A Semi-Nonparametric Estimator For Counts With An Endogenous Dummy Variable
Treating endogeneity and flexibility in such a way that efficiency is not sacrificed constitutes a rising point of interest in count data models. Endogeneity typically appears when unobservable characteristics affect both the count outcome and individuals decision represented by the dummy variable. Thus, we use numerical quadrature to integrate out the unobserved components. Also count data often shows empirical distributions that fit poorly the standard models in the literature. We estimate by Full Information Maximum Likelihood, where we allow for a polynomial expansion of the Poisson specification. Due to the multipe local optima appearing, we apply the Simulated Annealing optimization algorithm. We also develop statistics for sensibility analysis. Model evaluation is performed using measures of goodness of fit, information criteria, likelihood ratio and scores tests. We test our model using data on the number of trips by households and number of physician office visits. In the first case, a low polynomial degree suffices to yield a good fit, while in the latter, results are still to come.
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