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Testable implications of general equilibrium models: an integer programming approach

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  • Laurens CHERCHYE
  • Thomas DEMUYNCK
  • Bram DE ROCK

Abstract

Focusing on the testable implications on the equilibrium manifold, we show that the rationalizability problem is NP-complete. Subsequently, we present an integer programming (IP) approach to characterizing general equilibrium models. This approach avoids the use of the Tarski-Seidenberg algorithm for quantifier elimination that is commonly used in the literature. The IP approach naturally applies to settings with any number of observations, which is attractive for empirical applications. In addition, it can easily be adjusted to analyze the testable implications of alternative general equilibrium models (that include, e.g., public goods, externalities and/or production). Further, we show that the IP framework can easily address recoverability questions (pertaining to the structural model that underlies the observed equilibrium behavior), and account for empirical issues when bringing the IP methodology to the data (such as goodness-of-fit and power). Finally, we show how to develop easy-to-implement heuristics that give a quick (but possibly inconclusive) answer to whether or not the data satisfy the general equilibrium models.

Suggested Citation

  • Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2009. "Testable implications of general equilibrium models: an integer programming approach," Working Papers Department of Economics ces09.14, KU Leuven, Faculty of Economics and Business, Department of Economics.
  • Handle: RePEc:ete:ceswps:ces09.14
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    References listed on IDEAS

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    1. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    2. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    3. Ruediger Bachmann, 2006. "Testable Implications of Pareto Efficiency and Individualrationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 489-504, November.
    4. Andrés Carvajal & John Quah, 2009. "A Nonparametric Analysis of the Cournot Model," Economics Papers 2009-W15, Economics Group, Nuffield College, University of Oxford.
    5. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for Deciding Collectively Rational Consumption Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 38(2), pages 173-204, August.
    6. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    7. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
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    10. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
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    12. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The revealed preference approach to collective consumption behavior: nonparametric testing and sharing rule recovery," ULB Institutional Repository 2013/98560, ULB -- Universite Libre de Bruxelles.
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    14. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    15. 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.
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    17. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
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    Citations

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    Cited by:

    1. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2015. "Is utility transferable? a revealed preference analysis," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    3. Donald J. Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Cowles Foundation Discussion Papers 1865R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2012.
    4. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2011. "Testable implications of general equilibrium models: An integer programming approach," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 564-575.
    5. repec:eee:mateco:v:75:y:2018:i:c:p:19-30 is not listed on IDEAS
    6. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0053-5 is not listed on IDEAS
    7. Donald Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Levine's Working Paper Archive 786969000000000537, David K. Levine.
    8. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    9. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    10. Bart Smeulders & Laurens Cherchye & Bram Rock & Frits C. R. Spieksma & Fabrice Talla Nobibon, 2015. "Transitive preferences in multi-member households," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 243-254, October.
    11. Steven D. Silver, 2016. "A QUAIDS Model of Need-Based Structure in U.S. Personal Consumption 2006–2012," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 44(3), pages 303-323, September.

    More about this item

    Keywords

    General equilibrium; equilibrium manifold; exchange economies; production economies; NP-completeness; nonparametric restrictions; GARP; integer programming.;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D10 - Microeconomics - - Household Behavior - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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