Asymptotics for GMM Estimators with Weak Instruments

43 Pages Posted: 16 Jul 2000 Last revised: 19 Jul 2010

See all articles by James H. Stock

James H. Stock

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Harvard University - Harvard Kennedy School (HKS)

Jonathan H. Wright

Johns Hopkins University - Department of Economics

Date Written: July 1996

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

Stock, James H. and Wright, Jonathan H., Asymptotics for GMM Estimators with Weak Instruments (July 1996). NBER Working Paper No. t0198, Available at SSRN: https://ssrn.com/abstract=225138

James H. Stock (Contact Author)

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Jonathan H. Wright

Johns Hopkins University - Department of Economics ( email )

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