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Bayesian estimation of agent-based models via adaptive particle Markov chain Monte Carlo

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  • Lux, Thomas

Abstract

Over the last decade, agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community. While most available papers have pursued a frequentist approach adopting either likelihood-based algorithms or simulated moment estimators, here we explore Bayesian estimation using a Markov chain Monte Carlo approach (MCMC). One major problem in the design of MCMC estimators is finding a parametrization that leads to a reasonable acceptance probability for new draws from the proposal density. With agent-based models the appropriate choice of the proposal density and its parameters becomes even more complex since such models often require a numerical approximation of the likelihood. This brings in additional factors affecting the acceptance rate as it will also depend on the approximation error of the likelihood. In this paper, we take advantage of a number of recent innovations in MCMC: We combine Particle Filter Markov Chain Monte Carlo (PMCMC) as proposed by Andrieu et al. (2010) with adaptive choice of the proposal distribution and delayed rejection in order to identify an appropriate design of the MCMC estimator. We illustrate the methodology using two well-known behavioral asset pricing models.

Suggested Citation

  • Lux, Thomas, 2020. "Bayesian estimation of agent-based models via adaptive particle Markov chain Monte Carlo," Economics Working Papers 2020-01, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:202001
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    References listed on IDEAS

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    1. Grazzini, Jakob & Richiardi, Matteo G. & Tsionas, Mike, 2017. "Bayesian estimation of agent-based models," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 26-47.
    2. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    3. Zhang, Jingjing & Dennis, Todd E. & Landers, Todd J. & Bell, Elizabeth & Perry, George L.W., 2017. "Linking individual-based and statistical inferential models in movement ecology: A case study with black petrels (Procellaria parkinsoni)," Ecological Modelling, Elsevier, vol. 360(C), pages 425-436.
    4. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.
    5. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    6. Edward P. Herbst & Frank Schorfheide, 2016. "Bayesian Estimation of DSGE Models," Economics Books, Princeton University Press, edition 1, number 10612.
    7. Nils Bertschinger & Iurii Mozzhorin & Sitabhra Sinha, 2018. "Reality-check for Econophysics: Likelihood-based fitting of physics-inspired market models to empirical data," Papers 1803.03861, arXiv.org.
    8. Franke, Reiner & Westerhoff, Frank, 2012. "Structural stochastic volatility in asset pricing dynamics: Estimation and model contest," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1193-1211.
    9. Pitt, Michael K. & Silva, Ralph dos Santos & Giordani, Paolo & Kohn, Robert, 2012. "On some properties of Markov chain Monte Carlo simulation methods based on the particle filter," Journal of Econometrics, Elsevier, vol. 171(2), pages 134-151.
    10. A. Doucet & M. K. Pitt & G. Deligiannidis & R. Kohn, 2015. "Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator," Biometrika, Biometrika Trust, vol. 102(2), pages 295-313.
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    More about this item

    Keywords

    Agents-based models; Makov chain Monte Carlo; particle filter;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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