Three Essays on Extremal Quantiles

Abstract

<p>Extremal quantile index is a concept that the quantile index will drift to zero (or one)</p><p>as the sample size increases. The three chapters of my dissertation consists of three</p><p>applications of this concept in three distinct econometric problems. In Chapter 2, I</p><p>use the concept of extremal quantile index to derive new asymptotic properties and</p><p>inference method for quantile treatment effect estimators when the quantile index</p><p>of interest is close to zero. In Chapter 3, I rely on the concept of extremal quantile</p><p>index to achieve identification at infinity of the sample selection models and propose</p><p>a new inference method. Last, in Chapter 4, I use the concept of extremal quantile</p><p>index to define an asymptotic trimming scheme which can be used to control the</p><p>convergence rate of the estimator of the intercept of binary response models.</p>