Bias in Poisson Pseudo-Maximum Likelihood estimation of structural gravity models: how much of a problem for applied research?

Theory-consistent (‘structural’) gravity models are commonly used to model bilateral trade. Extensive simulations suggest that the Poisson Pseudo-Maximum Likelihood (PPML) estimator performs well in that setting. However, an influential review by (‘HM’) includes a simulation where PPML exhibits significant bias, which leads them to recommend a toolbox approach, including PPML and other estimators. I show that PPML’s bias is related to the noisiness of the data. A more realistic error variance assumption reveals that even for the same distribution type as HM, PPML’s bias is 4% rather than the 27% they report.