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

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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.
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    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. 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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    6. 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.
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    1. is not listed on IDEAS
    2. Xiaohong Chen & Min Seong Kim & Sokbae Lee & Myung Hwan Seo & Myunghyun Song, 2025. "SLIM: Stochastic Learning and Inference in Overidentified Models," Cowles Foundation Discussion Papers 2472, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    5. 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.
    6. Jean-Jacques Forneron & Liang Zhong, 2023. "Convexity Not Required: Estimation of Smooth Moment Condition Models," Papers 2304.14386, arXiv.org, revised Jul 2025.
    7. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    8. Jean-Jacques Forneron, 2023. "Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models," Papers 2301.07196, arXiv.org, revised Aug 2025.
    9. 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.
    10. 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.
    11. 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.
    12. Xiaohong Chen & Min Seong Kim & Sokbae Lee & Myung Hwan Seo & Myunghyun Song, 2025. "SLIM: Stochastic Learning and Inference in Overidentified Models," Papers 2510.20996, arXiv.org, revised Oct 2025.
    13. repec:awi:wpaper:0462 is not listed on IDEAS
    14. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    15. Sangdai Ryoo, 2002. "Testing for Sunspot in the Foreign Exchange Market," International Economic Journal, Taylor & Francis Journals, vol. 16(3), pages 39-58.
    16. 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.
    17. 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.
    18. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    19. 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.

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    JEL classification:

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

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