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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. 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.
  2. 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.
  3. Seung C. Ahn & Young H. Lee & Peter Schmidt, 2006. "Panel Data Models with Multiple Time-Varying Individual Effects," Working Papers 0702, University of Crete, Department of Economics.
  4. PETER McADAM & ALPO WILLMAN, 2013. "Technology, Utilization, and Inflation: What Drives the New Keynesian Phillips Curve?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(8), pages 1547-1579, December.
  5. Theodoridis, Konstantinos, 2011. "An efficient minimum distance estimator for DSGE models," Bank of England working papers 439, Bank of England.
  6. Hayakawa, Kazuhiko & Pesaran, M. Hashem, 2012. "Robust Standard Errors in Transformed Likelihood Estimation of Dynamic Panel Data Models," IZA Discussion Papers 6583, Institute for the Study of Labor (IZA).
  7. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
  8. Martins, Luis F. & Gabriel, Vasco J., 2014. "Linear instrumental variables model averaging estimation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 709-724.
  9. 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.
  10. Rachida Ouysse, 2014. "On the performance of block-bootstrap continuously updated GMM for a class of non-linear conditional moment models," Computational Statistics, Springer, vol. 29(1), pages 233-261, February.
  11. 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.
  12. 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.
  13. Hayakawa, K. & Pesaran, M.H., 2012. "Robust Standard Errors in Transformed Likelihood Estimation of Dynamic Panel Models," Cambridge Working Papers in Economics 1224, Faculty of Economics, University of Cambridge.

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