Whitney K. Newey

A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions. (This abstract was borrowed from another version of this item.)

Estimating Vector Autoregressions with Panel Data

This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation. The results also show that lagged hours is important in the hours equation. Copyright 1988 by The Econometric Society.

Automatic Lag Selection in Covariance Matrix Estimation

We propose a nonparametric method for automatically selecting the number of autocovariances to use in computing a heteroskedasticity and autocorrelation consistent covariance matrix. For a given kernel for weighting the autocovariances, we prove that our procedure is asymptotically equivalent to one that is optimal under a mean squared error loss function. Monte Carlo simulations suggest that our procedure performs tolerably well, although it does result in size distortions.

Large sample estimation and hypothesis testing

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.

Hypothesis Testing with Efficient Method of Moments Estimation

Efficient method of moments estimation techniques include many commonly used techniques, including ordinary least squares, two- and three-stage least squares, quasi maximum likelihood, and versions of these for nonlinear environments. For models estimated by any efficient method of moments technique, the authors define analogues to the maximum likeliho od based Wald, likelihood ratio, Lagrange multiplier, and minimum chi-squared statistics. They prove the mutual asymptotic equivalence of the four in an environment that allows for disturbances that are auto correlated and heteroskedastic. They also describe a very convenient way to test a linear hypothesis in a linear model. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Efficient estimation of limited dependent variable models with endogenous explanatory variables

Abstract This paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables. General results on asymptotic efficiency of two-stage and Amemiya GLS estimators are derived and used to obtain a simple, asymptotically efficient estimator of the structural coefficients. This estimator can be calculated by applying GLS to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables. It is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi-square method.

Generalized method of moments specification testing

Abstract This paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions. It shows that any such test may fail against general misspecification that causes estimator inconsistency. The mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived. Applications to testing for exogeneity of a set of instrumental variables are presented.

Instrumental Variable Estimation of Nonparametric Models

In econometrics there are many occasions where knowledge of the structural relationship among dependent variables is required to answer questions of interest. This paper gives identification and estimation results for nonparametric conditional moment restrictions. We characterize identification of structural functions as completeness of certain conditional distributions, and give sufficient identification conditions for exponential families and discrete variables. We also give a consistent, nonparametric estimator of the structural function. The estimator is nonparametric two-stage least squares based on series approximation, which overcomes an ill-posed inverse problem by placing bounds on integrals of higher-order derivatives. Copyright The Econometric Society 2003.

The asymptotic variance of semiparametric estimators

This paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions. The general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean-square projections (including conditional expectations). Regularity conditions for the validity of the formula are also given, including primitive conditions for asymptotic normality when series estimators are present. New examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative. Copyright 1994 by The Econometric Society.

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper is about identification and estimation in a triangular nonparametric structural model with instrumental variables and non-additive errors. Identification and estimation is based on a control function consisting of the conditional distribution function of the endogenous variable given the instruments. We allow for a structural disturbance of arbitrary, unknown dimension while identifying interesting structural effects, such as quantile and average effects. We consider a two-step approach to estimation. We find that the convergence rate for the second-step structural estimator depends on the strength of the instrument.