Growth spillovers and market access in Africa

Growth spillovers and market access in Africa Abstract How much do countries in Africa benefit from their neighbours’ growth? This paper shows that neighbouring growth increases a country’s ‘foreign market access’ (FMA)—boosting export demand and increasing local output. Using luminosity data to exploit within-country variation, I find that between 1992 and 2012 domestic output responded to increases in FMA with an elasticity in the range 0.3 to 0.6. By reducing trade costs, countries can increase their FMA, and so increase the spillover of neighbouring growth into domestic growth. 1. Introduction With African growth averaging over 4% a year since the early 1990 s, there is increasing hope that much of the continent may have finally achieved ‘growth take-off’.1 The incidence of civil war has declined by most measures, and some post-conflict countries—such as Mozambique and Rwanda—have achieved steady and sustained economic progress.2 For many countries, the prosperity of their surrounding neighbourhood has increased markedly. In this paper, I ask to what extent African countries benefit from the growth of their neighbours. I focus on a specific channel: trade. I adapt the model of Donaldson and Hornbeck (2016) to express domestic output as a function of ‘foreign market access’ (FMA). Domestic districts benefit from international growth, as access to foreign markets increases; this boosts export demand and lowers prices, increasing local output. Guided by this theoretical framework, I use luminosity data to create a panel of sub-national district output between 1992 and 2012. I calculate each district’s FMA, and investigate to what extent increases in FMA are associated with increases in local output. Based on the model, FMA is calculated as a weighted sum of the output in all foreign African districts, with weights determined by the cost of trade and the elasticity of trade with respect to (WRT) trade costs. As actual trade costs are unobserved, I first estimate a gravity model to provide reasonable values for the trade cost parameters. As in much of the gravity literature, I find that trade declines significantly with distance and international borders, but increases when there is a common language, currency union (CU) or free trade agreement (see Head and Mayer, 2015, for a meta-analysis). Feeding the gravity estimates into the market access term, I find that increases in FMA are associated with significant and substantial increases in local output, with an elasticity in the range 0.3 to 0.6. The paper fits into an emerging economic geography literature, demonstrating the importance of access to international markets for an area’s prosperity (Redding and Venables, 2004; Head and Mayer, 2011). The contribution here is to exploit within-country variation. This is done through panel regressions of output (luminosity) on FMA at the district level, including both district and country-year fixed effects. The district fixed effects eliminate institutional and geographic factors, such as the disease environment, that might drive the correlation between output and market access. The country-year fixed effects absorb macroeconomic and political shocks, which have often been sufficiently large in Africa to dwarf other sources of variation in output. The strategy here is therefore to ask whether those districts within a country that have cheaper access to foreign African markets respond more to output changes in those markets than districts within the same country that have more costly access. The analysis is particularly relevant to Africa, a continent of historically low growth and still home to the majority of the world’s very poorest countries. With a third of the population being landlocked, and manufacturing centres continuing to agglomerate in East Asia, penetrating global markets may be unrealistic in the near-term (Radelet and Sachs, 1998; Collier, 2008). As a result, African economic integration is now a top priority of donors and policymakers. For the landlocked in particular, Collier and O’Connell argue that ‘the most obvious growth strategy for such a country is to service the markets of its neighbours’ (2007, p. 38). In this vein, as a calibration exercise I demonstrate the importance of South Africa to its immediate neighbours. As this dominant regional economy grows, larger markets are available to its neighbours, creating growth spillovers. The baseline results suggest that each additional percentage point of South African growth is reflected in around 0.3 percentage points of growth for each of its neighbours. By lowering trade costs, neighbouring countries can increase their access to expanding regional markets and so increase such growth spillovers. The paper proceeds as follows. Section 2 discusses the theoretical connection between output and market access, and develops an empirical FMA variable. Building on this, Section 3 presents the empirical framework which proceeds in two stages. First, a gravity model is used to estimate the FMA term. Second, district output is regressed on this market access term, generating my main results of interest. Section 4 discusses the data, Section 5 presents the results and Section 6 presents the South African calibration exercise. Section 7 concludes. 2. Theoretical framework 2.1 Output and market access To guide the empirical analysis, I adapt the model of Donaldson and Hornbeck (2016) to express the output of each district i as a log-linear function of its FMA. To do so, I make a number of reduced form simplifications to implement the model empirically, each of which is outlined in turn below. I then show how the gravity equation can be used to provide an estimable version of the model in the absence of data on trade costs. I take as a starting point the following equation (derived explicitly in Appendix A):   ln⁡(Yi)=γ0+ln⁡(Ti)+γ1ln⁡(MAi) (1) where Yi is the level of output in district i, γ0 is a constant3, Ti is the level of ‘technology’ in district i and MA is district i’s ‘market access’. The level of market access is given by the following expression:   MAi=∑jτij−θYjMAj (2) where τij≥1 is the cost of trade between districts i and j, modelled using the standard iceberg approach, and θ is the elasticity of trade WRT trade costs. Equation (1) therefore states that controlling for a district’s level of technology Ti, output increases log-linearly in market access. Market access is the sum of output in all districts j, each Yj being weighted by: (i) the cost of trading with I; and (ii) j’s own market access MAj. This second term captures the degree of competition for market j: if j itself has strong market access, then a smaller share of its imports is sourced from i and hence increases in import demand (coming from increases in Y j) are muted. Given a panel of observations on district output, eq. (1) therefore provides a testable prediction for the empirical analysis. 2.2 Implementing the model There are a number of challenges with implementing the model in eq. (1) empirically. Firstly, the market access term in (1) includes domestic output, as it is a weighted sum of the output in all districts j. This creates a clear endogeneity problem, and would require estimates of internal trade costs τii−θ in order to be implemented. A partial solution to the problem, pursued by Redding and Venables (2004), is to estimate internal trade costs and run the model with both ‘domestic’ and ‘foreign’ market access terms. An alternative approach, pursued by Mayer (2009) and by Donaldson and Hornbeck (2016), is to drop the inclusion of domestic output from the market access term. 4 As I am interested in international spillovers, this is the approach I follow here. Indeed, to concentrate on international spillovers, I include only foreign (African) districts in the calculation of MAi. I term this ‘foreign market access’ and denote it by FMAi.5 Secondly, eq. (1) remains an implicit function of Yi even when domestic districts are excluded from the calculation of market access. This is due to the MAj term in the denominator, which accounts for the degree of competition in the importing district j. Following Donaldson and Hornbeck (2016), I approximate the theoretically correct market access term with a simpler expression given by MAi=∑jτij−θYj. As noted by the authors, the two market access terms are highly correlated in practice but the approximation does not require each market access term to be explicitly derived from the model. Further, the authors show that the empirical results are extremely similar in both cases. As I work with FMA, my variable of interest is therefore given by FMAi=∑j∈Fτij−θYjMAj≈∑j∈Fτij−θYj, where F denotes the set of foreign districts. Allowing for randomness in the data and adding a time dimension, the manipulations of eq. (1) above suggest estimating the following specification:   ln⁡(Yict)=ϕ0+ϕ1ln⁡(FMAict)+δi+δct+ηict (3) where ϕ0 is a constant, Yict is the output of district i in country c in year t, FMAict=∑j∈Fτij−θYjt, δi and δct are district and country-year fixed effects respectively (to control for the productivity Ti of district i) and ηict is an error term. Without information on trade costs τij and the elasticity of trade WRT trade costs (θ), eq. (3) cannot be estimated directly. As an initial step in the empirical work, and departing from Donaldson and Hornbeck (2016), I therefore apply a gravity model to estimate these values. To generate my main results of interest, I then regress district output Yict on the estimated market access term FMÂict. 2.3 Gravity: constructing FMÂict As noted by Anderson and van Wincoop (2004), the trade cost τij is typically assumed to be multiplicatively separable in its factors, such that:   τij=∏m=1M(zijm)γm (4) where zij=(zij1...zijm...zijM) is the vector of trade cost factors between i and j (e.g. distance, shared language) and γm is the elasticity of τij WRT factor m. Substituting this expression into the FMA term, we have:   FMAi=∑j∈F[∏m=1M(zijm)−γmθ]Yj (5) and from the gravity equation (see Appendix A) we can get consistent estimates of the γmθ terms by running the following regression:   ln⁡(Xij)=φ0−θln⁡(τij)+δi+δj+εij=φ0−∑mγmθln⁡(zijm)+δi+δj+εij (6) where φ0 is a constant and εij is the error term. That is, if we observed trade flows between i and j, we could consistently estimate FMA. As I do not have district trade data, I will estimate (6) at the country level. The estimated coefficients allow me to construct FMA as:   FMÂict=∑j∈F[∏m=1M(zijm)−γmθ̂]Yjct (7) where the γmθ̂ terms are the estimated coefficients from (6). Taking a simple example to clarify this procedure, suppose that the only relevant trade cost is the distance between i and j. In this case, we have τij=distijγ from eq. (4) and ln⁡(Xij)=φ0−θγln⁡(distij)+δi+δj+εij from the gravity eq. (6). Suppose that from the gravity equation we estimate −θγ̂=−1.1, the median estimate from Head and Mayer (2015). From eq. (7) the market access term would therefore be given by FMÂict=∑j∈Fdistij−1.1Yjt. This example highlights that the market access term used here is a more general form of the well-known Harris (1954) ‘market potential’ term given by MPit=∑jYjtdistij. 2.4 Discussion The theoretical model underpinning eq. (1) is that of Donaldson and Hornbeck (2016). Perhaps the most contentious aspect of this model, for the context in which it is used here, is the assumption that labour is mobile across districts. This assumption is made to simplify the derivations (in Appendix A), and Alder (2015) shows that an alternative assumption of fully immobile labour still generates a log-linear relationship between output and market access in this framework. He notes that the main difference between the two approaches is the implied elasticity of output WRT market access. In this paper, I estimate this elasticity from the data, and use the theoretical framework for its prediction of a log-linear relationship. I also show that the empirical relationship is robust to many alternative calculations of FMÂ. The assumption made regarding the mobility of labour does have significant implications the underlying mechanisms of the model however. With mobile labour, an increase in output in district j will have two offsetting effects on output in district i: exports will increase and workers will migrate out of the district. In equilibrium, real wages are equalized across districts. With immobile labour, an increase in output in district j will again increase the exports of district i, which increases real wages in both districts (assuming, for example, that labour is paid a constant fraction of income as with the Cobb-Douglas production function). Districts with the cheapest access to j will see the largest increase in export demand, and so will see a larger increase in real wages. In equilibrium, districts with greater market access will therefore also have higher real wages (see, for example, Redding and Venables, 2004). In practice, in the context here it may be appropriate to assume mobile domestic labour, but immobile international labour. To capture such dynamics completely, a mixed regional/international model would be required. Although that exercise is not undertaken here, it is useful to think through the implications qualitatively, particularly for the counterfactual exercise in Section 6. Suppose for example that a particular domestic region i receives a boost to its FMA due to a large increase in output across the border in district j. Workers cannot migrate out of district i to district j (where the increase in output was larger), and instead workers will migrate into i from other domestic regions (whose FMA did not increase as much). District i would therefore receive an additional boost to its output due to internal migration.6 Under these assumptions, we would therefore still expect to see a positive relationship between changes in FMA and changes in domestic output. 3. Empirical strategy 3.1 Overview The primary question of interest is how changes in FMA affect domestic output. Based on the discussion in Section 2, my baseline specification is therefore given by:   ln⁡(Yict)=β0+β1ln⁡(FMÂict)+δi+δct+ɛict (8) where Yict is the output of district i in country c in year t, FMÂict is as defined in eq. (7), δi is a district fixed effect and δct is a country-year fixed effect. Due to data availability, I run this model on annual data over the period 1992–2012. In alternate specifications I also include a district-specific linear time trend, to allow for different growth paths of the districts. As discussed in Section 2, I estimate the parameters of FMÂict by first running a gravity model, specified in eq. (6). I estimate this model at the country-level due to the lack of district-level data. I note however that if these cross-country regressions provide biased estimates of the barriers to cross-district trade, then the resulting FMÂict will likely also be biased. Given that FMÂict is a function of several trade cost parameters, quantifying any resulting bias is extremely complex. Instead, I present the results of eq. (8) using three different estimates of θ to calculate FMÂict, and present the resulting elasticity as a range. A single year of trade data would suffice for consistency of the gravity equation, however I include the full set of trade observations between 1992 and 2012 for greater efficiency. As trade cost factors (zij) I include distance, a contiguity dummy, common language dummy, regional trade agreement (RTA) and CU dummies (Mayer 2009, Head and Mayer 2015). I note here that the only trade cost variable that varies within countries in the calculation of FMÂict is distance. In robustness checks however I extend this list to include a domestic ethnicity variable, which varies from district-to-district. 3.2 Discussion FMÂict is the sum of output in all foreign African districts, with each district weighted by the cost of trade with the domestic district. Although the cost of trade can vary over time, due to changes in the RTA and CU variables, changes in FMÂit are driven primarily by changes in foreign output. Specifically, an output change in a foreign district has more impact on the FMA of domestic districts with which it has lower trade costs (because FMA is a weighted sum of foreign output). The empirical approach is therefore to test whether those districts within a country that have cheaper access to foreign African markets respond more to output changes in those markets than districts within the same country that have more costly access. To implement this strategy, eq. (8) includes both district and country-year fixed effects. The district fixed effects control for time-invariant factors that could induce a spurious correlation between market access and district output in the cross-section. In Africa, prominent among such factors are the disease environment and physical geography. The country-year fixed effects control for political and macroeconomic shocks. Such shocks have been frequent and severe in Africa in the recent past: during the period studied for example, seve African countries witnessed a swing in real GDP of over 25% from the previous year. In the presence of these dramatic macro shocks, it is difficult to identify international growth correlations or spillovers when working with country-level data. Analysing districts within countries therefore allows for a cleaner identification of growth spillovers across countries by controlling for these political and macro shocks. It is important to note however that the fixed effects do not fully alleviate all endogeneity concerns with eq. (8). Most notably, the country-year fixed effects cannot account for the effect of local shocks that could drive a spurious correlation between output changes in any two districts i and j. Further, there is a feedback between the output of i and j as the FMA terms depend on each other. In Section 5.3 I attempt to account for these issues through a series of ‘identification’ and robustness checks, although it is not possible to discount them completely. Therefore, although the results here suggest a robust positive relationship between output and FMA, they do not establish causality. An additional limitation of the empirical approach is that African GDP (and therefore market access) has been growing over time, and so other factors that are also growing over time could drive a correlation between market access and output. The country-year fixed effects control for those factors that affect all districts within the country equally, but there may be some omitted factors for which this is not the case. It is possible for example that lights have been gradually spreading from major cities to hinterland districts that have lower market access. Relative to the major cities, hinterland districts would then have both a larger increase in their lights output and a larger increase in their market access (as, being closer to a border, their market access is more heavily influenced by other hinterland districts just across the border). Although it is not possible to control for such issues completely, it is noted that lights did not grow significantly faster on average in hinterland districts than capital districts over the period considered here.7Henderson et al. (2012) find a slightly higher increase in lights growth in hinterland areas of Africa than large cities, although they note that such a difference is extremely small. My preferred set of results also include district-specific time trends, so that I am testing to what extent a district’s lights output deviates from trend in response to changes in market access. 4. Data 4.1 Bilateral trade flows I construct a panel of bilateral imports using data from the UN Comtrade Database. I work with import reports as these are known to be more reliable than export reports (World Trade Organization, 2012). The dependent variable is the value of imports of country i from country j in year t. The independent variables are taken from the gravity database of Head et al. (2010) and Glick and Rose (2016). In particular, I take the time-invariant measures (distance, contiguity and common language) from Head et al. (2010) and the time-dependent variables (CU and RTA dummies) from Glick and Rose (2016). 4.2 District output and market access As sub-national output figures are extremely sparse in Africa, particularly in a time-series context, I use luminosity readings as a proxy. Described in detail in Henderson et al. (2012), luminosity data has now been used as a proxy for output in a variety of settings, including in Africa (Storeygard, 2016). I provide technical details on the luminosity data in Appendix B, and demonstrate that there is a robust correlation between lights and economic output, including at the sub-national level in Africa. I work with Administrative Level 1 districts, and sum the light readings within each district to generate a district-year panel dataset covering 1992 to 2012. To construct the FMÂict term, I calculate the distance from each district i to each foreign district j. Distances are calculated using the great circle distance from the largest city in each district, based on lights output in 2000.8 In calculating FMÂict, I restrict the set of foreign districts j to lie within the same UNECA ‘sub-region’ as i—these consist of West Africa, Central Africa, Eastern Africa and Southern Africa. (The Admin 1 districts of any immediate neighbour that is not in the same UNECA ‘sub-region’ are also included in the calculation of FMÂict.)9 The motivation for this is that: (i) the vast majority of intra-African trade takes place within the same sub-region; and (ii) when considering trade flows across sub-regions, the relative locations of districts within the same country becomes trivial relative to the overall distance between domestic and foreign districts. Running eq. (8) including two FMÂict terms, one calculated from foreign districts within the same UNECA sub-region as i, and one calculated from foreign districts outside the UNECA sub-region, shows that only the first is significant. In addition, the main results of interest (presented in Table 3) remain strongly significant if FMÂict is calculated using all foreign African districts. For the baseline results in Table 3, I exclude all observations from countries that are in conflict according to the UCDP/PRIO Armed Conflict Database.10 Conflicts tend to be concentrated in particular districts within a country, and so some districts suffer large falls in output regardless of changes in their market access. It therefore seems sensible to exclude all districts of a country for years in which the country is in conflict. In Appendix B I show that the results are robust to including all observations, including conflict years. Summary statistics are presented in Table 1, showing that FMÂict is, on average, calculated as a weighted sum of the output of 140 foreign districts, and the average distance between districts is over 1,000 km. Further, as discussed in Appendix B, the average growth of lights output over the period was consistent with the growth of official GDP. As the lights data are available between 1992 and 2012, the summary statistics and all subsequent analysis covers this period. All mainland sub-Saharan African countries are included except for Equatorial Guinea, which is dropped (as in Henderson et al. 2012) because almost all of the light output is from gas flares. As a tiny country, it also has only one mainland district. Table 1. Summary statistics   Mean  Median  s.d.  Min  Max  Countries  40          Districts  530          Observations  11,130          Districts per country  13.25  10.50  10.66  3  40  District growth (lights)  0.05  0.04  0.07  −1.00  0.24  Country growth (lights)  0.04  0.04  0.02  0.00  0.10  Country growth (GDP)  0.04  0.04  0.02  −0.01  0.09  Partner districts  140.17  129  55.72  46  218  Distance (km)  1,248.64  1,164.91  659.00  68.10  2,927.13    Mean  Median  s.d.  Min  Max  Countries  40          Districts  530          Observations  11,130          Districts per country  13.25  10.50  10.66  3  40  District growth (lights)  0.05  0.04  0.07  −1.00  0.24  Country growth (lights)  0.04  0.04  0.02  0.00  0.10  Country growth (GDP)  0.04  0.04  0.02  −0.01  0.09  Partner districts  140.17  129  55.72  46  218  Distance (km)  1,248.64  1,164.91  659.00  68.10  2,927.13  Notes: Growth rates are compound annual averages, and must be multiplied by 100 for a percentage figure. Source: Author's calculations. 5. Results 5.1 Gravity model Table 2 presents the results of running eq. (6), a structural gravity model, for the sub-Saharan African sample between 1992 and 2012. The set of control variables follows Mayer (2009), and consists of distance (km), contiguity (denoted border), common language, RTA membership and CU membership. This is a standard set of controls in the gravity literature (see, for example, Head and Mayer, 2015), although in alternate columns I exclude the potentially endogenous RTA and CU variables. Columns (1) and (2) include importer and exporter fixed effects and columns (3) to (6) include a full-set of importer-year and exporter-year fixed effects. This is now best practice in the literature (Anderson and van Wincoop, 2004), as it most closely follows the theoretical gravity model (eq. [6]). Finally, columns (5) to (6) are estimated using a Poisson pseudo-maximum-likelihood (PPML) estimator (Santos Silva and Tenreyro, 2006) instead of ordinary least squares (OLS). Table 3. District output and market access (1992–2012)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(FMÂ1)  0.466***  0.411***            (0.152)  (0.120)          ln⁡(FMÂ2)      0.398***  0.343***            (0.136)  (0.111)      ln⁡(FMÂ3)          0.689***  0.550***            (0.199)  (0.165)  Time trend  No  Yes  No  Yes  No  Yes  Obs.  8,956  8,956  8,956  8,956  8,956  8,956  Districts  508  508  508  508  508  508  R-Squared  0.58  0.75  0.58  0.75  0.58  0.75    (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(FMÂ1)  0.466***  0.411***            (0.152)  (0.120)          ln⁡(FMÂ2)      0.398***  0.343***            (0.136)  (0.111)      ln⁡(FMÂ3)          0.689***  0.550***            (0.199)  (0.165)  Time trend  No  Yes  No  Yes  No  Yes  Obs.  8,956  8,956  8,956  8,956  8,956  8,956  Districts  508  508  508  508  508  508  R-Squared  0.58  0.75  0.58  0.75  0.58  0.75  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by district) in parentheses. FMÂ1 is calculated using the estimates of column (2) from Table 2; FMÂ2 is calculated using the estimates of column (4) from Table 2; FMÂ3 is calculated using the estimates of column (6) from Table 2. Alternative columns include a linear district-specific time trend. Source: Author's calculations. The variables enter significantly throughout, with each taking the expected sign: trade declines with distance, but increases when there is a common border, language, CU or RTA. A number of the coefficients are larger than previous estimates however. In each specification for example, the coefficient on the RTA dummy is greater than 0.7. Although estimates of RTA effects vary widely, Head and Mayer’s (2015) meta-analysis finds a median estimate of 0.28 from structural gravity models. A satisfactory explanation for this finding would require further research, although I note here that the positive relationship between FMA and output is robust to the alternative estimates in Table 2 as well as those from Head and Mayer (2015). The coefficient on distance, particularly in the OLS regressions, is also slightly larger than typical estimates. (Head and Mayer, 2015, find a median coefficient on distance of -1.14 from structural gravity regressions with a standard deviation of 0.4.) This is perhaps less surprising than the RTA effect, as the poor state of African infrastructure (Limao and Venables, 2001) and logistics services (Arvis et al., 2010) both suggest that transport costs rise rapidly with distance. In practice, it is likely that African trade is even more geographically concentrated than the estimates here suggest. Survey evidence shows that informal cross-border trade occurs on a substantial scale across the continent, with volumes in some areas comparable to official trade (Lesser and Moisé-Leeman, 2009; Afrika and Ajumbo, 2012). Much of this trade is in food, agriculture and low-quality manufactures, meaning that much of it is concentrated around border districts (Lesser and Moisé-Leeman, 2009; Golub, 2015). Hence overall trade likely declines more rapidly in distance than official trade: the estimates here may in fact underestimate the true effect of distance on trade in Africa. 5.2 District output and market access Having generated estimates for the trade cost parameters, I can now consider the effect of FMA on district output. To do so I substitute the coefficients from Table 2 into my expression for market access, FMÂict from eq. (7), and regress district output on this estimated market access term—eq. (8). The results from eq. (8) are presented in Table 3. I consider three alternative estimates of market access: FMÂ1 is calculated using column (2) from Table 2, FMÂ2 uses column (4) from Table 3 and FMÂ3 uses column (6) from Table 2. That is, the different market access terms are calculated from eq. (7) using estimates from the three different specifications in Table 2: OLS (CFE), OLS (CYFE) and Poisson (CYFE). Table 2. Gravity results (1992–2012)   OLS (CFE)   OLS (CYFE)   PPML (CYFE)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(dist)  −1.992***  −1.567***  −2.001***  −1.491***  −0.868***  −1.286***    (0.103)  (0.129)  (0.108)  (0.139)  (0.180)  (0.192)  border  0.908***  0.953***  0.909***  0.975***  1.201  0.419*    (0.201)  (0.193)  (0.209)  (0.200)  (0.234)  (0.228)  lang.  0.854***  0.572***  0.864***  0.593***  1.233***  0.569*    (0.118)  (0.141)  (0.123)  (0.146)  (0.207)  (0.289)  RTA    0.828***    1.024***    0.773***      (0.155)    (0.180)    (0.190)  CU    0.858**    0.790**    0.485      (0.346)    (0.363)    (0.496)  Obs.  13,710  13,710  13,710  13,710  13,736  13,711  R-squared  0.56  0.57  0.60  0.61  0.76  0.92    OLS (CFE)   OLS (CYFE)   PPML (CYFE)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(dist)  −1.992***  −1.567***  −2.001***  −1.491***  −0.868***  −1.286***    (0.103)  (0.129)  (0.108)  (0.139)  (0.180)  (0.192)  border  0.908***  0.953***  0.909***  0.975***  1.201  0.419*    (0.201)  (0.193)  (0.209)  (0.200)  (0.234)  (0.228)  lang.  0.854***  0.572***  0.864***  0.593***  1.233***  0.569*    (0.118)  (0.141)  (0.123)  (0.146)  (0.207)  (0.289)  RTA    0.828***    1.024***    0.773***      (0.155)    (0.180)    (0.190)  CU    0.858**    0.790**    0.485      (0.346)    (0.363)    (0.496)  Obs.  13,710  13,710  13,710  13,710  13,736  13,711  R-squared  0.56  0.57  0.60  0.61  0.76  0.92  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by country) in parentheses. Columns (1) and (2) include a full set of importer and exporter dummies and columns (3) to (6) include a full set of importer-year and exporter-year dummies. Dist is the distance in km between countries, border is a dummy equal to 1 if two countries share a common border, lang is a common language dummy, RTA and CU are Regional Trade Agreement and Currency Union dummies respectively. Source: Author's calculations. In all columns of Table 3, FMA has a positive and highly significant effect on district output. I consider the results in columns (4) and (6) to be the best estimates, as the parameters of the FMÂ term are estimated using a full set of importer and exporter-year fixed effects, and any long-term district growth paths are controlled for with the district time trend. These estimates put the elasticity of district output WRT FMA in the range 0.3 to 0.6. These district-level estimates are comparable to those from previous country-level work. Mayer (2009) regresses income per capita on a measure of ‘foreign market potential’ between 1960 and 2003, finding an elasticity of 0.88 from a random effects model and 0.57 when including country fixed effects.11 In earlier work, Redding and Venables (2004) apply the same approach as Mayer on a single cross-section of countries in 1996, and find an elasticity of 0.48 on their measure of market access. 5.3 Identification and robustness The results presented in Table 3 show that there is a robust correlation between changes in a district’s FMA and changes in its own output. Based on the theoretical framework of Section 2, I argue that this is driven by trade: as FMA increases, demand for local goods increases which drives increases in local production. In this sub-section, I aim to establish that trade is indeed the driving mechanism, and try to address some of the primary endogeneity concerns. To do so, I present a number of falsification and robustness checks in Table 4.12 Table 4. Identification and robustness checks   (1)  (2)  (3)  (4)  (5)  (6)  Panel A: OLS ( FMÂ2)              ln⁡(FMÂ2)    0.425***  0.472***  0.334***  0.342***  0.391***      (0.388)  (0.151)  (0.111)  (0.111)  (0.114)  ln⁡(FMÂ_D)  0.317***              (0.114)            ln⁡(FMÂ_ND)  0.212              (0.300)            Conflict_neigh        −0.055              (0.035)      Obs.  3,560  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Panel B: PPML ( FMÂ3)              ln⁡(FMÂ3)    0.711**  0.799***  0.538***  0.550***  0.549**      (0.203)  (0.237)  (0.163)  (0.165)  (0.252)  ln⁡(FMÂ_D)  0.526***              (0.168)            ln⁡(FMÂ_ND)  0.262              (0.376)            Conflict_neigh        −0.058              (0.036)      Obs.  8,164  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75    (1)  (2)  (3)  (4)  (5)  (6)  Panel A: OLS ( FMÂ2)              ln⁡(FMÂ2)    0.425***  0.472***  0.334***  0.342***  0.391***      (0.388)  (0.151)  (0.111)  (0.111)  (0.114)  ln⁡(FMÂ_D)  0.317***              (0.114)            ln⁡(FMÂ_ND)  0.212              (0.300)            Conflict_neigh        −0.055              (0.035)      Obs.  3,560  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Panel B: PPML ( FMÂ3)              ln⁡(FMÂ3)    0.711**  0.799***  0.538***  0.550***  0.549**      (0.203)  (0.237)  (0.163)  (0.165)  (0.252)  ln⁡(FMÂ_D)  0.526***              (0.168)            ln⁡(FMÂ_ND)  0.262              (0.376)            Conflict_neigh        −0.058              (0.036)      Obs.  8,164  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by district) in parentheses. FMÂ2 is calculated using the estimates of column (4) from Table 2; FMÂ3 is calculated using the estimates of column (6) from Table 2. FMÂD is calculated using only foreign countries with which the domestic country had diplomatic relations, and FMÂND across countries without diplomatic relations. All columns include a district-specific linear time trend. Source: Author's calculations. Firstly, if the effect of FMA is working through trade, we would expect to find a smaller effect between countries that do not have trading relationships with each other.13 To test this, I gather data on diplomatic relations from the Correlates of War’s Diplomatic Exchange Database, and classify countries based on whether they had diplomatic relations with each other over the period (1992–2012). For each district, I then calculate two FMÂ terms: one across countries with which it had diplomatic relations ( FMÂ_D), and another across districts in countries with which it did not ( FMÂ_ND). Reassuringly, in column (1) we see that the FMÂ term is significant only amongst countries with diplomatic relations. Secondly, there may be localized shocks, such as higher commodity prices or cross-border investment projects, that simultaneously benefit neighbouring districts. This would generate a positive correlation between output and market access, but not due to the trade channel posited here. To reduce such concerns, column (2) excludes all districts within 100 km of the domestic district when calculating FMÂ.14 Column (3) drops the closest foreign district, so that any localized shock would have to cover a number of districts to drive the correlation between FMA and domestic output. In both cases, the FMÂ term remains highly significant. Column (4) controls for neighbouring conflicts, which can spill across national borders through refugee flows, direct violence or destruction of infrastructure. This acts like a specific localized shock, generating a simultaneous (negative) shock to both FMA and domestic output. To control for this, I create a dummy variable (denoted conflict_neigh) that equals 1 if a district’s nearest neighbour is in conflict in year t.15 In column (4) this variable enters negatively but insignificantly, whereas the coefficient on FMÂ remains largely unchanged and highly significant.16 Finally, columns (5) and (6) address potential reverse causality from domestic output to FMA. This occurs because an increase in domestic output increases every foreign district’s FMA, increasing their output, which in turn increases the domestic district’s FMA. In practice, this concern is reduced because every district’s FMA term is calculated based on the output of a large number of districts (140 on average, see Table 2). Still, it may be the case that some districts are large enough to individually affect output in the the wider area in a meaningful way. To account for this possibility, column (5) drops all observations from the economically largest district of each country. Column (6) drops all observations from the largest country in each UNECA sub-region. Hence even when eq. (8) is run only with economically small districts, the FMÂ term remains positive and significant. The results in Table 4 support the view that the relationship between FMÂ and domestic output is driven by trade. In Appendix C, I provide a number of more general robustness checks. I remove outliers in terms of changes in luminosity or FMÂ;17 remove observations in which the annual increase in luminosity is greater than 10%; account for common ethnicity in the calculation of FMÂ;18 restrict the sample to districts that have a positive light reading in every year; drop countries with a population below 5 million in 2000; calculate FMÂ using the median structural gravity estimates of Head and Mayer (2015); and calculate market access by simply summing the output of all foreign districts within 500 km of the domestic district.19 In all cases the FMÂ term remains positive and significant. 6. South African growth spillovers In this section, I quantify the importance of South Africa to the wider regional economy, by considering the impact of higher South African growth on each of its neighbours. South Africa remains by far the largest economy in the southern region, and as it economy expands, larger markets are accessible to its neighbours. In the context of the model, higher South African growth increases the FMA of its neighbours, and so boosts their own output. Those neighbours with the lowest trade costs benefit the most, as their FMA increases the most. To demonstrate this, I suppose that each South African district grew by an additional 1 percentage point per year between 1992 and 2012, and then re-calculate the FMA of each neighbouring-country district under this scenario. Based on the relationship between output and FMA, estimated in Table 3, I can then calculate the implied growth of the neighbouring districts due to FMA over the period under both the actual and alternative scenarios.20 As output increases log-linearly in FMA, we can calculate changes in output due to FMA as Δln⁡(Yit)=β^Δln⁡(FMÂit), implying that:   Yit−Yit−1Yit−1=(FMÂitFMÂit−1)β^−1 (9) where Yit−Yit−1Yit−1 is the growth of Yi between 1992 and 2012. I thus calculate implied output growth, using (9), under both the actual and alternative scenarios. The difference between the two gives an estimate of the ‘growth spillovers’ resulting from faster South African growth.21 The results are presented in Table 5, which uses β^=0.343 from Table 3 to calculate (9). The first two columns present the actual observed growth rates in each country; the first using official GDP figures, and the second using the luminosity data. It is notable that the luminosity data tracks GDP relatively well across the six countries—capturing the rapid growth in Mozambique and the stagnation in Zimbabwe. Table 5. Effect of higher South African growth   Actual Growth   Implied Growth due to FMA^it     GDP  Lights  Previous  New  Diff  Botswana  4.5  5.5  0.7  1.0  0.31  Lesotho  4.0  5.3  0.6  0.9  0.34  Mozambique  8.5  6.9  2.4  2.7  0.26  Namibia  3.9  2.5  0.7  1.0  0.30  Swaziland  3.3  3.3  0.6  0.9  0.33  Zimbabwe  −0.3  0.4  2.5  2.8  0.26    Actual Growth   Implied Growth due to FMA^it     GDP  Lights  Previous  New  Diff  Botswana  4.5  5.5  0.7  1.0  0.31  Lesotho  4.0  5.3  0.6  0.9  0.34  Mozambique  8.5  6.9  2.4  2.7  0.26  Namibia  3.9  2.5  0.7  1.0  0.30  Swaziland  3.3  3.3  0.6  0.9  0.33  Zimbabwe  −0.3  0.4  2.5  2.8  0.26  Notes: All figures are annual percentage compound growth rates between 1992 and 2012. The GDP figures are taken from the World Bank World Development Index and are in constant US dollars. Source: Author's calculations. The final three columns present the implied growth in output due only to changes in FMA, i.e. due to increases in the output of neighbouring economies. The ‘previous’ column presents the results of calculating eq. (9) for each country, using the actual South African output figures. In Botswana for example, actual growth over the period averaged 5.5% per year (using the lights data). Based on changes in FMA alone, the model predicts that growth in Botswana would have averaged 0.7% per year over the period. The ‘new’ column shows the implied growth rate under the scenario of faster South African growth, and the final column calculates the difference—i.e. the change in annual growth as a result of 1 percentage point higher South African growth. The largest gains accrue to Lesotho and Swaziland, the countries with the lowest trade costs with South Africa (driven primarily by shorter distances than the other neighbours). The smallest gains accrue to Mozambique and Zimbabwe, although even here the spillover effects are reasonably large. 7. Conclusion This paper considers how African countries are affected by the growth of their neighbours. Adapting the model of Donaldson and Hornbeck (2016), I show that a district’s output can be expressed as a function of its ‘market access’. Higher growth elsewhere increases market access, increasing the demand for local goods. To concentrate on international spillovers, I include only foreign (African) districts in the calculation of market access for the empirical work. I am able to conduct the empirical work at the sub-national level by exploiting luminosity data to generate a panel of district output over 1992–2012. This advances both previous work on spillovers in Africa (Collier and O’Connell 2007; Roberts and Deichmann, 2011) and the related market access literature (Redding and Venables, 2004; Mayer, 2009), which work with country-level data. My empirical work shows that FMA is an important determinant of the growth of domestic districts: increases in FMA are reflected in significant district growth, with an elasticity between 0.3 and 0.6. I noted in the introduction that African economic integration is now a top priority of policymakers. In large part, this stems from the difficulty that most countries face in penetrating global markets. Agglomeration forces have clustered manufacturing activity in East Asia, generating concerns that African countries have ‘missed the boat’ of globalization (see World Bank, 2002; Collier, 2008). For the landlocked countries, higher freight and insurance costs multiply this challenge (Limao and Venables, 2001; Faye et al. 2004). The World Bank (2009) argues that ‘for small countries far from world markets but close to a large developing country [such as South Africa], their best prospects often lie in growth in the dominant economy’ (p. 272). I provide evidence here to support that claim, and show that by reducing trade costs such prospects are improved. Supplementary material Supplementary material—the Appendix and data files—is available online at the OUP website. Footnotes 1 Throughout the paper, I use ‘Africa’ to refer to sub-Saharan Africa. The average growth of real GDP in Africa was 4.1% between 1992 and 2012, based on World Bank figures. 2 Based on the UCDP/PRIO Armed Conflict Database for example, there were seven sub-Saharan African countries involved in ‘intense’ conflicts—those resulting in at least 1,000 deaths per year—in 1990. By 2012, this dropped to just two (Somalia and Sudan). See also: http://www.economist.com/blogs/baobab/2013/11/civil-wars. 3 γ0 is treated as a constant, although it includes the aggregate utility level U¯ which in practice is not necessarily constant over time. As I am implementing a simplified (‘reduced form’) version of the model, discussed below, I abstract from this complication here. 4 Redding and Venables (2004) outline a similar trade model to the one presented here but with immobile labour. Their model derives output per capita in country i (yi) as a log-linear function of the country’s market access. They use income per capita as a proxy for yi and consider various approximations to calculate internal trade costs τii for the (domestic) market access term. Mayer (2009) extends the Redding and Venables approach to a panel setting. He presents empirical results both with approximations for τii, and with domestic output dropped from the market access term. Both approaches show strongly significant effects of market access on income per capita. 5 This is also consistent with my approach of using cross-country gravity regressions to estimate the trade cost function (below). 6 See Overman et al. (2010) for a more detailed discussion of the spatial implications of an output shock in a particular region. 7 I denote a ‘capital district’ here as the largest district in each country based on lights output in 2000. Lights output grew in capital districts by 5% per year on average. Across other districts, they grew by 4% per year on average. 8 I take the centroid of the largest city (contiguous block of urban cells) based on light output in 2000. To accurately calculate distance, I then project these points to the African Sinusoidal (projected) coordinate system. Geodesic distances, that take into account the curvature of the globe, are then calculated using the Generate Near Table tool. All steps are done in ArcMap 10.2.1. 9 UNECA is the United Nations Economic Commission for Africa. See http://www.uneca.org/pages/subregional-offices. 10 Only ‘intense’ conflict years are excluded, which are those that result in a minimum of 1,000 battle-related deaths. 11 Mayer’s (2009) ‘foreign market potential’ term is, from his model, very similar to that used here. His empirical approach is quite different however. Rather than including a measure of market potential directly, he demonstrates that it can be captured by the country fixed effect coefficients from an initial gravity regression. That approach is not applicable here because I am calculating market access for sub-national units. 12 Each column in Table 4 includes the district-specific linear time trend. 13 The effect would not necessarily be zero, as informal cross-border trade takes place on a substantial scale across the continent (Lesser and Moisé-Leeman, 2009). This is likely the case even amongst countries with poor official relations. 14 I drop if distance >100 km, hence this is based on the distance between the largest ‘cities’ in the two districts. 15 Neighbouring conflicts are defined in the same way as domestic conflicts (Section 4), as a year in which there are 1,000 or more battle-related deaths according to the UCDP/PRIO Armed Conflicts Database. 16 The neighbouring conflict variable enters significantly if the district-specific linear time trend is excluded. 17 For each variable, I remove all observations greater (in absolute value) than the mean plus or minus 2 standard deviations. 18 I generate a dummy equal to 1 if two districts share a common ethnic group, based on the geospatial data held by the International Conflict Research Group at ETH Zurich. To calculate FMÂ in this case I first scale this variable to the country level and include this in the gravity regressions. For brevity I have not provided these gravity results, but they are available on request. 19 This is to approximate the ‘intuitive’ market access term suggested by Baum-Snow et al. (2015). 20 There are additional feedback effects that are abstracted from here. In particular, higher South African growth increases the growth of its neighbours, which in turn reinforces South African growth. Given the relative size of South African economy, such feedback effects are likely to be very small, and are ignored here for simplicity. More generally, the results in this Section are provided primarily to illustrate the magnitude of the estimated effects, and should be interpreted in this vein. 21 We are ultimately interested in the response of GDP in district i (denoted zi) to changes in GDP in district j (denoted zj), rather than the response of lights in i (denoted yi) to lights in j (denoted yj). The two elasticities are the same however. Denote the ‘GDP elasticity’ by ɛ1≡dzidzjzjzi and the ‘lights elasticity’ by: ɛ2≡dyidyjyjyi. We have also estimated the elasticity of GDP to lights in Section 4, denoted by: ɛ3≡dzidyiyizi. From the chain rule: dzidzj=dzidyidyidyjdyjdzj and so, multiplying by: zjzi,   ɛ1=dzidzjzjzi=(dzidyiyizi)︸ɛ3(dyidyjyjyi)︸ɛ2(dyjdzjzjyj)︸ɛ3−1=ɛ2 Acknowledgements This paper formed a chapter of my PhD thesis, and I am grateful to my supervisor Tim Besley for his advice throughout the project, as well as my examiners Gharad Bryan and Tony Venables. I also thank Jane Ansell, Zelda Brutti, Vernon Henderson, Guy Michaels, Adam Storeygard, Silvana Tenreyro, two anonymous referees and participants at the LSE Development and Growth Seminars and the Econometric Society World Congress in Montreal for very helpful feedback. References Afrika J.-G. K., Ajumbo G. ( 2012) Informal cross border trade in Africa: implications and policy recommendations, Africa Economic Brief 3 , African Development Bank, Washington, DC. Alder S. ( 2015) Chinese roads in India: the effect of transport infrastructure on economic development, mimeo, University of North Carolina at Chapel Hill, NC. Anderson J., van Wincoop E. ( 2004) Trade costs, Journal of Economic Literature , 42, 691– 751. Google Scholar CrossRef Search ADS   Arvis J.-F., Raballand G., Marteau J.-F. ( 2010) The Cost of Being Landlocked , The World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Baum-Snow N., Brandt L., Henderson V., Turner M., Zhang Q. ( 2015) Transport infrastructure, urban growth and market access in China, mimeo, International Growth Centre, LSE, London. Collier P. ( 2008) The Bottom Billion: Why the Poorest Countries are Failing and What Can be Done About it , Oxford University Press, Oxford. Collier P., O’Connell S. ( 2007) Opportunities and choices, in The Political Economy of Economic Growth in Africa, 1960–2000 , Cambridge University Press, Cambridge. Google Scholar CrossRef Search ADS   Donaldson D., Hornbeck R. ( 2016) Railroads and American economic growth: a market access approach, Quarterly Journal of Economics , 131, 799– 858. Google Scholar CrossRef Search ADS   Faye M.A., McArthur J., Sachs J., Snow T. ( 2004) The challenges facing landlocked developing countries, Journal of Human Development , 5, 31– 68. Google Scholar CrossRef Search ADS   Glick R., Rose A.K. ( 2016) Currency unions and trade: a post-EMU reassessment, mimeo, University of California, Berkeley, CA. Golub S. ( 2015) Informal cross-border trade and smuggling in Africa, in Morrissey O., Lopez R., Sharma K. (eds) Handbook of Trade and Development , Edward Elgar, Cheltenham. Google Scholar CrossRef Search ADS   Harris C.D. ( 1954) The market as a factor in the localization of industry in the United States, Annals of the Association of American Geographers , 44, 315– 48. Head K., Mayer T. ( 2011) Gravity, market potential and economic development, Journal of Economic Geography , 11, 281– 94. Google Scholar CrossRef Search ADS   Head K., Mayer T. ( 2015) Gravity equations: workhorse, toolkit and cookbook, in Helpman E., Rogoff K., Gopinath G. (eds) Handbook of International Economics Volume 4 , Elsevier, Amsterdam. Google Scholar CrossRef Search ADS   Head K., Mayer T., Ries J. ( 2010) The erosion of colonial trade linkages after independence, Journal of International Economics , 81, 1– 14. Google Scholar CrossRef Search ADS   Henderson J.V., Storeygard A., Weil D.N. ( 2012) Measuring economic growth from outer space, American Economic Review , 102, 994– 1028. Google Scholar CrossRef Search ADS PubMed  Lesser C., Moisé-Leeman E. ( 2009) Informal cross-border trade and trade facilitation reform in sub-Saharan Africa, Trade Policy Working Paper No. 86 , OECD Publishing, Paris. Limao N., Venables A.J. ( 2001) Infrastructure, geographical disadvantage, transport costs and trade, The World Bank Economic Review , 15, 451– 79. Google Scholar CrossRef Search ADS   Mayer T. ( 2009) Market potential and development, CEPII Working Paper No. 2009–24, CEPII, Paris. Overman H., Rice P., Venables A.J. ( 2010) Economic linkages across space, Regional Studies , 44, 17– 33. Google Scholar CrossRef Search ADS   Radelet S., Sachs J. ( 1998) Shipping costs, manufactured exports and economic growth, mimeo, Harvard University, Cambridge, MA. Redding S., Venables A.J. ( 2004) Economic geography and international inequality, Journal of International Economics , 62, 53– 82. Google Scholar CrossRef Search ADS   Roberts M., Deichmann U. ( 2011) International growth spillovers, geography and infrastructure, The World Economy , 34, 1507– 33. Google Scholar CrossRef Search ADS   Santos Silva J.M.C., Tenreyro S. ( 2006) ‘The log of gravity’, The Review of Economics and Statistics , 88, 641– 58. Google Scholar CrossRef Search ADS   Storeygard A. ( 2016) Farther on down the road: transport costs, trade and urban growth in sub-Saharan Africa, Review of Economic Studies , 83, 1263– 95. Google Scholar CrossRef Search ADS   World Bank ( 2002) Globalization, Growth, and Poverty , The World Bank, Washington, DC. World Bank ( 2009) World Development Report 2009: Reshaping Economic Geography , The World Bank, Washington, DC. World Trade Organization ( 2012) A Practical Guide to Trade Policy Analysis , WTO Publications, Geneva. © Crown copyright 2017 All rights reserved This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Economic Papers Oxford University Press

Growth spillovers and market access in Africa

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Abstract

Abstract How much do countries in Africa benefit from their neighbours’ growth? This paper shows that neighbouring growth increases a country’s ‘foreign market access’ (FMA)—boosting export demand and increasing local output. Using luminosity data to exploit within-country variation, I find that between 1992 and 2012 domestic output responded to increases in FMA with an elasticity in the range 0.3 to 0.6. By reducing trade costs, countries can increase their FMA, and so increase the spillover of neighbouring growth into domestic growth. 1. Introduction With African growth averaging over 4% a year since the early 1990 s, there is increasing hope that much of the continent may have finally achieved ‘growth take-off’.1 The incidence of civil war has declined by most measures, and some post-conflict countries—such as Mozambique and Rwanda—have achieved steady and sustained economic progress.2 For many countries, the prosperity of their surrounding neighbourhood has increased markedly. In this paper, I ask to what extent African countries benefit from the growth of their neighbours. I focus on a specific channel: trade. I adapt the model of Donaldson and Hornbeck (2016) to express domestic output as a function of ‘foreign market access’ (FMA). Domestic districts benefit from international growth, as access to foreign markets increases; this boosts export demand and lowers prices, increasing local output. Guided by this theoretical framework, I use luminosity data to create a panel of sub-national district output between 1992 and 2012. I calculate each district’s FMA, and investigate to what extent increases in FMA are associated with increases in local output. Based on the model, FMA is calculated as a weighted sum of the output in all foreign African districts, with weights determined by the cost of trade and the elasticity of trade with respect to (WRT) trade costs. As actual trade costs are unobserved, I first estimate a gravity model to provide reasonable values for the trade cost parameters. As in much of the gravity literature, I find that trade declines significantly with distance and international borders, but increases when there is a common language, currency union (CU) or free trade agreement (see Head and Mayer, 2015, for a meta-analysis). Feeding the gravity estimates into the market access term, I find that increases in FMA are associated with significant and substantial increases in local output, with an elasticity in the range 0.3 to 0.6. The paper fits into an emerging economic geography literature, demonstrating the importance of access to international markets for an area’s prosperity (Redding and Venables, 2004; Head and Mayer, 2011). The contribution here is to exploit within-country variation. This is done through panel regressions of output (luminosity) on FMA at the district level, including both district and country-year fixed effects. The district fixed effects eliminate institutional and geographic factors, such as the disease environment, that might drive the correlation between output and market access. The country-year fixed effects absorb macroeconomic and political shocks, which have often been sufficiently large in Africa to dwarf other sources of variation in output. The strategy here is therefore to ask whether those districts within a country that have cheaper access to foreign African markets respond more to output changes in those markets than districts within the same country that have more costly access. The analysis is particularly relevant to Africa, a continent of historically low growth and still home to the majority of the world’s very poorest countries. With a third of the population being landlocked, and manufacturing centres continuing to agglomerate in East Asia, penetrating global markets may be unrealistic in the near-term (Radelet and Sachs, 1998; Collier, 2008). As a result, African economic integration is now a top priority of donors and policymakers. For the landlocked in particular, Collier and O’Connell argue that ‘the most obvious growth strategy for such a country is to service the markets of its neighbours’ (2007, p. 38). In this vein, as a calibration exercise I demonstrate the importance of South Africa to its immediate neighbours. As this dominant regional economy grows, larger markets are available to its neighbours, creating growth spillovers. The baseline results suggest that each additional percentage point of South African growth is reflected in around 0.3 percentage points of growth for each of its neighbours. By lowering trade costs, neighbouring countries can increase their access to expanding regional markets and so increase such growth spillovers. The paper proceeds as follows. Section 2 discusses the theoretical connection between output and market access, and develops an empirical FMA variable. Building on this, Section 3 presents the empirical framework which proceeds in two stages. First, a gravity model is used to estimate the FMA term. Second, district output is regressed on this market access term, generating my main results of interest. Section 4 discusses the data, Section 5 presents the results and Section 6 presents the South African calibration exercise. Section 7 concludes. 2. Theoretical framework 2.1 Output and market access To guide the empirical analysis, I adapt the model of Donaldson and Hornbeck (2016) to express the output of each district i as a log-linear function of its FMA. To do so, I make a number of reduced form simplifications to implement the model empirically, each of which is outlined in turn below. I then show how the gravity equation can be used to provide an estimable version of the model in the absence of data on trade costs. I take as a starting point the following equation (derived explicitly in Appendix A):   ln⁡(Yi)=γ0+ln⁡(Ti)+γ1ln⁡(MAi) (1) where Yi is the level of output in district i, γ0 is a constant3, Ti is the level of ‘technology’ in district i and MA is district i’s ‘market access’. The level of market access is given by the following expression:   MAi=∑jτij−θYjMAj (2) where τij≥1 is the cost of trade between districts i and j, modelled using the standard iceberg approach, and θ is the elasticity of trade WRT trade costs. Equation (1) therefore states that controlling for a district’s level of technology Ti, output increases log-linearly in market access. Market access is the sum of output in all districts j, each Yj being weighted by: (i) the cost of trading with I; and (ii) j’s own market access MAj. This second term captures the degree of competition for market j: if j itself has strong market access, then a smaller share of its imports is sourced from i and hence increases in import demand (coming from increases in Y j) are muted. Given a panel of observations on district output, eq. (1) therefore provides a testable prediction for the empirical analysis. 2.2 Implementing the model There are a number of challenges with implementing the model in eq. (1) empirically. Firstly, the market access term in (1) includes domestic output, as it is a weighted sum of the output in all districts j. This creates a clear endogeneity problem, and would require estimates of internal trade costs τii−θ in order to be implemented. A partial solution to the problem, pursued by Redding and Venables (2004), is to estimate internal trade costs and run the model with both ‘domestic’ and ‘foreign’ market access terms. An alternative approach, pursued by Mayer (2009) and by Donaldson and Hornbeck (2016), is to drop the inclusion of domestic output from the market access term. 4 As I am interested in international spillovers, this is the approach I follow here. Indeed, to concentrate on international spillovers, I include only foreign (African) districts in the calculation of MAi. I term this ‘foreign market access’ and denote it by FMAi.5 Secondly, eq. (1) remains an implicit function of Yi even when domestic districts are excluded from the calculation of market access. This is due to the MAj term in the denominator, which accounts for the degree of competition in the importing district j. Following Donaldson and Hornbeck (2016), I approximate the theoretically correct market access term with a simpler expression given by MAi=∑jτij−θYj. As noted by the authors, the two market access terms are highly correlated in practice but the approximation does not require each market access term to be explicitly derived from the model. Further, the authors show that the empirical results are extremely similar in both cases. As I work with FMA, my variable of interest is therefore given by FMAi=∑j∈Fτij−θYjMAj≈∑j∈Fτij−θYj, where F denotes the set of foreign districts. Allowing for randomness in the data and adding a time dimension, the manipulations of eq. (1) above suggest estimating the following specification:   ln⁡(Yict)=ϕ0+ϕ1ln⁡(FMAict)+δi+δct+ηict (3) where ϕ0 is a constant, Yict is the output of district i in country c in year t, FMAict=∑j∈Fτij−θYjt, δi and δct are district and country-year fixed effects respectively (to control for the productivity Ti of district i) and ηict is an error term. Without information on trade costs τij and the elasticity of trade WRT trade costs (θ), eq. (3) cannot be estimated directly. As an initial step in the empirical work, and departing from Donaldson and Hornbeck (2016), I therefore apply a gravity model to estimate these values. To generate my main results of interest, I then regress district output Yict on the estimated market access term FMÂict. 2.3 Gravity: constructing FMÂict As noted by Anderson and van Wincoop (2004), the trade cost τij is typically assumed to be multiplicatively separable in its factors, such that:   τij=∏m=1M(zijm)γm (4) where zij=(zij1...zijm...zijM) is the vector of trade cost factors between i and j (e.g. distance, shared language) and γm is the elasticity of τij WRT factor m. Substituting this expression into the FMA term, we have:   FMAi=∑j∈F[∏m=1M(zijm)−γmθ]Yj (5) and from the gravity equation (see Appendix A) we can get consistent estimates of the γmθ terms by running the following regression:   ln⁡(Xij)=φ0−θln⁡(τij)+δi+δj+εij=φ0−∑mγmθln⁡(zijm)+δi+δj+εij (6) where φ0 is a constant and εij is the error term. That is, if we observed trade flows between i and j, we could consistently estimate FMA. As I do not have district trade data, I will estimate (6) at the country level. The estimated coefficients allow me to construct FMA as:   FMÂict=∑j∈F[∏m=1M(zijm)−γmθ̂]Yjct (7) where the γmθ̂ terms are the estimated coefficients from (6). Taking a simple example to clarify this procedure, suppose that the only relevant trade cost is the distance between i and j. In this case, we have τij=distijγ from eq. (4) and ln⁡(Xij)=φ0−θγln⁡(distij)+δi+δj+εij from the gravity eq. (6). Suppose that from the gravity equation we estimate −θγ̂=−1.1, the median estimate from Head and Mayer (2015). From eq. (7) the market access term would therefore be given by FMÂict=∑j∈Fdistij−1.1Yjt. This example highlights that the market access term used here is a more general form of the well-known Harris (1954) ‘market potential’ term given by MPit=∑jYjtdistij. 2.4 Discussion The theoretical model underpinning eq. (1) is that of Donaldson and Hornbeck (2016). Perhaps the most contentious aspect of this model, for the context in which it is used here, is the assumption that labour is mobile across districts. This assumption is made to simplify the derivations (in Appendix A), and Alder (2015) shows that an alternative assumption of fully immobile labour still generates a log-linear relationship between output and market access in this framework. He notes that the main difference between the two approaches is the implied elasticity of output WRT market access. In this paper, I estimate this elasticity from the data, and use the theoretical framework for its prediction of a log-linear relationship. I also show that the empirical relationship is robust to many alternative calculations of FMÂ. The assumption made regarding the mobility of labour does have significant implications the underlying mechanisms of the model however. With mobile labour, an increase in output in district j will have two offsetting effects on output in district i: exports will increase and workers will migrate out of the district. In equilibrium, real wages are equalized across districts. With immobile labour, an increase in output in district j will again increase the exports of district i, which increases real wages in both districts (assuming, for example, that labour is paid a constant fraction of income as with the Cobb-Douglas production function). Districts with the cheapest access to j will see the largest increase in export demand, and so will see a larger increase in real wages. In equilibrium, districts with greater market access will therefore also have higher real wages (see, for example, Redding and Venables, 2004). In practice, in the context here it may be appropriate to assume mobile domestic labour, but immobile international labour. To capture such dynamics completely, a mixed regional/international model would be required. Although that exercise is not undertaken here, it is useful to think through the implications qualitatively, particularly for the counterfactual exercise in Section 6. Suppose for example that a particular domestic region i receives a boost to its FMA due to a large increase in output across the border in district j. Workers cannot migrate out of district i to district j (where the increase in output was larger), and instead workers will migrate into i from other domestic regions (whose FMA did not increase as much). District i would therefore receive an additional boost to its output due to internal migration.6 Under these assumptions, we would therefore still expect to see a positive relationship between changes in FMA and changes in domestic output. 3. Empirical strategy 3.1 Overview The primary question of interest is how changes in FMA affect domestic output. Based on the discussion in Section 2, my baseline specification is therefore given by:   ln⁡(Yict)=β0+β1ln⁡(FMÂict)+δi+δct+ɛict (8) where Yict is the output of district i in country c in year t, FMÂict is as defined in eq. (7), δi is a district fixed effect and δct is a country-year fixed effect. Due to data availability, I run this model on annual data over the period 1992–2012. In alternate specifications I also include a district-specific linear time trend, to allow for different growth paths of the districts. As discussed in Section 2, I estimate the parameters of FMÂict by first running a gravity model, specified in eq. (6). I estimate this model at the country-level due to the lack of district-level data. I note however that if these cross-country regressions provide biased estimates of the barriers to cross-district trade, then the resulting FMÂict will likely also be biased. Given that FMÂict is a function of several trade cost parameters, quantifying any resulting bias is extremely complex. Instead, I present the results of eq. (8) using three different estimates of θ to calculate FMÂict, and present the resulting elasticity as a range. A single year of trade data would suffice for consistency of the gravity equation, however I include the full set of trade observations between 1992 and 2012 for greater efficiency. As trade cost factors (zij) I include distance, a contiguity dummy, common language dummy, regional trade agreement (RTA) and CU dummies (Mayer 2009, Head and Mayer 2015). I note here that the only trade cost variable that varies within countries in the calculation of FMÂict is distance. In robustness checks however I extend this list to include a domestic ethnicity variable, which varies from district-to-district. 3.2 Discussion FMÂict is the sum of output in all foreign African districts, with each district weighted by the cost of trade with the domestic district. Although the cost of trade can vary over time, due to changes in the RTA and CU variables, changes in FMÂit are driven primarily by changes in foreign output. Specifically, an output change in a foreign district has more impact on the FMA of domestic districts with which it has lower trade costs (because FMA is a weighted sum of foreign output). The empirical approach is therefore to test whether those districts within a country that have cheaper access to foreign African markets respond more to output changes in those markets than districts within the same country that have more costly access. To implement this strategy, eq. (8) includes both district and country-year fixed effects. The district fixed effects control for time-invariant factors that could induce a spurious correlation between market access and district output in the cross-section. In Africa, prominent among such factors are the disease environment and physical geography. The country-year fixed effects control for political and macroeconomic shocks. Such shocks have been frequent and severe in Africa in the recent past: during the period studied for example, seve African countries witnessed a swing in real GDP of over 25% from the previous year. In the presence of these dramatic macro shocks, it is difficult to identify international growth correlations or spillovers when working with country-level data. Analysing districts within countries therefore allows for a cleaner identification of growth spillovers across countries by controlling for these political and macro shocks. It is important to note however that the fixed effects do not fully alleviate all endogeneity concerns with eq. (8). Most notably, the country-year fixed effects cannot account for the effect of local shocks that could drive a spurious correlation between output changes in any two districts i and j. Further, there is a feedback between the output of i and j as the FMA terms depend on each other. In Section 5.3 I attempt to account for these issues through a series of ‘identification’ and robustness checks, although it is not possible to discount them completely. Therefore, although the results here suggest a robust positive relationship between output and FMA, they do not establish causality. An additional limitation of the empirical approach is that African GDP (and therefore market access) has been growing over time, and so other factors that are also growing over time could drive a correlation between market access and output. The country-year fixed effects control for those factors that affect all districts within the country equally, but there may be some omitted factors for which this is not the case. It is possible for example that lights have been gradually spreading from major cities to hinterland districts that have lower market access. Relative to the major cities, hinterland districts would then have both a larger increase in their lights output and a larger increase in their market access (as, being closer to a border, their market access is more heavily influenced by other hinterland districts just across the border). Although it is not possible to control for such issues completely, it is noted that lights did not grow significantly faster on average in hinterland districts than capital districts over the period considered here.7Henderson et al. (2012) find a slightly higher increase in lights growth in hinterland areas of Africa than large cities, although they note that such a difference is extremely small. My preferred set of results also include district-specific time trends, so that I am testing to what extent a district’s lights output deviates from trend in response to changes in market access. 4. Data 4.1 Bilateral trade flows I construct a panel of bilateral imports using data from the UN Comtrade Database. I work with import reports as these are known to be more reliable than export reports (World Trade Organization, 2012). The dependent variable is the value of imports of country i from country j in year t. The independent variables are taken from the gravity database of Head et al. (2010) and Glick and Rose (2016). In particular, I take the time-invariant measures (distance, contiguity and common language) from Head et al. (2010) and the time-dependent variables (CU and RTA dummies) from Glick and Rose (2016). 4.2 District output and market access As sub-national output figures are extremely sparse in Africa, particularly in a time-series context, I use luminosity readings as a proxy. Described in detail in Henderson et al. (2012), luminosity data has now been used as a proxy for output in a variety of settings, including in Africa (Storeygard, 2016). I provide technical details on the luminosity data in Appendix B, and demonstrate that there is a robust correlation between lights and economic output, including at the sub-national level in Africa. I work with Administrative Level 1 districts, and sum the light readings within each district to generate a district-year panel dataset covering 1992 to 2012. To construct the FMÂict term, I calculate the distance from each district i to each foreign district j. Distances are calculated using the great circle distance from the largest city in each district, based on lights output in 2000.8 In calculating FMÂict, I restrict the set of foreign districts j to lie within the same UNECA ‘sub-region’ as i—these consist of West Africa, Central Africa, Eastern Africa and Southern Africa. (The Admin 1 districts of any immediate neighbour that is not in the same UNECA ‘sub-region’ are also included in the calculation of FMÂict.)9 The motivation for this is that: (i) the vast majority of intra-African trade takes place within the same sub-region; and (ii) when considering trade flows across sub-regions, the relative locations of districts within the same country becomes trivial relative to the overall distance between domestic and foreign districts. Running eq. (8) including two FMÂict terms, one calculated from foreign districts within the same UNECA sub-region as i, and one calculated from foreign districts outside the UNECA sub-region, shows that only the first is significant. In addition, the main results of interest (presented in Table 3) remain strongly significant if FMÂict is calculated using all foreign African districts. For the baseline results in Table 3, I exclude all observations from countries that are in conflict according to the UCDP/PRIO Armed Conflict Database.10 Conflicts tend to be concentrated in particular districts within a country, and so some districts suffer large falls in output regardless of changes in their market access. It therefore seems sensible to exclude all districts of a country for years in which the country is in conflict. In Appendix B I show that the results are robust to including all observations, including conflict years. Summary statistics are presented in Table 1, showing that FMÂict is, on average, calculated as a weighted sum of the output of 140 foreign districts, and the average distance between districts is over 1,000 km. Further, as discussed in Appendix B, the average growth of lights output over the period was consistent with the growth of official GDP. As the lights data are available between 1992 and 2012, the summary statistics and all subsequent analysis covers this period. All mainland sub-Saharan African countries are included except for Equatorial Guinea, which is dropped (as in Henderson et al. 2012) because almost all of the light output is from gas flares. As a tiny country, it also has only one mainland district. Table 1. Summary statistics   Mean  Median  s.d.  Min  Max  Countries  40          Districts  530          Observations  11,130          Districts per country  13.25  10.50  10.66  3  40  District growth (lights)  0.05  0.04  0.07  −1.00  0.24  Country growth (lights)  0.04  0.04  0.02  0.00  0.10  Country growth (GDP)  0.04  0.04  0.02  −0.01  0.09  Partner districts  140.17  129  55.72  46  218  Distance (km)  1,248.64  1,164.91  659.00  68.10  2,927.13    Mean  Median  s.d.  Min  Max  Countries  40          Districts  530          Observations  11,130          Districts per country  13.25  10.50  10.66  3  40  District growth (lights)  0.05  0.04  0.07  −1.00  0.24  Country growth (lights)  0.04  0.04  0.02  0.00  0.10  Country growth (GDP)  0.04  0.04  0.02  −0.01  0.09  Partner districts  140.17  129  55.72  46  218  Distance (km)  1,248.64  1,164.91  659.00  68.10  2,927.13  Notes: Growth rates are compound annual averages, and must be multiplied by 100 for a percentage figure. Source: Author's calculations. 5. Results 5.1 Gravity model Table 2 presents the results of running eq. (6), a structural gravity model, for the sub-Saharan African sample between 1992 and 2012. The set of control variables follows Mayer (2009), and consists of distance (km), contiguity (denoted border), common language, RTA membership and CU membership. This is a standard set of controls in the gravity literature (see, for example, Head and Mayer, 2015), although in alternate columns I exclude the potentially endogenous RTA and CU variables. Columns (1) and (2) include importer and exporter fixed effects and columns (3) to (6) include a full-set of importer-year and exporter-year fixed effects. This is now best practice in the literature (Anderson and van Wincoop, 2004), as it most closely follows the theoretical gravity model (eq. [6]). Finally, columns (5) to (6) are estimated using a Poisson pseudo-maximum-likelihood (PPML) estimator (Santos Silva and Tenreyro, 2006) instead of ordinary least squares (OLS). Table 3. District output and market access (1992–2012)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(FMÂ1)  0.466***  0.411***            (0.152)  (0.120)          ln⁡(FMÂ2)      0.398***  0.343***            (0.136)  (0.111)      ln⁡(FMÂ3)          0.689***  0.550***            (0.199)  (0.165)  Time trend  No  Yes  No  Yes  No  Yes  Obs.  8,956  8,956  8,956  8,956  8,956  8,956  Districts  508  508  508  508  508  508  R-Squared  0.58  0.75  0.58  0.75  0.58  0.75    (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(FMÂ1)  0.466***  0.411***            (0.152)  (0.120)          ln⁡(FMÂ2)      0.398***  0.343***            (0.136)  (0.111)      ln⁡(FMÂ3)          0.689***  0.550***            (0.199)  (0.165)  Time trend  No  Yes  No  Yes  No  Yes  Obs.  8,956  8,956  8,956  8,956  8,956  8,956  Districts  508  508  508  508  508  508  R-Squared  0.58  0.75  0.58  0.75  0.58  0.75  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by district) in parentheses. FMÂ1 is calculated using the estimates of column (2) from Table 2; FMÂ2 is calculated using the estimates of column (4) from Table 2; FMÂ3 is calculated using the estimates of column (6) from Table 2. Alternative columns include a linear district-specific time trend. Source: Author's calculations. The variables enter significantly throughout, with each taking the expected sign: trade declines with distance, but increases when there is a common border, language, CU or RTA. A number of the coefficients are larger than previous estimates however. In each specification for example, the coefficient on the RTA dummy is greater than 0.7. Although estimates of RTA effects vary widely, Head and Mayer’s (2015) meta-analysis finds a median estimate of 0.28 from structural gravity models. A satisfactory explanation for this finding would require further research, although I note here that the positive relationship between FMA and output is robust to the alternative estimates in Table 2 as well as those from Head and Mayer (2015). The coefficient on distance, particularly in the OLS regressions, is also slightly larger than typical estimates. (Head and Mayer, 2015, find a median coefficient on distance of -1.14 from structural gravity regressions with a standard deviation of 0.4.) This is perhaps less surprising than the RTA effect, as the poor state of African infrastructure (Limao and Venables, 2001) and logistics services (Arvis et al., 2010) both suggest that transport costs rise rapidly with distance. In practice, it is likely that African trade is even more geographically concentrated than the estimates here suggest. Survey evidence shows that informal cross-border trade occurs on a substantial scale across the continent, with volumes in some areas comparable to official trade (Lesser and Moisé-Leeman, 2009; Afrika and Ajumbo, 2012). Much of this trade is in food, agriculture and low-quality manufactures, meaning that much of it is concentrated around border districts (Lesser and Moisé-Leeman, 2009; Golub, 2015). Hence overall trade likely declines more rapidly in distance than official trade: the estimates here may in fact underestimate the true effect of distance on trade in Africa. 5.2 District output and market access Having generated estimates for the trade cost parameters, I can now consider the effect of FMA on district output. To do so I substitute the coefficients from Table 2 into my expression for market access, FMÂict from eq. (7), and regress district output on this estimated market access term—eq. (8). The results from eq. (8) are presented in Table 3. I consider three alternative estimates of market access: FMÂ1 is calculated using column (2) from Table 2, FMÂ2 uses column (4) from Table 3 and FMÂ3 uses column (6) from Table 2. That is, the different market access terms are calculated from eq. (7) using estimates from the three different specifications in Table 2: OLS (CFE), OLS (CYFE) and Poisson (CYFE). Table 2. Gravity results (1992–2012)   OLS (CFE)   OLS (CYFE)   PPML (CYFE)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(dist)  −1.992***  −1.567***  −2.001***  −1.491***  −0.868***  −1.286***    (0.103)  (0.129)  (0.108)  (0.139)  (0.180)  (0.192)  border  0.908***  0.953***  0.909***  0.975***  1.201  0.419*    (0.201)  (0.193)  (0.209)  (0.200)  (0.234)  (0.228)  lang.  0.854***  0.572***  0.864***  0.593***  1.233***  0.569*    (0.118)  (0.141)  (0.123)  (0.146)  (0.207)  (0.289)  RTA    0.828***    1.024***    0.773***      (0.155)    (0.180)    (0.190)  CU    0.858**    0.790**    0.485      (0.346)    (0.363)    (0.496)  Obs.  13,710  13,710  13,710  13,710  13,736  13,711  R-squared  0.56  0.57  0.60  0.61  0.76  0.92    OLS (CFE)   OLS (CYFE)   PPML (CYFE)   (1)  (2)  (3)  (4)  (5)  (6)  ln⁡(dist)  −1.992***  −1.567***  −2.001***  −1.491***  −0.868***  −1.286***    (0.103)  (0.129)  (0.108)  (0.139)  (0.180)  (0.192)  border  0.908***  0.953***  0.909***  0.975***  1.201  0.419*    (0.201)  (0.193)  (0.209)  (0.200)  (0.234)  (0.228)  lang.  0.854***  0.572***  0.864***  0.593***  1.233***  0.569*    (0.118)  (0.141)  (0.123)  (0.146)  (0.207)  (0.289)  RTA    0.828***    1.024***    0.773***      (0.155)    (0.180)    (0.190)  CU    0.858**    0.790**    0.485      (0.346)    (0.363)    (0.496)  Obs.  13,710  13,710  13,710  13,710  13,736  13,711  R-squared  0.56  0.57  0.60  0.61  0.76  0.92  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by country) in parentheses. Columns (1) and (2) include a full set of importer and exporter dummies and columns (3) to (6) include a full set of importer-year and exporter-year dummies. Dist is the distance in km between countries, border is a dummy equal to 1 if two countries share a common border, lang is a common language dummy, RTA and CU are Regional Trade Agreement and Currency Union dummies respectively. Source: Author's calculations. In all columns of Table 3, FMA has a positive and highly significant effect on district output. I consider the results in columns (4) and (6) to be the best estimates, as the parameters of the FMÂ term are estimated using a full set of importer and exporter-year fixed effects, and any long-term district growth paths are controlled for with the district time trend. These estimates put the elasticity of district output WRT FMA in the range 0.3 to 0.6. These district-level estimates are comparable to those from previous country-level work. Mayer (2009) regresses income per capita on a measure of ‘foreign market potential’ between 1960 and 2003, finding an elasticity of 0.88 from a random effects model and 0.57 when including country fixed effects.11 In earlier work, Redding and Venables (2004) apply the same approach as Mayer on a single cross-section of countries in 1996, and find an elasticity of 0.48 on their measure of market access. 5.3 Identification and robustness The results presented in Table 3 show that there is a robust correlation between changes in a district’s FMA and changes in its own output. Based on the theoretical framework of Section 2, I argue that this is driven by trade: as FMA increases, demand for local goods increases which drives increases in local production. In this sub-section, I aim to establish that trade is indeed the driving mechanism, and try to address some of the primary endogeneity concerns. To do so, I present a number of falsification and robustness checks in Table 4.12 Table 4. Identification and robustness checks   (1)  (2)  (3)  (4)  (5)  (6)  Panel A: OLS ( FMÂ2)              ln⁡(FMÂ2)    0.425***  0.472***  0.334***  0.342***  0.391***      (0.388)  (0.151)  (0.111)  (0.111)  (0.114)  ln⁡(FMÂ_D)  0.317***              (0.114)            ln⁡(FMÂ_ND)  0.212              (0.300)            Conflict_neigh        −0.055              (0.035)      Obs.  3,560  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Panel B: PPML ( FMÂ3)              ln⁡(FMÂ3)    0.711**  0.799***  0.538***  0.550***  0.549**      (0.203)  (0.237)  (0.163)  (0.165)  (0.252)  ln⁡(FMÂ_D)  0.526***              (0.168)            ln⁡(FMÂ_ND)  0.262              (0.376)            Conflict_neigh        −0.058              (0.036)      Obs.  8,164  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75    (1)  (2)  (3)  (4)  (5)  (6)  Panel A: OLS ( FMÂ2)              ln⁡(FMÂ2)    0.425***  0.472***  0.334***  0.342***  0.391***      (0.388)  (0.151)  (0.111)  (0.111)  (0.114)  ln⁡(FMÂ_D)  0.317***              (0.114)            ln⁡(FMÂ_ND)  0.212              (0.300)            Conflict_neigh        −0.055              (0.035)      Obs.  3,560  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Panel B: PPML ( FMÂ3)              ln⁡(FMÂ3)    0.711**  0.799***  0.538***  0.550***  0.549**      (0.203)  (0.237)  (0.163)  (0.165)  (0.252)  ln⁡(FMÂ_D)  0.526***              (0.168)            ln⁡(FMÂ_ND)  0.262              (0.376)            Conflict_neigh        −0.058              (0.036)      Obs.  8,164  8,956  8,956  8,172  7,633  7,633  Districts  470  508  508  468  445  445  R-squared  0.74  0.75  0.75  0.75  0.75  0.75  Notes: *** p < 0.01, ** p < 0.05, * p < 0.1. Robust standard errors (clustered by district) in parentheses. FMÂ2 is calculated using the estimates of column (4) from Table 2; FMÂ3 is calculated using the estimates of column (6) from Table 2. FMÂD is calculated using only foreign countries with which the domestic country had diplomatic relations, and FMÂND across countries without diplomatic relations. All columns include a district-specific linear time trend. Source: Author's calculations. Firstly, if the effect of FMA is working through trade, we would expect to find a smaller effect between countries that do not have trading relationships with each other.13 To test this, I gather data on diplomatic relations from the Correlates of War’s Diplomatic Exchange Database, and classify countries based on whether they had diplomatic relations with each other over the period (1992–2012). For each district, I then calculate two FMÂ terms: one across countries with which it had diplomatic relations ( FMÂ_D), and another across districts in countries with which it did not ( FMÂ_ND). Reassuringly, in column (1) we see that the FMÂ term is significant only amongst countries with diplomatic relations. Secondly, there may be localized shocks, such as higher commodity prices or cross-border investment projects, that simultaneously benefit neighbouring districts. This would generate a positive correlation between output and market access, but not due to the trade channel posited here. To reduce such concerns, column (2) excludes all districts within 100 km of the domestic district when calculating FMÂ.14 Column (3) drops the closest foreign district, so that any localized shock would have to cover a number of districts to drive the correlation between FMA and domestic output. In both cases, the FMÂ term remains highly significant. Column (4) controls for neighbouring conflicts, which can spill across national borders through refugee flows, direct violence or destruction of infrastructure. This acts like a specific localized shock, generating a simultaneous (negative) shock to both FMA and domestic output. To control for this, I create a dummy variable (denoted conflict_neigh) that equals 1 if a district’s nearest neighbour is in conflict in year t.15 In column (4) this variable enters negatively but insignificantly, whereas the coefficient on FMÂ remains largely unchanged and highly significant.16 Finally, columns (5) and (6) address potential reverse causality from domestic output to FMA. This occurs because an increase in domestic output increases every foreign district’s FMA, increasing their output, which in turn increases the domestic district’s FMA. In practice, this concern is reduced because every district’s FMA term is calculated based on the output of a large number of districts (140 on average, see Table 2). Still, it may be the case that some districts are large enough to individually affect output in the the wider area in a meaningful way. To account for this possibility, column (5) drops all observations from the economically largest district of each country. Column (6) drops all observations from the largest country in each UNECA sub-region. Hence even when eq. (8) is run only with economically small districts, the FMÂ term remains positive and significant. The results in Table 4 support the view that the relationship between FMÂ and domestic output is driven by trade. In Appendix C, I provide a number of more general robustness checks. I remove outliers in terms of changes in luminosity or FMÂ;17 remove observations in which the annual increase in luminosity is greater than 10%; account for common ethnicity in the calculation of FMÂ;18 restrict the sample to districts that have a positive light reading in every year; drop countries with a population below 5 million in 2000; calculate FMÂ using the median structural gravity estimates of Head and Mayer (2015); and calculate market access by simply summing the output of all foreign districts within 500 km of the domestic district.19 In all cases the FMÂ term remains positive and significant. 6. South African growth spillovers In this section, I quantify the importance of South Africa to the wider regional economy, by considering the impact of higher South African growth on each of its neighbours. South Africa remains by far the largest economy in the southern region, and as it economy expands, larger markets are accessible to its neighbours. In the context of the model, higher South African growth increases the FMA of its neighbours, and so boosts their own output. Those neighbours with the lowest trade costs benefit the most, as their FMA increases the most. To demonstrate this, I suppose that each South African district grew by an additional 1 percentage point per year between 1992 and 2012, and then re-calculate the FMA of each neighbouring-country district under this scenario. Based on the relationship between output and FMA, estimated in Table 3, I can then calculate the implied growth of the neighbouring districts due to FMA over the period under both the actual and alternative scenarios.20 As output increases log-linearly in FMA, we can calculate changes in output due to FMA as Δln⁡(Yit)=β^Δln⁡(FMÂit), implying that:   Yit−Yit−1Yit−1=(FMÂitFMÂit−1)β^−1 (9) where Yit−Yit−1Yit−1 is the growth of Yi between 1992 and 2012. I thus calculate implied output growth, using (9), under both the actual and alternative scenarios. The difference between the two gives an estimate of the ‘growth spillovers’ resulting from faster South African growth.21 The results are presented in Table 5, which uses β^=0.343 from Table 3 to calculate (9). The first two columns present the actual observed growth rates in each country; the first using official GDP figures, and the second using the luminosity data. It is notable that the luminosity data tracks GDP relatively well across the six countries—capturing the rapid growth in Mozambique and the stagnation in Zimbabwe. Table 5. Effect of higher South African growth   Actual Growth   Implied Growth due to FMA^it     GDP  Lights  Previous  New  Diff  Botswana  4.5  5.5  0.7  1.0  0.31  Lesotho  4.0  5.3  0.6  0.9  0.34  Mozambique  8.5  6.9  2.4  2.7  0.26  Namibia  3.9  2.5  0.7  1.0  0.30  Swaziland  3.3  3.3  0.6  0.9  0.33  Zimbabwe  −0.3  0.4  2.5  2.8  0.26    Actual Growth   Implied Growth due to FMA^it     GDP  Lights  Previous  New  Diff  Botswana  4.5  5.5  0.7  1.0  0.31  Lesotho  4.0  5.3  0.6  0.9  0.34  Mozambique  8.5  6.9  2.4  2.7  0.26  Namibia  3.9  2.5  0.7  1.0  0.30  Swaziland  3.3  3.3  0.6  0.9  0.33  Zimbabwe  −0.3  0.4  2.5  2.8  0.26  Notes: All figures are annual percentage compound growth rates between 1992 and 2012. The GDP figures are taken from the World Bank World Development Index and are in constant US dollars. Source: Author's calculations. The final three columns present the implied growth in output due only to changes in FMA, i.e. due to increases in the output of neighbouring economies. The ‘previous’ column presents the results of calculating eq. (9) for each country, using the actual South African output figures. In Botswana for example, actual growth over the period averaged 5.5% per year (using the lights data). Based on changes in FMA alone, the model predicts that growth in Botswana would have averaged 0.7% per year over the period. The ‘new’ column shows the implied growth rate under the scenario of faster South African growth, and the final column calculates the difference—i.e. the change in annual growth as a result of 1 percentage point higher South African growth. The largest gains accrue to Lesotho and Swaziland, the countries with the lowest trade costs with South Africa (driven primarily by shorter distances than the other neighbours). The smallest gains accrue to Mozambique and Zimbabwe, although even here the spillover effects are reasonably large. 7. Conclusion This paper considers how African countries are affected by the growth of their neighbours. Adapting the model of Donaldson and Hornbeck (2016), I show that a district’s output can be expressed as a function of its ‘market access’. Higher growth elsewhere increases market access, increasing the demand for local goods. To concentrate on international spillovers, I include only foreign (African) districts in the calculation of market access for the empirical work. I am able to conduct the empirical work at the sub-national level by exploiting luminosity data to generate a panel of district output over 1992–2012. This advances both previous work on spillovers in Africa (Collier and O’Connell 2007; Roberts and Deichmann, 2011) and the related market access literature (Redding and Venables, 2004; Mayer, 2009), which work with country-level data. My empirical work shows that FMA is an important determinant of the growth of domestic districts: increases in FMA are reflected in significant district growth, with an elasticity between 0.3 and 0.6. I noted in the introduction that African economic integration is now a top priority of policymakers. In large part, this stems from the difficulty that most countries face in penetrating global markets. Agglomeration forces have clustered manufacturing activity in East Asia, generating concerns that African countries have ‘missed the boat’ of globalization (see World Bank, 2002; Collier, 2008). For the landlocked countries, higher freight and insurance costs multiply this challenge (Limao and Venables, 2001; Faye et al. 2004). The World Bank (2009) argues that ‘for small countries far from world markets but close to a large developing country [such as South Africa], their best prospects often lie in growth in the dominant economy’ (p. 272). I provide evidence here to support that claim, and show that by reducing trade costs such prospects are improved. Supplementary material Supplementary material—the Appendix and data files—is available online at the OUP website. Footnotes 1 Throughout the paper, I use ‘Africa’ to refer to sub-Saharan Africa. The average growth of real GDP in Africa was 4.1% between 1992 and 2012, based on World Bank figures. 2 Based on the UCDP/PRIO Armed Conflict Database for example, there were seven sub-Saharan African countries involved in ‘intense’ conflicts—those resulting in at least 1,000 deaths per year—in 1990. By 2012, this dropped to just two (Somalia and Sudan). See also: http://www.economist.com/blogs/baobab/2013/11/civil-wars. 3 γ0 is treated as a constant, although it includes the aggregate utility level U¯ which in practice is not necessarily constant over time. As I am implementing a simplified (‘reduced form’) version of the model, discussed below, I abstract from this complication here. 4 Redding and Venables (2004) outline a similar trade model to the one presented here but with immobile labour. Their model derives output per capita in country i (yi) as a log-linear function of the country’s market access. They use income per capita as a proxy for yi and consider various approximations to calculate internal trade costs τii for the (domestic) market access term. Mayer (2009) extends the Redding and Venables approach to a panel setting. He presents empirical results both with approximations for τii, and with domestic output dropped from the market access term. Both approaches show strongly significant effects of market access on income per capita. 5 This is also consistent with my approach of using cross-country gravity regressions to estimate the trade cost function (below). 6 See Overman et al. (2010) for a more detailed discussion of the spatial implications of an output shock in a particular region. 7 I denote a ‘capital district’ here as the largest district in each country based on lights output in 2000. Lights output grew in capital districts by 5% per year on average. Across other districts, they grew by 4% per year on average. 8 I take the centroid of the largest city (contiguous block of urban cells) based on light output in 2000. To accurately calculate distance, I then project these points to the African Sinusoidal (projected) coordinate system. Geodesic distances, that take into account the curvature of the globe, are then calculated using the Generate Near Table tool. All steps are done in ArcMap 10.2.1. 9 UNECA is the United Nations Economic Commission for Africa. See http://www.uneca.org/pages/subregional-offices. 10 Only ‘intense’ conflict years are excluded, which are those that result in a minimum of 1,000 battle-related deaths. 11 Mayer’s (2009) ‘foreign market potential’ term is, from his model, very similar to that used here. His empirical approach is quite different however. Rather than including a measure of market potential directly, he demonstrates that it can be captured by the country fixed effect coefficients from an initial gravity regression. That approach is not applicable here because I am calculating market access for sub-national units. 12 Each column in Table 4 includes the district-specific linear time trend. 13 The effect would not necessarily be zero, as informal cross-border trade takes place on a substantial scale across the continent (Lesser and Moisé-Leeman, 2009). This is likely the case even amongst countries with poor official relations. 14 I drop if distance >100 km, hence this is based on the distance between the largest ‘cities’ in the two districts. 15 Neighbouring conflicts are defined in the same way as domestic conflicts (Section 4), as a year in which there are 1,000 or more battle-related deaths according to the UCDP/PRIO Armed Conflicts Database. 16 The neighbouring conflict variable enters significantly if the district-specific linear time trend is excluded. 17 For each variable, I remove all observations greater (in absolute value) than the mean plus or minus 2 standard deviations. 18 I generate a dummy equal to 1 if two districts share a common ethnic group, based on the geospatial data held by the International Conflict Research Group at ETH Zurich. To calculate FMÂ in this case I first scale this variable to the country level and include this in the gravity regressions. For brevity I have not provided these gravity results, but they are available on request. 19 This is to approximate the ‘intuitive’ market access term suggested by Baum-Snow et al. (2015). 20 There are additional feedback effects that are abstracted from here. In particular, higher South African growth increases the growth of its neighbours, which in turn reinforces South African growth. Given the relative size of South African economy, such feedback effects are likely to be very small, and are ignored here for simplicity. More generally, the results in this Section are provided primarily to illustrate the magnitude of the estimated effects, and should be interpreted in this vein. 21 We are ultimately interested in the response of GDP in district i (denoted zi) to changes in GDP in district j (denoted zj), rather than the response of lights in i (denoted yi) to lights in j (denoted yj). The two elasticities are the same however. Denote the ‘GDP elasticity’ by ɛ1≡dzidzjzjzi and the ‘lights elasticity’ by: ɛ2≡dyidyjyjyi. We have also estimated the elasticity of GDP to lights in Section 4, denoted by: ɛ3≡dzidyiyizi. From the chain rule: dzidzj=dzidyidyidyjdyjdzj and so, multiplying by: zjzi,   ɛ1=dzidzjzjzi=(dzidyiyizi)︸ɛ3(dyidyjyjyi)︸ɛ2(dyjdzjzjyj)︸ɛ3−1=ɛ2 Acknowledgements This paper formed a chapter of my PhD thesis, and I am grateful to my supervisor Tim Besley for his advice throughout the project, as well as my examiners Gharad Bryan and Tony Venables. I also thank Jane Ansell, Zelda Brutti, Vernon Henderson, Guy Michaels, Adam Storeygard, Silvana Tenreyro, two anonymous referees and participants at the LSE Development and Growth Seminars and the Econometric Society World Congress in Montreal for very helpful feedback. References Afrika J.-G. K., Ajumbo G. 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Published: Apr 1, 2018

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