From periphery to core: measuring agglomeration effects using high-speed rail

From periphery to core: measuring agglomeration effects using high-speed rail Abstract We analyze the economic impact of the German high-speed rail (HSR) connecting Cologne and Frankfurt, which provides plausibly exogenous variation in access to surrounding economic mass. We find a causal effect of about 8.5% on average of the HSR on the GDP of three counties with intermediate stops. We make further use of the variation in bilateral transport costs between all counties in our study area induced by the HSR to identify the strength and spatial scope of agglomeration forces. Our most careful estimate points to an elasticity of output with respect to market potential of 12.5%. The strength of the spillover declines by 50% every 30 min of travel time, diminishing to 1% after about 200 min. Our results further imply an elasticity of per-worker output with respect to economic density of 3.8%, although the effects seem driven by worker and firm selection. 1. Introduction ‘A major new high-speed rail line will generate many thousands of construction jobs over several years, as well as permanent jobs for rail employees and increased economic activity in the destinations these trains serve.’ —US President Barack Obama, 16 April 2009 One of the most fundamental and uncontroversial ideas in economic geography and urban economics is that firms and households benefit from access to economic markets due to various forms of agglomeration economies (Marshall, 1920). The mutually reinforcing effects of spatial density and productivity can theoretically account for the highly uneven distribution of economic activity between and within regions. The strong belief that economic agents benefit from an ease of interaction has always motivated large (public) expenditures into transport infrastructures, e.g. ports, airports, highways or railways. A striking example of an expensive, but increasingly popular transport mode is high-speed rail (HSR). The costs of implementing an HSR network in Britain, which mainly consists of a Y-shaped connection of London to Birmingham, Leeds and Manchester of about 500 km length are scheduled to amount to as much as £42 (about US$63) billion at present (Storeygard, 2012). The US Department of Transportation (2009) has announced its strategic plan, which proposes the construction of completely new rail lines that will feature velocities of possibly up to 400 km/h (250 mph). The plan has already identified US$8 billion plus US$1 billion per year for 5 years in the federal budget just to jump-start a program that would only be comparable to the interstate highway program of the 20th century. The perhaps most spectacular HSR considered to date is a 7000 km line connecting the Russian and Chinese capitals Moscow and Beijing, currently estimated at 1.5 trillion yuan (US$242 billion) (Phillips, 2015). The willingness to commit large amounts of public money to the development of HSR bears witness to the confidence that HSR will deliver a substantial economic impact. The wider economic impacts such infrastructures deliver, however, naturally depend on the strength and the spatial scope of the agglomeration economies they enhance.1 Estimating such agglomeration effects is empirically challenging. The density of economic activity and the productivity at a given location are not only potentially mutually dependent, but also potentially simultaneously determined by location fundamentals, such as a favorable geography or good institutions. The main challenge in estimating the strength and the spatial scope of agglomeration effects, therefore, is to find exogenous variation in access to the surrounding economic mass. While transport infrastructures, such as a new HSR, generate such variation in access to economic mass, the allocation of transport infrastructure is typically nonrandom, thus generating additional identification problems. In this article, we provide causal estimates of the strength and the spatial scope of agglomeration effects using a variation of the market potential approach, which links economic outcomes at a given locality to economic activity at surrounding localities via a transportation network. To disentangle the effects of market potential from other determinants of economic outcomes our identification stems exclusively from changes in transport technology, which affect the effective distance between all pairs of locations in a region.2 Specifically, we exploit the variation in bilateral transport costs between all counties located in the German federal states of North Rhine-Westphalia, Hesse and Rhineland-Palatinate that was induced by the Cologne–Frankfurt HSR. With this research design we are able to control for unobserved time-invariant variation in location fundamentals and circumvent some of the typical challenges in estimating the effects of spatial density on economic outcomes. Given the particular institutional setting we argue that the HSR analyzed provides variation in bilateral transport costs that is credibly exogenous, creating a natural experiment with identifying variation that is as good as random.3 The Cologne–Frankfurt HSR was inaugurated in 2002. The line is part of the Trans-European Networks and facilitates train velocities of up to 300 km/h. The HSR reduced travel time between both metropolises by more than 55% in comparison to the old rail connection and by more than 35% in comparison to the automobile. Along the HSR line, intermediate stops were created in the towns of Limburg, Montabaur and Siegburg. It is noteworthy that given the small population of less than 25,000 and 15,000 inhabitants, in particular, the stops in Limburg and Montabaur are unusual within the German if not European HSR network. Following the connection to the HSR line the two towns are within 40 min of Cologne and Frankfurt, which are the centers of the two largest German agglomerations, but also less than 10 min of each other. The final routing of the line and the location of the intermediate stops were the result of a political bargaining process among the rail carrier, three federal states and several business lobby and environmental activist groups that lasted almost 40 years. We argue that the institutional particularities, which we describe in more detail in Section 2, allow us to make the helpful identifying assumptions that the routing and the timing of the connection of Limburg, Montabaur and Siegburg and the timing of the connection of all other stations are exogenous to the levels and trends of economic development. Based on the exogenous variation provided, we are able to identify the causal impact of HSR on local economic development as well as the strength and the spatial scope of agglomeration economies promoted by the line. In the first step, we assess the effect of the HSR on the local economies within the counties of the intermediate stops using program evaluation techniques. In the second step, we correlate the growth in effective density, which we express in market potential form (Harris, 1954), to the economic growth across counties within our study area. The market potential expresses effective density as the transport cost weighted sum of the GDP of all counties in the study area. The measure takes into account the effect of the HSR on bilateral transport costs between all counties in our study area. Since the HSR is used exclusively for passenger service, we implicitly disentangle the effects of facilitated human interactions from the transport costs of tradable goods, i.e. the trade channel. The spillovers we capture thus include Marshallian externalities related to knowledge diffusion and labor market pooling and the effects of improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs, but not freight costs. Theoretically, one effect of the HSR is to upgrade the accessibility of formerly peripheral areas, which at least during a transition period offers the benefit of relatively low land prices, and may thus become attractive to firms. Indeed, our results point to a positive economic impact of HSR. On average, 6 years after the opening of the line, the GDP in the counties of the intermediate stops exceeds the counterfactual trend established via a group of synthetic counties by 8.5%.4 We find an elasticity of GDP with respect to effective density, i.e. market potential, of about 12.5% in our most conservative model. The elasticity of output per worker with respect to effective density is, at 10%, only marginally smaller. Because our measure of effective density is spatially smoothed the variance across counties is naturally lower than in conventional density measures. Normalized by the log ratio of the standard deviations of effective density over actual density our results imply an elasticity of productivity with respect to employment density of 3.8%, which is close to previous estimates derived from cross-sectional research designs (e.g. Ciccone and Hall, 1996).5 The effect, however, seems to be driven to a significant extent by selection, i.e. a compositional change in industry and worker qualification (Combes et al., 2011, 2012). We further estimate that the strength of economic spillovers halves every 30 min of travel time and is near to zero after about 200 min. The spillovers we detect are significantly less localized than in previous studies that have identified spillover effects from within-city variation (Arzaghi and Henderson, 2008; Ahlfeldt and Wendland, 2013; Ahlfeldt et al. 2015), but are more localized than the scope of spatial interactions inferred from empirical New Economic Geography (NEG) models with a stronger emphasis on trade costs (Hanson, 2005).6 Our research connects to a large and growing literature on the nature of agglomeration economies reviewed in detail in Duranton and Puga (2004) and Rosenthal and Strange (2004). A standard approach in this literature has been to regress economic outcome measures, such as wages, against some measure of agglomeration, typically employment or population density.7 A smaller literature has exploited presumably exogenous variation in the surrounding concentration of economic activity. Rosenthal and Strange (2008) and Combes et al. (2010) use geology to instrument for density. Greenstone et al. (2010) analyze the effects of the openings of large manufacturing plants on incumbent plants. Another related strand has analyzed the impact of natural experiments such as trade liberalization (Hanson, 1996, 1997), wartime bombing (Davis and Weinstein, 2002), the decrease in the economic relevance of portage sites (Bleakley and Lin, 2014) and the Tennessee Valley Authority (Kline and Moretti, 2014) on the spatial distribution of economic activity. At the intersection of both strands, Redding and Sturm (2008) have exploited the effects of the variation in access to the surrounding economic mass created by the division and unification of Germany on city growth. Ahlfeldt et al. (2015) use the within-city variation in surrounding economic mass induced by the division and reunification of Berlin, Germany, to identify the strength and spatial scope of spillovers among residents and among firms as well as the rate at which commuting probabilities decline in time distance. Our main contributions to this literature are 2-fold. First, we estimate the agglomeration effects based on the variation in surrounding economic mass created by new transport infrastructures, which allows for a relatively robust separation of spillover effects from unobserved locational fundamental effects. Second, we contribute to a relatively small literature that has provided estimates of the rate of spatial decay in spillovers. The relatively strong spatial decay in spatial spillovers substantiates the intuition that moving people is more costly than moving goods. Another growing strand in the literature to which we contribute is concerned with the economic effects of transport infrastructure. Overall, the evidence suggests that a well-developed transport infrastructure enhances trade (Duranton et al., 2014; Donaldson, 2015), promotes economic growth (Banerjee et al., 2012; Duranton and Turner, 2012), and, at a more local level, increases property prices (Baum-Snow and Kahn, 2000; Gibbons and Machin, 2005). There is also evidence of asymmetric impacts on labor markets, in particular, of a relative increase in demand for skilled workers in skill-abundant regions (Michaels, 2008). The evidence on the impact on the spatial distribution of economic activity is more mixed. Within metropolitan areas radial connections tend to facilitate suburbanization and, thus, benefit peripheral areas (Baum-Snow, 2007; Kopecky and Suen, 2010; Baum-Snow et al., 2017).8 However, there is also evidence that within larger regions reductions in trade costs between regions due to better road networks favor core regions at the expense of peripheral regions (Faber, 2014). Empirically, the literature evaluating the economic effects of transport infrastructure has been concerned with the nonrandom allocation of transport infrastructure, which is usually built to accommodate existing or expected demand. Instrumental variables based on historic transport networks (Duranton and Turner, 2012), counterfactual least-cost networks (Faber, 2014) or straight-line connections among regional centers (Banerjee et al., 2012) have emerged as a standard approach to establishing a causal relationship. The alternative and potentially complementary strategy adopted here is the so-called inconsequential units approach (Redding and Turner, 2015). This approach rests on the assumption that the main purpose of a transport infrastructure is often to connect regional agglomerations and that the connection of localities along the way is not necessarily intended (Chandra and Thompson, 2000; Michaels, 2008). Our contribution to this line of research is, again, 2-fold. First, we provide evidence of the economic impacts of HSR, an increasingly important but empirically understudied transport mode, exploiting a source of exogenous variation. Second, we show that peripheral regions can benefit from a better connectivity to core regions if the cost of human interaction is reduced but trade costs remain unchanged.9 This evidence complements the extant literature suggesting that HSR primarily benefits large cities, but not necessarily remote counties (Zheng and Kahn, 2013; Lin, 2014; Qin, 2016). The evidence of positive effects emerging from Marshallian externalities is also complementary to the recent evidence of negative effects on peripheral regions operating through a trade channel (Faber, 2014). Our results similarly complement literature on suburbanization (Baum-Snow, 2007; Garcia-López, 2012; Garcia-López et al., 2015) by showing that a HSR is less likely to decentralize population to suburbs than a highway. The next section introduces the institutional setting in more detail and discusses the data used. In Section 3, we conduct a program evaluation with a focus on the impact of HSR on the economies of the counties of the intermediate stations. In Section 4, we then exploit the full variation the HSR induced in bilateral transport costs between all counties in our study area to estimate the strength and spatial scope of agglomeration effects. The final section concludes. 2. Background and data 2.1. The Cologne–Frankfurt HSR line The HSR line from Cologne to Frankfurt/Main is part of the priority axis Paris–Brussels–Cologne–Amsterdam–London (PBKAL), which is 1 of 14 projects of the Trans-European Transport Network (TEN-T) as endorsed by the European Commission in 1994. In comparison to the old track alongside the river Rhine, the new HSR connects the Rhine/Ruhr area (including Cologne) and the Rhine/Main area (including Frankfurt) almost directly, reducing track length from 222 km to 177 km.10 The new track is designed exclusively for passenger transport and allows train velocities of up to 300 km/h. Due to both facts, travel time between the two main stations was reduced from 2 h, 13 min to 59 min (Brux, 2002). Preparatory works for the construction of the HSR started in December 1995. The major construction work—on the various tunnels and bridges—began in 1998. The HSR line was completed at the end of 2001. After a test period, the HSR line was put into operation in 2002. The total cost of the project was €6 billion (European Commission, 2005, 17). The broader areas of Rhine-Ruhr and Rhine-Main have long been considered to be the largest German economic agglomerations. The rail lines connecting the two centers along both Rhine riverbanks were among the European rail corridors with the heaviest usage. They had represented a traditional bottleneck since the early 1970s, when usage already exceeded capacity. The first plans for constructing an HSR line between Cologne and Frankfurt, consequently, date back to as far as the early 1970s. Since then, it has taken more than 30 years until the opening. A reason for the long time period was the complex evolution process of infrastructure projects in Germany. Several variants at the left-hand and right-hand side of the Rhine were discussed during decades of negotiations. Taking into account the difficult geography of the Central German Uplands, it was ultimately decided to construct a right-hand side connection that would largely follow the highway A3 in an attempt to minimize construction and environmental costs as well as travel time between the major centers. These benefits came at the expense of leaving relatively large cities like Koblenz and the state capitals Wiesbaden (Hesse) and Mainz (Rhineland Palatinate) aside. Due to the federal system of the Federal Republic of Germany, the states (Länder) have a strong influence on infrastructure projects that affect their territories (Sartori, 2008, 3–8). Three federal states were concerned with the subject project: North Rhine-Westphalia, Rhineland-Palatine and Hesse. While Cologne lies in North Rhine-Westphalia and Frankfurt is located in Hesse, no stop was planned within the state of Rhineland-Palatine after the plans to connect Koblenz were abandoned in 1989. The announcement of the exact routing, however, suddenly opened opportunities for communities along the line to lobby in favor of their connection. Limburg, supported by Hesse, was the first city to make a case. Somewhat later in the process, the local political and economic actors in Montabaur also managed to convince the state authorities of Rhineland-Palatinate to support their case. It was argued that from Montabaur the hinterland of the state could be connected via an existing regional line. The case of Montabaur was facilitated by the decision to build the new Limburg station at the southeastern fringe of the city in Eschhofen. The originally proposed site (Limburg-Staffel) was significantly closer than Montabaur and, given the already short distance, would have made an additional stop in Montabaur almost impossible to justify. During a long lobbying process menacing a blockade of the planning and political decision process, the three federal states eventually negotiated three intermediate stops along the HSR line, one in each of the concerned federal states. While Bonn/Siegburg and Limburg represented the shares of North Rhine-Westphalia and Hesse, a new station in Montabaur ensured the connection of Rhineland-Palatinate. At the end of this process, Montabaur, with a population of less than 20,000—the by far smallest city on the German HSR network—found itself within 40 min of the regional centers Cologne and Frankfurt and within 20 min of the international airports Frankfurt and Cologne-Bonn. Anecdotal evidence suggests that this exceptional upgrade in terms of accessibility improved the attractiveness of the city as a business location. A new congress center was opened and more than 50 firms settled in an industrial park built adjacent to the rail station11; 1&1, a leading provider of communication services, even moved their headquarters to that location. A number of local manufacturing companies in the wider catchment area expanded their capacities in response to the improvement in connectivity (Egenolf, 2008). Mainstream media reported a major success story as early as 2007, citing city officials who claim that the HSR brought at least 600 new jobs to the town (Sorge, 2007). Since then, the number has climbed to 1800 (Hergert, 2015). Several newspapers cite executives of various local firms such as 1&1 (telecommunications), Emc2 (consulting), Friedhelm-Loh (electrical engineering), ADG (congress centre), Itac (software), MTE Deutschland (milling machines), all of which suggest that the HSR was a major factor in their decisions to locate or expand business activity in Montabaur (Sorge, 2007; Rhein-Zeitung, 2012; Hergert, 2015). As an example, ADG representatives highlight that the new congress center would not have been viable without the fast connection (less than 30 min) to the major airports (Frankfurt and Cologne/Bonn). Among the major advantages reported were the ease of maintaining business relations and an improved access to a highly qualified labor pool. Various representatives, from Itac, 1&1, and others, stress that the HSR enables them to draw from a much larger labor market, which now includes the major agglomerations Cologne and Frankfurt. In selected firms, more than 80% of the managerial positions are held by in-commuters. As an example, two-thirds of the 1600 employees working for 1&1, commute into town, most of them by HSR (Hergert, 2015). These newspaper reports align well with the mayor’s HSR impact summary. According to Edmund Schaaf, employment has increased by 1400 jobs (subject to social insurance contributions) over the past 15 years, which is almost 10 times the increase in population of 150. Altogether, the anecdotal evidence suggests that the unexpectedly high passenger numbers of 3000 per day, about 10 times the original forecasts (Müller, 2012), are driven by people working, not living, in the city. This pattern is also consistent with the numbers reported for Limburg, where over the same period the number of in-commuters increased from 13,000 to 17,500 (Hergert, 2015). Notwithstanding this local impact, the intermediate stops have been very controversial in terms of their economic viability. The cities of Montabaur and Limburg only exhibit approximately 12,500 and 34,000 habitants. Furthermore, the distance between these two small cities is barely 20 km and the high-speed Intercity-Express (ICE) train needs only 9 min between the two stops, which is in contrast to the concept of high-velocity travelling that has its comparative advantages at much larger distances. The advantage of this institutional setting for our empirical analysis is that it is reasonable to assume that the routing of the track was exogenous in the sense that it was determined by geographical constraints, construction costs and environmental concerns. Compared to the considered alternative route discussed in more detail in Section 3.3, the population living within the immediate catchment areas of the intermediate stops along the selected route amounts to less than a half.12 The locations of the eventually chosen intermediate stops was constrained by the proposed routing and the need to accommodate three stops at reasonable distances in three different federal states, disentangling political lobbying for intermediate stops from other regional policies. Most importantly, the connection of the intermediate stations was not driven by existing or expected demand—in fact, these stations were heavily opposed by the operating rail carrier Deutsche Bahn. Thus, we consider the resulting variation in accessibility provided by the rail line as exogenous to the economic outcomes we observe. Furthermore, it is reasonable to argue that the timing of the inauguration was exogenous to contemporary economic trends for the entire line. When the plans for a connection of Frankfurt and Cologne were first drafted in the 1970s, it was virtually impossible to foresee changes in economic conditions in the late 1990s. 2.2. Data and study area Our study area comprises the German federal states Hesse, North Rhine-Westphalia and Rhineland-Palatinate, to which the HSR connects. In 1996, 6 years before the opening of the HSR, the total population of the study area was about 28 million, thus somewhat less than California and about the size of Belgium and the Netherlands together. The share at the total German population was about 34%. The share at German GDP was slightly higher at 36%. For the 115 counties (NUTS3 regions) in the three federal states, we collect data from various official sources: GDP, population, gross value added (GVA) by industry sectors from the German Federal Statistical Office13; number of in- and out-commuter, employment (at workplace and residence) and share of workforce holding an academic degree (at workplace) from the Federal Employment Agency. Municipality level population is obtained from the Federal Office for Building and Regional Planning. We use these data primarily to identify the most important cities within each county, which we define as their economic centers. We collected data from 1992 to 1995 (depending on data availability) to 2009. The average county in our study area in 1996 had a population of about 241K, which is significantly larger than the average county in the rest of the country (157K). In terms of output per worker, our study area is fairly similar to the rest of the country (€71.5K vs. €70.8K). Also, the shares of various industries at the regional GVA are remarkably similar. Descriptive statistics are presented in section 2 of the Supplementary Appendix, where we also present a map that illustrates the location of the study area and the HSR within Germany. 3. Program evaluation The intermediate stops Limburg, Montabaur and Siegburg on the Cologne–Frankfurt HSR were, as we argue, an accidental result of political bargaining and not rational transport planning. The new stations thus provide plausibly exogenous variation in transport services that can be exploited to detect economic impact using established program evaluation techniques. In this section, we analyze the economic effects of the opening of the HSR—the treatment—on the economies of the counties of the intermediate stops, the treated counties. Specifically, we compare the evolution of various economic outcome measures in the treated counties to control counties that provide a counterfactual. 3.1. Treated versus synthetic counties We note that at this stage we ignore Cologne and Frankfurt because these regional centers are arguably major generators of transport demand, so the routing of the HSR line cannot be considered exogenous to their economic performance. As these cities potentially benefit from improved transport services we also exclude them from the group of control counties. Besides, on the exogeneity of the treatment the credibility of a quasi-experimental comparison rests on the assumption that the treatment and control group would have followed the same trend in the absence of the treatment. To ensure a valid comparison we create a comparison group consisting of three synthetic counties, one for each of the treated counties in which the HSR stops Limburg, Montabaur and Siegburg are located. With this approach, we avoid problems arising in conventional difference-in-differences (DD) analysis if the number of treated subjects is small relative to the number of control subjects (Cameron and Miller 2015). We follow the procedure developed by Abadie and Gardeazabal (2003), who define a synthetic region as a weighted combination of nontreated regions. The optimal combination of weights is determined by two objectives. First, a synthetic county should match its treated counterpart as closely as possible in terms of the following economic growth predictors: GDP per worker, population density, ratio of out-commuters over in-commuters, the shares of construction, mining, services, retail, manufacturing and finance at GVA, and the share of workers holding a university degree in the workforce at workplace. Formally, this problem is defined as minW∈WX1-X0W′VX1-X0W, where W is a vector of non-negative weights of the non-treated counties in the synthetic county that must sum to one, X1 is a vector of pre-opening values of k economic growth predictors for the treated county, X0 is a matrix containing the same information for the non-treated counties, and V is a diagonal matrix with nonnegative elements that determine the relative importance of the growth predictors. The solution to this problem, the vector of optimal weights of nontreated counties W*, depends on V, which leads to the second objective. We search for the optimal combination V* which produces a synthetic control county that best matches the respective treated county in terms of the pre-construction growth trend. Formally, this second problem is defined as V*=argminV∈νZ1-Z0W*V′Z1-Z0W*(V), where Z1 a is vector of pre-construction observations of an economic outcome measure Y for the treated county and Z0 is a matrix with the same information for the nontreated counties.14 Table 1 summarizes the pretreatment characteristics of the home counties of the intermediate HSR stops, the synthetic control counties and all other nontreated counties in the study areas. Each synthetic county is the result of a separate implementation of the procedure outlined above. In each case the economic outcome measure Y, used to find the optimal weights matrix W* is the log of GDP. The pre-period covers all years prior to 1998, when the substantial construction works began and after—more than 25 years of negotiations—confidence was created so that the HSR would eventually materialize. The values for the k growth predictors for a given synthetic county are given by the vector X1*=X0W*, i.e. a weighted combination of nontreated counties. The treated counties (and the synthetic counties) are characterized by below-average productivity, tend to be residential locations and have a low share of workers holding university degrees. With few exceptions, the synthetic counties resemble their treated counterparts closely in observable characteristics, certainly more closely than the average of the nontreated counties. Table 1 Pretreatment characteristics: treated versus synthetic controls   Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  All nontreated counties  Predictor variable  Treat  Synth  Treat  Synth  Treat  Synth  Mean  S.D.  GDP/worker (€, K)  63.8  69.0  64.9  64.5  74.9  74.7  69.3  7.9  Ratio out/in-commuting  0.51  0.30  0.51  0.50  0.36  0.38  1.09  1.00  Population/sq. km land area  227  424  193  178  464  463  771  813  Industry share: Const. (%)  4.6  4.6  4.0  4.0  2.9  2.9  2.8  1.1  Industry share: Mining (%)  9.2  9.2  14.1  13.9  10.8  10.8  13.7  5.1  Industry share: Services (%)  36.2  36.2  31.9  31.7  36.2  36.1  33.5  4.9  Industry share: Retail (%)  8.0  8.9  8.7  8.7  8.5  8.5  8.8  2.1  Industry share: Manufact. (%)  13.8  13.8  18.1  18.0  13.8  13.7  16.5  4.9  Industry share: Finance (%)  16.1  15.9  12.1  12.0  15.1  15.0  12.8  2.8  Share higher education (%)  5.1  4.7  3.7  3.6  6.7  6.7  6.5  3.1    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  All nontreated counties  Predictor variable  Treat  Synth  Treat  Synth  Treat  Synth  Mean  S.D.  GDP/worker (€, K)  63.8  69.0  64.9  64.5  74.9  74.7  69.3  7.9  Ratio out/in-commuting  0.51  0.30  0.51  0.50  0.36  0.38  1.09  1.00  Population/sq. km land area  227  424  193  178  464  463  771  813  Industry share: Const. (%)  4.6  4.6  4.0  4.0  2.9  2.9  2.8  1.1  Industry share: Mining (%)  9.2  9.2  14.1  13.9  10.8  10.8  13.7  5.1  Industry share: Services (%)  36.2  36.2  31.9  31.7  36.2  36.1  33.5  4.9  Industry share: Retail (%)  8.0  8.9  8.7  8.7  8.5  8.5  8.8  2.1  Industry share: Manufact. (%)  13.8  13.8  18.1  18.0  13.8  13.7  16.5  4.9  Industry share: Finance (%)  16.1  15.9  12.1  12.0  15.1  15.0  12.8  2.8  Share higher education (%)  5.1  4.7  3.7  3.6  6.7  6.7  6.5  3.1  Note: The reported values are means across all years prior to 1998 (when construction began) except for the share of workers (at workplace) holding a university degree, which refers to 1999, the earliest year for which data was available. The weighting has achieved its first-order purpose of creating comparison counties that are more similar to the treated than the naïve control group of all nontreated counties. None of the synthetic counties depend solely on one county, nor are the important donors (with high weights) within a likely spillover range (see section 3-A in the Supplementary Appendix). We are thus ready to use the weights matrices (one for each treated county) to approximate vectors of counterfactual outcomes for the synthetic counties. We begin with Westerwaldkreis, home to the HSR stop Montabaur. As introduced in Section 2, Montabaur features particularly prominently in the media as an example of how communities can benefit from access to HSR. Using log GDP as an outcome variable, the left panel of Figure 1 compares the actual realizations (solid lines) to a vector of counterfactual values (dashed line) for the synthetic control county Y1*=Y0W*, where Y0 is a matrix containing the economic outcomes of all nontreated counties for all years. Both trend lines are normalized to zero in the first period. Up to 1998, the two lines followed each other closely, which indicates that the weighting also achieved the second-order purpose of equalizing pre-trends. After 1998, actual economic growth surpasses the counterfactual growth, in particular during the construction period. This pattern is indicative of some anticipation effects. Some firms moved to or expanded their businesses before the station was actually served, perhaps in an attempt to seek first-mover advantages and occupy the best possible spots in the business park close to the station. Figure 1 View largeDownload slide Westerwaldkreis (Montabaur) versus synthetic control county. Notes: Solid (dashed) line shows the trend line for Westerwaldkreis where Montabaur is situated (the synthetic control county). Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrix underlying the synthetic county. Figure 1 View largeDownload slide Westerwaldkreis (Montabaur) versus synthetic control county. Notes: Solid (dashed) line shows the trend line for Westerwaldkreis where Montabaur is situated (the synthetic control county). Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrix underlying the synthetic county. To gain further insights into other dimensions of economic impact we have used the procedure outlined above to create synthetic control counties and counterfactual trends for each of the three treated counties and a number of alternative outcomes. The right panel in Figure 1 exemplarily illustrates the resulting trend lines for the actual and the counterfactual log number of in-commuters in Westerwaldkreis. This comparison substantiates the impression that the county was perceived as an economically more attractive location once it was clear that it would be connected to the HSR line. Figure 2 provides an overview of the various comparisons between the actual and counterfactual trends we did for the three treated counties and six alternative outcome measures. In each panel we plot the differences between the trend lines (actual–counterfactual) for a different outcome measure. We further add an extrapolated linear trend fitted into the pre (before 1998) observations to allow for an intuitive comparison of the relative trends before and after construction began. Figure 2 View largeDownload slide Relative trends for treated counties versus. synthetic control counties. Notes: Solid lines represent the differences between the trend lines for a treated county and the synthetic control county. Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrices underlying the synthetic counties. Dashed lines are extrapolated linear fits using observations before 1998. Figure 2 View largeDownload slide Relative trends for treated counties versus. synthetic control counties. Notes: Solid lines represent the differences between the trend lines for a treated county and the synthetic control county. Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrices underlying the synthetic counties. Dashed lines are extrapolated linear fits using observations before 1998. The positive impacts on economic activity suggested by Figure 1 for Montabaur seem to generalize to the two other intermediate stops. We find positive deviations from the relative pre-trend in GDP after the construction began (Limburg) or the line was completed (Siegburg). Similar positive turns in relative trends are evident in the share of in-commuters. The other outcome measures yield more mixed patterns and, in general, suggest that the HSR increased the attractiveness of the three affected counties as places to work rather than places to live. 3.2. Econometric analysis For a more formal test of the economic impact of the HSR on the group of treated counties, we make use of the following DD specification:   logYit=θTi×t>2002t+∑n=19982002θnTi×t=n+ϑTi×t-2003t+ϑPTi×t-2003t×t>2002t+μi+φt+εit, (3.1) where i and t index counties (treated and nontreated) and years, Ti is a dummy variable that is 1 for the treated counties of Montabaur, Limburg and Siegburg and 0 otherwise, t>2002 similarly indexes years after 2002, t=n similarly indexes a year n, t-2003 is a yearly trend taking a value of zero in 2003, and μi and φt are county and year fixed effects and εit is a random error term. This specification allows for a short-run impact on the level of the economic outcome variable θTi×t>2002t as well as a long-run impact on its trend ϑPTi×t-2003t×t>2002t while controlling for heterogeneity in pre-trends across the treated and the control counties ϑTi×t-2003t. The cumulated percentage impact in a given (post) year is defined as expθ^+ϑ^P×t-2003-1.15 The new stations have provided transport services since 2002, but a high degree of confidence regarding the eventual completion of the line have existed since 1998 when the substantial construction works began. We therefore add a number of short-run DD terms ∑n=19982002θnTi×t=n which absorb the effects during the construction period so that our treatment estimates are based on a comparison between the pre-construction (t < 1998) to the post-completion period (t > 2002). Essentially, the model produces empirical estimates of the cumulated effect (and its significance) which correspond to the differences between the solid and the dashed lines in Figure 2 during the post period. Standard errors are clustered on counties to account for serial correlation as recommended by Bertrand et al. (2004). We begin with the presentation of the empirical results for the outcome measure log GDP in Table 2. We use the groups of all nontreated (1–3) as well as the synthetic counties (4–6) as control groups and, in each case, complement the presentation of the results of the full models (3) and (6) with simplified versions of the model. Columns (1) and (4) provide a simple mean comparison (conditional on county and year fixed effects) of the difference in log GDP across the groups of treated and non-treated as well as the pre (before 2003) and post (from 2003 onward) periods. Columns (2) and (5) control for effects during the construction years, but do not control for trends. Table 2 Treatment effect on GDP   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP  Control group  Nontreated counties  Synthetic counties  T × (Year > 2002) [ θ]  0.057*** (0.006)  0.072*** (0.008)  −0.002 (0.011)  0.049** (0.014)  0.051** (0.016)  0.046* (0.018)  T × (Year > 2002) × (Year − 2003) [ ϑP]      −0.001 (0.003)      0.006 (0.003)  Cumulated effect      −0.003      0.066*  after 3 years      (0.017)      (0.027)  Cumulated effect      −0.005      0.084*  after 6 years      (0.024)      (0.036)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  Yes  —  Yes  Yes  T × (Year − 2003)  —  —  Yes  —  —  Yes  R2  0.997  0.997  0.997  0.999  0.999  0.999  N  2034  2034  2034  108  108  108    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP  Control group  Nontreated counties  Synthetic counties  T × (Year > 2002) [ θ]  0.057*** (0.006)  0.072*** (0.008)  −0.002 (0.011)  0.049** (0.014)  0.051** (0.016)  0.046* (0.018)  T × (Year > 2002) × (Year − 2003) [ ϑP]      −0.001 (0.003)      0.006 (0.003)  Cumulated effect      −0.003      0.066*  after 3 years      (0.017)      (0.027)  Cumulated effect      −0.005      0.084*  after 6 years      (0.024)      (0.036)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  Yes  —  Yes  Yes  T × (Year − 2003)  —  —  Yes  —  —  Yes  R2  0.997  0.997  0.997  0.999  0.999  0.999  N  2034  2034  2034  108  108  108  Notes: Standard errors in parentheses are clustered on counties. T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. The results, relatively consistently point to a positive and significant impact of the HSR on GDP. Ignoring trends, GDP in the treated counties grew by about 7% more in the treated counties than in the remaining ones if the comparison is made between the periods before construction began and after construction ended (2). The effect is slightly larger than in the basic model (1), which is consistent with the anticipation effects found in the visual inspection of the trend lines. The effect is also roughly in line with the average differences between the actual relative trend (solid lines) and linearly extrapolation pre-trends (dashed lines) during the post-period in the upper-left panel of Figure 2. Once we control for relative trends, the treatment effect disappears. As there is no positive impact on (post) trends, the implication is that the model attributes the relative differences between the before and after period to heterogeneous trends that existed prior to the treatment. Our preferred models, which compare the trends in the treated counties to the synthetic counties, yield a somewhat different picture. Consistently, all models (4–6) point to a GDP growth in the group of treated counties that exceeds the control group by about 5% in the short run. The full model (6) also suggests a positive long-run impact on the GDP trend, which is just about not statistically significant. The cumulated effects after 3 (2006) and 6 (2009) years, which are a combination of the short-run level and long-run trend effects amount to statistically significant effects of about 6.5–8.5% and are thus within the range of the effects suggested by Table 2, column (2) and Figure 2 (upper-left). The estimates reported in Table 2 are robust to using different donor pools (counties from which the algorithm can draw) and predictors (covariates the algorithm seeks to balance) (see section 3-B in the Supplementary Appendix). In Table 3, we replicate the least (1) and most (6) demanding models from Table 2 separately for each of the treated counties. We find positive effects on each of the treated counties, which are roughly within the range of the effects derived from the pooled models. After 6 years, each of the treated counties exceeded its synthetic counterpart by about 7–10% in terms of GDP. Table 3 Treatment effects on GDP by treated county   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  Control group  Nontreat  Synth  Nontreat  Synth  Nontreat  Synth  Treat × (Year > 2002) [ θ]  0.056*** (0.006)  0.033** (0.010)  0.058*** (0.006)  0.049 (0.030)  0.057*** (0.006)  0.057** (0.023)  Treat × (Year > 2002) × (Year − 2003) [ ϑP]    0.005* (0.002)    0.007* (0.004)    0.005 (0.003)  Cumulated effect    0.050***    0.073*    0.074**  after 3 years    (0.009)    (0.039)    (0.026)  Cumulated effect    0.067***    0.097*    0.089**  after 6 years    (0.013)    (0.049)    (0.031)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  —  Yes  —  Yes  T × (Year − 2003)  —  Yes  —  Yes  —  Yes  R2  0.997  1.000  0.997  1.000  0.997  1.000  N  1998  36  1998  36  1998  36    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  Control group  Nontreat  Synth  Nontreat  Synth  Nontreat  Synth  Treat × (Year > 2002) [ θ]  0.056*** (0.006)  0.033** (0.010)  0.058*** (0.006)  0.049 (0.030)  0.057*** (0.006)  0.057** (0.023)  Treat × (Year > 2002) × (Year − 2003) [ ϑP]    0.005* (0.002)    0.007* (0.004)    0.005 (0.003)  Cumulated effect    0.050***    0.073*    0.074**  after 3 years    (0.009)    (0.039)    (0.026)  Cumulated effect    0.067***    0.097*    0.089**  after 6 years    (0.013)    (0.049)    (0.031)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  —  Yes  —  Yes  T × (Year − 2003)  —  Yes  —  Yes  —  Yes  R2  0.997  1.000  0.997  1.000  0.997  1.000  N  1998  36  1998  36  1998  36  Notes: Standard errors in parentheses are robust in columns (2), (4) and (6) and clustered on counties in columns (1), (3) and (5). T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4, applies the most demanding specification (comparison to synthetic control counties controlling for trends) to different outcome measures. We find a positive and statistically significant effect on per-worker GDP, which is roughly within the range of the GDP impact just discussed. Economic growth thus seems to have come at least in part, if not entirely, through an increase in productivity (of the labor force). It is noteworthy, however, that the naïve DD specification (used in Table 2, column 2) yields significantly positive effects on per-worker GDP and workplace employment of roughly similar magnitude (see section 3-C in the Supplementary Appendix). The naïve DD specification also adds to the results reported Table 4, column 5 in that the positive point estimate of the in-commuter effect is statistically significant. This is in line with the results of a complementary analysis of bilateral commuting flows within the study area summarized in Figure 3 and laid out in more detail in Supplementary Appendix section 3-E. Confirming the anecdotal evidence reported in Section 2.1, the analysis shows that firms in Montabaur and Limburg have been drawing employees from a wider labor market since the opening of the HSR. The analysis also reveals that at the intensive margin (variation in reduction of commuting times), there seems to be a HSR effect on out-commuting. Table 4 Treatment effect on other economic outcomes   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP/ worker  Ln workplace employment  Ln residence employment  Ln population  Ln no. of in-commuters  Ln no. of out- commuters  Control group  Synthetic counties  T × (Year > 2002) [ θ]  0.056*** (0.010)  −0.020 (0.032)  −0.025 (0.014)  −0.009 (0.015)  0.030 (0.086)  −0.015 (0.030)  T × (Year > 2002) × (Year − 2003) [ ϑP]  0.002 (0.004)  −0.001 (0.006)  −0.005*** (0.001)  −0.004* (0.002)  0.010 (0.011)  −0.007 (0.004)  Cumulated effect  0.065**  −0.023  −0.040**  −0.022  0.062  −0.035  after 3 years  (0.021)  (0.050)  (0.014)  (0.021)  (0.123)  (0.039)  Cumulated effect  0.072*  −0.025  −0.055**  −0.034  0.095  −0.055  after 6 years  (0.034)  (0.069)  (0.015)  (0.026)  (0.158)  (0.049)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  Yes  Yes  Yes  Yes  Yes  Yes  T × (Year − 2003)  Yes  Yes  Yes  Yes  Yes  Yes  R2  0.983  0.999  1.000  1.000  0.998  0.999  N  102  102  102  120  96  96    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP/ worker  Ln workplace employment  Ln residence employment  Ln population  Ln no. of in-commuters  Ln no. of out- commuters  Control group  Synthetic counties  T × (Year > 2002) [ θ]  0.056*** (0.010)  −0.020 (0.032)  −0.025 (0.014)  −0.009 (0.015)  0.030 (0.086)  −0.015 (0.030)  T × (Year > 2002) × (Year − 2003) [ ϑP]  0.002 (0.004)  −0.001 (0.006)  −0.005*** (0.001)  −0.004* (0.002)  0.010 (0.011)  −0.007 (0.004)  Cumulated effect  0.065**  −0.023  −0.040**  −0.022  0.062  −0.035  after 3 years  (0.021)  (0.050)  (0.014)  (0.021)  (0.123)  (0.039)  Cumulated effect  0.072*  −0.025  −0.055**  −0.034  0.095  −0.055  after 6 years  (0.034)  (0.069)  (0.015)  (0.026)  (0.158)  (0.049)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  Yes  Yes  Yes  Yes  Yes  Yes  T × (Year − 2003)  Yes  Yes  Yes  Yes  Yes  Yes  R2  0.983  0.999  1.000  1.000  0.998  0.999  N  102  102  102  120  96  96  Notes: Standard errors in parentheses are clustered on counties. T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. Figure 3 View largeDownload slide HSR effects on bilateral commuting flows from and to HSR municipalities. Notes: In-commuter models use flows from all municipalities in the study area into intermediate HSR municipalities. Out-commuter models use flows from intermediate HSR municipalities to all municipalities in the study area. First difference in number of commuters is the difference between the average number of commuters from 1992 to 1995 and the average number of commuters from 2010 to 2012. First difference in travel time is based on the transport cost matrices summarized in Figure 5. Observations weighted by the average number of commuters (across all period). Figure 3 View largeDownload slide HSR effects on bilateral commuting flows from and to HSR municipalities. Notes: In-commuter models use flows from all municipalities in the study area into intermediate HSR municipalities. Out-commuter models use flows from intermediate HSR municipalities to all municipalities in the study area. First difference in number of commuters is the difference between the average number of commuters from 1992 to 1995 and the average number of commuters from 2010 to 2012. First difference in travel time is based on the transport cost matrices summarized in Figure 5. Observations weighted by the average number of commuters (across all period). Overall, the results of the econometric analysis support the key finding of the visual trend inspection that the HSR increased the attractiveness of the locations close to the intermediate stations as places to work, but not necessarily as places to live. A further breakdown by industry (in section 3-D in the Supplementary Appendix) shows that treatment effects are driven by financial services and other nonpublic services. This confirms anecdotal evidence citing the positive effects on firms specializing in consulting (Emc2), telecommunications (1&1), software (Itac) or events (ADG). 3.3. Falsification As with any program evaluation, the key identification challenge in our empirical exercise is to find a credible counterfactual for the treated group. To ensure a valid comparison we have constructed a synthetic control group which resembles the treated counties in terms of observable characteristics and pretreatment trends. In addition, we have made use of an econometric model that controls for heterogeneity in pre-trends between the treated and the control counties. We argue that this degree of sophistication helps to reduce the risk of erroneously attributing different macroeconomic trends that result from differences between the groups of treated and control counties to the HRS. But we acknowledge that there is, ultimately, no formal way of affirming that the true counterfactual trend has been established. What can be done is to evaluate the likelihood that our empirical design reveals a treatment effect where, in effect, there is no treatment. We summarize the results of three falsification tests here and refer to the Supplementary Appendix (sections 3-F, 3-G, 3-H) for a detailed discussion. We begin with a classic ‘placebo’ study. We apply our empirical strategy to an HSR which was considered during the planning stage but never built. The track would also have had three intermediate stops in each of the involved federal states and would have passed through the economically and politically relevant cities of Bonn (the former federal capital located in North Rhine-Westphalia), Koblenz (the largest city in northern Rhineland-Palatinate) and Wiesbaden (the state capital of Hesse). The results are easily summarized. The mean treatment effect on the GDP across the three cities is near to and not statistically different from zero in all specifications. The separate treatment estimates by treated county produce significant estimates with mixed signs in the naïve DD specification, but no significant cumulative effects using synthetic counties as comparisons (although Wiesbaden has a near to 10% significance level positive long-run effect). We do not find any significant effect of the other outcome measures either, although there are large and positive point estimates for per-worker GDP (but even larger standard errors). Focusing on GDP as an outcome measure, we next conduct a placebo test in the spirit of Abadie et al. (2010). For every county in the donor pool (non-HSR counties), we use a synthetic county generated by the same method as in the baseline model to estimate a placebo treatment effect. We find that the actual average treatment effect (across the three intermediate towns) is outside the 90% confidence interval in the right tail of the distribution of placebo treatment effects (1000 random combinations of three placebo-treated counties). The key insight from this placebo test is that the method employed is unlikely to yield treatment effects similar to the ones estimated for the HSR counties by chance. This, placebo test, however, could be favorable to the actual treated counties because these are not randomly located in space. Instead, the treated counties are within a relatively close distance (compared to the average distance between counties in the study area) located almost exactly along a straight line. It is therefore more likely that unobserved spatially correlated characteristics have a similar impact on economic trends of the actual treated counties than for the randomly selected placebo-treated counties. To address this concern, we refine the selection process of placebo-treated counties to make the test more demanding. Again, we run a series of 1000 similar models, however, this time requiring that the placebo-treated counties are connected by a placebo HSR. In each iteration of the placebo test, we first randomly select one county as one endpoint of a placebo HSR (the placebo Cologne). Second, we randomly select another endpoint (the placebo Frankfurt) from all counties within a 140–180 km range (in terms of straight-line distances) of the first endpoint (the distance between Cologne and Frankfurt is 160 km). Third, we pick the three counties whose economic center (the largest city) is closest to a straight line connecting the two endpoints and define them as the treated counties (the placebo intermediate stops). Fourth, we create synthetic comparison counties for each of the placebo-treated counties according to our standard procedure. Fifth, we estimate the naïve DD model (Table 2, column (3) model, which uses all nontreated control counties and does not control for trends) as well as our preferred model (Table 2, column (6) model, which uses synthetic control counties and controls for trends) and save the point estimates and significance levels. Of the 1000 tests, 8.4% (24%) deliver significant treatment effects after 6 years using our preferred (naïve) DD model; 5.6% (8.2%) iterations resulted in treatment effects that were significant (at the 10% level) and at least as large as our benchmark estimates. The mean of the point estimate is very close to zero. Notably, the standard deviation across placebo point estimates with 8.6% (5.4%) is relatively large compared to our 8.4% (5.7%) treatment estimate. We conclude that it is unlikely that our empirical specification delivers significant treatment effects that are spurious. 4. Agglomeration effects Given the results presented so far it seems fair to conclude that the HSR has had a positive impact on the economies of the counties of the intermediate stops. This impact is in line with the idea that an increase in (market) accessibility should increase the attractiveness of a location as a place of production. In the next step, we seek to model the change in accessibility pattern induced by the HSR more fully to gain insights into the strength and the spatial scope of agglomeration forces. 4.1. Empirical strategy In our baseline empirical model, we assume that the output in county i in year t denoted by Qit depends on effective density Dit as well as arbitrary county effects ci and year effects dt.   lnQit=δ1lnDit+ci+dt+εit, (4.1) where δ1 is the elasticity of output with respect to effective density for marginal changes in D and εit is a random error. We hypothesize that, all else equal, access to a larger economic mass should increase firm productivity and lead to higher economic output. We model effective density as a function of output across all counties j within reach and, thus, assume a black-box agglomeration force that depends on the productivity of all non-land inputs. Specifically, we allow for bilateral productivity externalities between all counties, assuming that the spillover effect declines exponentially in a measure of effective distance Eij between regions i and j, which takes into account the availability of transport infrastructure. Our measure of effective density thus takes the market potential form (Harris, 1954), which is popular in the theoretical (Fujita and Ogawa, 1982; Lucas and Rossi-Hansberg, 2002) and empirical (Ahlfeldt et al., 2015; Ahlfeldt and Wendland, 2013) agglomeration economics literature. Similar measures have been used in the empirical NEG literature (Hanson, 2005; Redding and Sturm, 2008).   Dit=∑jQje-δ2Eij, (4.2) where δ2>0 determines the rate of spatial decay of the productivity effect in effective distance between two regions i and j.16 The strength of the market potential formulation is that it effectively allows the productivity effect of spatial externalities to vary in effective distance to the surrounding economic mass without imposing arbitrary discrete classifications. Instead of assuming that externalities operate within the administrative borders of a region or contiguous groups of regions, our measure of effective density also accounts for externalities across such borders. Estimating the parameters of interest δ1 and δ2 is challenging for a variety of reasons. First, it is difficult to control all location factors subsumed in ci, which impact on productivity and are potentially correlated with the agglomerations measure. Second, there is a mechanical endogeneity problem because the dependent variable output (Qit) also appears in the market potential of regions i = j. Unobserved shocks to output can therefore lead to a spurious correlation between the outcome measure and effective density. The problem is nontrivial given that internal effective distance Eij=i is typically short so that the Qij=i receives a relatively high weight. Third, it is likely that shocks to outputs are spatially correlated so that the same problem also applies to nearby areas i and j. The first problem can be addressed by estimating Equation (4.1) in differences so that unobserved time-invariant location factors are differentiated out as, for example, in Hanson (2005). Informed by the program evaluation results, we take long differences over the construction period from 1998 to 2002 in our baseline estimation, but we consider alternative end dates in an alternative specification. The second problem, in principle, can be mitigated by aggregating right-hand side areas j to larger spatial units (e.g. Hanson, 2005) or replacing Qij=i with imputed values (Ahlfeldt and Wendland, 2013). Both strategies come at the cost of losing information. The third problem is even more difficult to address since shocks to output at nearby regions are likely correlated not only in levels but also in trends. Our empirical strategy addresses the abovementioned problems by exploiting the variation in bilateral transport times created by the HSR. We set the output levels at all locations j to Qjt=1998 in both periods, so that the identification comes exclusively from changes in effective distance. Our estimation equation thus takes the following form:   lnQi,t=2002-lnQi,t=1998=δ0+δ1ln∑jQj,t=1998e-δ2Eij,t=2002-ln∑jQj,t=1998e-δ2Eij,t=1998+Δεi (4.3) We stress that this specification differs from a conventional first-difference approach in that the first difference in the market potential is driven by changes in the travel time, but not output. Specification (4.3) is estimated using a nonlinear least squares estimator to simultaneously determine both parameters of interest (δ1 and δ2). With the estimated parameters it is then possible to express the effect of an increase in economic mass at j by one unit of initial market potential of county i on the outcome of county i as a function of the bilateral effective distance:   ∂log(Qi)∂(Qj)×∑jQje-δ2Eij=δ1^exp(-δ2^Eij) (4.4) Similar increases in economic mass are expected to benefit a county more if it happens in a county within a shorter effective distance. We consider several alterations of specification (4.3) for the purposes of validation, falsification and evaluation of robustness. We estimate Equation (4.3) using the GVA in various industry sectors as an outcome variable. We consider a grid search over a large parameter space δ1,δ2 to evaluate whether the agglomeration and spillover parameters are credibly separately identified. We contrast our results with those derived from a market potential specification that allows for more flexibility in the spatial decay. We allow for trends correlated with initial sectorial composition, workforce qualification and exposure to agglomeration. We also control for trends pre-existing the construction of the HSR and explore the temporal pattern of adjustment using an alternative panel specification. Importantly, we use instrumental variables to restrict the identifying variation to the portion that is not only exogenous with respect to the timing, but also with respect to the routing of the HSR. For falsification, we make use of the placebo HSR, which was considered but never built, and public sector GVA as an outcome, which we expect not to respond to the HSR, at least in the short run. Finally, we replicate the main stages of the analysis using per-worker GDP as a dependent variable to connect more closely to the literature on the productivity effects of density. In this alternative specification we will also control for changes in the industry sector structure and workforce qualification to address selection effects. 4.2. Approximation of effective distance To implement the empirical strategy laid out above we require empirical approximations of the bilateral travel costs between each pair of counties in the study area, the effective distance. To compute our measures of effective distance we make use of a Geographic Information System (GIS) and the information on transport infrastructure displayed in Figure 4. In connecting two counties we refer to the largest cities within the pair of counties as the respective centers of economic mass (the black dots in Figure 4). In computing the effective distance we assume that transport costs are incurred exclusively in terms of travel time and that route choice is based on travel time minimization. The identifying variation stems exclusively from the HSR line in question. We abstract from any other change in transport technology. Figure 4 View largeDownload slide The transport infrastructure in the study area. Note: Market potential based on Equation (4.2) and the decay parameter estimate (δ2) from Table 5, column (1). Figure 4 View largeDownload slide The transport infrastructure in the study area. Note: Market potential based on Equation (4.2) and the decay parameter estimate (δ2) from Table 5, column (1). To solve for the least-cost matrix connecting all potential origins and destinations we assign travel times to each fraction of the transport network, which are based on the network distance and the following speeds: 160 km/h for HSR, which is roughly in line with the 70-min journey along the 180 km Cologne-Frankfurt HSR line; 80 km/h for conventional rail, which is roughly in line with the 140-min journey along the 205 km conventional rail line; 100 km/h for motorways and 80 km/h on the other primary roads. In combining these transport modes we experiment with different procedures. In our benchmark cost matrix we allow travellers to change from roads to conventional rail in any city (they all have rail stations) and from any mode to HSR at the dedicated HSR stations (white circles in Figure 4) if in the respective period HSR is available. For robustness checks, we compute travel times according to two alternative decision rules. In one version, travellers can choose either the automobile or rail, including HSR if available, but they are not allowed to switch mode during a journey. In a further alternative, we eliminate the automobile altogether. Since the automobile is typically the more competitive mode, the resulting change in travel time reflects an upper bound of the true accessibility gain. In each case, we approximate the average internal travel time within a region i = j as the travel time that corresponds to a journey at 80 km/h (primary road) along a distance that corresponds to two-thirds of the radius of a circle with the same surface area. Figure 5 summarizes the distribution of travel times across the 1152=13,225 county pairs in the situations with and without HRS according to the baseline decision rule and the rail-only alternative. Evidently, the introduction of HSR had a significant impact on the competitiveness of the rail network as reflected by the major shift in the distribution of rail travel times (dashed lines) toward the distribution of road travel times (black solid line). Prior to HSR, the road network offered faster connections for almost all county pairs so that the road travel time matrix effectively describes the least-cost matrix (black solid lines). As expected, adding HSR as a potential mode that can be combined with the automobile reduces travel times significantly on a number of routes, especially on those that would otherwise take 50 min or more (red solid line). Figure 5 View largeDownload slide Distributions of bilateral travel times. Notes: Black (gray) solid line shows the distribution of bilateral travel times on roads (the fastest combination of car and rail including HSR). Black (gray) dashed line shows the distributions for rail excluding (including) HSR. Vertical lines denote the respective means of the distributions. Figure 5 View largeDownload slide Distributions of bilateral travel times. Notes: Black (gray) solid line shows the distribution of bilateral travel times on roads (the fastest combination of car and rail including HSR). Black (gray) dashed line shows the distributions for rail excluding (including) HSR. Vertical lines denote the respective means of the distributions. 4.3. Market potential effects on output: baseline results Column (1) in Table 5 summarizes the results of estimating the model given by Equation (4.3) using ln regional GDP as the economic outcome. The estimates point to positive spillover effects, which decay in distance. Given an 18.5% elasticity of output with respect to market potential, a doubling in market potential implies an increase in GDP by 20% (= exp(0.185)−1). The strength of spillovers decays by 2.3% every minute, which corresponds to a half-life travel time of about 30 min. It takes about 200 min before the strength of the spillovers diminish to around 1%. The black line in Figure 6 illustrates the implied productivity effect of an increase in economic mass at location j by one unit of total market potential at location i. Based on this estimated spatial decay, we illustrate the change in market potential in Figure 1. Not surprisingly, Montabaur (the primary town in its county) experiences the largest accessibility gain from HSR. Combining the change in market potential by 0.34 log points with the estimated market potential elasticity the predicted increase in GDP for Montabaur is about 6%, which is close to the cumulated effect after 3 years detected in the ‘Program Evaluation’ section. Table 5 Market potential effects on output by sectors   (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Sector  All  Construction  Mining  Manufacturing  Financial services  Other services  Δln Market potential ( δ1)  0.185*** (0.051)  0.360** (0.167)  0.320** (0.124)  0.331*** (0.118)  0.379*** (0.116)  0.155 (0.094)  Decay ( δ2)  0.022**  0.021  0.033  0.032*  0.014  0.010    (0.011)  (0.014)  (0.022)  (0.018)  (0.013)  (0.022)  R2  0.054  0.036  0.030  0.037  0.050  0.021  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Sector  All  Construction  Mining  Manufacturing  Financial services  Other services  Δln Market potential ( δ1)  0.185*** (0.051)  0.360** (0.167)  0.320** (0.124)  0.331*** (0.118)  0.379*** (0.116)  0.155 (0.094)  Decay ( δ2)  0.022**  0.021  0.033  0.032*  0.014  0.010    (0.011)  (0.014)  (0.022)  (0.018)  (0.013)  (0.022)  R2  0.054  0.036  0.030  0.037  0.050  0.021  N  115  115  115  115  115  115  Notes: Estimation method is nonlinear least squares in all models. Robust standard errors (in parentheses) of the market potential coefficient δ1 are heteroskedasticity robust and computed in separate ordinary least squares (OLS) regressions holding the decay parameters ( δ2) constant at the levels estimated in the non-linear least squares (NLS) models reported in the table. The market potential of region i is the transport cost weighted sum of output in all regions j. The change in market potential is driven by changes in travel cost between regions exclusively. Regional output is held constant at 1998 level. *p < 0.1, **p < 0.05, ***p < 0.01. Figure 6 View largeDownload slide Market potential effect on output by effective distance. Notes: The figure shows the effect of a hypothetical increase in output at county j by one unit of initial market potential at county i on log output of county i. The figure illustrates agglomeration spillover effects as defined as in Equation (4.4). Estimates of δ1 and δ2 from Table 2. Figure 6 View largeDownload slide Market potential effect on output by effective distance. Notes: The figure shows the effect of a hypothetical increase in output at county j by one unit of initial market potential at county i on log output of county i. The figure illustrates agglomeration spillover effects as defined as in Equation (4.4). Estimates of δ1 and δ2 from Table 2. The remaining columns in Table 5 present results according to Equation (4.3) replacing regional GDP with the GVA of various industry sectors as the outcome variable. The estimated spillover effects are visualized in Figure 6 as gray lines. The estimates are generally within the range of column (1). For some sectors the parameters are, however, estimated less precisely. The results also suggest that the market potential elasticity estimated in column (1) is brought down somewhat by sectors that are apparently less susceptible to agglomeration benefits, namely services other than financial services. For construction, mining, manufacturing and financial services the elasticity of output with respect to market potential is relatively large. As the HSR line is used exclusively for passenger transport, we expect to capture Marshallian externalities related to human interactions. Candidates are knowledge spillovers due to formal and informal meetings, improved labor market access and matching, as well as improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs but not freight costs. Our results are thus principally comparable to Ahlfeldt et al. (2015) and Ahlfeldt and Wendland (2013) who have estimated the effects of spillovers on productivity from within-city variation. These studies have found spillover effects that are significantly more localized. The spillover effect in these studies decays to near to zero within about half a kilometer, which is in line with Arzaghi and Henderson (2008) who also focus on within-city variation. Compared to these studies the lower spatial decay suggests that we are capturing different types of spatial externalities. While the steep spillover decay in the within-city studies points to a dominating role of face-to-face contacts that purposely or accidently happen at high frequency in the immediate neighborhood (Storper and Venables, 2004), our results suggest that the HSR effects operate at an intermediate range and through the benefits of shared inputs and labor pools, labor market matching or increases in consumer and producer market access. This interpretation is also in line with the significantly lower spatial decay found in an empirical NEG studies with an emphasis on trade costs (Hanson, 2005). 4.4. Market potential effects on output: validation, robustness and falsification As in any market potential equation, the elasticity and decay parameters are not necessarily separably identified. In fact, it is only the (ad hoc) functional form of the spatial decay imposed in the market potential formulation (Equation (4.2)) that allows us to separately estimate the market potential elasticity ( δ1) and the decay parameter ( δ2). In general terms, a larger decay parameter δ2 implies that more distant regions enter the market potential with a lower weight, reducing the degree of implicit spatial smoothing. The resulting larger variation in the market potential normally implies a lower estimate of the elasticity parameter δ1. As there could be multiple combinations of these critical parameters that fit the data we have run a grid-search over 500 possible values of δ1 and δ2(0.001–0.5) resulting in 250,000 parameter combinations for each of the models reported in Table 5. For each parameter combination, we compute the root sum of the square deviations between the observed and predicted changes in regional output. As illustrated in Figure 7, we find relatively clearly defined global minima, supporting the parametric estimates presented in Table 5 and Figure 6. This robustness check using an alternative approach to identifying the elasticity and decay parameters increases our confidence in the point estimates of the decay parameters estimated with large standard errors reported in Table 5. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Figure 7 View large Download slide Market potential effect on output: Grid searches over parameter space. Notes: Dark shades indicate a low root sum of square error in ‘predicted change log output’—'actual change log output', where predicted change in log output and actual change in log output are normalized to have a zero mean. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Output is measured in GDP for all non-public sectors, and GVA for all other sectors. Services exclude financial services (Finance) and public services. Class thresholds correspond to the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th and 99th percentile in the distribution within the parameter space delta 2 = {0,0.1}. White circles denote NLS point estimates from Table 5. X-axis in ln scale. Figure 7 View large Download slide Market potential effect on output: Grid searches over parameter space. Notes: Dark shades indicate a low root sum of square error in ‘predicted change log output’—'actual change log output', where predicted change in log output and actual change in log output are normalized to have a zero mean. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Output is measured in GDP for all non-public sectors, and GVA for all other sectors. Services exclude financial services (Finance) and public services. Class thresholds correspond to the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th and 99th percentile in the distribution within the parameter space delta 2 = {0,0.1}. White circles denote NLS point estimates from Table 5. X-axis in ln scale. In Table 6, we present a series of alterations of the baseline model in column (1) of Table 5. We fix the decay parameter to the value estimated in the baseline model (Table 5, column (1)) so the market potential elasticity remains comparable across alternative models. In columns (1–3), we control for trends that may be correlated with but are economically unrelated to the change in market potential and potentially confound the estimates. The purpose of these models is, thus, similar to the matching on observables we imposed in the construction of synthetic counties in the ‘Program Evaluation’ section. In model (4), we additionally control for the (1992–1997) pre-trend in log GDP to account for the possibility that unobserved county characteristics determine long-run growth trends.17 This control serves a similar purpose to the matching on pre-trends in the construction of the synthetic counties and the control for heterogeneity in pre-trends in the program evaluation DD model. The market potential elasticity decreases somewhat but remains significant and within the range of the baseline estimate. In model (5), we exploit that the timing and the routing of the HSR line can be assumed to be exogenous for the intermediate stops (Limburg, Montabaur, Siegburg) while ‘only’ the timing (and not the routing) is exogenous for the endpoints Cologne and Frankfurt. To restrict the variation in change in market potential to the fraction that is most plausibly exogenous we instrument the change in market potential with three indicator variables, each denoting one of the counties in which the intermediate stops are located. The market potential elasticity remains significant, but decreases somewhat further to about 12.5%. The instruments are strong (F-stat > 10) and while we prefer to justify the instruments on theoretical grounds (they restrict the identification to plausibly exogenous variation), we note that a Sargan-Hansen test does not reject validity. In model (6), we use GVA in the public sector instead of total GDP as the left-hand side measure of output. We view this model as a placebo test because the spatial distribution of this sector is unlikely to be determined by economic agglomeration forces, at least in the short run. In line with this interpretation we find a nonstatistically significant near to zero agglomeration effect. So far we have estimated the agglomeration effects induced by the HSR line assuming that economic adjustments took place between 1998 and 2002. This choice is based on the results presented in the ‘Program Evaluation’ section, where we find that each of the counties of the intermediate stops experienced a substantial impact over this period. To evaluate the temporal pattern of the adjustment and to empirically substantiate the chosen adjustment period, we estimate a time-varying treatment effects model such as in Ahlfeldt and Maennig (2015), where the treatment measure is the change in market potential used in Table 6. With this model, we estimate a series of market potential elasticities, each of which is identified from a comparison between long-differences in log GDP and log market potential taken over a treatment year n and the base year 1998. We set up the model such that the identifying variation corresponds to our most conservative long-difference model in Table 6, column (5), i.e. we control for trends correlated with observables and restrict the identifying variation to the intermediate stops using instrumental variables. The exact details of the specification are in the notes to Figure 8, which presents the resulting estimated market potential elasticity series. Figure 8 View largeDownload slide Market potential elasticity: Time-varying estimates. Notes: The figure is based on the following panel specification: lnQit=∑n≠1998δ1,nΔlnDi×(t=n)+Xitbt+ci+dt+εit, where Qit is the output measured as GDP of county i in year t, n indexes treatment years from 1992 to 2009, excluding the base year 1998, ΔlnDi is the change in market potential assuming the decay parameter estimated in Table 5, column (1), Xit is a vector year effects interacted with a vector of the following variables: industry shares at total 1998 GVA (construction, manufacturing, mining, financial services and other nonpublic services), the share of the workforce (at place of work) holding a university degree in 1998, the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. bt is a matrix of coefficients for each variable–year combination. ci and dt are county and year effects as in Equation (4.1). We instrument the vector of change in market potential × year interaction terms ΔlnDi×(t=n) using a full set of interaction terms between year effects and three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. Black dots represent point estimates of δ1,n and the gray shaded area denotes the 95% confidence intervals (standard errors clustered on the counties). Vertical dashed lines frame the period over which long-difference are taken in Tables 5 and 6. The upper horizontal dashed lines indicates the market potential elasticity estimated in Table 6, column (5) model, which in terms of the identifying variation is comparable to the model presented. Figure 8 View largeDownload slide Market potential elasticity: Time-varying estimates. Notes: The figure is based on the following panel specification: lnQit=∑n≠1998δ1,nΔlnDi×(t=n)+Xitbt+ci+dt+εit, where Qit is the output measured as GDP of county i in year t, n indexes treatment years from 1992 to 2009, excluding the base year 1998, ΔlnDi is the change in market potential assuming the decay parameter estimated in Table 5, column (1), Xit is a vector year effects interacted with a vector of the following variables: industry shares at total 1998 GVA (construction, manufacturing, mining, financial services and other nonpublic services), the share of the workforce (at place of work) holding a university degree in 1998, the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. bt is a matrix of coefficients for each variable–year combination. ci and dt are county and year effects as in Equation (4.1). We instrument the vector of change in market potential × year interaction terms ΔlnDi×(t=n) using a full set of interaction terms between year effects and three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. Black dots represent point estimates of δ1,n and the gray shaded area denotes the 95% confidence intervals (standard errors clustered on the counties). Vertical dashed lines frame the period over which long-difference are taken in Tables 5 and 6. The upper horizontal dashed lines indicates the market potential elasticity estimated in Table 6, column (5) model, which in terms of the identifying variation is comparable to the model presented. As expected, we find no significant response in the spatial distribution of economic activity to the market potential shock for treatment years n < 1998, while the estimates of the market potential elasticity converge to the estimate in Table 6, column (5), relatively quickly for treatment years n > 1998. By 2000, still in anticipation of the opening of the line in 2002, the spatial economy seems to have adjusted to the market potential shock as the time-varying estimates of the elasticity then remain relatively stable for a number of consecutive years. This pattern is suggestive of an impact of the HSR on the level, but not the trend of economic activity. In 2006, however, we observe a further relative shift in economic activity in regions which benefited from the HSR. Looking at the overall trend in the economic adjustment, this shift seems somewhat detached from the market potential shock, and it remains ultimately difficult to assert whether or not this shift is causally related to the HSR. We have conducted a number of further alterations of our baseline model, which we briefly discuss in the remainder of this subsection. A more detailed discussion can be found in the Supplementary Appendix. The exponential functional form of the spatial decay in spillovers, while popular in the theoretical and empirical literature (e.g. Fujita and Ogawa, 1982; Lucas and Rossi-Hansberg, 2002; Ahlfeldt et al., 2015), is ad hoc and other functional forms are theoretically imaginable. We have estimated an alternative version of our benchmark model in which the market potential is captured as the total GDP within several mutually exclusive 20-min travel time bins (e.g. 0–20 min, 20–40 min, etc.). For each travel time bin a separate market potential elasticity is estimated, thus allowing for a more flexible pattern in the spatial decay. When comparing the predicted effects of the change in market potential on GDP in this alternative model to our baseline model, we find an approximately linear relationship, suggesting that our results are not driven by an inappropriate functional form of the spatial decay (see Supplementary Appendix section 4-B). On a related note, we have addressed the insignificant sectoral market potential decay parameters by estimating the market potential elasticity imposing the decay parameter estimated across all sectors, which is highly significant. With the exception of ‘other non-public services’, whose effect is already not significant in Table 5, the market potential estimates remain within close range of the results reported in Table 5 (see Supplementary Appendix section 4-B). We have experimented with alternative travel choice models underlying the construction of travel times. In one alternative choice model, we disallow switching from train to automobile or vice versa along a journey. In another alternative choice model, we disallow the use of the automobile altogether. The results remain qualitatively unchanged and quantitatively within the range of the results presented here (see Supplementary Appendix section 4-C). We have also experimented with alternative instrumental variables to restrict the identification to variation in the change in market potential to the fraction that arises from the intermediate transport stations. In particular, we consider the log straight-line distance to Montabaur and indictor variables for the counties of the intermediate stops as well as the adjacent counties as alternatives. The results remain close to those reported in Table 6 (see Supplementary Appendix section 4-D). Finally, we have also replicated the main stages of our analysis replacing the actual HSR with the considered but never built placebo HSR, which we introduced in the previous section. We find no robust evidence of HSR effects in this falsification exercise (see Supplementary Appendix section 4-E). 4.5. Market potential effects on productivity As discussed in the introduction, a large literature has analyzed agglomeration effects by regressing a measure of productivity against a measure of density. In order to connect to this literature and to assess to which extent the market potential (effective density) effect on GDP discussed above is attributable to an increase in productivity of the labor force (rather than an expansion of the labor force), we replicate our baseline model using the ratio of GDP over the total employment (at workplace) as a dependent variable. The empirical specification used shared similarities with the nominal wage equation estimated in the NEG literature (e.g. Hanson, 2005) . In Table 7, we present the results of three OLS (columns (1)–(3)) and three 2SLS (columns (4)–(6)) estimations. In each case, we present unconditional correlations between per-worker GDP growth and change in log market potential, a version using the same controls as in Table 6, column (4), and one version where we additionally account for changes in the industry structure and the skill composition of the workforce. The instrumental variables used are the same as in Table 6, column (5). Table 7 Productivity effects   (1)  (2)  (3)  (4)  (5)  (6)    ΔLn (GDP/Employment (workplace)) 1998–2002    OLS  OLS  OLS  2SLS  2SLS  2SLS  Δln Market potential ( δ1)  0.066 (0.059)  0.132** (0.058)  0.009 (0.048)  0.170*** (0.055)  0.108* (0.062)  0.042 (0.059)  Industry shares  −  Yes  Yes  −  Yes  Yes  Degree share  −  Yes  Yes  −  Yes  Yes  Agglomeration effects  −  Yes  Yes  −  Yes  Yes  Δln GDP/Employment (workplace) 1992–1997  −  Yes  Yes  −  Yes  Yes  Composition effects  −  −  Yes  −  −  Yes  R2  0.007  0.148  0.495  −  0.147  0.487  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    ΔLn (GDP/Employment (workplace)) 1998–2002    OLS  OLS  OLS  2SLS  2SLS  2SLS  Δln Market potential ( δ1)  0.066 (0.059)  0.132** (0.058)  0.009 (0.048)  0.170*** (0.055)  0.108* (0.062)  0.042 (0.059)  Industry shares  −  Yes  Yes  −  Yes  Yes  Degree share  −  Yes  Yes  −  Yes  Yes  Agglomeration effects  −  Yes  Yes  −  Yes  Yes  Δln GDP/Employment (workplace) 1992–1997  −  Yes  Yes  −  Yes  Yes  Composition effects  −  −  Yes  −  −  Yes  R2  0.007  0.148  0.495  −  0.147  0.487  N  115  115  115  115  115  115  Notes: Robust standard errors in parentheses are heteroscedasticity robust. Δln Market potential ( δ1) is based on Equation (4.2) and the decay parameter ( δ1) from Table 5, column (1). Industry shares are shares at total 1998 GVA in the following sectors: construction, manufacturing, mining, financial services and other services. Degree share is the share for the workforce (at place of work) holding a university degree in 1999. Agglomeration effects include the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. Composition effects are 1998–2002 changes in industry shares and 1999–2002 degree share. Instrumental variables in columns (4)–(6) are three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. *p < 0.1, **p < 0.05, ***p < 0.01. The preferred results in columns (2) and (5) suggest that the increase we find in GDP is driven by an increase in worker productivity, rather than an expansion of the workforce, as the estimated elasticity is within the range of the models in Table 6. In comparing these results to the literature on the productivity effects of density it is important to acknowledge that unlike conventional density measures, our market potential takes into account the economic activity in surrounding regions, albeit with a lower weight. As a measure of effective density the market potential therefore introduces a spatial autocorrelation, which reduces variation in effective density across counties. It turns out that the standard deviation in the 1998 log market potential across counties in our data is almost three times the standard deviation in the 1998 log employment density. Our elasticity of productivity with respect to effective density is, therefore, not directly comparable to the majority of estimates in the agglomeration economics literature as a 1% increase in market potential, on average, implies a much larger percentage increase in density. Normalized by the log ratio of the standard deviations of effective density (market potential) over density (employment per area), our results imply a 3.8% elasticity of productivity with respect to employment density, which is close to previous estimates derived from cross-sectional research designs (e.g. Ciccone and Hall, 1996; Ciccone, 2002). Once we control for changes in the industry sector and skill composition the productivity effect is substantially reduced and is no longer significantly different from zero (columns (3) and (6)). One interpretation is that the increase in per-worker output is driven by a relative expansion of, on average, more productive and skill-intensive sectors, which benefit particularly from HSR. This may suggest that the economic adjustments are primarily due to selection instead of agglomeration effects (Combes et al., 2012). Another interpretation is that our controls for sector and skill composition are endogenous and we may be over-controlling, a bad control problem as discussed by Angrist and Pischke (2009). 5. External validity Before we draw conclusions in the next section, some words are due on the external validity of our findings. As with most attempts to improve identification, our variant of the inconsequential units approach (Redding and Turner, 2015) provides local treatment effect estimates as we infer a causal effect from a large accessibility shock on small towns. If marginal agglomeration benefits were concave in city size, HSR effects could be smaller for the typically connected large cities. It is not possible for us to test for such a concave relationship since our inconsequential units approach is not suited for large metropolitan areas that are connected purposely (implying a potential for reverse causality). That said, the fact that the implied elasticity of productivity with respect to a density of 3.8% (previous subsection) is close to the average of comparable estimates in the literate (Melo et al., 2009), is at least suggestive that our results have some generalizability. As with every case study, some factors are specific to our context and are worth considering before transferring conclusions to other contexts. As mentioned in Section 2.1, the Cologne–Frankfurt HSR was built parallel to a highway (A3) and the presence of such a substitute may affect the effects of the HSR as much as the technology of the HSR itself. If one is willing to accept that our estimated parameters hold some external validity, our market potential approach can be used to compute counterfactual outcomes as follows:   Δln(Qi)̂=δ^1ln∑jQj,t=1998e-δ^2Eij,t=post-ln∑jQj,t=1998e-δ^2Eij,t=pre (5.1) where δ^1 is our preferred estimate of the elasticity of output with respect to effective density and δ^2 is our preferred estimate of the spatial decay. All variables are defined as in Equation (4.3). It is possible to compare predicted outcomes Δln(Qi)̂ across different scenarios by solving Equation (7.1) assuming different speeds on the rail and road network in the transport matrices Eij,t=(pre,post) before (pre) and after (post) the HSR opening. In Table 8, we first increase the speed on the HSR (1–4, 2 is the actual scenario) before we eliminate the highway (5) and increase the speed of the highway (6). Without the highway (5), the effects on the three intermediate towns would have been even larger and roughly as large the effect of an HSR operating at a 40 km/h (25%) higher average speed (assuming there are no complementarities between the HSR and the highway). In keeping with intuition, increasing the speed on the highway by 20 km/h (6) has roughly the same effects as reducing the speed of the HSR by about 20 km/h. Table 8 Counterfactual scenarios   (1)  (2)  (3)  (4)  (5)  (6)  HSR speed (km/h)  140  160  180  200  160  160  Highway speed (km/h)  100  100  100  100  0  120  Limburg GDP effect (%)  3.16  4.55  5.73  6.75  6.62  2.37  Montabaur GDP effect (%)  4.85  6.40  7.65  8.71  9.14  4.02  Siegburg GDP effect (%)  1.63  2.25  2.79  3.27  3.29  1.33  Total GDP effect (€, billion)  5.16  7.90  10.46  12.88  10.99  4.53  Extra GDP effect in % of actual (2)  −34.74  0  32.41  63.03  39.01  −42.67    (1)  (2)  (3)  (4)  (5)  (6)  HSR speed (km/h)  140  160  180  200  160  160  Highway speed (km/h)  100  100  100  100  0  120  Limburg GDP effect (%)  3.16  4.55  5.73  6.75  6.62  2.37  Montabaur GDP effect (%)  4.85  6.40  7.65  8.71  9.14  4.02  Siegburg GDP effect (%)  1.63  2.25  2.79  3.27  3.29  1.33  Total GDP effect (€, billion)  5.16  7.90  10.46  12.88  10.99  4.53  Extra GDP effect in % of actual (2)  −34.74  0  32.41  63.03  39.01  −42.67  Notes: Table illustrates the relative and aggregate GDP effects of the HSR under different average speeds of the two modes (first two lines). Counterfactual outcomes are computed as Δln(Qi)̂=δ̂1ΔDî, where δ̂1 is our preferred estimate of the elasticity of output with respect to effective density. In computing the transport matrixes used to compute ΔDî we assume that individuals strictly choose the fastest route between any pairs of counties. They can switch between rail and car at any rail station. Another feature of the analyzed institutional context is complementary investments into infrastructure. Minor upgrades were made to the Siegburger Bahn (new overhead system, accessibility at selected stations), a light rail connecting Bonn to Siegburg (one of the intermediate stops). Station terminal buildings were newly constructed or expanded in Limburg, Montabaur and Siegburg, including some improvements to existing facilities, such as bus stops (Roggendorf and Schmidt, 1999). Much of the new or expanded business activity discussed in Section 2.1 is located in new business parks developed close to the new HSR stations. It is difficult to create a counterfactual describing the situation with the HSR, but without such complementary investments, because the anecdotal evidence overwhelmingly suggests that these measures would have had little impact without the HSR. We believe that the economic effects are best understood as originating from the combination of a substantial accessibility benefit and complementary measures that facilitate firms taking advantage of it. Our results, therefore, generalize to other contexts to the extent that similar complementary policies usually accompany the rollout of HSR. A final word concerns the entrepreneur Ralph Dommermuth, who founded one of the world’s largest web hosting companies (1&1) in his birthplace Montabaur. He is also an important investor involved in the development of the business park close to the Montabaur HSR station. Like the other stakeholders cited in Section 2, he stresses the role of the HSR as a critical ingredient for economic development, in particular the access to a wider labor market pool the HSR offers (Ferdinand, 2015). Yet, it seems possible that personal attachments to his birthplace partially motivated his strong engagement as an investor, implying that without a similarly wealthy and engaged citizen the HSR effects in Montabaur could have been more moderate or, at least, delayed. 6. Conclusion We analyze the economic effects of the Cologne–Frankfurt HSR in Germany, which connects the two major economic core regions in Germany and a number of peripheral regions along the way. Due to the institutional setting the HSR represents one of the rare occasions where transport improvements provide plausibly exogenous variation in access to surrounding economic mass. We find that the average GDP in the counties of the intermediate stops 6 years after the opening of the line exceeds a counterfactual trend by 8.5%. We make further use of the quasi-experimental variation provided by the HSR to contribute to a literature that has focused on estimating the strength and scope spatial scope of agglomeration effects. We find an elasticity of output with respect to effective density, i.e. market potential, of about 12.5% in our most conservative model. Our results further imply an elasticity of productivity with respect to density of 3.8%, which is well within the range of existing cross-sectional estimates. The strength of spillovers halves every 30 min of travel time and is near to zero after about 200 minutes. The spillovers we detect are significantly less localized than in previous studies that have identified similar spillover effects from within-city variation, but more localized than those found in the empirical NEG literature with an emphasis on trade cost. The benefits HSR has delivered to the peripheral regions operate through knowledge diffusion and labor market pooling and the effects of improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs, and thus, Marshallian externalities (Marshall, 1920). Our results complement recent evidence suggesting that improved transport linkages can benefit core regions at the expense of peripheral regions through a trade channel (Faber, 2014). Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Footnotes 1 The transport appraisal literature distinguishes between user benefits, which mainly capture the value of shorter travel times, and wider economic impacts, such as agglomeration benefits due to higher effective density, moves to more productive jobs and output changes in imperfectly competitive markets (Department for Transport, 2014). 2 Storeygard (2012) uses changes in oil prices interacted with static distance measures as a source of variation in transport cost over time. 3 Complementary literature has modeled the mutual dependence of demand for and supply of transport infrastructure (Levinson, 2008; Xie and Levinson, 2010). 4 We create a synthetic equivalents for each treated county following Abadie and Gardeazabal (2003). 5 Reviewing 729 estimates across 34 studies, Melo et al. (2009) find a mean elasticity of 5.8%. 6 See Head and Mayer (2004) for a review of this literature. For an introduction into the theoretical and empirical literature on agglomeration, productivity and trade, see e.g. Ottaviano et al. (2002), Behrens et al. (2014) or Sato and Zenou (2015). 7 Examples include Ciccone (2002), Ciccone and Hall (1996), Dekle & Eaton (1999), Glaeser and Maré (2001), Henderson, Kuncoro and Turner (1995), Moretti (2004), Rauch (1993) and Sveikauskas (1975). 8 Such a tendency of decentralization in response to reductions in transport costs is in line with standard urban models in the spirit of Alonso (1964), Mills (1967) and Muth (1969). 9 This finding is in line with evidence suggesting that well-developed transport infrastructures are associated with less spatial concentration (Ramcharan, 2009) 10 The straight-line distance between Cologne Main Station and Frankfurt Main Station is 152 km. 11 Among them: Landesbetrieb Mobilität RLP Autobahnamt, Unternehmensberatung Emc², Industrie- und Handelskammer (IHK), Ingenieurgesellschaft Ruffert und Partner, Objektverwalter S.K.E.T, Cafe Latino, Kantine Genuss & Harmonie. 12 Using GIS we find a 2002 population of 438,540 living within 10 km from Limburg, Montabaur, and Siegburg, while 1,020,474 residents lived within the same distance from Bonn, Koblenz and Wiesbaden. All distances are measured between municipality centroids as the crow flies. 13 These data are available at the website www.regionalstatistik.de. 14 We use the Stata ado file synth compiled by Hainmueller, Abadie and Diamond to generate the synthetic control counties. 15 The respective standard error is exp(var(θ^)+(t−2003)2×var(ϑ^P)+2×(t−2003)×cov(θ^,ϑ^P))−1 16 Our internal effective distance Eij=idepends on the land area of county i so that our measure corresponds to a standard density measure for the within county externalities. 17 We take the lagged log GDP long-difference over the period 1992–1997 instead of 1992–1998 to avoid a mechanical endogeneity problem that would arise if the 1998 log GDP was entered on both sides of the equation. Table 6 Agglomeration effects: expanded models   (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP all sectors 1998–2002  Δln GVA public services1998–2002    OLS  OLS  OLS  OLS  2SLS  OLS  Δln Market potential ( δ1)  0.149*** (0.048)  0.154*** (0.046)  0.154** (0.066)  0.138** (0.068)  0.125** (0.054)  −0.014 (0.081)  Industry shares  Yes  Yes  Yes  Yes  Yes  −  Degree share  −  Yes  Yes  Yes  Yes  −  Agglomeration effects  −  −  Yes  Yes  Yes  −  Δln GDP all sectors 1992–1997  −  −  −  Yes  Yes  −  F-stat (Cragg-Donald)  −  −  −  −  23.95  −  Hansen J (p-value)  −  −  −  −  0.33  −  R2  0.123  0.145  0.220  0.235  0.235  0.000  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP all sectors 1998–2002  Δln GVA public services1998–2002    OLS  OLS  OLS  OLS  2SLS  OLS  Δln Market potential ( δ1)  0.149*** (0.048)  0.154*** (0.046)  0.154** (0.066)  0.138** (0.068)  0.125** (0.054)  −0.014 (0.081)  Industry shares  Yes  Yes  Yes  Yes  Yes  −  Degree share  −  Yes  Yes  Yes  Yes  −  Agglomeration effects  −  −  Yes  Yes  Yes  −  Δln GDP all sectors 1992–1997  −  −  −  Yes  Yes  −  F-stat (Cragg-Donald)  −  −  −  −  23.95  −  Hansen J (p-value)  −  −  −  −  0.33  −  R2  0.123  0.145  0.220  0.235  0.235  0.000  N  115  115  115  115  115  115  Notes: Robust standard errors in parentheses are heteroscedasticity robust. Δln Market potential ( δ1) is based on Equation (4.2) and the decay parameter ( δ1) from Table 5, column (1). Industry shares are shares at total 1998 GVA in the following sectors: construction, manufacturing, mining, financial services and other services. Degree share is the share for the workforce (at place of work) holding a university degree in 1998. Agglomeration effects include the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. Instrumental variables in column (5) are three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. *p < 0.1, **p < 0.05, ***p < 0.01. Acknowledgements We thank seminar and conference participants at Berkeley, Barcelona, London, Jönköping, Kiel, New York, San Francisco and Vancouver, and especially Gilles Duranton, Henry Overman, Ian Gordon, Stephan Heblich, David King and Jeffrey Lin as well as two anonymous referees and the editor for valuable comments and suggestions. We gratefully acknowledge Per Kropp from the Institute for Employment Research for sharing commuting data. Patricia Schikora provided excellent research assistance. References Abadie A., Diamond A., Hainmueller J. ( 2010) Synthetic control methods for comparative case studies: estimating the effect of California’s tobacco control program. Journal of the American Statistical Association , 105: 493– 505. Google Scholar CrossRef Search ADS   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   Ahlfeldt G. M., Maennig W. 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From periphery to core: measuring agglomeration effects using high-speed rail

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Abstract

Abstract We analyze the economic impact of the German high-speed rail (HSR) connecting Cologne and Frankfurt, which provides plausibly exogenous variation in access to surrounding economic mass. We find a causal effect of about 8.5% on average of the HSR on the GDP of three counties with intermediate stops. We make further use of the variation in bilateral transport costs between all counties in our study area induced by the HSR to identify the strength and spatial scope of agglomeration forces. Our most careful estimate points to an elasticity of output with respect to market potential of 12.5%. The strength of the spillover declines by 50% every 30 min of travel time, diminishing to 1% after about 200 min. Our results further imply an elasticity of per-worker output with respect to economic density of 3.8%, although the effects seem driven by worker and firm selection. 1. Introduction ‘A major new high-speed rail line will generate many thousands of construction jobs over several years, as well as permanent jobs for rail employees and increased economic activity in the destinations these trains serve.’ —US President Barack Obama, 16 April 2009 One of the most fundamental and uncontroversial ideas in economic geography and urban economics is that firms and households benefit from access to economic markets due to various forms of agglomeration economies (Marshall, 1920). The mutually reinforcing effects of spatial density and productivity can theoretically account for the highly uneven distribution of economic activity between and within regions. The strong belief that economic agents benefit from an ease of interaction has always motivated large (public) expenditures into transport infrastructures, e.g. ports, airports, highways or railways. A striking example of an expensive, but increasingly popular transport mode is high-speed rail (HSR). The costs of implementing an HSR network in Britain, which mainly consists of a Y-shaped connection of London to Birmingham, Leeds and Manchester of about 500 km length are scheduled to amount to as much as £42 (about US$63) billion at present (Storeygard, 2012). The US Department of Transportation (2009) has announced its strategic plan, which proposes the construction of completely new rail lines that will feature velocities of possibly up to 400 km/h (250 mph). The plan has already identified US$8 billion plus US$1 billion per year for 5 years in the federal budget just to jump-start a program that would only be comparable to the interstate highway program of the 20th century. The perhaps most spectacular HSR considered to date is a 7000 km line connecting the Russian and Chinese capitals Moscow and Beijing, currently estimated at 1.5 trillion yuan (US$242 billion) (Phillips, 2015). The willingness to commit large amounts of public money to the development of HSR bears witness to the confidence that HSR will deliver a substantial economic impact. The wider economic impacts such infrastructures deliver, however, naturally depend on the strength and the spatial scope of the agglomeration economies they enhance.1 Estimating such agglomeration effects is empirically challenging. The density of economic activity and the productivity at a given location are not only potentially mutually dependent, but also potentially simultaneously determined by location fundamentals, such as a favorable geography or good institutions. The main challenge in estimating the strength and the spatial scope of agglomeration effects, therefore, is to find exogenous variation in access to the surrounding economic mass. While transport infrastructures, such as a new HSR, generate such variation in access to economic mass, the allocation of transport infrastructure is typically nonrandom, thus generating additional identification problems. In this article, we provide causal estimates of the strength and the spatial scope of agglomeration effects using a variation of the market potential approach, which links economic outcomes at a given locality to economic activity at surrounding localities via a transportation network. To disentangle the effects of market potential from other determinants of economic outcomes our identification stems exclusively from changes in transport technology, which affect the effective distance between all pairs of locations in a region.2 Specifically, we exploit the variation in bilateral transport costs between all counties located in the German federal states of North Rhine-Westphalia, Hesse and Rhineland-Palatinate that was induced by the Cologne–Frankfurt HSR. With this research design we are able to control for unobserved time-invariant variation in location fundamentals and circumvent some of the typical challenges in estimating the effects of spatial density on economic outcomes. Given the particular institutional setting we argue that the HSR analyzed provides variation in bilateral transport costs that is credibly exogenous, creating a natural experiment with identifying variation that is as good as random.3 The Cologne–Frankfurt HSR was inaugurated in 2002. The line is part of the Trans-European Networks and facilitates train velocities of up to 300 km/h. The HSR reduced travel time between both metropolises by more than 55% in comparison to the old rail connection and by more than 35% in comparison to the automobile. Along the HSR line, intermediate stops were created in the towns of Limburg, Montabaur and Siegburg. It is noteworthy that given the small population of less than 25,000 and 15,000 inhabitants, in particular, the stops in Limburg and Montabaur are unusual within the German if not European HSR network. Following the connection to the HSR line the two towns are within 40 min of Cologne and Frankfurt, which are the centers of the two largest German agglomerations, but also less than 10 min of each other. The final routing of the line and the location of the intermediate stops were the result of a political bargaining process among the rail carrier, three federal states and several business lobby and environmental activist groups that lasted almost 40 years. We argue that the institutional particularities, which we describe in more detail in Section 2, allow us to make the helpful identifying assumptions that the routing and the timing of the connection of Limburg, Montabaur and Siegburg and the timing of the connection of all other stations are exogenous to the levels and trends of economic development. Based on the exogenous variation provided, we are able to identify the causal impact of HSR on local economic development as well as the strength and the spatial scope of agglomeration economies promoted by the line. In the first step, we assess the effect of the HSR on the local economies within the counties of the intermediate stops using program evaluation techniques. In the second step, we correlate the growth in effective density, which we express in market potential form (Harris, 1954), to the economic growth across counties within our study area. The market potential expresses effective density as the transport cost weighted sum of the GDP of all counties in the study area. The measure takes into account the effect of the HSR on bilateral transport costs between all counties in our study area. Since the HSR is used exclusively for passenger service, we implicitly disentangle the effects of facilitated human interactions from the transport costs of tradable goods, i.e. the trade channel. The spillovers we capture thus include Marshallian externalities related to knowledge diffusion and labor market pooling and the effects of improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs, but not freight costs. Theoretically, one effect of the HSR is to upgrade the accessibility of formerly peripheral areas, which at least during a transition period offers the benefit of relatively low land prices, and may thus become attractive to firms. Indeed, our results point to a positive economic impact of HSR. On average, 6 years after the opening of the line, the GDP in the counties of the intermediate stops exceeds the counterfactual trend established via a group of synthetic counties by 8.5%.4 We find an elasticity of GDP with respect to effective density, i.e. market potential, of about 12.5% in our most conservative model. The elasticity of output per worker with respect to effective density is, at 10%, only marginally smaller. Because our measure of effective density is spatially smoothed the variance across counties is naturally lower than in conventional density measures. Normalized by the log ratio of the standard deviations of effective density over actual density our results imply an elasticity of productivity with respect to employment density of 3.8%, which is close to previous estimates derived from cross-sectional research designs (e.g. Ciccone and Hall, 1996).5 The effect, however, seems to be driven to a significant extent by selection, i.e. a compositional change in industry and worker qualification (Combes et al., 2011, 2012). We further estimate that the strength of economic spillovers halves every 30 min of travel time and is near to zero after about 200 min. The spillovers we detect are significantly less localized than in previous studies that have identified spillover effects from within-city variation (Arzaghi and Henderson, 2008; Ahlfeldt and Wendland, 2013; Ahlfeldt et al. 2015), but are more localized than the scope of spatial interactions inferred from empirical New Economic Geography (NEG) models with a stronger emphasis on trade costs (Hanson, 2005).6 Our research connects to a large and growing literature on the nature of agglomeration economies reviewed in detail in Duranton and Puga (2004) and Rosenthal and Strange (2004). A standard approach in this literature has been to regress economic outcome measures, such as wages, against some measure of agglomeration, typically employment or population density.7 A smaller literature has exploited presumably exogenous variation in the surrounding concentration of economic activity. Rosenthal and Strange (2008) and Combes et al. (2010) use geology to instrument for density. Greenstone et al. (2010) analyze the effects of the openings of large manufacturing plants on incumbent plants. Another related strand has analyzed the impact of natural experiments such as trade liberalization (Hanson, 1996, 1997), wartime bombing (Davis and Weinstein, 2002), the decrease in the economic relevance of portage sites (Bleakley and Lin, 2014) and the Tennessee Valley Authority (Kline and Moretti, 2014) on the spatial distribution of economic activity. At the intersection of both strands, Redding and Sturm (2008) have exploited the effects of the variation in access to the surrounding economic mass created by the division and unification of Germany on city growth. Ahlfeldt et al. (2015) use the within-city variation in surrounding economic mass induced by the division and reunification of Berlin, Germany, to identify the strength and spatial scope of spillovers among residents and among firms as well as the rate at which commuting probabilities decline in time distance. Our main contributions to this literature are 2-fold. First, we estimate the agglomeration effects based on the variation in surrounding economic mass created by new transport infrastructures, which allows for a relatively robust separation of spillover effects from unobserved locational fundamental effects. Second, we contribute to a relatively small literature that has provided estimates of the rate of spatial decay in spillovers. The relatively strong spatial decay in spatial spillovers substantiates the intuition that moving people is more costly than moving goods. Another growing strand in the literature to which we contribute is concerned with the economic effects of transport infrastructure. Overall, the evidence suggests that a well-developed transport infrastructure enhances trade (Duranton et al., 2014; Donaldson, 2015), promotes economic growth (Banerjee et al., 2012; Duranton and Turner, 2012), and, at a more local level, increases property prices (Baum-Snow and Kahn, 2000; Gibbons and Machin, 2005). There is also evidence of asymmetric impacts on labor markets, in particular, of a relative increase in demand for skilled workers in skill-abundant regions (Michaels, 2008). The evidence on the impact on the spatial distribution of economic activity is more mixed. Within metropolitan areas radial connections tend to facilitate suburbanization and, thus, benefit peripheral areas (Baum-Snow, 2007; Kopecky and Suen, 2010; Baum-Snow et al., 2017).8 However, there is also evidence that within larger regions reductions in trade costs between regions due to better road networks favor core regions at the expense of peripheral regions (Faber, 2014). Empirically, the literature evaluating the economic effects of transport infrastructure has been concerned with the nonrandom allocation of transport infrastructure, which is usually built to accommodate existing or expected demand. Instrumental variables based on historic transport networks (Duranton and Turner, 2012), counterfactual least-cost networks (Faber, 2014) or straight-line connections among regional centers (Banerjee et al., 2012) have emerged as a standard approach to establishing a causal relationship. The alternative and potentially complementary strategy adopted here is the so-called inconsequential units approach (Redding and Turner, 2015). This approach rests on the assumption that the main purpose of a transport infrastructure is often to connect regional agglomerations and that the connection of localities along the way is not necessarily intended (Chandra and Thompson, 2000; Michaels, 2008). Our contribution to this line of research is, again, 2-fold. First, we provide evidence of the economic impacts of HSR, an increasingly important but empirically understudied transport mode, exploiting a source of exogenous variation. Second, we show that peripheral regions can benefit from a better connectivity to core regions if the cost of human interaction is reduced but trade costs remain unchanged.9 This evidence complements the extant literature suggesting that HSR primarily benefits large cities, but not necessarily remote counties (Zheng and Kahn, 2013; Lin, 2014; Qin, 2016). The evidence of positive effects emerging from Marshallian externalities is also complementary to the recent evidence of negative effects on peripheral regions operating through a trade channel (Faber, 2014). Our results similarly complement literature on suburbanization (Baum-Snow, 2007; Garcia-López, 2012; Garcia-López et al., 2015) by showing that a HSR is less likely to decentralize population to suburbs than a highway. The next section introduces the institutional setting in more detail and discusses the data used. In Section 3, we conduct a program evaluation with a focus on the impact of HSR on the economies of the counties of the intermediate stations. In Section 4, we then exploit the full variation the HSR induced in bilateral transport costs between all counties in our study area to estimate the strength and spatial scope of agglomeration effects. The final section concludes. 2. Background and data 2.1. The Cologne–Frankfurt HSR line The HSR line from Cologne to Frankfurt/Main is part of the priority axis Paris–Brussels–Cologne–Amsterdam–London (PBKAL), which is 1 of 14 projects of the Trans-European Transport Network (TEN-T) as endorsed by the European Commission in 1994. In comparison to the old track alongside the river Rhine, the new HSR connects the Rhine/Ruhr area (including Cologne) and the Rhine/Main area (including Frankfurt) almost directly, reducing track length from 222 km to 177 km.10 The new track is designed exclusively for passenger transport and allows train velocities of up to 300 km/h. Due to both facts, travel time between the two main stations was reduced from 2 h, 13 min to 59 min (Brux, 2002). Preparatory works for the construction of the HSR started in December 1995. The major construction work—on the various tunnels and bridges—began in 1998. The HSR line was completed at the end of 2001. After a test period, the HSR line was put into operation in 2002. The total cost of the project was €6 billion (European Commission, 2005, 17). The broader areas of Rhine-Ruhr and Rhine-Main have long been considered to be the largest German economic agglomerations. The rail lines connecting the two centers along both Rhine riverbanks were among the European rail corridors with the heaviest usage. They had represented a traditional bottleneck since the early 1970s, when usage already exceeded capacity. The first plans for constructing an HSR line between Cologne and Frankfurt, consequently, date back to as far as the early 1970s. Since then, it has taken more than 30 years until the opening. A reason for the long time period was the complex evolution process of infrastructure projects in Germany. Several variants at the left-hand and right-hand side of the Rhine were discussed during decades of negotiations. Taking into account the difficult geography of the Central German Uplands, it was ultimately decided to construct a right-hand side connection that would largely follow the highway A3 in an attempt to minimize construction and environmental costs as well as travel time between the major centers. These benefits came at the expense of leaving relatively large cities like Koblenz and the state capitals Wiesbaden (Hesse) and Mainz (Rhineland Palatinate) aside. Due to the federal system of the Federal Republic of Germany, the states (Länder) have a strong influence on infrastructure projects that affect their territories (Sartori, 2008, 3–8). Three federal states were concerned with the subject project: North Rhine-Westphalia, Rhineland-Palatine and Hesse. While Cologne lies in North Rhine-Westphalia and Frankfurt is located in Hesse, no stop was planned within the state of Rhineland-Palatine after the plans to connect Koblenz were abandoned in 1989. The announcement of the exact routing, however, suddenly opened opportunities for communities along the line to lobby in favor of their connection. Limburg, supported by Hesse, was the first city to make a case. Somewhat later in the process, the local political and economic actors in Montabaur also managed to convince the state authorities of Rhineland-Palatinate to support their case. It was argued that from Montabaur the hinterland of the state could be connected via an existing regional line. The case of Montabaur was facilitated by the decision to build the new Limburg station at the southeastern fringe of the city in Eschhofen. The originally proposed site (Limburg-Staffel) was significantly closer than Montabaur and, given the already short distance, would have made an additional stop in Montabaur almost impossible to justify. During a long lobbying process menacing a blockade of the planning and political decision process, the three federal states eventually negotiated three intermediate stops along the HSR line, one in each of the concerned federal states. While Bonn/Siegburg and Limburg represented the shares of North Rhine-Westphalia and Hesse, a new station in Montabaur ensured the connection of Rhineland-Palatinate. At the end of this process, Montabaur, with a population of less than 20,000—the by far smallest city on the German HSR network—found itself within 40 min of the regional centers Cologne and Frankfurt and within 20 min of the international airports Frankfurt and Cologne-Bonn. Anecdotal evidence suggests that this exceptional upgrade in terms of accessibility improved the attractiveness of the city as a business location. A new congress center was opened and more than 50 firms settled in an industrial park built adjacent to the rail station11; 1&1, a leading provider of communication services, even moved their headquarters to that location. A number of local manufacturing companies in the wider catchment area expanded their capacities in response to the improvement in connectivity (Egenolf, 2008). Mainstream media reported a major success story as early as 2007, citing city officials who claim that the HSR brought at least 600 new jobs to the town (Sorge, 2007). Since then, the number has climbed to 1800 (Hergert, 2015). Several newspapers cite executives of various local firms such as 1&1 (telecommunications), Emc2 (consulting), Friedhelm-Loh (electrical engineering), ADG (congress centre), Itac (software), MTE Deutschland (milling machines), all of which suggest that the HSR was a major factor in their decisions to locate or expand business activity in Montabaur (Sorge, 2007; Rhein-Zeitung, 2012; Hergert, 2015). As an example, ADG representatives highlight that the new congress center would not have been viable without the fast connection (less than 30 min) to the major airports (Frankfurt and Cologne/Bonn). Among the major advantages reported were the ease of maintaining business relations and an improved access to a highly qualified labor pool. Various representatives, from Itac, 1&1, and others, stress that the HSR enables them to draw from a much larger labor market, which now includes the major agglomerations Cologne and Frankfurt. In selected firms, more than 80% of the managerial positions are held by in-commuters. As an example, two-thirds of the 1600 employees working for 1&1, commute into town, most of them by HSR (Hergert, 2015). These newspaper reports align well with the mayor’s HSR impact summary. According to Edmund Schaaf, employment has increased by 1400 jobs (subject to social insurance contributions) over the past 15 years, which is almost 10 times the increase in population of 150. Altogether, the anecdotal evidence suggests that the unexpectedly high passenger numbers of 3000 per day, about 10 times the original forecasts (Müller, 2012), are driven by people working, not living, in the city. This pattern is also consistent with the numbers reported for Limburg, where over the same period the number of in-commuters increased from 13,000 to 17,500 (Hergert, 2015). Notwithstanding this local impact, the intermediate stops have been very controversial in terms of their economic viability. The cities of Montabaur and Limburg only exhibit approximately 12,500 and 34,000 habitants. Furthermore, the distance between these two small cities is barely 20 km and the high-speed Intercity-Express (ICE) train needs only 9 min between the two stops, which is in contrast to the concept of high-velocity travelling that has its comparative advantages at much larger distances. The advantage of this institutional setting for our empirical analysis is that it is reasonable to assume that the routing of the track was exogenous in the sense that it was determined by geographical constraints, construction costs and environmental concerns. Compared to the considered alternative route discussed in more detail in Section 3.3, the population living within the immediate catchment areas of the intermediate stops along the selected route amounts to less than a half.12 The locations of the eventually chosen intermediate stops was constrained by the proposed routing and the need to accommodate three stops at reasonable distances in three different federal states, disentangling political lobbying for intermediate stops from other regional policies. Most importantly, the connection of the intermediate stations was not driven by existing or expected demand—in fact, these stations were heavily opposed by the operating rail carrier Deutsche Bahn. Thus, we consider the resulting variation in accessibility provided by the rail line as exogenous to the economic outcomes we observe. Furthermore, it is reasonable to argue that the timing of the inauguration was exogenous to contemporary economic trends for the entire line. When the plans for a connection of Frankfurt and Cologne were first drafted in the 1970s, it was virtually impossible to foresee changes in economic conditions in the late 1990s. 2.2. Data and study area Our study area comprises the German federal states Hesse, North Rhine-Westphalia and Rhineland-Palatinate, to which the HSR connects. In 1996, 6 years before the opening of the HSR, the total population of the study area was about 28 million, thus somewhat less than California and about the size of Belgium and the Netherlands together. The share at the total German population was about 34%. The share at German GDP was slightly higher at 36%. For the 115 counties (NUTS3 regions) in the three federal states, we collect data from various official sources: GDP, population, gross value added (GVA) by industry sectors from the German Federal Statistical Office13; number of in- and out-commuter, employment (at workplace and residence) and share of workforce holding an academic degree (at workplace) from the Federal Employment Agency. Municipality level population is obtained from the Federal Office for Building and Regional Planning. We use these data primarily to identify the most important cities within each county, which we define as their economic centers. We collected data from 1992 to 1995 (depending on data availability) to 2009. The average county in our study area in 1996 had a population of about 241K, which is significantly larger than the average county in the rest of the country (157K). In terms of output per worker, our study area is fairly similar to the rest of the country (€71.5K vs. €70.8K). Also, the shares of various industries at the regional GVA are remarkably similar. Descriptive statistics are presented in section 2 of the Supplementary Appendix, where we also present a map that illustrates the location of the study area and the HSR within Germany. 3. Program evaluation The intermediate stops Limburg, Montabaur and Siegburg on the Cologne–Frankfurt HSR were, as we argue, an accidental result of political bargaining and not rational transport planning. The new stations thus provide plausibly exogenous variation in transport services that can be exploited to detect economic impact using established program evaluation techniques. In this section, we analyze the economic effects of the opening of the HSR—the treatment—on the economies of the counties of the intermediate stops, the treated counties. Specifically, we compare the evolution of various economic outcome measures in the treated counties to control counties that provide a counterfactual. 3.1. Treated versus synthetic counties We note that at this stage we ignore Cologne and Frankfurt because these regional centers are arguably major generators of transport demand, so the routing of the HSR line cannot be considered exogenous to their economic performance. As these cities potentially benefit from improved transport services we also exclude them from the group of control counties. Besides, on the exogeneity of the treatment the credibility of a quasi-experimental comparison rests on the assumption that the treatment and control group would have followed the same trend in the absence of the treatment. To ensure a valid comparison we create a comparison group consisting of three synthetic counties, one for each of the treated counties in which the HSR stops Limburg, Montabaur and Siegburg are located. With this approach, we avoid problems arising in conventional difference-in-differences (DD) analysis if the number of treated subjects is small relative to the number of control subjects (Cameron and Miller 2015). We follow the procedure developed by Abadie and Gardeazabal (2003), who define a synthetic region as a weighted combination of nontreated regions. The optimal combination of weights is determined by two objectives. First, a synthetic county should match its treated counterpart as closely as possible in terms of the following economic growth predictors: GDP per worker, population density, ratio of out-commuters over in-commuters, the shares of construction, mining, services, retail, manufacturing and finance at GVA, and the share of workers holding a university degree in the workforce at workplace. Formally, this problem is defined as minW∈WX1-X0W′VX1-X0W, where W is a vector of non-negative weights of the non-treated counties in the synthetic county that must sum to one, X1 is a vector of pre-opening values of k economic growth predictors for the treated county, X0 is a matrix containing the same information for the non-treated counties, and V is a diagonal matrix with nonnegative elements that determine the relative importance of the growth predictors. The solution to this problem, the vector of optimal weights of nontreated counties W*, depends on V, which leads to the second objective. We search for the optimal combination V* which produces a synthetic control county that best matches the respective treated county in terms of the pre-construction growth trend. Formally, this second problem is defined as V*=argminV∈νZ1-Z0W*V′Z1-Z0W*(V), where Z1 a is vector of pre-construction observations of an economic outcome measure Y for the treated county and Z0 is a matrix with the same information for the nontreated counties.14 Table 1 summarizes the pretreatment characteristics of the home counties of the intermediate HSR stops, the synthetic control counties and all other nontreated counties in the study areas. Each synthetic county is the result of a separate implementation of the procedure outlined above. In each case the economic outcome measure Y, used to find the optimal weights matrix W* is the log of GDP. The pre-period covers all years prior to 1998, when the substantial construction works began and after—more than 25 years of negotiations—confidence was created so that the HSR would eventually materialize. The values for the k growth predictors for a given synthetic county are given by the vector X1*=X0W*, i.e. a weighted combination of nontreated counties. The treated counties (and the synthetic counties) are characterized by below-average productivity, tend to be residential locations and have a low share of workers holding university degrees. With few exceptions, the synthetic counties resemble their treated counterparts closely in observable characteristics, certainly more closely than the average of the nontreated counties. Table 1 Pretreatment characteristics: treated versus synthetic controls   Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  All nontreated counties  Predictor variable  Treat  Synth  Treat  Synth  Treat  Synth  Mean  S.D.  GDP/worker (€, K)  63.8  69.0  64.9  64.5  74.9  74.7  69.3  7.9  Ratio out/in-commuting  0.51  0.30  0.51  0.50  0.36  0.38  1.09  1.00  Population/sq. km land area  227  424  193  178  464  463  771  813  Industry share: Const. (%)  4.6  4.6  4.0  4.0  2.9  2.9  2.8  1.1  Industry share: Mining (%)  9.2  9.2  14.1  13.9  10.8  10.8  13.7  5.1  Industry share: Services (%)  36.2  36.2  31.9  31.7  36.2  36.1  33.5  4.9  Industry share: Retail (%)  8.0  8.9  8.7  8.7  8.5  8.5  8.8  2.1  Industry share: Manufact. (%)  13.8  13.8  18.1  18.0  13.8  13.7  16.5  4.9  Industry share: Finance (%)  16.1  15.9  12.1  12.0  15.1  15.0  12.8  2.8  Share higher education (%)  5.1  4.7  3.7  3.6  6.7  6.7  6.5  3.1    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  All nontreated counties  Predictor variable  Treat  Synth  Treat  Synth  Treat  Synth  Mean  S.D.  GDP/worker (€, K)  63.8  69.0  64.9  64.5  74.9  74.7  69.3  7.9  Ratio out/in-commuting  0.51  0.30  0.51  0.50  0.36  0.38  1.09  1.00  Population/sq. km land area  227  424  193  178  464  463  771  813  Industry share: Const. (%)  4.6  4.6  4.0  4.0  2.9  2.9  2.8  1.1  Industry share: Mining (%)  9.2  9.2  14.1  13.9  10.8  10.8  13.7  5.1  Industry share: Services (%)  36.2  36.2  31.9  31.7  36.2  36.1  33.5  4.9  Industry share: Retail (%)  8.0  8.9  8.7  8.7  8.5  8.5  8.8  2.1  Industry share: Manufact. (%)  13.8  13.8  18.1  18.0  13.8  13.7  16.5  4.9  Industry share: Finance (%)  16.1  15.9  12.1  12.0  15.1  15.0  12.8  2.8  Share higher education (%)  5.1  4.7  3.7  3.6  6.7  6.7  6.5  3.1  Note: The reported values are means across all years prior to 1998 (when construction began) except for the share of workers (at workplace) holding a university degree, which refers to 1999, the earliest year for which data was available. The weighting has achieved its first-order purpose of creating comparison counties that are more similar to the treated than the naïve control group of all nontreated counties. None of the synthetic counties depend solely on one county, nor are the important donors (with high weights) within a likely spillover range (see section 3-A in the Supplementary Appendix). We are thus ready to use the weights matrices (one for each treated county) to approximate vectors of counterfactual outcomes for the synthetic counties. We begin with Westerwaldkreis, home to the HSR stop Montabaur. As introduced in Section 2, Montabaur features particularly prominently in the media as an example of how communities can benefit from access to HSR. Using log GDP as an outcome variable, the left panel of Figure 1 compares the actual realizations (solid lines) to a vector of counterfactual values (dashed line) for the synthetic control county Y1*=Y0W*, where Y0 is a matrix containing the economic outcomes of all nontreated counties for all years. Both trend lines are normalized to zero in the first period. Up to 1998, the two lines followed each other closely, which indicates that the weighting also achieved the second-order purpose of equalizing pre-trends. After 1998, actual economic growth surpasses the counterfactual growth, in particular during the construction period. This pattern is indicative of some anticipation effects. Some firms moved to or expanded their businesses before the station was actually served, perhaps in an attempt to seek first-mover advantages and occupy the best possible spots in the business park close to the station. Figure 1 View largeDownload slide Westerwaldkreis (Montabaur) versus synthetic control county. Notes: Solid (dashed) line shows the trend line for Westerwaldkreis where Montabaur is situated (the synthetic control county). Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrix underlying the synthetic county. Figure 1 View largeDownload slide Westerwaldkreis (Montabaur) versus synthetic control county. Notes: Solid (dashed) line shows the trend line for Westerwaldkreis where Montabaur is situated (the synthetic control county). Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrix underlying the synthetic county. To gain further insights into other dimensions of economic impact we have used the procedure outlined above to create synthetic control counties and counterfactual trends for each of the three treated counties and a number of alternative outcomes. The right panel in Figure 1 exemplarily illustrates the resulting trend lines for the actual and the counterfactual log number of in-commuters in Westerwaldkreis. This comparison substantiates the impression that the county was perceived as an economically more attractive location once it was clear that it would be connected to the HSR line. Figure 2 provides an overview of the various comparisons between the actual and counterfactual trends we did for the three treated counties and six alternative outcome measures. In each panel we plot the differences between the trend lines (actual–counterfactual) for a different outcome measure. We further add an extrapolated linear trend fitted into the pre (before 1998) observations to allow for an intuitive comparison of the relative trends before and after construction began. Figure 2 View largeDownload slide Relative trends for treated counties versus. synthetic control counties. Notes: Solid lines represent the differences between the trend lines for a treated county and the synthetic control county. Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrices underlying the synthetic counties. Dashed lines are extrapolated linear fits using observations before 1998. Figure 2 View largeDownload slide Relative trends for treated counties versus. synthetic control counties. Notes: Solid lines represent the differences between the trend lines for a treated county and the synthetic control county. Vertical lines indicate the period of substantial construction activity. Years up to 1997 were used in the construction of the weights matrices underlying the synthetic counties. Dashed lines are extrapolated linear fits using observations before 1998. The positive impacts on economic activity suggested by Figure 1 for Montabaur seem to generalize to the two other intermediate stops. We find positive deviations from the relative pre-trend in GDP after the construction began (Limburg) or the line was completed (Siegburg). Similar positive turns in relative trends are evident in the share of in-commuters. The other outcome measures yield more mixed patterns and, in general, suggest that the HSR increased the attractiveness of the three affected counties as places to work rather than places to live. 3.2. Econometric analysis For a more formal test of the economic impact of the HSR on the group of treated counties, we make use of the following DD specification:   logYit=θTi×t>2002t+∑n=19982002θnTi×t=n+ϑTi×t-2003t+ϑPTi×t-2003t×t>2002t+μi+φt+εit, (3.1) where i and t index counties (treated and nontreated) and years, Ti is a dummy variable that is 1 for the treated counties of Montabaur, Limburg and Siegburg and 0 otherwise, t>2002 similarly indexes years after 2002, t=n similarly indexes a year n, t-2003 is a yearly trend taking a value of zero in 2003, and μi and φt are county and year fixed effects and εit is a random error term. This specification allows for a short-run impact on the level of the economic outcome variable θTi×t>2002t as well as a long-run impact on its trend ϑPTi×t-2003t×t>2002t while controlling for heterogeneity in pre-trends across the treated and the control counties ϑTi×t-2003t. The cumulated percentage impact in a given (post) year is defined as expθ^+ϑ^P×t-2003-1.15 The new stations have provided transport services since 2002, but a high degree of confidence regarding the eventual completion of the line have existed since 1998 when the substantial construction works began. We therefore add a number of short-run DD terms ∑n=19982002θnTi×t=n which absorb the effects during the construction period so that our treatment estimates are based on a comparison between the pre-construction (t < 1998) to the post-completion period (t > 2002). Essentially, the model produces empirical estimates of the cumulated effect (and its significance) which correspond to the differences between the solid and the dashed lines in Figure 2 during the post period. Standard errors are clustered on counties to account for serial correlation as recommended by Bertrand et al. (2004). We begin with the presentation of the empirical results for the outcome measure log GDP in Table 2. We use the groups of all nontreated (1–3) as well as the synthetic counties (4–6) as control groups and, in each case, complement the presentation of the results of the full models (3) and (6) with simplified versions of the model. Columns (1) and (4) provide a simple mean comparison (conditional on county and year fixed effects) of the difference in log GDP across the groups of treated and non-treated as well as the pre (before 2003) and post (from 2003 onward) periods. Columns (2) and (5) control for effects during the construction years, but do not control for trends. Table 2 Treatment effect on GDP   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP  Control group  Nontreated counties  Synthetic counties  T × (Year > 2002) [ θ]  0.057*** (0.006)  0.072*** (0.008)  −0.002 (0.011)  0.049** (0.014)  0.051** (0.016)  0.046* (0.018)  T × (Year > 2002) × (Year − 2003) [ ϑP]      −0.001 (0.003)      0.006 (0.003)  Cumulated effect      −0.003      0.066*  after 3 years      (0.017)      (0.027)  Cumulated effect      −0.005      0.084*  after 6 years      (0.024)      (0.036)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  Yes  —  Yes  Yes  T × (Year − 2003)  —  —  Yes  —  —  Yes  R2  0.997  0.997  0.997  0.999  0.999  0.999  N  2034  2034  2034  108  108  108    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP  Control group  Nontreated counties  Synthetic counties  T × (Year > 2002) [ θ]  0.057*** (0.006)  0.072*** (0.008)  −0.002 (0.011)  0.049** (0.014)  0.051** (0.016)  0.046* (0.018)  T × (Year > 2002) × (Year − 2003) [ ϑP]      −0.001 (0.003)      0.006 (0.003)  Cumulated effect      −0.003      0.066*  after 3 years      (0.017)      (0.027)  Cumulated effect      −0.005      0.084*  after 6 years      (0.024)      (0.036)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  Yes  —  Yes  Yes  T × (Year − 2003)  —  —  Yes  —  —  Yes  R2  0.997  0.997  0.997  0.999  0.999  0.999  N  2034  2034  2034  108  108  108  Notes: Standard errors in parentheses are clustered on counties. T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. The results, relatively consistently point to a positive and significant impact of the HSR on GDP. Ignoring trends, GDP in the treated counties grew by about 7% more in the treated counties than in the remaining ones if the comparison is made between the periods before construction began and after construction ended (2). The effect is slightly larger than in the basic model (1), which is consistent with the anticipation effects found in the visual inspection of the trend lines. The effect is also roughly in line with the average differences between the actual relative trend (solid lines) and linearly extrapolation pre-trends (dashed lines) during the post-period in the upper-left panel of Figure 2. Once we control for relative trends, the treatment effect disappears. As there is no positive impact on (post) trends, the implication is that the model attributes the relative differences between the before and after period to heterogeneous trends that existed prior to the treatment. Our preferred models, which compare the trends in the treated counties to the synthetic counties, yield a somewhat different picture. Consistently, all models (4–6) point to a GDP growth in the group of treated counties that exceeds the control group by about 5% in the short run. The full model (6) also suggests a positive long-run impact on the GDP trend, which is just about not statistically significant. The cumulated effects after 3 (2006) and 6 (2009) years, which are a combination of the short-run level and long-run trend effects amount to statistically significant effects of about 6.5–8.5% and are thus within the range of the effects suggested by Table 2, column (2) and Figure 2 (upper-left). The estimates reported in Table 2 are robust to using different donor pools (counties from which the algorithm can draw) and predictors (covariates the algorithm seeks to balance) (see section 3-B in the Supplementary Appendix). In Table 3, we replicate the least (1) and most (6) demanding models from Table 2 separately for each of the treated counties. We find positive effects on each of the treated counties, which are roughly within the range of the effects derived from the pooled models. After 6 years, each of the treated counties exceeded its synthetic counterpart by about 7–10% in terms of GDP. Table 3 Treatment effects on GDP by treated county   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  Control group  Nontreat  Synth  Nontreat  Synth  Nontreat  Synth  Treat × (Year > 2002) [ θ]  0.056*** (0.006)  0.033** (0.010)  0.058*** (0.006)  0.049 (0.030)  0.057*** (0.006)  0.057** (0.023)  Treat × (Year > 2002) × (Year − 2003) [ ϑP]    0.005* (0.002)    0.007* (0.004)    0.005 (0.003)  Cumulated effect    0.050***    0.073*    0.074**  after 3 years    (0.009)    (0.039)    (0.026)  Cumulated effect    0.067***    0.097*    0.089**  after 6 years    (0.013)    (0.049)    (0.031)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  —  Yes  —  Yes  T × (Year − 2003)  —  Yes  —  Yes  —  Yes  R2  0.997  1.000  0.997  1.000  0.997  1.000  N  1998  36  1998  36  1998  36    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP    Limburg- Weilburg (Limburg)  Westerwaldkreis (Montabaur)  Rhein-Siegkreis (Siegburg)  Control group  Nontreat  Synth  Nontreat  Synth  Nontreat  Synth  Treat × (Year > 2002) [ θ]  0.056*** (0.006)  0.033** (0.010)  0.058*** (0.006)  0.049 (0.030)  0.057*** (0.006)  0.057** (0.023)  Treat × (Year > 2002) × (Year − 2003) [ ϑP]    0.005* (0.002)    0.007* (0.004)    0.005 (0.003)  Cumulated effect    0.050***    0.073*    0.074**  after 3 years    (0.009)    (0.039)    (0.026)  Cumulated effect    0.067***    0.097*    0.089**  after 6 years    (0.013)    (0.049)    (0.031)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  —  Yes  —  Yes  —  Yes  T × (Year − 2003)  —  Yes  —  Yes  —  Yes  R2  0.997  1.000  0.997  1.000  0.997  1.000  N  1998  36  1998  36  1998  36  Notes: Standard errors in parentheses are robust in columns (2), (4) and (6) and clustered on counties in columns (1), (3) and (5). T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. Table 4, applies the most demanding specification (comparison to synthetic control counties controlling for trends) to different outcome measures. We find a positive and statistically significant effect on per-worker GDP, which is roughly within the range of the GDP impact just discussed. Economic growth thus seems to have come at least in part, if not entirely, through an increase in productivity (of the labor force). It is noteworthy, however, that the naïve DD specification (used in Table 2, column 2) yields significantly positive effects on per-worker GDP and workplace employment of roughly similar magnitude (see section 3-C in the Supplementary Appendix). The naïve DD specification also adds to the results reported Table 4, column 5 in that the positive point estimate of the in-commuter effect is statistically significant. This is in line with the results of a complementary analysis of bilateral commuting flows within the study area summarized in Figure 3 and laid out in more detail in Supplementary Appendix section 3-E. Confirming the anecdotal evidence reported in Section 2.1, the analysis shows that firms in Montabaur and Limburg have been drawing employees from a wider labor market since the opening of the HSR. The analysis also reveals that at the intensive margin (variation in reduction of commuting times), there seems to be a HSR effect on out-commuting. Table 4 Treatment effect on other economic outcomes   (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP/ worker  Ln workplace employment  Ln residence employment  Ln population  Ln no. of in-commuters  Ln no. of out- commuters  Control group  Synthetic counties  T × (Year > 2002) [ θ]  0.056*** (0.010)  −0.020 (0.032)  −0.025 (0.014)  −0.009 (0.015)  0.030 (0.086)  −0.015 (0.030)  T × (Year > 2002) × (Year − 2003) [ ϑP]  0.002 (0.004)  −0.001 (0.006)  −0.005*** (0.001)  −0.004* (0.002)  0.010 (0.011)  −0.007 (0.004)  Cumulated effect  0.065**  −0.023  −0.040**  −0.022  0.062  −0.035  after 3 years  (0.021)  (0.050)  (0.014)  (0.021)  (0.123)  (0.039)  Cumulated effect  0.072*  −0.025  −0.055**  −0.034  0.095  −0.055  after 6 years  (0.034)  (0.069)  (0.015)  (0.026)  (0.158)  (0.049)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  Yes  Yes  Yes  Yes  Yes  Yes  T × (Year − 2003)  Yes  Yes  Yes  Yes  Yes  Yes  R2  0.983  0.999  1.000  1.000  0.998  0.999  N  102  102  102  120  96  96    (1)  (2)  (3)  (4)  (5)  (6)    Ln GDP/ worker  Ln workplace employment  Ln residence employment  Ln population  Ln no. of in-commuters  Ln no. of out- commuters  Control group  Synthetic counties  T × (Year > 2002) [ θ]  0.056*** (0.010)  −0.020 (0.032)  −0.025 (0.014)  −0.009 (0.015)  0.030 (0.086)  −0.015 (0.030)  T × (Year > 2002) × (Year − 2003) [ ϑP]  0.002 (0.004)  −0.001 (0.006)  −0.005*** (0.001)  −0.004* (0.002)  0.010 (0.011)  −0.007 (0.004)  Cumulated effect  0.065**  −0.023  −0.040**  −0.022  0.062  −0.035  after 3 years  (0.021)  (0.050)  (0.014)  (0.021)  (0.123)  (0.039)  Cumulated effect  0.072*  −0.025  −0.055**  −0.034  0.095  −0.055  after 6 years  (0.034)  (0.069)  (0.015)  (0.026)  (0.158)  (0.049)  County effects  Yes  Yes  Yes  Yes  Yes  Yes  Year effects  Yes  Yes  Yes  Yes  Yes  Yes  Constr. years × T  Yes  Yes  Yes  Yes  Yes  Yes  T × (Year − 2003)  Yes  Yes  Yes  Yes  Yes  Yes  R2  0.983  0.999  1.000  1.000  0.998  0.999  N  102  102  102  120  96  96  Notes: Standard errors in parentheses are clustered on counties. T is a 0,1 indicator variable indexing the treated counties. Cumulated effects computed as expθ^+ϑ^P×t-2003-1. Cumulated standard errors computed as expvarθ^+t-20032×var(ϑ^P)+2×t-2003×cov(θ^,ϑ^P)-1. Constr, years × T indicates treatment T × year n interaction terms ∑n=19982002θnTi×t=n. *p < 0.1, **p < 0.05, ***p < 0.01. Figure 3 View largeDownload slide HSR effects on bilateral commuting flows from and to HSR municipalities. Notes: In-commuter models use flows from all municipalities in the study area into intermediate HSR municipalities. Out-commuter models use flows from intermediate HSR municipalities to all municipalities in the study area. First difference in number of commuters is the difference between the average number of commuters from 1992 to 1995 and the average number of commuters from 2010 to 2012. First difference in travel time is based on the transport cost matrices summarized in Figure 5. Observations weighted by the average number of commuters (across all period). Figure 3 View largeDownload slide HSR effects on bilateral commuting flows from and to HSR municipalities. Notes: In-commuter models use flows from all municipalities in the study area into intermediate HSR municipalities. Out-commuter models use flows from intermediate HSR municipalities to all municipalities in the study area. First difference in number of commuters is the difference between the average number of commuters from 1992 to 1995 and the average number of commuters from 2010 to 2012. First difference in travel time is based on the transport cost matrices summarized in Figure 5. Observations weighted by the average number of commuters (across all period). Overall, the results of the econometric analysis support the key finding of the visual trend inspection that the HSR increased the attractiveness of the locations close to the intermediate stations as places to work, but not necessarily as places to live. A further breakdown by industry (in section 3-D in the Supplementary Appendix) shows that treatment effects are driven by financial services and other nonpublic services. This confirms anecdotal evidence citing the positive effects on firms specializing in consulting (Emc2), telecommunications (1&1), software (Itac) or events (ADG). 3.3. Falsification As with any program evaluation, the key identification challenge in our empirical exercise is to find a credible counterfactual for the treated group. To ensure a valid comparison we have constructed a synthetic control group which resembles the treated counties in terms of observable characteristics and pretreatment trends. In addition, we have made use of an econometric model that controls for heterogeneity in pre-trends between the treated and the control counties. We argue that this degree of sophistication helps to reduce the risk of erroneously attributing different macroeconomic trends that result from differences between the groups of treated and control counties to the HRS. But we acknowledge that there is, ultimately, no formal way of affirming that the true counterfactual trend has been established. What can be done is to evaluate the likelihood that our empirical design reveals a treatment effect where, in effect, there is no treatment. We summarize the results of three falsification tests here and refer to the Supplementary Appendix (sections 3-F, 3-G, 3-H) for a detailed discussion. We begin with a classic ‘placebo’ study. We apply our empirical strategy to an HSR which was considered during the planning stage but never built. The track would also have had three intermediate stops in each of the involved federal states and would have passed through the economically and politically relevant cities of Bonn (the former federal capital located in North Rhine-Westphalia), Koblenz (the largest city in northern Rhineland-Palatinate) and Wiesbaden (the state capital of Hesse). The results are easily summarized. The mean treatment effect on the GDP across the three cities is near to and not statistically different from zero in all specifications. The separate treatment estimates by treated county produce significant estimates with mixed signs in the naïve DD specification, but no significant cumulative effects using synthetic counties as comparisons (although Wiesbaden has a near to 10% significance level positive long-run effect). We do not find any significant effect of the other outcome measures either, although there are large and positive point estimates for per-worker GDP (but even larger standard errors). Focusing on GDP as an outcome measure, we next conduct a placebo test in the spirit of Abadie et al. (2010). For every county in the donor pool (non-HSR counties), we use a synthetic county generated by the same method as in the baseline model to estimate a placebo treatment effect. We find that the actual average treatment effect (across the three intermediate towns) is outside the 90% confidence interval in the right tail of the distribution of placebo treatment effects (1000 random combinations of three placebo-treated counties). The key insight from this placebo test is that the method employed is unlikely to yield treatment effects similar to the ones estimated for the HSR counties by chance. This, placebo test, however, could be favorable to the actual treated counties because these are not randomly located in space. Instead, the treated counties are within a relatively close distance (compared to the average distance between counties in the study area) located almost exactly along a straight line. It is therefore more likely that unobserved spatially correlated characteristics have a similar impact on economic trends of the actual treated counties than for the randomly selected placebo-treated counties. To address this concern, we refine the selection process of placebo-treated counties to make the test more demanding. Again, we run a series of 1000 similar models, however, this time requiring that the placebo-treated counties are connected by a placebo HSR. In each iteration of the placebo test, we first randomly select one county as one endpoint of a placebo HSR (the placebo Cologne). Second, we randomly select another endpoint (the placebo Frankfurt) from all counties within a 140–180 km range (in terms of straight-line distances) of the first endpoint (the distance between Cologne and Frankfurt is 160 km). Third, we pick the three counties whose economic center (the largest city) is closest to a straight line connecting the two endpoints and define them as the treated counties (the placebo intermediate stops). Fourth, we create synthetic comparison counties for each of the placebo-treated counties according to our standard procedure. Fifth, we estimate the naïve DD model (Table 2, column (3) model, which uses all nontreated control counties and does not control for trends) as well as our preferred model (Table 2, column (6) model, which uses synthetic control counties and controls for trends) and save the point estimates and significance levels. Of the 1000 tests, 8.4% (24%) deliver significant treatment effects after 6 years using our preferred (naïve) DD model; 5.6% (8.2%) iterations resulted in treatment effects that were significant (at the 10% level) and at least as large as our benchmark estimates. The mean of the point estimate is very close to zero. Notably, the standard deviation across placebo point estimates with 8.6% (5.4%) is relatively large compared to our 8.4% (5.7%) treatment estimate. We conclude that it is unlikely that our empirical specification delivers significant treatment effects that are spurious. 4. Agglomeration effects Given the results presented so far it seems fair to conclude that the HSR has had a positive impact on the economies of the counties of the intermediate stops. This impact is in line with the idea that an increase in (market) accessibility should increase the attractiveness of a location as a place of production. In the next step, we seek to model the change in accessibility pattern induced by the HSR more fully to gain insights into the strength and the spatial scope of agglomeration forces. 4.1. Empirical strategy In our baseline empirical model, we assume that the output in county i in year t denoted by Qit depends on effective density Dit as well as arbitrary county effects ci and year effects dt.   lnQit=δ1lnDit+ci+dt+εit, (4.1) where δ1 is the elasticity of output with respect to effective density for marginal changes in D and εit is a random error. We hypothesize that, all else equal, access to a larger economic mass should increase firm productivity and lead to higher economic output. We model effective density as a function of output across all counties j within reach and, thus, assume a black-box agglomeration force that depends on the productivity of all non-land inputs. Specifically, we allow for bilateral productivity externalities between all counties, assuming that the spillover effect declines exponentially in a measure of effective distance Eij between regions i and j, which takes into account the availability of transport infrastructure. Our measure of effective density thus takes the market potential form (Harris, 1954), which is popular in the theoretical (Fujita and Ogawa, 1982; Lucas and Rossi-Hansberg, 2002) and empirical (Ahlfeldt et al., 2015; Ahlfeldt and Wendland, 2013) agglomeration economics literature. Similar measures have been used in the empirical NEG literature (Hanson, 2005; Redding and Sturm, 2008).   Dit=∑jQje-δ2Eij, (4.2) where δ2>0 determines the rate of spatial decay of the productivity effect in effective distance between two regions i and j.16 The strength of the market potential formulation is that it effectively allows the productivity effect of spatial externalities to vary in effective distance to the surrounding economic mass without imposing arbitrary discrete classifications. Instead of assuming that externalities operate within the administrative borders of a region or contiguous groups of regions, our measure of effective density also accounts for externalities across such borders. Estimating the parameters of interest δ1 and δ2 is challenging for a variety of reasons. First, it is difficult to control all location factors subsumed in ci, which impact on productivity and are potentially correlated with the agglomerations measure. Second, there is a mechanical endogeneity problem because the dependent variable output (Qit) also appears in the market potential of regions i = j. Unobserved shocks to output can therefore lead to a spurious correlation between the outcome measure and effective density. The problem is nontrivial given that internal effective distance Eij=i is typically short so that the Qij=i receives a relatively high weight. Third, it is likely that shocks to outputs are spatially correlated so that the same problem also applies to nearby areas i and j. The first problem can be addressed by estimating Equation (4.1) in differences so that unobserved time-invariant location factors are differentiated out as, for example, in Hanson (2005). Informed by the program evaluation results, we take long differences over the construction period from 1998 to 2002 in our baseline estimation, but we consider alternative end dates in an alternative specification. The second problem, in principle, can be mitigated by aggregating right-hand side areas j to larger spatial units (e.g. Hanson, 2005) or replacing Qij=i with imputed values (Ahlfeldt and Wendland, 2013). Both strategies come at the cost of losing information. The third problem is even more difficult to address since shocks to output at nearby regions are likely correlated not only in levels but also in trends. Our empirical strategy addresses the abovementioned problems by exploiting the variation in bilateral transport times created by the HSR. We set the output levels at all locations j to Qjt=1998 in both periods, so that the identification comes exclusively from changes in effective distance. Our estimation equation thus takes the following form:   lnQi,t=2002-lnQi,t=1998=δ0+δ1ln∑jQj,t=1998e-δ2Eij,t=2002-ln∑jQj,t=1998e-δ2Eij,t=1998+Δεi (4.3) We stress that this specification differs from a conventional first-difference approach in that the first difference in the market potential is driven by changes in the travel time, but not output. Specification (4.3) is estimated using a nonlinear least squares estimator to simultaneously determine both parameters of interest (δ1 and δ2). With the estimated parameters it is then possible to express the effect of an increase in economic mass at j by one unit of initial market potential of county i on the outcome of county i as a function of the bilateral effective distance:   ∂log(Qi)∂(Qj)×∑jQje-δ2Eij=δ1^exp(-δ2^Eij) (4.4) Similar increases in economic mass are expected to benefit a county more if it happens in a county within a shorter effective distance. We consider several alterations of specification (4.3) for the purposes of validation, falsification and evaluation of robustness. We estimate Equation (4.3) using the GVA in various industry sectors as an outcome variable. We consider a grid search over a large parameter space δ1,δ2 to evaluate whether the agglomeration and spillover parameters are credibly separately identified. We contrast our results with those derived from a market potential specification that allows for more flexibility in the spatial decay. We allow for trends correlated with initial sectorial composition, workforce qualification and exposure to agglomeration. We also control for trends pre-existing the construction of the HSR and explore the temporal pattern of adjustment using an alternative panel specification. Importantly, we use instrumental variables to restrict the identifying variation to the portion that is not only exogenous with respect to the timing, but also with respect to the routing of the HSR. For falsification, we make use of the placebo HSR, which was considered but never built, and public sector GVA as an outcome, which we expect not to respond to the HSR, at least in the short run. Finally, we replicate the main stages of the analysis using per-worker GDP as a dependent variable to connect more closely to the literature on the productivity effects of density. In this alternative specification we will also control for changes in the industry sector structure and workforce qualification to address selection effects. 4.2. Approximation of effective distance To implement the empirical strategy laid out above we require empirical approximations of the bilateral travel costs between each pair of counties in the study area, the effective distance. To compute our measures of effective distance we make use of a Geographic Information System (GIS) and the information on transport infrastructure displayed in Figure 4. In connecting two counties we refer to the largest cities within the pair of counties as the respective centers of economic mass (the black dots in Figure 4). In computing the effective distance we assume that transport costs are incurred exclusively in terms of travel time and that route choice is based on travel time minimization. The identifying variation stems exclusively from the HSR line in question. We abstract from any other change in transport technology. Figure 4 View largeDownload slide The transport infrastructure in the study area. Note: Market potential based on Equation (4.2) and the decay parameter estimate (δ2) from Table 5, column (1). Figure 4 View largeDownload slide The transport infrastructure in the study area. Note: Market potential based on Equation (4.2) and the decay parameter estimate (δ2) from Table 5, column (1). To solve for the least-cost matrix connecting all potential origins and destinations we assign travel times to each fraction of the transport network, which are based on the network distance and the following speeds: 160 km/h for HSR, which is roughly in line with the 70-min journey along the 180 km Cologne-Frankfurt HSR line; 80 km/h for conventional rail, which is roughly in line with the 140-min journey along the 205 km conventional rail line; 100 km/h for motorways and 80 km/h on the other primary roads. In combining these transport modes we experiment with different procedures. In our benchmark cost matrix we allow travellers to change from roads to conventional rail in any city (they all have rail stations) and from any mode to HSR at the dedicated HSR stations (white circles in Figure 4) if in the respective period HSR is available. For robustness checks, we compute travel times according to two alternative decision rules. In one version, travellers can choose either the automobile or rail, including HSR if available, but they are not allowed to switch mode during a journey. In a further alternative, we eliminate the automobile altogether. Since the automobile is typically the more competitive mode, the resulting change in travel time reflects an upper bound of the true accessibility gain. In each case, we approximate the average internal travel time within a region i = j as the travel time that corresponds to a journey at 80 km/h (primary road) along a distance that corresponds to two-thirds of the radius of a circle with the same surface area. Figure 5 summarizes the distribution of travel times across the 1152=13,225 county pairs in the situations with and without HRS according to the baseline decision rule and the rail-only alternative. Evidently, the introduction of HSR had a significant impact on the competitiveness of the rail network as reflected by the major shift in the distribution of rail travel times (dashed lines) toward the distribution of road travel times (black solid line). Prior to HSR, the road network offered faster connections for almost all county pairs so that the road travel time matrix effectively describes the least-cost matrix (black solid lines). As expected, adding HSR as a potential mode that can be combined with the automobile reduces travel times significantly on a number of routes, especially on those that would otherwise take 50 min or more (red solid line). Figure 5 View largeDownload slide Distributions of bilateral travel times. Notes: Black (gray) solid line shows the distribution of bilateral travel times on roads (the fastest combination of car and rail including HSR). Black (gray) dashed line shows the distributions for rail excluding (including) HSR. Vertical lines denote the respective means of the distributions. Figure 5 View largeDownload slide Distributions of bilateral travel times. Notes: Black (gray) solid line shows the distribution of bilateral travel times on roads (the fastest combination of car and rail including HSR). Black (gray) dashed line shows the distributions for rail excluding (including) HSR. Vertical lines denote the respective means of the distributions. 4.3. Market potential effects on output: baseline results Column (1) in Table 5 summarizes the results of estimating the model given by Equation (4.3) using ln regional GDP as the economic outcome. The estimates point to positive spillover effects, which decay in distance. Given an 18.5% elasticity of output with respect to market potential, a doubling in market potential implies an increase in GDP by 20% (= exp(0.185)−1). The strength of spillovers decays by 2.3% every minute, which corresponds to a half-life travel time of about 30 min. It takes about 200 min before the strength of the spillovers diminish to around 1%. The black line in Figure 6 illustrates the implied productivity effect of an increase in economic mass at location j by one unit of total market potential at location i. Based on this estimated spatial decay, we illustrate the change in market potential in Figure 1. Not surprisingly, Montabaur (the primary town in its county) experiences the largest accessibility gain from HSR. Combining the change in market potential by 0.34 log points with the estimated market potential elasticity the predicted increase in GDP for Montabaur is about 6%, which is close to the cumulated effect after 3 years detected in the ‘Program Evaluation’ section. Table 5 Market potential effects on output by sectors   (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Sector  All  Construction  Mining  Manufacturing  Financial services  Other services  Δln Market potential ( δ1)  0.185*** (0.051)  0.360** (0.167)  0.320** (0.124)  0.331*** (0.118)  0.379*** (0.116)  0.155 (0.094)  Decay ( δ2)  0.022**  0.021  0.033  0.032*  0.014  0.010    (0.011)  (0.014)  (0.022)  (0.018)  (0.013)  (0.022)  R2  0.054  0.036  0.030  0.037  0.050  0.021  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Δln GVA 1998–2002  Sector  All  Construction  Mining  Manufacturing  Financial services  Other services  Δln Market potential ( δ1)  0.185*** (0.051)  0.360** (0.167)  0.320** (0.124)  0.331*** (0.118)  0.379*** (0.116)  0.155 (0.094)  Decay ( δ2)  0.022**  0.021  0.033  0.032*  0.014  0.010    (0.011)  (0.014)  (0.022)  (0.018)  (0.013)  (0.022)  R2  0.054  0.036  0.030  0.037  0.050  0.021  N  115  115  115  115  115  115  Notes: Estimation method is nonlinear least squares in all models. Robust standard errors (in parentheses) of the market potential coefficient δ1 are heteroskedasticity robust and computed in separate ordinary least squares (OLS) regressions holding the decay parameters ( δ2) constant at the levels estimated in the non-linear least squares (NLS) models reported in the table. The market potential of region i is the transport cost weighted sum of output in all regions j. The change in market potential is driven by changes in travel cost between regions exclusively. Regional output is held constant at 1998 level. *p < 0.1, **p < 0.05, ***p < 0.01. Figure 6 View largeDownload slide Market potential effect on output by effective distance. Notes: The figure shows the effect of a hypothetical increase in output at county j by one unit of initial market potential at county i on log output of county i. The figure illustrates agglomeration spillover effects as defined as in Equation (4.4). Estimates of δ1 and δ2 from Table 2. Figure 6 View largeDownload slide Market potential effect on output by effective distance. Notes: The figure shows the effect of a hypothetical increase in output at county j by one unit of initial market potential at county i on log output of county i. The figure illustrates agglomeration spillover effects as defined as in Equation (4.4). Estimates of δ1 and δ2 from Table 2. The remaining columns in Table 5 present results according to Equation (4.3) replacing regional GDP with the GVA of various industry sectors as the outcome variable. The estimated spillover effects are visualized in Figure 6 as gray lines. The estimates are generally within the range of column (1). For some sectors the parameters are, however, estimated less precisely. The results also suggest that the market potential elasticity estimated in column (1) is brought down somewhat by sectors that are apparently less susceptible to agglomeration benefits, namely services other than financial services. For construction, mining, manufacturing and financial services the elasticity of output with respect to market potential is relatively large. As the HSR line is used exclusively for passenger transport, we expect to capture Marshallian externalities related to human interactions. Candidates are knowledge spillovers due to formal and informal meetings, improved labor market access and matching, as well as improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs but not freight costs. Our results are thus principally comparable to Ahlfeldt et al. (2015) and Ahlfeldt and Wendland (2013) who have estimated the effects of spillovers on productivity from within-city variation. These studies have found spillover effects that are significantly more localized. The spillover effect in these studies decays to near to zero within about half a kilometer, which is in line with Arzaghi and Henderson (2008) who also focus on within-city variation. Compared to these studies the lower spatial decay suggests that we are capturing different types of spatial externalities. While the steep spillover decay in the within-city studies points to a dominating role of face-to-face contacts that purposely or accidently happen at high frequency in the immediate neighborhood (Storper and Venables, 2004), our results suggest that the HSR effects operate at an intermediate range and through the benefits of shared inputs and labor pools, labor market matching or increases in consumer and producer market access. This interpretation is also in line with the significantly lower spatial decay found in an empirical NEG studies with an emphasis on trade costs (Hanson, 2005). 4.4. Market potential effects on output: validation, robustness and falsification As in any market potential equation, the elasticity and decay parameters are not necessarily separably identified. In fact, it is only the (ad hoc) functional form of the spatial decay imposed in the market potential formulation (Equation (4.2)) that allows us to separately estimate the market potential elasticity ( δ1) and the decay parameter ( δ2). In general terms, a larger decay parameter δ2 implies that more distant regions enter the market potential with a lower weight, reducing the degree of implicit spatial smoothing. The resulting larger variation in the market potential normally implies a lower estimate of the elasticity parameter δ1. As there could be multiple combinations of these critical parameters that fit the data we have run a grid-search over 500 possible values of δ1 and δ2(0.001–0.5) resulting in 250,000 parameter combinations for each of the models reported in Table 5. For each parameter combination, we compute the root sum of the square deviations between the observed and predicted changes in regional output. As illustrated in Figure 7, we find relatively clearly defined global minima, supporting the parametric estimates presented in Table 5 and Figure 6. This robustness check using an alternative approach to identifying the elasticity and decay parameters increases our confidence in the point estimates of the decay parameters estimated with large standard errors reported in Table 5. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Figure 7 View large Download slide Market potential effect on output: Grid searches over parameter space. Notes: Dark shades indicate a low root sum of square error in ‘predicted change log output’—'actual change log output', where predicted change in log output and actual change in log output are normalized to have a zero mean. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Output is measured in GDP for all non-public sectors, and GVA for all other sectors. Services exclude financial services (Finance) and public services. Class thresholds correspond to the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th and 99th percentile in the distribution within the parameter space delta 2 = {0,0.1}. White circles denote NLS point estimates from Table 5. X-axis in ln scale. Figure 7 View large Download slide Market potential effect on output: Grid searches over parameter space. Notes: Dark shades indicate a low root sum of square error in ‘predicted change log output’—'actual change log output', where predicted change in log output and actual change in log output are normalized to have a zero mean. A more detailed description of the objective function is in the Supplementary Appendix (section 4-A). Output is measured in GDP for all non-public sectors, and GVA for all other sectors. Services exclude financial services (Finance) and public services. Class thresholds correspond to the 1st, 5th, 10th, 25th, 50th, 75th, 90th, 95th and 99th percentile in the distribution within the parameter space delta 2 = {0,0.1}. White circles denote NLS point estimates from Table 5. X-axis in ln scale. In Table 6, we present a series of alterations of the baseline model in column (1) of Table 5. We fix the decay parameter to the value estimated in the baseline model (Table 5, column (1)) so the market potential elasticity remains comparable across alternative models. In columns (1–3), we control for trends that may be correlated with but are economically unrelated to the change in market potential and potentially confound the estimates. The purpose of these models is, thus, similar to the matching on observables we imposed in the construction of synthetic counties in the ‘Program Evaluation’ section. In model (4), we additionally control for the (1992–1997) pre-trend in log GDP to account for the possibility that unobserved county characteristics determine long-run growth trends.17 This control serves a similar purpose to the matching on pre-trends in the construction of the synthetic counties and the control for heterogeneity in pre-trends in the program evaluation DD model. The market potential elasticity decreases somewhat but remains significant and within the range of the baseline estimate. In model (5), we exploit that the timing and the routing of the HSR line can be assumed to be exogenous for the intermediate stops (Limburg, Montabaur, Siegburg) while ‘only’ the timing (and not the routing) is exogenous for the endpoints Cologne and Frankfurt. To restrict the variation in change in market potential to the fraction that is most plausibly exogenous we instrument the change in market potential with three indicator variables, each denoting one of the counties in which the intermediate stops are located. The market potential elasticity remains significant, but decreases somewhat further to about 12.5%. The instruments are strong (F-stat > 10) and while we prefer to justify the instruments on theoretical grounds (they restrict the identification to plausibly exogenous variation), we note that a Sargan-Hansen test does not reject validity. In model (6), we use GVA in the public sector instead of total GDP as the left-hand side measure of output. We view this model as a placebo test because the spatial distribution of this sector is unlikely to be determined by economic agglomeration forces, at least in the short run. In line with this interpretation we find a nonstatistically significant near to zero agglomeration effect. So far we have estimated the agglomeration effects induced by the HSR line assuming that economic adjustments took place between 1998 and 2002. This choice is based on the results presented in the ‘Program Evaluation’ section, where we find that each of the counties of the intermediate stops experienced a substantial impact over this period. To evaluate the temporal pattern of the adjustment and to empirically substantiate the chosen adjustment period, we estimate a time-varying treatment effects model such as in Ahlfeldt and Maennig (2015), where the treatment measure is the change in market potential used in Table 6. With this model, we estimate a series of market potential elasticities, each of which is identified from a comparison between long-differences in log GDP and log market potential taken over a treatment year n and the base year 1998. We set up the model such that the identifying variation corresponds to our most conservative long-difference model in Table 6, column (5), i.e. we control for trends correlated with observables and restrict the identifying variation to the intermediate stops using instrumental variables. The exact details of the specification are in the notes to Figure 8, which presents the resulting estimated market potential elasticity series. Figure 8 View largeDownload slide Market potential elasticity: Time-varying estimates. Notes: The figure is based on the following panel specification: lnQit=∑n≠1998δ1,nΔlnDi×(t=n)+Xitbt+ci+dt+εit, where Qit is the output measured as GDP of county i in year t, n indexes treatment years from 1992 to 2009, excluding the base year 1998, ΔlnDi is the change in market potential assuming the decay parameter estimated in Table 5, column (1), Xit is a vector year effects interacted with a vector of the following variables: industry shares at total 1998 GVA (construction, manufacturing, mining, financial services and other nonpublic services), the share of the workforce (at place of work) holding a university degree in 1998, the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. bt is a matrix of coefficients for each variable–year combination. ci and dt are county and year effects as in Equation (4.1). We instrument the vector of change in market potential × year interaction terms ΔlnDi×(t=n) using a full set of interaction terms between year effects and three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. Black dots represent point estimates of δ1,n and the gray shaded area denotes the 95% confidence intervals (standard errors clustered on the counties). Vertical dashed lines frame the period over which long-difference are taken in Tables 5 and 6. The upper horizontal dashed lines indicates the market potential elasticity estimated in Table 6, column (5) model, which in terms of the identifying variation is comparable to the model presented. Figure 8 View largeDownload slide Market potential elasticity: Time-varying estimates. Notes: The figure is based on the following panel specification: lnQit=∑n≠1998δ1,nΔlnDi×(t=n)+Xitbt+ci+dt+εit, where Qit is the output measured as GDP of county i in year t, n indexes treatment years from 1992 to 2009, excluding the base year 1998, ΔlnDi is the change in market potential assuming the decay parameter estimated in Table 5, column (1), Xit is a vector year effects interacted with a vector of the following variables: industry shares at total 1998 GVA (construction, manufacturing, mining, financial services and other nonpublic services), the share of the workforce (at place of work) holding a university degree in 1998, the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. bt is a matrix of coefficients for each variable–year combination. ci and dt are county and year effects as in Equation (4.1). We instrument the vector of change in market potential × year interaction terms ΔlnDi×(t=n) using a full set of interaction terms between year effects and three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. Black dots represent point estimates of δ1,n and the gray shaded area denotes the 95% confidence intervals (standard errors clustered on the counties). Vertical dashed lines frame the period over which long-difference are taken in Tables 5 and 6. The upper horizontal dashed lines indicates the market potential elasticity estimated in Table 6, column (5) model, which in terms of the identifying variation is comparable to the model presented. As expected, we find no significant response in the spatial distribution of economic activity to the market potential shock for treatment years n < 1998, while the estimates of the market potential elasticity converge to the estimate in Table 6, column (5), relatively quickly for treatment years n > 1998. By 2000, still in anticipation of the opening of the line in 2002, the spatial economy seems to have adjusted to the market potential shock as the time-varying estimates of the elasticity then remain relatively stable for a number of consecutive years. This pattern is suggestive of an impact of the HSR on the level, but not the trend of economic activity. In 2006, however, we observe a further relative shift in economic activity in regions which benefited from the HSR. Looking at the overall trend in the economic adjustment, this shift seems somewhat detached from the market potential shock, and it remains ultimately difficult to assert whether or not this shift is causally related to the HSR. We have conducted a number of further alterations of our baseline model, which we briefly discuss in the remainder of this subsection. A more detailed discussion can be found in the Supplementary Appendix. The exponential functional form of the spatial decay in spillovers, while popular in the theoretical and empirical literature (e.g. Fujita and Ogawa, 1982; Lucas and Rossi-Hansberg, 2002; Ahlfeldt et al., 2015), is ad hoc and other functional forms are theoretically imaginable. We have estimated an alternative version of our benchmark model in which the market potential is captured as the total GDP within several mutually exclusive 20-min travel time bins (e.g. 0–20 min, 20–40 min, etc.). For each travel time bin a separate market potential elasticity is estimated, thus allowing for a more flexible pattern in the spatial decay. When comparing the predicted effects of the change in market potential on GDP in this alternative model to our baseline model, we find an approximately linear relationship, suggesting that our results are not driven by an inappropriate functional form of the spatial decay (see Supplementary Appendix section 4-B). On a related note, we have addressed the insignificant sectoral market potential decay parameters by estimating the market potential elasticity imposing the decay parameter estimated across all sectors, which is highly significant. With the exception of ‘other non-public services’, whose effect is already not significant in Table 5, the market potential estimates remain within close range of the results reported in Table 5 (see Supplementary Appendix section 4-B). We have experimented with alternative travel choice models underlying the construction of travel times. In one alternative choice model, we disallow switching from train to automobile or vice versa along a journey. In another alternative choice model, we disallow the use of the automobile altogether. The results remain qualitatively unchanged and quantitatively within the range of the results presented here (see Supplementary Appendix section 4-C). We have also experimented with alternative instrumental variables to restrict the identification to variation in the change in market potential to the fraction that arises from the intermediate transport stations. In particular, we consider the log straight-line distance to Montabaur and indictor variables for the counties of the intermediate stops as well as the adjacent counties as alternatives. The results remain close to those reported in Table 6 (see Supplementary Appendix section 4-D). Finally, we have also replicated the main stages of our analysis replacing the actual HSR with the considered but never built placebo HSR, which we introduced in the previous section. We find no robust evidence of HSR effects in this falsification exercise (see Supplementary Appendix section 4-E). 4.5. Market potential effects on productivity As discussed in the introduction, a large literature has analyzed agglomeration effects by regressing a measure of productivity against a measure of density. In order to connect to this literature and to assess to which extent the market potential (effective density) effect on GDP discussed above is attributable to an increase in productivity of the labor force (rather than an expansion of the labor force), we replicate our baseline model using the ratio of GDP over the total employment (at workplace) as a dependent variable. The empirical specification used shared similarities with the nominal wage equation estimated in the NEG literature (e.g. Hanson, 2005) . In Table 7, we present the results of three OLS (columns (1)–(3)) and three 2SLS (columns (4)–(6)) estimations. In each case, we present unconditional correlations between per-worker GDP growth and change in log market potential, a version using the same controls as in Table 6, column (4), and one version where we additionally account for changes in the industry structure and the skill composition of the workforce. The instrumental variables used are the same as in Table 6, column (5). Table 7 Productivity effects   (1)  (2)  (3)  (4)  (5)  (6)    ΔLn (GDP/Employment (workplace)) 1998–2002    OLS  OLS  OLS  2SLS  2SLS  2SLS  Δln Market potential ( δ1)  0.066 (0.059)  0.132** (0.058)  0.009 (0.048)  0.170*** (0.055)  0.108* (0.062)  0.042 (0.059)  Industry shares  −  Yes  Yes  −  Yes  Yes  Degree share  −  Yes  Yes  −  Yes  Yes  Agglomeration effects  −  Yes  Yes  −  Yes  Yes  Δln GDP/Employment (workplace) 1992–1997  −  Yes  Yes  −  Yes  Yes  Composition effects  −  −  Yes  −  −  Yes  R2  0.007  0.148  0.495  −  0.147  0.487  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    ΔLn (GDP/Employment (workplace)) 1998–2002    OLS  OLS  OLS  2SLS  2SLS  2SLS  Δln Market potential ( δ1)  0.066 (0.059)  0.132** (0.058)  0.009 (0.048)  0.170*** (0.055)  0.108* (0.062)  0.042 (0.059)  Industry shares  −  Yes  Yes  −  Yes  Yes  Degree share  −  Yes  Yes  −  Yes  Yes  Agglomeration effects  −  Yes  Yes  −  Yes  Yes  Δln GDP/Employment (workplace) 1992–1997  −  Yes  Yes  −  Yes  Yes  Composition effects  −  −  Yes  −  −  Yes  R2  0.007  0.148  0.495  −  0.147  0.487  N  115  115  115  115  115  115  Notes: Robust standard errors in parentheses are heteroscedasticity robust. Δln Market potential ( δ1) is based on Equation (4.2) and the decay parameter ( δ1) from Table 5, column (1). Industry shares are shares at total 1998 GVA in the following sectors: construction, manufacturing, mining, financial services and other services. Degree share is the share for the workforce (at place of work) holding a university degree in 1999. Agglomeration effects include the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. Composition effects are 1998–2002 changes in industry shares and 1999–2002 degree share. Instrumental variables in columns (4)–(6) are three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. *p < 0.1, **p < 0.05, ***p < 0.01. The preferred results in columns (2) and (5) suggest that the increase we find in GDP is driven by an increase in worker productivity, rather than an expansion of the workforce, as the estimated elasticity is within the range of the models in Table 6. In comparing these results to the literature on the productivity effects of density it is important to acknowledge that unlike conventional density measures, our market potential takes into account the economic activity in surrounding regions, albeit with a lower weight. As a measure of effective density the market potential therefore introduces a spatial autocorrelation, which reduces variation in effective density across counties. It turns out that the standard deviation in the 1998 log market potential across counties in our data is almost three times the standard deviation in the 1998 log employment density. Our elasticity of productivity with respect to effective density is, therefore, not directly comparable to the majority of estimates in the agglomeration economics literature as a 1% increase in market potential, on average, implies a much larger percentage increase in density. Normalized by the log ratio of the standard deviations of effective density (market potential) over density (employment per area), our results imply a 3.8% elasticity of productivity with respect to employment density, which is close to previous estimates derived from cross-sectional research designs (e.g. Ciccone and Hall, 1996; Ciccone, 2002). Once we control for changes in the industry sector and skill composition the productivity effect is substantially reduced and is no longer significantly different from zero (columns (3) and (6)). One interpretation is that the increase in per-worker output is driven by a relative expansion of, on average, more productive and skill-intensive sectors, which benefit particularly from HSR. This may suggest that the economic adjustments are primarily due to selection instead of agglomeration effects (Combes et al., 2012). Another interpretation is that our controls for sector and skill composition are endogenous and we may be over-controlling, a bad control problem as discussed by Angrist and Pischke (2009). 5. External validity Before we draw conclusions in the next section, some words are due on the external validity of our findings. As with most attempts to improve identification, our variant of the inconsequential units approach (Redding and Turner, 2015) provides local treatment effect estimates as we infer a causal effect from a large accessibility shock on small towns. If marginal agglomeration benefits were concave in city size, HSR effects could be smaller for the typically connected large cities. It is not possible for us to test for such a concave relationship since our inconsequential units approach is not suited for large metropolitan areas that are connected purposely (implying a potential for reverse causality). That said, the fact that the implied elasticity of productivity with respect to a density of 3.8% (previous subsection) is close to the average of comparable estimates in the literate (Melo et al., 2009), is at least suggestive that our results have some generalizability. As with every case study, some factors are specific to our context and are worth considering before transferring conclusions to other contexts. As mentioned in Section 2.1, the Cologne–Frankfurt HSR was built parallel to a highway (A3) and the presence of such a substitute may affect the effects of the HSR as much as the technology of the HSR itself. If one is willing to accept that our estimated parameters hold some external validity, our market potential approach can be used to compute counterfactual outcomes as follows:   Δln(Qi)̂=δ^1ln∑jQj,t=1998e-δ^2Eij,t=post-ln∑jQj,t=1998e-δ^2Eij,t=pre (5.1) where δ^1 is our preferred estimate of the elasticity of output with respect to effective density and δ^2 is our preferred estimate of the spatial decay. All variables are defined as in Equation (4.3). It is possible to compare predicted outcomes Δln(Qi)̂ across different scenarios by solving Equation (7.1) assuming different speeds on the rail and road network in the transport matrices Eij,t=(pre,post) before (pre) and after (post) the HSR opening. In Table 8, we first increase the speed on the HSR (1–4, 2 is the actual scenario) before we eliminate the highway (5) and increase the speed of the highway (6). Without the highway (5), the effects on the three intermediate towns would have been even larger and roughly as large the effect of an HSR operating at a 40 km/h (25%) higher average speed (assuming there are no complementarities between the HSR and the highway). In keeping with intuition, increasing the speed on the highway by 20 km/h (6) has roughly the same effects as reducing the speed of the HSR by about 20 km/h. Table 8 Counterfactual scenarios   (1)  (2)  (3)  (4)  (5)  (6)  HSR speed (km/h)  140  160  180  200  160  160  Highway speed (km/h)  100  100  100  100  0  120  Limburg GDP effect (%)  3.16  4.55  5.73  6.75  6.62  2.37  Montabaur GDP effect (%)  4.85  6.40  7.65  8.71  9.14  4.02  Siegburg GDP effect (%)  1.63  2.25  2.79  3.27  3.29  1.33  Total GDP effect (€, billion)  5.16  7.90  10.46  12.88  10.99  4.53  Extra GDP effect in % of actual (2)  −34.74  0  32.41  63.03  39.01  −42.67    (1)  (2)  (3)  (4)  (5)  (6)  HSR speed (km/h)  140  160  180  200  160  160  Highway speed (km/h)  100  100  100  100  0  120  Limburg GDP effect (%)  3.16  4.55  5.73  6.75  6.62  2.37  Montabaur GDP effect (%)  4.85  6.40  7.65  8.71  9.14  4.02  Siegburg GDP effect (%)  1.63  2.25  2.79  3.27  3.29  1.33  Total GDP effect (€, billion)  5.16  7.90  10.46  12.88  10.99  4.53  Extra GDP effect in % of actual (2)  −34.74  0  32.41  63.03  39.01  −42.67  Notes: Table illustrates the relative and aggregate GDP effects of the HSR under different average speeds of the two modes (first two lines). Counterfactual outcomes are computed as Δln(Qi)̂=δ̂1ΔDî, where δ̂1 is our preferred estimate of the elasticity of output with respect to effective density. In computing the transport matrixes used to compute ΔDî we assume that individuals strictly choose the fastest route between any pairs of counties. They can switch between rail and car at any rail station. Another feature of the analyzed institutional context is complementary investments into infrastructure. Minor upgrades were made to the Siegburger Bahn (new overhead system, accessibility at selected stations), a light rail connecting Bonn to Siegburg (one of the intermediate stops). Station terminal buildings were newly constructed or expanded in Limburg, Montabaur and Siegburg, including some improvements to existing facilities, such as bus stops (Roggendorf and Schmidt, 1999). Much of the new or expanded business activity discussed in Section 2.1 is located in new business parks developed close to the new HSR stations. It is difficult to create a counterfactual describing the situation with the HSR, but without such complementary investments, because the anecdotal evidence overwhelmingly suggests that these measures would have had little impact without the HSR. We believe that the economic effects are best understood as originating from the combination of a substantial accessibility benefit and complementary measures that facilitate firms taking advantage of it. Our results, therefore, generalize to other contexts to the extent that similar complementary policies usually accompany the rollout of HSR. A final word concerns the entrepreneur Ralph Dommermuth, who founded one of the world’s largest web hosting companies (1&1) in his birthplace Montabaur. He is also an important investor involved in the development of the business park close to the Montabaur HSR station. Like the other stakeholders cited in Section 2, he stresses the role of the HSR as a critical ingredient for economic development, in particular the access to a wider labor market pool the HSR offers (Ferdinand, 2015). Yet, it seems possible that personal attachments to his birthplace partially motivated his strong engagement as an investor, implying that without a similarly wealthy and engaged citizen the HSR effects in Montabaur could have been more moderate or, at least, delayed. 6. Conclusion We analyze the economic effects of the Cologne–Frankfurt HSR in Germany, which connects the two major economic core regions in Germany and a number of peripheral regions along the way. Due to the institutional setting the HSR represents one of the rare occasions where transport improvements provide plausibly exogenous variation in access to surrounding economic mass. We find that the average GDP in the counties of the intermediate stops 6 years after the opening of the line exceeds a counterfactual trend by 8.5%. We make further use of the quasi-experimental variation provided by the HSR to contribute to a literature that has focused on estimating the strength and scope spatial scope of agglomeration effects. We find an elasticity of output with respect to effective density, i.e. market potential, of about 12.5% in our most conservative model. Our results further imply an elasticity of productivity with respect to density of 3.8%, which is well within the range of existing cross-sectional estimates. The strength of spillovers halves every 30 min of travel time and is near to zero after about 200 minutes. The spillovers we detect are significantly less localized than in previous studies that have identified similar spillover effects from within-city variation, but more localized than those found in the empirical NEG literature with an emphasis on trade cost. The benefits HSR has delivered to the peripheral regions operate through knowledge diffusion and labor market pooling and the effects of improved access to intermediated goods and consumer markets to the extent that the ease of communication reduces transaction costs, and thus, Marshallian externalities (Marshall, 1920). Our results complement recent evidence suggesting that improved transport linkages can benefit core regions at the expense of peripheral regions through a trade channel (Faber, 2014). Supplementary material Supplementary data for this paper are available at Journal of Economic Geography online. Footnotes 1 The transport appraisal literature distinguishes between user benefits, which mainly capture the value of shorter travel times, and wider economic impacts, such as agglomeration benefits due to higher effective density, moves to more productive jobs and output changes in imperfectly competitive markets (Department for Transport, 2014). 2 Storeygard (2012) uses changes in oil prices interacted with static distance measures as a source of variation in transport cost over time. 3 Complementary literature has modeled the mutual dependence of demand for and supply of transport infrastructure (Levinson, 2008; Xie and Levinson, 2010). 4 We create a synthetic equivalents for each treated county following Abadie and Gardeazabal (2003). 5 Reviewing 729 estimates across 34 studies, Melo et al. (2009) find a mean elasticity of 5.8%. 6 See Head and Mayer (2004) for a review of this literature. For an introduction into the theoretical and empirical literature on agglomeration, productivity and trade, see e.g. Ottaviano et al. (2002), Behrens et al. (2014) or Sato and Zenou (2015). 7 Examples include Ciccone (2002), Ciccone and Hall (1996), Dekle & Eaton (1999), Glaeser and Maré (2001), Henderson, Kuncoro and Turner (1995), Moretti (2004), Rauch (1993) and Sveikauskas (1975). 8 Such a tendency of decentralization in response to reductions in transport costs is in line with standard urban models in the spirit of Alonso (1964), Mills (1967) and Muth (1969). 9 This finding is in line with evidence suggesting that well-developed transport infrastructures are associated with less spatial concentration (Ramcharan, 2009) 10 The straight-line distance between Cologne Main Station and Frankfurt Main Station is 152 km. 11 Among them: Landesbetrieb Mobilität RLP Autobahnamt, Unternehmensberatung Emc², Industrie- und Handelskammer (IHK), Ingenieurgesellschaft Ruffert und Partner, Objektverwalter S.K.E.T, Cafe Latino, Kantine Genuss & Harmonie. 12 Using GIS we find a 2002 population of 438,540 living within 10 km from Limburg, Montabaur, and Siegburg, while 1,020,474 residents lived within the same distance from Bonn, Koblenz and Wiesbaden. All distances are measured between municipality centroids as the crow flies. 13 These data are available at the website www.regionalstatistik.de. 14 We use the Stata ado file synth compiled by Hainmueller, Abadie and Diamond to generate the synthetic control counties. 15 The respective standard error is exp(var(θ^)+(t−2003)2×var(ϑ^P)+2×(t−2003)×cov(θ^,ϑ^P))−1 16 Our internal effective distance Eij=idepends on the land area of county i so that our measure corresponds to a standard density measure for the within county externalities. 17 We take the lagged log GDP long-difference over the period 1992–1997 instead of 1992–1998 to avoid a mechanical endogeneity problem that would arise if the 1998 log GDP was entered on both sides of the equation. Table 6 Agglomeration effects: expanded models   (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP all sectors 1998–2002  Δln GVA public services1998–2002    OLS  OLS  OLS  OLS  2SLS  OLS  Δln Market potential ( δ1)  0.149*** (0.048)  0.154*** (0.046)  0.154** (0.066)  0.138** (0.068)  0.125** (0.054)  −0.014 (0.081)  Industry shares  Yes  Yes  Yes  Yes  Yes  −  Degree share  −  Yes  Yes  Yes  Yes  −  Agglomeration effects  −  −  Yes  Yes  Yes  −  Δln GDP all sectors 1992–1997  −  −  −  Yes  Yes  −  F-stat (Cragg-Donald)  −  −  −  −  23.95  −  Hansen J (p-value)  −  −  −  −  0.33  −  R2  0.123  0.145  0.220  0.235  0.235  0.000  N  115  115  115  115  115  115    (1)  (2)  (3)  (4)  (5)  (6)    Δln GDP all sectors 1998–2002  Δln GVA public services1998–2002    OLS  OLS  OLS  OLS  2SLS  OLS  Δln Market potential ( δ1)  0.149*** (0.048)  0.154*** (0.046)  0.154** (0.066)  0.138** (0.068)  0.125** (0.054)  −0.014 (0.081)  Industry shares  Yes  Yes  Yes  Yes  Yes  −  Degree share  −  Yes  Yes  Yes  Yes  −  Agglomeration effects  −  −  Yes  Yes  Yes  −  Δln GDP all sectors 1992–1997  −  −  −  Yes  Yes  −  F-stat (Cragg-Donald)  −  −  −  −  23.95  −  Hansen J (p-value)  −  −  −  −  0.33  −  R2  0.123  0.145  0.220  0.235  0.235  0.000  N  115  115  115  115  115  115  Notes: Robust standard errors in parentheses are heteroscedasticity robust. Δln Market potential ( δ1) is based on Equation (4.2) and the decay parameter ( δ1) from Table 5, column (1). Industry shares are shares at total 1998 GVA in the following sectors: construction, manufacturing, mining, financial services and other services. Degree share is the share for the workforce (at place of work) holding a university degree in 1998. Agglomeration effects include the 1998 market potential, population density, the 1997 log GDP as well as straight-line distances to Frankfurt and Cologne. Instrumental variables in column (5) are three indicator variations, each denoting one of the counties in which the intermediate stops Limburg, Montabaur and Siegburg are located. *p < 0.1, **p < 0.05, ***p < 0.01. 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