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. For the analysis of treatment effects, under some circumstances, the average treatment effect can be estimated via a linear CRC model. We give the identification conditions for the average slopes of a linear CRC model with a general nonparametric correlation between regressors and random coefficients. We construct a √ n consistent estimator for the average slopes via varying coefficient regression. The identification of binary response panel data models with unobserved heterogeneity is difficult. We base identification conditions and estimation on the framework of the model with a special regressor, which is a major approach proposed by Lewbel (1998, 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 transfer 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. Simulations are given to show the finite sample advantage of our estimators.