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A Practitioner's Guide to Robust Covariance Matrix Estimation

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  • Wouter J. Den Haan
  • Andrew T. Levin

Abstract

This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments. The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentrated) objective function as a stochastic process. The general results are specialized to two leading cases, linear instrumental variables regression and GMM estimation of Euler equations obtained from the consumption-based capital asset pricing model with power utility. Numerical results of the latter model confirm that finite sample distributions can deviate substantially from normality, and indicate that these deviations are captured by the weak instruments asymptotic approximations.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0197.

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Date of creation: Jun 1996
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Publication status: published as Handbook of Statistics 15. edited by G.S. Maddala and C.R. Rao, 1997
Handle: RePEc:nbr:nberte:0197

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  1. Martin S. Eichenbaum & Lars Peter Hansen & Kenneth J. Singleton, 1986. "A Time Series Analysis of Representative Agent Models of Consumption andLeisure Choice Under Uncertainty," NBER Working Papers 1981, National Bureau of Economic Research, Inc.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Wouter J. Den Haan & Andrew Levin, 1996. "Inferences from Parametric and Non-Parametric Covariance Matrix Estimation Procedures," NBER Technical Working Papers 0195, National Bureau of Economic Research, Inc.
  4. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
  5. Craig Burnside & Martin Eichenbaum, 1994. "Small sample properties of generalized method of moments based Wald tests," Working Paper Series, Macroeconomic Issues 94-12, Federal Reserve Bank of Chicago.
  6. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
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