Endogeneity in Semiparametric Binary Random Coe¢ cient Models,Discussion paper

In this paper we consider endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further specification of the distribution of the unobserved random components. As a particularly relevant example for a structural model where no semiparametric estimator has of yet been analyzed, we consider the binary random coefficients model with endogenous regressors. However, many of the arguments we make hold more generally in all endogenous binary choice models with heteroscedas-ticity. We focus on the estimation of a centrality parameter β, because even in random coefficient models usually an average effect and not the entire distribution of coefficients is of interest. We use a control function IV assumption to identify a centrality parame-ter that has the interpretation of a local average structural effect of the regressor on the latent variable, and establish identification based on the mean ratio of derivatives of two functions of the instruments. We propose an estimator based on sample counterparts, and discuss the large sample behavior. In particular, we show n consistency and derive the asymptotic distribution. In the same framework, we propose tests for heteroscedasticity, overidentification and endogeneity. We analyze the small sample performance through a simulation study. An application of the model to IO demand data concludes this paper