Bootstrapping the GMM Overidentification Test Under First-Order Underidentification

48 Pages Posted: 3 Jun 2014

See all articles by Prosper Dovonon

Prosper Dovonon

Concordia University, Quebec

Sílvia Gonçalves

University of Montreal - Department of Economics

Date Written: April 2, 2014


The main contribution of this paper is to study the applicability of the bootstrap to estimating the distribution of the standard test of overidentifying restrictions of Hansen (1982) when the model is globally identified but the rank condition fails to hold (lack of first order local identification). An important example for which these conditions are verified is the popular test of common conditionally heteroskedastic features proposed by Engle and Kozicki (1993). As Dovonon and Renault (2013) show, the Jacobian matrix for this model is identically zero at the true parameter value, resulting in a highly nonstandard limiting distribution that complicates the computation of critical values. We first show that the standard bootstrap method of Hall and Horowitz (1996) fails to consistently estimate the distribution of the overidentification restrictions test under lack of first order identification. We then propose a new bootstrap method that is asymptotically valid in this context. The modification consists of adding an additional term that recenters the bootstrap moment conditions in a way as to ensure that the bootstrap Jacobian matrix is zero when evaluated at the GMM estimate.

Keywords: Bootstrapping, overidentification, overidentification

Suggested Citation

Dovonon, Prosper and Goncalves, Silvia, Bootstrapping the GMM Overidentification Test Under First-Order Underidentification (April 2, 2014). CIRANO - Scientific Publications 2014s-25. Available at SSRN: or

Prosper Dovonon (Contact Author)

Concordia University, Quebec ( email )

1455 de Maisonneuve Blvd. W.
Montreal, Quebec H3G 1MB

Silvia Goncalves

University of Montreal - Department of Economics ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7

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