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Possibly Ill-behaved Posteriors in Econometric Models

Author

Listed:
  • Lennart Hoogerheide

    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    (Erasmus University Rotterdam)

Abstract

Highly non-elliptical posterior distributions may occur in several econometric models, in particular, when the likelihood information is allowed to dominate and data information is weak. We explain the issue of highly non-elliptical posteriors in a model for the effect of education on income using data from the well-known Angrist and Krueger (1991) study and discuss how a so-called Information Matrix or Jeffreys' prior may be used as a `regularization prior' that in combination with the likelihood yields posteriors with desirable properties. We further consider an 8-dimensional bimodal posterior distribution in a 2-regime mixture model for the real US GNP growth. In order to perform a Bayesian posterior analysis using indirect sampling methods in these models, one has to find a good candidate density. In a recent paper - Hoogerheide, Kaashoek and Van Dijk (2007) - a class of neural network functions was introduced as candidate densities in case of non-elliptical posteriors. In the present paper, the connection between canonical model structures, non-elliptical credible sets, and more sophisticated neural network simulation techniques is explored. In all examples considered in this paper – a bimodal distribution of Gelman and Meng (1991) and posteriors in IV and mixture models - the mixture of Student's t distributions is clearly a much better candidate than a Student's t candidate, yielding far more precise estimates of posterior means after the same amount of computing time, whereas the Student's t candidate almost completely misses substantial parts of the parameter space.

Suggested Citation

  • Lennart Hoogerheide & Herman K. van Dijk, 2008. "Possibly Ill-behaved Posteriors in Econometric Models," Tinbergen Institute Discussion Papers 08-036/4, Tinbergen Institute, revised 18 Apr 2008.
  • Handle: RePEc:tin:wpaper:20080036
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    References listed on IDEAS

    as
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    8. Hoogerheide, Lennart & Kleibergen, Frank & van Dijk, Herman K., 2007. "Natural conjugate priors for the instrumental variables regression model applied to the Angrist-Krueger data," Journal of Econometrics, Elsevier, vol. 138(1), pages 63-103, May.
    9. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
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    Citations

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    Cited by:

    1. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
    2. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    3. Tsionas, Mike G., 2019. "Multi-objective optimization using statistical models," European Journal of Operational Research, Elsevier, vol. 276(1), pages 364-378.
    4. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2009. "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i03).
    5. Grazian, Clara & Robert, Christian P., 2018. "Jeffreys priors for mixture estimation: Properties and alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 149-163.
    6. repec:jss:jstsof:29:i03 is not listed on IDEAS
    7. David, D. & Hoogerheide, L.F. & van Dijk, H.K., 2008. "The AdMit Package," Econometric Institute Research Papers EI 2008-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    More about this item

    Keywords

    instrumental variables; vector error correction model; mixture model; importance sampling; Markov chain Monte Carlo; neural network;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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