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GMM with Many Moment Conditions

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Author Info
Peter C. B. Phillips
Chirok Han

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Abstract

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak) instruments and some panel data models covering moderate time spans and with correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter. A prominent role in the asymptotic theory is played by two different sources of signal emanating from the moment conditions themselves and from the variability across moment conditions. When the moment conditions are weak, convergence holds because variation across the moment conditions produces a signal that is sufficient in itself to achieve convergence. However, this signal may not be sufficiently informative about the true value of the parameter being estimated, in which case the limit may not correspond to the true parameter. Conditions under which GMM estimators are consistent under such circumstances are given. Some preliminary theory characterizing the limit distribution is provided and a small simulation study is reported

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Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 525.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:525

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Related research
Keywords: GMM; IV; Large numbers of instruments; Pseudo true value; Signal; Signal Variability; Weak instrumentation;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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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.:
  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-91, September.
  3. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February. [Downloadable!] (restricted)
    Other versions:
  4. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
    Other versions:
  5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  6. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-36, June.
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  7. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  8. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-78, May. [Downloadable!] (restricted)
  9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  10. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation, Yale University. [Downloadable!]
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  11. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
  12. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December. [Downloadable!] (restricted)
  13. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  14. John C. Chao & Norman R. Swanson, 2003. "Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments," Departmental Working Papers 200312, Rutgers University, Department of Economics. [Downloadable!]
  15. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July. [Downloadable!] (restricted)
  16. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management. [Downloadable!]
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  17. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March. [Downloadable!] (restricted)
  18. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  19. Anderson, T W, 1977. "Asymptotic Expansions of the Distributions of Estimates in Simultaneous Equations for Alternative Parameter Sequences," Econometrica, Econometric Society, vol. 45(2), pages 509-18, March. [Downloadable!] (restricted)
  20. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier. [Downloadable!] (restricted)
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  21. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Alastair R. Hall & Sanggohn Han & Otilia Boldea, 2009. "Capital Requirements and Business Cycles with Credit Market Imperfections," Centre for Growth and Business Cycle Research Discussion Paper Series 125, Economics, The Univeristy of Manchester. [Downloadable!]
  2. Giovanni Forchini, 2006. "The Asymptotic distribution of the LIML Estimator in a Partially Identified Structural Equation," Monash Econometrics and Business Statistics Working Papers 1/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  3. Chirok Han & Peter C.B. Phillips, 2007. "GMM Estimation for Dynamic Panels with Fixed Effects and Strong Instruments at Unity," Cowles Foundation Discussion Papers 1599, Cowles Foundation, Yale University. [Downloadable!]
  4. Maurice J.G. Bun & Frank Windmeijer, 2007. "The Weak Instrument Problem of the System GMM Estimator in Dynamic Panel Data Models," Bristol Economics Discussion Papers 07/595, Department of Economics, University of Bristol, UK. [Downloadable!]
    Other versions:
  5. Mehmet Caner, 2005. "Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Fixed and Many Moment Asymptotics," Econometrics 0509018, EconWPA. [Downloadable!]
    Other versions:
  6. John Chao & Norman Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Departmental Working Papers 200421, Rutgers University, Department of Economics. [Downloadable!]
    Other versions:
  7. PREMINGER, Arie & HAFNER, Christian M., 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," CORE Discussion Papers 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  8. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
  9. Fabel, Oliver & Pascalau, Razvan, 2007. "Recruitment of Seemingly Overeducated Personnel: Insider-Outsider Effects on Fair Employee Selection Practices," MPRA Paper 7218, University Library of Munich, Germany. [Downloadable!]
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