Endogeneity in Semiparametric Binary Random Coe-cient Models

TL;DR: In this article, the authors consider the case of endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further speciflcation of the distribution of the unobserved random components.

Abstract: In this paper we consider the case of endogenous regressors in the binary choice model under a weak median exclusion restriction, but without further speciflcation of the distribution of the unobserved random components. As a particularly relevant example for a model where no semiparametric estimator has of yet been analyzed, we consider the binary random coe‐cients model with endogenous regressors. However, many of the arguments we make hold more generally in all endogenous binary choice models with heteroscedasticity. We focus on the estimation of a centrality parameter fl, because even in random coe‐cient models usually an average efiect and not the entire distribution of coe‐cients is of interest. We use a control function IV assumption to identify a centrality parameter that has the interpretation of a local average structural efiect of the regressor on the latent variable, and establish identiflcation 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 p n consistency and derive the asymptotic distribution. In the same framework, we propose tests for heteroscedasticity, overidentiflcation and endogeneity. We analyze the small sample performance through a simulation study. An application of the model to IO demand data concludes this paper.