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). Results from a broad Monte Carlo study provide novel evidence on important features of this approach in nonlinear settings. We find differences in the finite sample performance of various likelihood-based tests under correct specification and when the outcome equation is misspecified due to neglected over-dispersion or non-linearity. We compare alternative 2SRI procedures and uncover that standardizing the variance of the first stage residuals leads to higher power of the test and reduces the bias of the treatment coefficients. An original application in health economics corroborates our findings.