Further Results on the Limiting Distribution of GMM Sample Moment Conditions

Nikolay Gospodinov, Raymond Kan, and Cesare Robotti
Working Paper 2010-11
July 2010

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In this paper, we extend the results in Hansen (1982) regarding the asymptotic distribution of generalized method of moments (GMM) sample moment conditions. In particular, we show that the part of the scaled sample moment conditions that gives rise to degeneracy in the asymptotic normal distribution is T-consistent and has a nonstandard limiting distribution. We derive the asymptotic distribution for a given linear combination of the sample moment conditions and show how to conduct statistical inference. We demonstrate the finite-sample properties of the proposed asymptotic approximation using simulation.

JEL classification: C13, C32, G12

Key words: GMM

The authors thank Jonathan Wright and Chu Zhang for helpful comments and suggestions. Gospodinov gratefully acknowledges financial support from Fonds de Recherche sur la Société et la Culture (FQRSC), Institut de Finance Mathématique de Montréal (IFM2), and the Social Sciences and Humanities Research Council of Canada. Kan gratefully acknowledges financial support from the National Bank Financial of Canada, the Social Sciences and Humanities Research Council of Canada, and the Center for Financial Innovation and Stability at the Federal Reserve Bank of Atlanta. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Nikolay Gospodinov (corresponding author), Concordia University and CIREQ, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8, 514-848-2424, ext. 3935, nikolay.gospodinov@concordia.ca; Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, kan@chass.utoronto.ca; or Cesare Robotti, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8543, cesare.robotti@atl.frb.org.

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