Large sample estimation and hypothesis testing

TLDR

Asymptotic distribution theory is the main tool for studying properties of econometric estimators and tests. The paper presents conditions for consistency, asymptotic normality, and efficiency of a broad class of extremum estimators. The authors develop consistent asymptotic variance estimators, specialize the results to MLE, GMM, and two‑step, nonsmooth, and semiparametric estimators, and illustrate the theory with numerous examples.

Abstract

Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests. We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators). Consistent asymptotic variance estimators are given to enable approximation of the asymptotic distribution. Asymptotic efficiency is another desirable property then considered. Throughout the chapter, the general results are also specialized to common econometric estimators (e.g. MLE and GMM), and in specific examples we work through the conditions for the various results in detail. The results are also extended to two-step estimators (with finite-dimensional parameter estimation in the first step), estimators derived from nonsmooth objective functions, and semiparametric two-step estimators (with nonparametric estimation of an infinite-dimensional parameter in the first step). Finally, the trinity of test statistics is considered within the quite general setting of GMM estimation, and numerous examples are given.