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Generalized Method of Moments With Many Weak Moment Conditions

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  • Whitney K. Newey
  • Frank Windmeijer

Abstract

Using many moment conditions can improve efficiency but makes the usual generalized method of moments (GMM) inferences inaccurate. Two-step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias, but the usual standard errors are too small in instrumental variable settings. In this paper we give a new variance estimator for GEL that addresses this problem. It is consistent under the usual asymptotics and, under many weak moment asymptotics, is larger than usual and is consistent. We also show that the Kleibergen (2005) Lagrange multiplier and conditional likelihood ratio statistics are valid under many weak moments. In addition, we introduce a jackknife GMM estimator, but find that GEL is asymptotically more efficient under many weak moments. In Monte Carlo examples we find that t-statistics based on the new variance estimator have nearly correct size in a wide range of cases. Copyright 2009 The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 3 (05)
Pages: 687-719

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Handle: RePEc:ecm:emetrp:v:77:y:2009:i:3:p:687-719

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Cited by:
  1. Kazuhiko Hayakawa & M. Hashem Pesaran, 2012. "Robust Standard Errors in Transformed Likelihood Estimation of Dynamic Panel Data Models," Working Paper Series 38_12, The Rimini Centre for Economic Analysis.
  2. Ahn, Seung C. & Lee, Young H. & Schmidt, Peter, 2013. "Panel data models with multiple time-varying individual effects," Journal of Econometrics, Elsevier, vol. 174(1), pages 1-14.
  3. McAdam, Peter & Willman, Alpo, 2011. "Technology, utilization and inflation: what drives the New Keynesian Phillips Curve?," Working Paper Series 1369, European Central Bank.
  4. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
  5. Moritz Schularick & Solomos Solomou, 2011. "Tariffs and economic growth in the first era of globalization," Journal of Economic Growth, Springer, vol. 16(1), pages 33-70, March.
  6. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.
  7. Martins, Luis F. & Gabriel, Vasco J., 2014. "Linear instrumental variables model averaging estimation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 709-724.
  8. Todd, Prono, 2009. "Simple, Skewness-Based GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 30994, University Library of Munich, Germany, revised 30 Jul 2011.
  9. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
  10. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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