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

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  • Donald W. K. Andrews

Abstract

To obtain consistency and asymptotic normality, a generalized method of moments (GAM) estimator typically is defined to be an approximate global minimizer of a GAM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. To alleviate this problem, the author proposes a stopping-rule (SR) procedure for computing GAM 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, 1997. "A Stopping Rule for the Computation of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 65(4), pages 913-932, July.
    • Handle: RePEc:ecm:emetrp:v:65:y:1997:i:4:p:913-932
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    References listed on IDEAS

    as
    1. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. 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.
    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. Veall, Michael R, 1990. "Testing for a Global Maximum in an Econometric Context," Econometrica, Econometric Society, vol. 58(6), pages 1459-1465, November.
    6. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
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    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. 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.
    3. Jean-Jacques Forneron & Liang Zhong, 2023. "Convexity Not Required: Estimation of Smooth Moment Condition Models," Papers 2304.14386, arXiv.org.
    4. 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.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    7. 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.
    8. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    9. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Feb 2023.
    10. 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.
    11. 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.
    12. 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.
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    14. Sangdai Ryoo, 2002. "Testing for Sunspot in the Foreign Exchange Market," International Economic Journal, Taylor & Francis Journals, vol. 16(3), pages 39-58.
    15. 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.
    16. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.

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    JEL classification:

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

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