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



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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    References listed on IDEAS

    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. 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.
    2. Bal√°zs Cserna, 2008. "Application of the Generalized Method of Moments for Estimating Continuous-Time Models of U.S. Short-Term Interest Rates," Working Papers 0462, University of Heidelberg, Department of Economics, revised Jan 2008.
    3. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.
    4. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(01), pages 74-113, February.
    5. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    6. 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.
    7. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    8. 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.

    More about this item


    Computation; generalized method of moments estimator; global optimization; j-step estimator; stopping rule;

    JEL classification:

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


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