Journal of Economic Geography

Kono, Tatsuhito;Joshi, Kirti Kusum

2017 Journal of Economic Geography

doi: 10.1093/jeg/lbx021

Abstract In a continuous city with three distinct land use zones consisting of business, condominiums and detached houses, we derive the formulae which simultaneously optimize regulations on building size, lot size and the three zonal boundaries under the existence of agglomeration economies and traffic congestion. The formulae show that the optimal regulations require a combination of downward and upward adjustments to the market sizes of buildings within both the business zone and the condominium zone, followed by minimum lot size regulation in the housing zone. The outer boundaries of the condominium and housing zones should be regulated inward whereas the optimal business zone boundary regulation depends on the trade-off between agglomeration economies and traffic congestion costs. 1. Introduction Land use regulations are common urban policies for managing spatial externalities1 caused by high concentration of population in cities. Spatial externalities can be positive or negative. For instance, concentration of workers enhances communication and thus facilitates exchange of innovative ideas (see Rauch, 1993; Ciccone and Hall, 1996; Duranton and Puga, 2001; Moretti, 2004). In contrast, concentration of population also has negative effects such as traffic congestion. In order to internalize such spatial externalities, local governments generally intervene in the urban space market through simultaneous enforcement of multiple regulations on building size and lot size, and by zoning the city into different land uses. For example, the City of Portland in the USA has imposed zonal land use restrictions and floor area ratio regulation (FARR) as well as an urban growth boundary (UGB) regulation.2 This article explores how multiple land use regulations should be simultaneously imposed across a city under the existence of agglomeration economies and traffic congestion. Considering a monocentric and continuous city with three distinct land use zones consisting of business, condominiums and detached houses, we derive the formulae—composed entirely of observable variables—which allow simultaneous optimization of regulations on building size, lot size and the three zonal boundaries across the city. In addition, from the formulae, we derive some theoretical properties of optimal land use regulations with new interpretation. Land use regulations are used as practical alternatives to superior policies—such as congestion pricing against traffic congestion—which are often politically infeasible, as discussed in Lindsey and Verhoef (2001) or King et al. (2007), or incomplete for unavoidable reasons such as enormous implementation costs. In fact, current practical applications of congestion pricing are far from the first-best congestion pricing, and moreover, the applications are limited to a few advanced cities only (e.g., London, Milan, Oslo, Singapore, and Stockholm). In contrast, land use regulations are very common worldwide. In the USA, 92% of the jurisdictions in the 50 largest metropolitan areas have zoning ordinances of one kind or another in place, and only 5% of the metropolitan population live in jurisdictions without zoning (Pendall et al., 2006). However, it is not an easy task for local governments to rationally design optimal land use regulations because they have to take into account the change in the distortions caused by the regulations as well as spatial externalities. Land use interventions and their effects on the welfare level of urban residents have been discussed in many previous studies (see Brueckner (2009) for a survey of theoretical analyses, or Evans (1999) for a survey of empirical investigations). However, although most real-world cities are simultaneously regulated under multiple rules, previous studies examine one land use regulation at a time (or at most, one regulation in the presence of UGB regulation). In related literature, many papers including Pasha (1996) and Wheaton (1998) explore lot size regulation but ignore business area zoning or building size regulation, while Helpman and Pines (1977) and Stull (1974) determine optimal zoning between manufacturing and residential areas without considering regulations on building size or lot size, and Rossi-Hansberg (2004) simulates the same in the existence of agglomeration spillovers of firms. Arnott and MacKinnon (1977), Bertaud and Brueckner (2005) and Brueckner and Sridhar (2012) study the welfare cost of building size regulation in isolation. When optimality of regulation is analyzed by considering only one regulation despite the presence of other regulations, we might actually obtain a nonoptimal result. For example, Kanemoto (1977) shows that in a congested monocentric city, a properly chosen UGB is welfare improving whereas Pines and Sadka (1985) and Wheaton (1998), using the same model, show that controlling lot size3 without UGB can lead to a first-best policy, implying that in the presence of lot size regulation, UGB regulation is unnecessary. This demonstrates that simultaneous consideration of multiple land use regulations gives a different optimal solution than when addressing a single regulation. Some recent papers have demonstrated the need of multiple regulations or at least variations within a single regulation. For instance, Joshi and Kono (2009), Kono et al. (2010, 2012), and Pines and Kono (2012) show that optimal FARRs consist of maximum and minimum FARRs in combination. By definition, floor area ratio (FAR) is the ratio of the total floor area of a building to the size of the plot on which the building is built. FARR is the most common form of building size regulation. Optimal regulations such as those achieved in the aforementioned studies are second-best policies substitutable for the first-best policies. Indeed, according to numerical simulations in Kono et al. (2012), optimal FAR and UGB regulations increase social welfare by approximately 70–85% of the welfare gain of the first-best policy. However, these studies do not consider what happens to the ‘optimal’ regulation if, for example, in addition to the FARR, lot sizes of detached dwellings are also regulated or land use zoning is also in place. Against this backdrop, this article addresses an important research gap on simultaneous imposition of multiple land use regulations across a city. We consider a monocentric city with three distinct land use zones—consisting of business, condominiums and housing lots—which closely resemble land use observed in real-world cities. The city has agglomeration economies in the business zone and traffic congestion across the city. Three points are noted for this setup. First, the setting of geography and residents’ preference plays an important role on the properties of optimal land use regulations. For example, by setting mixed-use zones in a monocentric and non-monocentric city having residents with idiosyncratic tastes, and in a system of cities with homogeneous residents, respectively, Anas and Rhee (2006, 2007) and Anas and Pines (2008) show that an expansive UGB may be necessary, which contradicts the traditional conclusions based on a monocentric city model. A monocentric city with homogeneous residents and firms, which we adopt, is a basic model. The results from a monocentric city model should be reasonably valid for any modifications on the model as long as the fundamental relationship between population (or employment) density and commuting costs is preserved (Brueckner, 2007; Sridhar, 2007). Secondly, distinction between the central city residential land use and that in the suburb is important for the study of certain urban phenomena. For example, using a two-zone model, Brueckner and Helsley (2011) relate urban blight with urban sprawl, and determine price-based corrective policies as well as a UGB regulation to shift population from the suburb back to the central city. However, Anas and Pines (2013), assuming local public goods with scale economies, demonstrate that this conclusion is not true in a system of cities, as population should be shifted by UGBs being imposed to create more and smaller cities. In any geographical setting, distinction between center and suburb is, therefore, a key factor. Thirdly, assuming the presence of unpriced traffic congestion and agglomeration spillovers of firms, we analytically explore the second-best adjustment to firm and residential density through land use regulations that include not only zoning but also regulations on building size and lot size. In a related paper, Rossi-Hansberg (2004), besides addressing optimal zoning between business and residential areas, also examines the first-best distribution of workers and residents in a city in the presence of spatial production externalities and uncongested commuting costs. This first-best distribution is achieved by location-variable labor subsidies, which are equivalent to transportation subsidies (Helsley and Strange, 2007). However, the optimal location-varying building size regulation, which is targeted by the current paper, cannot achieve the first-best distribution of workers because of the residual deadweight losses in the regulated building size markets (see Figure 3 in the current article). In a more recent paper, Rhee et al. (2014) also treat land use regulations in cities with agglomeration economies and traffic congestion. A key difference compared with our article lies in the geographical setting. The theoretical model of Rhee et al. (2014) assumes only two discrete zones with mixed land uses allowed in each zone,4 whereas our model addresses a continuous city with three different land use zones. Applying optimal control theory to the continuous city, our model achieves optimal density regulation that changes continuously from the center. In addition, we separately treat FARR and lot size regulation because building-size regulation necessarily generates deadweight loss caused by the regulation itself (see Kono et al., 2012) whereas lot size regulation has no deadweight losses (see Wheaton, 1998). Under building size regulation, households can choose their optimal floor size within the regulated buildings. That is, building size regulation controls population density indirectly, whereas lot size regulation does this directly. In addition, we design optimal regulations on multiple zonal boundaries between the business zone, condominium zone and lot housing zone. We also show by how much the building size, the lot size and the zone sizes should differ from those determined at the market equilibrium. The differences are shown in the formulae composed of empirically observable economic variables. All these results are useful for policy makers to design optimal density and zonal regulations in a monocentric city.5 The remaining portion of the article is organized as follows. In Section 2, we present and explain key results even before we introduce our model later in Section 3 so as to facilitate understanding of our inherently complicated theoretical exercise on optimal simultaneous regulations. Section 4 derives necessary conditions for maximizing social welfare using regulations. Section 5 explores optimal regulations on FAR, lot size and multiple zonal boundaries, using the necessary conditions. Finally, Section 6 concludes the article. 2. Key results As mentioned above, our monocentric city model is divided into business zone consisting of firms, condominium zone and lot housing zone. The objective of our study is to find optimal FARR and lot size zoning in the presence of optimal zonal boundaries. In other words, using FARR, lot size zoning and zonal boundary controls as planning tools, this study aims to determine optimal firm density in the business zone and optimal population density in the residential zones. The city population, and thereby the worker population, is fixed. Workers in the business zone (or firms) benefit from agglomeration economies, but residents across the city (including workers in the business zone) also face congestion externality while commuting to and within the business zone. With this setup, our results are summarized as follows. Result 1 (Optimal firm density in business zone).When agglomeration economies are weaker than traffic congestion costs, the optimal firm density in the business zone tends to be higher (resp. lower) in the more central (resp. peripheral) locations relative to the market firm density, economizing on commuting costs. The reverse case is similarly explained. Result 2 (Optimal size of business zone).Enlargement of the business zone decreases agglomeration economies but reduces total commuting distance and hence traffic congestion costs; the optimal size of the business zone depends on the net effect. Result 3 (Optimal population density in residential zones).Relative to the market population density in the residential zones consisting of condominiums followed by detached houses, the optimal population density is higher (resp. lower) in the more central (resp. peripheral) locations. Result 4 (Optimal size of residential zones).In the optimal case, the residential zones are more compact relative to the market equilibrium case, economizing on traffic congestion costs. Note that minimum (resp. maximum) FARR leads to upward (resp. downward) adjustment to market building size and hence density. Likewise, minimum lot size zoning leads to lower population density. The following sections derive these results rigorously and interpret them intuitively. 3. The model 3.1. The city The model city is closed, monocentric and linear with a width of unity and size defined by m∈[−MH,MH], where m denotes distance from the city center. We assume that each zone is sufficiently large relative to the size of a lot such that the location of a lot or building can be expressed in terms of m. Following a real-world urban land use pattern, and as depicted in Figure 1, which shows only the right half of the symmetrical city, the city is divided into the following three zones in successive order: (i) the central business district (CBD) or business zone, Zone B (m∈[0,MB]), consisting of office buildings, (ii) the condominium zone, Zone C (m∈[MB,MC]) and (iii) extending to the urban boundary, the lot housing zone, Zone H (m∈[MC,MH]), consisting of single-family houses. Figure 1 View largeDownload slide The model city. Figure 1 View largeDownload slide The model city. Zone B and Zone C are regulated by FARR. We assume that all buildings are built on lots of equal size which is normalized to unity; therefore, the FAR of a building is equivalent to its total floor supply. Let Fk′( k′∈{B,C}) denote the FAR of a building in zone k′. Likewise, the lots within Zone H are regulated; let fH denote the lot consumption per household in the zone. The city is inhabited by identical households. One member of each household commutes to the CBD, where all firms, and thereby jobs, are located. The city population is identified with the number of households, denoted 2N¯, which is divided equally between the two halves of the symmetric city. The city is closed, which implies that 2N¯ is exogenously fixed. Buildings in Zone B and Zone C are constructed by developers whereas, following most of the previous studies (e.g., Pines and Sadka, 1985), we ignore housing capital in Zone H, assuming that land is directly consumed by the residents. One possible interpretation is that households construct their houses using composite goods. Finally, we assume the so-called public land ownership under which residents share the city land equally. Hereafter, we basically model the right half of the city unless it is unavoidable to model both sides. 3.2. Externalities and regulations We consider two types of externalities: (i) agglomeration economies that arise from communication between firms in Zone B and (ii) traffic congestion across the city. To address these two externalities, FARR, lot size zoning and zonal regulation on zonal boundaries are imposed. The policy variables are as follows. Definition 1 (Policy Variables). The city government regulates (1) FAR at each location in Zone B and Zone C, i.e., Fk′(m), (k′∈{B,C}), m∈[0,MC], (2) lot size at each location in Zone H, i.e., fH(m), (m∈[MC,MH])under lot size regulation, and (3) three zonal boundaries, i.e., Mk, (k∈{B,C,H}). Firm density in Zone B and population density in Zone C are adjusted only by FARR, whereas in Zone H, only lot size regulation adjusts population density. As shown in Kono et al. (2012), FARR generates price distortions whereas lot size regulation generates no price distortion. 3.3. Firms’ behavior All firms are located within Zone B, and they have identical production function. We model single-worker production that uses floor area as an input besides labor. The production function is expressed as AX(fB), where A is the communication-based factor productivity function; fB is the per-firm floor area and X(fB) is the partial production function.6 Following Borukhov and Hochman (1977), O’Hara (1977), and Ogawa and Fujita (1980), we assume that each worker communicates inelastically with workers in the other firms. Although inelastic communication is less realistic, such inelastic bilateral communication trips can represent agglomeration economies in the sense that firms would concentrate more on saving social communication trip costs. This is why this setting has been used in the aforementioned previous theoretical studies. Although we focus only on the right side of the CBD, firms on the right-hand side communicate with firms all over the CBD including those on the left-hand side. For each firm, the number of trips to each other during a certain period is normalized to 1 without loss of generality. With the number of total workers, and thus the number of single-worker firms being 2N¯, the total communication trip for each firm is 2N¯−1. In this case, A=A(2N¯−1)≡A¯, which implies that A¯ is constant because 2N¯−1 is constant. The profit for a firm at m, denoted π(m), is then given by: π(m)=A¯X(fB)−g(m)−w(m)−rB(m)fB,  m∈[0,MB], (1) where g(m), w(m) and rB(m), respectively denote the communication trip cost, wage and floor rent for the firm at location m. The communication trip cost g(m) is defined as follows. A worker at m communicates with a worker at x at the cost of τ|x−m|, where |x−m| is the distance between the corresponding firms, and τ is the constant unit-distance cost. The worker communicates with all other workers; so the total communication trip cost borne by a worker at m, say G(m), is given by G(m)=∫−MBMBn˙B(x)[τ|x−m|]dx,  m∈[0,MB], (2) where n˙B(x)≡∂nB/∂x, which denotes worker density at x, and nB(m)=∫0mn˙B(x)dx is the number of total workers working at the firms located between the CBD center and location m. A dot over a variable, hereafter, denotes derivative of the variable with respect to distance. The trip cost G(m) is physically determined by the supply-side condition (or transport capacity). Workers must pay at least the supply-side cost, but they might be paying more (e.g., by driving inefficiently slowly or by consuming more fuel for unnecessary acceleration). Therefore, the relation between the communication trip cost G(m) and the actual payment g(m) is expressed as an inequality condition: g(m)≥G(m),  m∈[0,MB]. (3)7We differentiate the right-hand side of Equation (2) with respect to m, which yields dG(m)dm≡G˙(m)=2nB(m)τ, m∈[0,MB],8 (4)8and an initial condition is obtained as G(0)=2∫0MBn˙B(m)τmdm. (5) Rent bidding among firms yields π(m)=0. The bid rent is expressed as rB(g(m),w)=max fB(A¯X(fB)−g(m)−w(m)fB), m∈[0,MB]. (6) The first-order condition yields fBA¯∂X/∂fB−A¯X(fB)+g(m)+w(m)=0. (7) Thus, fB is the function of g(m) and w(m). As Equation (7) shows, a firm considers only its private communication costs, whereas its proximity to other firms may allow the latter to economize on their communication costs. This is what Kanemoto (1990) calls ‘locational externality’. Such locational externality can be adjusted by density regulations. However, under the assumption of an endogenous floor area consumption, the optimal FARR cannot lead to the first-best labor distribution.9 Finally, we define wage rate. Denoting the commuting cost from MB to m as tB(m), the wage w(m) should follow w(m)=w(MB)+tB(m), (8) because the wage at each location should compensate for the commuting cost tB(m). 3.4. Developers’ behavior Developers supply buildings in Zone B and Zone C under the FARR. Let πk′d, k′∈{B,C} denote developers’ profit from the construction of a building in zone k′, which is given by πk′d(mk′)=Fk′rk′(mk′)−Sk′(Fk′)−Rk′(mk′), k′∈{B,C},mB∈[0,MB],mC∈[MB,MC], (9) where Sk′(Fk′) denotes the total construction cost of FARR-regulated floor area Fk′. rk′ and Rk′ denote floor rent and land rent, respectively. Note that buildings are constructed on lots of equal size normalized to 1. Considering perfectly competitive developers, the zero-profit condition is given by πk′d(m)=0, k′∈{B,C}, which then yields Rk′(m)=Fk′(m)rk′(m)−Sk′(Fk′(m)), k′∈{B,C},mB∈[0,MB],mC∈[MB,MC]. (10) 3.5. Commuting cost—an external factor To consider congestion externality, we adopt transport functions à la Wheaton (1998) and Brueckner (2007). For simplicity, the commuting cost is divided into two parts: that within the residential area (i.e., Zone C and Zone H) and that within the business area (i.e., Zone B), denoted t(·) and tB(·), respectively (See Figure 1). The unit-distance commuting cost within the residential area t(m) borne by the resident at location m has the following condition: dt(m)dm≡t˙(m)≥ξ+δ[N¯−n(m)ρ(m)]γ,m∈[MB,MH], (11) where n(m) is the total commuter population residing beyond the CBD edge up to location x, and thus N¯−n(m) is the total commuter population that joins traffic at location m on the way toward the CBD. ξ is the free-flow commuting cost factor; δ and γ are positive parameters; and ρ(m) is the road capacity at location m, given exogenously. Equation (11) uses an inequality condition. The left-hand side is the demand-side cost, which a commuter pays, while the right-hand side is the supply-side cost, which is determined physically. Similar to the communication trip cost in the business area, commuters might be paying more than the supply-side cost.10 The total commuting cost is defined as t(m)≥∫MBm[ξ+δ[N¯−n(x)ρ(x)]γ]dx,m∈[MB, MH]. (12) Similarly, the commuting cost within the business zone borne by a worker employed at a firm located at m, tB(m), is defined as tB(m)≥∫mMB[ξ+δ[nB(x)ρ(x)]γ]dx, (13) and dtB(m)dm≡t˙B(m)≤−ξ−δ[nB(m)ρ(m)]γ,m∈[0, MB].11 (14) where nB(m) denotes number of firms located between the city center and location m. The right-hand side in both Equations (13) and (14) implies that there is congestion caused by commuting trips. Note that as distance m from the center decreases, the traffic volume, implied by nB(m), also decreases because most commuters would have already reached their firms.12 3.6. Household behavior Each household worker earns wage w per period by working in the CBD. The household’s expenditure comprises commuting, housing and non-housing commodity costs. Private cars are the only mode of commuting. For simplicity, we assume a quasi-linear utility function for households living in Zone C and H, denoted VC and VH, respectively, which is expressed as Vk″(mk″)=uk″(fk″(mk″))+zk″(mk″),13 k″∈{C,H}, mC∈[MB,MC] and mH∈[MC,MH]; here, uC and uH, respectively, denote household utility derived from the consumption of floor space fC(m) and from the consumption of lot size fH(m), and zk″ is the numeraire non-housing commodity. The income constraint is expressed as zk″+fk″rk″(m)=w(m)+[1/N¯]Φ−t(m)−tB(m), where t(m) is the round-trip commuting cost to the CBD edge borne by a household residing at location m, and Φ is the total profit from the land, that is, total differential land rent. [1/N¯]Φ on the right-hand side implies the assumption of public ownership of land. Using Equation (8), the income constraint can be simplified as zk″+fk″rk″(m)=w(MB)+[1/N¯]Φ−t(m). The total profit from the land, Φ, is expressed as Φ=∫0MB[RB(m)−RA]dm+∫MBMC[RC(m)−RA]dm+∫MCMH[rH(m)−RA]dm, (15) where RA is the agricultural rent, and rH is the land rent in Zone H. The maximization of household utility yields the demand function fC(rC(m)). Substituting this into the utility function yields zC(m)=−uC(fC(rC(m)))+VC(m), m∈[MB,MC]. Regarding Zone H, we obtain zH(m)=−uH(fH(m))+VH(m), m∈[MC,MH]. Note that under the lot size regulation, fH(m) is regulated, and therefore, cannot be chosen by a household, whereas as stated above, fC(m) is the function of rC(m) following utility maximization. Using the demand functions, the residents’ income constraints are expressed as w(MB)+1N¯Φ−t(m)=−uC(fC(rC(m)))+VC(m)+fC(rC(m))rC(m),m∈[MB,MC], (16) w(MB)+1N¯Φ−t(m)=−uH(fH(m))+VH(m)+fH(m)rH(m),m∈[MC,MH]. (17) 3.7. Market clearing conditions and definitions The equality of utilities among locations and market clearing conditions are shown here. First, Equation (18) implies that the household utility is equal everywhere, which is because households are indifferent regarding locations. VC(mC)=VH(mH)≡V, mC∈[MB,MC], mH∈[MC,MH], (18) Population function n(m) and transportation cost t(m) are both continuous at MC but are not necessarily smooth. So, to clearly distinguish these functions before and after MC, we define nC(m), nH(m), tC(m) and tH(m): nC(m) ≡{n(m)|m∈[MB,MC]} and tC(m) ≡{t(m)|m∈[MB,MC]},  (19) and nH(m)≡{n(m)|m∈[MC,MH]} and tH(m)≡{t(m)|m∈[MC,MH]}. (20) Next, as Equation (21) states, the total floor space consumed is balanced by total floor space supplied. Likewise, Equation (22) expresses the market equilibrium in floor space in Zone C. Next, Equation (23) expresses that in Zone H, the households at m consume fH(m) area of lot; therefore, total area consumed is equal to the unit land area supplied. Floor space in Zone B, fB(g(m),w(m))n˙B(m)=FB(m),m∈[0,MB], (21) Floor space in Zone C, fC(m)n˙C(m)=FC(m) where n˙C(m)≡∂nC(m)/∂m,m∈[MB,MC], (22) Lot supply in Zone H, n˙H(m)fH(m)=1,  where n˙H(m)≡∂nH(m)/∂m,m∈[MC,MH]. (23) Finally, as shown in Equation (24), because one household member works in the CBD, the total number of workers (left side) is equal to the household population N¯ (right side). Labor population,  ∫0MBn˙B(m)dm=N¯. (24) 4. Maximizing social welfare with land use regulations 4.1. Objective The objective of optimal regulations can be denoted as Definition 2 (see also Definition 1), using the social welfare composed of total utilities, W=N¯V, (25) where V is defined in Equation (18). Definition 2 (Optimal Regulations). Optimal FAR at each location in Zone B and Zone C, i.e., Fk′(m), k′∈{B,C}, m∈[0,MC], and optimal lot size at each location in Zone H, i.e., fH(m), m∈[MC,MH], and three optimal zonal boundaries MB,MC,MH are given by maximizing social welfare subject to the market equilibrium. Mathematically, [F,f,MB,MC,MH]=arg max F,f,MB,MC,MH W subject to eqs. (1) – (25), where F=(FB(mB),FC(mC))∀mB∈[0,MB], ∀mC∈[MB,MC] and f=fH(m)∀m∈[MC,MH]. The first-best optimum can be achieved by levying a Pigouvian toll on commuting equal to the gap between the marginal social cost and the private cost of travel; and a Pigouvian tax on each communication cost equal to the gap between the social marginal and private communication cost. Agglomeration economies enhancing A¯ are fixed because the city population is fixed. Aside from the first best, the current article explores optimization of the social welfare using land use regulations. 4.2. First-order conditions for optimal regulations Regulations affect social welfare W through changes in (i) agglomeration economies arising from communication in the business zone due to the distribution of firms, (ii) deadweight loss in the floor space and lot size market due to the distribution of residences, and (iii) commuting costs. The optimal control problem maximizing the social welfare subject to the market mechanism in Equations (1)–(25) is expressed in the Lagrangian, which is shown in Appendix A. Our model allows simultaneous optimization of FARR in the business and condominium zones, lot size regulations in lot housing zones and three zonal boundaries. The first-order conditions show the relationships among distortions caused by the regulations, agglomeration economies and congestion. We interpret these relationships in Appendix B. 5. Optimal regulations 5.1. Optimal FARR and lot size regulation This section obtains important properties of the optimal regulations on FAR and lot size. First, we consider shadow prices μk(m)(k=B,C,H) which directly show how and by how much the FAR or lot regulations should be imposed. As we show later in Proposition 1, these properties are important to determine land use regulation. Rigorous description of these properties is shown in Lemma 1 in Appendix C. We summarize the motion of μk(m) in Figure 2. Figure 2 View largeDownload slide The motion of shadow prices. Figure 2 View largeDownload slide The motion of shadow prices. From Equations (A.2) and (A.3) in Appendix A, it is evident that the sign of μk'(m)(k'∈{B,C}) is the reverse of Dk′(mk′)≡rk′(mk′)−∂Sk′(Fk′)/∂Fk′, where Dk′(mk′) denotes distortion in the floor space market caused by FARR as shown in Figure 3(a). Note that Dk′(m)=0, if the FAR is unregulated and determined by the market. An FAR greater (resp. smaller) than the market FAR implies Dk′(m)<0 (resp. Dk′(m)>0). Thus, combining Equation (A.2) with Lemma 1(1) while also using η=1 from Equations (A.7) and (A.11) yields Proposition 1(1). Likewise, combining Equation (A.3) and Lemma 1(2) using η=1 again yields Proposition 1(2). Next, DH≡∂uH/∂fH−rH denotes distortion in the lot supply market due to lot size regulation as shown in Figure 3(b). The combination of Equation (A.4) with Lemma 1(3) leads to DH<0 for any m∈(MC,MH], thereby yielding Proposition 1(3). Proposition 1 (Optimal FARR and lot size regulation in the presence of optimal zonal boundaries). Let superscript ‘ †’ refer to the market equilibrium case. Figure 3 View largeDownload slide Deadweight loss due to regulations: (a) FARR (left); (b) lot size regulation (right). Note: Subscripts ‘ †’ and ‘ ∗’, respectively, refer to the market equilibrium and optimal cases. Figure 3 View largeDownload slide Deadweight loss due to regulations: (a) FARR (left); (b) lot size regulation (right). Note: Subscripts ‘ †’ and ‘ ∗’, respectively, refer to the market equilibrium and optimal cases. Business zone:There is at least one sub-zone where FB(m)>FB†(m)and one other sub-zone where FB(m)<FB†(m), where m∈[0,MB]. In the two cases classified by whether communication costs are stronger than traffic congestion costs or not: Case (i) implying −2τ+δγnB(m)γ−1/ρ(m)γ<0 at any m∈[0,MB]:FB(m)>FB†(m) at any m∈[0,m⌣) and FB(m)<FB†(m) at any m∈(m⌣,MB], where m⌣∈(0,MB); Case (ii) implying −2τ+δγnB(m)γ−1/ρ(m)γ>0 at any m∈[0,MB]: FB(m)<FB†(m) at any m∈[0,m⌣) and FB(m)>FB†(mB) at any m∈(m⌣,MB], where m⌣∈(0,MB); Condominium zone: FC(m)>FC†(m) for any m∈[MB,m⌢) and FC(m)<FC†(m) at any m∈(m⌢,MC], where m⌢∈(MB,MC); Lot housing zone: fH(m)>fH†(m) at any m∈[MC,MH]. Case (i) in Proposition 1(1) implies that communication costs are stronger than traffic congestion costs in the business zone. Case (i) arises if the communication cost, τ, is sufficiently large. Case (ii) is the reverse condition, which arises if the transportation capacity, ρ(m), is sufficiently small, implying severe congestion in the business zone. Note that near the city center, the number of commuters is close to zero; so at m∈[0,ε] where ε=˙0, −2τ+δγnB(0)γ−1/ρ(0)γ<0. If ρ(m) is relatively large in the central area, Case (i) emerges because the communication cost for business people is generally high. In most developed cities with high wages, Case (i) is likely to hold. It is important to recall that Proposition 1 holds when optimal zonal boundaries are simultaneously imposed, which are presented later in Proposition 2. Results of Proposition 1 are depicted in Figure 4, and the implication is explained as follows. Figure 4 View largeDownload slide Optimal regulations. Note: For FARR in Zone B, regulations in bold letters hold in Case (i), and regulations in parenthesis hold in Case (ii). For the area regulation in the business zone, a decrease in the zone area hold in Case (i), and an increase in the zone area holds in Case (ii). Figure 4 View largeDownload slide Optimal regulations. Note: For FARR in Zone B, regulations in bold letters hold in Case (i), and regulations in parenthesis hold in Case (ii). For the area regulation in the business zone, a decrease in the zone area hold in Case (i), and an increase in the zone area holds in Case (ii). First, the combination of maximum and minimum FARRs results in an efficient labor distribution in order to optimize the total welfare composed of deadweight loss in the floor market and agglomeration benefits in the CBD. To achieve a certain labor distribution, if only conventional ‘maximum FARR’ is imposed, the total deadweight loss arising from FARR would be greater than that would arise from the combination of maximum and minimum FARRs. Whether minimum FARR is required in central locations or peripheral locations depends on the relative magnitude of −2τ and δγnB(m)γ−1/ρ(m)γ ( m∈[0,MB]). For example, in Case (i), that is, if −2τ+δγnB(m)γ−1/ρ(m)γ<0 (resp. in Case (ii), that is, −2τ+δγnB(m)γ−1/ρ(m)γ>0) in most parts of the business zone, the optimal policy requires enforcement of minimum (resp. maximum) FARR at the more central locations and maximum (resp. minimum) FARR at the peripheral locations. Recall that Case (i) is more likely to hold in developed cities. Next, in the condominium zone, the optimal policy requires enforcement of minimum FARR at the central locations and maximum FARR at the periopheral locations. Such regulations shift population in favor of more central locations, and thereby reduce traffic congestion caused by commuters from distant locations. See Kono et al. (2010) for a related discussion in detail. In the lot housing zone, however, the optimal regulation requires enforcement of minimum lot size regulation over the zone. As shown in Figure 3(b), DH denotes marginal deadweight loss in the lot size market at the given location. The optimal regulation addresses these deadweight losses. Given that the city also has UGB regulation that prevents sprawl, minimum lot size regulation reduces supply of housing lots and thereby decreases population in the suburb and ultimately reduces traffic congestion across the condominium zones and lot housing zone. 5.2. Optimal zonal boundaries We now examine how a change in each zonal boundary affects the social welfare under regulated FAR and lot size. From Lemma 2 in Appendix D, which summarizes the related first-order conditions of the welfare maximization, we directly derive Proposition 2, which shows optimal zoning conditions composed of only empirically observable variables. Proposition 2 (Optimal zonal boundaries in the presence of optimal FARR and lot size regulation).Let superscript ‘ †’ refer to the market equilibrium case. The optimal zonal boundaries are as follows. Whether the business zone should be more compact or larger than the market size depends on the trade-off between agglomeration economies and traffic congestion costs. More concretely, recalling the two cases defined in Proposition 1(1), MB<MB† in Case (i) whereas whether MB>MB† or MB<MB† is ambiguous in Case (ii); The boundary of Zone C should be shrunk relative to the market boundary. That is, MC<MC†; The boundary of Zone H, which is equal to the urban boundary, should be shrunk relative to the market boundary. That is, MH<MH†. The implication of Proposition 2(1) is explained as follows. Regarding the business zone, an enlargement of the zone decreases agglomeration economies resulting in a decrease in welfare. Simultaneously, it implies that the business area becomes closer for all residents. Accordingly, the congested commuting distances decrease. That implies a decrease in congestion cost of commuting in the residential floor market at location MB. The net effect is ambiguous. Proposition 2(2) implies that contraction of Zone C decreases the deadweight loss at Zone C edge by DC(MC)FC(MC) but increases the same at the inner edge of Zone H by DH(MC). The first exceeds the latter in absolute value. This can also be explained using the equation in Lemma 2(2). Proposition 2(3) implies that a marginal expansion of Zone H decreases social welfare. Expanding Zone H by a unit area means supplying additional lots, thereby increasing the population at the city edge by 1/fH(MH). Because the city is closed, such expansion results in reallocation of some households from the outer edge of Zone C to the city edge, noting that fH(m)(m∈[MC,MH]) is fixed by lot size regulation. Such relocation increases the commuting cost in Zone H by ∫MCMHδγ[[N−n(m)]/ρ(m)]γdm·[1/fH(MH)] (i.e., the first term in the right-hand side of equation of Lemma 2(3)). The relocation decreases the deadweight loss at the outer edge of Zone C by DC(MC)[fC(MC)/fH(MH)], where fC(MC)/fH(MH) implies decrease in the building size at the outer edge of Zone C because of the relocation of [1/fH(MH)] number of residents. This can also be explained using the equation in Lemma 2(3). Finally, we explore whether the total area of the city decreases or not. Although the areas of Zone C and Zone H should be shrunk relative to the market boundary, the optimal size of Zone B is ambiguous in Case (ii). When the congestion costs are large enough compared to agglomeration benefits, a larger Zone B is welfare improving because it reduces traffic congestion by reducing the distance between Zone B and the residential area. In such case, an optimal city can be larger than a market city if +ΔMB−ΔMC−ΔMH>0, where ΔMk(k∈{B,C,H}) denotes optimal change (‘+’ if expansion and ‘−’ if shrinkage) in the corresponding zonal boundary relative to the market equilibrium. 6. Summary and conclusion This article simultaneously optimizes multiple regulations—on building size, lot size and zonal boundaries—in a monocentric city with office buildings, condominiums and single-family dwellings in distinct but adjoining districts. We demonstrate the necessity of both minimum and maximum FARR in both business zone and condominium zone. Although Kono et al. (2010) achieve similar results in their treatment of condominiums, our results differ because we also consider office buildings. Accordingly, in our model, where minimum or maximum FARR should be imposed within the business zone, which has both agglomeration economies and congestion externalities, differs from that in condominium zone which has only congestion externalities. Although the optimal FARR in the business zone is ambiguous in our model, our results suggest that if agglomeration economies are relatively dominant over traffic congestion costs (such as in developed cities), it is more likely that the optimal policy requires enforcement of minimum FARR at the more central locations and maximum FARR at the more peripheral locations. The same applies non-ambiguously in the case of condominium zone, followed by minimum lot size regulation in the suburb. In the presence of optimal FARR and lot size regulation, we also explore optimal zonal boundaries. The optimal size of the business zone is ambiguous depending on the trade-off between agglomeration economies and traffic congestion costs but the outer boundaries of the condominium and housing lot zones should be shrunk. This has an important implication regarding what minimum lot size regulation achieves in our model, and how. Although minimum allowable lot size in the suburb is prevalent in most countries, especially in the USA, our interpretation of the necessity of minimum lot size regulation (see Proposition 2) is different. The objective of such zoning as being practiced is to promote low-density development but such a policy contributes to urban sprawl (Pasha, 1996), and thus increases congestion costs. That is why Pines and Sadka (1985) and Wheaton (1998) suggest maximum lot size regulation in the central area. But our model is able to alleviate congestion externality through minimum lot size regulation and without sprawl because it allows options for additional higher density in the central area through minimum FARR. Such result is achieved because of simultaneous consideration of multiple regulations. Our theoretical results are supplemented by some numerical examples which show how social welfare is affected by changes in the regulation (see Appendix E). The application of our results to real cities has some caveats. In this study, we have not assumed any other means of transport except automobiles. Buyukeren and Hiramatsu (2016), assuming a congested car mode and an uncongested public transit mode, analytically demonstrate that, under certain conditions, an expansionary UGB would be optimal. Hence, our results are not applicable to cities with multiple transport modes as they are. However, many cities have no railroad system, and even if they have one, it does not cover the whole city. Our results are applicable to areas without railroads within cities. In addition, some relevant transport policies might affect land use regulation drastically. Indeed, cordon pricing affects land use regulation (see Kono and Kawaguchi, 2017). Furthermore, although the current article only assumes homogeneous residents, we should explore how land use regulation affects heterogeneous residents before implementing the regulation. Another major limitation is that our model is a static city model, which treats the building stock as fully malleable as if it could be adjusted instantaneously. Fluctuations in productivity could cause fluctuations in demand for space in the city, which implies that the optimal FAR and zonal boundaries could change over time. Indeed, several recent papers have attempted to take account of dynamic aspects. For example, Joshi and Kono (2009) analyze optimal FARR in a dynamic setting in a growing city with two zones with congestion externality. Jou (2012) explores the optimal UGB in a monocentric city with uncertainty. Optimal dynamic regulations can thus be another subject of interest for further research. Footnotes 1 As Hanushek and Quigley (1990) note, fiscal objectives are other justification for land use regulation. 2 See http://www.portlandonline.com/auditor/index.cfm?c=28197 (last accessed on 23 March 2015). 3 Pines and Sadka (1985) use housing tax to control lot size. However, this is equivalent to lot size regulation in terms of social welfare. 4 Rhee et al. (2014) numerically simulate optimal regulations in a model with two or three zones on the right side of the city. Although the number of zones is still limited, they allow mixed use of industrial and residential uses in each zone. This point is different from our model. 5 Note that land use regulations can be replaced by equivalent property tax policies (see Pines and Kono, 2012). 6 Single-worker production is not so specific as Borukhov and Hochman (1977) note. If the production function is expressed as AΓ(Q,l), where Γ(Q,l) is one-degree homogeneous production function, Q is the total floor space for a firm, and l is the labor size, then we obtain a production function with one unit of labor, given by AX(fB)=AΓ(Q/l,1), where fB=Q/l. 7 Needless to say, a rational worker does not pay more than the supply-side cost unless she could improve her welfare which does not happen in the stable equilibrium. Hence, this expression is going to hold as an equality as a result of the rational worker’s optimal behavior. Nevertheless, this inequality expression is useful later for determining the sign of the shadow price (or Lagrange multiplier) of this constraint. Because the multiplier implies the value of the supply-side transport cost, the sign is negative, implying a natural result that an increase in the transport cost has a negative welfare effect. This is straightforwardly proved using the Kuhn–Tucker condition if we use an inequality condition. A similar method is used in Kono and Joshi (2012) and Kono and Kawaguchi (2017). 8 ddm∫−MBMBn˙B(x)[τ|x−m|]dx=[nB(MB)+nB(m)−[nB(MB)−nB(m)]]τ=2nB(m)τ,  m∈[0,MB]. 9 If the floor area is fixed as in O’Hara (1977) and Ogawa and Fujita (1980), the optimal FARR brings about no deadweight loss in the floor market because the demand is inelastic. But we focus on the deadweight loss brought by the FARR; so the assumption of endogenous elastic floor area is vital for the purpose of our article. To achieve the first-best distribution, as Helsley and Strange (2007) show, transportation subsidies should be imposed. 10 The discussion in footnote 7 also applies here by replacing ‘rational worker’ with ‘rational commuter’. In addition, note that this unnecessary travel cost is not equal to congestion pricing. The payment for congestion pricing will be returned to the society, but the unnecessary travel cost is lost by the society. 11 Differentiating Equation (13) with respect to m reverses its inequality sign because t˙B(m) is negative. 12 This is why formulation of Equation (14) differs from that of Equation (11). In Equation (11), N¯−n(m) denotes household (or commuter) population residing beyond location m (m∈[MB,MH]) that would be commuting to the CBD. In Equation (14), nB(m) denotes commuter population working at firms located over [0,x] (m∈[0,MB]) that would cross location m while commuting to the firms or while returning home. 13 Because the marginal utility with respect to income is constant over locations under the assumption of a quasi-linear utility, the derivation would be simple. In contrast, Pines and Kono (2012) use a general utility function (i.e., u(f,z)) to obtain the optimal FARR. However, in the current article treating multiple regulations, the derivation of the optimal regulations will be very complex if a general utility function is adopted. However, even in the latter case, the formula describing the optimal regulation will essentially be the same. Furthermore, if a change in the marginal utility with respect to income does not change much according to the regulations, the same properties regarding the optimal regulation are obtained. 14 The Lagrangian considers only the right-hand side of the city. However, communication costs in the right side of the city depend on the left side as well. Equations (4) and (5) include the left-side firms’ communication costs. So, we have to first consider dividing them by 2 for inclusion in the Lagrangian. But, because the city is symmetric, the left side’s symmetrical change should be considered, which can be done by multiplying the equations by 2 because the communication trips are inelastic. In conclusion, we can consider Equations (4) and (5) as they are. Further, note that this Lagrangian can be replaced with Hamiltonian, which generates the same first-order conditions. 15 λH(MC)=N¯−nC(MC) is proved simply by using Equations (A6), (A17), (A18) and (A19). 16 Totally differentiating Equation (16) yields −dtC=−[∂uC/∂fC−rC]·∂fC/∂rC·drC+fCdrC, where ∂uC/∂fC=rC because of the first order condition of the utility maximization. So, we obtain −1/fC=drC/dtC. Multiplying both sides by dfC/drC yields −[1/fC]dfC/drC=dfC/dtC. 17 A similar equation to Equation (A33) appears in Kanemoto (1977), Arnott and MacKinnon (1977), Arnott (1979), Pines and Sadka (1985) and Pines and Kono (2012). As explained in the main text, μC(m) expresses the distortion arising from the FARR in our model. In contrast, in the case of those previous papers, except for Pines and Kono (2012), the distortion arises from the allocation of land between road and residential areas, which is fixed in our model. Simultaneously controlling FARR with road area remains a future task. 18 The Harberger’s welfare formula is expressed as dW/dQ=∑iΞi∂Xi/∂Q where Ξi is the distortion (e.g., price minus marginal cost) in market i, X is the output in market i, and Q is the policy variable. 19 Note that market land rents between two adjacent zones are not equalized in the formulation of Lagrangian in Equation (A.1) or subsequent derivations. This should show that Proposition 1 is not derived with zonal boundaries set at market equilibrium. 20 See Lemma 1(1) for definition of Cases (i) and (ii). 21 Programs for the simulation are available upon request. 22 Programs solving the market equilibrium are composed of simultaneous equations only. In contrast, programs solving the optimal solution maximize the social welfare subject to multiple equations (conditions or constraints). In other words, the second-best optimum is a constrained nonlinear optimization subject to numerous constraints multiplied by the number of blocks our three-zone model city is divided into. We were able to numerically solve the market equilibrium only. Acknowledgements We appreciate the editor Kristian Behrens and anonymous reviewers for useful comments. Earlier versions of this paper were presented at an Urban Economic Association session of the North American Meetings of the Regional Science Association in Ottawa, Canada, the Applied Regional Science Conference in Toyama, Japan, and a seminar at Kyoto University. We are thankful to the participants at the meetings for their helpful comments and suggestions, in particular to T. Mori, S. Mun, J. Siodla, and Y. Yoshida. Furthermore, we are very grateful to the late Y. Hayashiyama, who kindly supported and reviewed our research. Despite assistance from many sources, any errors in the paper remain the sole responsibility of the authors. 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Lagrangian and Pontryagin's maximum principle The Lagrangian according to Definition 2 is as follows.14 L=  N¯V+∫MBMCκC(m)FC(m)fC(m)[w(MB)+1N¯Φ+uC(fC(rC(m)))−V−fC(rC(m))rC(m)−tC(m)]dm+∫MCMHκH(m)1fH(m)[w(MB)+1N¯Φ+uH(fH(m))−V−fH(m)rH(m)−tH(m)]dm−η[Φ−∫0MB[FB(m)rB(g(m),w(MB)+tB(m))−SB(FB)−RA]dm−∫MBMC[FC(m)rC(m)−SC(FC)−RA]dm−∫MCMH[rH(m)−RA]dm]+∫0MBϕB(m)[G˙(m)−2nB(m)τ]dm+θ[G(0)−2∫0MBn˙B(m)τmdm]+∫0MBω(m)[g(m)−G(m)]dm+∫0MBλB(m)[t˙B(m)+ξ+δ[nB(m)ρ(m)]γ]dm+∫0MBμB(m)[FB(m)fB(g(m),w(MB)+tB(m))−n˙B(m)]dm+∫MBMCλC(m)[t˙C(m)−ξ−δ[N¯−nC(m)ρ(m)]γ]dm+∫MBMCμC(m)[FC(m)fC(rC(m))−n˙C(m)]dm+∫MCMHλH(m)[t˙H(m)−ξ−δ[N¯−nH(m)ρ(m)]γ]dm+∫MCMHμH(m)[1fH−n˙H(m)]dm+ςn[nH(MC)−nC(MC)]+ςt[tH(MC)−tC(MC)], (A.1) where κk″(m), η, θ, ω(m), ϕB(m), ψB(m), λk(m), μk(m), ςn and ςt are shadow prices; k″∈{C,H} and k∈{B,C,H}. Because communication between firms takes place bilaterally, the constraint, G(0)=2∫0MBn˙B(m)τmdm from Equation (5), is necessary in Equation (A.1). As Tauchen and Witte (1984) and Fujita and Thisse (2002) show, the total communication cost in the CBD is expressed by double integrals; so the Lagrangian should treat this constraint specifically in addition to the constraint of G˙(m). This necessity is also intuitive because the boundary condition tB(0) depends on the endogenous labor distribution. The other boundary conditions are as follows. For Zone B, nB(0)=0, and nB(MB)=N¯. For Zone C, n(MB)=0. For Zone H, n(MH)=N¯. To obtain the first order conditions, we integrate the Lagrangian in Equation (A.1) by parts. After that, differentiating the Lagrangian with regard to the policy variables and the endogenous variables, we obtain the first order conditions (A.2)–(A.30). These expressions use the following relations: ∂rB/∂g=−1/fB and ∂rB/∂w=−1/fB. Also note that a dot denotes derivative with respect to distance from the center. ∂L∂FB(m)=0:η[rB(m)−∂SB∂FB(m)]+μB(m)1fB(g(m),w(m))=0, m∈[0,MB], (A.2) ∂L∂FC(m)=0:η[rC(m)−∂SC∂FC(m)]+μC(m)1fC(rC(m))=0, m∈[MB,MC], (A.3) ∂L∂fH(m)=0:κH(m)1fH[∂uH∂fH−rH]−μH(m)1fH(m)2=0, m∈[MC,MH], (A.4) where, for deriving Equations (A.3) and (A.4), Equations (16) and (17) have been used respectively, in addition to Equation (18); (A.5) ∂L∂rH(m)=0:−κH(m)+η=0, m∈[MC,MH], (A.6) ∂L∂V=0:N¯−∫MBMCκC(m)FCfCdm−∫MCMHκH(m)1fHdm=0, (A.7) ∂L∂w(MB)=0:∫MBMCκC(m)FCfCdm+∫MCMHκH(m)1fHdm         −η∫0MBFB(m)fB(m)dm+∫0MBμB(m)FB(m)fB(m)2∂fB∂w(MB)dm=0, (A.8) where for the last term, note that ∂w(m)/∂w(MB)=1 by virtue of Equation (8); ∂L∂tB(m)=0:−ηFB(m)fB(m)−μB(m)FB(m)fB(m)2∂fB∂tB−λ˙B(m)=0, (A.9) ∂L∂tB(0)=0:−λB(0)=0, (A.10) ∂L∂Φ=0:1N¯[∫MBMCκC(m)FCfCdm+∫MCMHκH(m)1fHdm]−η=0, (A.11) ∂L∂g(m)=0:−ηFB(m)fB(m)+ω(m)−μBFB(m)fB(m)2∂fB(m)∂g(m)=0, m∈[0,MB], (A.12) ∂L∂G(m)=0:−ϕ˙B(m)−ω(m)=0,m∈[0,MB], (A.13) ∂L∂G(0)=0:−ϕB(0)+θ=0, (A.14) where for deriving this condition, Equation (A.13) is used noting that the latter holds when m→0; ∂L∂G(MB)=0:ϕB(MB)=0, (A.15) ∂L∂tC(m)=0:−κC(m)FC(m)fC(m)−λ˙C(m)=0,m∈[MB,MC], (A.16) ∂L∂tH(m)=0:−κH(m)1fH(m)−λ˙H(m)=0,m∈[MC,MH], (A.17) ∂L∂tC(MC)=0:λC(MC)−ςt=0, (A.18) ∂L∂tH(MC)=0:−λH(MC)+ςt=0, and ∂L∂tH(MH)=0:λH(MH)=0, (A.19) ∂L∂nB(m)=0:2τ[θ−ϕB(m)]+μ˙B(m)+λB(m)δγ[nB(m)]γ−1ρ(m)γ=0, m∈[0,MB], (A.20) ∂L∂nC(m)=0:λC(m)δγ[N¯−nC(m)]γ−1ρ(m)γ+μ˙C(m)=0,m∈[MB,MC], (A.21) ∂L∂nH(m)=0:λH(m)δγ[N¯−nH(m)]γ−1ρ(m)γ+μ˙H(m)=0,m∈[MC,MH], (A.22) ∂L∂nH(MC)=0:μH(MC)+ςn=0, (A.23) ∂L∂nC(MC)=0:−μC(MC)−ςn=0, (A.24) ∂L∂MB=0:[FBrB(g(MB),w)−SB(FB)−RA]+μB(MB)FB(MB)fB−[FCrC(m)−SC(FC)−RA]−λB(MB)[ξ+δ[N¯ρ(MB)]γ]−λC(MB)[ξ+δ[N¯ρ(MB)]γ]−μC(MB)FC(MB)fC(rC(MB))=0. (A.25) To derive Equation (A.25), we used ϕB(MB)=0 from Equation (A.15) and η=1 from Equations (A.7) and (A.11). ∂L∂MC=0:[FC(MC)rC−SC(FC)−RA]−[rH(MC)−RA]+μC(MC)FC(MC)fC(rC(MC))−μH(MC)1fH(MC)=0. (A.26) To derive Equation (A.26), we used λC(MC)=λH(MC) by virtue of Equations (A.18) and (A.19). ∂L∂MH=0:[rH−RA]+μH(MH)1fH(MH)=0, (A.27) ∂L∂ω(m)≥0,ω(m)≥0,∂L∂ω(m)ω(m)=0, m∈[0,MB], (A.28) λB(m)∂L∂λB(m)=0,λB(m)≤0,∂L∂λB(m)≤0, (A.29) noting the sign of the corresponding constraint in Equation (13). λk″(m)∂L∂λk″(m)=0,λk″(m)≥0,∂L∂λk″(m)≥0,k″∈{C,H}. (A.30) The first-order conditions with respect to shadow prices, except for ω(m), λB(m), λC(m) and λH(m), are suppressed because they are obvious. Appendix B. Interpretation of optimal FARR and lot size regulation B.1 FARR in the business zone First, solving Equations (A.2), (A.9) and (A.10) and using η=1 from Equation (A.7) and Equation (A.11) yields λB(m)=−nB(m)+∫0m[rB(x)−∂SB∂FB]FB(x)fB∂fB∂tBdx, where λB(m) is the shadow price for the commuting cost within the business zone. Next, substituting Equation (A.13) into (A.12) to cancel out ω(m), and then integrating the result and using boundary condition ϕB(MB)=0 from Equation (A.15), yields −ϕB(m)=−[N¯−nB(m)]−∫mMBμB(x)FB(x)fB2∂fB∂gdx. From Equation (A.14), θ=ϕB(0), whereas ϕB(0) is obtained from the aforementioned equation involving −ϕB(m), thereby yielding θ=N¯+∫0MBμB(x)FB(x)fB2∂fB∂gdx. Substituting these three equations regarding λB(m), −ϕB(m), and θ as well as Equation (A.2) into (A.20) yields ΩB≡μ˙B(m)dm   =[nB(m)−∫0m[rB(x)−∂SB∂FB]FB(x)fB∂fB∂gdx]︸=θ−ϕB(m)>0[−2τ︸<0+δγ[nB(m)]γ−1ρ(m)γ︸>0]dm, m∈(0,MB]. (A.31) Note that μ˙B(m)dm=μB(m+dm)−μB(m), where μB(m) is the shadow price for the floor area containing FB/fB number of workers at location m. Therefore, Equation (A.31) implies a change in the social welfare from the relocation of one worker from location m to location m + dm due to a change in the FARR. Recall that we have supposed a symmetric distribution of firms with respect to the center, and have focused only on the right side of the city. In fact, the relocation should take place symmetrically on both sides. The combined effect of the relocation of one worker on communication costs and traffic congestion is −2τ+δγ[nB(m)]γ−1/[ρ(m)]γ in Equation (A.31). The first term, −2τ, is related to the increase in the communication cost for firms located over [0,MB]. The relocation of one worker from m to m + dm increases the communication cost of the firms located over [0,m], but decreases the communication cost of the firms located over [m,MB]. Likewise, the symmetrical left-side relocation of one worker from –m to –m–dm increases the communication cost of the firms located over both [0,m] and [m,MB]. Summing up, the total communication cost for all firms located over [0,m] increases by 2nB(m)τ and that for all the firms over [m,MB] increases by [N¯−nB(m)][τ−τ]=0. As a result, the change in the total communication cost for the firms in the right side of the city is 2nB(m)τdm. Furthermore, the change in the communication cost for the firms located at x∈[0,m] affects the respective floor market deadweight loss caused by FARR, which is expressed as −∫0mDB(x)[FB(x)/fB][∂fB/∂g]dx·[−2τ], noting that DB(x)≡rB(x)−∂SB/∂FB expresses the change in the deadweight loss in the floor market (see Figure 3). Next, the term δγ[nB(m)]γ−1/ρ(m)γ in Equation (A.31) is the saving in traffic congestion cost for the firms located over [0,m]. This change in the traffic congestion costs also affects the respective floor market distortions caused by FARR, which is expressed as −∫0mDB(x)[FB(x)/fB][∂fB/∂g]dx·δγ[nB(m)]γ−1/[ρ(m)]γ. This concludes interpretation of Equation (A.31). Next, from Equation (A.2), ΨB≡μ˙B(m)dm=−fB(m+dm)[rB(m+dm)−∂SB∂FB(m+dm)]+fB(m)[rB(m)−∂SB∂FB(m)], (A.32) recalling that η=1 from Equations (A.7) and (A.11). The relocation of one worker implies relocation of fB units of floor space. Accordingly, Equation (A.32) implies the total change in deadweight loss in the floor market, which arises from the FARR at m + dm and m. At the optimal condition, the social welfare change due to the change in the communication cost, expressed as ΩB in Equation (A.31), should be balanced with the change in the deadweight loss in the floor market expressed as ΨB in Equation (A.32). This is the interpretation of the first-order conditions with respect to FARR in the business zone. B.2 FARR in the condominium zone First, noting that η=1, combination of Equation (A.5) and Equation (A.16), by cancelling κC, yields λ˙C(m)+FC(m)/fC−[μC(m)/fC][FC(m)/fC2]dfC/drC=0. Rearrangement of Equation (A.3) yields −μC(m)/fC(m)=rC(m)−∂SC/∂FC. Substituting this into the above equation and integrating the result with respect to m, we obtain ∫mMCλ˙C(x)dx=−∫mMCn˙C(x)dx+∫mMC[rC(x)−∂SC/∂FC]n˙C(x)[dfC/dtC]dx, which leads to −λC(m)=−[N¯−nC(m)]+∫mMC[rC(x)−∂SC∂FC]n˙C(x)dfCdtCdx, (A.33) where the following relationships are used: λC(MC)=λH(MC)=N¯−n(MC),15 and −[1/fC]dfC/drC=dfC/dtC, which is obtained from differentiating Equation (16)16. Recalling the form of the Lagrangian in Equation (A.1), [−λC(m)] on the left-hand side of Equation (A.33) expresses the shadow price for the unit travel time at m (m∈[MB,MC]). Equation (A.33) is easily interpreted as follows.17 The first term on the right-hand side of Equation (A.33) is the direct effect of the total increase in travel time for all the commuters, that is, N¯−nC(m), passing through m. The second term is the effect of the change in the per-capita floor area consumption, dfC/dtC, beyond m, which is induced by the increase in the travel cost tC(x)(x∈[m,MC]). The change in the per-capita floor area consumption, dfC/dtC, multiplied by n˙C(x) gives the change in the total floor area F(x) at x. As explained earlier, the term rC(x)−∂SC/∂FC is the marginal change in the deadweight loss (or distortion) caused by the FARR (see Figure 3(a)). If FC is determined in the perfect competition, rC(x)=∂SC/∂FC, and correspondingly the second term on the right hand side of Equation (A.33) is zero. However, when the floor area is regulated, rC(x)≠∂SC/∂FC; that is, the second term is not zero. Next, we interpret the optimality condition of FARR by combining the first-order conditions. Substituting −λC(m) from Equation (A.33) into Equation (A.21) yields ΩC≡μ˙C(m)dm=−δγ[N¯−nC(m)]γ−1ρ(m)γ[N¯−nC(m)]+δγ[N¯−nC(m)]γ−1ρ(m)γ∫mMC[rC(x)−∂SC∂FC]n˙C(x)dfCdtCdx, (A.34) where δγ[N¯−nC(m)]γ−1/ρ(m)γ=∂tC(m)/∂n˙C(m). Next, differentiating Equation (A.3) with respect to m yields ΨC≡μ˙C(m)dm=−fC(m+dm)[rC(m+dm)−∂SC∂FCFC(m+dm)]+fC(m)[rC(m)−∂SC∂FCFC(m)]. (A.35) Because both ΩC and ΨC are equal to μ˙C(m)dm, the right-hand side of Equation (A.34) should be equal to the right-hand side of Equation (A.35) for the optimality of the FARR; that is, ΩC−ΨC=0. A similar case is interpreted in Kono et al. (2012) in detail. We present only a brief explanation here as follows. The relation ΩC−ΨC=0 for the optimality of FARR implies that under the relocation of one person from m to m + dm, the welfare increase associated with the deadweight loss in the FARR, that is, −ΨC should be cancelled out by the welfare increase associated with the increased travel cost, that is, ΩC. Importantly, ‘ ΩC−ΨC’is compatible with the Harberger’s welfare formula, which measures the welfare change in a distorted economy (see Harberger, 1971).18 B.3 Lot size regulation in the lot housing zone In detached housing zone, population density is directly adjusted whereas in the case of FARR, even if the building sizes are adjusted, per-capita floor area cannot be controlled by the government. Therefore, the second term in Equation (A.34) exists in the case of FARR but not in the case of lot size regulation. To check the difference, we can derive μ˙H(m) using Equations (A.6), (A.17), (A.19) and (A.22), as μ˙H(m)=−δγ[N¯−nH(m)]γ−1ρ(m)γ[N¯−nH(m)]. (A.36)Equation (A.36) does not have the term corresponding to the second term in Equation (A.34). However, the other first-order conditions are essentially the same. Appendix C. Lemma 1 Proof is shown after Lemma 1. Lemma 1 (Optimality condition for FARR and lot size regulation in the presence of optimal zonal boundaries).19 Business zone: The sign of μB(m)(m∈[0,MB]) depends on the sign of −2τ+δγnB(m)γ−1/ρ(m)γ which can be positive or negative; however, there is at least one location where μB(m) changes sign. Two cases arise: Case (i) implying −2τ+δγnB(m)γ−1/ρ(m)γ<0at any m∈[0,MB]: μB(m)>0at any m∈[0,m⌣)and μB(m)<0at any m∈(m⌣,MB]; Case (ii) implying −2τ+δγnB(m)γ−1/ρ(m)γ>0at any m∈[ε,MB], where ε=˙0: μB(m)<0at any m∈[ε,m⌣)and μB(m)>0at any m∈(m⌣,MB]; Condominium zone: μC(m)>0at any m∈[MB,m⌢)and μC(m)<0at any m∈(m⌢,MC]and μ(m⌢)=0where m⌢∈(MB,MC); Lot housing zone: μH(mH)<0at any m∈(MC,MH]and μH(MC)=μC(MC). Lemma 1 is proved as follows. Business zone: We prove Lemma 1(1) in two steps. First, noting that η=1 and ∫0MB[FB(m)/fB(m)]dm=N, combination of Equations (A.7) and (A.8) yields ∫0MBμB(m)[FB(m)/fB2][∂fB/∂w]dm=0. (A.37) This implies that the solution of μB(m) has one of the following two patterns: pattern 1) μB(m) is positive at some m and negative at other m, where m∈[0,MB], or pattern 2) μB(m) is zero all over m∈[0,MB]. In the second step, we will analyze the sign of μ˙B(m) in Equation (A.31). Noting that ∂fB/∂w=∂fB/∂g based on Equation (7), substituting Equation (A.37) into the equation θ=N¯+∫0MBμB(x)FB(x)fB2∂fB∂gdx (from Appendix B) yields θ=N¯, and substituting into (A.14) yields ϕB(0)=N¯. Note that ϕB(MB)=0 from (A.15). Next, Equations (A.13) and (A.28) show ϕ˙B(m)<0 at any m∈(0,MB) when ∂L/∂ω(m)=0 due to the complementary slackness. Therefore, θ−ϕB(m)>0, m∈(0,MB]. This explains why the first parenthesis in Equation (A.31) is positive. It thus turns out that the sign of μ˙B(m) is the same as that of [−2τ+δγ[nB(m)]γ−1/ρ(m)γ] which can be either positive or negative. This concludes the proof of Lemma 1(1). Condominium zone: A similar explanation as in the case of business zone applies. Noting that η=1, combination of Equations (A.5), (A.6) and (A.7) yields ∫MBMCμC(m)[FC(m)/fC2][∂fC/∂rC]dm=0. To hold this, the solution of μC(m) has one of the following two patterns: pattern 1) μC(m) is positive at some m and negative at other m, m∈[MB,MC], or pattern 2) μC(m) is zero all over m∈[MB,MC]. From Equation (A.21), μ˙C(m)=−λC(m)δγ[N−nC(m)]γ−1/ρ(m)γ, m∈(MB,MC). Accordingly, μ˙C(m)<0 because λC(m)>0 from Equation (A.30), where m∈(MB,MC). Therefore, we can exclude pattern 2) of the solution of μC(m). Finally, continuous μC(m) holds Lemma 1(2). Lot housing zone: From Equations (A.6) and (A.17), noting the condition λH(MH)=0, λH(m)=∫mMH1/fH(x)dx=N¯−nH(m). Substituting this into Equation (A.22) yields μ˙H(m)=−δγ[[N¯−nH(m)]/ρ(m)]γ<0,m∈(MC,MH). Equations (A.23) and (A.24) imply μH(MC)=μC(MC), where as proved earlier, μC(MC)<0. Therefore, μH(m)=μC(MC)− ∫MCmδγ[[N−n(x)]/ρ(x)]γdx<0, m∈[MC,MH). The results μ˙H(m)<0 and μH(m)<0 prove Lemma 1(3). Appendix D. Lemma 2 Proof is shown after Lemma 2. Lemma 2(1) is derived from the combination of Equations (A.2), (A.5), (A.25), and (A.33) using η=1 and ∫MBMCμC(m)[FC(m)/fC2][∂fC/∂rC]dm=0 (from the proof of Lemma 1(2)). Following relations are also used: λC(MB)=N¯ and, from Appendix B, λB(MB)=−N¯. The inequality conditions involving μk(k={B,C,H}) are obtained from Lemma 1. Lemma 2(2) is derived from the combination of Equations (A.3), (A.4), (A.6) and (A.26). μC(MC)=μH(MC) is obtained from Equations (A.23) and (A.24). μC(MC)<0 is from Lemma 1(2). Lemma 2(3) is derived from Equation (A.27) with μH(m)=μC(MC)−∫MCmδγ[[N−n(x)]/ρ(x)]γdx, which is obtained in the proof of Lemma 1. This concludes proof of Lemma 2. The equations in Lemma 2 are interpreted following Proposition 2. But first, we compare the optimal zonal boundaries with the market boundaries. If the boundary of Zone B is determined by the market, then FBrB(g(MB),w)−SB(FB)= FCrC(MB)−SC(FC) where the land rents are equal between Zones B and C. Lemma 2(1) shows that, in Case (i), FBrB(g(MB),w)−SB(FB)>FCrC(MB)−SC(FC) because the right-hand side of the first equation in Lemma 2(1) is greater than zero. However, in Case (ii), whether FBrB(g(MB),w)−SB(FB) is greater or less than FCrC(MB)−SC(FC) is ambiguous because the right hand side of the first equation in Lemma 2(1) can be either negative or positive. Likewise, if the boundary between Zone C and Zone H is determined by the market, then FC(MC)rC(MC)−SC(FC)=rH(MC). Lemma 2(2) shows that, in the optimal case, the sign of [FC(MC)rC−SC(FC)−RA]−[rH(MC)−RA] is same as that of the right side of the equation in Lemma 2(2). The right side can be arranged into DC(MC)FC(MC)−DH(MC)=fC(MC)DC(MC)[nC(MC)−nH(MC)], using the second equation in Lemma 2(2). This implies that the right side is greater than zero because DC(MC)>0 as denoted in Lemma 2(2) and [nC(MC)−nH(MC)]>0 because, by definition, a condominium has more households than a detached house. Correspondingly, in the optimal case, [FC(MC)rC−SC(FC)−RA]−[rH(MC)−RA]>0. Finally, if the urban boundary is determined in the market, then rH(MH)=RA. Lemma 2(3) shows that in the optimal case, rH(MH)>RA because the right-hand side of the equation in Lemma 2(3) is greater than zero. Appendix E. Numerical simulations In the Supplementary data, we present some numerical examples21 to demonstrate how social welfare in our model changes with FAR and/or zonal boundaries. This helps understand the property of optimal land use regulation, theoretically achieved in this article, in a quantitative manner. However, the numerical simulation does not completely trace our Propositions. The base simulation model is a market equilibrium model, not our maximization problem (that is, Definition 2).22 Our Propositions show what properties the optimal regulations possess, compared to the market equilibrium, while our numerical simulations only show how much a certain level of difference in the level of regulation from the market equilibrium changes the welfare. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

Basile, Roberto;Ciccarelli, Carlo

2017 Journal of Economic Geography

doi: 10.1093/jeg/lbx033

Abstract This study focuses on industrial location in Italy during the period 1871–1911, when manufacturing moved from artisanal to factory-based production processes. There is general agreement in the historical and economic literature that factor endowment and domestic market potential represented the main drivers of industrial location. We test the relative importance of the above drivers of location for the various manufacturing sectors using data at the provincial level. Estimation results reveal that the location of capital intensive sectors (such as chemicals, cotton, metalmaking and paper) was driven by domestic market potential and literacy. Once market potential and literacy are accounted for, the evidence on the effect of water endowment on industrial location is mixed, depending on the manufacturing sector considered. 1. Introduction Economic theory suggests that factor endowment and market access are the key determinants of industrial location. On the one hand, the neoclassical trade theory predicts that regional differences in factor endowments (such as mineral deposits, water supply and labor skills) contribute to determine regional comparative advantages and, therefore, regional specialization. On the other hand, the New Economic Geography (NEG) literature (Krugman, 1991; Fujita et al., 1999) suggests that an uneven spatial distribution of market access encourages firms to concentrate in regions with higher market potential, to benefit from increasing returns and to export goods and services to other regions. The relative effect of factor endowment and market access on industrial location can be hardly quantified using empirical data referring to modern economies, as the two forces tend to coexist and interact in a very complex way along with the effect of (endogenous) policy interventions. Midelfart-Knarvik and Overman (2002) show for instance that the European industrial policy strongly influenced the industrial location patterns across the EU regions. As long as industrial policies are endogenously driven by the actual spatial distribution of economic activities, it can be quite difficult to quantify the genuine (net of industrial policies) effect of comparative advantages and/or market potential on industrial location. However, the use of historical data covering the years following the political unification of a country (i.e., when the process of domestic market integration was taking its first steps, and no systematic regional industrial policy existed) may provide an opportunity to better contrast the different explanations for the spatial concentration of industry and, in particular, to appreciate the role of the home-market effect. Industrialization processes, the fall in transport costs and the integration of domestic markets may indeed generate the agglomeration forces that change the distribution of economic activities across space and reinforce spatial disparities over time. As a matter of fact, the economic history literature has increasingly drawn on NEG models to analyze national historical experiences and, due to its rising importance, the manufacturing sector has received most of the attention. Examples of studies in this direction are Wolf (2007) for Poland, Klein and Crafts (2012) for the USA, Rosés (2003), Tirado et al. (2002), and Martinez-Galarraga (2012) for Spain and Crafts and Mulatu (2005) for Britain. As far as Italy is concerned, A’Hearn and Venables (2013) explore the interactions between external trade and regional disparities since the unification of the country (in 1861). The authors argue that the economic superiority of Northern regions over the rest of the country was initially based on natural advantages (in particular the endowment of water), while from the late 1880s onwards domestic market access became a key determinant of industrial location, inducing dynamic industrial sectors to locate in regions with a large domestic market—that is, in the North. From 1945 onwards, however, with the gradual process of European integration, foreign market access became the decisive factor; and the North, once again, had the advantage of proximity to these markets. While we broadly agree with the periodization proposed by A’Hearn and Venables (2013), we believe that it requires further qualification. Specifically, in line with Rosés (2003) for Spain and Klein and Crafts (2012) for the USA, we believe that the relative importance of factor endowment and market potential for industrial location varies according to the technology prevailing in the various sectors. In particular, market potential is expected to be more important in industries characterized by increasing returns to scale (typically, high and medium capital intensive industries), while factor endowment should be more relevant in the remaining manufacturing sectors. On the basis of these considerations, we analyze the spatial location patterns of the various branches of the Italian manufacturing industry during the period 1871–1911. Specifically, we assess the relative importance of factor endowment (water abundance and labor skills) and domestic market potential for industrial location behavior in the early phases of Italian industrialization, distinguishing among the various manufacturing sectors. Our analysis is based on sectoral value added data at 1911 prices at the provincial level, recently produced by Ciccarelli and Fenoaltea (2013, 2014). Our results clearly show that as transportation costs decreased and institutional barriers to domestic trade were eliminated, Italian provinces became more and more specialized and manufacturing activity became increasingly concentrated in a few provinces, mostly belonging to the North-West. The estimation results corroborate the hypothesis that both comparative advantages and domestic market potential have been responsible for this process of spatial concentration. However, the econometric analysis also reveals a heterogeneous reaction of the location of various branches of manufacturing to domestic market potential and factor endowment. In particular, the location of medium and high capital intensive sectors (including chemicals, cotton, metalmaking, machinery and paper) was mainly driven by the domestic market potential and literacy. Water endowment represented an important driver of industrial location for sectors of heterogeneous nature (such as chemicals, silk and leather). The rest of the paper is organized as follows. Section 2 illustrates the spatial distribution of manufacturing industry over the sample period. Section 3 describes the hypotheses on the key drivers of industrial location. Section 4 reports the estimation results. Section 5 concludes. 2. The spatial diffusion of manufacturing activity in Italy: 1871–1911 2.1. Setting the scene Figure 1 illustrates the division of the Italian territory that roughly prevailed during the 1815–1860 period. The seven pre-unitarian states (Kingdom of Sardinia, Kingdom of Lombardy-Venetia, Duchy of Parma and Piacenza, Duchy of Modena and Reggio, Grand Duchy of Tuscany, Papal States and Kingdom of the Two Sicilies) were characterized by extremely different institutions and economic policies. The coin, monetary regimes and trade policies were different. Primary schooling was mandatory only in certain pre-unitarian states, mainly those in the North. Figure 1 View largeDownload slide Italian provinces at 1911 borders grouped into pre-unitarian states (1815–1860 ca.). Figure 1 View largeDownload slide Italian provinces at 1911 borders grouped into pre-unitarian states (1815–1860 ca.). Italy was unified in 1861, although Venetia and Latium were annexed to the country only in 1866 and 1870, respectively. Between 1861 and 1870, the national capital was moved from Turin to Florence and, finally, to Rome. Soon after the political unification, policy makers realized that there was an urgent need of statistical information. Decennial population censuses were established, and dozens of annual reports to the Italian Parliament and other official publications concerning the main economic sectors (public budget and taxation, international trade, railroads, public school system) were regularly produced. The new official historical statistics divided the Italian territory into 16 regions (compartimenti, roughly NUTS-2 units) and 69 provinces (province, roughly NUTS-3 units). The borders of these administrative units (shown in Figure 1 and in the Appendix) did not change between 1871 and 1911. 2.2. The structure of economic activity Between 1871 and 1911, the composition of Italy’s GDP changed considerably, with industry increasing (from about 15% to 25%) at the expense of agriculture. At the same time, a considerable sectoral reallocation within manufacturing occurred. Table 1 reports the sectoral distribution of manufacturing value added at benchmark years (1871, 1881, 1901, and 1911), when population censuses were taken. With few exceptions, sectors tied to the production of consumption goods (roughly those from 2.1 foodstuffs to 2.6 leather) show a constant reduction in their shares. Sectors tied to the production of durable goods (roughly those from 2.7 metalmaking to 2.11 paper) follow an opposite long-term trend, with a rapid acceleration in the 1901–1911 decade. The last column of Table 1 summarizes the 1871–1911 trends, with numbers below 1 indicating a reduction of the sectoral share, and vice versa. Table 1 Manufacturing sectors: value added sharesa (percentages) Sectors 1871 1881 1901 1911 1911/1871 2.1 Foodstuffs 33.5 30.4 25.4 21.5 0.6 2.2 Tobacco 1.6 1.3 0.9 0.7 0.4 2.3 Textiles 10.3 10.3 12.8 11.1 1.1     2.3.1 Cotton 1.3 1.9 5.2 4.8 3.7     2.3.2 Wool 1.8 2.0 2.4 2.3 1.3     2.3.3 Silk 3.9 3.8 4.3 3.3 0.8     2.3.4 Other natural fibers 3.2 2.5 0.9 0.7 0.2 2.4 Clothing 6.9 7.4 6.8 6.3 0.9 2.5 Wood 10.0 9.3 9.7 10.0 1.0 2.6 Leather 10.5 11.5 11.4 7.8 0.7 2.7 Metalmaking 0.6 1.0 1.7 3.1 5.2 2.8 Engineering 17.5 17.8 18.7 21.5 1.2     2.8.1 Shipbuilding 2.0 1.4 3.0 1.9 1.0     2.8.2 Machinery 2.9 4.3 7.4 10.5 3.6     2.8.3 Blacksmith 12.5 12.2 9.1 9.0 0.7 2.9 Non-metallic mineral products 3.6 4.2 4.2 6.6 1.8 2.10 Chemicals and rubber 2.1 2.4 3.0 4.3 2.0 2.11 Paper 2.7 3.5 4.8 6.3 2.3 2.12 Sundry 0.7 0.7 0.6 0.7 1.0 2. Total manufacturing 100.0 100.0 100.0 100.0 1.0 Sectors 1871 1881 1901 1911 1911/1871 2.1 Foodstuffs 33.5 30.4 25.4 21.5 0.6 2.2 Tobacco 1.6 1.3 0.9 0.7 0.4 2.3 Textiles 10.3 10.3 12.8 11.1 1.1     2.3.1 Cotton 1.3 1.9 5.2 4.8 3.7     2.3.2 Wool 1.8 2.0 2.4 2.3 1.3     2.3.3 Silk 3.9 3.8 4.3 3.3 0.8     2.3.4 Other natural fibers 3.2 2.5 0.9 0.7 0.2 2.4 Clothing 6.9 7.4 6.8 6.3 0.9 2.5 Wood 10.0 9.3 9.7 10.0 1.0 2.6 Leather 10.5 11.5 11.4 7.8 0.7 2.7 Metalmaking 0.6 1.0 1.7 3.1 5.2 2.8 Engineering 17.5 17.8 18.7 21.5 1.2     2.8.1 Shipbuilding 2.0 1.4 3.0 1.9 1.0     2.8.2 Machinery 2.9 4.3 7.4 10.5 3.6     2.8.3 Blacksmith 12.5 12.2 9.1 9.0 0.7 2.9 Non-metallic mineral products 3.6 4.2 4.2 6.6 1.8 2.10 Chemicals and rubber 2.1 2.4 3.0 4.3 2.0 2.11 Paper 2.7 3.5 4.8 6.3 2.3 2.12 Sundry 0.7 0.7 0.6 0.7 1.0 2. Total manufacturing 100.0 100.0 100.0 100.0 1.0 aThe table includes 12 manufacturing sectors (numbered from 2.1 to 2.12, as it is customary in the national account, where usually 1 refers to the extractive sector, 2 to manufacturing, 3 to constructions and 4 to the utilities). Textiles (2.3) and engineering (2.8) are further disaggregated, as detailed in the Appendix. Numbers need not to add due to rounding. Table 1 Manufacturing sectors: value added sharesa (percentages) Sectors 1871 1881 1901 1911 1911/1871 2.1 Foodstuffs 33.5 30.4 25.4 21.5 0.6 2.2 Tobacco 1.6 1.3 0.9 0.7 0.4 2.3 Textiles 10.3 10.3 12.8 11.1 1.1     2.3.1 Cotton 1.3 1.9 5.2 4.8 3.7     2.3.2 Wool 1.8 2.0 2.4 2.3 1.3     2.3.3 Silk 3.9 3.8 4.3 3.3 0.8     2.3.4 Other natural fibers 3.2 2.5 0.9 0.7 0.2 2.4 Clothing 6.9 7.4 6.8 6.3 0.9 2.5 Wood 10.0 9.3 9.7 10.0 1.0 2.6 Leather 10.5 11.5 11.4 7.8 0.7 2.7 Metalmaking 0.6 1.0 1.7 3.1 5.2 2.8 Engineering 17.5 17.8 18.7 21.5 1.2     2.8.1 Shipbuilding 2.0 1.4 3.0 1.9 1.0     2.8.2 Machinery 2.9 4.3 7.4 10.5 3.6     2.8.3 Blacksmith 12.5 12.2 9.1 9.0 0.7 2.9 Non-metallic mineral products 3.6 4.2 4.2 6.6 1.8 2.10 Chemicals and rubber 2.1 2.4 3.0 4.3 2.0 2.11 Paper 2.7 3.5 4.8 6.3 2.3 2.12 Sundry 0.7 0.7 0.6 0.7 1.0 2. Total manufacturing 100.0 100.0 100.0 100.0 1.0 Sectors 1871 1881 1901 1911 1911/1871 2.1 Foodstuffs 33.5 30.4 25.4 21.5 0.6 2.2 Tobacco 1.6 1.3 0.9 0.7 0.4 2.3 Textiles 10.3 10.3 12.8 11.1 1.1     2.3.1 Cotton 1.3 1.9 5.2 4.8 3.7     2.3.2 Wool 1.8 2.0 2.4 2.3 1.3     2.3.3 Silk 3.9 3.8 4.3 3.3 0.8     2.3.4 Other natural fibers 3.2 2.5 0.9 0.7 0.2 2.4 Clothing 6.9 7.4 6.8 6.3 0.9 2.5 Wood 10.0 9.3 9.7 10.0 1.0 2.6 Leather 10.5 11.5 11.4 7.8 0.7 2.7 Metalmaking 0.6 1.0 1.7 3.1 5.2 2.8 Engineering 17.5 17.8 18.7 21.5 1.2     2.8.1 Shipbuilding 2.0 1.4 3.0 1.9 1.0     2.8.2 Machinery 2.9 4.3 7.4 10.5 3.6     2.8.3 Blacksmith 12.5 12.2 9.1 9.0 0.7 2.9 Non-metallic mineral products 3.6 4.2 4.2 6.6 1.8 2.10 Chemicals and rubber 2.1 2.4 3.0 4.3 2.0 2.11 Paper 2.7 3.5 4.8 6.3 2.3 2.12 Sundry 0.7 0.7 0.6 0.7 1.0 2. Total manufacturing 100.0 100.0 100.0 100.0 1.0 aThe table includes 12 manufacturing sectors (numbered from 2.1 to 2.12, as it is customary in the national account, where usually 1 refers to the extractive sector, 2 to manufacturing, 3 to constructions and 4 to the utilities). Textiles (2.3) and engineering (2.8) are further disaggregated, as detailed in the Appendix. Numbers need not to add due to rounding. In 1911, foodstuffs, textiles and engineering alone represented more than 50% of total value added in manufacturing. Effectively, Ciccarelli and Proietti (2013) show that these three sectors explain much of the variability of sectoral specialization at the provincial level, and thus act as a sort of ‘sufficient statistic’ for the whole manufacturing industry during 1871–1911. In addition, Fenoaltea (2016) documents how vast and heterogeneous was the engineering sectors and Rosés (2003) bases his results for Spain on the separated components of the textile industry. For these reasons, we disaggregated the data on value added for the textile and engineering sectors into sub-sectors (this was not possible for foodstuffs due to the lack of historical data). Table 1 clearly shows the importance of this disaggregation. Within the textile sector, only cotton, more suitable to mechanization than other fibers, increased substantially its value added share over time. Within engineering, the size of the machinery component increased substantially. At the same time, however, traditional blacksmith activities, despite a declining trend, accounted for about half of value added of the engineering sector even at the end of our sample period. After all, 19th-century Italy was very much an agricultural country and the maintenance of agricultural tools (such as spades, hoes and ploughs) represented a substantial part of blacksmiths’ traditional activity. 2.3. Regional specialization and geographical concentration of manufacturing activity To analyze the dynamics of regional specialization, industrial concentration and the spatial distribution of industrial activities during 1871–1911, we use disaggregated data on manufacturing value added, vik(t), at 1911 prices in province i ( i=1,…,69), sector k ( k=1,…,17)and time t ( t=1871,1881,1901,1911) and compute, for each time t the location quotient LQik=(vik/∑kvik)/(∑kvik/∑i∑kvik) (see the Appendix for details on data and indices). In 1871, the manufacturing industry mainly clustered in a few Northern provinces (Figure 2). To some extent, it was however also present in the South. Naples and Palermo, the provinces with the ancient capitals of the Kingdom of the Two Sicilies, registered in particular noticeable LQ values (respectively, 1.41 and 1.32) in line with Turin (1.35) and Genoa (1.20) that, together with Milan (1.57), formed the vertices of the so-called ‘industrial triangle’. In 1911, the North-West reinforced its dominant position, while most of the Southern provinces worsened their relative position. Figure 2 View largeDownload slide Manufacturing: choropleth maps of LQ values. Figure 2 View largeDownload slide Manufacturing: choropleth maps of LQ values. The increase in spatial inequalities in Italian manufacturing activity is also revealed by the values of the Theil index of concentration (passing from 0.03 in 1871 to 0.08 in 1911) and of the Moran’s I index of spatial autocorrelation (passing from a statically non-significant negative value of −0.04 in 1871 to a significant value of 0.05 in 1911). Moreover, the average degree of industrial specialization of Italian provinces (measured by the Krugman index) increased monotonically over the sample period (passing from 0.26 to 0.38). The Krugman index increased particularly for selected provinces of the North-West (including Turin, Milan, Genoa, Novara, Como, Cremona and Bergamo) and Tuscany (Massa Carrara, Lucca, Pisa and Leghorn) (see the Appendix). These findings are in line with the predictions of Core-Periphery NEG models (Krugman, 1991), according to which, when interregional trade costs decrease,1 industrial activities characterized by increasing returns to scale tend to concentrate in the core regions (i.e., those with higher demand; home-market effect), while the remaining (peripheral) regions suffer de-industrialization. Increased competition, in the labor market for instance, may, however, create an inverted U-shape pattern: as trade costs continue to fall, a second stage of adjustment could occur when market forces operate to undermine the core–periphery pattern and reduce regional inequalities (Krugman and Venables, 1995; Puga, 1999). However, this second stage of adjustment refers to the most recent history of globalization, so we may conclude that the evolution of the spatial distribution of the overall manufacturing activity during the period 1871–1911 is a good fit for the predictions of the core–periphery model. The spatial diffusion of the overall manufacturing activity is nevertheless the net result of heterogeneous dynamics across the 17 manufacturing branches. To analyze sectoral developments, we combine the a-spatial Theil index and the Moran’s I index in a scatterplot for 1871 and 1911, excluding tobacco and sundry (Figure 3). The vertical and horizontal dashed lines denote median values and identify four patterns in the distribution of economic activities: (a) HL (high concentration and low spatial dependence), (b) HH (high concentration and high spatial dependence), (c) LH (low concentration and high spatial dependence) and (d) LL (low concentration and low spatial dependence). Figure 3 View largeDownload slide Spatial concentration: scatterplot between the a-spatial Theil index of concentration (y-axis), and the Moran index of spatial autocorrelation (x-axis). Figure 3 View largeDownload slide Spatial concentration: scatterplot between the a-spatial Theil index of concentration (y-axis), and the Moran index of spatial autocorrelation (x-axis). Shipbuilding and leather appear the most extreme cases. Shipbuilding belongs both in 1871 and 1911 to spatial pattern a (high Theil, low Moran). This means that this industry concentrated its activity in a small number of (coastal) areas that were not close to each other. In this kind of sector, indeed, economies of scale are reached by increasing the plant size and concentrating the production in a small number of locations. Leather, both in 1871 and 1911, belongs to spatial pattern c (low Theil and high Moran). Other sectors kept their position over time. Capital intensive metalmaking belongs in 1871 and 1911 to spatial pattern b (high concentration and high spatial dependence). Traditional economic activities tied to the agricultural sector such as clothing, foodstuffs and wood, but also blacksmiths and non-metallic mineral products belong, although with some difference, to spatial pattern c (as does leather). Within textiles, silk and cotton, always characterized by above median Theil index, moved from spatial pattern a to spatial pattern b, becoming strongly agglomerated in 1911. On the contrary the other natural fibers components moved from spatial pattern b to spatial pattern a. The reallocation of the textile industry is consistent with Fenoaltea (2011) for Italy. The above evidence is also in line with the international literature. Rosés (2003) and Wolf (2007) document, respectively, for 19th-century Spain and for Poland in 1925–1937 that metalmaking and textiles were increasingly concentrated. Within the engineering sector, shipbuilding, machinery and blacksmith differ tremendously in terms of concentration, but also on the spatial autocorrelation dimension. This confirms the importance of considering further disaggregated data for this industry. One further notes that fast growing sectors (such as machinery, paper and chemicals) present in 1911 about median values of Theil and Moran. Finally, one notices a substantial continuity in the ranking of sectors along the vertical dimension (with traditional sectors like foodstuffs, clothing, blacksmiths, but also wood being the most dispersed sectors). Indeed, the ranking of the Theil indices remained very stable over time (the rank correlation between the Theil indices in 1871 and in 1911 is 0.95 with a p-value of 0.000). Interestingly, the stability in the level of concentration across industries is a pattern also found in Crafts and Mulatu (2006) for 19th-century Britain. So far we have documented the significant specialization and concentration of manufacturing industry that occurred during the sample period. In the following section, we will explore the potential drivers of this spatial evolution. 3. Drivers of industrial location The literature analyzing the main determinants of regional industrial location in the late 19th and the early 20th centuries focuses on the role played by factor endowment and market potential. Crafts and Mulatu (2006) show that patterns of industrial location in Britain were rather persistent and only marginally affected by falling transport costs during 1871–1911. Factor endowment (coal abundance) had a stronger effect on overall industrial location than proximity to markets. However, the latter was an attraction for industries with large plant size, above all shipbuilding and textiles. In addition, educated workers were an important input for the chemical but not for the textile sector. Klein and Crafts (2012) consider industrial location in the USA during 1880–1920 and show that both agglomeration mechanisms related to market potential and natural advantages influenced industrial location, although the former were increasingly important for sectors where plant size was relatively large, mainly located in the manufacturing belt. Rosés (2003) analyzes 19th-century Spain and shows that, as transport costs decreased and barriers to domestic trade were eliminated, Spanish manufacturing industry became increasingly concentrated in a few regions. Both market potential and factor endowment contribute to explain industrial location. However, the home-market effect played a key role for modern industries producing heterogeneous goods and experiencing increasing returns to scale. Wolf (2007) shows that skilled labor and inter-industry linkages have an important explanatory power for the industrial location in the case of 1925–1937 Poland. Inspired by this literature, in the remaining part of this section we provide possible measures of factor endowment and market potential and posit some hypotheses on their role as main determinants of industrial location in the case of 19th-century Italy. 3.1. Factor endowment 3.1.1. Water supply The historical literature (e.g., Cafagna, 1989) stressed the central role of natural endowment (above all, water) for industrial location in 19th-century Italy. The point was recently reiterated by Fenoaltea (2011), providing perhaps the most careful and sharp account of Italian industrialization over the 1861–1913 period. According to Fenoaltea, ‘the roots of the success of the Northern regions seem […] environmental rather than historical’ (p. 231): thus, factor endowment, more than socioeconomic variables such as social capital or institutions. Modern (or factory-based) systems of production gradually replaced artisanal production and ‘gave a strong advantage to the locations with a year-round supply of water (for power and also in the specific case of textiles, for the repeated washing of the material); and in Italy such locations abound only on the northern edge of the Po valley, where the Alpine run-off offsets the lack of summer rain’. Moreover, when analyzing the location dynamics of the textile industry during 1871–1911, Fenoaltea (2011, 232) mentions among the natural advantages of northern regions ‘the water that flowed in the rivers, the water suspended in the air […]’ and the presence of ‘mountain glaciers’. Beyond representing a source of motive power and adequate climate for textile industry (as stressed by Italy’s economic historians), rivers are in principle important determinants of industrial location of most manufacturing activities. Water may indeed work as a production input for washing, cooling, boiling and so on for both modern industries (such as chemicals) and more traditional industrial activities. As an example of the latter, consider the case of leather. Each step of the manufacturing process to obtain leather from the skins of the animals (tanning, retanning and finishing) requires a considerable amount of fresh water (Sundar et al., 2001). These arguments, and the lack of a comprehensive supporting literature on the matter, suggest that it is virtually impossible to posit specific hypotheses on the (possibly heterogeneous) response of the location of the various manufacturing sectors to water abundance. In principle, any sector should have benefited from the presence of rivers. So, we will essentially let the data speak for themselves, and assess through the econometric analysis whether water supply significantly affected industrial location net of the effect of the other variables included in the model (i.e., market potential and literacy). To measure water endowment at provincial level, the present study considers two time-invariant variables. The first one is the number of rivers in a province weighted by their economic ‘relevance’. The historical source Annuario Statistico Italiano (1886, 22–27) provides an exhaustive list of rivers flowing through the 69 Italian provinces. These rivers are ranked, with a value ranging from 1 to 5, according to the weight assigned to them by the experts of the Italian Military Geographic Institute (IGM) in a publication that culminates a research project that started in the 1960s (IGM, 2007). The importance of each river is established on the basis of ‘the length of each river and its socio-economic relevance’ (IGM, 2007, preface). In the IGM ranking, a value of 1 means ‘high relevance’, while a value of 5 means ‘low relevance’. Thus, our first measure of water endowment in each province i is the weighted average of the number of rivers in the province using (1−IGMrank/6) as weights: RIVERi=∑r∈i(1−IGMrankr/6), where r refers to each river flowing through province i. The second variable is a dummy indicating whether the province belongs to the Alpine region. Italian rivers are essentially of two types: Alpine rivers and Apennine rivers. Alpine rivers typically descend from the Alps, flowing from the North into the upper bank of the Po river. The Alps work in a sense as a sponge that absorbs water in the autumn and winter, and releases water in the spring and summer, when the glaciers melt. Alpine rivers are therefore rich in water throughout the year, while the Apennine rivers are relatively dry during the summer season—limiting the regular development of factory-based manufacturing activities that are not organized on a seasonal basis. In addition, Alpine rivers also have a higher flow rate than the Apennine rivers. As we will document in our econometric analysis, the interaction between the continuous variable RIVERi and the Alpine region dummy variable proved to be of significant help for our understanding of industrial location of certain manufacturing sectors, and supports nicely the need for industrial use of a year-round supply of water considered by Fenoaltea (2011). The provincial distribution of these water-related variables is illustrated in Figure 4. Figure 4 View largeDownload slide Water endowment. (a) Rivers and (b) Alpine region. Panel (a) shows the geographical distribution of the RIVERi variable, measuring the (weighted) number of rivers flowing through province i; panel (b) shows the provinces belonging to the Alpine region, located on the left (northern) bank of the Po river. Figure 4 View largeDownload slide Water endowment. (a) Rivers and (b) Alpine region. Panel (a) shows the geographical distribution of the RIVERi variable, measuring the (weighted) number of rivers flowing through province i; panel (b) shows the provinces belonging to the Alpine region, located on the left (northern) bank of the Po river. 3.1.2. Literacy Data on literacy rates (share of individuals aged 6 years and above able to read and write) at the provincial level for the years 1871, 1881, 1901 and 1911 are those reported in the population censuses. Data on literacy rates for 1861 (used, as we will illustrate, as an instrument for literacy rates in 1871) are also from the population census. However, in 1861 Latium and Venetia were not part of Italy and census data are not available. To fill this gap, we proceed as follows. Estimates of literacy rates for the provinces of Venetia in 1861 are obtained by assuming a constant 1871–1861 ratio of literacy rates in the regions of Lombardy and Venetia (both part of the Habsburg Empire during 1815–1860 ca.). Similarly, the estimates of literacy rates for Latium in 1861 assume a constant 1871–1861 ratio of literacy rates of Latium on the one hand, and of the macro-area formed by Emilia, Umbria and the Marches on the other hand. The underlying assumption is that, between 1861 and 1871, literacy rates of the regions forming the Papal States (during 1815–1860 ca.) evolved similarly. Figure 5 illustrates the geographical distribution of literacy rates in 1871 and 1911. As a result of very different socioeconomic developments and pre-unitarian policies, the North-South regional divide is particularly marked (Ciccarelli and Weisdorf, 2016). In 1871, the north-western regions registered literacy rates of about 50%, central and north-eastern regions of about 30% and southern regions of about 15%. In 1911, after four decades of mandatory primary public schooling, literacy rates reached some 75% in the north-west, 55 in the north-east and in the center and about 35% in the south. Figure 5 View largeDownload slide Literacy rates. Share of population aged 6 years and above able to read and write. Figure 5 View largeDownload slide Literacy rates. Share of population aged 6 years and above able to read and write. 3.2. Market potential In order to analyze the importance of domestic market access as a key driver of the spatial distribution of economic activity, a sound measure of accessibility to demand is required. In line with Klein and Crafts (2012), we construct market potential estimates for each Italian province i between 1871 and 1911 using Harris (1954)’s formula, that is, as a weighted average of GDP (or total value added) of all provinces j2: MKTPOTit=∑j=1NGDPjt×dij−1, (1) with dij the great circle distance in kilometer between the centroids of provinces i and j.3 In practice, this indicator equates the potential demand for goods and services produced in a given location with that location’s proximity to consumer markets. Thus, it can be interpreted as the volume of economic activity to which a region has access to, after having taken into account the necessary transport costs to cover the distance to reach other provinces. An important point is that historical GDP estimates at the provincial level for the case of Italy are not available. Thus, we proxy for provincial GDP by allocating total regional GDP (NUTS-2 units) estimates for 1871, 1881, 1901 and 1911 to provinces (NUTS-3 units) using the provincial shares of regional population obtained by population census (see the Appendix for further details). Figure 6 shows that the values of Harris market potential are increasingly concentrated in north-western provinces. However, estimated market potential is also high in Florence, Rome, Naples and Palermo, that is the provinces with the pre-unitarian city capitals of, respectively, the Grand Duchy of Tuscany, the Papal States and the Kingdom of the Two Sicilies. This last evidence fits perfectly well with the intuition of Fenoaltea (2003, 1073–74) who, in his study on Italian regional industrialization, noticed that in the early 1870s ‘The industrial, manufacturing regions are those with the former capitals, of the preceding decades and centuries’ and that ‘In such a context the appropriate unit of analysis is not in fact the region, but (in Italy) the much smaller province’. Figure 6 View largeDownload slide Harris market potential. Figure 6 View largeDownload slide Harris market potential. 3.3. Expected sectoral effects of market potential and literacy The international literature, as we briefly summarized at the beginning of this section, shows that both market potential and factor endowment contribute to explain industrial location patterns in Britain, Poland, Spain and in the USA during the late 19th and early 20th centuries. However, the effects are generally sector-specific. Recall for instance that both Crafts and Mulatu (2006) for the UK and Klein and Crafts (2012) for the USA show that market potential was an attraction especially for industries with large plant size. This finding is important in that it supports the view that the effect of market potential may depend on the degree of scale economies prevailing in the various sectors. Effectively, economic geography theory predicts that economic activities with increasing returns to scale tend to establish themselves in regions that enjoy good market access, while the location of economic activities with constant returns technologies is mainly influenced by factor endowment. Sectoral differences may also exist in the effect of regional skill endowment on industrial location. Standard neoclassical trade theory (Heckscher–Ohlin model) predicts that high-skilled labor intensive industries tend to be concentrated in regions with higher endowment of high-skilled labor. Crafts and Mulatu (2006) show that in 19th-century Britain educated workers were an important input for the chemical sector, but not for textiles. Based on these economic geography arguments, one may broadly expect that the location of sectors characterized by high and medium capital to labor ratio (K/L), inherently tied to skill intensity and increasing returns to scale, was relatively more influenced by market potential. Table 2 groups the Italian manufacturing sectors into light and heavy industries depending on their capital intensity (the Appendix reports maps illustrating the spatial distribution of selected high and low K/L sectors). The table reports in particular data on horse-power per worker (HP/L), often used to proxy capital intensity (e.g., Broadberry and Crafts, 1990). The table is mostly based on the data from the first industrial census of 1911 given in Zamagni (1978), and the 0.6 for 1911 threshold for ‘K/L’ inferred from Federico (2006).4 It also uses the disaggregated data for the engineering sector by Fenoaltea (2016). There is little argument in the literature that metalmaking, paper and chemicals represent high ‘K/L’ sectors, while non-metallic mineral products, wood, leather and clothing are low ‘K/L’ sectors. Within the textile industry, cotton and wool belong to the high ‘K/L’ group, while silk belongs to the low one. The production of raw silk, an activity at the boundary between agriculture and manufacturing, is a very labor-intensive activity, suitable for water-rich and densely populated areas, such as the North-West of Italy. In addition, silk represented a leading component of Italian exports toward North-Western Europe, and being a luxury good, beyond the reach of most of 19th-century Italians (Federico and Tena-Junguito, 2014). As far as the engineering industry is concerned, Fenoaltea (2016) shows that the average value of K/L = 0.33 for the whole industry actually includes values as low as 0.20 for blacksmiths and as high as 0.60 for shipyards, reflecting the fact that the manufacturing of major naval vessels (but also steam locomotives) was far more sophisticated from a technological point of view than the maintenance of agricultural tools by blacksmiths.5 A final note on the foodstuffs sector is that, as warned by Zamagni (1978), the relatively high level of horse-power per worker should not be misinterpreted, since it was largely due to the traditional flour-milling industry. Table 2 Horse-power per worker (HP/L) in 1911 High HP/L Metalmaking 2.62 Chemicals and rubber 1.30 Foodstuffsa 0.94 Textiles     Cotton 0.85     Wool 0.78 Paper 0.73 Engineering     Machinery 0.61     Shipbuilding 0.60 Low HP/L Non-metallic mineral products 0.36 Wood 0.23 Engineering     Blacksmiths 0.20 Textiles     Silk 0.11 Leather 0.09 Clothing 0.07 High HP/L Metalmaking 2.62 Chemicals and rubber 1.30 Foodstuffsa 0.94 Textiles     Cotton 0.85     Wool 0.78 Paper 0.73 Engineering     Machinery 0.61     Shipbuilding 0.60 Low HP/L Non-metallic mineral products 0.36 Wood 0.23 Engineering     Blacksmiths 0.20 Textiles     Silk 0.11 Leather 0.09 Clothing 0.07 aFoodstuffs is net of sugar (with K/L = 2.18). Source: Zamagni (1978) and Fenoaltea (2016) for machinery, shipbuilding and blacksmiths. The ‘K/L’ figure for machinery is in particular the average of rail-guided vehicles, other heavy equipment and other ordinary machinery. Table 2 Horse-power per worker (HP/L) in 1911 High HP/L Metalmaking 2.62 Chemicals and rubber 1.30 Foodstuffsa 0.94 Textiles     Cotton 0.85     Wool 0.78 Paper 0.73 Engineering     Machinery 0.61     Shipbuilding 0.60 Low HP/L Non-metallic mineral products 0.36 Wood 0.23 Engineering     Blacksmiths 0.20 Textiles     Silk 0.11 Leather 0.09 Clothing 0.07 High HP/L Metalmaking 2.62 Chemicals and rubber 1.30 Foodstuffsa 0.94 Textiles     Cotton 0.85     Wool 0.78 Paper 0.73 Engineering     Machinery 0.61     Shipbuilding 0.60 Low HP/L Non-metallic mineral products 0.36 Wood 0.23 Engineering     Blacksmiths 0.20 Textiles     Silk 0.11 Leather 0.09 Clothing 0.07 aFoodstuffs is net of sugar (with K/L = 2.18). Source: Zamagni (1978) and Fenoaltea (2016) for machinery, shipbuilding and blacksmiths. The ‘K/L’ figure for machinery is in particular the average of rail-guided vehicles, other heavy equipment and other ordinary machinery. 4. Econometric analysis This section examines the relevance of factor endowment and (domestic) market potential in shaping the location of industries across Italian provinces during the period 1871–1911. Industrial location is measured in relative terms, that is by using the log of the location quotient, ln⁡(LQ). Market potential is measured by the log of Harris (1954) formula ( ln⁡(Mktpot)). As for factor endowment, we focus on labor skills and water abundance. Labor skills are measured by the log of literacy, ln⁡(Literacy), that is, the share of people aged 6 years and above who are able to read and write. Water supply is measured by the continuous, but time-invariant, variable ln⁡(River), and its interaction with the dummy variable Alpine, indicating if the province belongs to the Alpine region. Following Combes and Gobillon (2015), we test the effect of market potential, literacy and natural advantages in two steps. In the first step, we exploit the panel structure of the data (69 provinces for four time periods) to assess the effect of time-varying variables (i.e., ln⁡(Mktpot) and ln⁡(Literacy)), while in the second step we estimate the effect of time-invariant variables (i.e., water abundance). 4.1. The effect of market potential and literacy 4.1.1. Empirical strategy In this section, we discuss the estimated effects of the two time-varying variables (i.e., ln⁡(Mktpot) and ln⁡(Literacy)). Differently from Combes and Gobillon (2015), however, in this first step we control for time-invariant unobserved heterogeneity by using a simple semiparametric model with a smooth spatial trend (the so-called Geoadditive Model) (Lee and Durbán, 2011), rather than by introducing spatial-fixed effects. More formally, for each sector k, and denoting with i and t the province and time index, the model for the first step is specified as6: ln⁡(LQi,t)=α+β1ln⁡(Literacyi,t)+β2ln⁡(Mktpoti,t)+f1(Lati)+f2(Longi)+f12(Lati,Longi)+γt+εi,tεi,t ∼ iidN(0,σε2) i=1,…,N t=1,…,T. (2) Time-fixed effects (γt) are introduced in the model to control for time-related factor biases. Moreover, the geoadditive terms, that is, the smooth effect of the latitude— f1(Lati), of the longitude— f2(Longi), and of their interaction— f12(Lati,Longi)—work as control functions (CFs) to filter the spatial trend out of the residuals, and transfer it to the mean response in a model specification. Thus, they allow to capture the shape of the spatial distribution of the dependent variable, conditional on the determinants included in the model. These CFs also isolate stochastic spatial dependence in the residuals that is spatially autocorrelated unobserved heterogeneity (see also Basile et al., 2014). Thus, they can be regarded as an alternative to individual regional dummies (spatial-fixed effects) to capture unobserved spatial heterogeneity as long as the latter is smoothly distributed over space. Regional dummies peak significantly higher and lower levels of the mean response variable. If these peaks are smoothly distributed over a two-dimensional surface (i.e., if unobserved spatial heterogeneity is spatially auto-correlated), the smooth spatial trend is able to capture them.7 We simply demonstrate the validity of these statements by estimating the two competing models without explanatory variables (see the Appendix). A complication with the estimation of model (2) is given by the presence of endogenous variables— ln⁡(Mktpoti,t) and ln⁡(Literacyi,t)—on the right-hand side (r.h.s.). As for ln⁡(Mktpoti,t), NEG models describe a process characterized by reverse causality in which market potential, by attracting firms and workers, increases production in a particular location, and this, in turn, raises its market potential. ln⁡(Literacyi,t) may also be an endogenous variable. On the one hand, the availability of literate workers may foster the concentration of industrial activities in certain regions. On the other hand, however, more industrialized regions may provide an incentive to achieve education that is generally lacking in backward areas of the country. To address these issues, we extend the REML methodology to estimate the parameters of model (2) in a 2-stage ‘CF’ approach (Blundell and Powell, 2003), that is an alternative to standard instrumental variable/two-stage least square (IV–2SLS) methods. In the first stage, each endogenous variable is regressed on a set of conformable IVs (Z), using a semiparametric model. The residuals from the first stages are then included in the original model (2) to control for the endogeneity of ln⁡Mktpoti,t and ln⁡Literacyi,t. Since the second stage contains generated regressors (i.e., the first-step residuals), a bootstrap procedure is used to compute p-values [see Basile et al. (2014) for details on the bootstrap procedure]. This procedure requires finding good instruments, that is, variables that are correlated with the endogenous explanatory variables but not with the residuals of the regression. To control for the endogeneity of market potential, we follow the main empirical literature in using a measure of centrality of the region ( Centrality=∑idij−1) (Head and Mayer, 2006), and the geographical distance from the main economic center (i.e., the distance from Milan, DistMilani) (Redding and Venables, 2004; Wolf, 2007; Klein and Crafts, 2012; Martinez-Galarraga, 2012) as IVs. To control for the endogeneity of ln⁡Literacyi,t, we use its time lag ( ln⁡Literacyi,t−10). 4.1.2. Evidence for the whole manufacturing sector For the case of the whole manufacturing activity, we report in Table 3 the estimation results of the semiparametric CF approach, along with the estimation results of a fully parametric 2SLS. Obviously, we cannot use the within-group version of the 2SLS estimator, since two important instruments (DistMilani and Centralityi) are time invariant, while the third one ( ln⁡Literacyi,t−10) would be correlated with the within-group transformed error term. Thus, in order to control for spatial heterogeneity, we include a parametric nonlinear spatial trend (i.e., Lat, Lat2, Long, Long2, Lat × Long) on the r.h.s. of the pooled 2SLS model. Table 3 Whole manufacturing. Estimation results of the parametric IV (2SLS) approach and of the semiparametric control function (CF) approach Variable 2SLS Semiparametric CF Parametric terms     Intercept 5.003 −1.833***      (0.613) (0.001)      ln⁡(Mktpot) 0.610*** 0.468***      (0.000) (0.000)      ln⁡(Literacy) 0.015 0.235**      (0.934) (0.027)     Lat −0.487      (0.238)     Lat2 0.006      (0.153)     Long 0.268      (0.456)     Long2 −0.009**      (0.027)     Lat×Long −0.001      (0.940) Non-parametric terms      f1(Lat) 7.760***      (0.000)      f2(Long) 10.259***      (0.000)      f12(Lat,Long) 20.047***      (0.000)      h1(Res1) 3.007***      (0.078)      h2(Res2) 2.933***      (0.002) Diagnostics     Weak instr.-ln(Mktpot) 21.208*** 24.461*      (0.000) (0.000)     Weak instr.-ln(Literacy) 405.489*** 210.072***      (0.000) (0.000)     Wu–Hausman 10.535*** 33.056***      (0.000) (0.000)     Sargan 0.436 3.727      (0.509) (0.155) Variable 2SLS Semiparametric CF Parametric terms     Intercept 5.003 −1.833***      (0.613) (0.001)      ln⁡(Mktpot) 0.610*** 0.468***      (0.000) (0.000)      ln⁡(Literacy) 0.015 0.235**      (0.934) (0.027)     Lat −0.487      (0.238)     Lat2 0.006      (0.153)     Long 0.268      (0.456)     Long2 −0.009**      (0.027)     Lat×Long −0.001      (0.940) Non-parametric terms      f1(Lat) 7.760***      (0.000)      f2(Long) 10.259***      (0.000)      f12(Lat,Long) 20.047***      (0.000)      h1(Res1) 3.007***      (0.078)      h2(Res2) 2.933***      (0.002) Diagnostics     Weak instr.-ln(Mktpot) 21.208*** 24.461*      (0.000) (0.000)     Weak instr.-ln(Literacy) 405.489*** 210.072***      (0.000) (0.000)     Wu–Hausman 10.535*** 33.056***      (0.000) (0.000)     Sargan 0.436 3.727      (0.509) (0.155) Notes: Coefficients, e.d.f. and bootstrap p-values (in parenthesis). Time-fixed effects are included in both models. Number of observations: 276. Table 3 Whole manufacturing. Estimation results of the parametric IV (2SLS) approach and of the semiparametric control function (CF) approach Variable 2SLS Semiparametric CF Parametric terms     Intercept 5.003 −1.833***      (0.613) (0.001)      ln⁡(Mktpot) 0.610*** 0.468***      (0.000) (0.000)      ln⁡(Literacy) 0.015 0.235**      (0.934) (0.027)     Lat −0.487      (0.238)     Lat2 0.006      (0.153)     Long 0.268      (0.456)     Long2 −0.009**      (0.027)     Lat×Long −0.001      (0.940) Non-parametric terms      f1(Lat) 7.760***      (0.000)      f2(Long) 10.259***      (0.000)      f12(Lat,Long) 20.047***      (0.000)      h1(Res1) 3.007***      (0.078)      h2(Res2) 2.933***      (0.002) Diagnostics     Weak instr.-ln(Mktpot) 21.208*** 24.461*      (0.000) (0.000)     Weak instr.-ln(Literacy) 405.489*** 210.072***      (0.000) (0.000)     Wu–Hausman 10.535*** 33.056***      (0.000) (0.000)     Sargan 0.436 3.727      (0.509) (0.155) Variable 2SLS Semiparametric CF Parametric terms     Intercept 5.003 −1.833***      (0.613) (0.001)      ln⁡(Mktpot) 0.610*** 0.468***      (0.000) (0.000)      ln⁡(Literacy) 0.015 0.235**      (0.934) (0.027)     Lat −0.487      (0.238)     Lat2 0.006      (0.153)     Long 0.268      (0.456)     Long2 −0.009**      (0.027)     Lat×Long −0.001      (0.940) Non-parametric terms      f1(Lat) 7.760***      (0.000)      f2(Long) 10.259***      (0.000)      f12(Lat,Long) 20.047***      (0.000)      h1(Res1) 3.007***      (0.078)      h2(Res2) 2.933***      (0.002) Diagnostics     Weak instr.-ln(Mktpot) 21.208*** 24.461*      (0.000) (0.000)     Weak instr.-ln(Literacy) 405.489*** 210.072***      (0.000) (0.000)     Wu–Hausman 10.535*** 33.056***      (0.000) (0.000)     Sargan 0.436 3.727      (0.509) (0.155) Notes: Coefficients, e.d.f. and bootstrap p-values (in parenthesis). Time-fixed effects are included in both models. Number of observations: 276. All in all, the diagnostic tests of the 2SLS model provide encouraging evidence in favor of the chosen set of instruments. First, the Wu–Hausman test confirms that ln⁡Literacyi,t and ln⁡Mktpoti,t are endogenous. Second, the weak instrument tests confirm that the IVs are strongly correlated to the endogenous variables. Third, the Sargan test of overidentifying restrictions suggests that the DistMilani, Centralityi, and ln⁡Literacyi,t−10 are valid instruments, that is, they are uncorrelated with the error term, and thus they are correctly excluded from the estimated equation. Nevertheless, the estimated parametric 2SLS model does not properly control for unobserved spatial heterogeneity. From Table 3 it emerges indeed that the spatial variables (Lat, Lat2, Long, Long2, Lat × Long) are weakly significant. The spatial trend in the data (i.e., the smooth spatial heterogeneity) is much better captured by the semiparametric geoadditive model as indicated by the high significance of the smooth terms f1, f2, and f12 (in column semiparametric CF).8 The smooth functions of the residuals from the two first stages ( h1(Res1) and h2(Res2)) work as CFs to correct the estimated parameters for the endogeneity bias. The statistical significance of these smooth terms can also be used as endogeneity tests. In Table 3 we also report a test of the joint significance of h1(Res1) and h2(Res2), similar to the Wu–Hausman test in the parametric 2SLS approach, as well as two weak-instrument tests using the results of the semiparametric first stages (which confirm that the excluded instruments are strongly correlated to the endogenous variables, thus rejecting the hypothesis of weak instruments). Unfortunately, there is not a well-known and widely accepted test for the validity of the conditional mean restrictions imposed by the CF approach (overidentification test). A practically feasible way of testing such restrictions consists of including the excluded instruments in the CF estimate, and testing their significance. They should not be significant since the CF should pick up all of the correlation between the structural error term and (X, Z). In our case, all the external instruments turned out to be strictly exogenous. The CF estimation results for the whole manufacturing industry show that, after controlling for unobserved heterogeneity and after correcting for the endogeneity bias, the variables ln⁡(Literacy) and ln⁡(Mktpot) enter the model significantly and positively, thus proving to be important drivers of industrial location during the sample period. In particular, the positive effect of market potential corroborates the hypothesis that even during the early stage of Italy’s industrialization firms tended to settle in regions with the highest market potential (i.e., in the North West). Moreover, the elasticity of Mktpot (0.47) is much higher than that of Literacy (0.24). 4.1.3. The heterogeneous effect of market potential and literacy across sectors Table 4 looks within manufacturing and provides the estimation results of model (2) for each industrial sector. Again, the model includes a smooth spatial trend to control for unobserved spatial heterogeneity, time dummies to control for unobserved time heterogeneity and smooth terms of first-stage residuals as CFs to correct the inconsistency due to the endogeneity of ln⁡(Mktpot) and ln⁡(Literacy).9 Table 4 Marginal effects of ln(Mktpot) and ln(Literacy) Sectors Market potential Literacy Whole manufacturing 0.468*** 0.235**      (0.000) (0.027) High HP/L sectors     Metalmaking 1.502*** 1.976***      (0.000) (0.002)     Chemicals and rubber 0.653*** 0.670**      (0.000) (0.044)     Foodstuffs −0.286*** 0.272***      (0.000) (0.002)     Cotton 2.815*** −0.244      (0.000) (0.817)     Wool 0.775* −1.475*      (0.073) (0.058)     Other natural fibers 0.614** 0.220      (0.018) (0.701)     Paper 0.969*** 0.320      (0.000) (0.217)     Machinery 0.687*** 0.105      (0.000) (0.629)     Shipbuilding 0.475 2.659**      (0.469) (0.015) Low HP/L sectors     Non-metallic mineral products 0.023 −0.770***      (0.862) (0.001)     Wood −0.191*** 0.199**      (0.001) (0.019)     Blacksmith −0.222*** −0.184*      (0.000) (0.054)     Silk 2.199*** −1.035      (0.000) (0.321)     Leather −0.453*** −0.005      (0.000) (0.963)     Clothing 0.017 0.126      (0.876) (0.406) Sectors Market potential Literacy Whole manufacturing 0.468*** 0.235**      (0.000) (0.027) High HP/L sectors     Metalmaking 1.502*** 1.976***      (0.000) (0.002)     Chemicals and rubber 0.653*** 0.670**      (0.000) (0.044)     Foodstuffs −0.286*** 0.272***      (0.000) (0.002)     Cotton 2.815*** −0.244      (0.000) (0.817)     Wool 0.775* −1.475*      (0.073) (0.058)     Other natural fibers 0.614** 0.220      (0.018) (0.701)     Paper 0.969*** 0.320      (0.000) (0.217)     Machinery 0.687*** 0.105      (0.000) (0.629)     Shipbuilding 0.475 2.659**      (0.469) (0.015) Low HP/L sectors     Non-metallic mineral products 0.023 −0.770***      (0.862) (0.001)     Wood −0.191*** 0.199**      (0.001) (0.019)     Blacksmith −0.222*** −0.184*      (0.000) (0.054)     Silk 2.199*** −1.035      (0.000) (0.321)     Leather −0.453*** −0.005      (0.000) (0.963)     Clothing 0.017 0.126      (0.876) (0.406) Notes: Coefficients and bootstrap p-values (in parenthesis). The number of observations for each sector is 276 (69 province by four time points). Table 4 Marginal effects of ln(Mktpot) and ln(Literacy) Sectors Market potential Literacy Whole manufacturing 0.468*** 0.235**      (0.000) (0.027) High HP/L sectors     Metalmaking 1.502*** 1.976***      (0.000) (0.002)     Chemicals and rubber 0.653*** 0.670**      (0.000) (0.044)     Foodstuffs −0.286*** 0.272***      (0.000) (0.002)     Cotton 2.815*** −0.244      (0.000) (0.817)     Wool 0.775* −1.475*      (0.073) (0.058)     Other natural fibers 0.614** 0.220      (0.018) (0.701)     Paper 0.969*** 0.320      (0.000) (0.217)     Machinery 0.687*** 0.105      (0.000) (0.629)     Shipbuilding 0.475 2.659**      (0.469) (0.015) Low HP/L sectors     Non-metallic mineral products 0.023 −0.770***      (0.862) (0.001)     Wood −0.191*** 0.199**      (0.001) (0.019)     Blacksmith −0.222*** −0.184*      (0.000) (0.054)     Silk 2.199*** −1.035      (0.000) (0.321)     Leather −0.453*** −0.005      (0.000) (0.963)     Clothing 0.017 0.126      (0.876) (0.406) Sectors Market potential Literacy Whole manufacturing 0.468*** 0.235**      (0.000) (0.027) High HP/L sectors     Metalmaking 1.502*** 1.976***      (0.000) (0.002)     Chemicals and rubber 0.653*** 0.670**      (0.000) (0.044)     Foodstuffs −0.286*** 0.272***      (0.000) (0.002)     Cotton 2.815*** −0.244      (0.000) (0.817)     Wool 0.775* −1.475*      (0.073) (0.058)     Other natural fibers 0.614** 0.220      (0.018) (0.701)     Paper 0.969*** 0.320      (0.000) (0.217)     Machinery 0.687*** 0.105      (0.000) (0.629)     Shipbuilding 0.475 2.659**      (0.469) (0.015) Low HP/L sectors     Non-metallic mineral products 0.023 −0.770***      (0.862) (0.001)     Wood −0.191*** 0.199**      (0.001) (0.019)     Blacksmith −0.222*** −0.184*      (0.000) (0.054)     Silk 2.199*** −1.035      (0.000) (0.321)     Leather −0.453*** −0.005      (0.000) (0.963)     Clothing 0.017 0.126      (0.876) (0.406) Notes: Coefficients and bootstrap p-values (in parenthesis). The number of observations for each sector is 276 (69 province by four time points). The results were obtained by pooling the data over the 69 provinces and the four census years (1871, 1881, 1901 and 1911). For each parametric term, we report the estimated coefficient and the corresponding bootstrapped p-value. In line with our expectations, during the period 1871–1911 market potential turned out to be a key driver of the industrial location in the case of high HP/L industries. The coefficient associated to the variable ln⁡(Mktpot) is indeed positive and strongly significant in the case of metalmaking, chemicals, paper, machinery, cotton, wool and other natural fibers. The elasticity of this variable is particularly high in the case of cotton (2.8) and metalmaking (1.5). There are, however, two exceptions. The first is shipbuilding, for which the effect of market potential is not statistically significant. But in this case, the industrial location was obviously driven by the presence of a port, independently of the market potential of the region. The second exception is foodstuffs, for which the effect is negative and significant. Census data for 1911 inform us that some 50% and more of this industrial activity was accounted for by the first- and second-stage processing of wheat and other cereals (flour-milling industry, and the baking of bread, biscuits and pasta production). These activities need often to locate close to cities, regardless of their position in the urban hierarchy. Moreover, the mild climate of the South of Italy represented a strong comparative advantage for the production of some foodstuffs, such as pasta asciutta (literally ‘dry pasta’) traditionally desiccated through simple exposition to the air. The effect of ln⁡(Mktpot) was instead negative (or not significant) in the case of low HP/L industries. Silk represents an isolated, yet important, exception. It was a labor intensive sector for which the estimated effect of market potential is sizeable (2.2), and highly significant. Recall, however, that silk production was increasingly concentrated in northern provinces and largely exported to northern European countries. Thus, it is likely that proximity to northern Europe and decreasing international physical transport costs associated with railway development, more than domestic market potential, were at the heart of the relocation of the silk industry to the northern Italian provinces.10 These findings are consistent with the predictions of the Core–Periphery NEG model (Krugman, 1991), according to which economic activities with increasing returns to scale tend to establish themselves in regions that enjoy good market access. A region with a larger market potential is also characterized by a more generous compensation of local factors, while small regions that are far from the large market will have lower local wages compared to regions close to the industrial core. Thus, if everything else is unchanged, and if the firms all achieve constant returns to scale (as in the case of low HP/L industries), the increase in the price of local factors (labor, land and so on) will reduce the profitability of all the firms at that location. Within high HP/L sectors, shipbuildings, metalmaking, foodstuffs and chemicals proved to be knowledge-intensive sectors requiring educated labor force, mainly located in the north-western regions. While, for most traditional low HP/L sectors, often tied to agriculture, literacy has a negative impact or is not significant, with wood representing the only exception. 4.2. The effect of water endowment 4.2.1. Empirical strategy and evidence for the whole manufacturing sector Similarly to Combes and Gobillon (2015), in the second step of our empirical strategy we assess the effect of time-invariant variables (i.e., Alpine, ln River and their interaction). However, instead of regressing the estimated-fixed effects, αî, on Alpinei, ln⁡(Riveri) and Alpinei×ln⁡(Riveri), we regress the estimated values of the spatial trend ( fspt̂i) on these three variables. That is, we estimate the following interaction model using OLS: fspt̂i=α+β1Alpinei+β2ln⁡(Riveri)++β3Alpinei×ln⁡(Riveri)+εiεi∼iidN(0,σε2)i=1,…,Nfspt̂i=f1̂(Lati)+f2̂(Longi)+f12̂(Lati,Longi). (3) As expected, however, the OLS residuals turned out to be spatially autocorrelated. For the case of the whole manufacturing sector, the standardized Moran I test statistic on the residuals is equal to 4.539 and its p-value is 0.000. In fact, Alpinei, ln⁡(Riveri) and Alpinei×ln⁡(Riveri) capture only a portion of the large spatial heterogeneity which characterizes the spatial distribution of the location quotient net of the effect of market potential and literacy, that is, the spatial distribution of fspt̂i (the adjusted R2 of the model is 0.31). Heterogeneity among provinces, induced by an uneven distribution of immobile resources (such as natural harbors) and amenities (climate) may also be at the origin of a variety of comparative advantages. This unobserved heterogeneity may also be spatially correlated, thus introducing spatial autocorrelation in the residuals. In order to control for spatial autocorrelation, we use a semiparametric spatial filter (Tiefelsdorf and Griffith, 2007). As is well known, spatial filtering uses a set of spatial proxy variables, which are extracted as eigenvectors from the spatial weights matrix, and implants these vectors as control variables into the model. These control variables identify and isolate the stochastic spatial dependencies among observations, thus allowing model building to proceed as if the observations were independent. Specifically, we used the function SpatialFiltering from the R library spdep. This function selects eigenvectors in a semiparametric spatial filtering approach (as proposed by Tiefelsdorf and Griffith, 2007) to remove spatial dependence from linear models. The optimal subset of eigenvectors is identified by an objective function that minimizes spatial autocorrelation, that is, by finding the single eigenvector which reduces the standard variate of Moran’s I for regression residuals most, and continuing until no candidate eigenvector reduces the value by more than a tolerance value. This subset of eigenvectors is a proxy either for those spatially autocorrelated exogenous factors that have not been incorporated into a model, or for an underlying spatial process that ties the observations together. Furthermore, incorporation of all relevant eigenvectors into a model should leave the remaining residual component spatially uncorrelated. Consequently, standard statistical modeling and estimation techniques as well as interpretations can be employed for spatially filtered models. The spatially filtered OLS estimates of model (3) confirm the widely accepted idea that, over the analyzed period, the whole manufacturing activity was mainly located in proximity to Alpine rivers. Figure 7 displays in panel (a) the changes in the marginal effect of Alpine conditional on the values of ln⁡River, that is ∂fspt̂̂∂Alpine=β1+β3ln⁡River, while it shows in panel (b) the changes in the marginal effect of the continuous variable ln⁡River conditional on the values of the dummy variable Alpine, that is ∂fspt̂̂∂ln⁡River=β2+β3Alpine. Figure 7 View largeDownload slide Whole manufacturing. Marginal effect of ln(River) and Alpine with simulated 95% confidence intervals. (a) Estimated coefficient of Alpine by ln(River) and (b) Estimated coefficient of ln(River) by Alpine. Figure 7 View largeDownload slide Whole manufacturing. Marginal effect of ln(River) and Alpine with simulated 95% confidence intervals. (a) Estimated coefficient of Alpine by ln(River) and (b) Estimated coefficient of ln(River) by Alpine. The two plots, created using the R function interplot, also include simulated 95% pointwise confidence intervals (obtained using the simulation function from the R package arm of Gelman and Hill, 2006) around these marginal effects. The plot in panel (a) shows that, with increasing importance of the river (along the horizontal axis), the magnitude of the marginal effect of Alpine on the location of the whole manufacturing sector also increases (along the vertical axis). The ‘dot-and-whisker’ plot in panel (b) shows the effect of ln⁡River (measuring the importance of the river) conditional on the dummy variable Alpine. On the one hand, when Alpine = 1 (i.e., when the province belongs to the Alpine region), the simulated 95% confidence interval around the marginal effect of ln⁡River is above (and does not contain) the horizontal zero line. On the other hand, when Alpine = 0 (i.e., when the province does not belong to the Alpine region), the simulated 95% confidence interval around the marginal effect of ln⁡River is below (and does not contain) the horizontal zero line. Thus, for manufacturing, there is a positive effect of Alpine rivers, as widely suggested by previous qualitative studies of historical nature stressing the importance of water as a source of motive power and, more generally, to sustain manufacturing activities that required water throughout the year. 4.2.2. The heterogeneous effect of water endowment across sectors Table 5 shows that, once the effect of market potential and literacy is accounted for, the marginal effect of ln⁡River when Alpine = 1 is positive and statistically significant for 6 out of 15 industries. They are evenly shared between low HP/L industries (clothing, silk and leather) and high HP/L sector (chemicals, foodstuffs and other natural fibers). In the case of chemical products, we find in particular the same result holding for the whole manufacturing industry (i.e., a positive marginal effect of Alpine rivers and a negative effect of Apennine rivers). The estimated effect is instead negative or insignificant for the remaining industries. Apennine rivers have instead a positive effect in the cases of wool, silk, blacksmith and leather. Table 5 Marginal effect of ln(River) conditional on Alpine Sectors Alpine = 0 Lower bound Upper bound Alpine = 1 Lower bound Upper bound Manufacturing −0.208* −0.281 −0.133 0.127* 0.013 0.241 High HP/L sectors     Metalmaking −0.294* −0.532 −0.059 −0.283 −0.632 0.074     Chemicals and rubber −0.198* −0.333 −0.064 0.430* 0.221 0.646     Foodstuffs 0.055 −0.018 0.130 0.150* 0.041 0.257     Cotton −0.200 −0.459 0.049 −1.023* −1.389 −0.656     Wool 0.712* 0.256 1.162 −0.002 −0.679 0.681     Other natural fibers 0.029 −0.130 0.189 0.528* 0.292 0.767     Paper −0.095 −0.215 0.025 −0.225* −0.403 −0.052     Machinery −0.040 −0.098 0.015 0.031 −0.054 0.114     Shipbuilding −1.460* −2.254 −0.661 −0.557 −1.730 0.643 Low HP/L sectors     Non-metallic mineral products 0.045 −0.074 0.164 −0.397* −0.589 −0.204     Wood −0.026 −0.091 0.039 0.051 −0.051 0.152     Blacksmith 0.089* 0.046 0.132 −0.033 −0.101 0.035     Silk 0.492* 0.016 0.961 0.731* 0.034 1.452     Leather 0.075* 0.009 0.141 0.156* 0.062 0.250     Clothing 0.078 −0.036 0.188 0.189* 0.018 0.361 Sectors Alpine = 0 Lower bound Upper bound Alpine = 1 Lower bound Upper bound Manufacturing −0.208* −0.281 −0.133 0.127* 0.013 0.241 High HP/L sectors     Metalmaking −0.294* −0.532 −0.059 −0.283 −0.632 0.074     Chemicals and rubber −0.198* −0.333 −0.064 0.430* 0.221 0.646     Foodstuffs 0.055 −0.018 0.130 0.150* 0.041 0.257     Cotton −0.200 −0.459 0.049 −1.023* −1.389 −0.656     Wool 0.712* 0.256 1.162 −0.002 −0.679 0.681     Other natural fibers 0.029 −0.130 0.189 0.528* 0.292 0.767     Paper −0.095 −0.215 0.025 −0.225* −0.403 −0.052     Machinery −0.040 −0.098 0.015 0.031 −0.054 0.114     Shipbuilding −1.460* −2.254 −0.661 −0.557 −1.730 0.643 Low HP/L sectors     Non-metallic mineral products 0.045 −0.074 0.164 −0.397* −0.589 −0.204     Wood −0.026 −0.091 0.039 0.051 −0.051 0.152     Blacksmith 0.089* 0.046 0.132 −0.033 −0.101 0.035     Silk 0.492* 0.016 0.961 0.731* 0.034 1.452     Leather 0.075* 0.009 0.141 0.156* 0.062 0.250     Clothing 0.078 −0.036 0.188 0.189* 0.018 0.361 Notes: Coefficients and bootstrap confidence intervals. The number of observations for each sector is 69. Table 5 Marginal effect of ln(River) conditional on Alpine Sectors Alpine = 0 Lower bound Upper bound Alpine = 1 Lower bound Upper bound Manufacturing −0.208* −0.281 −0.133 0.127* 0.013 0.241 High HP/L sectors     Metalmaking −0.294* −0.532 −0.059 −0.283 −0.632 0.074     Chemicals and rubber −0.198* −0.333 −0.064 0.430* 0.221 0.646     Foodstuffs 0.055 −0.018 0.130 0.150* 0.041 0.257     Cotton −0.200 −0.459 0.049 −1.023* −1.389 −0.656     Wool 0.712* 0.256 1.162 −0.002 −0.679 0.681     Other natural fibers 0.029 −0.130 0.189 0.528* 0.292 0.767     Paper −0.095 −0.215 0.025 −0.225* −0.403 −0.052     Machinery −0.040 −0.098 0.015 0.031 −0.054 0.114     Shipbuilding −1.460* −2.254 −0.661 −0.557 −1.730 0.643 Low HP/L sectors     Non-metallic mineral products 0.045 −0.074 0.164 −0.397* −0.589 −0.204     Wood −0.026 −0.091 0.039 0.051 −0.051 0.152     Blacksmith 0.089* 0.046 0.132 −0.033 −0.101 0.035     Silk 0.492* 0.016 0.961 0.731* 0.034 1.452     Leather 0.075* 0.009 0.141 0.156* 0.062 0.250     Clothing 0.078 −0.036 0.188 0.189* 0.018 0.361 Sectors Alpine = 0 Lower bound Upper bound Alpine = 1 Lower bound Upper bound Manufacturing −0.208* −0.281 −0.133 0.127* 0.013 0.241 High HP/L sectors     Metalmaking −0.294* −0.532 −0.059 −0.283 −0.632 0.074     Chemicals and rubber −0.198* −0.333 −0.064 0.430* 0.221 0.646     Foodstuffs 0.055 −0.018 0.130 0.150* 0.041 0.257     Cotton −0.200 −0.459 0.049 −1.023* −1.389 −0.656     Wool 0.712* 0.256 1.162 −0.002 −0.679 0.681     Other natural fibers 0.029 −0.130 0.189 0.528* 0.292 0.767     Paper −0.095 −0.215 0.025 −0.225* −0.403 −0.052     Machinery −0.040 −0.098 0.015 0.031 −0.054 0.114     Shipbuilding −1.460* −2.254 −0.661 −0.557 −1.730 0.643 Low HP/L sectors     Non-metallic mineral products 0.045 −0.074 0.164 −0.397* −0.589 −0.204     Wood −0.026 −0.091 0.039 0.051 −0.051 0.152     Blacksmith 0.089* 0.046 0.132 −0.033 −0.101 0.035     Silk 0.492* 0.016 0.961 0.731* 0.034 1.452     Leather 0.075* 0.009 0.141 0.156* 0.062 0.250     Clothing 0.078 −0.036 0.188 0.189* 0.018 0.361 Notes: Coefficients and bootstrap confidence intervals. The number of observations for each sector is 69. Overall, the results shed a new light on the interpretation of the much debated role of water endowment on industrial location in 19th-century Italy. The historical literature stressed that during the early development of the Italian manufacturing industry, Alpine regions had a comparative advantage (over central and southern ones) stemming from water endowment. Effectively, even when the effect of market potential and literacy is duly accounted for, there is still room left for water endowment as a driver of industrial location. However, this role appears to be inherently tied to the nature of the industrial sector considered, and cannot simply be attributed to a generic Alpine/Apennine divide. Consider the case of the silk and leather industries. The descriptive analysis (reported in the Appendix) shows that silk was increasingly agglomerated in the Alpine region, while leather was spatially diffused in the South. Both industries made an intensive use of fresh water, not just as a source of motive power, but also and more generally in the various steps of their production process. For both industries, the empirical results of Table 5 show effectively that the proximity to a river was relevant independently of its position (either Alpine or Apennine). 5. Conclusions Using a new set of provincial (NUTS-3 units) data on industrial value added at 1911 prices, this paper analyzed the spatial location patterns of manufacturing activity in Italy during the period 1871–1911. Specifically, we tested the relative effect of tangible factors, such as market size and factor endowment (water abundance and literacy), as the main drivers of industrial location, ruling out the role of intangible factors such as knowledge spillovers. The results show that, after the political and economic unification of the country in 1861, Italian provinces became more and more specialized, and manufacturing activity became increasingly concentrated in a few provinces, mostly belonging to the North-West part of the country. The estimation results corroborate the hypothesis that both comparative advantages (water endowment effect) and market potential (home-market effect) have been responsible for this process of spatial concentration. These findings are in line with those available in the literature for other countries (see, e.g., Rosés (2003) for 19th-century Spain). The capital/labor (‘K/L’) ratio, related to both skill-intensity and increasing-returns-to scale, provided useful guidance in the analysis of sectoral developments. The role of market potential as a driver of industrial location emerged clearly for medium-high ‘K/L’ sectors mostly tied to the production of durable and capital goods (metalmaking, chemicals, machinery and paper), but also of consumer goods (cotton and wool). In addition, the location of metalmaking and chemicals was positively related to the availability of more educated labor force. Furthermore, once the effect of market potential and literacy is accounted for, we find evidence that the location of some traditional industries characterized by a low K/L ratio (such as silk and leather) was mainly driven by water endowment. There are of course more historical industrial location developments in heaven and earth than in our theoretical and empirical models. The case of shipbuilding, where only literacy emerged as an important driver of industrial location, does not fit well for instance within our interpretive scheme. With these caveats in mind, our results confirm the importance of using data that are disaggregated at the sectoral level when investigating the main factors influencing regional industrial location. Our findings are in line with the Core–Periphery NEG model (Krugman, 1991) that predicts increasing polarization and regional specialization as a result of economic integration. In this model, agglomeration economies derive from the interaction among economies of scale, transportation costs and market size, while intangible external economies (such as information spillovers) do not play any role. Today NEG models are strongly criticized on the basis of the observation that they focus on forces and processes that were important a century ago but are much less relevant today. The NEG approach seems less and less applicable to the actual location patterns of advanced economies. Nevertheless, the current economic geography of fast-growing countries like Brazil, China and India is highly reminiscent of the economic geography of Western countries during the 19th century, and it fits well into the NEG framework. Historical analyses like the one presented in this paper might thus help our understanding of the current process of economic modernization of developing countries. Footnotes 1 The increasing domestic market integration (decreasing trade costs) during the sample period can be documented through several evidences. First, in the early 1860s internal trade barriers were eliminated, and the mild external trade tariff previously adopted by the Kingdom of Savoy was extended to the rest of the country (Ciccarelli and Proietti, 2013). Second, internal transport costs were reduced through the development of the railway network: 8 km in 1839, 2400 km in 1860, 9100 km in 1880, and 15,300 km in 1910, when the network was essentially completed (ISTAT, 1958, 137). Finally, the reduction in shipping and railway rates during 1870–1910 is documented in Missiaia (201648). 2 Harris (1954)’s formula can be derived from a NEG theoretical model (Combes et al., 2008). An alternative way of obtaining a structural estimate of market potential based on NEG models was proposed by Redding and Venables (2004). The latter, however, requires data on bilateral trade flows that are not available at regional level for our sample period. 3 In order to measure Harris’ market potential, we rely on geodesic distances between locations. Recent historical studies (see e.g., Martínez-Galarraga, 2014) consider more sophisticated measures of bilateral transport costs. These measures take into consideration different transport modes, the routes used in the transportation of commodities by mode and the respective freight rates; they also take into account that their evolution over time can vary for a number of reasons. The adoption of this approach is beyond the scope of the present paper, since it requires a large amount of historical information that is not available using current data sources. Rather, it will be considered as an objective of our future research agenda. 4 Federico (2006) distinguishes between light industries and heavy industries. The former are those that ‘are featured by a (relatively) low capital intensity and by the prevailing orientation toward the final consumer’, the latter ‘are more capital-intensive and produce mainly inputs for other sectors’. The author (see in particular Table 2.6 therein), uses the industrial census of 1927 and considers as heavy industries those with a ‘K/L’ value above 0.7. Our data refer to 1911, and a 0.6 threshold for ‘K/L’ dovetails better with the data at hand. 5 The historical data and methodology used in Zamagni (1978) and Fenoaltea (2016) for the engineering sector differ, so that the average ‘K/L’ value for the year 1911 proposed by Zamagni (1978) (‘K/L’ = 0.51) and by Fenoaltea (2016) (‘K/L’ = 0.33) are difficult to compare. 6 This specification is different from the one used in the related literature (e.g., by Ellison and Glaeser, 1999; Midelfart-Knarvik et al., 2000; Wolf, 2007). These authors pool the data by regions, sectors and time, and regress the location quotient on a set of interactions between the vectors of location characteristics (factor endowment and market potential) and a vector of industry characteristics (measuring industries’ factor intensities and the share of intermediate inputs in GDP). Our dataset is rich enough to avoid considering the above interaction and pooling of the data, and it allows us to estimate separate models for each industrial sector. 7 The smooth components of the spatial trend in equation 2—f1, f2 and f12—are approximated by tensor product smoothers (Wood, 2006). As is well known, any semiparametric model can be expressed as a mixed model and, thus, it is possible to estimate all the parameters using restricted maximum-likelihood methods (REMLs). To estimate this model, we used the method described by Wood (2006) which allows for automatic and integrated smoothing parameters selection through the minimization of the REML. Wood has implemented this approach in the R package mgcv. 8 For the nonparametric smooth terms (i.e., the spatial trend and the first-stage residuals), Table 3 also shows the estimated degree of freedom (e.d.f.), a broad measure of nonlinearity (an e.d.f. equal to 1 indicates linearity, while a value higher than 1 indicates nonlinearity). 9 The results for these controls are not reported in Table 4, but are available upon request. 10 Up to the late 1880s, when Italy started a nonsense trade-war with France, nearly half of Italy’s total exports, albeit rather limited in size, were directed to the French market (Federico et al., 2011, 42–43). Acknowledgements We are grateful to Brian A'Hearn, Stefano Fachin, and Jacob Weisdorf for useful comments and suggestions. 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PIEDMONT: Alessandria (AL), Cuneo (CN), Novara (NO), Turin (TO) LIGURIA: Genoa (GE), Porto Maurizio (PM) LOMBARDY: Bergamo (BG), Brescia (BS), Como (CO), Cremona (CR), Mantua (MN), Milan (MI), Pavia (PV), Sondrio (SO) VENETIA: Belluno (BL), Padua (PD), Rovigo (RO), Treviso (TV), Udine (UD), Venice (VE), Verona (VR), Vicenza (VI) EMILIA: Bologna (BO), Ferrara (FE), Forlí (FO), Modena (MO), Parma (PR), Piacenza (PC), Ravenna(RA), Reggio Emilia (RE) TUSCANY: Arezzo (AR), Florence (FI), Grosseto (GR), Leghorn (LI), Lucca (LU), Massa Carrara (MS), Pisa (PI), Siena (SI) MARCHES: Ancona (AN), Ascoli Piceno (AP), Macerata (MC), Pesaro (PE) UMBRIA: Perugia (PG) LATIUM: Rome (RM) ABRUZZI: Aquila (AQ), Campobasso (CB), Chieti (CH), Teramo (TE) CAMPANIA: Avellino (AV), Benevento (BN), Caserta (CE), Naples (NA), Salerno (SA) APULIA: Bari (BA), Foggia (FG), Lecce (LE) BASILICATA: Potenza (PZ) CALABRIA: Catanzaro (CZ), Cosenza (CS), Reggio Calabria (RC) SICILY: Caltanissetta (CL), Catania (CT), Girgenti (AG), Messina (ME), Palermo (PA), Syracuse (SR), Trapani (TP) SARDINIA: Cagliari (CA), Sassari (SS) View largeDownload slide View largeDownload slide A.2. Data A.2.1. Value added for manufacturing sectors Provincial value added data at 1911 prices for the 12 manufacturing sectors listed in Table 1 are from Ciccarelli and Fenoaltea (2013). The data are available at http://onlinelibrary.wiley.com/doi/10/j.1468-0289.2011.00643.x/full (see in particular the Supplementary Materia). Ciccarelli and Fenoaltea obtained the provincial (i.e., NUTS 3) figures as follows. They first produced annual 1861–1913 regional (i.e., NUTS 2) value added data at 1911 prices as a result of a long-term project sponsored by the bank of Italy (Ciccarelli and Fenoaltea, 2009, 2014) (see https://www.bancaditalia.it/pubblicazioni/altre-pubblicazioni-storiche/produzione-industriale-1861-1913/). The regional estimates of industrial value added are based, whenever possible and depending on the availability of historical sources, on physical production data. To give an example, consider the chemical industry. The historical sources are extremely detailed and allow one to essentially track the 1861–1913 physical production of about 100 products (sulfuric acid, soda nitric acid, Leblanc hydrochloric acid, matches, superphosphate, Thomas slang, etc.) separately for each of the 16 regions. These physical production regional series (say, tons of output) are weighted by a unitarian value added (lire of value added per ton, or other physical unit) evaluated at the national level for the year 1911 and based on historical data on capital and wages. Regional 1861–1913 value added series at 1911 prices for the whole chemical sector are then obtained by summation of the separated regional series referring to the various products. The regional estimates thus account for differences in productivity among regions and industrial sectors. Once the regional value added data for each industrial sector (VAREGIO) were obtained, the authors allocated them to provinces (VAPROV), by using the provincial labor force shares (LFSHPROV) of regional totals, separately for each industrial sector. For each given region and time, provincial value added in province i and sector j has been obtained as: VAPROVi,j=VAREGIOj*LFSHPROVi,j. As a consequence, while annual 1861–1913 regional estimates (VAREGIO) are based on a rich set of detailed historical sources, provincial estimates (VAPROV) rest essentially on the information on the labor force as reported in the population censuses and, thus, are only available for the years 1871, 1881, 1901 and 1911 (the 1891 population census was not taken, and the first industrial census was carried out in 1911). Following this approach, we used the population censuses of 1871, 1881, 1901 and 1911 to further disaggregate at the provincial level the regional value added data for the textile and engineering industries. Detailed regional value added data for the textile industry and its sectoral components (wool, silk, cotton and other natural fibers) are reported in Fenoaltea (2004), while regional value added data for the engineering industry and its sectoral components (shipbuilding, machinery and blacksmith) are provided by Ciccarelli and Fenoaltea (2014). It is worth noticing that population censuses do not generally report information on industrial sectors, rather on individual professions. The latter, as is customary, must be mapped into industrial sectors, which always involves a certain degree of arbitrariness. The details are too numerous to be even partially illustrated here. However, just to give the basic idea, we allocated, province by province, and census year by census year, to the cotton sectors professions such as cotton spinner or cotton weaver, and to the blacksmith sector professions such as blacksmith or coppersmith. Finally, we illustrate the geographical distribution of location quotients. For the reason of space, we consider metalmaking and leather as representative of ‘high’ and ‘low’ K/L sectors, respectively. We consider instead separately the main sectoral components of the textile industry (cotton and silk). Figure A1 illustrates the case of ‘high’ K/L sectors in 1871 and 1911. There is a clear predominance of the West side on Central and Northern Italy. Among northern provinces, a marked difference between sub-Alpine provinces and those along the Po valley is evident. At the same time, however, some reallocation within the Center is also evident, with a shift away from the coastal Tyrrhenian regions (Latium and Southern Tuscany). In the South light colors prevail in 1871 and 1911, especially so along the backbone represented by the Central and Southern Apennines provinces down to Calabria, at the toe of Italy’s boot. Figure A1 View largeDownload slide Metalmaking (high K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figure A1 View largeDownload slide Metalmaking (high K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figure A2 considers ‘low’ K/L sectors in 1871 and 1911. There is little change here. In 1871, and even more in 1911, a clear North-South gradient or spatial trend is present. It is interesting to note that Figure A1 and Figure A2 essentially complement each other, suggesting possibly alternative driving forces for their industrial location. Figure A2 View largeDownload slide Leather (low K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figure A2 View largeDownload slide Leather (low K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figures A3 and A4 refer finally to the geographical distribution of cotton and silk, representing, together with metalmaking, the most agglomerated sectors in 1911. The predominant role of Alpine regions emerges clearly, with Piedmont and Lombardy alone accounting for about 75% of value added in textiles in 1913 (Fenoaltea, 2004). However, the sectoral reallocation between 1871 and 1911, with the whitening of the maps for the southern provinces of Campania and Sicily is also evident, especially for the cotton industry. These facts are largely consistent with the progressive mechanization of the cotton industry, also sustained by rising protection, with import duties increased during the late 1870s and 1880s (Fenoaltea, 2004). It is also interesting to note that silk producers were instead traditionally favorable to free trade (Cafagna, 1989; Fenoaltea, 2011). Figure A3 View largeDownload slide Cotton (high K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figure A3 View largeDownload slide Cotton (high K/L): choropleth maps of LQ values. (a) 1871 and (b) 1911. Figure A4 View largeDownload slide Silk (low K/L): choropleth maps of LQ values. (a) Year: 1871 and (b) Year: 1911. Figure A4 View largeDownload slide Silk (low K/L): choropleth maps of LQ values. (a) Year: 1871 and (b) Year: 1911. A.2.2. Gross domestic product Historical GDP estimates at the provincial level for the case of Italy are not available. Thus, we proxy for provincial GDP by allocating total regional GDP (NUTS-2 units) estimates for 1871, 1881, 1901 and 1911 to provinces (NUTS-3 units) using the provincial shares of regional population obtained by population censuses. Data on GDP at historical borders (NUTS-2 units) were kindly provided by E. Felice. GDP includes of course industry, agriculture and services. It is important to stress that the industrial component of the regional GDP estimates by Felice is largely based on the statistical reconstructions by Ciccarelli and Fenoaltea considered before [we refer the reader to Felice (2013) for further details]. A.3. Geoadditive model versus fixed effects model In this appendix, we compare the estimation results of the geoadditive model and the fixed effects model using as dependence variable the location quotient for the whole manufacturing sector. Starting from a model without explanatory variables, we report in Figure A5 the choropleth map of the estimated fixed effects, αî, from a simple model like ln⁡(LQi,t)=αi+εi,t along with the choropleth map of the predicted values of the spatial trend, sptî=f1̂+f2̂+f12̂,obtained from the estimation of a simple geoadditive model without explanatory variables, ln⁡(LQi,t)=α+f1(noi)+f2(ei)+f12(noi,ei)+εi,t. Figure A5 View largeDownload slide Whole manufacturing. Comparing estimated-fixed effects and spatial trend. (a) Estimated-fixed effects and (b) Estimated spatial trend. Figure A5 View largeDownload slide Whole manufacturing. Comparing estimated-fixed effects and spatial trend. (a) Estimated-fixed effects and (b) Estimated spatial trend. By comparing Figure A5 and Figure 2, we may conclude that both models capture well the spatial distribution of the location quotient for the whole manufacturing activity. Extending the two models to include the two time-varying variables (the log of Harris market potential and the log of labor skills), we get the results reported in Table A1 which confirm that the two approaches can be used as alternative specifications to control for unobserved spatial heterogeneity. The sign of the coefficients estimated with the two models is the same, although the magnitude and level of significance is a bit different. However, the model with spatial trend has an important advantage over the fixed effects model. In particular, the geoadditive model allows us to save degrees of freedom. The fixed effect model uses 69 + 2 = 71 degrees of freedom (one coefficient for each of the 69 regional dummies, plus two parameters for the two explanatory variables), while the model with the spatial trend uses 45 effective degrees of freedom (e.d.f. for the spatial trend plus three parameters for the intercept and the two explanatory variables). To estimate the geoadditive model, we used a number of knots equal to 14 for each of the two univariate components of the spatial trend—f1 and f2—and seven knots for the bivariate term—f12. Thus, in total we used 14 + 14 + 49 = 77 knots, that is, a large number of knots (larger than the number of fixed effects!) to better capture nonlinearities in the spatial trend. However, the penalized spline method reduced the number of effectively used parameters (i.e., the e.d.f.) to 45 (exactly 45.123). It is worth noticing that the degree of smoothing, that is the degree of penalization, is automatically determined by the REML estimation procedure, and thus there is no arbitrary choice from the researcher. This suggests that we do not need to remove all the between-group variability in the model to filter the spatial unobserved heterogeneity. What really matters is to remove any systematic spatial pattern from the residuals which might be correlated to the explanatory variables (i.e., the source of endogeneity). We conclude that the spatial trend model must be preferred to the fixed effects model as a way to control spatial heterogeneity and to get reasonable results of the effects of the explanatory variables. Table A1 Whole manufacturing Variable Fixed effects Geoadditive model Intercept −1.290*** (0.444) Ln(Mktpot) 0.096** 0.144*** (0.048) (0.047) Ln(Literacy) −0.262*** −0.363*** (0.054) (0.056) Variable Fixed effects Geoadditive model Intercept −1.290*** (0.444) Ln(Mktpot) 0.096** 0.144*** (0.048) (0.047) Ln(Literacy) −0.262*** −0.363*** (0.054) (0.056) Notes: Estimation results of the parametric-fixed effect model and of the semiparametric geoadditive model. Coefficients and standard errors (in parenthesis). Number of observations: 276 (69 provinces by four points in time). Table A1 Whole manufacturing Variable Fixed effects Geoadditive model Intercept −1.290*** (0.444) Ln(Mktpot) 0.096** 0.144*** (0.048) (0.047) Ln(Literacy) −0.262*** −0.363*** (0.054) (0.056) Variable Fixed effects Geoadditive model Intercept −1.290*** (0.444) Ln(Mktpot) 0.096** 0.144*** (0.048) (0.047) Ln(Literacy) −0.262*** −0.363*** (0.054) (0.056) Notes: Estimation results of the parametric-fixed effect model and of the semiparametric geoadditive model. Coefficients and standard errors (in parenthesis). Number of observations: 276 (69 provinces by four points in time). A.4. Specialization, concentration and spatial dependence A.4.1. Krugman specialization index We address the question of how specialized were Italian provinces by using Krugman’s specialization index Ki that, for a given point in time (t), is defined as: Ki=∑k|(sik−si−k)|0≤Ki≤2, where sik=(vik)/(∑kvik), and si−k is the share of industry k in the national total net of province i. Thus, the Krugman index provides a measure of the difference in the specialization of a given province when compared with the remaining provinces of the country. It takes the value of 0 if there is no difference, and the value of 2 if a province has no industries in common with the rest of Italy. Figure A6 illustrates the territorial distribution of Ki in 1871 and 1911. Figure A6 View largeDownload slide Specialization: Krugman index. Figure A6 View largeDownload slide Specialization: Krugman index. A.4.2. Theil index of concentration The relative Theil index of concentration (Ck) is based on the normalized location quotient, that is LQik normalized by the ratio between vi (manufacturing value added in province i) over V (manufacturing value added in Italy): Ck=∑iviVln⁡(LQik). The higher the value of Ck, the higher the concentration of industry k. The relative Theil index Ck provides useful information about the extent to which industries are concentrated in a limited number of areas, but it does not take into consideration whether those areas are close together or far apart. In other words, it does not take into account the spatial structure of the data. Every region is treated as an island, and its position in space relative to other regions is not taken into account. Thus, the relative Theil index, Ck(t), is an a-spatial measure of concentration: the same degree of concentration can be compatible with very different localization schemes. For example, two industries may appear equally geographically concentrated, while one is located in two neighboring regions, and the other splits between the northern and the southern part of the country. As pointed out by Arbia et al. (2013), a more accurate analysis of the spatial distribution of economic activities requires the combination of traditional measures of geographical concentration and methodologies that account for spatial dependence, in that they provide different and complementary information about the concentration of the various sectors. A.4.3. Moran’s I index of spatial dependence Spatial autocorrelation is present when the values of one variable observed at nearby locations are more similar than those observed in locations that are far apart. More precisely, positive spatial autocorrelation occurs when high or low values of a variable tend to cluster together in space and negative spatial autocorrelation when high values are surrounded by low values and vice versa. Among the spatial dependence measures the most widely used is the Moran’s I index based, as is well known, on a comparison of LQik at any location with the value of the same variable at surrounding locations. The most widely used is the Moran’s I index: I=(N∑i∑jwij)(∑i∑jwij(LQi−LQ¯)(LQj−LQ¯)∑i(LQi−LQ¯)2), (4) where N is the total number of provinces, LQi and LQj are the observed values of the location quotient for the locations i and j (with mean LQ¯), and the first term is a scaling constant. This statistic compares the value of a continuous variable at any location with the value of the same variable at surrounding locations. The spatial structure of the data is formally expressed in a spatial weight matrix W with generic elements wij (with i≠j). In this paper, we employ a row-standardized spatial weights matrix (W), whose elements wij on the main diagonal are set to zero whereas wij = 1 if dij<d¯ and wij = 0 if dij>d¯, with dij the great circle distance between the centroids of region i and region j and d¯ a cut-off distance (equal to 112 km, corresponding to the minimum distance which allows all provinces to have at least one neighbor). Table A2 reports the calculated value of the Theil and Moran indices for the years 1871, 1881, 1901 and 1911 with data disaggregated by sector. Table A2 Industry concentration: Theil index and Moran’s I (1) (2) (3) (4) (5) (6) (7) (8) Theil Moran 1871 1881 1901 1911 1871 1881 1901 1911 2.1 Foodstuffs 0.02 0.02 0.04 0.06 0.15 0.31 0.25 0.29 (−0.02) (0.00) (0.00) (0.00) 2.2 Tobacco 1.23 1.05 1.04 0.81 −0.04 0.00 0.02 0.01 (−0.63) (−0.41) (−0.32) (−0.38) 2.3 Textiles 0.26 0.30 0.45 0.45 0.33 0.38 0.47 0.49 (0.00) (0.00) (0.00) (0.00)     2.3.1 Cotton 0.90 0.91 0.70 0.63 0.04 0.08 0.39 0.44 (0.23) (0.11) (0.00) (0.00)     2.3.2 Wool 1.09 1.21 1.40 1.30 0.03 0.02 0.00 0.00 (0.27) (0.27) (0.42) (0.41)     2.3.3 Silk 1.44 1.45 1.14 1.04 0.04 0.04 0.13 0.26 (0.04) (0.08) (0.00) (0.00)     2.3.4 Other natural fibers 0.27 0.37 0.23 0.40 0.19 0.45 0.07 −0.06 (0.00) (0.00) (0.14) (0.73) 2.4 Clothing 0.11 0.13 0.10 0.11 0.29 0.30 0.40 0.35 (0.00) (0.00) (0.00) (0.00) 2.5 Wood 0.02 0.02 0.03 0.05 0.11 0.10 0.22 0.37 (−0.05) (−0.06) (0.00) (0.00) 2.6 Leather 0.05 0.06 0.11 0.16 0.60 0.62 0.69 0.73 (0.00) (0.00) (0.00) (0.00) 2.7 Metalmaking 0.38 0.57 0.86 0.74 0.28 0.26 0.17 0.17 (0.00) (0.00) (0.00) (0.00) 2.8 Engineering 0.05 0.03 0.06 0.07 0.17 0.19 0.12 0.02 (−0.01) (0.00) (−0.03) (−0.34)     2.8.1 Shipbuildings 1.95 1.56 1.67 1.79 0.00 −0.01 −0.02 −0.06 (0.34) (0.49) (0.55) (0.78)     2.8.2 Machinery 0.16 0.09 0.22 0.19 0.02 0.35 0.06 0.08 (0.32) (0.00) (0.16) (0.10)     2.8.3 Blacksmith 0.04 0.03 0.04 0.02 0.35 0.37 0.43 0.11 (0.00) (0.00) (0.00) (0.05) 2.9 Non-metallic mineral products 0.17 0.17 0.19 0.09 0.20 0.08 0.12 0.11 (0.00) (−0.03) (0.00) (−0.02) 2.10 Chemicals and rubber 0.18 0.16 0.23 0.17 −0.04 0.15 0.00 0.05 (−0.61) (−0.02) (−0.40) (−0.19) 2.11 Paper and printing 0.21 0.21 0.17 0.16 0.11 0.07 0.06 0.07 (−0.05) (−0.12) (−0.17) (−0.13) 2.12 Sundry 0.33 0.89 0.62 0.46 0.05 0.00 0.01 0.15 (−0.19) (−0.37) (−0.36) (−0.01) 2. Total manufacturing 0.03 0.04 0.07 0.08 0.05 0.00 0.01 0.15 (−0.47) (−0.41) (−0.09) (−0.02) (1) (2) (3) (4) (5) (6) (7) (8) Theil Moran 1871 1881 1901 1911 1871 1881 1901 1911 2.1 Foodstuffs 0.02 0.02 0.04 0.06 0.15 0.31 0.25 0.29 (−0.02) (0.00) (0.00) (0.00) 2.2 Tobacco 1.23 1.05 1.04 0.81 −0.04 0.00 0.02 0.01 (−0.63) (−0.41) (−0.32) (−0.38) 2.3 Textiles 0.26 0.30 0.45 0.45 0.33 0.38 0.47 0.49 (0.00) (0.00) (0.00) (0.00)     2.3.1 Cotton 0.90 0.91 0.70 0.63 0.04 0.08 0.39 0.44 (0.23) (0.11) (0.00) (0.00)     2.3.2 Wool 1.09 1.21 1.40 1.30 0.03 0.02 0.00 0.00 (0.27) (0.27) (0.42) (0.41)     2.3.3 Silk 1.44 1.45 1.14 1.04 0.04 0.04 0.13 0.26 (0.04) (0.08) (0.00) (0.00)     2.3.4 Other natural fibers 0.27 0.37 0.23 0.40 0.19 0.45 0.07 −0.06 (0.00) (0.00) (0.14) (0.73) 2.4 Clothing 0.11 0.13 0.10 0.11 0.29 0.30 0.40 0.35 (0.00) (0.00) (0.00) (0.00) 2.5 Wood 0.02 0.02 0.03 0.05 0.11 0.10 0.22 0.37 (−0.05) (−0.06) (0.00) (0.00) 2.6 Leather 0.05 0.06 0.11 0.16 0.60 0.62 0.69 0.73 (0.00) (0.00) (0.00) (0.00) 2.7 Metalmaking 0.38 0.57 0.86 0.74 0.28 0.26 0.17 0.17 (0.00) (0.00) (0.00) (0.00) 2.8 Engineering 0.05 0.03 0.06 0.07 0.17 0.19 0.12 0.02 (−0.01) (0.00) (−0.03) (−0.34)     2.8.1 Shipbuildings 1.95 1.56 1.67 1.79 0.00 −0.01 −0.02 −0.06 (0.34) (0.49) (0.55) (0.78)     2.8.2 Machinery 0.16 0.09 0.22 0.19 0.02 0.35 0.06 0.08 (0.32) (0.00) (0.16) (0.10)     2.8.3 Blacksmith 0.04 0.03 0.04 0.02 0.35 0.37 0.43 0.11 (0.00) (0.00) (0.00) (0.05) 2.9 Non-metallic mineral products 0.17 0.17 0.19 0.09 0.20 0.08 0.12 0.11 (0.00) (−0.03) (0.00) (−0.02) 2.10 Chemicals and rubber 0.18 0.16 0.23 0.17 −0.04 0.15 0.00 0.05 (−0.61) (−0.02) (−0.40) (−0.19) 2.11 Paper and printing 0.21 0.21 0.17 0.16 0.11 0.07 0.06 0.07 (−0.05) (−0.12) (−0.17) (−0.13) 2.12 Sundry 0.33 0.89 0.62 0.46 0.05 0.00 0.01 0.15 (−0.19) (−0.37) (−0.36) (−0.01) 2. Total manufacturing 0.03 0.04 0.07 0.08 0.05 0.00 0.01 0.15 (−0.47) (−0.41) (−0.09) (−0.02) Note: p-values in parenthesis. Table A2 Industry concentration: Theil index and Moran’s I (1) (2) (3) (4) (5) (6) (7) (8) Theil Moran 1871 1881 1901 1911 1871 1881 1901 1911 2.1 Foodstuffs 0.02 0.02 0.04 0.06 0.15 0.31 0.25 0.29 (−0.02) (0.00) (0.00) (0.00) 2.2 Tobacco 1.23 1.05 1.04 0.81 −0.04 0.00 0.02 0.01 (−0.63) (−0.41) (−0.32) (−0.38) 2.3 Textiles 0.26 0.30 0.45 0.45 0.33 0.38 0.47 0.49 (0.00) (0.00) (0.00) (0.00)     2.3.1 Cotton 0.90 0.91 0.70 0.63 0.04 0.08 0.39 0.44 (0.23) (0.11) (0.00) (0.00)     2.3.2 Wool 1.09 1.21 1.40 1.30 0.03 0.02 0.00 0.00 (0.27) (0.27) (0.42) (0.41)     2.3.3 Silk 1.44 1.45 1.14 1.04 0.04 0.04 0.13 0.26 (0.04) (0.08) (0.00) (0.00)     2.3.4 Other natural fibers 0.27 0.37 0.23 0.40 0.19 0.45 0.07 −0.06 (0.00) (0.00) (0.14) (0.73) 2.4 Clothing 0.11 0.13 0.10 0.11 0.29 0.30 0.40 0.35 (0.00) (0.00) (0.00) (0.00) 2.5 Wood 0.02 0.02 0.03 0.05 0.11 0.10 0.22 0.37 (−0.05) (−0.06) (0.00) (0.00) 2.6 Leather 0.05 0.06 0.11 0.16 0.60 0.62 0.69 0.73 (0.00) (0.00) (0.00) (0.00) 2.7 Metalmaking 0.38 0.57 0.86 0.74 0.28 0.26 0.17 0.17 (0.00) (0.00) (0.00) (0.00) 2.8 Engineering 0.05 0.03 0.06 0.07 0.17 0.19 0.12 0.02 (−0.01) (0.00) (−0.03) (−0.34)     2.8.1 Shipbuildings 1.95 1.56 1.67 1.79 0.00 −0.01 −0.02 −0.06 (0.34) (0.49) (0.55) (0.78)     2.8.2 Machinery 0.16 0.09 0.22 0.19 0.02 0.35 0.06 0.08 (0.32) (0.00) (0.16) (0.10)     2.8.3 Blacksmith 0.04 0.03 0.04 0.02 0.35 0.37 0.43 0.11 (0.00) (0.00) (0.00) (0.05) 2.9 Non-metallic mineral products 0.17 0.17 0.19 0.09 0.20 0.08 0.12 0.11 (0.00) (−0.03) (0.00) (−0.02) 2.10 Chemicals and rubber 0.18 0.16 0.23 0.17 −0.04 0.15 0.00 0.05 (−0.61) (−0.02) (−0.40) (−0.19) 2.11 Paper and printing 0.21 0.21 0.17 0.16 0.11 0.07 0.06 0.07 (−0.05) (−0.12) (−0.17) (−0.13) 2.12 Sundry 0.33 0.89 0.62 0.46 0.05 0.00 0.01 0.15 (−0.19) (−0.37) (−0.36) (−0.01) 2. Total manufacturing 0.03 0.04 0.07 0.08 0.05 0.00 0.01 0.15 (−0.47) (−0.41) (−0.09) (−0.02) (1) (2) (3) (4) (5) (6) (7) (8) Theil Moran 1871 1881 1901 1911 1871 1881 1901 1911 2.1 Foodstuffs 0.02 0.02 0.04 0.06 0.15 0.31 0.25 0.29 (−0.02) (0.00) (0.00) (0.00) 2.2 Tobacco 1.23 1.05 1.04 0.81 −0.04 0.00 0.02 0.01 (−0.63) (−0.41) (−0.32) (−0.38) 2.3 Textiles 0.26 0.30 0.45 0.45 0.33 0.38 0.47 0.49 (0.00) (0.00) (0.00) (0.00)     2.3.1 Cotton 0.90 0.91 0.70 0.63 0.04 0.08 0.39 0.44 (0.23) (0.11) (0.00) (0.00)     2.3.2 Wool 1.09 1.21 1.40 1.30 0.03 0.02 0.00 0.00 (0.27) (0.27) (0.42) (0.41)     2.3.3 Silk 1.44 1.45 1.14 1.04 0.04 0.04 0.13 0.26 (0.04) (0.08) (0.00) (0.00)     2.3.4 Other natural fibers 0.27 0.37 0.23 0.40 0.19 0.45 0.07 −0.06 (0.00) (0.00) (0.14) (0.73) 2.4 Clothing 0.11 0.13 0.10 0.11 0.29 0.30 0.40 0.35 (0.00) (0.00) (0.00) (0.00) 2.5 Wood 0.02 0.02 0.03 0.05 0.11 0.10 0.22 0.37 (−0.05) (−0.06) (0.00) (0.00) 2.6 Leather 0.05 0.06 0.11 0.16 0.60 0.62 0.69 0.73 (0.00) (0.00) (0.00) (0.00) 2.7 Metalmaking 0.38 0.57 0.86 0.74 0.28 0.26 0.17 0.17 (0.00) (0.00) (0.00) (0.00) 2.8 Engineering 0.05 0.03 0.06 0.07 0.17 0.19 0.12 0.02 (−0.01) (0.00) (−0.03) (−0.34)     2.8.1 Shipbuildings 1.95 1.56 1.67 1.79 0.00 −0.01 −0.02 −0.06 (0.34) (0.49) (0.55) (0.78)     2.8.2 Machinery 0.16 0.09 0.22 0.19 0.02 0.35 0.06 0.08 (0.32) (0.00) (0.16) (0.10)     2.8.3 Blacksmith 0.04 0.03 0.04 0.02 0.35 0.37 0.43 0.11 (0.00) (0.00) (0.00) (0.05) 2.9 Non-metallic mineral products 0.17 0.17 0.19 0.09 0.20 0.08 0.12 0.11 (0.00) (−0.03) (0.00) (−0.02) 2.10 Chemicals and rubber 0.18 0.16 0.23 0.17 −0.04 0.15 0.00 0.05 (−0.61) (−0.02) (−0.40) (−0.19) 2.11 Paper and printing 0.21 0.21 0.17 0.16 0.11 0.07 0.06 0.07 (−0.05) (−0.12) (−0.17) (−0.13) 2.12 Sundry 0.33 0.89 0.62 0.46 0.05 0.00 0.01 0.15 (−0.19) (−0.37) (−0.36) (−0.01) 2. Total manufacturing 0.03 0.04 0.07 0.08 0.05 0.00 0.01 0.15 (−0.47) (−0.41) (−0.09) (−0.02) Note: p-values in parenthesis. A.5. The sectorial effects of Alpine regions as a function of river The following figure shows the estimated marginal effects of the dummy Alpine, conditional on the effect of market potential and literacy, as a function of the river variable. Alpine provinces show a comparative advantage in the location of industrial activity in the case of machinery, cotton, silk, blacksmith and non-metallic mineral products. Figure A7 View largeDownload slide Estimated coefficient of Alpine by ln(River) with simulated 95% confidence intervals. Figure A7 View largeDownload slide Estimated coefficient of Alpine by ln(River) with simulated 95% confidence intervals. © The Author (2017). Published by Oxford University Press. All rights reserved. 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Gershenson, Seth;Hayes, Michael S

2017 Journal of Economic Geography

doi: 10.1093/jeg/lbx014

Abstract We document externalities of the police shooting of an unarmed black teenager and the resultant civic unrest experienced in Ferguson, MO. Difference-in-differences estimates compare Ferguson-area schools to neighboring schools in the greater St. Louis area and find that the unrest led to statistically significant, arguably causal declines in elementary school students’ math and reading achievement. Attendance is one mechanism through which this effect operated, as chronic absence increased by 5% in Ferguson-area schools. Impacts were concentrated in the bottom of the achievement distribution and spilled over into majority black schools throughout the greater St. Louis area. 1. Introduction The August 2014 police shooting of Michael Brown, an unarmed black teenager, in Ferguson, MO prompted local protests against real and perceived racial inequities in police departments’ treatment of citizens and communities in the Ferguson-area northwest of St. Louis. These protests quickly attracted activists and media coverage from across the country. Similar protests, and accompanying civic unrest, spread to several major American cities during the latter half of 2014, both in response to the events in Ferguson and to similar incidents in which unarmed black males were killed by police. Notable examples include the killings of 43-year-old Eric Garner in New York and 12-year-old Tamir Rice in Cleveland. Unrest in Ferguson and in other parts of the country continued into 2015, when the officers involved in previous incidents were neither indicted nor formally charged. New, external events generated renewed unrest in Ferguson, such as the death of Freddie Gray while in police custody in Baltimore in April 2015. Ensuing protests, demonstrations, civic unrest, riots, and growth of socio-political movements (e.g. Black Lives Matter) renewed public discussion of racial differences in citizens’ exposure to, and interactions with, law enforcement and the criminal justice system.1 Of course, whether these events and movements create long run, permanent changes in policing practices, racial segregation and living conditions in inner city, historically disadvantaged communities remains to be seen. In the short run, however, episodes of civic unrest associated with protests potentially impose both direct and indirect costs on society. These knock-on costs are in addition to the direct effects (e.g. trauma and stress) of the shooting itself, though it is difficult, if not impossible, to disentangle the effects of each shock. This is not to say that demonstrations and protests associated with social movements are ‘bad’ in the sense that they necessarily reduce social welfare. Indeed, they may be catalysts for change that alleviate social injustices, establish human rights and create social benefits that far outweigh any associated costs. Rather, understanding the size, distribution and burdens of these costs is crucial for policymakers and community leaders seeking to minimize short-run harm. For example, direct costs of the riots in Ferguson include upwards of $4 million in property damage (Unglesbee, 2014) and as much as $20 million in spending by local and state governments, mainly for overtime for first responders (Davis, 2014). Wenger (2015a, 2015b) reports similar direct costs of the 2015 Baltimore riots. There are other potential short-run costs that policymakers and institutions can potentially mitigate. However, such costs have received relatively little attention thus far, perhaps because they are inherently difficult to quantify. Doing so is important, as identifying the nature and magnitude of negative externalities is paramount to devising effective and efficient policy responses. The current study investigates one potential class of such indirect costs: the causal effect of a police shooting and the subsequent prolonged, acute civic unrest associated with the incident on schools and student achievement. Identifying the impact of highly publicized, racially charged citizen–police interactions and the ensuing civic unrest, on student outcomes is important for at least three reasons. First, there is likely room for schools and communities to intervene and mitigate the associated harms. Second, educational success is likely to play a key role in breaking cycles of poverty and violence in disadvantaged neighborhoods, given the well-documented association between educational attainment and earnings (Card, 1999; Blundell et al., 2005), civic engagement (Dee, 2004; Milligan et al., 2004) and crime (Lochner and Moretti, 2004; Deming, 2011; Machin et al., 2011). Finally, in an era of consequential accountability in which schools are sanctioned for low aggregate performance on standardized tests (e.g. Figlio and Loeb, 2011), sanctions that result from shootings, civic unrest and other communitywide shocks outside schools’ control present additional hurdles that schools serving disadvantaged communities must overcome. The police shooting of Michael Brown in Ferguson, MO provides an ideal natural experiment with which to analyze the impact of intense, prolonged civic unrest and attention to racial disparities in interactions with the criminal justice system following a racially charged incident on student achievement: the shooting occurred on the eve of the 2014–2015 school year and intermittent protests occurred throughout the subsequent 9 months (i.e. the entirety of the 2014–2015 school year). While Ferguson schools were already relatively low performing and serving disproportionately large numbers of high-needs students compared to other schools in the St. Louis area, it is possible that the added stress and distractions associated with the shooting and subsequent protests, riots, violence, out of town visitors and media attention further harmed student achievement, through some combination of causing student and teacher absences, shifting classroom time from curricular instruction to discussion of current events, changing home and parental behaviors, causing mental stress and concern for the safety of students’ neighborhoods and family members and by disrupting learning environments. To account for preexisting differences between schools in the Ferguson area and schools in other parts of the state, we attempt to identify the impact of the events in Ferguson using difference-in-differences (DD) methods that explicitly control for preexisting differences (and differential trends) between schools.2 We do so using school-level data on annual academic achievement and student attendance, both overall and for the subset of high-needs students, from 2010 to 2015.3 This article contributes to a growing body of literature that investigates the effects of exposure to stressors such as acute violence, natural disasters and communitywide violence (i.e. civil wars) on student achievement. Particularly relevant to the context of urban centers in the USA, a series of papers by Patrick Sharkey and coauthors (Sharkey, 2010; Sharkey et al., 2012, 2014) estimate the effect of students’ geographical proximity to homicides on various cognitive measures and standardized tests in inner city neighborhoods in Chicago and New York by exploiting arguably random temporal variation in homicides within neighborhoods. Beland and Kim (2016) estimate the impact of school shootings (i.e. homicides that occurred on school grounds) using a similar identification strategy. While these studies consistently find evidence of a short-run effect of exposure to one-off incidents of acute violence on student achievement, their implications for the harm attributable to unexpected, longer lasting neighborhood- or city-level disruptions is unclear. One of the few studies to investigate the impact of sustained exposure to a communitywide traumatic event in the US context is Gershenson and Tekin (2015). The authors find that exposure to the ‘Beltway Sniper’ attacks, which occurred during a three week period in October 2002, reduced primary school students’ math achievement. They use a DD strategy that compares schools in the I-95 corridor that were within five miles of a sniper attack to those that were not, which is similar to the DD strategy applied in the current study. While Gershenson and Tekin (2015) provide evidence that less acute, longer-term exposure to external stressors can harm student achievement, the stress and disruption attributable to the police shooting and resultant civic unrest in Ferguson was fundamentally different in at least two ways. First, it was sustained, with intermittent outbreaks of extreme disruption, over an entire academic year. Second, the source of the stress was not a random targeting, but rather a specific incident that caused long simmering racial and socioeconomic tensions in the community to erupt. Thus, the current study contributes to this literature by documenting the short-run impact of a police shooting and the subsequent, sustained civic unrest in a relatively segregated, disadvantaged community on students’ educational outcomes. Additionally, we investigate some potential mechanisms through which such effects operate. The article proceeds as follows: Section 2 reviews the timeline of events in Ferguson, MO that precipitated and sustained the civic unrest throughout the 2015 academic year and describes the geography and district catchment areas used to define the treatment. Section 3 describes the data. Section 4 describes the identification strategy. The school-level DD results are presented in Section 5. Section 6 concludes. 2. Background 2.1. Ferguson Timeline The civic unrest in Ferguson, MO began shortly after Michael Brown, an 18-year-old black male, was shot and killed by a white police officer on 9 August 2014.4 Brown was unarmed and some witnesses claimed that he was surrendering at the time he was shot. Shortly thereafter, crowds gathered at the scene, and later that evening some rioting and looting occurred on nearby West Florissant Avenue. For the next 10 days or so, the Ferguson area witnessed several tense standoffs and encounters between protestors and police. There was a heavy media presence as well. A strong police response, which included militaristic vehicles and arms, may have escalated the tension. Tensions eased as Brown’s funeral was held on 25 August, though a series of sporadic protests, arrests and announcements from the authorities occurred throughout September and October. A second round of intense violence, riots and standoffs between protestors and police occurred in the second half of November 2014, this time due to a grand jury’s failure to indict the police officer involved in the shooting of Michael Brown. This series of protests and rioting lasted for about 1 week. Protests spread to other cities across the country in response to the grand jury’s decision. Smaller outbreaks of violence in Ferguson occurred in March and April of 2015, in response to the Ferguson police chief’s resignation and the death of Freddie Gray in police custody in Baltimore, respectively. The cycle of civic unrest came full circle when additional looting and shootings occurred in concert with demonstrations and protests commemorating the 1-year anniversary of Brown’s death in August 2015. Thus, from the time of the shooting 2 weeks before school was scheduled to start, throughout the entire 2014–2015 academic year and into the subsequent summer vacation, residents of Ferguson experienced a persistent, elevated state of civic unrest, disruption, stress and violence. This is in addition to the initial trauma caused by the shooting of an unarmed black graduate of an area high school. Viewed through the lens of a natural experiment, the disruptions experienced in Ferguson throughout the 2014–2015 academic year provide leverage with which to identify their impacts on short-run student outcomes. 2.2. Ferguson Geography The St. Louis Metropolitan Statistical Area (MSA) straddles the Mississippi River and includes counties in both Missouri and Illinois.5 According to the 2010 US Census, the MSA was home to about 2.8 million individuals and was about 77% white, 18% black, 2.5% Hispanic and 2.1% Asian. St. Louis County, in which Ferguson is located, is the most populous county in the MSA. We restrict our analysis to the St. Louis MSA because its labor market and demographics are quite different from those in other parts of Missouri. We further restrict our analytic sample to schools and districts on the Missouri side of the MSA, because the Missouri and Illinois tests are not directly comparable. Defining the ‘treated group’ is not straightforward for several reasons. First, media reports and discussion of the unrest frequently refer to the city of Ferguson, which is technically accurate as this is the jurisdiction in which the shooting of Michael Brown and much of the looting and protests occurred. However, Ferguson-Florissant School District is not synonymous with Ferguson City. In fact, Ferguson City proper contains several smaller school districts, notably Riverview Gardens District, whose catchment area includes the specific sites of Brown’s shooting and the initial protests on West Florissant Ave. Moreover, Brown himself actually completed high school in the Normandy District, which is adjacent to the South of both the Ferguson and Riverview Gardens districts. A fourth independent school district, Jennings, is surrounded by these three districts, and by St. Louis City District to the East. Thus, as the map in Figure 1 makes clear, it is potentially misleading to consider Ferguson as the sole ‘treated’ district. In the baseline school-level DD models, we, therefore, consider schools in the geographically contiguous block of four districts (Ferguson, Jennings, Normandy and Riverview Gardens) as treated. We also estimate models that allow the treatment effect to vary across these four districts and investigate the sensitivity of the main results to using a broader definition of treatment that adds three additional geographically contiguous districts to the treatment group: St. Louis City, University City and Hazelwood. The main results are robust to these, and to alternative configurations, of the treatment group, as well as to including all MO schools in the control group. We also use a triple-difference specification to test whether majority black schools in the MSA, but outside the immediate vicinity of Ferguson, were affected by the racial tensions exacerbated by fear of police interactions, discussions and protests associated with the shooting of Michael Brown. Figure 1 View largeDownload slide Map of Ferguson-area districts. Notes: Baseline treatment districts are contained in a square and include Ferguson, Jennings, Normandy, and Riverview Gardens. Extended treatment districts include Hazelwood, University City, and St. Louis City, which are circled. Stars indicate the districts that comprise Ferguson’s synthetic control (Ritenour and Maplewood-Richmond Heights). The Eastern border is the Mississippi River, which separates Missouri from Illinois. Hazelwood’s Northern border is the Missouri River. All bold black lines demarcate counties. Online Appendix Figure A.1 available as Supplementary data shows all counties in the St. Louis MSA. Source: Missouri Department of Elementary and Secondary Education. Figure 1 View largeDownload slide Map of Ferguson-area districts. Notes: Baseline treatment districts are contained in a square and include Ferguson, Jennings, Normandy, and Riverview Gardens. Extended treatment districts include Hazelwood, University City, and St. Louis City, which are circled. Stars indicate the districts that comprise Ferguson’s synthetic control (Ritenour and Maplewood-Richmond Heights). The Eastern border is the Mississippi River, which separates Missouri from Illinois. Hazelwood’s Northern border is the Missouri River. All bold black lines demarcate counties. Online Appendix Figure A.1 available as Supplementary data shows all counties in the St. Louis MSA. Source: Missouri Department of Elementary and Secondary Education. 3. Data We analyze school-level data from 2010 to 2015 made available by Missouri’s Department of Elementary and Secondary Education via their Comprehensive Data System.6 Achievement data comes from school-level aggregate performance on Missouri Assessment Program (MAP) standardized tests that are administered in grades 3–8 and in certain high school subjects between March and May of each academic year. Exact testing dates vary by district and by grade level. For example, in Ferguson in 2015, the grade-3 tests were administered in the first two weeks of April and the grade-5 tests were administered in the second two weeks of April. The state codes student performance on these exams into four mutually exclusive performance categories: advanced, proficient, basic and below basic. The percent of all schools’ and districts’ students that fit in each category are publicly released. The empirical analysis focuses on the top and bottom categories, as we find that changes in advanced are approximately offset by changes in proficient, and changes in below basic are approximately offset by changes in basic.7 In addition to aggregate performance measures, in accordance with the No Child Left Behind Act (NCLB), the state also reports aggregate performance measures separately by student subgroups. Specifically, the state reports results for what it calls ‘Super Subgroup’ students, who are high-needs students who are in at least one of the following specific subgroups: black, Hispanic, students with disabilities, English language learners (ELL) or low-income students.8 Because many students in the Ferguson area qualify for Super-subgroup status, we report results both overall and for the Super subgroup, as the latter ensures that the DD analyses compare the performance of high-needs students in treated and control schools.9 Missouri’s Comprehensive Data System also provides a wealth of information about schools in the state, which we summarize along with the academic performance data in Table 1.10 We report means separately by treatment status for schools in the St. Louis MSA, which highlights baseline differences between Ferguson-area schools and other schools in the MSA.11 There are 53 schools in the 4 treated districts and 439 schools elsewhere in the MSA. Several stark differences emerge. First, in both reading and math, Ferguson-area schools perform significantly worse than control schools: on average, students in Ferguson-area schools are about twice as likely to score ‘Below Basic’ and less than half as likely to score ‘Advanced’ as students in other districts in the MSA. Table 1 Descriptive statistics for St. Louis MSA Public Schools Ferguson-area schools Control schools Mean SD Mean SD Reading achievement     % Below (All students) 19.0 11.6 9.0 10.4     % Advanced (All students) 7.5 5.3 23.3 13.4     % Below (Super subgroup) 19.4 11.5 12.7 10.2     % Advanced (Super subgroup) 6.7 4.4 14.5 8.7 Math achievement     % Below (All students) 23.7 15.8 23.7 15.8     % Advanced (All students) 5.2 4.6 5.2 4.6     % Below (Super subgroup) 24.1 15.9 24.1 15.9     % Advanced (Super subgroup) 4.7 4.3 4.7 4.3 Attendance     All students 80.8 11.3 89.8 7.6     Male students 79.3 11.7 89.5 7.7     Female students 82.5 11.4 90.0 7.8     IEP students 75.1 12.9 85.0 9.8     FRL students 79.8 11.5 84.6 8.6 School characteristics     Average admin salary $94,656 18,753 $92,612 21,489     # of FTE teachers 29.5 17.6 39.7 24.1     Average teacher salary $57,696 4998 $53,127 7371     Average teacher experience 13.9 2.8 12.2 2.5     % Teachers w/masters 63.4 12.8 65.7 16.4     Total enrollment 474.6 319.4 585 406.5     Student to teacher ratio 15.8 2.3 14.3 2.3     % White students 6.9 10.2 64.5 32.5     % Black students 89.5 13.3 27.2 33.3     % Hispanic students 1.4 2.8 3.3 3.3     % Asian students 0.4 0.6 3.2 4.1     % Multiracial students 1.7 2.4 1.5 2     % Other race students 0.5 0.6 3.5 4.1     % LEP students 0.7 2.6 3.5 6.2     % FRL students 82 14.7 44.6 27.7     N (School years) 300 2513     N (Unique schools) 53 439     N (Unique districts) 4 46     N (Years) 6 6 Ferguson-area schools Control schools Mean SD Mean SD Reading achievement     % Below (All students) 19.0 11.6 9.0 10.4     % Advanced (All students) 7.5 5.3 23.3 13.4     % Below (Super subgroup) 19.4 11.5 12.7 10.2     % Advanced (Super subgroup) 6.7 4.4 14.5 8.7 Math achievement     % Below (All students) 23.7 15.8 23.7 15.8     % Advanced (All students) 5.2 4.6 5.2 4.6     % Below (Super subgroup) 24.1 15.9 24.1 15.9     % Advanced (Super subgroup) 4.7 4.3 4.7 4.3 Attendance     All students 80.8 11.3 89.8 7.6     Male students 79.3 11.7 89.5 7.7     Female students 82.5 11.4 90.0 7.8     IEP students 75.1 12.9 85.0 9.8     FRL students 79.8 11.5 84.6 8.6 School characteristics     Average admin salary $94,656 18,753 $92,612 21,489     # of FTE teachers 29.5 17.6 39.7 24.1     Average teacher salary $57,696 4998 $53,127 7371     Average teacher experience 13.9 2.8 12.2 2.5     % Teachers w/masters 63.4 12.8 65.7 16.4     Total enrollment 474.6 319.4 585 406.5     Student to teacher ratio 15.8 2.3 14.3 2.3     % White students 6.9 10.2 64.5 32.5     % Black students 89.5 13.3 27.2 33.3     % Hispanic students 1.4 2.8 3.3 3.3     % Asian students 0.4 0.6 3.2 4.1     % Multiracial students 1.7 2.4 1.5 2     % Other race students 0.5 0.6 3.5 4.1     % LEP students 0.7 2.6 3.5 6.2     % FRL students 82 14.7 44.6 27.7     N (School years) 300 2513     N (Unique schools) 53 439     N (Unique districts) 4 46     N (Years) 6 6 Notes: Ferguson-area (treatment) schools are schools in the following school districts: Ferguson, Normandy, Jennings and Riverview Gardens. Control schools are all other schools in the St. Louis MSA on the Missouri side of the Mississippi River. Super subgroup includes high needs students who are black, Hispanic, low-income or have an IEP. Attendance rates are the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). Table 1 Descriptive statistics for St. Louis MSA Public Schools Ferguson-area schools Control schools Mean SD Mean SD Reading achievement     % Below (All students) 19.0 11.6 9.0 10.4     % Advanced (All students) 7.5 5.3 23.3 13.4     % Below (Super subgroup) 19.4 11.5 12.7 10.2     % Advanced (Super subgroup) 6.7 4.4 14.5 8.7 Math achievement     % Below (All students) 23.7 15.8 23.7 15.8     % Advanced (All students) 5.2 4.6 5.2 4.6     % Below (Super subgroup) 24.1 15.9 24.1 15.9     % Advanced (Super subgroup) 4.7 4.3 4.7 4.3 Attendance     All students 80.8 11.3 89.8 7.6     Male students 79.3 11.7 89.5 7.7     Female students 82.5 11.4 90.0 7.8     IEP students 75.1 12.9 85.0 9.8     FRL students 79.8 11.5 84.6 8.6 School characteristics     Average admin salary $94,656 18,753 $92,612 21,489     # of FTE teachers 29.5 17.6 39.7 24.1     Average teacher salary $57,696 4998 $53,127 7371     Average teacher experience 13.9 2.8 12.2 2.5     % Teachers w/masters 63.4 12.8 65.7 16.4     Total enrollment 474.6 319.4 585 406.5     Student to teacher ratio 15.8 2.3 14.3 2.3     % White students 6.9 10.2 64.5 32.5     % Black students 89.5 13.3 27.2 33.3     % Hispanic students 1.4 2.8 3.3 3.3     % Asian students 0.4 0.6 3.2 4.1     % Multiracial students 1.7 2.4 1.5 2     % Other race students 0.5 0.6 3.5 4.1     % LEP students 0.7 2.6 3.5 6.2     % FRL students 82 14.7 44.6 27.7     N (School years) 300 2513     N (Unique schools) 53 439     N (Unique districts) 4 46     N (Years) 6 6 Ferguson-area schools Control schools Mean SD Mean SD Reading achievement     % Below (All students) 19.0 11.6 9.0 10.4     % Advanced (All students) 7.5 5.3 23.3 13.4     % Below (Super subgroup) 19.4 11.5 12.7 10.2     % Advanced (Super subgroup) 6.7 4.4 14.5 8.7 Math achievement     % Below (All students) 23.7 15.8 23.7 15.8     % Advanced (All students) 5.2 4.6 5.2 4.6     % Below (Super subgroup) 24.1 15.9 24.1 15.9     % Advanced (Super subgroup) 4.7 4.3 4.7 4.3 Attendance     All students 80.8 11.3 89.8 7.6     Male students 79.3 11.7 89.5 7.7     Female students 82.5 11.4 90.0 7.8     IEP students 75.1 12.9 85.0 9.8     FRL students 79.8 11.5 84.6 8.6 School characteristics     Average admin salary $94,656 18,753 $92,612 21,489     # of FTE teachers 29.5 17.6 39.7 24.1     Average teacher salary $57,696 4998 $53,127 7371     Average teacher experience 13.9 2.8 12.2 2.5     % Teachers w/masters 63.4 12.8 65.7 16.4     Total enrollment 474.6 319.4 585 406.5     Student to teacher ratio 15.8 2.3 14.3 2.3     % White students 6.9 10.2 64.5 32.5     % Black students 89.5 13.3 27.2 33.3     % Hispanic students 1.4 2.8 3.3 3.3     % Asian students 0.4 0.6 3.2 4.1     % Multiracial students 1.7 2.4 1.5 2     % Other race students 0.5 0.6 3.5 4.1     % LEP students 0.7 2.6 3.5 6.2     % FRL students 82 14.7 44.6 27.7     N (School years) 300 2513     N (Unique schools) 53 439     N (Unique districts) 4 46     N (Years) 6 6 Notes: Ferguson-area (treatment) schools are schools in the following school districts: Ferguson, Normandy, Jennings and Riverview Gardens. Control schools are all other schools in the St. Louis MSA on the Missouri side of the Mississippi River. Super subgroup includes high needs students who are black, Hispanic, low-income or have an IEP. Attendance rates are the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). Second, there is also an attendance differential between treated and control schools, for both male and female students, that is less pronounced among low-income, free- or reduced price lunch (FRL) students.12 The attendance rates reported in Missouri refer to the percentage of a school’s students who were absent fewer than 10% of school days. Being absent more than 10% of school days is a common definition of chronic absence (Balfanz and Byrnes, 2012), so the reported attendance rates are best interpreted as the percentage of students who are not chronically absent. These are informative measures of school attendance, which is an important input in the education production function: chronically absent students score about 0.12 test-score standard deviations lower than students who are rarely absent (Gershenson et al., 2017). Attendance is an intermediate educational outcome that may have been affected by the civic unrest in Ferguson, and therefore a possible channel through which the unrest in Ferguson harmed academic achievement. Finally, Table 1 summarizes numerous school characteristics. Teachers and administrators have higher salaries in treated schools, on average, than their counterparts in control schools. Ferguson-area teachers are also slightly more experienced than their counterparts elsewhere in the MSA. However, student–teacher ratios are larger in treated districts. Finally, the socio-demographic composition of the enrollments in Ferguson-area schools is quite different from the rest of the MSA: these schools are 90% black and 82% FRL, on average, while control schools are only 27% black and 45% FRL. This concentration of low income, racial minority students has been a focus of many discussions of the events that precipitated the civic unrest in Ferguson (e.g. Goodman, H.A., 2014; Kneebone, 2014). These differences underscore the importance of accounting for preexisting differences between treated and control schools in the econometric analysis and the value of the super-subgroup performance measures, which facilitate comparisons of high-needs students in and outside Ferguson. Figures 2 and 3 motivate the empirical analysis by providing suggestive evidence of a departure from trend in Ferguson-area schools in 2015 that is unlikely to be due to chance. Figure 2 plots the average school’s deviance from the MSA-wide school average in percent below basic in math in each year, separately for control and treated schools. We report these figures relative to the MSA-wide, year-specific mean to account for MSA-wide changes to the tests and make the results comparable over time. Two aspects of Figure 2 are worth noting. First, trends in overall and super-subgroup math achievement in both treated and control schools are similar in the pre-treatment period (2010–2014). This suggests that any effects of the events in Ferguson are not driven by preexisting differential trends between treated and control groups, though we formally test this assumption below. Second, the trend line for control schools continues to be flat in 2015, the treatment year, while there is a notable uptick in the frequency of below-basic scores in treated schools in 2015, both overall and among Super-subgroup students. Indeed, Figure 2 shows that what was approximately a ten percentage point gap between treated and control schools in percent below basic in math roughly doubled to a 20 percentage point gap in 2015, both overall and among high-needs students.13Online Appendix Figure A.2 available as Supplementary data shows a similar pattern in the doubling of the treatment-control gap in the percent of students scoring below basic in reading. Accordingly, for brevity, the main analyses focus on math achievement. Figure 2 View largeDownload slide School average ‘Percent Below Basic’ in math rates (a) Percent below basic in math, all students; (b) Percent below basic in math, super subgroup. Notes: Ferguson-area schools include all schools in four Missouri school districts including Ferguson, Jennings, Normandy and Riverview Gardens. Control schools include all other public schools in the St. Louis MSA. Each dot represents the annual school average deviation from the MSA, year-specific mean. Figure 2 View largeDownload slide School average ‘Percent Below Basic’ in math rates (a) Percent below basic in math, all students; (b) Percent below basic in math, super subgroup. Notes: Ferguson-area schools include all schools in four Missouri school districts including Ferguson, Jennings, Normandy and Riverview Gardens. Control schools include all other public schools in the St. Louis MSA. Each dot represents the annual school average deviation from the MSA, year-specific mean. Figure 3 View largeDownload slide Distribution of annual within-school changes in ‘Percent Below Basic’ in math (a) Changes from 2014 to 2015; (b) Changes from 2013 to 2014; (c) Changes from 2012 to 2013. Notes: In panel A, Treatment = 54.5% of top 5% schools and 60.0% of top 1% schools. In panel B, Treatment = 33.3% of top 5% schools and 20.0% of top 1% schools. In panel C, Treatment = 26.1% of top 5% schools and 20% of top 1% schools. Figure 3 View largeDownload slide Distribution of annual within-school changes in ‘Percent Below Basic’ in math (a) Changes from 2014 to 2015; (b) Changes from 2013 to 2014; (c) Changes from 2012 to 2013. Notes: In panel A, Treatment = 54.5% of top 5% schools and 60.0% of top 1% schools. In panel B, Treatment = 33.3% of top 5% schools and 20.0% of top 1% schools. In panel C, Treatment = 26.1% of top 5% schools and 20% of top 1% schools. Figure 3 addresses the stylized fact that test scores are noisy and prone to mean reversion by plotting the full distribution of within-school, year-to-year changes in percent below basic in math for the 2012–2013, 2013–2014 and 2014–2015 transitions. Treated Ferguson-area schools are shaded black and control schools are shaded gray. Panel A shows a preponderance of black in the distribution’s right tail, indicating that most Ferguson-area schools exhibited relatively large increases in percent below basic. Specifically, more than half of the top 5% declines and 60% of the top 1% declines occurred in the Ferguson area, despite Ferguson schools representing only about 11% of all schools. This is in stark contrast to panels B and C of Figure 3, which present analogous figures for the two transitions before the unrest in Ferguson. Here, Ferguson-area schools constitute only 20% of the top 1% declines and only 26 to 33% of top 5% declines. As in Figures 2 and 3 suggests that while Ferguson-area schools were underperforming relative to other schools in the St. Louis MSA, they experienced a pronounced departure from trend in 2015, the year following the shooting. 4. Identification Strategy As suggested by Figures 2 and 3, Ferguson-area (treated) schools are systematically different from other schools in the MSA and there may have been secular statewide changes in student performance over the period 2010–2015. We address these confounding factors by using school-level data to estimate a variety of DD style regressions that control for school fixed effects (FE), year FE, time-varying observed school characteristics and school-specific time trends. The preferred baseline model conditions on time-varying school characteristics, school FE, year FE and school-specific linear time trends. Specifically, we estimate models of the form Yst=τFergusons×1{t=2015}+βXst+θs+δt+γtθs+ɛst, (1) where s and t index schools and academic years, respectively; Y is a school-level outcome; Ferguson is a binary indicator equal to one if the school was in one of the four districts in the immediate vicinity of the protests, and zero otherwise; 1{·} is the indicator function; X is a vector of the time-varying school characteristics summarized in Table 1; θ and δ are school and year FE, respectively; and ɛ is an idiosyncratic error. Equation (1) will also be augmented to condition on quadratic school time trends. The parameter of interest is τ, which represents the departure from trend of Ferguson-area schools in the 2015 academic year. Standard errors are clustered at the district level, which makes inference robust to arbitrary serial correlation within schools and districts, as schools are nested in districts. The key identifying assumption for OLS estimation of Equation (1) is a variant of the parallel slopes assumption: that is conditional on school-specific linear time trends, schools in and outside the Ferguson area were trending similarly before the 2015 school year. We provide two pieces of empirical evidence that suggest this assumption holds. First, we estimate versions of Equation (1) that either restrict β = 0, restrict γ = 0, replace the linear school time trends with linear district time trends or augment the model to include quadratic school time trends. Importantly, if estimates of τ are similar across these alternative specifications, the baseline results are unlikely to be the result of differential preexisting trends between ‘treated’ and ‘control’ schools. Second, we estimate event study versions of Equation (1) that interact Ferguson with each year indicator, which provides a direct test for ‘effects’ of the events in years before their occurrence in 2015. If the event study analysis yields significant ‘effects’ in Ferguson in the years before 2015, we would be concerned that the DD estimates of Equation (1) are biased by preexisting differential trends in the treated schools. As shown in Section 5.4, the results of these sensitivity analyses corroborate a causal interpretation of OLS estimates of τ in Equation (1). 5.Results This section presents the results. Section 5.1 presents estimates of the baseline DD model (Equation (1)). Section 5.2 investigates whether the effects persisted into the 2016 school year. Section 5.3 tests for heterogeneous responses to the events in Ferguson. Finally, Section 5.4 probes the robustness of the DD estimates and tests the ‘parallel slopes’ identifying assumption. 5.1. Baseline DD Estimates Table 2 reports estimates of the baseline DD regression model specified in Equation (1). Each cell of Table 2 reports the DD estimate of τ from a unique regression. The models estimated in column 1, which pool all schools, document practically large, statistically significant effects on the percentage of students scoring ‘below basic’ in math. Overall, there was a 16.9 percentage point increase in the share of students who scored ‘below basic’, which constitutes a substantively large doubling of the previous year’s share. The effect on the fraction of Super-subgroup students scoring below basic is smaller, yet still statistically and economically significant: among this high-needs population, the share of students scoring below basic increased by 10.9 percentage points (68%). These point estimates are consistent with the patterns observed in Figure 2. There are also modest, negative effects on ‘Percent Advanced’ in math, though the point estimate is not statistically significant for Super-subgroup students. While these point estimates are smaller in magnitude and less precisely estimated than those for ‘Below Basic’, in the treated Ferguson-area districts, only a small base of students ever score ‘Advanced’. These results are troubling, as they suggest that many marginal students fell further behind while some high achievers were harmed as well.14 Table 2 Baseline school-level DD estimates of effects on student math achievement School type All schools Elementary Middle High (1) (2) (3) (4) A. Math achievement, below basic All students 16.9*** 18.4*** 16.2*** 11.3 (4.6) (4.1) (4.9) (12.2) Super subgroup 10.9** 12.8*** 8.0* 6.6 (4.4) (3.8) (4.3) (12.8) B. Math achievement, advanced All Students −6.2*** −9.9*** −1.9 −1.0 (2.1) (2.9) (4.4) (2.9) Super Subgroup −1.6 −4.1 −1.2 2.2 (2.1) (2.8) (4.2) (2.5) N (school years) 2813 1744 495 574 School type All schools Elementary Middle High (1) (2) (3) (4) A. Math achievement, below basic All students 16.9*** 18.4*** 16.2*** 11.3 (4.6) (4.1) (4.9) (12.2) Super subgroup 10.9** 12.8*** 8.0* 6.6 (4.4) (3.8) (4.3) (12.8) B. Math achievement, advanced All Students −6.2*** −9.9*** −1.9 −1.0 (2.1) (2.9) (4.4) (2.9) Super Subgroup −1.6 −4.1 −1.2 2.2 (2.1) (2.8) (4.2) (2.5) N (school years) 2813 1744 495 574 Notes: Each cell reports the estimate of τ for a unique regression that controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each panel represents a different dependent variable: percent below basic or percent advanced. Standard errors are clustered by school district. DD = difference-in-difference. ***p < 0.01, **p < 0.05, and *p < 0.1. Table 2 Baseline school-level DD estimates of effects on student math achievement School type All schools Elementary Middle High (1) (2) (3) (4) A. Math achievement, below basic All students 16.9*** 18.4*** 16.2*** 11.3 (4.6) (4.1) (4.9) (12.2) Super subgroup 10.9** 12.8*** 8.0* 6.6 (4.4) (3.8) (4.3) (12.8) B. Math achievement, advanced All Students −6.2*** −9.9*** −1.9 −1.0 (2.1) (2.9) (4.4) (2.9) Super Subgroup −1.6 −4.1 −1.2 2.2 (2.1) (2.8) (4.2) (2.5) N (school years) 2813 1744 495 574 School type All schools Elementary Middle High (1) (2) (3) (4) A. Math achievement, below basic All students 16.9*** 18.4*** 16.2*** 11.3 (4.6) (4.1) (4.9) (12.2) Super subgroup 10.9** 12.8*** 8.0* 6.6 (4.4) (3.8) (4.3) (12.8) B. Math achievement, advanced All Students −6.2*** −9.9*** −1.9 −1.0 (2.1) (2.9) (4.4) (2.9) Super Subgroup −1.6 −4.1 −1.2 2.2 (2.1) (2.8) (4.2) (2.5) N (school years) 2813 1744 495 574 Notes: Each cell reports the estimate of τ for a unique regression that controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each panel represents a different dependent variable: percent below basic or percent advanced. Standard errors are clustered by school district. DD = difference-in-difference. ***p < 0.01, **p < 0.05, and *p < 0.1. Of course, assuming that elementary, middle and high schools were affected in the same ways is unrealistic, as the school contexts differ substantially and older students have more agency over intermediate inputs such as attendance. Accordingly, columns 2–4 of Table 2 show that the overall effects reported in column 1 were primarily driven by the response in elementary schools, which is consistent with the results of Gershenson and Tekin (2015) and Sharkey et al. (2014).15 The estimated effects in high schools are generally in the same direction, but smaller in magnitude and never statistically significant. Sharkey et al. (2014) hypothesize that this could be because older students, who have grown up in disadvantaged neighborhoods, are more resilient to unexpected shocks and disruption. Alternatively, this result could be due to cognitive ability being more malleable at younger ages (e.g. Cunha et al., 2006). Table 3 investigates a potential channel through which the events in Ferguson might have harmed student achievement. The absence of student- or teacher-level data limits the channels that we can investigate, but school data on the percentage of students who were not chronically absent is reported. Specifically, this variable measures the percent of students who are absent less than 10% of school days. The causal link between attendance and achievement is well established (e.g. Goodman, J., 2014; Aucejo and Romano, 2016; Gershenson et al., 2017), and it is plausible that the civic unrest in Ferguson affected student attendance by creating safety concerns over the commute to school, causing students to disengage from school more generally, or distracting parents from ensuring that students attended school on a regular basis. Column 1 of Table 3 reports baseline DD estimates of the impact of the events in Ferguson on Ferguson-area schools’ overall attendance rates and attendance rates for specific socio-demographic groups. Columns 2–4 do the same separately for elementary, middle and high schools. Thus, each cell in Table 3 reports the DD estimate of τ for a unique regression. Table 3 Baseline school-level DD estimates of effects on student attendance School type Outcome All Schools Elementary Middle High (1) (2) (3) (4) Total attendance rate −3.1*** −4.2*** −1.8 −1.0 (0.8) (0.5) (2.3) (4.9) Male attendance rate −2.8*** −3.9*** −2.9 0.6 (0.5) (0.7) (2.0) (4.9) Female attendance rate −3.5*** −4.8*** −0.4 −2.5 (1.0) (0.5) (2.6) (4.9) IEP attendance rate −2.8*** −3.8* −4.5 −0.0 (0.9) (1.9) (3.5) (5.1) FRL attendance rate −0.8 −2.3** 0.8 1.2 (0.6) (1.0) (2.1) (4.1) N (school years) 2813 1744 495 574 School type Outcome All Schools Elementary Middle High (1) (2) (3) (4) Total attendance rate −3.1*** −4.2*** −1.8 −1.0 (0.8) (0.5) (2.3) (4.9) Male attendance rate −2.8*** −3.9*** −2.9 0.6 (0.5) (0.7) (2.0) (4.9) Female attendance rate −3.5*** −4.8*** −0.4 −2.5 (1.0) (0.5) (2.6) (4.9) IEP attendance rate −2.8*** −3.8* −4.5 −0.0 (0.9) (1.9) (3.5) (5.1) FRL attendance rate −0.8 −2.3** 0.8 1.2 (0.6) (1.0) (2.1) (4.1) N (school years) 2813 1744 495 574 Notes: Each cell reports the coefficient estimate on the interaction between the ‘treated school’ and 2015 indicators from a unique regression that controls for school and year FE, linear district time trends and time-varying school characteristics. The dependent variable, attendance rate, is the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). Standard errors are clustered by school district. IEP = Individualized Education Plan. FRL = Free or reduced price lunch. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 3 Baseline school-level DD estimates of effects on student attendance School type Outcome All Schools Elementary Middle High (1) (2) (3) (4) Total attendance rate −3.1*** −4.2*** −1.8 −1.0 (0.8) (0.5) (2.3) (4.9) Male attendance rate −2.8*** −3.9*** −2.9 0.6 (0.5) (0.7) (2.0) (4.9) Female attendance rate −3.5*** −4.8*** −0.4 −2.5 (1.0) (0.5) (2.6) (4.9) IEP attendance rate −2.8*** −3.8* −4.5 −0.0 (0.9) (1.9) (3.5) (5.1) FRL attendance rate −0.8 −2.3** 0.8 1.2 (0.6) (1.0) (2.1) (4.1) N (school years) 2813 1744 495 574 School type Outcome All Schools Elementary Middle High (1) (2) (3) (4) Total attendance rate −3.1*** −4.2*** −1.8 −1.0 (0.8) (0.5) (2.3) (4.9) Male attendance rate −2.8*** −3.9*** −2.9 0.6 (0.5) (0.7) (2.0) (4.9) Female attendance rate −3.5*** −4.8*** −0.4 −2.5 (1.0) (0.5) (2.6) (4.9) IEP attendance rate −2.8*** −3.8* −4.5 −0.0 (0.9) (1.9) (3.5) (5.1) FRL attendance rate −0.8 −2.3** 0.8 1.2 (0.6) (1.0) (2.1) (4.1) N (school years) 2813 1744 495 574 Notes: Each cell reports the coefficient estimate on the interaction between the ‘treated school’ and 2015 indicators from a unique regression that controls for school and year FE, linear district time trends and time-varying school characteristics. The dependent variable, attendance rate, is the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). Standard errors are clustered by school district. IEP = Individualized Education Plan. FRL = Free or reduced price lunch. ***p < 0.01, **p < 0.05 and *p < 0.1. Overall, the first entry in column 1 shows that the events in Ferguson led to a 3.1 percentage point decrease in the attendance measure, which means that chronic-absence rates increased by this amount. This effect is strongly statistically significant and represents an approximate decline of 4% in treated schools. The effect was similar for both male and female students, and Individual Educational Plan (IEP) students. The elementary school estimates in column 2 are quite similar to those in column 1, while the estimates for middle and high schools in columns 3 and 4, respectively, tend to be smaller and are imprecisely estimated. This is the same pattern observed for math achievement in Table 2. Overall, the absence results presented in Table 3 are consistent with a causal interpretation of the main result of Table 2: that the events in Ferguson before and during the 2015 school year harmed student achievement in area elementary schools. Moreover, these results suggest that increased absenteeism was an important channel through which the events in Ferguson harmed student achievement in area elementary schools. Because the impacts on both achievement and attendance are concentrated almost entirely in elementary schools, subsequent analyses focus exclusively on elementary schools. 5.2. Persistence Having uncovered arguably causal effects of the disruptions experienced in the Ferguson area during the 2014–2015 school year on student attendance and spring-2015 test scores, a natural, policy-relevant question arises: did student achievement recover or remain depressed in subsequent school years? The models estimated in Table 4 address this question by utilizing an additional year of data and an augmented version of the baseline model (Equation (1)) that allows for such effects to persist in 2016. Generally, the ‘long-run’ effects in 2016 are in the same direction, but smaller in magnitude and less precisely estimated, than the immediate effects in 2015. In only one instance is the long-run effect in 2016 individually statistically significant: column 1 shows that the overall increase in percent below basic persisted into 2016, though this effect is only half as large as the immediate impact in 2015. Still, the effects on percent below basic in 2016 are significantly smaller than those in 2015. The long-run impacts on percent advanced and attendance rates in 2016 are not statistically significant. Table 4 Persistence of effects on elementary student achievement and attendance Outcome: Below basic, math Advanced, math Attendance Students: All Super subgroup All Super subgroup All FRL (1) (2) (3) (4) (5) (6) 2015 × Treated 17.6*** 13.4*** −9.8*** −6.0*** −3.1*** −1.9* (4.0) (4.0) (2.3) (1.5) (0.7) (1.0) 2016 × Treated 8.5** 4.1 −7.0 −3.5 −1.9 −0.8 (3.4) (3.1) (5.0) (3.7) (1.3) (1.7) Diff. (p-value) 0.00 0.00 0.53 0.55 0.27 0.36 N (school years) 2002 1992 1968 1934 2031 1990 Outcome: Below basic, math Advanced, math Attendance Students: All Super subgroup All Super subgroup All FRL (1) (2) (3) (4) (5) (6) 2015 × Treated 17.6*** 13.4*** −9.8*** −6.0*** −3.1*** −1.9* (4.0) (4.0) (2.3) (1.5) (0.7) (1.0) 2016 × Treated 8.5** 4.1 −7.0 −3.5 −1.9 −0.8 (3.4) (3.1) (5.0) (3.7) (1.3) (1.7) Diff. (p-value) 0.00 0.00 0.53 0.55 0.27 0.36 N (school years) 2002 1992 1968 1934 2031 1990 Notes: Each column reports coefficient estimates from a unique regression that controls for school and year FE, linear district time trends and time-varying school characteristics. Attendance is the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). The super-subgroup (high needs) classification includes students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 4 Persistence of effects on elementary student achievement and attendance Outcome: Below basic, math Advanced, math Attendance Students: All Super subgroup All Super subgroup All FRL (1) (2) (3) (4) (5) (6) 2015 × Treated 17.6*** 13.4*** −9.8*** −6.0*** −3.1*** −1.9* (4.0) (4.0) (2.3) (1.5) (0.7) (1.0) 2016 × Treated 8.5** 4.1 −7.0 −3.5 −1.9 −0.8 (3.4) (3.1) (5.0) (3.7) (1.3) (1.7) Diff. (p-value) 0.00 0.00 0.53 0.55 0.27 0.36 N (school years) 2002 1992 1968 1934 2031 1990 Outcome: Below basic, math Advanced, math Attendance Students: All Super subgroup All Super subgroup All FRL (1) (2) (3) (4) (5) (6) 2015 × Treated 17.6*** 13.4*** −9.8*** −6.0*** −3.1*** −1.9* (4.0) (4.0) (2.3) (1.5) (0.7) (1.0) 2016 × Treated 8.5** 4.1 −7.0 −3.5 −1.9 −0.8 (3.4) (3.1) (5.0) (3.7) (1.3) (1.7) Diff. (p-value) 0.00 0.00 0.53 0.55 0.27 0.36 N (school years) 2002 1992 1968 1934 2031 1990 Notes: Each column reports coefficient estimates from a unique regression that controls for school and year FE, linear district time trends and time-varying school characteristics. Attendance is the percentage of a school’s students who were absent fewer than 10% of school days (i.e. who were not chronically absent). The super-subgroup (high needs) classification includes students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Overall, the results in Table 4 suggest that the disruptions experienced in Ferguson during the 2014–2015 school year had modest, if any, lasting impact on elementary school students’ academic performance and attendance habits in the 2015–2016 school year. The lack of strongly persistent effects is consistent with previous research on the impact of similar community traumatic events: for example, Gershenson and Tekin (2015) find no evidence that exposure to the Beltway Sniper attacks harmed student achievement in the following school year. This could be due to parents and school administrators responding in the following academic year to reverse the immediate negative effects observed in 2015. Unfortunately, data limitations prohibit testing these hypotheses. However, this is not an implausible scenario given the considerable national attention received by these schools and neighborhoods in the aftermath of the shooting. Of course, even if the effects on test scores faded out, effects on socio-emotional and attitudinal outcomes might persist in ways that affect long-run socioeconomic outcomes (e.g. Chetty et al., 2011). Nonetheless, it is comforting that the negative impacts on test scores and attendance associated with the unrest in Ferguson appear to be short lived. The reason that this lack of persistence is comforting is that while reversing the harmful impacts of community traumatic events on student achievement may be possible, doing so would require the reallocation of scarce resources. 5.3. Heterogeneity The racially charged events and conversations in Ferguson might well have affected predominantly black schools and communities across the St. Louis MSA, even those not in close proximity to the shooting and subsequent unrest in the Ferguson area. For example, stress, fear and concern caused by the highly publicized shooting of an unarmed black teenager could easily distract students in other parts of the MSA, especially given the amount of national media attention that Ferguson received. Accordingly, we estimate a triple-difference version of Equation (1) that allows the racially charged events in Ferguson to affect all majority-black schools in the MSA, and for this effect to differ in Ferguson-area schools, which themselves are uniformly majority black. Estimates of these triple-difference models are reported in Table 5. Table 5 School-level DDD estimates of effects on student achievement and attendance Outcome: Below basic, Math Attendance Students: All students Super subgroup All students (1) (2) (3) (4) (5) (6) 2015 × Black 14.9*** 12.2*** 8.7*** 6.1*** −2.7*** −2.1*** (2.3) (2.3) (2.2) (2.1) (0.5) (0.6) 2015 × Black × Ferguson 8.1** 7.6* −1.8** (3.5) (3.9) (0.8) Outcome: Below basic, Math Attendance Students: All students Super subgroup All students (1) (2) (3) (4) (5) (6) 2015 × Black 14.9*** 12.2*** 8.7*** 6.1*** −2.7*** −2.1*** (2.3) (2.3) (2.2) (2.1) (0.5) (0.6) 2015 × Black × Ferguson 8.1** 7.6* −1.8** (3.5) (3.9) (0.8) Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Black is a binary indicator equal to one if the school’s enrollment is more than 50% black, and zero otherwise. All Ferguson-area schools are more than 50% black. Each column reports coefficient estimates from a single regression, in which indicators for each of the four ‘treated’ districts are interacted with the 2015 indicator. Each regression controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Attendance reflects the percentage of a school’s students who were absent fewer than 10% of school days. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 5 School-level DDD estimates of effects on student achievement and attendance Outcome: Below basic, Math Attendance Students: All students Super subgroup All students (1) (2) (3) (4) (5) (6) 2015 × Black 14.9*** 12.2*** 8.7*** 6.1*** −2.7*** −2.1*** (2.3) (2.3) (2.2) (2.1) (0.5) (0.6) 2015 × Black × Ferguson 8.1** 7.6* −1.8** (3.5) (3.9) (0.8) Outcome: Below basic, Math Attendance Students: All students Super subgroup All students (1) (2) (3) (4) (5) (6) 2015 × Black 14.9*** 12.2*** 8.7*** 6.1*** −2.7*** −2.1*** (2.3) (2.3) (2.2) (2.1) (0.5) (0.6) 2015 × Black × Ferguson 8.1** 7.6* −1.8** (3.5) (3.9) (0.8) Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Black is a binary indicator equal to one if the school’s enrollment is more than 50% black, and zero otherwise. All Ferguson-area schools are more than 50% black. Each column reports coefficient estimates from a single regression, in which indicators for each of the four ‘treated’ districts are interacted with the 2015 indicator. Each regression controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Attendance reflects the percentage of a school’s students who were absent fewer than 10% of school days. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Before estimating the full triple-difference model, column 1 of Table 5 simply changes the treatment indicator in the baseline model from ‘Ferguson area’ to ‘majority black’. The resulting point estimate in column 1 is smaller than the analogous estimate in column 2 of Table 2, but is similarly positive and statistically significant. Intuitively, this suggests that the impact of the events in Ferguson was not isolated to the four ‘treated’ districts in the immediate vicinity of the shooting and subsequent unrest, though the effects were larger in magnitude in districts physically closer to the epicenter of the unrest. Column 2 formalizes this idea by estimating a triple-interaction model that allows the response of majority-black schools to vary by proximity to Ferguson. As expected, the triple-interaction term shows that the effects were significantly larger in magnitude in Ferguson-area schools. Columns 3 and 4 repeat this exercise for the subset of super-subgroup students, where a similar pattern is observed: the impact of the events in Ferguson was significantly larger in the majority-black schools in the Ferguson area than in other majority-black schools in the St. Louis MSA. Specifically, the overall and super-subgroup effects of the civic unrest in Ferguson on percent below basic in math were 66% and 125% larger, respectively, in Ferguson-area elementary schools than in majority-black elementary schools elsewhere in the MSA. Similarly, column 6 shows that the effects of the events in Ferguson on elementary school attendance rates were 86% larger in the Ferguson area than in majority-black schools elsewhere in the MSA. These results are consistent with a causal impact of the events in Ferguson on student achievement in Ferguson-area elementary schools. Moreover, these results suggest that attendance was an important, but not the only, mechanism through which student learning was affected. One interpretation of the triple-difference estimates reported in Table 5 is that the psychic costs of stress and changes in the allocation of instructional time away from academic topics covered by MAP tests and towards conversations about race, social and criminal justice and inequality were more important channels through which achievement was affected than direct disruptions to schools, households and neighborhoods in the Ferguson area. That the impact spread to other parts of the MSA, state and nation is plausible, as the nightly news coverage of the events in Ferguson, New York, Baltimore, Cleveland and elsewhere made racial inequities in the US salient and a topic of conversation in majority-black schools.16 Together with the effect on student attendance, these findings reinforce the main result of the baseline school-level DD analyses: the police shooting and subsequent civic unrest experienced in Ferguson, MO had a nontrivial, arguably causal impact on elementary school students’ academic achievement, which occurred at least partly due to an increase in chronic absenteeism, and was concentrated at the bottom of the achievement distribution. It is also possible that the four distinct districts that comprise the ‘Ferguson Area’ treatment group were differentially affected. Table 6 tests this hypothesis by estimating an augmented version of the baseline model (Equation (1)) in which the treatment indicator is disaggregated into four separate district indicators. In all models, the four-interaction terms (district-specific treatments) are jointly statistically significant. While the main result of a positive, sizable and statistically significant effect on the percent Below Basic is upheld in all four ‘treated’ districts, the effect is about twice as large in Ferguson and Normandy as it is in Jennings and Riverview Gardens. This is perhaps unsurprising, as Ferguson was the name mentioned in most media accounts of the events and home to much of the violence that occurred along W. Florissant Ave and Normandy is the district that Michael Brown graduated from. Thus, for different reasons, it is intuitive that the impact on achievement was more severe in these districts. Column 5 shows that the impact on attendance was fairly constant across districts. Table 6 Geographic heterogeneity in effect of unrest on student outcomes Below basic, math Advanced, math Attendance All students Super subgroup All students Super subgroup All students (1) (2) (3) (4) (5) 2015 × Ferguson 23.3*** 17.9*** −11.6*** −4.0 −3.0*** (2.9) (2.4) (3.0) (2.9) (0.6) 2015 × Jennings 12.4*** 8.0*** −10.9*** −8.5*** −3.8*** (2.3) (1.1) (1.6) (0.9) (0.6) 2015 × Normandy 18.0*** 12.6*** −6.1** −3.4** −3.8*** (3.5) (2.2) (2.3) (1.4) (0.8) 2015 × Riverview Gardens 14.6*** 7.0** −7.7** 0.3 −4.5*** (3.5) (2.8) (3.6) (3.6) (0.6) Tests of equality (p-values) Ferguson = Jennings 0.00 0.00 0.72 0.13 0.11 Ferguson = Normandy 0.00 0.00 0.01 0.81 0.31 Ferguson = Riverview Gardens 0.00 0.00 0.00 0.00 0.00 Jennings = Normandy 0.00 0.00 0.00 0.00 0.99 Jennings = Riverview Gardens 0.16 0.64 0.23 0.02 0.15 Normandy = Riverview Gardens 0.00 0.00 0.50 0.24 0.30 Below basic, math Advanced, math Attendance All students Super subgroup All students Super subgroup All students (1) (2) (3) (4) (5) 2015 × Ferguson 23.3*** 17.9*** −11.6*** −4.0 −3.0*** (2.9) (2.4) (3.0) (2.9) (0.6) 2015 × Jennings 12.4*** 8.0*** −10.9*** −8.5*** −3.8*** (2.3) (1.1) (1.6) (0.9) (0.6) 2015 × Normandy 18.0*** 12.6*** −6.1** −3.4** −3.8*** (3.5) (2.2) (2.3) (1.4) (0.8) 2015 × Riverview Gardens 14.6*** 7.0** −7.7** 0.3 −4.5*** (3.5) (2.8) (3.6) (3.6) (0.6) Tests of equality (p-values) Ferguson = Jennings 0.00 0.00 0.72 0.13 0.11 Ferguson = Normandy 0.00 0.00 0.01 0.81 0.31 Ferguson = Riverview Gardens 0.00 0.00 0.00 0.00 0.00 Jennings = Normandy 0.00 0.00 0.00 0.00 0.99 Jennings = Riverview Gardens 0.16 0.64 0.23 0.02 0.15 Normandy = Riverview Gardens 0.00 0.00 0.50 0.24 0.30 Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each column reports coefficient estimates from a single regression, in which indicators for each of the four ‘treated’ districts are interacted with the 2015 indicator. Each regression controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 6 Geographic heterogeneity in effect of unrest on student outcomes Below basic, math Advanced, math Attendance All students Super subgroup All students Super subgroup All students (1) (2) (3) (4) (5) 2015 × Ferguson 23.3*** 17.9*** −11.6*** −4.0 −3.0*** (2.9) (2.4) (3.0) (2.9) (0.6) 2015 × Jennings 12.4*** 8.0*** −10.9*** −8.5*** −3.8*** (2.3) (1.1) (1.6) (0.9) (0.6) 2015 × Normandy 18.0*** 12.6*** −6.1** −3.4** −3.8*** (3.5) (2.2) (2.3) (1.4) (0.8) 2015 × Riverview Gardens 14.6*** 7.0** −7.7** 0.3 −4.5*** (3.5) (2.8) (3.6) (3.6) (0.6) Tests of equality (p-values) Ferguson = Jennings 0.00 0.00 0.72 0.13 0.11 Ferguson = Normandy 0.00 0.00 0.01 0.81 0.31 Ferguson = Riverview Gardens 0.00 0.00 0.00 0.00 0.00 Jennings = Normandy 0.00 0.00 0.00 0.00 0.99 Jennings = Riverview Gardens 0.16 0.64 0.23 0.02 0.15 Normandy = Riverview Gardens 0.00 0.00 0.50 0.24 0.30 Below basic, math Advanced, math Attendance All students Super subgroup All students Super subgroup All students (1) (2) (3) (4) (5) 2015 × Ferguson 23.3*** 17.9*** −11.6*** −4.0 −3.0*** (2.9) (2.4) (3.0) (2.9) (0.6) 2015 × Jennings 12.4*** 8.0*** −10.9*** −8.5*** −3.8*** (2.3) (1.1) (1.6) (0.9) (0.6) 2015 × Normandy 18.0*** 12.6*** −6.1** −3.4** −3.8*** (3.5) (2.2) (2.3) (1.4) (0.8) 2015 × Riverview Gardens 14.6*** 7.0** −7.7** 0.3 −4.5*** (3.5) (2.8) (3.6) (3.6) (0.6) Tests of equality (p-values) Ferguson = Jennings 0.00 0.00 0.72 0.13 0.11 Ferguson = Normandy 0.00 0.00 0.01 0.81 0.31 Ferguson = Riverview Gardens 0.00 0.00 0.00 0.00 0.00 Jennings = Normandy 0.00 0.00 0.00 0.00 0.99 Jennings = Riverview Gardens 0.16 0.64 0.23 0.02 0.15 Normandy = Riverview Gardens 0.00 0.00 0.50 0.24 0.30 Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each column reports coefficient estimates from a single regression, in which indicators for each of the four ‘treated’ districts are interacted with the 2015 indicator. Each regression controls for school and year FE, linear school time trends and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. 5.4. Sensitivity Analysis This section presents evidence that the key identifying ‘parallel trends’ assumption made by the DD identification strategy is valid, and thus that the OLS estimates of Equation (1) and its variants presented in Sections 5.1–5.3 can be given causal interpretations. We begin by showing that estimates of τ are robust to conditioning on time-varying school characteristics, linear school and district time trends and quadratic school time trends. Specifically, column 1 of Table 7 reports estimates of parsimonious specifications that condition only on school and year FE. Moving from left to right, each column of Table 7 augments the model estimated in column 1 to include a richer conditioning set: column 2 adds time-varying school controls, column 3 adds linear district-specific time trends, column 4 adds linear school-specific time trends (which subsume the district trends) and column 5 adds quadratic school-specific time trends. Panels A and B of Table 7 report the DD estimates for percent below basic in math and percent advanced in math, respectively, both for all students and for Super-subgroup students. Each cell of Table 7, therefore, reports the DD estimate of τ from a unique regression. Online Appendix Table A.5 available as Supplementary data reports analogous results for reading (ELA) achievement, which are similarly robust to model specification. Table 7 School level DD estimates (1) (2) (3) (4) (5) A. Math achievement, below basic     All students 18.6*** 19.1*** 17.9*** 18.4*** 17.7*** (3.5) (3.6) (3.6) (4.1) (4.3)     Super subgroup 14.2*** 13.5*** 12.4*** 12.8*** 12.6*** (3.4) (3.4) (3.3) (3.8) (4.3) B. Math achievement, advanced     All students −9.8*** −10.1*** −9.6*** −9.9*** −11.6*** (1.9) (2.7) (3.1) (2.9) (4.1)     Super subgroup −5.6*** −4.0* −3.8 −4.1 −4.4 (1.1) (2.1) (2.9) (2.8) (3.2)     School and year FE √ √ √ √ √     School controls √ √ √ √     Linear district trends √     Linear school trends √ √     Quadratic school trends √ (1) (2) (3) (4) (5) A. Math achievement, below basic     All students 18.6*** 19.1*** 17.9*** 18.4*** 17.7*** (3.5) (3.6) (3.6) (4.1) (4.3)     Super subgroup 14.2*** 13.5*** 12.4*** 12.8*** 12.6*** (3.4) (3.4) (3.3) (3.8) (4.3) B. Math achievement, advanced     All students −9.8*** −10.1*** −9.6*** −9.9*** −11.6*** (1.9) (2.7) (3.1) (2.9) (4.1)     Super subgroup −5.6*** −4.0* −3.8 −4.1 −4.4 (1.1) (2.1) (2.9) (2.8) (3.2)     School and year FE √ √ √ √ √     School controls √ √ √ √     Linear district trends √     Linear school trends √ √     Quadratic school trends √ Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each cell reports the estimate of τ for a unique regression. Outcomes are school performance rates for either all students or for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each panel represents a different dependent variable: percent below basic or percent advanced, in either math or reading. Standard errors are clustered by school district. FE = fixed effects. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 7 School level DD estimates (1) (2) (3) (4) (5) A. Math achievement, below basic     All students 18.6*** 19.1*** 17.9*** 18.4*** 17.7*** (3.5) (3.6) (3.6) (4.1) (4.3)     Super subgroup 14.2*** 13.5*** 12.4*** 12.8*** 12.6*** (3.4) (3.4) (3.3) (3.8) (4.3) B. Math achievement, advanced     All students −9.8*** −10.1*** −9.6*** −9.9*** −11.6*** (1.9) (2.7) (3.1) (2.9) (4.1)     Super subgroup −5.6*** −4.0* −3.8 −4.1 −4.4 (1.1) (2.1) (2.9) (2.8) (3.2)     School and year FE √ √ √ √ √     School controls √ √ √ √     Linear district trends √     Linear school trends √ √     Quadratic school trends √ (1) (2) (3) (4) (5) A. Math achievement, below basic     All students 18.6*** 19.1*** 17.9*** 18.4*** 17.7*** (3.5) (3.6) (3.6) (4.1) (4.3)     Super subgroup 14.2*** 13.5*** 12.4*** 12.8*** 12.6*** (3.4) (3.4) (3.3) (3.8) (4.3) B. Math achievement, advanced     All students −9.8*** −10.1*** −9.6*** −9.9*** −11.6*** (1.9) (2.7) (3.1) (2.9) (4.1)     Super subgroup −5.6*** −4.0* −3.8 −4.1 −4.4 (1.1) (2.1) (2.9) (2.8) (3.2)     School and year FE √ √ √ √ √     School controls √ √ √ √     Linear district trends √     Linear school trends √ √     Quadratic school trends √ Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each cell reports the estimate of τ for a unique regression. Outcomes are school performance rates for either all students or for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each panel represents a different dependent variable: percent below basic or percent advanced, in either math or reading. Standard errors are clustered by school district. FE = fixed effects. ***p < 0.01, **p < 0.05 and *p < 0.1. Importantly, the estimates are remarkably stable across columns, within rows of Table 7. In other words, the baseline DD estimates are robust to controlling (or not) for time-variant school characteristics and various school and district time trends. This stability strongly suggests that the DD estimates are not biased by preexisting differential trends (i.e. failure of the parallel trends assumption) (Angrist and Pischke, 2009). We address this issue further by estimating event-study specifications, which are presented in Table 8. Table 8 School-level math achievement event study estimates Below basic Advanced All students Super subgroup All students Super subgroup (1) (2) (3) (4) 2011 × Treated 0.5 0.9 −0.1 0.1 (0.5) (0.5) (1.0) (0.9) 2012 × Treated 0.1 1.2 0.2 −0.1 (0.7) (0.9) (1.1) (1.0) 2013 × Treated −0.6 0.1 1.2 1.3 (0.6) (0.7) (1.5) (1.6) 2014 × Treated 1.1 1.5* 0.8 0.5 (0.8) (0.9) (1.2) (1.1) 2015 × Treated 19.4*** 14.3*** −9.7*** −3.6* 0.5 0.9 -0.1 0.1 Below basic Advanced All students Super subgroup All students Super subgroup (1) (2) (3) (4) 2011 × Treated 0.5 0.9 −0.1 0.1 (0.5) (0.5) (1.0) (0.9) 2012 × Treated 0.1 1.2 0.2 −0.1 (0.7) (0.9) (1.1) (1.0) 2013 × Treated −0.6 0.1 1.2 1.3 (0.6) (0.7) (1.5) (1.6) 2014 × Treated 1.1 1.5* 0.8 0.5 (0.8) (0.9) (1.2) (1.1) 2015 × Treated 19.4*** 14.3*** −9.7*** −3.6* 0.5 0.9 -0.1 0.1 Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each column reports the coefficient estimates on the interactions between the ‘treated school’ and year indicators from a unique event-study regression that controls for school and year FE and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each row represents a different dependent variable: percent below basic or percent advanced, in math. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. Table 8 School-level math achievement event study estimates Below basic Advanced All students Super subgroup All students Super subgroup (1) (2) (3) (4) 2011 × Treated 0.5 0.9 −0.1 0.1 (0.5) (0.5) (1.0) (0.9) 2012 × Treated 0.1 1.2 0.2 −0.1 (0.7) (0.9) (1.1) (1.0) 2013 × Treated −0.6 0.1 1.2 1.3 (0.6) (0.7) (1.5) (1.6) 2014 × Treated 1.1 1.5* 0.8 0.5 (0.8) (0.9) (1.2) (1.1) 2015 × Treated 19.4*** 14.3*** −9.7*** −3.6* 0.5 0.9 -0.1 0.1 Below basic Advanced All students Super subgroup All students Super subgroup (1) (2) (3) (4) 2011 × Treated 0.5 0.9 −0.1 0.1 (0.5) (0.5) (1.0) (0.9) 2012 × Treated 0.1 1.2 0.2 −0.1 (0.7) (0.9) (1.1) (1.0) 2013 × Treated −0.6 0.1 1.2 1.3 (0.6) (0.7) (1.5) (1.6) 2014 × Treated 1.1 1.5* 0.8 0.5 (0.8) (0.9) (1.2) (1.1) 2015 × Treated 19.4*** 14.3*** −9.7*** −3.6* 0.5 0.9 -0.1 0.1 Notes: The analytic sample contains 1744 unique school-year observations, 50 unique districts, 302 unique elementary schools and 6 academic years (2010–2015). Each column reports the coefficient estimates on the interactions between the ‘treated school’ and year indicators from a unique event-study regression that controls for school and year FE and time-varying school characteristics. Outcomes are school performance rates for both all students and for super-subgroup (high-needs) students who are black, Hispanic, eligible for FRL, have an IEP or ELL. Each row represents a different dependent variable: percent below basic or percent advanced, in math. Standard errors are clustered by school district. ***p < 0.01, **p < 0.05 and *p < 0.1. The robustness of the baseline results to controlling for school and district-specific time trends, and for time-varying school observables, suggests that the DD estimates are not driven by preexisting differential trends in the treated (Ferguson-area) schools. In Table 8, we formally test this assumption using an event study version of Equation (1) that fully interacts the Ferguson indicator with the full set of year FE. Relative to the omitted 2010 reference group, the other 2011–2014 pre-treatment interactions tend to be statistically insignificant and small in magnitude. In fact, they are often the opposite sign of the actual 2015 treatment effect, which itself remains similar in magnitude to the baseline estimates reported in Table 2 and strongly statistically significant for three of the four outcomes. Coupled with the results in Table 7, the event study estimates reported in Table 8 provide further evidence that the main identifying assumption holds and, as a result, that the baseline DD estimates can be given a causal interpretation. 6. Conclusion This article documents the negative impact of a police shooting, and the many months of civic unrest that followed, on student achievement in Ferguson, MO. While we cannot separately identify the impacts of the shooting and the subsequent unrest, we find statistically significant, arguably causal effects of the bundle of treatments on students’ math and reading achievement in Ferguson-area elementary schools relative to other schools in the St. Louis MSA. Smaller negative effects are found in majority-black schools elsewhere in the MSA. These DD and triple-difference estimates are not driven by preexisting differential trends in treated schools and are robust to controlling for time-varying school characteristics and linear and quadratic school-specific time trends. Effects are relatively large, particularly at the lower end of the math-score distribution. For example, a conservative estimate suggests that the fraction of high-needs students scoring ‘below basic’ in math increased by about 10 percentage points following the unrest. Reductions in achievement were concentrated in elementary schools, and were at least partly driven by corresponding increases in student absences: the rate of chronic absence increased by about four percentage points (5%) in Ferguson-area elementary schools. However, attendance is unlikely the sole mechanism through which the events in Ferguson affected student achievement in the area, as smaller, but statistically significant, declines in achievement occurred in other majority-black school districts farther away from the physical unrest. For example, the events in Ferguson might have affected schools through other channels, such as creating stress and causing teachers and parents to reallocate instructional time away from math and reading skills and towards non-tested topics such as race, inequality and the criminal justice system. Of course, without objective data on these intermediate outcomes, it is impossible to definitively say to what extent the disruptions in Ferguson affected student achievement through these channels, in Ferguson or elsewhere in the MSA, state and country. Because decreased attendance and lost instructional time are likely mechanisms through which the events in Ferguson may have affected achievement, we contextualize our results by comparing them to those from similar analyses of the impact of disruptions to school schedules on school-level proficiency rates. For example, Marcotte and Hemelt (2008) find that 10 unscheduled, weather-related school closings reduced third- and fifth-grade math proficiency rates by between 5 and 7 percentage points in Maryland. Similarly, Gershenson and Tekin (2015) find that proximity to the 2002 Beltway Sniper Attacks reduced schools’ fifth-grade math proficiency rates by about 5 percentage points in schools serving black and low-income communities. These effects are similar in size to the conservative triple-difference estimates reported in Table 5 and smaller than the baseline estimates in Table 2 of the current study. That the effects of the events in Ferguson are larger than those of the beltway sniper attacks is intuitive, since even if the two events created similar levels of stress and safety concerns, the unrest in Ferguson played out over an entire school year while those in the sniper case lasted about 3 weeks, early in the school year. Still, these impacts are large enough to change schools’ standings under consequential accountability regimes such as No Child Left Behind (Marcotte and Hemelt, 2008; Gershenson and Tekin, 2015). The attendance results in the current study furthers our understanding of the mechanisms through which external disruptions to school environments and school schedules can affect student achievement and highlight the importance of attendance in the education production function (Goodman, J., 2014; Gershenson et al., 2017). More generally, these results highlight the potential benefits of local and state interventions that respond to community traumatic events, civic unrest and related distractions and disruptions to schools. For example, providing additional resources, support and guidance to affected schools and communities might reduce the harm to achievement associated with such events. Weems et al. (2009) describe one school-based intervention that reduced test anxiety in a predominantly black sample of students who were exposed to Hurricane Katrina. This type of reactive policy and support would be further justified by the fact that the police shooting and subsequent civic unrest in Ferguson occurred in what were already relatively disadvantaged and under-resourced schools and communities. Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Footnotes 1 See, for example, Mullainathan’s (2015) piece in the New York Times. More recently, three police shootings of black men in Baton Rouge, LA, Dallas, TX and St. Paul, MN in July 2016 have touched off another round of discussion and protests regarding black communities’ relationships with law enforcement agencies and the criminal justice system. 2 District-level synthetic control method (SCM) analyses (Abadie and Gardeazabal, 2003) yield qualitatively similar results. 3 We henceforth refer to academic years by spring semester. 4 Detailed timelines are available from numerous media outlets, including The Telegraph and The New York Times (part 1, part 2). 5 The six St. Louis MSA counties in Missouri are Lincoln, Warren, St. Charles, Franklin, Jefferson and St. Louis County (which contains Ferguson). St. Louis is an independent city in Missouri in the MSA. Online Appendix Figure A.1 available as Supplementary data shows a map of the entire MSA. 6 See http://mcds.dese.mo.gov/Pages/default.aspx. 7 Specifically, see Online Appendix Table A.1 available as Supplementary data, which reports the estimated impact on the percent of students scoring in each of the four mutually exclusive achievement categories. In any given column (specification), the four point estimates sum to approximately zero, as these categories are both mutually exclusive and inclusive of all students. 8 Low-income is measured by students’ eligibility for FRL. 9 We focus on the Super-subgroup designation rather than race-specific results because there is insufficient within-school variation in race with which to make valid comparisons between treatment and control schools. 10 See Online Appendix Table A.2 available as Supplementary data similarly summarizes the subset of elementary schools. 11 As described in Section 2, the baseline ‘treatment’ group includes schools in four districts: Ferguson, Jennings, Normandy and Riverview gardens. 12 Unfortunately, attendance is not reported at the Super-subgroup level. 13 It is also possible to use the Synthetic Control Method (SCM) (Abadie and Gardeazabal, 2003; Abadie et al., 2010) to identify a ‘synthetic’ Ferguson school district to serve as the control group. As a robustness check, we implement a SCM using Ferguson as the sole treated district. We exclude the other six Ferguson-area districts that comprise the ‘broad treatment’ from the donor pool, which consists of all other districts in the St. Louis MSA. The SCM identifies a ‘synthetic Ferguson’ that is a weighted average of two districts: Ritenour and Maplewood-Richmond Heights. Both are nearby Ferguson and visible in the map in Figure 1. The SCM results are plotted in Online Appendix Figure A.3 available as Supplementary data. The top panel plots the percent below basic in math in the real and synthetic Ferguson districts, relative to the statewide mean, from 2010 to 2015. From 2010 to 2014, Ferguson and its synthetic control follow the same pattern and are nearly overlapping. This is consistent with the raw data plotted in Figure 2 and indicates that the SCM matching algorithm identified a valid synthetic control. In 2015, there is an increase in the percentage of students scoring below basic in math in both the actual and synthetic Ferguson districts. However, the increase in the real Ferguson is noticeably steeper than that in the synthetic control. This difference indicates an impact of more than 10 percentage points, which is similar in size to the impacts identified in the school-level DD analyses. The smaller uptick in the synthetic Ferguson is consistent with spillover effects of the acute unrest in the Ferguson area on neighboring, majority-black districts. The bottom panel plots the annual difference between Ferguson and its synthetic control in each year. Before treatment, this difference fluctuates around zero. The departure from this trend in 2015 can be interpreted as the impact of the unrest on math achievement in the district. 14 See Online Appendix Table A.3 available as Supplementary data shows that the main results presented in Table 2 are robust to weighting by school enrollments (Solon et al., 2015) and to using a broader definition of ‘treatment’ that includes three additional nearby school districts. 15 See Online Appendix Table A.4 available as Supplementary data shows that this interpretation is robust to instead looking separately at performance on end-of-year math tests in third, fifth and eighth grades, and in high school Algebra 1 exams. Specifically, the effects are concentrated on third- and fifth-grade tests. 16 Another possible interpretation of the triple interaction terms in Table 5 is that they represent lower bounds of the impact of the civic unrest in Ferguson on math achievement. This would be the case if, for example, some other event or policy shock disproportionately affected majority-black schools in the St. Louis MSA in 2015. Acknowledgments The authors thank David Deming, Dave Marcotte, Nicholas Papageorge and seminar participants at the College Board and the 2016 SOLE Meetings for providing helpful comments. Elizabeth Pancotti provided helpful research assistance. This manuscript was previously circulated as IZA Discussion Paper No. 10091, entitled ‘Short-Run Externalities of Civic Unrest: Evidence from Ferguson, Missouri’. Any remaining errors are our own. References Abadie A. , Gardeazabal J. ( 2003 ) The economic costs of conflict: a case study of the Basque Country . American Economic Review , 93 : 113 – 132 . Google Scholar CrossRef Search ADS Abadie A. , Diamond A. , Hainmueller J. ( 2010 ) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program . 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( 2014 ) Ferguson resulted from Republican talking points that ignore the economic segregation of blacks in America . Huff Post Politics . Available online at: http://www.huffingtonpost.com/h-a-goodman/ferguson-resulted-from-re_b_5680955.html [Accessed 27 October 2015]. Goodman J. ( 2014 ) Flaking out: student absences and snow days as disruptions of instructional time. NBER Working Paper No. 20221. Kneebone E. ( 2014 ) Ferguson, Mo. Emblematic of Growing Suburban Poverty. Brookings – f The Avenue. Available online at: http://www.brookings.edu/blogs/the-avenue/posts/2014/08/15-ferguson-suburban-poverty [Accessed 27 October 2015]. Lochner L. , Enrico M . ( 2004 ) The effect of education on crime: evidence from prison inmates, arrests, and self-reports . American Economic Review , 94 : 155 – 189 . Google Scholar CrossRef Search ADS Machin S. , Marie O. , Vujic S. ( 2011 ) The crime reducing effect of education . The Economic Journal , 121 : 463 – 484 . 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Ramos, Roberto;Moral-Benito, Enrique

2017 Journal of Economic Geography

doi: 10.1093/jeg/lbx038

Abstract We use a dataset of Spanish exporters with rich spatial information to document the existence of agglomeration economies by export destination. More specifically, we show that, for a large set of export destinations, exporters are geographically too close to be the result of a random outcome. We also analyze the variables that explain the cross-destination heterogeneity in agglomeration. We find that firms selling to countries with worse institutions, a dissimilar language and a different currency are significantly more agglomerated. These results suggest that the value provided by agglomeration is higher concerning destinations where entry is more difficult. 1. Introduction It is now a well-established fact that a large amount of industries are geographically concentrated. This finding together with the observation that firms are on average more productive in denser areas have attracted much attention from economists and policy-makers, who have built a large body of research on the foundations and effects of agglomeration economies. In this article we study a specific form of these agglomeration economies, namely those accruing to export firms. Our main contribution is to uncover the fact that exporters are geographically concentrated by export destination, which is consistent with the existence of agglomeration economies associated with the process of selling abroad. Reaching foreign markets entails additional costs, hence the traditional forces leading to industry agglomeration, namely sharing, matching and learning mechanisms, see Marshall (1920) and Duranton and Puga (2004), apply to this process, and naturally vary by export destination. We are not the first to emphasize the existence of destination-specific export spillovers. In a regression framework, Koenig (2009), Koenig et al. (2010) and Choquette and Meinen (2015) show that the decision to sell to a certain destination is positively affected by the pool of local exporters selling to that destination, while Cassey and Schmeiser (2013) show evidence of clustering by export destination in Russian regions. Our main step forward in this literature is to document the existence of destination-specific agglomeration economies using a firm level dataset with rich spatial information that allows us to apply a nonparametric standard test of agglomeration: Duranton and Overman (2005). This method improved on previous approaches, such as Ellison and Glaeser (1997), Maurel and Sédillot (1999), and Devereux et al. (2004), for two reasons. First, it treats space as continuous, as opposed to using an arbitrary set of spatial units. And second, it allows assessing the statistical significance of departures from randomness.1 The use of the Duranton and Overman (2005) test allows us to refine and expand the results of the extant literature in two fundamental ways. First, we uncover destination-specific exporter agglomeration beyond the overall concentration of exporters with respect to domestic firms and the industry agglomeration of exports to each country. That is, for each destination the counterfactual is built solely from exporters operating in the industries exported to the destination. This addresses a crucial issue: industries are geographically concentrated, and different countries demand goods from different industries. Then, agglomeration by export destination might be the result of countries buying goods intensively from agglomerated industries. We show that exporters are significantly concentrated over and above what would be expected from the fact that exporters to individual countries are concentrated by sector and sectors are concentrated geographically. Furthermore, by restricting the analysis to export firms, we account for different location patterns between domestic and export firms. And second, we compute a continuous index measuring the extent of geographical agglomeration of exporters to each destination. This allows us to investigate the characteristics that explain the cross-destination heterogeneity in agglomeration levels. Our baseline results indicate that for more than half of export destinations exporters are significantly concentrated, i.e. they are too close to be the result of a random outcome.2 We also perform a battery of robustness checks to account for other mechanisms that would result in agglomeration by export destination without relying on export-destination spillovers. There are two mechanisms that are worth emphasizing. First, large firms are able to reach a larger set of destinations, hence agglomeration by destination could be the result of large exporters being concentrated with respect to small exporters. And second, it is documented that firms go hierarchically to more and more destinations. Then agglomeration by popular destinations could induce agglomeration by less popular destinations if exporters to the former disproportionately export to the latter. By restricting the counterfactual, we show that our results are not the mechanical consequence of these and other mechanisms that would result in spurious agglomeration. Our results also show that the level of agglomeration varies meaningfully across destinations. We find that exporters to countries with a dissimilar language, lower institutional quality and a different currency are significantly more agglomerated. We interpret this finding as evidence suggesting that agglomeration provides higher value in countries where entry is more difficult. Overall, our findings are consistent with the existence of externalities in the process of selling to some countries. Although thus far the literature has been to some extent unable to empirically verify the specific driving mechanisms, several possibilities have been rationalized in theoretical models.3 For example, Segura-Cayuela and Vilarrubia (2008) and Fernandes and Tang (2014) emphasize that firms entering foreign markets reveal information, hence reducing the uncertainty faced by potential entrants. Also, Krautheim (2012) and Cassey and Schmeiser (2013) explore the channel of cost reductions brought by a larger number of exporters in the setting of the Melitz (2003) model. On the empirical front, our results are consistent with Lovely et al. (2005), who show, using the Ellison and Glaeser index, that US exporter headquarter activity is more agglomerated when firms sell to countries less integrated in the world economy and with worse credit ratings. Moreover, Koenig (2009), Wagner and Zahler (2015) and Cadot et al. (2013) show that the presence of neighboring export firms and pioneers in foreign markets are significantly associated with a higher probability of foreign entry, suggesting that the flow of information between nearby firms and signals revealed by successful exporters are important in this context. Also, a recent contribution by Paravisini et al. (2015) finds that the distribution of bank lending is skewed toward firms exporting to the same destination, which suggests that agglomeration may be associated with credit markets. We are able to link the observed patterns of concentration across destinations to cultural and institutional differences across importing countries. Beyond this, our article also remains silent on the specific mechanisms driving the clustering by export destination. Yet, our findings as well as those of the literature give new understandings regarding the behavior of export firms and provide useful policy insights on how to help firms access foreign markets. The rest of the article is organized as follows. Section 2 describes the dataset. Section 3 explains the methodology, presents the baseline results and performs a set of robustness checks. Section 4 delves into the determinants of the cross-destination variation in agglomeration levels. Section 5 concludes. 2. Data We use the firm-level data compiled by the Bank of Spain to construct the Balance of Payments statistics for Spain. The dataset contains information on firms making transactions with foreign agents if they are worth more than €12,000 and they are performed through a bank. Therefore, the dataset is likely to exclude only the smallest exporters. In the baseline analysis, we rely on 2007 data and we use previous years to check the stability of the results over time.4 The dataset has several advantages for the study of the geographical location of exporters. First, it is made up from administrative records and it has a large coverage. For example, it accounts for 97% of aggregate exports in 2007 and both transactions within the EU and to third countries are observed. Second, it contains information on total sales of every firm to each export destination. And third, it provides the zip code of every exporter. Hence, we can compute distances between firms and study the agglomeration of export firms by destination. The zip code provided is that of the headquarters, thus our focus in on headquarter agglomeration rather than on establishment agglomeration. We argue that this feature is likely to play a small role in the results, as we estimate that around 91% of exporters in our data have just one plant.5 Moreover, Koenig (2009), Koenig et al. (2010) and Choquette and Meinen (2015) show that export spillovers are not affected by including either single-plant exporters or the headquarter of all exporters. Having said this, focusing on headquarters points to externalities stemming from information flows, rather than cost-sharing mechanisms, which are more likely to be linked to establishments. There is one limitation of the dataset that is worth noting: it has no information on the type of goods being traded. Rather, it only provides the exporter four-digit industry code. In our baseline results, we rely on two-digit industry codes to control for the industry composition of exports. Focusing on two-digit industries provides sufficiently large bins for drawing the counterfactual exporters, which increases the precision of the confidence bands. Yet, it makes us account for the varieties being exported only to a certain extent (see also Section 3.3.5). Besides, the dataset does not include firm characteristics beyond industry, fiscal id and total exports to each country. For this reason, for the robustness check described in Section 3.3.1, we approximate firm size with total firm exports. Table 1 shows some descriptive statistics of the exporters included in our dataset in 2007. Our analysis is restricted to manufacturing firms and export destinations with at least 10 exporters. The data include more than 18,000 exporters located in close to 3200 zip codes, out of a total of around 11,000 zip codes in Spain. The median exporter sells to two destinations and the median zip code hosts two export firms. See also Table A1 in the Appendix for a description of the main variables used in the article and Table A2 for the destinations included in the sample. Table 1 Descriptive statistics: exporters in 2007 (balance of payments) Mean Percentiles (Std. Dev.) 25 50 75 (1) (2) (3) (4) Panel A: exporters (N = 18,715) Total exports (thousand €) 6745 54 255 1435 (100,757) Destinations (N = 166) 5.19 1 2 6 (7.82) Panel B: zip codes (N = 3192) Number exporters 5.89 1 2 6 (10.05) Mean Percentiles (Std. Dev.) 25 50 75 (1) (2) (3) (4) Panel A: exporters (N = 18,715) Total exports (thousand €) 6745 54 255 1435 (100,757) Destinations (N = 166) 5.19 1 2 6 (7.82) Panel B: zip codes (N = 3192) Number exporters 5.89 1 2 6 (10.05) Notes: This table shows descriptive statistics of Spanish manufacturing exporters in 2007 included in the Balance of Payments micro data. The panel A shows statistics of total exports and number of export destinations per exporter. The panel B shows moments of the distribution of the number of export firms located in the zip codes hosting at least one export firm. N corresponds to the number of distinct observations. Table 1 Descriptive statistics: exporters in 2007 (balance of payments) Mean Percentiles (Std. Dev.) 25 50 75 (1) (2) (3) (4) Panel A: exporters (N = 18,715) Total exports (thousand €) 6745 54 255 1435 (100,757) Destinations (N = 166) 5.19 1 2 6 (7.82) Panel B: zip codes (N = 3192) Number exporters 5.89 1 2 6 (10.05) Mean Percentiles (Std. Dev.) 25 50 75 (1) (2) (3) (4) Panel A: exporters (N = 18,715) Total exports (thousand €) 6745 54 255 1435 (100,757) Destinations (N = 166) 5.19 1 2 6 (7.82) Panel B: zip codes (N = 3192) Number exporters 5.89 1 2 6 (10.05) Notes: This table shows descriptive statistics of Spanish manufacturing exporters in 2007 included in the Balance of Payments micro data. The panel A shows statistics of total exports and number of export destinations per exporter. The panel B shows moments of the distribution of the number of export firms located in the zip codes hosting at least one export firm. N corresponds to the number of distinct observations. Table 2 Most localized destinations Rank Country N Localization Rank Country N Localization 1 West Bank and Gaza 36 0.29 6 Montenegro 61 0.10 2 Iraq 23 0.18 7 Andorra 887 0.09 3 Suriname 18 0.18 8 Aruba 19 0.09 4 Chad 18 0.16 9 Tanzania 42 0.08 5 Albania 168 0.11 10 Armenia 53 0.08 Rank Country N Localization Rank Country N Localization 1 West Bank and Gaza 36 0.29 6 Montenegro 61 0.10 2 Iraq 23 0.18 7 Andorra 887 0.09 3 Suriname 18 0.18 8 Aruba 19 0.09 4 Chad 18 0.16 9 Tanzania 42 0.08 5 Albania 168 0.11 10 Armenia 53 0.08 Notes: This table shows the 10 destinations to which exporters exhibit the highest level of agglomeration, according to the country index of localization defined in Section 3.1. Table 2 Most localized destinations Rank Country N Localization Rank Country N Localization 1 West Bank and Gaza 36 0.29 6 Montenegro 61 0.10 2 Iraq 23 0.18 7 Andorra 887 0.09 3 Suriname 18 0.18 8 Aruba 19 0.09 4 Chad 18 0.16 9 Tanzania 42 0.08 5 Albania 168 0.11 10 Armenia 53 0.08 Rank Country N Localization Rank Country N Localization 1 West Bank and Gaza 36 0.29 6 Montenegro 61 0.10 2 Iraq 23 0.18 7 Andorra 887 0.09 3 Suriname 18 0.18 8 Aruba 19 0.09 4 Chad 18 0.16 9 Tanzania 42 0.08 5 Albania 168 0.11 10 Armenia 53 0.08 Notes: This table shows the 10 destinations to which exporters exhibit the highest level of agglomeration, according to the country index of localization defined in Section 3.1. 3. Localization of exporters by export destination In this section, we provide evidence that exporters are significantly agglomerated by export destination by applying the methodology developed by Duranton and Overman (2005), henceforth DO. Among other advantages discussed in the introduction, this methodology allows us to account for the fact that exports to a country are concentrated by sector and sectors are concentrated geographically. Furthermore, it allows controlling for other forces leading to agglomeration by export destination, such as the concentration of large vs small exporters, sequential exporting and the concentration of exporters in large cities, which we discuss below. Before turning to the baseline results, we describe briefly our application of DO. 3.1. Methodology: application of Duranton and Overman (2005) In this section, we give a succinct overview on how we use DO to uncover agglomeration by export destination, see Appendix B for a more comprehensive explanation and technical details. In our baseline analysis, we use data from 2007 and we consider the 166 destinations with at least 10 exporters. For each country, we kernel-estimate the distribution of bilateral distances of exporters to the country by applying to the zip code coordinates the haversine formula, which computes the shortest distance over the Earth’s surface. We then compare this distribution with 1000 counterfactual distributions built as follows. For each two-digit industry, we draw 1000 independent random samples from exporters in the industry; each draw of size the actual number of exporters to the country operating in that industry. Then, we aggregate each draw across the different industries to collect 1000 random samples that replicate the industry composition of exports to the country. Note also that the size of each random draw is the same as the actual number of exporters to the country. We then estimate the distance distribution of each random draw. The resulting counterfactual distributions control for two mechanisms that might result in spurious agglomeration by export destination. First, the fact that exporters have special characteristics relative to nonexporters (see, e.g., Bernard et al. (2003)) and hence they may agglomerate with respect to domestic firms. Indeed, Behrens and Bougna (2015) show that this is the case in 14–16% Canadian industries and the literature on export spillovers has documented that pools of local exporters affects positively the decision to enter foreign markets, see for example Koenig (2009). And second, the fact that the industry composition of exports differs across countries. For example, one country may demand heavily goods from an industry that is highly concentrated. Therefore, exporters to this country can be concentrated either because of industry concentration or because of exporter concentration. By making the random draws replicate the destination-specific industry composition of exports, we are able to disentangle the latter from the former. We then rank, for each kilometer, the 1000 counterfactual distributions in ascending order and define a localization threshold as the percentile that makes 95% of the counterfactual distributions lie below it across all distances. Note that to compare the estimated density with the counterfactual distributions we focus on distances below 100 kilometers, which are more relevant to explain interactions between exporters. This distance horizon has no substantial effects on the results, as shown in Section 3.3.5. We define exporters to a country to be significantly localized if the actual distance distribution is above the localization threshold in at least one kilometer. We also define a dispersion threshold as the percentile that makes 5% of the simulations lie below it across all distances. Given that densities must sum up to one, localization at some distances implies dispersion at others. Therefore, we define exporters to a country to be dispersed if the actual distance distribution is below the dispersion threshold in at least one kilometer and the country does not exhibit localization. These definitions follow DO.6 Finally, we also construct the country version of the industry quantitative index of localization defined by DO. This country index is computed as the sum across distances of the difference between the density of the actual distance distribution and the localization threshold if the former is above the latter and zero otherwise. This index gives a measure of the amount of exporter localization by export destination. 3.2. Baseline results In our baseline results we find significant agglomeration for a large number of export destinations: of the 166 countries in our sample, firms exporting to 107 (64%) are significantly agglomerated, whereas only one destination exhibits dispersion. Figure 1A displays the share of destinations in which exporters exhibit significant localization at each distance. Close to 60% of destinations exhibit significant agglomeration at distances below 40 kilometers, this share decreasing fast at larger distances. This pattern resembles that found by DO regarding industry agglomeration. With respect to the amount of agglomeration at each distance, Panel B plots for each kilometer the sum across destinations of the difference between the distance distribution and the localization threshold when the former is above the latter. As can be seen, the largest amount of agglomeration takes place at very small distances. Again, this result is in line with industry agglomeration patterns. Figure 1 View largeDownload slide Localization of exporters by export destination. Notes: This figure shows the pattern of agglomeration by export destination. (A) Displays the share of destinations to which exporters exhibit significant localization at each level of distance, whereas (B) shows the amount of localization at each distance, i.e. the sum across destinations of the difference between the distance distribution and the localization threshold when the former is above the latter. Figure 1 View largeDownload slide Localization of exporters by export destination. Notes: This figure shows the pattern of agglomeration by export destination. (A) Displays the share of destinations to which exporters exhibit significant localization at each level of distance, whereas (B) shows the amount of localization at each distance, i.e. the sum across destinations of the difference between the distance distribution and the localization threshold when the former is above the latter. Table 2 shows the destinations exhibiting the highest country index of agglomeration and Table A2 in the Appendix reports the value of the index for all destinations. The largest amount of agglomeration is found in rather small destinations, accounting for only 1.4% of all firm-country relationships in 2007. However, larger countries, such as the main EU countries and the USA, also exhibit significant agglomeration. Overall, 85.8% of firm-country relationships correspond to significantly localized destinations. It is also worth highlighting that the extent of agglomeration varies widely across destinations, being the standard deviation of the country index twice as large as the mean. At first sight it is not straightforward to uncover a systematic pattern of cross-destination agglomeration, probably due to the fact that several determinants act in opposing directions. For example, some agglomeration is expected to happen next to the border of neighboring countries. Indeed, one destination exhibiting very large agglomeration is Andorra, with which Spain shares a border. However, nearby countries such as those belonging to the EU have good business practices, which undermines the value of agglomeration in overcoming trade barriers. Hence, we would expect exporters to these countries to be less agglomerated. We acknowledge that given the nature of our data it is very hard to disentangle the specific mechanisms driving agglomeration by export destination. Yet in Section 4 we discuss several possibilities and show some evidence via regression analysis. Before this, we perform several robustness checks in the next section. 3.3. Robustness checks In this section we check the sensitivity of the baseline results to restricting the counterfactual. In doing so, we control for some concentration patterns that would result in agglomeration by export destination without relying on export-destination spillovers. Specifically, we take into account the different concentration patterns of large vs small exporters, the role of sequential exporting, the concentration of firms in large cities, the stability of the results over time and others. 3.3.1. Controlling for destinations served by large vs small exporters The heterogeneous firms literature has documented that there is a substantial amount of heterogeneity within exporters, one important dimension of this heterogeneity being size. This is a relevant issue for the study of agglomeration by destination, since it has been documented that large exporters reach a larger set of export destinations, see Helpman et al. (2008) and Eaton et al. (2011). Therefore, our baseline results raise the concern that agglomeration by destination could be the result of large exporters being agglomerated with respect to small exporters. Being this the case, our findings would not exist among exporters of comparable size. We carry out four tests to address this issue. First, we repeat the baseline exercise with subsamples of the largest exporters. Specifically, we consider exporters above the median and above the 75-th percentile of total firm exports. Second, we explicitly control for the size of exporters when building the counterfactual. To be precise, we restrict further the counterfactual by conditioning on 10 and 20 bins of total firm exports. That is, we construct counterfactual distributions from exporters in the same industry and the same size bin, replicating for each destination the distribution of these variables observed in the data. Hence, this procedure estimates destination-specific agglomeration patterns beyond the concentration of exporters, industries and exporters of comparable size.7 Figure 2 shows the results of these tests. Focusing on the sample of the largest exporters (those above percentile 75) reduces the number of agglomerated destinations to 49%, from 64% in the baseline. A similar result arises when we restrict the counterfactual to 10 or 20 bins of total firm exports, see Figure 2A. Hence, some portion of the localization patterns can be explained by the agglomeration of firms of similar size, although this portion is small and the bulk of the baseline results is preserved. Indeed, the destinations to which exporters are no longer significantly agglomerated are those with the lowest degree of agglomeration in the baseline, see the scatter plot in Figure 2B. This suggests that the lower agglomeration levels can be explained (at least partly) by the smaller populations from which the random samples of the counterfactual simulations are drawn. For example, the median number of exporters per industry is 626, whereas the median number of exporters per industry and size bin is 37. Hence, it is reassuring that a more stringent counterfactual preserves the finding of significant agglomeration to a large set of export destinations, in this case to half of the total. Figure 2 View largeDownload slide Localization controlling for exporter size. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for the size of exporters. (A) Shows the share of localized destinations at each level of distance. The red dashed and the green short-dashed lines are built from samples of the largest exporters: those above the median and the 75 percentile of total firm exports, respectively. The blue dash-dotted and the orange long-dashed lines are obtained from counterfactuals that control for 10 and 20 bins, respectively, of total firm exports (as well as the industry composition of exports). (B) Displays the correlation between the country index of agglomeration and that from the simulations accounting for 20 bins of exporter size. The value of this correlation is 0.98. Figure 2 View largeDownload slide Localization controlling for exporter size. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for the size of exporters. (A) Shows the share of localized destinations at each level of distance. The red dashed and the green short-dashed lines are built from samples of the largest exporters: those above the median and the 75 percentile of total firm exports, respectively. The blue dash-dotted and the orange long-dashed lines are obtained from counterfactuals that control for 10 and 20 bins, respectively, of total firm exports (as well as the industry composition of exports). (B) Displays the correlation between the country index of agglomeration and that from the simulations accounting for 20 bins of exporter size. The value of this correlation is 0.98. 3.3.2. Controlling for sequential exporting In our empirical specification each destination is treated independently. Given that some firms export to more than one country, this creates a possible dependence of agglomeration patterns across certain markets. Indeed, a large literature has documented that firms go hierarchically to more and more destinations, see for example Albornoz et al. (2012) and Chaney (2014). Therefore, if exporters to one destination are agglomerated and a subset of these exporters disproportionately exports to another destination, this destination will also exhibit agglomeration. We partially addressed this concern when controlling for firm size in the previous subsection, as exporters of the same size are more likely to share some destinations. Here we explore further this issue. First, we inspect if the average number of export destinations of exporters to countries that exhibit significant agglomeration is higher than that of exporters to countries that do not exhibit agglomeration. Finding so would suggest that the large number of agglomerated destinations could be the result of these countries attracting exporters that sell to many (possibly agglomerated) countries. Second, we restrict the counterfactual in the spirit of the previous subsection in order to control for the ability of exporters to sell to more and more difficult destinations. Regarding the first analysis, we find that the distribution of the average number of export destinations of exporters to agglomerated countries lies to the left of the distribution of the average number of export destinations of exporters to countries that do not exhibit agglomeration, see Figure 3. For example, the average number of export destinations of exporters selling to countries that exhibit agglomeration is on average 25.1, whereas this statistic is 27.8 regarding exporters to countries that do not exhibit agglomeration. This provides evidence, at least to a first approximation, against the concern that agglomerated destinations are so because exporters selling there sell also to many other countries. Figure 3 View largeDownload slide Average number of destinations of exporters selling to localized vs nonlocalized destinations. Notes: This figure shows the cross-destination distribution of the average number of destinations reached by exporters. The white bars correspond to countries that exhibit significant agglomeration whereas the gray bars to countries that do not exhibit significant concentration. Figure 3 View largeDownload slide Average number of destinations of exporters selling to localized vs nonlocalized destinations. Notes: This figure shows the cross-destination distribution of the average number of destinations reached by exporters. The white bars correspond to countries that exhibit significant agglomeration whereas the gray bars to countries that do not exhibit significant concentration. Regarding the second exercise, we carry out two additional robustness checks. First, we condition the counterfactual on two bins: exporters selling to only one destination (which represents roughly 40% of exporters) and exporters selling to more than one country. And second, we condition on how ‘difficult’ are the destinations each exporter sells to. We proceed as follows, we rank the destinations in our sample from the highest to the lowest number of exporters, that is, from the most popular to the least popular destinations. We then split the sample in five quintiles, the bottom quintile containing the most popular destinations and the top quintile the least popular. We then assign each exporter to the quintile of the most difficult destination it sells to. Therefore, firms selling to difficult countries are assigned to the top quintile, whereas exporters reaching only the most popular destinations are assigned to the bottom quintile. Hence, we condition the counterfactual to exporters of the same industry and of the same ability to reach difficult destinations. Figure 4 shows that accounting for sequential exporting gives similar results to controlling for firm-size bins. Figure 4A shows that 40% of destinations exhibit significant agglomeration at small distances, a percentage that gradually declines as distance increases. This is a lower share of localized destinations as compared to the baseline. Reassuringly, we find that the relative agglomeration patterns across countries are preserved. Figure 4B displays a high correlation between the baseline country index of agglomeration and that accounting for the difficulty of reaching each destination. Those countries exhibiting the largest amount of agglomeration in the baseline are still those with the highest levels in the more restricted counterfactual. It is worth noting also that the extent of agglomeration is reduced: the average index of significantly agglomerated destinations is around two thirds that of the baseline. This suggests that sequential exporting can be relevant in determining the extent of agglomeration by export destination, yet the smaller samples from which the counterfactual simulations are drawn may partly explain this result. Figure 4 View largeDownload slide Localization controlling for sequential exporting. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for sequential exporting. (A) Shows the share of localized destinations at each level of distance. The red dashed line is obtained from a counterfactual that controls for two groups of firms according to the number of countries they sell to: one or more than one. The green dotted line is obtained from a counterfactual of 5 bins according to the most difficult destination each exporter is able to sell to. The degree of difficulty of each destination is assessed according to the total number of exporters. Both counterfactuals account also for the industry composition of exports. (B) Displays the correlation between the country index of agglomeration and that from the simulations accounting for the difficulty of reaching each destination. The value of this correlation is 0.97. Figure 4 View largeDownload slide Localization controlling for sequential exporting. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for sequential exporting. (A) Shows the share of localized destinations at each level of distance. The red dashed line is obtained from a counterfactual that controls for two groups of firms according to the number of countries they sell to: one or more than one. The green dotted line is obtained from a counterfactual of 5 bins according to the most difficult destination each exporter is able to sell to. The degree of difficulty of each destination is assessed according to the total number of exporters. Both counterfactuals account also for the industry composition of exports. (B) Displays the correlation between the country index of agglomeration and that from the simulations accounting for the difficulty of reaching each destination. The value of this correlation is 0.97. 3.3.3. Controlling for destinations served by exporters in large cities Exporters located in large cities might be able to reach a larger set of export destinations, for instance by using better transport facilities, such as airports. Then, if some exporters concentrate in large cities and large cities disproportionately export to difficult destinations, exporters to these destinations will be spatially agglomerated. If this is the case, the destination-specific agglomeration economies would not exist within cities of comparable size. We perform two tests to address this concern. First, we exclude from our sample those firms located in Madrid and Barcelona, which are the largest municipalities in Spain, accounting for around 13% of export firms. Second, we control for the size of each city where each exporter is located when building the counterfactual distributions. We construct city-size bins with cutoffs given by 10 thousand, 100 thousand, 250 thousand and 1 million people.8 We then restrict the counterfactual to exporters in the same industry and the same population bin, replicating for each destination the distribution of these two variables observed in the data. Figure 5A shows that excluding firms located in the largest municipalities has a small effect on the results. At low distances the share of localized destinations does not change, whereas at larger distances agglomeration is higher. Indeed, 60% of destinations exhibit agglomeration until around 70 km, which is a larger scale of agglomeration than that of the baseline. Accounting for city-size bins reduces the extent of agglomeration at small distances, although to a limited extent. The total number of localized destinations goes down from 64% in the baseline to 62%. Figure 5B compares the country index of agglomeration with that of the baseline. We find that they are very highly correlated (0.98) and most of the countries lie very close to the 45° line. Indeed, those destinations for which agglomeration is no longer significant are those that exhibit very low levels in the first place. Hence, it seems that the baseline results cannot be explained by firms located in the largest municipalities or in locations of certain size. Figure 5 View largeDownload slide Localization controlling for city size. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for the size of cities where exporters are located. (A) Shows the share of localized destinations at each level of distance. The red dashed line corresponds to the sample excluding exporters located in Madrid and Barcelona. The green short-dashed line is built from a counterfactual that controls for 5 bins of city size (as well as the industry composition of exports). (B) Displays the correlation between the baseline country index of agglomeration and that from the simulations controlling for city-size bins. The value of this correlation is 0.98. Figure 5 View largeDownload slide Localization controlling for city size. Notes: This figure compares the baseline results of agglomeration by export destination with those controlling for the size of cities where exporters are located. (A) Shows the share of localized destinations at each level of distance. The red dashed line corresponds to the sample excluding exporters located in Madrid and Barcelona. The green short-dashed line is built from a counterfactual that controls for 5 bins of city size (as well as the industry composition of exports). (B) Displays the correlation between the baseline country index of agglomeration and that from the simulations controlling for city-size bins. The value of this correlation is 0.98. 3.3.4. Stability of the results over time In this subsection we check the stability of the results over time. A recent strand of literature documents that a large portion of exporter-destination relationships are short-lived, see Besedes and Prusa (2006), Nitsch (2009) and Békés and Muraközy (2012). This raises the concern that the agglomeration patterns uncovered so far could vary over time. We carry out two tests to address this issue. First, we repeat the baseline analysis for the years 2003 and 2005. And second, we restrict the baseline sample to continuous exporters from 2005 to 2007. Note that this exercise involves restricting the sample to those firm-country relationships that exist during three consecutive years (2005, 2006 and 2007). This criterion implies dropping around 40% of the exporters in the original sample. Note also that the agglomeration patterns by destination are computed only for continuous exporters to that destination, the counterfactual being random draws of continuous exporters to that and other destinations that satisfy the industry criterion. This implies that the number of destinations is reduced to 121. Figure 6 shows the results. The patterns of agglomeration by destination hold broadly across years, being the share of localized destinations very similar in 2003, 2005 and 2007 (Figure 6A). This is also true for the sample of continuous exporters between 2005 and 2007. The share of localized destinations is 60% vs 64% in the baseline and the scale of agglomeration at short distances is very similar. This finding highlights that agglomeration by a significant amount of export destinations is also a feature of the exporters most able to establish permanent trade relationships. In terms of the country index of agglomeration, the results over time are also relatively stable. The correlation between the 2007 index and that of 2005 and 2003 is 0.66 and 0.75, respectively. The Figure 6B shows the scatterplot between the baseline index and that of the continuous exporters sample. The correlation amounts to 0.71.9 Figure 6 View largeDownload slide Localization across different years. Notes: This figure shows agglomeration by export destination across different years and for the sample of continuous exporters in 2007 (i.e. exporter-destination relationships that exist during 2005 to 2007). (A) Shows the share of localized destinations at each distance. (B) Displays the correlation between the baseline country index of agglomeration and that obtained from the continuous exporter sample. The value of this correlation is 0.71. Note that this panel excludes two destinations with highly localized exporters in both the baseline and the continuous exporter sample in order to keep a meaningful scale. Figure 6 View largeDownload slide Localization across different years. Notes: This figure shows agglomeration by export destination across different years and for the sample of continuous exporters in 2007 (i.e. exporter-destination relationships that exist during 2005 to 2007). (A) Shows the share of localized destinations at each distance. (B) Displays the correlation between the baseline country index of agglomeration and that obtained from the continuous exporter sample. The value of this correlation is 0.71. Note that this panel excludes two destinations with highly localized exporters in both the baseline and the continuous exporter sample in order to keep a meaningful scale. 3.3.5. Additional robustness checks In our counterfactual simulations, we controlled for the industry composition of exports up to two-digit industries. This level of aggregation might be too coarse if countries demand specific varieties of a product that are locally produced. This concern could be partly addressed by using detailed enough product codes such as HS-6, yet our data do not contain such information. As an additional robustness check, we controlled in the counterfactual simulations for the industry composition of exports up to four-digit industries, at the cost of losing degrees of freedom when building the counterfactual. We find that the number of destinations with agglomerated exporters is 57%, slightly less than in the baseline but still high. Moreover, the patterns of agglomeration resemble that of the baseline. The share of localized destinations is close to 50% until about 40 km, decreasing fast from that distance on, see Figure 7A. Figure 7 View largeDownload slide Additional robustness checks. Notes: This figure shows additional robustness checks on the baseline results. (A) Shows agglomeration by export destination at each distance when the counterfactual controls for four-digit industries vs two-digit industries in the baseline. (B) Extends the distance horizon at which the density and the counterfactual distributions are compared to 200 and 400 km vs 100 km in the baseline. Figure 7 View largeDownload slide Additional robustness checks. Notes: This figure shows additional robustness checks on the baseline results. (A) Shows agglomeration by export destination at each distance when the counterfactual controls for four-digit industries vs two-digit industries in the baseline. (B) Extends the distance horizon at which the density and the counterfactual distributions are compared to 200 and 400 km vs 100 km in the baseline. Finally, we also checked if the agglomeration patterns vary when considering an extended distance horizon over which the distance distribution and the counterfactual are compared. Note that DO focus on 180 km, which corresponds approximately to the median distance of manufacturing plants in the UK, and Ellison et al. (2010) provide results for the USA over thresholds ranging from 100 to 1000 miles. Figure 7B shows that extending the distance horizon to 200 and 400 km from the 100-km baseline deliver similar agglomeration patterns. Note that the value of the K-densities is independent of the distance horizon over which they are evaluated. The slightly lower number of countries exhibiting agglomeration is the result of the higher localization threshold needed to fulfill the criterion that 95% of the counterfactual distributions lie below it across all distances, which leads to wider confidence bands. Also, the country indices of agglomeration have a large correlation with respect to the baseline, of 0.99 and 0.93, respectively. 4. Factors behind agglomeration by destination In this section, we aim at identifying the variables that explain the cross-destination variation in agglomeration levels documented above. The process of selling abroad involves both fixed and variable costs, such as learning about the foreign market, establishing a distribution network, tailoring the products to foreign tastes and regulations, clearing the goods through customs, etc. Therefore, the industry agglomeration sources emphasized by the literature, related to sharing, matching and learning mechanisms (see for instance Duranton and Puga (2004)) may also lead, at least to some extent, to agglomeration by export destination. Indeed, there exist potential gains from pooling the costs of selling abroad and from extracting the information revealed by nearby exporters as shown, for instance, by Segura-Cayuela and Vilarrubia (2008) and Fernandes and Tang (2014). Agglomeration may also be the result of geographical proximity to the importing country, which would lead to export firms being concentrated close to the border. To shed some light on the determinants of agglomeration by export destination, we regress the country index of agglomeration on a set of country characteristics borrowed from the gravity literature, which connects trade flows with size and trade barriers, see Helpman et al. (2008). If agglomeration results in lower transport costs, this literature provides a natural guideline to assess the cross-destination heterogeneity in exporter agglomeration. Then, we include proxies of geographical distance, cultural similarity, transaction costs and institutions among other determinants. To take into account the left-censored nature of the dependent variable, we specify the following Tobit model: Localizationc=β0+β1Spanishc+β2Institutional Qualityc+β3Euroc+β4Contiguityc+β5Log Distance to Capitalc+β6Log Per Capita GDPc+β7Log Number of Exportersc+β8Log Populationc+εc. (1) Our variables capturing trade barriers are the following. Cultural similarity is proxied by a dummy variable taking value one if Spanish is spoken in the destination country, and zero otherwise. The institutional environment in the importing country is captured by the principal factor of the six dimensions comprising the Worldwide Governance Indicators, namely rule of law, political stability, control of corruption, government effectiveness, regulatory quality, and voice and accountability (see Appendix C for details). We also include a dummy taking value one if the euro is the currency of the destination. Finally, we add the log average distance between exporters and the destination’s capital and a dummy taking value one if the destination shares a border with Spain. In a different specification, we include the average distance of exporters to the closest port from which shipments are sent to the country.10 Finally, we add a set of controls including per capita GDP, population, and the log number of firms exporting to the country. The latter depends also on export costs. We include it to facilitate the reading of the results: we compare the extent of exporter agglomeration across destinations reached by the same number of firms, and assess how this varies according to characteristics such as language, institutions and distance.11 Note finally that we rescale the dependent variable by its standard deviation to ease the interpretation of the coefficients. Table 3 shows the results. In column (1) we find that, conditional on the rest of the covariates, exporters to countries with a different language, a different currency and a worse business environment are significantly more geographically agglomerated. The most significant variable is language: if Spanish is spoken in the importing country, agglomeration decreases by 0.89 standard deviations.12 In column (2) we restrict the sample to the destinations not belonging to the European Union, where entry is more difficult and hence the value provided by agglomeration is potentially larger. In this specification language and the institutional environment become more important in explaining the concentration of exporters. Speaking Spanish reduces the extent of agglomeration by 1.3 standard deviations and a one standard deviation increase in the business environment is associated with a 0.66 standard deviations decrease in agglomeration, both results pointing to a positive relationship between agglomeration and the difficulty in conducting businesses abroad.13 Our findings in columns (1) and (2) suggest also that distance plays no role in explaining the concentration of exporters. In column (3) we replace the exporter average distance to the country’s capital with the average distance to the closest port shipping to the country. This measure does not have explanatory power in accounting for exporter concentration either. Table 3 Factors behind exporters’ agglomeration by destination Baseline Non-EU Ports Immigrants Region Exporters’ FE Size (1) (2) (3) (4) (5) (6) Dep. variable: country index of exporters’ localization Spanish −0.8901*** −1.2840*** −1.1375*** −0.9416** −0.9035 −1.2434** (0.3358) (0.3750) (0.3200) (0.3305) (0.8289) (0.4834) Institutional Quality −0.4756* −0.6561** −0.5395** −0.2008 −0.3968* −0.7163** (0.2437) (0.3035) (0.2577) (0.1622) (0.2251) (0.3092) Euro −0.6491** −0.2722 0.3424 −0.9010*** −0.7463* (0.3052) (0.2548) (0.2001) (0.3264) (0.4362) Contiguity 0.7024 −0.7600 0.6388*** 0.6165 1.4376 (1.0417) (0.8099) (0.2175) (0.9288) (1.2682) Log Distance to Capital −0.1684 0.0043 0.2156 −0.2861 −0.2592 (0.1914) (0.2008) (0.1614) (0.3398) (0.2521) Log Distance to Port 0.0833 (0.2651) Log Per Capita GDP 0.2849 0.3498 0.3386* 0.7116*** 0.1605 0.3276 (0.1963) (0.2370) (0.1914) (0.2309) (0.1655) (0.2079) Log Number of Exporters 0.1371 0.2096 0.1474 −0.6587** −0.0083 0.1746 (0.1701) (0.2110) (0.1398) (0.2321) (0.2122) (0.1919) Log Population −0.0148 −0.0060 0.0628 0.2162 0.0268 −0.0476 (0.1111) (0.1360) (0.0941) (0.1322) (0.1419) (0.1334) Dispersion of Immigrants −2.3675*** (0.7900) Region Fixed Effects No No No No Yes No Observations 150 123 141 28 150 150 Pseudo R2 0.04 0.04 0.04 0.62 0.10 0.05 Log Likelihood −201.60 −165.90 −184.60 −8.67 −187.60 −181.40 Baseline Non-EU Ports Immigrants Region Exporters’ FE Size (1) (2) (3) (4) (5) (6) Dep. variable: country index of exporters’ localization Spanish −0.8901*** −1.2840*** −1.1375*** −0.9416** −0.9035 −1.2434** (0.3358) (0.3750) (0.3200) (0.3305) (0.8289) (0.4834) Institutional Quality −0.4756* −0.6561** −0.5395** −0.2008 −0.3968* −0.7163** (0.2437) (0.3035) (0.2577) (0.1622) (0.2251) (0.3092) Euro −0.6491** −0.2722 0.3424 −0.9010*** −0.7463* (0.3052) (0.2548) (0.2001) (0.3264) (0.4362) Contiguity 0.7024 −0.7600 0.6388*** 0.6165 1.4376 (1.0417) (0.8099) (0.2175) (0.9288) (1.2682) Log Distance to Capital −0.1684 0.0043 0.2156 −0.2861 −0.2592 (0.1914) (0.2008) (0.1614) (0.3398) (0.2521) Log Distance to Port 0.0833 (0.2651) Log Per Capita GDP 0.2849 0.3498 0.3386* 0.7116*** 0.1605 0.3276 (0.1963) (0.2370) (0.1914) (0.2309) (0.1655) (0.2079) Log Number of Exporters 0.1371 0.2096 0.1474 −0.6587** −0.0083 0.1746 (0.1701) (0.2110) (0.1398) (0.2321) (0.2122) (0.1919) Log Population −0.0148 −0.0060 0.0628 0.2162 0.0268 −0.0476 (0.1111) (0.1360) (0.0941) (0.1322) (0.1419) (0.1334) Dispersion of Immigrants −2.3675*** (0.7900) Region Fixed Effects No No No No Yes No Observations 150 123 141 28 150 150 Pseudo R2 0.04 0.04 0.04 0.62 0.10 0.05 Log Likelihood −201.60 −165.90 −184.60 −8.67 −187.60 −181.40 Notes: This table shows the regression of the country index of exporters’ localization (i.e. a variable capturing to what extent exporters to each export destination are significantly agglomerated) against measures of export costs, comparative advantage and several covariates. The specification is a tobit model described in Equation (1). Column (1) presents the baseline regression. Column (2) restricts the sample to countries not in the European Union. Column (3) replaces the variable distance with the average distance to the closest port shipping to the country. Column (4) introduces a measure of the concentration of immigrants from each country, proxied as the median distance between them. Column (5) introduces seven region fixed effects: Western Europe, Eastern Europe, Western and Central Asia, South-East Asia, Northern Africa, Central and Southern Africa, Central America and Caribbean, North America, South America, and Oceania. Finally, in column (6) the dependent variable is the country index built from a counterfactual that controls for firm-size bins (Section 3.3.1). Robust standard errors are in parenthesis. Significance levels: *10%; **5%; ***1%. Table 3 Factors behind exporters’ agglomeration by destination Baseline Non-EU Ports Immigrants Region Exporters’ FE Size (1) (2) (3) (4) (5) (6) Dep. variable: country index of exporters’ localization Spanish −0.8901*** −1.2840*** −1.1375*** −0.9416** −0.9035 −1.2434** (0.3358) (0.3750) (0.3200) (0.3305) (0.8289) (0.4834) Institutional Quality −0.4756* −0.6561** −0.5395** −0.2008 −0.3968* −0.7163** (0.2437) (0.3035) (0.2577) (0.1622) (0.2251) (0.3092) Euro −0.6491** −0.2722 0.3424 −0.9010*** −0.7463* (0.3052) (0.2548) (0.2001) (0.3264) (0.4362) Contiguity 0.7024 −0.7600 0.6388*** 0.6165 1.4376 (1.0417) (0.8099) (0.2175) (0.9288) (1.2682) Log Distance to Capital −0.1684 0.0043 0.2156 −0.2861 −0.2592 (0.1914) (0.2008) (0.1614) (0.3398) (0.2521) Log Distance to Port 0.0833 (0.2651) Log Per Capita GDP 0.2849 0.3498 0.3386* 0.7116*** 0.1605 0.3276 (0.1963) (0.2370) (0.1914) (0.2309) (0.1655) (0.2079) Log Number of Exporters 0.1371 0.2096 0.1474 −0.6587** −0.0083 0.1746 (0.1701) (0.2110) (0.1398) (0.2321) (0.2122) (0.1919) Log Population −0.0148 −0.0060 0.0628 0.2162 0.0268 −0.0476 (0.1111) (0.1360) (0.0941) (0.1322) (0.1419) (0.1334) Dispersion of Immigrants −2.3675*** (0.7900) Region Fixed Effects No No No No Yes No Observations 150 123 141 28 150 150 Pseudo R2 0.04 0.04 0.04 0.62 0.10 0.05 Log Likelihood −201.60 −165.90 −184.60 −8.67 −187.60 −181.40 Baseline Non-EU Ports Immigrants Region Exporters’ FE Size (1) (2) (3) (4) (5) (6) Dep. variable: country index of exporters’ localization Spanish −0.8901*** −1.2840*** −1.1375*** −0.9416** −0.9035 −1.2434** (0.3358) (0.3750) (0.3200) (0.3305) (0.8289) (0.4834) Institutional Quality −0.4756* −0.6561** −0.5395** −0.2008 −0.3968* −0.7163** (0.2437) (0.3035) (0.2577) (0.1622) (0.2251) (0.3092) Euro −0.6491** −0.2722 0.3424 −0.9010*** −0.7463* (0.3052) (0.2548) (0.2001) (0.3264) (0.4362) Contiguity 0.7024 −0.7600 0.6388*** 0.6165 1.4376 (1.0417) (0.8099) (0.2175) (0.9288) (1.2682) Log Distance to Capital −0.1684 0.0043 0.2156 −0.2861 −0.2592 (0.1914) (0.2008) (0.1614) (0.3398) (0.2521) Log Distance to Port 0.0833 (0.2651) Log Per Capita GDP 0.2849 0.3498 0.3386* 0.7116*** 0.1605 0.3276 (0.1963) (0.2370) (0.1914) (0.2309) (0.1655) (0.2079) Log Number of Exporters 0.1371 0.2096 0.1474 −0.6587** −0.0083 0.1746 (0.1701) (0.2110) (0.1398) (0.2321) (0.2122) (0.1919) Log Population −0.0148 −0.0060 0.0628 0.2162 0.0268 −0.0476 (0.1111) (0.1360) (0.0941) (0.1322) (0.1419) (0.1334) Dispersion of Immigrants −2.3675*** (0.7900) Region Fixed Effects No No No No Yes No Observations 150 123 141 28 150 150 Pseudo R2 0.04 0.04 0.04 0.62 0.10 0.05 Log Likelihood −201.60 −165.90 −184.60 −8.67 −187.60 −181.40 Notes: This table shows the regression of the country index of exporters’ localization (i.e. a variable capturing to what extent exporters to each export destination are significantly agglomerated) against measures of export costs, comparative advantage and several covariates. The specification is a tobit model described in Equation (1). Column (1) presents the baseline regression. Column (2) restricts the sample to countries not in the European Union. Column (3) replaces the variable distance with the average distance to the closest port shipping to the country. Column (4) introduces a measure of the concentration of immigrants from each country, proxied as the median distance between them. Column (5) introduces seven region fixed effects: Western Europe, Eastern Europe, Western and Central Asia, South-East Asia, Northern Africa, Central and Southern Africa, Central America and Caribbean, North America, South America, and Oceania. Finally, in column (6) the dependent variable is the country index built from a counterfactual that controls for firm-size bins (Section 3.3.1). Robust standard errors are in parenthesis. Significance levels: *10%; **5%; ***1%. In column (4) we quantify the role of immigrants in explaining agglomeration across countries. Specifically, we test whether the local concentration of immigrants can explain some of the patterns that we document. A line of research has shown that immigrants help overcome trade barriers, for example by providing specific knowledge about their home countries. For instance, Herander and Saavedra (2005) find an effect of local immigrant groups on export volumes in the USA. To delve into this issue, we construct an origin-specific index of immigrant dispersion, defined as the median distance between immigrants from each country (a higher distance meaning more dispersion). Our analysis is restricted to the 28 countries for which we have information on the population distribution across municipalities, therefore we raise a flag of caution on interpreting the results. With this caveat in mind, column (4) shows that there is a significant relationship between the dispersion of immigrants and the agglomeration of firms selling to their home countries. Conditional on the rest of controls, a 10% increase in the dispersion of immigrants is associated with a 0.53 standard deviation decrease in the degree of agglomeration. Therefore, agglomeration by destinations whose immigrants exhibit some concentration is found to be higher. Note that this result provides some evidence against export spillovers, since the agglomeration of people from the same country may lead to the agglomeration of exporters to their country of origin, even if no information between exporters is shared.14 In column (5) we add region fixed effects. We include 10 region dummies: Western Europe, Eastern Europe, Western and Central Asia, South-East Asia, Northern Africa, Central and Southern Africa, North America, Central America and Caribbean, South America and Oceania. We find that the coefficient associated with language barely changes with respect to the baseline, although it is imprecisely estimated, whereas that of institutional quality is somewhat lower, though it is still statistically significant. Interestingly, controlling for regions increases the estimated effect of the currency: belonging to the euro area reduces the extent of agglomeration by 0.90 standard deviations. These results suggest that the mechanisms connecting agglomeration with trade barriers hold also within broad geographic and economic areas. Finally, column (6) replaces the baseline country index of agglomeration with that obtained from the counterfactual that accounts for 20 bins of exporter size, see Section 3.3.1. This is a pertinent analysis because restricting the counterfactual in some cases reduced the number of significantly agglomerated destinations. However, given the high correlation between the country indices of agglomeration, the results tend to confirm the baseline findings. In fact, the point estimates are even larger in absolute value regarding language, institutional quality and currency. Adding the other country indices constructed in Section 3.3 confirms the baseline estimates. Overall, the previous results suggest that there exists a relationship between trade barriers to enter a country and the degree of spatial agglomeration of exporters selling to it. One limitation of this approach is that the precise mechanism driving these patterns cannot be uncovered, and we cannot rule out that other omitted factors may contaminate this relationship, hence we do not pursue causality. However, they show an insightful correlation between proxies of export costs and the extent of geographical concentration that is systematic and robust. Moreover, the results suggest that agglomeration can be more effective concerning those destinations from which information is more valuable and, in this regard, they inform the theoretical and empirical literature on export spillovers and learning from neighboring firms cited in the introduction. 5. Concluding remarks In this article, we document the existence of agglomeration economies that accrue to firms selling to certain foreign markets. In the pursuit of shedding light on the interpretation of our results, we show that these patterns of geographical concentration are not driven by the spatial location of large vs small exporters, hierarchical exporting or exporters located in large cities. Moreover, we find that these location patterns are quite stable over time. Regarding the determinants of agglomeration, we show that the cross-destination variability in agglomeration levels can be partly explained by language, currency and institutional quality, being agglomeration higher the larger export costs are. These findings are consistent with the existence of externalities in selling to certain foreign countries, having implications for international trade. For example, agglomeration might reduce destination-specific fixed costs, which would rationalize why firms do not follow a strict hierarchy of export destinations, a fact uncovered by Eaton et al. (2011). Also, some policy implications can be derived. The pattern of concentration by export destination suggests that easing the flow of information from exporters to potential entrants can pay off. Moreover, the fact that concentration is higher concerning more difficult destinations suggests that the benefits of these policies can be specially helpful in countries where entry is more difficult. Also, helping companies penetrate new markets can lead nearby firms to follow them. Interestingly, given how we defined the counterfactual, these benefits are not restricted to firms of the same industry, rather they can extend to firms belonging to different industries. The nature of our data prevents us from digging deeper into the specific channels through which agglomeration economies might work. More detailed data would allow to disentangling some sources of export spillovers, such as those related to information (via headquarters) from those linked to costs (via establishments). Also, a larger time span and more categories of goods would allow a geographical analysis of new products exported and new markets accessed. In general, we think that there is room in the literature to test empirically which are the most important channels through which agglomeration economies in international trade operate. Case studies or natural experiments seem a suitable framework to disentangle specific mechanisms playing a role in generating export spillovers. We see this avenue of further research as promising. Footnotes 1 The existing literature on export spillovers studies the agglomeration of exporters in the same administrative unit or economic area. This entails the so-called ‘border effect’ problem, which involves several issues. First, it amounts to treat symmetrically plants not belonging to the same spatial unit, regardless of the distance that separates them. Second, it involves the arbitrary decision of which spatial unit to take. This is relevant, as different levels of aggregation can lead to very different results. Furthermore, it has been showed that bigger units produce more pronounced correlations. This is called the Modifiable Areal Unit Problem (MAUP), see Openshaw and Taylor (1979) and Openshaw (1984). And third, the previous problem and the fact that spatial units are not often defined on the basis of economic significance make the comparison of results across spatial units difficult to interpret. 2 Although localization can be defined as agglomeration controlling for that of general manufacturing, as in Duranton and Overman (2005), in this article we use the words agglomeration, localization and concentration interchangeably, as the indices explicitly control for the overall concentration of exporters and do not lead to confusion. 3 On the mechanisms driving industry agglomeration, see Klepper (2010), who analyzes the historical clustering of firms in Detroit and Silicon Valley, and Ellison et al. (2010), who test the Marshall (1920) theories of industry agglomeration using coagglomeration patterns. 4 The dataset extends to 2013, but the export threshold was increased in 2008 to €50,000. For this reason and to avoid the results being contaminated from the crisis, we use data up to 2007. 5 This estimation is as follows. According to the 2009 Spanish Survey on Business Strategies, 93.1% of firms with less than 200 employees and 62.5% of firms with more than 200 employees have only one plant. In our data 94.5% of exporters have less than 200 employees (vs 99.1% of all firms), then we estimate that the percentage of single-plant exporters is approximately 91.4%. 6 In DO the localization and dispersion thresholds are referred to as global confidence bands. Note that they allow making statements about the overall agglomeration patterns, since they are neutral with respect to distances (at a given distance horizon). DO report local confidence intervals too, constructed as the 5-th and 95-th percentiles of the ranked counterfactual distributions at each kilometer. These intervals only allow local statements to be made, i.e. deviations from randomness at a given distance. Note that the percentiles associated with the localization thresholds are above the 95-th percentile, since the ranking of the counterfactual distributions varies across distances. At the baseline distance horizon of 100 km, they range (across countries) between the 96.4-th and the 99.5-th. 7 Each size bin contains the same number of exporters. The median amount of total exports is given by €0.25 million and the percentile 75 by €1.4 million. 8 The distribution of exporters across the five resulting bins is: 30%, 32%, 15%, 11% and 13%. 9 Note that to keep a meaningful scale this figure excludes two destinations with highly localized exporters in both the baseline and the continuous exporters sample. 10 We do not include it in the baseline because we lack data on exports from Spanish ports to 13 countries and the distance variables are never significant. Also, including the simple distance between the most populated cities yields very similar results. 11 Moreover, Helpman et al. (2008) shows the importance of accounting for the extensive margin of trade in the gravity equation framework. We also checked that excluding this variable does not affect the overall results. 12 Note that our baseline regression is performed on 150 countries because we lack data on 16 small countries. GDP data are missing in 14 countries and institutional quality in 6 observations. 13 We also inspected the role of some specific elements of the institutional environment by replacing the institutional factor in column (1) by each Governance Indicator (one by one). We found that a better rule of law, less corruption and more political stability are significantly associated with lower agglomeration, whereas the rest yielded nonsignificant associations. Moreover, we also found that specific measures of investor protection, such as the number of procedures required to enforce a contract, are also negatively and significantly associated with agglomeration. We also tried another proxies of import costs such as the number of days and the number of documents required to import goods, but found that the estimates were not statistically significant. 14 Note also that the coefficients of some variables change substantially with respect to the baseline (column 1). We found that they can be mainly explained by a composition effect, since repeating the baseline regression with the 28 countries did not yield large changes in the covariate estimates with respect to those obtained in column (4). 15 Given that our aim is to uncover agglomeration of export firms, we treat each firm as one observation and therefore we do not weigh the distances when estimating the distribution. An alternative would be consider the agglomeration of export values and hence weigh distances by exports to the country. There are three reasons that advise us against this strategy. First, the construction of the counterfactual involves firms that do not export to the country, hence they lack a weight. Second, if total firm exports were used as weights, we would disregard the specialization of firms to certain markets, given that weights would not have variation across export destinations. And third, total exports is a highly skewed variable, hence a few firms could distort the results. Acknowledgements This article was previously circulated under the title ‘Agglomeration Matters for Trade’. We are very grateful to Guillermo Caruana, Rosario Crinó and Claudio Michelacci for their constant guidance and help. We are also thankful to César Alonso, Pol Antràs, Manuel Arellano, Stéphane Bonhomme, David Dorn, Gino Gancia, Manuel García-Santana, Horacio Larreguy, Carlos Llano, Marc Melitz, Guy Michaels, Hannes Mueller, Diego Puga, Rafael Repullo, Rubén Segura-Cayuela, Andrei Shleifer, the editor, at least two anonymous referees, and seminar participants at CEMFI, European Winter Meeting of the Econometric Society (Konstanz), SAEe Vigo, IMT Lucca, Universität Mannheim, IAE, CESifo, 2013 Annual Meeting of the Society for Economic Dynamics (Seoul), 67th European Meeting of the Econometric Society (Gothenburg), 2013 Barcelona Workshop on Regional and Urban Economics, Banco de España, Universidad de Murcia, XVII Conference on International Economics (A Coruña), and Universidad Autónoma de Madrid for comments and useful discussions. We are also grateful to Patry Tello for providing us the exporter dataset. 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Control of Corruption Kaufmann et al. (2009) Extent to which public power is exercised for private gain, including corruption, as well as ‘capture’ of the state by elites and private interests. Regulatory Quality Kaufmann et al. (2009) Ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development. Political Stability Kaufmann et al. (2009) Likelihood that the government will be destabilized or overthrown by unconstitutional or violent means. Government Effectiveness Kaufmann et al. (2009) Quality of public services, the civil service, policy formulation and implementation, and credibility of the government’s commitment to such policies. Voice and Accountability Kaufmann et al. (2009) Extent to which a country’s citizens are able to participate in selecting their government, as well as freedom of expression, freedom of association and a free media. Euro 1 if the country’s currency is the euro. Contiguity Mayer and Zignago (2011) 1 for contiguity with respect to Spain. Distance to Country’s Capital Average distance of exporters to the country’s capital. Distance to Ports Puertos del Estado Distance between zip code and closest port from which shipments are sent to the country. We assume that from the three main Portuguese ports (Aveiro, Leixoes and Lisbon), all countries are reached. Per capita GDP World Bank Log Real per Capita GDP in constant 2000 US dollars. Population World Bank Country’s population. Location of Immigrants Instituto Nacional de Estadística Number of immigrants in each municipality by country of origin. European Union 1 if the country belongs to the European Union. Doing Business Index World Bank Ranking of economies that assess business regulations and their enforcement. Contract Enforcement World Bank Number of procedures required to enforce a contract. Time to Import World Bank Number of calendar days necessary to comply with all the procedures required to import goods. Variables Source Definition Zip code coordinates Geonames Distance between zip codes Apply haversine formula to the zip code coordinates. Spanish Mayer and Zignago (2011) 1 if a Spanish is spoken by at least 9% of the population. Rule of Law Kaufmann et al. (2009) Quality of contract enforcement, property rights, the police, the courts, and likelihood of crime and violence. Control of Corruption Kaufmann et al. (2009) Extent to which public power is exercised for private gain, including corruption, as well as ‘capture’ of the state by elites and private interests. Regulatory Quality Kaufmann et al. (2009) Ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development. Political Stability Kaufmann et al. (2009) Likelihood that the government will be destabilized or overthrown by unconstitutional or violent means. Government Effectiveness Kaufmann et al. (2009) Quality of public services, the civil service, policy formulation and implementation, and credibility of the government’s commitment to such policies. Voice and Accountability Kaufmann et al. (2009) Extent to which a country’s citizens are able to participate in selecting their government, as well as freedom of expression, freedom of association and a free media. Euro 1 if the country’s currency is the euro. Contiguity Mayer and Zignago (2011) 1 for contiguity with respect to Spain. Distance to Country’s Capital Average distance of exporters to the country’s capital. Distance to Ports Puertos del Estado Distance between zip code and closest port from which shipments are sent to the country. We assume that from the three main Portuguese ports (Aveiro, Leixoes and Lisbon), all countries are reached. Per capita GDP World Bank Log Real per Capita GDP in constant 2000 US dollars. Population World Bank Country’s population. Location of Immigrants Instituto Nacional de Estadística Number of immigrants in each municipality by country of origin. European Union 1 if the country belongs to the European Union. Doing Business Index World Bank Ranking of economies that assess business regulations and their enforcement. Contract Enforcement World Bank Number of procedures required to enforce a contract. Time to Import World Bank Number of calendar days necessary to comply with all the procedures required to import goods. Notes: This table shows the definitions and sources of the main variables used throughout the article. Table A1 Data definitions and sources Variables Source Definition Zip code coordinates Geonames Distance between zip codes Apply haversine formula to the zip code coordinates. Spanish Mayer and Zignago (2011) 1 if a Spanish is spoken by at least 9% of the population. Rule of Law Kaufmann et al. (2009) Quality of contract enforcement, property rights, the police, the courts, and likelihood of crime and violence. Control of Corruption Kaufmann et al. (2009) Extent to which public power is exercised for private gain, including corruption, as well as ‘capture’ of the state by elites and private interests. Regulatory Quality Kaufmann et al. (2009) Ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development. Political Stability Kaufmann et al. (2009) Likelihood that the government will be destabilized or overthrown by unconstitutional or violent means. Government Effectiveness Kaufmann et al. (2009) Quality of public services, the civil service, policy formulation and implementation, and credibility of the government’s commitment to such policies. Voice and Accountability Kaufmann et al. (2009) Extent to which a country’s citizens are able to participate in selecting their government, as well as freedom of expression, freedom of association and a free media. Euro 1 if the country’s currency is the euro. Contiguity Mayer and Zignago (2011) 1 for contiguity with respect to Spain. Distance to Country’s Capital Average distance of exporters to the country’s capital. Distance to Ports Puertos del Estado Distance between zip code and closest port from which shipments are sent to the country. We assume that from the three main Portuguese ports (Aveiro, Leixoes and Lisbon), all countries are reached. Per capita GDP World Bank Log Real per Capita GDP in constant 2000 US dollars. Population World Bank Country’s population. Location of Immigrants Instituto Nacional de Estadística Number of immigrants in each municipality by country of origin. European Union 1 if the country belongs to the European Union. Doing Business Index World Bank Ranking of economies that assess business regulations and their enforcement. Contract Enforcement World Bank Number of procedures required to enforce a contract. Time to Import World Bank Number of calendar days necessary to comply with all the procedures required to import goods. Variables Source Definition Zip code coordinates Geonames Distance between zip codes Apply haversine formula to the zip code coordinates. Spanish Mayer and Zignago (2011) 1 if a Spanish is spoken by at least 9% of the population. Rule of Law Kaufmann et al. (2009) Quality of contract enforcement, property rights, the police, the courts, and likelihood of crime and violence. Control of Corruption Kaufmann et al. (2009) Extent to which public power is exercised for private gain, including corruption, as well as ‘capture’ of the state by elites and private interests. Regulatory Quality Kaufmann et al. (2009) Ability of the government to formulate and implement sound policies and regulations that permit and promote private sector development. Political Stability Kaufmann et al. (2009) Likelihood that the government will be destabilized or overthrown by unconstitutional or violent means. Government Effectiveness Kaufmann et al. (2009) Quality of public services, the civil service, policy formulation and implementation, and credibility of the government’s commitment to such policies. Voice and Accountability Kaufmann et al. (2009) Extent to which a country’s citizens are able to participate in selecting their government, as well as freedom of expression, freedom of association and a free media. Euro 1 if the country’s currency is the euro. Contiguity Mayer and Zignago (2011) 1 for contiguity with respect to Spain. Distance to Country’s Capital Average distance of exporters to the country’s capital. Distance to Ports Puertos del Estado Distance between zip code and closest port from which shipments are sent to the country. We assume that from the three main Portuguese ports (Aveiro, Leixoes and Lisbon), all countries are reached. Per capita GDP World Bank Log Real per Capita GDP in constant 2000 US dollars. Population World Bank Country’s population. Location of Immigrants Instituto Nacional de Estadística Number of immigrants in each municipality by country of origin. European Union 1 if the country belongs to the European Union. Doing Business Index World Bank Ranking of economies that assess business regulations and their enforcement. Contract Enforcement World Bank Number of procedures required to enforce a contract. Time to Import World Bank Number of calendar days necessary to comply with all the procedures required to import goods. Notes: This table shows the definitions and sources of the main variables used throughout the article. Table A2 List of destinations Country N Localization Country N Localization Country N Localization Afghanistan 13 0.0000 Gambia 20 0.0000 The Netherlands 3010 0.0190 Albania 168 0.1108 Georgia 101 0.0025 New Caledonia 34 0.0000 Algeria 826 0.0027 Germany 6427 0.0174 New Zealand 278 0.0036 Andorra 887 0.0903 Ghana 72 0.0000 Nicaragua 63 0.0000 Angola 89 0.0000 Gibraltar 90 0.0000 Niger 44 0.0000 Antigua and Barbuda 20 0.0000 Greece 1768 0.0178 Nigeria 99 0.0560 Argentina 818 0.0100 Guam 10 0.0000 Norway 733 0.0004 Armenia 53 0.0794 Guatemala 226 0.0000 Oman 103 0.0017 Aruba 19 0.0876 Guinea 19 0.0000 Pakistan 189 0.0407 Australia 795 0.0128 Haiti 13 0.0000 Panama 492 0.0000 Austria 1620 0.0148 Honduras 107 0.0000 Paraguay 67 0.0193 Azerbaijan 28 0.0024 Hong Kong SAR, China 708 0.0315 Peru 435 0.0001 Bahamas, The 48 0.0000 Hungary 778 0.0276 Philippines 191 0.0096 Bahrain 154 0.0329 Iceland 160 0.0001 Poland 1627 0.0182 Bangladesh 67 0.0285 India 643 0.0232 Portugal 6861 0.0000 Barbados 32 0.0000 Indonesia 228 0.0136 Qatar 212 0.0445 Belarus 89 0.0000 Iran, Islamic Rep. 463 0.0109 Romania 902 0.0205 Belgium 3500 0.0217 Iraq 23 0.1835 Russian Federation 915 0.0189 Belize 79 0.0089 Ireland 1308 0.0000 San Marino 19 0.0000 Benin 26 0.0000 Israel 732 0.0307 Saudi Arabia 854 0.0134 Bermuda 16 0.0000 Italy 5166 0.0116 Senegal 86 0.0000 Bolivia 96 0.0000 Jamaica 48 0.0085 Serbia 178 0.0185 Bosnia and Herzegovina 103 0.0422 Japan 829 0.0222 Seychelles 31 0.0000 Brazil 1048 0.0269 Jordan 358 0.0154 Sierra Leone 15 0.0313 British Virgin Islands 124 0.0087 Kazakhstan 102 0.0000 Singapore 429 0.0335 Bulgaria 511 0.0151 Kenya 81 0.0000 Slovak Republic 447 0.0099 Burkina Faso 30 0.0000 Korea, Dem. People’s Rep. 38 0.0000 Slovenia 412 0.0224 Cabo Verde 22 0.0000 Korea, Rep. 561 0.0271 Solomon Islands 11 0.0000 Cameroon 47 0.0000 Kuwait 335 0.0331 South Africa 729 0.0262 Canada 848 0.0057 Kyrgyz Republic 188 0.0114 Sri Lanka 50 0.0000 Cayman Islands 20 0.0000 Latvia 679 0.0255 Sudan 43 0.0163 Chad 18 0.1599 Lebanon 494 0.0139 Suriname 18 0.1829 Chile 872 0.0001 Libya 152 0.0127 Swaziland 21 0.0359 China 1007 0.0102 Liechtenstein 56 0.0159 Sweden 1264 0.0051 Colombia 642 0.0117 Lithuania 642 0.0137 Switzerland 2095 0.0112 Congo, Dem. Rep. 19 0.0000 Luxembourg 282 0.0080 Syrian Arab Republic 166 0.0339 Congo, Rep. 15 0.0000 Macao SAR, China 34 0.0010 Taiwan, China 458 0.0229 Costa Rica 274 0.0000 Macedonia, FYR 66 0.0732 Tanzania 42 0.0844 Croatia 328 0.0147 Madagascar 23 0.0000 Thailand 343 0.0204 Cuba 314 0.0000 Malaysia 281 0.0026 Togo 17 0.0000 Cyprus 708 0.0236 Mali 22 0.0000 Trinidad and Tobago 97 0.0000 Czech Republic 1080 0.0245 Malta 247 0.0121 Tunisia 743 0.0061 Côte d’Ivoire 76 0.0009 Marshall Islands 10 0.0011 Turkey 1385 0.0367 Denmark 1286 0.0184 Mauritania 56 0.0000 Uganda 13 0.0000 Dominica 80 0.0000 Mauritius 65 0.0000 Ukraine 311 0.0052 Dominican Republic 456 0.0000 Mexico 1964 0.0051 United Arab Emirates 962 0.0086 Ecuador 337 0.0008 Micronesia, Fed. Sts. 30 0.0487 United Kingdom 5521 0.0120 Egypt, Arab Rep. 588 0.0254 Moldova 45 0.0000 United States 3882 0.0106 El Salvador 128 0.0000 Monaco 99 0.0348 Uruguay 247 0.0091 Equatorial Guinea 60 0.0000 Montenegro 61 0.0958 Uzbekistan 10 0.0000 Estonia 380 0.0254 Morocco 1703 0.0000 Venezuela, RB 675 0.0056 Ethiopia 28 0.0000 Mozambique 19 0.0000 Vietnam 128 0.0005 Finland 897 0.0029 Namibia 38 0.0154 Virgin Islands (U.S.) 22 0.0068 France 8946 0.0250 Nauru 15 0.0000 West Bank and Gaza 36 0.2886 French Polynesia 20 0.0000 Nepal 12 0.0000 Yemen, Rep. 86 0.0313 Gabon 41 0.0000 Country N Localization Country N Localization Country N Localization Afghanistan 13 0.0000 Gambia 20 0.0000 The Netherlands 3010 0.0190 Albania 168 0.1108 Georgia 101 0.0025 New Caledonia 34 0.0000 Algeria 826 0.0027 Germany 6427 0.0174 New Zealand 278 0.0036 Andorra 887 0.0903 Ghana 72 0.0000 Nicaragua 63 0.0000 Angola 89 0.0000 Gibraltar 90 0.0000 Niger 44 0.0000 Antigua and Barbuda 20 0.0000 Greece 1768 0.0178 Nigeria 99 0.0560 Argentina 818 0.0100 Guam 10 0.0000 Norway 733 0.0004 Armenia 53 0.0794 Guatemala 226 0.0000 Oman 103 0.0017 Aruba 19 0.0876 Guinea 19 0.0000 Pakistan 189 0.0407 Australia 795 0.0128 Haiti 13 0.0000 Panama 492 0.0000 Austria 1620 0.0148 Honduras 107 0.0000 Paraguay 67 0.0193 Azerbaijan 28 0.0024 Hong Kong SAR, China 708 0.0315 Peru 435 0.0001 Bahamas, The 48 0.0000 Hungary 778 0.0276 Philippines 191 0.0096 Bahrain 154 0.0329 Iceland 160 0.0001 Poland 1627 0.0182 Bangladesh 67 0.0285 India 643 0.0232 Portugal 6861 0.0000 Barbados 32 0.0000 Indonesia 228 0.0136 Qatar 212 0.0445 Belarus 89 0.0000 Iran, Islamic Rep. 463 0.0109 Romania 902 0.0205 Belgium 3500 0.0217 Iraq 23 0.1835 Russian Federation 915 0.0189 Belize 79 0.0089 Ireland 1308 0.0000 San Marino 19 0.0000 Benin 26 0.0000 Israel 732 0.0307 Saudi Arabia 854 0.0134 Bermuda 16 0.0000 Italy 5166 0.0116 Senegal 86 0.0000 Bolivia 96 0.0000 Jamaica 48 0.0085 Serbia 178 0.0185 Bosnia and Herzegovina 103 0.0422 Japan 829 0.0222 Seychelles 31 0.0000 Brazil 1048 0.0269 Jordan 358 0.0154 Sierra Leone 15 0.0313 British Virgin Islands 124 0.0087 Kazakhstan 102 0.0000 Singapore 429 0.0335 Bulgaria 511 0.0151 Kenya 81 0.0000 Slovak Republic 447 0.0099 Burkina Faso 30 0.0000 Korea, Dem. People’s Rep. 38 0.0000 Slovenia 412 0.0224 Cabo Verde 22 0.0000 Korea, Rep. 561 0.0271 Solomon Islands 11 0.0000 Cameroon 47 0.0000 Kuwait 335 0.0331 South Africa 729 0.0262 Canada 848 0.0057 Kyrgyz Republic 188 0.0114 Sri Lanka 50 0.0000 Cayman Islands 20 0.0000 Latvia 679 0.0255 Sudan 43 0.0163 Chad 18 0.1599 Lebanon 494 0.0139 Suriname 18 0.1829 Chile 872 0.0001 Libya 152 0.0127 Swaziland 21 0.0359 China 1007 0.0102 Liechtenstein 56 0.0159 Sweden 1264 0.0051 Colombia 642 0.0117 Lithuania 642 0.0137 Switzerland 2095 0.0112 Congo, Dem. Rep. 19 0.0000 Luxembourg 282 0.0080 Syrian Arab Republic 166 0.0339 Congo, Rep. 15 0.0000 Macao SAR, China 34 0.0010 Taiwan, China 458 0.0229 Costa Rica 274 0.0000 Macedonia, FYR 66 0.0732 Tanzania 42 0.0844 Croatia 328 0.0147 Madagascar 23 0.0000 Thailand 343 0.0204 Cuba 314 0.0000 Malaysia 281 0.0026 Togo 17 0.0000 Cyprus 708 0.0236 Mali 22 0.0000 Trinidad and Tobago 97 0.0000 Czech Republic 1080 0.0245 Malta 247 0.0121 Tunisia 743 0.0061 Côte d’Ivoire 76 0.0009 Marshall Islands 10 0.0011 Turkey 1385 0.0367 Denmark 1286 0.0184 Mauritania 56 0.0000 Uganda 13 0.0000 Dominica 80 0.0000 Mauritius 65 0.0000 Ukraine 311 0.0052 Dominican Republic 456 0.0000 Mexico 1964 0.0051 United Arab Emirates 962 0.0086 Ecuador 337 0.0008 Micronesia, Fed. Sts. 30 0.0487 United Kingdom 5521 0.0120 Egypt, Arab Rep. 588 0.0254 Moldova 45 0.0000 United States 3882 0.0106 El Salvador 128 0.0000 Monaco 99 0.0348 Uruguay 247 0.0091 Equatorial Guinea 60 0.0000 Montenegro 61 0.0958 Uzbekistan 10 0.0000 Estonia 380 0.0254 Morocco 1703 0.0000 Venezuela, RB 675 0.0056 Ethiopia 28 0.0000 Mozambique 19 0.0000 Vietnam 128 0.0005 Finland 897 0.0029 Namibia 38 0.0154 Virgin Islands (U.S.) 22 0.0068 France 8946 0.0250 Nauru 15 0.0000 West Bank and Gaza 36 0.2886 French Polynesia 20 0.0000 Nepal 12 0.0000 Yemen, Rep. 86 0.0313 Gabon 41 0.0000 Notes: N denotes the number of exporters and Localization is the country index of localization, which measures the amount of geographical concentration exhibiting exporters to each destination. Table A2 List of destinations Country N Localization Country N Localization Country N Localization Afghanistan 13 0.0000 Gambia 20 0.0000 The Netherlands 3010 0.0190 Albania 168 0.1108 Georgia 101 0.0025 New Caledonia 34 0.0000 Algeria 826 0.0027 Germany 6427 0.0174 New Zealand 278 0.0036 Andorra 887 0.0903 Ghana 72 0.0000 Nicaragua 63 0.0000 Angola 89 0.0000 Gibraltar 90 0.0000 Niger 44 0.0000 Antigua and Barbuda 20 0.0000 Greece 1768 0.0178 Nigeria 99 0.0560 Argentina 818 0.0100 Guam 10 0.0000 Norway 733 0.0004 Armenia 53 0.0794 Guatemala 226 0.0000 Oman 103 0.0017 Aruba 19 0.0876 Guinea 19 0.0000 Pakistan 189 0.0407 Australia 795 0.0128 Haiti 13 0.0000 Panama 492 0.0000 Austria 1620 0.0148 Honduras 107 0.0000 Paraguay 67 0.0193 Azerbaijan 28 0.0024 Hong Kong SAR, China 708 0.0315 Peru 435 0.0001 Bahamas, The 48 0.0000 Hungary 778 0.0276 Philippines 191 0.0096 Bahrain 154 0.0329 Iceland 160 0.0001 Poland 1627 0.0182 Bangladesh 67 0.0285 India 643 0.0232 Portugal 6861 0.0000 Barbados 32 0.0000 Indonesia 228 0.0136 Qatar 212 0.0445 Belarus 89 0.0000 Iran, Islamic Rep. 463 0.0109 Romania 902 0.0205 Belgium 3500 0.0217 Iraq 23 0.1835 Russian Federation 915 0.0189 Belize 79 0.0089 Ireland 1308 0.0000 San Marino 19 0.0000 Benin 26 0.0000 Israel 732 0.0307 Saudi Arabia 854 0.0134 Bermuda 16 0.0000 Italy 5166 0.0116 Senegal 86 0.0000 Bolivia 96 0.0000 Jamaica 48 0.0085 Serbia 178 0.0185 Bosnia and Herzegovina 103 0.0422 Japan 829 0.0222 Seychelles 31 0.0000 Brazil 1048 0.0269 Jordan 358 0.0154 Sierra Leone 15 0.0313 British Virgin Islands 124 0.0087 Kazakhstan 102 0.0000 Singapore 429 0.0335 Bulgaria 511 0.0151 Kenya 81 0.0000 Slovak Republic 447 0.0099 Burkina Faso 30 0.0000 Korea, Dem. People’s Rep. 38 0.0000 Slovenia 412 0.0224 Cabo Verde 22 0.0000 Korea, Rep. 561 0.0271 Solomon Islands 11 0.0000 Cameroon 47 0.0000 Kuwait 335 0.0331 South Africa 729 0.0262 Canada 848 0.0057 Kyrgyz Republic 188 0.0114 Sri Lanka 50 0.0000 Cayman Islands 20 0.0000 Latvia 679 0.0255 Sudan 43 0.0163 Chad 18 0.1599 Lebanon 494 0.0139 Suriname 18 0.1829 Chile 872 0.0001 Libya 152 0.0127 Swaziland 21 0.0359 China 1007 0.0102 Liechtenstein 56 0.0159 Sweden 1264 0.0051 Colombia 642 0.0117 Lithuania 642 0.0137 Switzerland 2095 0.0112 Congo, Dem. Rep. 19 0.0000 Luxembourg 282 0.0080 Syrian Arab Republic 166 0.0339 Congo, Rep. 15 0.0000 Macao SAR, China 34 0.0010 Taiwan, China 458 0.0229 Costa Rica 274 0.0000 Macedonia, FYR 66 0.0732 Tanzania 42 0.0844 Croatia 328 0.0147 Madagascar 23 0.0000 Thailand 343 0.0204 Cuba 314 0.0000 Malaysia 281 0.0026 Togo 17 0.0000 Cyprus 708 0.0236 Mali 22 0.0000 Trinidad and Tobago 97 0.0000 Czech Republic 1080 0.0245 Malta 247 0.0121 Tunisia 743 0.0061 Côte d’Ivoire 76 0.0009 Marshall Islands 10 0.0011 Turkey 1385 0.0367 Denmark 1286 0.0184 Mauritania 56 0.0000 Uganda 13 0.0000 Dominica 80 0.0000 Mauritius 65 0.0000 Ukraine 311 0.0052 Dominican Republic 456 0.0000 Mexico 1964 0.0051 United Arab Emirates 962 0.0086 Ecuador 337 0.0008 Micronesia, Fed. Sts. 30 0.0487 United Kingdom 5521 0.0120 Egypt, Arab Rep. 588 0.0254 Moldova 45 0.0000 United States 3882 0.0106 El Salvador 128 0.0000 Monaco 99 0.0348 Uruguay 247 0.0091 Equatorial Guinea 60 0.0000 Montenegro 61 0.0958 Uzbekistan 10 0.0000 Estonia 380 0.0254 Morocco 1703 0.0000 Venezuela, RB 675 0.0056 Ethiopia 28 0.0000 Mozambique 19 0.0000 Vietnam 128 0.0005 Finland 897 0.0029 Namibia 38 0.0154 Virgin Islands (U.S.) 22 0.0068 France 8946 0.0250 Nauru 15 0.0000 West Bank and Gaza 36 0.2886 French Polynesia 20 0.0000 Nepal 12 0.0000 Yemen, Rep. 86 0.0313 Gabon 41 0.0000 Country N Localization Country N Localization Country N Localization Afghanistan 13 0.0000 Gambia 20 0.0000 The Netherlands 3010 0.0190 Albania 168 0.1108 Georgia 101 0.0025 New Caledonia 34 0.0000 Algeria 826 0.0027 Germany 6427 0.0174 New Zealand 278 0.0036 Andorra 887 0.0903 Ghana 72 0.0000 Nicaragua 63 0.0000 Angola 89 0.0000 Gibraltar 90 0.0000 Niger 44 0.0000 Antigua and Barbuda 20 0.0000 Greece 1768 0.0178 Nigeria 99 0.0560 Argentina 818 0.0100 Guam 10 0.0000 Norway 733 0.0004 Armenia 53 0.0794 Guatemala 226 0.0000 Oman 103 0.0017 Aruba 19 0.0876 Guinea 19 0.0000 Pakistan 189 0.0407 Australia 795 0.0128 Haiti 13 0.0000 Panama 492 0.0000 Austria 1620 0.0148 Honduras 107 0.0000 Paraguay 67 0.0193 Azerbaijan 28 0.0024 Hong Kong SAR, China 708 0.0315 Peru 435 0.0001 Bahamas, The 48 0.0000 Hungary 778 0.0276 Philippines 191 0.0096 Bahrain 154 0.0329 Iceland 160 0.0001 Poland 1627 0.0182 Bangladesh 67 0.0285 India 643 0.0232 Portugal 6861 0.0000 Barbados 32 0.0000 Indonesia 228 0.0136 Qatar 212 0.0445 Belarus 89 0.0000 Iran, Islamic Rep. 463 0.0109 Romania 902 0.0205 Belgium 3500 0.0217 Iraq 23 0.1835 Russian Federation 915 0.0189 Belize 79 0.0089 Ireland 1308 0.0000 San Marino 19 0.0000 Benin 26 0.0000 Israel 732 0.0307 Saudi Arabia 854 0.0134 Bermuda 16 0.0000 Italy 5166 0.0116 Senegal 86 0.0000 Bolivia 96 0.0000 Jamaica 48 0.0085 Serbia 178 0.0185 Bosnia and Herzegovina 103 0.0422 Japan 829 0.0222 Seychelles 31 0.0000 Brazil 1048 0.0269 Jordan 358 0.0154 Sierra Leone 15 0.0313 British Virgin Islands 124 0.0087 Kazakhstan 102 0.0000 Singapore 429 0.0335 Bulgaria 511 0.0151 Kenya 81 0.0000 Slovak Republic 447 0.0099 Burkina Faso 30 0.0000 Korea, Dem. People’s Rep. 38 0.0000 Slovenia 412 0.0224 Cabo Verde 22 0.0000 Korea, Rep. 561 0.0271 Solomon Islands 11 0.0000 Cameroon 47 0.0000 Kuwait 335 0.0331 South Africa 729 0.0262 Canada 848 0.0057 Kyrgyz Republic 188 0.0114 Sri Lanka 50 0.0000 Cayman Islands 20 0.0000 Latvia 679 0.0255 Sudan 43 0.0163 Chad 18 0.1599 Lebanon 494 0.0139 Suriname 18 0.1829 Chile 872 0.0001 Libya 152 0.0127 Swaziland 21 0.0359 China 1007 0.0102 Liechtenstein 56 0.0159 Sweden 1264 0.0051 Colombia 642 0.0117 Lithuania 642 0.0137 Switzerland 2095 0.0112 Congo, Dem. Rep. 19 0.0000 Luxembourg 282 0.0080 Syrian Arab Republic 166 0.0339 Congo, Rep. 15 0.0000 Macao SAR, China 34 0.0010 Taiwan, China 458 0.0229 Costa Rica 274 0.0000 Macedonia, FYR 66 0.0732 Tanzania 42 0.0844 Croatia 328 0.0147 Madagascar 23 0.0000 Thailand 343 0.0204 Cuba 314 0.0000 Malaysia 281 0.0026 Togo 17 0.0000 Cyprus 708 0.0236 Mali 22 0.0000 Trinidad and Tobago 97 0.0000 Czech Republic 1080 0.0245 Malta 247 0.0121 Tunisia 743 0.0061 Côte d’Ivoire 76 0.0009 Marshall Islands 10 0.0011 Turkey 1385 0.0367 Denmark 1286 0.0184 Mauritania 56 0.0000 Uganda 13 0.0000 Dominica 80 0.0000 Mauritius 65 0.0000 Ukraine 311 0.0052 Dominican Republic 456 0.0000 Mexico 1964 0.0051 United Arab Emirates 962 0.0086 Ecuador 337 0.0008 Micronesia, Fed. Sts. 30 0.0487 United Kingdom 5521 0.0120 Egypt, Arab Rep. 588 0.0254 Moldova 45 0.0000 United States 3882 0.0106 El Salvador 128 0.0000 Monaco 99 0.0348 Uruguay 247 0.0091 Equatorial Guinea 60 0.0000 Montenegro 61 0.0958 Uzbekistan 10 0.0000 Estonia 380 0.0254 Morocco 1703 0.0000 Venezuela, RB 675 0.0056 Ethiopia 28 0.0000 Mozambique 19 0.0000 Vietnam 128 0.0005 Finland 897 0.0029 Namibia 38 0.0154 Virgin Islands (U.S.) 22 0.0068 France 8946 0.0250 Nauru 15 0.0000 West Bank and Gaza 36 0.2886 French Polynesia 20 0.0000 Nepal 12 0.0000 Yemen, Rep. 86 0.0313 Gabon 41 0.0000 Notes: N denotes the number of exporters and Localization is the country index of localization, which measures the amount of geographical concentration exhibiting exporters to each destination. Appendix B. Details on the Application of Duranton and Overman (2005) In this section we explain in detail the application of DO to uncover agglomeration by export destination. We proceed as follows. For each export destination we compute the unique bilateral distances between exporters by applying the haversine formula to the zip code coordinates. Next, we estimate the distribution of bilateral distances of each country via kernel estimation. As in DO, we use a Gaussian kernel, choosing the bandwidth so as to minimize the mean integrated squared error. Distances are reflected around zero, using the method proposed by Silverman (1986) to avoid giving positive densities to negative distances. Note also that firms within the same zip code are computed as being separated by 0 kilometers. The kernel density estimation for country c at every kilometer d ( K^c(d)) reads as follows: Kc^(d)=2nc(nc−1)h∑i=1nc−1∑j=i+1ncf(d−di,jh), (2) where nc is the number of export firms to country c, h is the bandwidth and f is the Gaussian probability density function.15Figure 8A shows the spatial distribution of exporters to India in 2007. The existence of several clusters of exporters is apparent. Figure 8B plots the histogram and the kernel estimation of the distance distribution. The high density at very small distances stems from the large number of exporters that are located within very close zip codes. The second peak in the distribution at around 400 kilometers marks the distance that separates the clusters. Figure 8 View largeDownload slide Distribution of distances of firms exporting to India. Notes: This figure plots the spatial distribution of exporters to India in 2007 (A) and the histogram of the unique bilateral distances between them as well as the kernel estimate of the probability density function (B). Figure 8 View largeDownload slide Distribution of distances of firms exporting to India. Notes: This figure plots the spatial distribution of exporters to India in 2007 (A) and the histogram of the unique bilateral distances between them as well as the kernel estimate of the probability density function (B). To test for significant agglomeration, the observed spatial distribution is compared with the counterfactual. As stated in the main text, the counterfactual controls for both the spatial distribution of exporters, which may be agglomerated with respect to domestic firms, as well as the industry composition of exports to each country. We proceed as follows. For each pair of country and two-digit industry, we draw 1000 random samples from exporters in the industry; each draw of size the actual number of exporters to the country operating in that industry. Then, for each country we aggregate each draw across the different industries to collect 1000 random samples of size nc (the actual number of exporters to the country) with an industry composition that replicates the one observed in the data. In our baseline analysis we carry out the test of significant agglomeration at distances below 100 km. As in DO we construct two tests, one of localization and one of dispersion, both with a significance level of 95%. We do the following. For each kilometer, we rank our 1000 counterfactual distributions in ascending order and then pick the percentile that makes 95% of the counterfactual distributions lie below it across all distances. When it is not possible to find a percentile making exactly 95% of the simulations be below it, we use linear interpolation. Note that in our baseline results all the percentiles fulfilling this criterion range between the 96.4-th and the 99.5-th. This percentile is referred to as the localization threshold, whereas a dispersion threshold is defined in a similar way, i.e. the percentile that makes 5% of the counterfactual distributions lie below it across all distances. Note that in DO the localization and dispersion thresholds are referred to as global confidence bands. The Figure 9A plots the density of the distance distribution below 100 km and a small sample of the counterfactual distributions. The Figure 9B displays the localization and dispersion thresholds (the upper and lower dashed lines, respectively). Figure 9 View largeDownload slide Localization and dispersion thresholds of India. Notes: (A) shows the estimated distance density of exporters to India in 2007 as well as a sample of 20 counterfactual distributions. (B) Displays the localization and dispersion thresholds, represented by the upper and lower dashed lines, respectively. The shaded area between the distance distribution and the localization threshold constitutes the country index of agglomeration. Figure 9 View largeDownload slide Localization and dispersion thresholds of India. Notes: (A) shows the estimated distance density of exporters to India in 2007 as well as a sample of 20 counterfactual distributions. (B) Displays the localization and dispersion thresholds, represented by the upper and lower dashed lines, respectively. The shaded area between the distance distribution and the localization threshold constitutes the country index of agglomeration. We define exporters to a destination to be significantly localized if the distance distribution is above the localization threshold in at least one kilometer. Similarly, exporters to a destination are defined to be dispersed if the distance distribution is below the dispersion threshold in at least one kilometer and the country does not exhibit localization. Note that the latter condition stems from the fact that densities sum up to one, hence localization at some distances implies dispersion at others. Following these criteria, Figure 9B shows that exporters to India are significantly localized. Note finally that localization and dispersion can be assessed at each distance, by comparing the distance distribution and the thresholds at each kilometer. In the example, localization takes place at distances below 70 km. Finally, we define a country index of agglomeration as the sum across distances of the difference between the distance distribution and the localization threshold if the former is above the latter and zero otherwise. This index accounts for the amount of exporter agglomeration by destination and it is the counterpart of the industry index of agglomeration defined by DO. In Figure 9B it is depicted as the shaded area between the distance density and the upper dashed line. Appendix C. Details on the Principal Component Analysis In Section 4, we create an index of institutional quality by applying a principal component analysis (PCA) on the World Bank Worldwide Governance Indicators (WGI). These measures account for six dimensions of governance, namely voice and accountability, political stability and absence of violence, government effectiveness, regulatory quality, rule of law, and control of corruption, see Kaufmann et al. (2010). Given the high correlation between these measures, a PCA is a useful tool to summarize all the information and construct a synthetic index that accounts for the overall institutional quality in each country. The PCA finds a set of uncorrelated linear combinations of the measures that accounts for most of the variance. In our case, the first of such combinations accounts for 88% of the variance and constitutes the index of institutional quality that we include in Table 3. Figure 10 plots the correlation of the institutional quality index with the rule of law (WGI), the Doing Business Index, investor protection and time to import goods. The high correlations suggest that our index of institutional quality provides a good approximation of the business environment that firms face when exporting to every foreign country. Figure 10 View largeDownload slide Correlation of the synthetic index of institutional quality (PCA) with other measures. This figure shows the correlation of our synthetic index of institutional quality, computed from a PCA on the Worldwide Governance Indicators, with other measures proxying the institutional environment of every country. Figure 10 View largeDownload slide Correlation of the synthetic index of institutional quality (PCA) with other measures. This figure shows the correlation of our synthetic index of institutional quality, computed from a PCA on the Worldwide Governance Indicators, with other measures proxying the institutional environment of every country. © The Author (2017). Published by Oxford University Press. All rights reserved. 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