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Indirect Likelihood Inference

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  • Michael Creel
  • Dennis Kristensen

Abstract

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.

Suggested Citation

  • Michael Creel & Dennis Kristensen, "undated". "Indirect Likelihood Inference," Working Papers 558, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:558
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    References listed on IDEAS

    as
    1. Michael Creel & Dennis Kristensen, 2012. "Estimation of dynamic latent variable models using simulated non‐parametric moments," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 490-515, October.
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    5. Gouriéroux, Christian & Phillips, Peter C.B. & Yu, Jun, 2010. "Indirect inference for dynamic panel models," Journal of Econometrics, Elsevier, vol. 157(1), pages 68-77, July.
    6. Canova, Fabio & Sala, Luca, 2009. "Back to square one: Identification issues in DSGE models," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 431-449, May.
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    11. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
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    Cited by:

    1. Creel, Michael, 2017. "Neural nets for indirect inference," Econometrics and Statistics, Elsevier, vol. 2(C), pages 36-49.
    2. 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.
    3. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.

    More about this item

    Keywords

    indirect inference; maximum-likelihood; simulation-based methods; bias correction; Bayesian estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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