centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Bias and Consistency in Three-way Gravity Models

Authors: Martin Weidner and Thomas Zylkin
Date: 07 January 2020
Type: cemmap Working Paper, CWP1/20
DOI: 10.1920/wp.cem.2020.120


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. 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.

Download full version

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us