IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1120.html
   My bibliography  Save this paper

A Stopping Rule for the Computation of Generalized Method of Moments Estimators

Author

Abstract

To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a local optimization algorithm. This yields an estimator that is not necessarily consistent and asymptotically normal. The use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function, which makes it difficult to know when to stop the algorithm. To alleviate these problems of global and local optimization, we propose a stopping-rule (SR) procedure for computing GMM estimators. The SR procedure eliminates the need for global search with high probability. And, it provides an explicit SR for problems of stability that may arise with local optimization problems.

Suggested Citation

  • Donald W.K. Andrews, 1996. "A Stopping Rule for the Computation of Generalized Method of Moments Estimators," Cowles Foundation Discussion Papers 1120, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1120
    Note: CFP 945.
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d11/d1120.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. Veall, Michael R, 1990. "Testing for a Global Maximum in an Econometric Context," Econometrica, Econometric Society, vol. 58(6), pages 1459-1465, November.
    3. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    4. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation for Research in Economics, Yale University.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
    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. Le‐Yu Chen & Sokbae Lee, 2018. "Exact computation of GMM estimators for instrumental variable quantile regression models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 553-567, June.
    2. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    3. Michael Creel & Jiti Gao & Han Hong & Dennis Kristensen, 2016. "Bayesian Indirect Inference and the ABC of GMM," Monash Econometrics and Business Statistics Working Papers 1/16, Monash University, Department of Econometrics and Business Statistics.
    4. Jean-Jacques Forneron & Liang Zhong, 2023. "Convexity Not Required: Estimation of Smooth Moment Condition Models," Papers 2304.14386, arXiv.org.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. 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.
    7. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    8. Bilias, Yannis & Florios, Kostas & Skouras, Spyros, 2019. "Exact computation of Censored Least Absolute Deviations estimator," Journal of Econometrics, Elsevier, vol. 212(2), pages 584-606.
    9. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    10. Christopher R. Knittel & Konstantinos Metaxoglou, 2008. "Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings," NBER Working Papers 14080, National Bureau of Economic Research, Inc.
    11. repec:awi:wpaper:0462 is not listed on IDEAS
    12. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    13. Sangdai Ryoo, 2002. "Testing for Sunspot in the Foreign Exchange Market," International Economic Journal, Taylor & Francis Journals, vol. 16(3), pages 39-58.
    14. Grammig, Joachim & Wellner, Marc, 2002. "Modeling the interdependence of volatility and inter-transaction duration processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 369-400, February.
    15. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    16. Don S. Poskitt, 2020. "On GMM Inference: Partial Identification, Identification Strength, and Non-Standard," Monash Econometrics and Business Statistics Working Papers 40/20, Monash University, Department of Econometrics and Business Statistics.

    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. 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.
    2. Calzolari, Giorgio, 1992. "Stima delle equazioni simultanee non-lineari: una rassegna [Estimation of nonlinear simultaneous equations: a survey]," MPRA Paper 24123, University Library of Munich, Germany, revised 1992.
    3. Heinz König & Michael Lechner, 1994. "Some Recent Developments in Microeconometrics - A Survey," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 130(III), pages 299-331, September.
    4. Michael Creel & Jiti Gao & Han Hong & Dennis Kristensen, 2016. "Bayesian Indirect Inference and the ABC of GMM," Monash Econometrics and Business Statistics Working Papers 1/16, Monash University, Department of Econometrics and Business Statistics.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    7. Hansen, Lars Peter & Heaton, John & Luttmer, Erzo G J, 1995. "Econometric Evaluation of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 8(2), pages 237-274.
    8. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    9. Epstein, Larry G. & Zin, Stanley E., 2001. "The independence axiom and asset returns," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 537-572, December.
    10. Lapo Filistrucchi & Tobias J. Klein, 2013. "Price Competition in Two-Sided Markets with Heterogeneous Consumers and Network Effects," Working Papers 13-20, NET Institute.
    11. repec:hal:wpspec:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    12. Igal Hendel, 1994. "Estimating Multiple-Discrete Choice Models: An Application to Computeri-zzation Returns," NBER Technical Working Papers 0168, National Bureau of Economic Research, Inc.
    13. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    14. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 613-654.
    15. 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.
    16. Anindya Biswas & Biswajit Mandal, 2016. "Estimating Preference Parameters From Stock Returns Using Simulated Method Of Moments," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-13, March.
    17. Yi Deng, 2003. "A Dynamic Stochastic Analysis of International Patent Application and Renewal Processes," Computing in Economics and Finance 2003 189, Society for Computational Economics.
    18. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    19. Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441, Elsevier.
    20. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    21. Zila, Eric & Kukacka, Jiri, 2023. "Moment set selection for the SMM using simple machine learning," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 366-391.

    More about this item

    Keywords

    Computation; generalized method of moments estimator; global optimization; j-step estimator; stopping rule;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:cwl:cwldpp:1120. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.