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.