ESSAYS IN NONSTANDARD ECONOMETRICS

Abstract

This dissertation studies some nonstandard econometric problems by first presenting the failure of existing standard methods that rely on asymptotic normality and then providing corresponding valid alternatives. Chapter 1 examines the threshold model and develops new method for statistic inference about the parameters. The standard method of conducting inference cannot satisfy the size constraint in the empirically important situation where the coefficient change is not statistically large, while the new test is uniformly valid. In additional, the new test/confidence interval is designed to have the best weighted average power/length among all methods that control size uniformly. Chapters 2 and 3 study statistic inference and estimation about tail properties of some underlying distribution, such as high quantile and tail conditional expectation. These two chapters are based on the papers coauthored with my advisor, Prof. Ulrich K. Müller. We develop a new asymptotic embedding which relies on the sole assumption that only the largest k tail observations are approximately stemming from a generalized Pareto tail, for a fixed and given k. This new approach has a much better small sample performance than the standard methods that assume an asymptotically infinite k, especially when the sample size is only moderately large.