Bias and consistency in three-way gravity models

Abstract

We study the incidental parameter problem in "three-way" Poisson Pseudo-Maximum Likelihood ("PPML") gravity models recently recommended for identifying the effects of trade policies and in other network panel data settings. Despite the number and variety of fixed effects this model entails, we confirm it is consistent for small $T$ and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when $T$ is small. At the same time, asymptotic confidence intervals in fixed-$T$ panels are not correctly centered at the true point estimates, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables.