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Bayesian Indirect Inference and the ABC of GMM

Author

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  • Michael Creel
  • Jiti Gao
  • Han Hong
  • Dennis Kristensen

Abstract

We propose and study local linear and polynomial based nonparametric regression methods for implementing Approximate Bayesian Computation (ABC) style indirect inference and GMM estimators. These estimators do not need to rely on numerical optimization or Markov Chain Monte Carlo (MCMC) simulations. They provide an effective complement to the classical M-estimators and to MCMC methods, and can be applied to both likelihood and method of moment based models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of estimated posterior quantiles for confidence interval construction. We also show that in this setting, local linear kernel regression methods have theoretical advantages over local constant kernel methods that are also reflected in finite sample simulation results. Our results apply to both exactly and over identified models.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2016-1
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp01-16.pdf
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    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. Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona School of Economics.
    3. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    7. Jiti Gao & Han Hong, 2014. "A Computational Implementation of GMM," Monash Econometrics and Business Statistics Working Papers 24/14, Monash University, Department of Econometrics and Business Statistics.
    8. Ruge-Murcia, Francisco, 2012. "Estimating nonlinear DSGE models by the simulated method of moments: With an application to business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 914-938.
    9. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    10. Han Hong, 2007. "A Statistical Inquiry into the Plausibility of Recursive Utility," Journal of Financial Econometrics, Oxford University Press, vol. 5(4), pages 523-559, Fall.
    11. Creel, Michael & Kristensen, Dennis, 2016. "On selection of statistics for approximate Bayesian computing (or the method of simulated moments)," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 99-114.
    12. 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.
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    Cited by:

    1. Forneron, Jean-Jacques & Ng, Serena, 2018. "The ABC of simulation estimation with auxiliary statistics," Journal of Econometrics, Elsevier, vol. 205(1), pages 112-139.
    2. Valerio Scalone, 2018. "Estimating Non-Linear DSGEs with the Approximate Bayesian Computation: an application to the Zero Lower Bound," Working papers 688, Banque de France.

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    More about this item

    Keywords

    GMM-estimators; Laplace transformations; ABC estimators; nonparametric regressions; simulation-based estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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