Three-way gravity models with multiplicative unobserved effects

Abstract

Summary This paper investigates three-way gravity models with multiplicative unobserved effects, which are popular in bilateral trade analysis and many other contexts. Such models are usually estimated by the fixed effects Poisson pseudo maximum likelihood method. As an alternative, we extend the estimation strategy proposed by Jochmans (2017) to our new settings by constructing moment conditions that are independent of the unobserved effects. Our method entails estimation of the conditional mean of a variety of functional forms. The generalized method of moments (GMM) estimator based on these moment conditions is N-consistent and asymptotically normally distributed. We also discuss the estimation of dynamic models by extending the linear feedback models to our three-way settings. Through various simulation designs, we show that our GMM estimator outperforms the competing Poisson pseudo maximum likelihood estimator. As an empirical application, we estimate the effects of the currency unions on exports.