Consistency of the fixed effects Poisson estimator with multiplicative measurement error and unbalanced panels

We study the asymptotic properties of the popular fixed effects Poisson (FEP) estimator in two scenarios important for empirical research. First, we allow for multiplicative measurement error and characterize when the FEP estimator consistently estimates the parameters. Second, we allow for unbalanced panels and characterize when the estimator is consistent under the complete cases. We propose simple tests to determine whether selection is systematically related to unobserved time-varying shocks, which can cause the FEP estimator to be inconsistent. A simulation shows that the predictions of the theoretical findings hold in reasonable sample sizes.