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A Markov Chain Monte Carlo procedure to generate revealed preference consistent datasets

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  • Demuynck, Thomas

Abstract

This paper presents Markov-Chain-Monte-Carlo (MCMC) procedures to sample uniformly from the collection of datasets that satisfy some revealed preference test. The MCMC for the GARP test combines a Gibbs-sampler with a simple hit and run step. It is shown that the MCMC has the uniform distribution as its unique invariant distribution and that it converges to this distribution at an exponential rate.

Suggested Citation

  • Demuynck, Thomas, 2021. "A Markov Chain Monte Carlo procedure to generate revealed preference consistent datasets," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    • Handle: RePEc:eee:mateco:v:97:y:2021:i:c:s0304406821000860
    DOI: 10.1016/j.jmateco.2021.102523
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    References listed on IDEAS

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    1. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    2. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    3. Timothy K. M. Beatty & Ian A. Crawford, 2011. "How Demanding Is the Revealed Preference Approach to Demand?," American Economic Review, American Economic Association, vol. 101(6), pages 2782-2795, October.
    4. Jan Heufer, 2014. "Generating Random Optimising Choices," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 295-305, October.
    5. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 183-188, April.
    6. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    7. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    8. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    9. Claude J. P. Bélisle & H. Edwin Romeijn & Robert L. Smith, 1993. "Hit-and-Run Algorithms for Generating Multivariate Distributions," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 255-266, May.
    10. Matthew Polisson & John K.-H. Quah & Ludovic Renou, 2020. "Revealed Preferences over Risk and Uncertainty," American Economic Review, American Economic Association, vol. 110(6), pages 1782-1820, June.
    11. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 99-110.
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    Cited by:

    1. Thomas Demuynck & Tom Potoms, 2022. "Testing revealed preference models with unobserved randomness: a column generation approach," Working Papers ECARES 2022-42, ULB -- Universite Libre de Bruxelles.
    2. Hjertstrand, Per, 2021. "Power against random expenditure allocation for revealed preference tests," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 36-45.

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    More about this item

    Keywords

    Revealed preference; Markov Chain Monte Carlo; Bronars power;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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