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