Testing Exogeneity of Multinomial Regressors in Count Data Models: Does Two-stage Residual Inclusion Work?

We study a simple exogeneity test in count data models with possibly endogenous multinomial treatment. The test is based on Two Stage Residual Inclusion (2SRI), an estimation method which has been proved to be consistent for a general class of nonlinear parametric models. Results from a broad set of simulation experiments provide novel evidence on important features of this approach. We find differences in the finite sample performance of various likelihood-based tests, analyze their robustness to misspecification arising from neglected over-dispersion or from incorrect specification of the first stage model, and uncover that standardizing the variance of the first stage residuals leads to better results. An original application to testing the endogeneity status of insurance in a model of healthcare demand corroborates our Monte Carlo findings.