Small Sample Properties of Generalized Method of Moments Based Wald Tests

50 Pages Posted: 11 Jul 2000

See all articles by A. Craig Burnside

A. Craig Burnside

Duke University - Department of Economics; University of Glasgow - Department of Economics; National Bureau of Economic Research (NBER)

Martin Eichenbaum

Northwestern University; National Bureau of Economic Research (NBER)

Date Written: May 1994

Abstract

This paper assesses the small sample properties of Generalized Method of Moments (GMM) based Wald statistics. The analysis is conducted assuming that the data generating process corresponds to (i) a simple vector white noise process and (ii) an equilibrium business cycle model. Our key findings are that the small sample size of the Wald tests exceeds their asymptotic size, and that their size increases uniformly with the dimensionality of joint hypotheses. For tests involving even moderate numbers of moment restrictions, the small sample size of the tests greatly exceeds their asymptotic size. Relying on asymptotic distribution theory leads one to reject joint hypothesis tests far too often. We argue that the source of the problem is the difficulty of estimating the spectral density matrix of the GMM residuals, which is needed to conduct inference in a GMM environment. Imposing restrictions implied by the underlying economic model being investigated or the null hypothesis being tested on this spectral density matrix can lead to substantial improvements in the small sample properties of the Wald tests.

Suggested Citation

Burnside, Craig and Eichenbaum, Martin, Small Sample Properties of Generalized Method of Moments Based Wald Tests (May 1994). NBER Working Paper No. t0155, Available at SSRN: https://ssrn.com/abstract=225114

Craig Burnside (Contact Author)

Duke University - Department of Economics ( email )

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University of Glasgow - Department of Economics

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Martin Eichenbaum

Northwestern University ( email )

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National Bureau of Economic Research (NBER)

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