Cross-sectional Gravity Models, PPML Estimation, and the Bias Correction of the Two-Way Cluster-Robust Standard Errors*

Abstract

In cross-section gravity models the two-way cluster-robust standard errors of the Poisson pseudo maximum likelihood (PPML) estimates tend to be considerably downward biased. However, two-way clustering can be avoided if intra-cluster correlation is induced by country-specific trade shocks with uniform pass through (equi-correlation) and the gravity model includes exporter and importer country fixed effects. In this case the pseudo-within-transformation of the PPML estimator projects out the corresponding components of the disturbances. In Monte Carlo simulations the Pustejovsky and Tipton (2018) bias correction for independent disturbances (i.e. ignoring clustering) reveals just a small downward bias of the estimated standard errors and confidence intervals with nearly correct coverage rates. Under deviations from equi-correlation the bias is somewhat larger, but still comparable to the bias of the cluster-robust standard errors with Pustejovsky and Tipton (2018) bias correction.