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Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura

  • Richard Smith

    ()

    (Institute for Fiscal Studies and University of Cambridge)

Initially this discussion briefly reviews the contributions of Andrews and Stock and Kitamura, henceforth A, S and K respectively. Because the breadth of material covered by AS and K is so vast, we concentrate only on a few topics. Generalized empirical likelihood (GEL) provides the focus for the discussion. By defining an appropriate set of nonlinear moment conditions, GEL estimation yields objects which mirror in an asymptotic sense those which form the basis of the exact theory in AS allowing the definition of asymptotically pivotal test statistics appropriate for weakly identified models, the acceptance regions of which may then be inverted to provide asymptotically valid con- fidence interval estimators for the parameters of interest. The general minimum distance approach of Corcoran (1998) which parallels the information theoretic development of EL in K is briefly reviewed. A new class of estimators mirroring Schennach (2004) is suggested which shares the same asymptotic bias properties of EL and possess a well-defined limit distribution under misspecification.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1305.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP13/05.

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Length: 21 pp.
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:ifs:cemmap:13/05
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  1. Donald W.K. Andrews & Marcelo J. Moreira & James H. Stock, 2004. "Optimal Invariant Similar Tests for Instrumental Variables Regression," Cowles Foundation Discussion Papers 1476, Cowles Foundation for Research in Economics, Yale University.
  2. Patrik Guggenberger & Richard Smith, 2005. "Generalized empirical likelihood tests in time series models with potential identification failure," CeMMAP working papers CWP01/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
  4. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
  5. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
  6. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  7. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  8. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
  9. Patrik Buggenberger & Richard Smith, 2003. "Generalized empirical likelihood estimators and tests under partial, weak and strong identification," CeMMAP working papers CWP08/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
  11. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
  12. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  13. Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
  14. Richard Paap & Frank Kleibergen, 2004. "Generalized Reduced Rank Tests using the Singular Value Decomposition," Econometric Society 2004 Australasian Meetings 195, Econometric Society.
  15. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
  16. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  17. Imbens, Guido W, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 359-83, July.
  18. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
  19. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-87, October.
  20. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
  21. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  22. Mehmet Caner, 2005. "Exponential Tilting with Weak Instruments: Estimation and Testing," Econometrics 0509017, EconWPA.
  23. Bryan W. Brown & Whitney K. Newey, 1998. "Efficient Semiparametric Estimation of Expectations," Econometrica, Econometric Society, vol. 66(2), pages 453-464, March.
  24. Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
  25. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
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