Variable Scaling And Joint Hypothesis Testing In PPML

The enormous gravity-model-of-trade literature has illustrated important advantages of estimation via Poisson Pseudo Maximum Likelihood (PPML). That literature’s prioritization of parameter estimation over hypothesis testing has left questions of testing in the PPML framework underexplored. In this paper we show analytically that scaling the dependent variable can affect the outcome of some joint hypothesis tests, but not others. Likelihood-ratio, model-based Wald, and model-based Lagrange Multiplier test statistics depend on scale, and therefore do not support scale-invariant inference. Wald and Lagrange Multiplier tests constructed with heteroskedasticity-robust sandwich adjustments are invariant to scale. We illustrate these points empirically with an application from the literature on Revealed Comparative Advantage.