Abstract
I document the existence of discontinuities in short- and long-term growth rates of satellite-recorded nighttime lights per capita across national borders, with growth rates of nighttime lights increasing abruptly as one crosses a border from a slower-growing country into a faster-growing one. I show that growth discontinuities are not driven by any special set of borders, or by differences in geographic and climatic conditions on the different sides of borders. I investigate multiple explanations for growth discontinuities, including differences in the determinants of growth across borders and differences in the extent to which borders form barriers to flows of goods, capital or people. I present evidence that differences in the quality of the rule of law are consistently helpful in explaining differences in growth between two countries at their border, and conclude that national-level variables such as institutions and policies may have rapid and important effects on growth.
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Notes
Ruthenia had been a part of the Kingdom of Hungary since 1526, and of the Habsburg empire (which included Hungary, Slovakia, and the parts of Poland and Romania that are visible in this picture) since 1699. After the collapse of the Habsburg empire as a result of World War I, Ruthenia became a part of Czechoslovakia in 1918. Ruthenia was annexed by the Soviet Union in 1945 as a result of World War II, and attached to the Ukrainian Socialist Soviet Republic, which became the independent country of Ukraine in 1991.
The recorded brightness of lights may depend on cloud cover, humidity and other atmospheric conditions in a region, but it is implausible that national borders consistently conform to atmospheric fronts. Robustness checks with controls for temprerature, precipitation, altitude and slope on both sides of borders do not alter the results.
Michalopoulos and Papaioannou (2014) implicitly consider a model with this property when investigating the lack of a discontinuity in economic activity at African borders at which an ethnicity was split between two countries during the Scramble for Africa. The find that, at least in Africa, local institutions, as proxied by ethnic institutions, matter more than national institutions (proxied by rule of law as measured by the World Bank) do. As I look at a model of growth rates rather than levels, and as I do not analyze borders that split rather than separate ethnicities, I do not claim that my results contradict Michalopoulos and Papaioannou (2014). In Sect. 5.2 I find some evidence that cultural similarities across borders in genetic distance from the UK or in the official language are correlated with smaller growth discontinuities at borders.
The nighttime lights maps are available for download from the URL http://www.ngdc.noaa.gov/dmsp/downloadV4composites.html.
Chen and Nordhaus (2010) use \(d=3/2\) in their related, though different, specification of the relationship between DN and output density.
I conduct the estimation by performing nonlinear least squares using the Matlab routine fmincon, in which I impose the constraint that \( c_{0} \) and \(c_{1}\) cannot be negative.
In addition to measuring the growth rate of calibrated lights per capita, I also present results in which the dependent variable is constructed as the growth in light density, which is measured as
$$\begin{aligned} \ln \left( 0.01+\sum _{j=0}^{63}j*v_{j,i}\right) \end{aligned}$$(2)following Michalopoulos and Papaioannou (2014). The resulting dependent variable has a correlation of greater than 0.98 with the lights per capita variable, even conditional on other covariates of my baseline specification (see sect. 3.4). Therefore, I present only results for lights per capita in the main text, and relegate results for light density to Appendix I. My results typically are robust across the different ways of computing the dependent variable. The similarity of results using light density and results using lights per capita is consistent with population not being disproportionately low or high on faster growing sides of borders, which is one of the findings in this paper.
This grid does not coincide with integer lines of latitude and longitude, so there are no problems of the grid falling exactly upon a border.
It is useful to recognize that the sample of borders overrepresents landlocked countries, because the latter have more neighbors than coastal countries by definition, and completely excludes countries that are islands (like Japan or Australia). While landlocked countries tend to be poorer than coastal countries, it is unclear whether this should affect the difference-based estimates in the paper. Estimates by region tend to be similar to the global estimates. Moreover, population-weighting the observations should reduce the bias towards countries that are less developed and support lower population densities.
If we were to look at the levels, rather than the growth rates of nighttime lights, we would see lights in Mexico at the border be much lower than lights in the U.S. at the border, except for the last 10 miles of the Mexican border, where the lights would be equal to the U.S. lights. These last 10 miles are likely accounted for by overglow, border-specific infrastructure, or an especially high intensity of foreign investment even relative to the rest of northern Mexico.
These are local linear discontinuity estimates, whose construction is discussed below.
I perform all analyses separately for 5-year growth rates and 18-year growth rates.
This result is most closely related to Card and Lee (2008).
In particular, it is easy to see that if growth were continuous at borders, then \(\gamma \) would be zero.
The climatic variables are: (1) Annual Mean Temperature, (2) Mean Diurnal Range, (3) Isothermality, (4) Temperature Seasonality, (5) Max Temperature of Warmest Month, (6) Min Temperature of Coldest Month, (7) Temperature Annual Range, (8) Mean Temperature of Wettest Quarter, (9) Mean Temperature of Driest Quarter, (10) Mean Temperature of Warmest Quarter, (11) Mean Temperature of Coldest Quarter, (12) Annual Precipitation, (13) Precipitation of Wettest Month, (14) Precipitation of Driest Month, (15) Precipitation Seasonality, (16) Precipitation of Wettest Quarter, (17) Precipitation of Driest Quarter, (18) Precipitation of Warmest Quarter, and (19) Precipitation of Coldest Quarter. The land cover categories are: (0) Body of Water, (1) Evergreen Needleleaf Forest, (2) Evergreen Broadleaf Forest, (3) Deciduous Needleleaf Forest, (4) Deciduous Broadleaf Forest, (5) Mixed Forest, (6) Closed Shrublands, (7) Open Shrublands, (8) Woody Savannas, (9) Savannas, (10) Grasslands, (11) Permanent Wetlands, (12) Croplands, (13) Cropland / Natural Vegetation Mosaic.
The Americas are treated as a single continent because they are contiguous, and the number of borders in the Americas is comparable to that in Europe, Asia or Africa. Since the latter three continents form a continuous landmass, I define Russia, Turkey and Egypt to be part of two continents at once. I count the borders of these countries to belong to the continent of the bordering country: e.g. Russia’s border with Estonia is a European border, but Russia’s border with China is an Asian border.
The fractal dimension of a curve is computed by superimposing square grids of varying grid sizes over the curve, counting up the number of grid cells intersected by the curve for each size, and running a regression of the log number of intersections on log grid size. The negative of the slope coefficient (minus one) is the fractal index of the border. See Alesina et al. (2011) (AEM) for greater details.
I do not succeed in replicating the results of AEM, most likely because of the worse resolution of the border map that I have available to use. The fractal dimension indices for countries that I obtain have a statistically significant correlation with AEM’s of 0.55. In results not reported, I use an alternative method of approximating the fractal dimension of borders by simply taking the average of the fractal dimensions of the bordering countries. I obtain the same results when I use this second method.
In this paper, I use the term “rugged” to mean that terrain has high average slope. I note that this is somewhat different from the concept of ruggedness in Nunn and Puga (2012), but is close in spirit.
Since I have ruggedness for every border piece, I can allow a border to have both rugged and flat border pieces. Hence, the numbers of borders having rugged and flat border pieces do not need to add up to the total number of borders (though they come fairly close, suggesting that most borders are either completely rugged or completely flat).
The gas flares data are available country by country from the DMSP-OLS website. I am very grateful to Matthew Lowe (http://economics.mit.edu/grad/mlowe) for sharing his version of these datasets merged together.
Clearly, the gas producing the flares is wasted rather than captured, and the extent to which flares are produced depends on how lax environmental regulations are, so the gas flares do not measure the quantity of fossil fuel extraction. However, it is reasonable to believe that the presence of flares should indicate that at least some fossil fuel extraction activity is taking place.
It does not make sense to regress growth differentials directly on the border permeability measures because there is nothing in the regression that would explain the sign of the growth differential: the constant and border permeability measures can only explain the magnitude of the differential.
I can also compute versions of these regressions in which all the cross-border flow measures are included simultaneously. This approach has the advantage of capturing the effect of controlling for a broader measure of cross-border flows on growth discontinuities at borders, although the coefficients on the interaction effects become more difficult to interpret. The regressions then become
$$\begin{aligned} \left| \Delta \tilde{g}_{i,b,t}\right| =\alpha +\sum _{j=1}^{4}d_{j}T_{b}^{j}+\varepsilon _{i,b,t} \end{aligned}$$(11)and
$$\begin{aligned} \tilde{g}_{i,b,t}= & {} \alpha _{b,t}+\beta u_{i,b,t}+\sum _{j=1}^{4}\tilde{\beta } _{j}u_{i,b,t}\times T_{b}^{j}+\varepsilon _{i,b,t}\\ \tilde{g}_{i,b,t}= & {} \chi _{b,t}+\gamma g_{i,t}+\sum _{j=1}^{J}\tilde{\gamma } _{j}g_{i,t}\times T_{b}^{j}+\upsilon _{i,b,t}\nonumber \end{aligned}$$(12)Estimates from these equations are presented in Appendix Table A1.
Additionally, I perform sample splits of the data along borders with high and low cross-border flows according to the four measures I consider. Appendix Table A3 presents estimates from this approaches. The results are qualitatively similar, although it appears that growth discontinuities may be weaker at borders with above-median trade flows for some measures of growth. The interaction-based specification is preferable to the sample split because it allows the extent of cross-border flows to have a more continuous effect on the size of the border discontinuity.
Following Sect. 3, we can also rewrite these equations as
$$\begin{aligned} \Delta \tilde{g}_{i,b,t}=\beta \Delta u_{i,b,t}+\tilde{\beta }\Delta u_{i,b,t}*T_{b}+\Delta \varepsilon _{i,b,t} \end{aligned}$$and
$$\begin{aligned} \Delta \tilde{g}_{i,b,t}=\gamma \Delta g_{i,t}+\tilde{\gamma }\Delta g_{i,t}*T_{b}+\Delta \upsilon _{i,b,t} \end{aligned}$$to highlight that the border permeability terms should attenuate the effect of the national growth differences upon the growth differences at the border.
This approach is the same as performing a sample split of the data along borders with high and low cross-border flows, with the exception that interactions allow the “split” variable to be continuous.
Another way in which culture may interact with borders is if an ethnic group with the same culture is split by a border and made part of two different countries. The estimation technique that I use should difference out this common cultural component on both sides of borders. This subject has been explored at greater length in Michalopoulos and Papaioannou (2014).
Analogously to the cross-border flow analysis, I compute estimates for the all-at-once regression and for using sample split. They are presented in Appendix Tables A2 and A4. The results are generally consistent with a weaker role for cultural variables in explaining border discontinuities than is Table 10.
Results for growth in light density are somewhat weaker and statistically insignificant unless controls for population, area, climate and local public goods are included, but show the same pattern of coefficients as the results presented, and become numerically similar to results presented once the additional controls specified are included. This is most likely because my growth of light density at a border variable is uncalibrated to GDP, unlike my growth of lights per capita variable. Using growth of calibrated light density at a border restores significance to the rule of law coefficient estimates. Results for growth in light density are included in the Online Appendix I.
In particular, there is a 0.85 correlation between total road length in the DCW and total road length as reported by the World Bank. There is a 0.55 correlation between total telephone line length in the DCW and total telephone line length as reported by the World Bank.
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Acknowledgements
I would like to thank Daron Acemoglu, Jerry Hausman, James Snyder and Amy Finkelstein for guidance and advice. I would like to thank Melissa Dell, Esther Duflo, Susan Elmes, Chris Elvidge, Jens Hainmueller, Horacio Larreguy, Anna Mikusheva, Serena Ng, Elias Papaioannou, Jack Porter, Bernard Salanie, Whitney Newey, and participants at the Political Economy Breakfast at MIT and the Econometrics Lunch at Columbia University for very insightful comments. I am very grateful to Oded Galor and four anonymous referees for insightful and useful comments. I would like to thank Daniel Sheehan and the MIT GIS lab for assistance with geographic software. I am very grateful to John Grigsby for truly superb and dedicated research assistance. I am very grateful to the Paul and Daisy Soros Fellowship for New Americans for intellectual stimulation, and to the National Science Foundation Graduate Research Fellowship Program and the Institute of Humane Studies for funding. The paper does not necessarily represent the views of the above individuals and organizations, of the Federal Reserve Bank of New York, or of the Federal Reserve System. All remaining errors are my own.
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Pinkovskiy, M.L. Growth discontinuities at borders. J Econ Growth 22, 145–192 (2017). https://doi.org/10.1007/s10887-016-9139-2
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DOI: https://doi.org/10.1007/s10887-016-9139-2