Three Essays on Quantile Regression

Abstract

The first chapter studies identification, estimation, and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption. We show identification of dose-response functions under the assumption that selection to treatment is based on observables. We consider estimation of dose-response functions through moment restriction models with generalized residual functions which are possibly non-smooth, and propose a semiparametric two-step estimator. This general formulation includes average and quantile treatment effects as special cases. The asymptotic properties of the estimator are derived. We also develop statistical inference procedures and show the validity of a bootstrap approach to implement these methods in practice. Monte Carlo simulations demonstrate that the test statistics have good finite sample properties. Finally, we apply the proposed methods to estimate unconditional average and quantile effects of mothers' weight gain and age on birthweight. The second chapter develops a new minimum distance quantile regression (MD-QR) estimator for panel data models with fixed effects. We establish consistency and derive the limiting distribution of the MD-QR estimator for panels with a large number of cross-sections and time-series. The limit theory allows for both sequential and joint limits. The proposed estimator is efficient in the class of minimum distance estimators. In addition, the MD-QR estimator is computationally fast, especially for large cross-sections. Monte Carlo simulations are conducted to evaluate finite sample performance. Finally, we illustrate the use of the estimator with a simple application to the investment equation model. The third chapter proposes tests for slope homogeneity across individuals in quantile regression fixed effects panel data models. The tests are based on the Swamy statistic. We establish the asymptotic null distribution of the tests under large panel data, with sequential and joint limits. Monte Carlo experiments show good performance of the proposed tests in finite samples in terms of size and power. Finally, we test and reject the hypothesis of homogeneous speed of capital structure adjustment across firms using a panel dataset.