The Surprising Bias of PPML Estimates of Structural Gravity Models With Two‐Way Fixed Effects

The previous literature has shown that the Poisson Pseudo‐Maximum Likelihood (PPML) estimator provides consistent and asymptotically unbiased estimates of the parameters of structural gravity models with two‐way fixed effects, although their standard errors need correction. We show that, notwithstanding this result, PPML suffers from bias in small samples. Surprisingly, that bias is evident in the types of samples typically used for gravity models, which can involve tens of thousands of observations. We explore the nature and extent of the bias both theoretically and through simulations, and we show that bias corrections based on the bootstrap and split‐sample jackknife can attenuate but not necessarily eliminate it. An empirical application suggests that, especially at the sectoral level, the bias we have identified could be significant, particularly in settings where point estimates are of primary importance, such as when gravity model estimates of the impact of a trade agreement or some other non‐tariff policy are used in a second stage general equilibrium impact assessment of a counterfactual policy change.