This dissertation focus on censored quantile regression with endogenous regressors and for panel data with fixed effects.

The first chapter investigates a censored regression model with endogenous regressors. For the purpose of identification and estimation, we use the general instrumental variable technique instead of the commonly used control function approach. Under the distributional exclusion assumption, a continuum of moment conditions shall be obtained. We integrate these moment conditions over a range of quantiles to improve estimation efficiency, which results in a set of finite dimensional parameters and an infinite dimensional quantile function to be estimated jointly. Our proposed estimator is straightforward to implement by combining a convex minimization problem, K...[ Read more ]

This dissertation focus on censored quantile regression with endogenous regressors and for panel data with fixed effects.

The first chapter investigates a censored regression model with endogenous regressors. For the purpose of identification and estimation, we use the general instrumental variable technique instead of the commonly used control function approach. Under the distributional exclusion assumption, a continuum of moment conditions shall be obtained. We integrate these moment conditions over a range of quantiles to improve estimation efficiency, which results in a set of finite dimensional parameters and an infinite dimensional quantile function to be estimated jointly. Our proposed estimator is straightforward to implement by combining a convex minimization problem, Kaplan-Meier estimator and a low-dimensional, sometimes a merely one-dimensional, minimization search. Consistency and asymptotic normality are established under regularity conditions, and small scale Monte Carlo experiments show good and stable performance of our estimator. We also provide an empirical application to illustrate the proposed estimation method.

The second chapter investigates estimation of a censored quantile regression (QR) model for panel data with fixed effect. We proposed a sequential estimation procedure which applies standard panel QR method to observations in informative subsets selected sequentially. Our sequential procedure does not make any parametric assumption on the censoring probability so as to avoid possible model misspecification. The proposed estimator is computationally convenient and achieves the same asymptotic efficiency as Powell's estimator. In order to establish asymptotic normality, the number of time periods T is required to grow much faster than the number of individuals N. This requirement is more restrictive than that in nonlinear panel data literature where T increases at a rate up to N. Under this weaker condition, we consider a smoothed sequential estimator which is consistent and asymptotically normal with a bias in the mean. Based on the expression of the bias term, we also consider an analytic bias correction procedure. A small Monte Carlo simulation is conducted to assess the finite sample performance of our estimators and the results show that they have stable and good performance.