Abstract
This paper studies the change in the distance elasticity of trade between 1948 and 2006. The elasticity sharply increased, when gravity equations are estimated by ordinary least squares in log form (log-OLS), while it was broadly stable or slightly increasing, depending on the specification, based on Poisson pseudo-maximal likehood (PPML) in levels, a standard estimator. We show that such a divergence is due to the increased heterogeneity of trade flows. However, gamma pseudo-maximal likehood, which should be consistent under the assumptions that make PPML so appealing, generate estimates that are significantly different from PPML and actually closer to log-OLS. We provide tentative solutions to this puzzle.
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Notes
Indeed, according to the meta-analysis carried out by Disdier and Head (2008), trade decreases with distance by at least the same amount today than 30 years ago, with an increase in the distance elasticity of trade since the late eighties.
Another suggestion has been provided by Lin and Sim (2012). They argue that an increase in the extensive margin of trade at longer distances and in the intensive margin at shorter distances might artificially generate higher distance coefficients in absolute terms.
SST actually suggest testing the adequacy of a particular value of \(\lambda _1\) from a Taylor expansion of (3), which they apply in the empirical part of their paper. Unfortunately, this procedure is subject to the same problem as for the negative binomial estimator: it artificially depends on the unit choice of trade flows, and could therefore be misleading. Details are available upon request.
In contrast, the NLS estimator of the trade level specification, although consistent, is inefficient in that case because it does not give enough weights to small flows.
http://www.cepii.fr/anglaisgraph/bdd/distances.htm, Centre d’Etudes Prospectives et d’Informations Internationales.
Compared with Fontagné and Zignago, FTA data has been updated beyond 2000. In total, 47 FTAs are covered. The first FTA in the database is the European Economic Community, which treaty was signed on March 25th, 1957.
Unlike Baier and Bergstrand, elasticities are here allowed to vary through time.
To be consistent with the gravity specification in levels, the geometric mean of trade flows is used as the dependant variable. By comparison, Baier and Bergstrand use a specification in logs with elasticities with respect to distance, border, colonial link, etc., that are constant through time, and reduce the number of fixed effects by keeping only one out of 5 years.
In 1986, Portugal and Spain joined the EU and Finland joined the EFTA. The scope of the FTA between the EU and the EFTA countries was also broadened as a result. The estimated FTA parameter increased from 0.56 in 1985 to 0.82 in 1986 and then dropped back to about 0.50 from 1993. Notwithstanding this possible collinearity issue, all the results presented in this paper are robust to the exclusion of the FTA variable. The only notable difference is that the mid-1980s trough in the PPML specification is smaller when the FTA variable is excluded.
For \(\lambda _1 = 0\), NLS or maximum likelihood leads to almost identical estimates.
More precisely, the ratio of the estimated standard deviation of the distance parameter is 2.4 on average, and 1.8 for the last available year (2006).
PPML and GPML lead also to differences in other parameters of interest. For example, sharing an FTA increases trade by 48 and 27 %, on average through time, according to PPML and GPML, respectively. Details are available upon request.
The sensitivity of GPML to the inclusion/exclusion of zeros is not a problem as such since small flows are given more weight with GPML and excluding them might lead to selection bias.
We are thankful to one anonymous referee to have pushed us in this direction.
In doing so, data corresponding to trade between large and small countries are lost.
We are especially grateful to one anonymous referee for having pushed us in this direction.
References
Anderson, J., & van Wincoop, E. (2003). Gravity with gravitas: A solution to the border puzzle. American Economic Review, 93(1), 170–192.
Baier, S. L., & Bergstrand, J. H. (2007). Do free trade agreements actually increase members international trade? Journal of International Economics, 71(1), 72–95.
Baldwin, R., & Taglioni, D. (2006). Gravity for dummies and dummies for gravity equations. (CEPR Discussion Paper 5850). London: Centre for Economic Policy Research.
Berthelon, M., & Freund, C. (2008). On the conservation of distance in international trade. Journal of International Economics, 75(2), 310–320.
Bosquet, C., & Boulhol, H. (2014). Applying the GLM variance assumption to overcome the scale-dependence of the negative binomial QGPML estimator. Econometric Reviews, 33(7), 772–784.
Buch, C. M., Kleinert, J., & Toubal, F. (2004). The distance puzzle: On the interpretation of the distance coefficient in gravity equations. Economics Letters, 83(3), 293–298.
Carrère, C., de Melo, J., & Wilson, J. (2013). The distance puzzle and low-income countries: An update. Journal of Economic Surveys, 27(4), 717–742.
Coe, D. T., Subramanian, A., & Tamirisa, N. (2007). The missing globalization puzzle: Evidence of the declining importance of distance. IMF Staff Papers, 54(1), 34–58.
Disdier, A.-C., & Head, K. (2008). The puzzling persistence of the distance effect on bilateral trade. The Review of Economics and Statistics, 90(1), 37–48.
Fontagné, L., & Zignago, S. (2007). A re-evaluation of the impact of regional agreements on trade patterns. Economie Internationale, 109(1), 31–51.
Golub, S., & Tomasik, B. (2008). Measures of international transport cost for OECD countries. (OECD Economics Department Working Papers 609). Paris: Organisation for Economic Co-operation and Development.
Head, K., & Mayer, T. (2013). Gravity equations: Workhorse, toolkit, and cookbook. (CEPR Discussion Paper 9322). London: Centre for Economic Policy Research.
Head, K., Mayer, T., & Ries, J. (2009). How remote is the offshoring threat? European Economic Review, 53(4), 429–444.
Hummels, D. (2007). Transportation costs and international trade in the second era of globalization. Journal of Economic Perspectives, 21(3), 131–154.
Leamer, E. (2007). A flat world, a level playing field, a small world after all, or none of the above? Review of Thomas L. Friedman’s the world is flat. Journal of Economic Literature, 45(1), 83–126.
Lin, F., & Sim, N. C. (2012). Death of distance and the distance puzzle. Economics Letters, 116(2), 225–228.
Manning, W. G., & Mullahy, J. (2001). Estimating log models: To transform or not to transform? Journal of Health Economics, 20(4), 461–494.
Santos Silva, J., & Tenreyro, S. (2006). The log of gravity. The Review of Economics and Statistics, 88(4), 641–658.
Santos Silva, J., & Tenreyro, S. (2011). Further simulation evidence on the performance of the poisson pseudo-maximum likelihood estimator. Economics Letters, 112(2), 220–222.
Wooldridge, J. M. (2002). Introductory Econometrics: A Modern Approach. Cincinnati, OH: South-Western College Publishing.
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We are particulary grateful to Thierry Mayer who provided data as well as useful suggestions at an early stage. We warmly thank Keith Head, Joao Santos Silva, Pierre-Philippe Combes, Lionel Fontagné and two anonymous referees for useful comments, as well as participants of the GREQAM PhD Students lunch seminar, the IXth RIEF doctoral meeting, the 24th EEA annual congress, the 58th AFSE annual congress and the ASSET annual congress.
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Bosquet, C., Boulhol, H. What is really puzzling about the “distance puzzle”. Rev World Econ 151, 1–21 (2015). https://doi.org/10.1007/s10290-014-0201-x
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DOI: https://doi.org/10.1007/s10290-014-0201-x