Binary response correlated random coefficient panel data models

In this paper, we consider binary response correlated random coefficient (CRC) panel data models which are frequently used in the analysis of treatment effects and demand of products. We focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors. Our identification conditions and estimation are based on the framework of the model with a special regressor, which is a novel approach proposed by Lewbel, 1998, Lewbel, 2000 to solve the heterogeneity and endogeneity problem in the binary response models. With the help of the additional information on the special regressor, we can transform a binary response CRC model to a linear moment relation. We also construct a semiparametric estimator for the average slopes and derive the n-normality result. Further, we propose a nonparametric method to test the correlations between random coefficients and regressors. Simulations are given to show the finite sample performance of our estimators and test statistics.