What is really puzzling about the “distance puzzle”


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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  1. 1.

    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.

  2. 2.

    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.

  3. 3.

    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.

  4. 4.

    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.

  5. 5.

    http://www.cepii.fr/anglaisgraph/bdd/distances.htm, Centre d’Etudes Prospectives et d’Informations Internationales.

  6. 6.

    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.

  7. 7.

    Unlike Baier and Bergstrand, elasticities are here allowed to vary through time.

  8. 8.

    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.

  9. 9.

    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.

  10. 10.

    The log of the residual is directly related to the bias as Eqs. (1), (4) and (5) imply that \(E(\ln u|Z) \approx -\frac{1}{2} {\text{Var}}(u|Z)\).

  11. 11.

    For \(\lambda _1 = 0\), NLS or maximum likelihood leads to almost identical estimates.

  12. 12.

    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).

  13. 13.

    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.

  14. 14.

    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.

  15. 15.

    We are thankful to one anonymous referee to have pushed us in this direction.

  16. 16.

    In doing so, data corresponding to trade between large and small countries are lost.

  17. 17.

    We are especially grateful to one anonymous referee for having pushed us in this direction.


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Corresponding author

Correspondence to Clément Bosquet.

Additional information

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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  • Distance puzzle
  • Gravity equations
  • Pseudo-maximum likelihood methods

JEL Classification

  • F10
  • F15
  • C13
  • C21
  • C23