PPML and Heavy-Tailed Trade and Factor Flows: Why Standard Inference Fails and How to Fix It

Peter Egger, Ting Ji and Yulong Wang

No 21998, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: The Poisson pseudo-maximum likelihood (PPML) estimator is widely used for estimating bilateral gravity equations. Its consistency requires only a correctly specified conditional mean. Conventional inference, however, also requires finite-variance scores and Gaussian limits. We show that these conditions fail: bilateral flows are Pareto-tailed, PPML scores have a stable limit under a structural gravity data-generating process, and sandwich confidence intervals are too narrow. We retain PPML for point estimation but replace sandwich inference with an m-out-of-n bootstrap robust to heavy tails. Across three bilateral data settings, the correction is large and overturns conventionally significant gravity coefficients.

Keywords: PPML estimation; Gravity equation; Heavy tails; Non-Gaussian limit; Bootstrap (search for similar items in EconPapers)
JEL-codes: C13 C51 F14 (search for similar items in EconPapers)
Date: 2026-09
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