Chapter 36LARGE SAMPLE ESTIMATION TESTING AND HYPOTHESIS Large sample distribution theory is the cornerstone of statistical inference for econometric models. The limiting distribution of a statistic gives approximate distributional results that are often straightforward to derive, even in complicated econometric models. | Chapter 36 LARGE SAMPLE ESTIMATION AND HYPOTHESIS TESTING WHITNEY K. NEWEY Massachusetts Institute of Technology DANIEL McFADDEN University of California Berkeley Contents Abstract 2113 1. Introduction 2113 2. Consistency 2120 . The basic consistency theorem 2121 . Identification 2124 . The maximum likelihood estimator 2124 . Nonlinear least squares 2125 . Generalized method of moments 2126 . Classical minimum distance 2128 . Uniform convergence and continuity 2129 . Consistency of maximum likelihood 2131 . Consistency of GMM 2132 . Consistency without compactness 2133 . Stochastic equicontinuity and uniform convergence 2136 . Least absolute deviations examples 2138 . Maximum score 2138 . Censored least absolute deviations 2140 3. Asymptotic normality 2141 . The basic results 2143 . Asymptotic normality for MLE 2146 . Asymptotic normality for GMM 2148 We are grateful to the NSF for financial support and to Y. Ait-Sahalia J. Porter J. Powell J. Robins P. Ruud and T. Stoker for helpful comments. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science B. V. All rights reserved 2112 . Newey and D. McFadden . One-step theorems 2150 . Technicalities 2152 4. Consistent asymptotic variance estimation 2153 . The basic results 2155 . Variance estimation for MLE 2157 . Asymptotic variance estimation for GMM 2160 5. Asymptotic efficiency 2162 . Efficiency of maximum likelihood estimation 2162 . Optimal minimum distance estimation 2164 . A general efficiency framework 2165 . Solving for the smallest asymptotic variance 2168 . Feasible efficient estimation 2171 . Technicalities 2173 6. Two-step estimators 2175 . Two-step estimators as joint GMM estimators 2176 . The effect of first-step estimation on second-step standard errors 2179 . Consistent asymptotic variance estimation for two-step estimators 2182 7. Asymptotic normality with