The Large Sample Behaviour of the Generalized Method of Moments Estimator in Misspecified Models

This paper presents the limiting distribution theory for the GMM estimator when the estimation is based on a population moment condition which is subject to non--local (or fixed) misspecification. It is shown that if the parameter vector is overidentified then the weighting matrix plays a far more fundamental role than it does in the corresponding analysis for correctly specified models. Specifically, the rate of convergence of the estimator depends on the rate of convergence of the weighting matrix to its probability limit. The analysis is presented for four particular choices of weighting matrix which are commonly used in practice. In each case the limiting distribution theory is different, and also different from the limiting distribution in a correctly specified model. Statistics are proposed which allow the researcher to test hypotheses about the parameters in misspecified models.

[1]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[2]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[3]  W. Newey,et al.  Hypothesis Testing with Efficient Method of Moments Estimation , 1987 .

[4]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[5]  Alastair R. Hall,et al.  Covariance Matrix Estimation and the Power of the Overidentifying Restrictions Test , 2000 .

[6]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis , 1991, Journal of Political Economy.

[7]  W. Newey,et al.  Generalized method of moments specification testing , 1985 .

[8]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[9]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[10]  N. Davies.  Multiple Time Series , 2005 .

[11]  G. Constantinides,et al.  Habit Persistence and Durability in Aggregate Consumption: Empirical Tests , 1991 .

[12]  M. Ogaki,et al.  Measuring noise in inventory models , 2022 .

[13]  Costas Meghir,et al.  INTERTEMPORAL NONSEPARABILITY OR BORROWING RESTRICTIONS? A DISAGGREGATE ANALYSIS USING A U.S. CONSUMPTION PANEL , 1996 .

[14]  A. Gallant,et al.  Nonlinear Statistical Models , 1988 .

[15]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[16]  David R. Brillinger,et al.  Time Series: Data Analysis and Theory. , 1982 .

[17]  Ravi Jagannathan,et al.  Assessing Specification Errors in Stochastic Discount Factor Models , 1994 .

[18]  J. Wooldridge.  Estimation and inference for dependent processes , 1994 .

[19]  P. Dhrymes.  Mathematics for econometrics , 1978 .

[20]  Ravi Jagannathan,et al.  Implications of Security Market Data for Models of Dynamic Economies , 1990, Journal of Political Economy.

[21]  Bruce E. Hansen,et al.  Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes , 1992 .

[22]  P. Phillips,et al.  On the behavior of inconsistent instrumental variable estimators , 1982 .

[23]  Lars Peter Hansen,et al.  Seasonality and approximation errors in rational expectations models , 1993 .

[24]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[25]  M. Watson.  Measures of Fit for Calibrated Models , 1991, Journal of Political Economy.

[26]  H. White,et al.  A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models , 1988 .

[27]  David E. Tyler.  The Asymptotic Distribution of Principal Component Roots Under Local Alternatives to Multiple Roots , 1983 .

[28]  John H. Cochrane,et al.  A Cross-Sectional Test of an Investment-Based Asset Pricing Model , 1996, Journal of Political Economy.

[29]  Erzo G. J. Luttmer,et al.  Econometric Evaluation of Asset Pricing Models , 1993 .

[30]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[31]  Francis X. Diebold,et al.  Dynamic Equilibrium Economies: A Framework for Comparing Models and Data , 1995 .

[32]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .