A Count Data Model with Dual Endogenous Binary Variables

Abstract

Count regression models are widely used in many scientific disciplines. Nevertheless, some binary explanatory variables could be endogenous during the process of generating the count dependent variable, thus simultaneous equations bias arises. Except for some numerically intensive simulation-based approaches, existing studies can only handle one endogenous binary variable. We extend this strand of the literature by estimating a Poisson model with dual endogenous binary regressors using a two-stage quasi-maximum likelihood (2SQML) approach. Our method is fast, easily implemented, and has promising finite sample performance under a Poisson model with two-way fixed effects specification consisting of hundreds of parameters. We also take our approach to trade data and find that signing a preferential trade agreement (PTA) has a strong positive impact
on bilateral trade flows. In contrast, a bilateral investment treaty (BIT) has a negative effect on trade when the endogeneity of these two binary variables is taken into account.

Keywords: Endogenous binary variables; Quasi-maximum likelihood; Poisson regression; Two-stage estimation; Gravity model of international trade

JEL Classification: F1, C25, C26