This article is concerned with semiparametric estimation of a partially linear transformation model under conditional quantile restriction with no parametric restriction imposed either on the link functional form or on the error term distribution. We describe for the finite-dimensional parameter a $\sqrt n$-consistent estimator which combines the features of Chen (2010)’s maximum integrated score estimator as well as Lee (2003)’s average quantile regression. We show the remaining two infinite-dimensional unknown functions in the model can be separately identified and propose estimators for these functions based on the marginal integration method. Furthermore, a simple approach is proposed to estimate the average partial quantile effect. Two important extensions, i.e., random censoring as well as estimating a transformation model with an endogenous regressor are also considered.
Summary In this paper, we consider the semiparametric identification and estimation of a heteroskedastic binary choice model with endogenous dummy regressors and no parametric restriction on error term distribution. Our approach addresses various drawbacks associated with previous estimators proposed for this model. It allows for (i) general multiplicative heteroskedasticity in both selection and outcome equations, (ii) a nonparametric selection mechanism, and (iii) multiple discrete endogenous regressors. The resulting three-stage estimator is shown to be asymptotically normal, with a convergence rate that can be arbitrarily close to n −1/2 if certain smoothness assumptions are satisfied. Simulation results show that our estimator performs reasonably well in finite samples. Our approach is then used to study the intergenerational transmission of smoking habits in British households.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.