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

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.

Bio

I am associate professor of economics at the college of business, Lehigh University. My research develops econometric methods for empirical settings where standard tools break down, especially with data exhibiting heavy tails, extreme values, and non-existent moments. My recent work covers robust inference for clustered data, tail-index regression in high dimensions, growth-at-risk forecasting, and estimation in gravity models of trade, with applications to income inequality, health expenditure, earnings dynamics, and auctions. I hold a Ph.D. and M.A. in Economics from Princeton University, an M.A. in Economics from UCLA, and a B.A. in Finance from Tsinghua University. Outside academia, I was a Senior Economist at Amazon.com, applying causal inference and forecasting to workforce analytics and other large-scale business problems. I am also a licensed realtor in New Jersey and New York, where I build data-driven housing valuation models from large-scale transaction data.