Bootstrapping the GMM overidentification test under first-order underidentification. (English) Zbl 1391.62052
Summary: 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 L. P. Hansen [Econometrica 50, 1029–1054 (1982; Zbl 0502.62098)] 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 R. F. Engle and S. Kozicki [“Testing for common features”, J. Bus. Econ. Stat. 11, No. 4, 369–380 (1993; doi:10.2307/1391623)]. As P. Dovonon and E. Renault [Econometrica 81, No. 6, 2561–2586 (2013; Zbl 1326.62224)] 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 GMM bootstrap 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.
We first show that the standard GMM bootstrap 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.
MSC:
| 62F40 | Bootstrap, jackknife and other resampling methods |
| 62F03 | Parametric hypothesis testing |
| 62F10 | Point estimation |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
GMM; GMM overidentification test; rank deficiency; second-order local identification; bootstrapReferences:
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