Pareto Distributions in International Trade: Hard to Identify, Easy to Estimate
45 Pages Posted: 5 Dec 2016
Date Written: November 13, 2016
We show that, in heterogeneous-firm international trade models, common forms of heterogeneity and uncertainty drive a (multiplicative random) wedge between the observable exports distribution and the latent distribution of firm productivity. Even if the latter is exactly Pareto distributed, this wedge, correlated with firm productivity, distorts the exports data, often making it look log-normally distributed. We show this distortion to be quantitatively relevant, meaning that empirical evidence of a log-normal exports distribution does not preclude an underlying Pareto distribution for productivity. Furthermore, this wedge renders common maximum-likelihood and quantile-based estimators misspecified, hence inconsistent. We provide general conditions in a broad class of international trade models under which, despite this misspecification issue, the tail of the exports distribution can be used to estimate the power exponent of the productivity distribution consistently -- provided the sample size of left-truncated export data is large enough.
Keywords: Pareto, power law, international trade, productivity distribution, misspecification
JEL Classification: F12, F14
Suggested Citation: Suggested Citation