The Poisson quasi-maximum likelihood estimator: a solution to the ‘adding up’ problem in gravity models

Abstract

This article shows that the Poisson Quasi-Maximum Likelihood (QML) estimator applied to the gravity model produces estimates in which, summing across all partners, actual and estimated total trade flows are identical. Other methods such as OLS do not have this desirable property. Indeed, Poisson is the only QML estimator that preserves total trade flows. This result is an additional reason for preferring Poisson as a workhorse gravity model estimator.

Keywords:

• international trade
• gravity model
• Poisson
• Quasi-Maximum Likelihood estimator

JEL Classification:

• F10
• C10

Notes

The findings, interpretations and conclusions expressed in this article are entirely those of the authors. They do not represent the view of the World Bank, its Executive Directors or the countries they represent.

¹The following development refers to a matrix of flows, but it applies to any list of allocation variables and not just a matrix.

²Partial derivatives are noted by the subscript 1 or 2 depending on the variable.