IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/14-05.html
   My bibliography  Save this paper

Efficient information theoretic inference for conditional moment restrictions

Author

Listed:
  • Richard Smith

    (Institute for Fiscal Studies and University of Cambridge)

Abstract

The generalized method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie-Read power divergence family of discrepancies. This approach is similar in spirit to the empirical likelihood methods of Kitamura, Tripathi and Ahn (2004) and Tripathi and Kitamura (2003). These efficient local methods avoid the necessity of explicit estimation of the conditional Jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations.

Suggested Citation

  • Richard Smith, 2005. "Efficient information theoretic inference for conditional moment restrictions," CeMMAP working papers CWP14/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:14/05
    as

    Download full text from publisher

    File URL: https://cemmap.ifs.org.uk/wps/cwp1405.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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, January.
    3. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-366, July.
    4. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-517, October.
    5. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    6. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    7. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    8. 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.
    9. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    10. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    11. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    12. Joel L. Horowitz, 1998. "Bootstrap Methods for Covariance Structures," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 39-61.
    13. 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.
    14. Whitney K. Newey & Joaquim J. S. Ramalho Ramalho & Richard Smith, 2003. "Asymptotic bias for GMM and GEL estimators with estimated nuisance parameters," CeMMAP working papers CWP05/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Joel L. Horowitz, 1996. "Bootstrap Methods For Covariance Structures," Econometrics 9610003, University Library of Munich, Germany.
    16. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    17. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    18. 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 262-280, July.
    19. Back, Kerry & Brown, David P, 1993. "Implied Probabilities in GMM Estimators," Econometrica, Econometric Society, vol. 61(4), pages 971-975, July.
    20. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    2. Daniel Becker & Alois Kneip & Valentin Patilea, 2021. "Semiparametric inference for partially linear regressions with Box-Cox transformation," Papers 2106.10723, arXiv.org.
    3. Lavergne, Pascal & Nguimkeu, Pierre, 2016. "A Hausman Specification Test of Conditional Moment Restrictions," TSE Working Papers 16-743, Toulouse School of Economics (TSE).
    4. Fan, Yanqin & Gentry, Matthew & Li, Tong, 2011. "A new class of asymptotically efficient estimators for moment condition models," Journal of Econometrics, Elsevier, vol. 162(2), pages 268-277, June.
    5. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    6. Ron Mittelhammer & George Judge, 2009. "A Minimum Power Divergence Class of CDFs and Estimators for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 33-49, April.
    7. Almeida, Caio & Garcia, René, 2012. "Assessing misspecified asset pricing models with empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 170(2), pages 519-537.
    8. Berger, Yves G. & Patilea, Valentin, 2022. "A semi-parametric empirical likelihood approach for conditional estimating equations under endogenous selection," Econometrics and Statistics, Elsevier, vol. 24(C), pages 151-163.
    9. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    10. Crudu, Federico & Sándor, Zsolt, 2011. "On the finite-sample properties of conditional empirical likelihood estimators," MPRA Paper 34116, University Library of Munich, Germany.
    11. Zhentao Shi & Huanhuan Zheng, 2018. "Structural estimation of behavioral heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 690-707, August.
    12. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    13. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richard Smith, 2005. "Local GEL methods for conditional moment restrictions," CeMMAP working papers CWP15/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    3. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    4. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    5. Jeffrey M. Wooldridge, 2004. "Estimating average partial effects under conditional moment independence assumptions," CeMMAP working papers CWP03/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. 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, January.
    7. Hahn, Jinyong & Newey, Whitney K. & Smith, Richard J., 2014. "Neglected heterogeneity in moment condition models," Journal of Econometrics, Elsevier, vol. 178(P1), pages 86-100.
    8. Ramalho Joaquim J.S., 2005. "Small Sample Bias of Alternative Estimation Methods for Moment Condition Models: Monte Carlo Evidence for Covariance Structures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-20, March.
    9. Joachim Inkmann, 2000. "Finite Sample Properties of One-Step, Two-Step and Bootstrap Empirical Likelihood Approaches to Efficient GMM Estimation," Econometric Society World Congress 2000 Contributed Papers 0332, Econometric Society.
    10. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    11. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    12. Fan, Yanqin & Gentry, Matthew & Li, Tong, 2011. "A new class of asymptotically efficient estimators for moment condition models," Journal of Econometrics, Elsevier, vol. 162(2), pages 268-277, June.
    13. Parente, Paulo M.D.C. & Smith, Richard J., 2017. "Tests of additional conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 200(1), pages 1-16.
    14. Whitney K. Newey & Joaquim J.S. Ramalho & Richard J. Smith, 2003. "A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter," Economics Working Papers 5_2003, University of Évora, Department of Economics (Portugal).
    15. Stefan Boes, 2010. "Count Data Models with Correlated Unobserved Heterogeneity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 382-402, September.
    16. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    17. Whitney K. 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.
    18. Shane M. Sherlund, 2004. "Quasi Empirical Likelihood Estimation of Moment Condition Models," Econometric Society 2004 North American Summer Meetings 507, Econometric Society.
    19. 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.
    20. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers CWP23/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Conditional Moment Restrictions; Local Cressie-Read Minimum Discrepancy; GMM; Semi-Parametric Efficiency;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:14/05. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.