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Asymptotics for GMM Estimators with Weak Instruments

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  • James H. Stock
  • Jonathan Wright

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 instrument asymptotic approximations.

Suggested Citation

  • James H. Stock & Jonathan Wright, 1996. "Asymptotics for GMM Estimators with Weak Instruments," NBER Technical Working Papers 0198, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0198
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    Cited by:

    1. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    2. Biorn, Erik & Klette, Tor Jakob, 1998. "Panel data with errors-in-variables: essential and redundant orthogonality conditions in GMM-estimation," Economics Letters, Elsevier, vol. 59(3), pages 275-282, June.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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