Bootstrapping the GMM overidentification test Under first-order underidentification
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.
|Date of creation:||01 Apr 2014|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (514) 985-4000
Fax: (514) 985-4039
Web page: http://www.cirano.qc.ca/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
- Donald W. K. Andrews, 2002.
"Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators,"
Econometric Society, vol. 70(1), pages 119-162, January.
- Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230, Cowles Foundation for Research in Economics, Yale University.
- Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2001.
- Dovonon, Prosper & Renault, Eric, 2011.
"Testing for Common GARCH Factors,"
40224, University Library of Munich, Germany.
- repec:oup:restud:v:49:y:1982:i:1:p:151-53 is not listed on IDEAS
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2014s-25. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Webmaster)
If references are entirely missing, you can add them using this form.