IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v76y2023i4d10.1007_s00199-023-01489-x.html
   My bibliography  Save this article

Computing revealed preference goodness-of-fit measures with integer programming

Author

Listed:
  • Thomas Demuynck

    (Université Libre de Bruxelles)

  • John Rehbeck

    (The Ohio State University)

Abstract

This paper develops mixed integer linear programming (MILP) formulations to compute various revealed preference goodness-of-fit measures. We provide MILP formulations to compute the Houtman–Maks index, the average Varian index, and the minimum cost index when there are linear budgets. Next, we provide MILPs to compute minimal “measurement error” in expenditures, prices, and quantities. Finally, we extend our results to non-linear budgets. As a proof of concept, we compute various goodness-of-fit measures for experimental choice data sets from the literature. The maximal computation time is less than 3 s for all measures examined on these datasets.

Suggested Citation

  • Thomas Demuynck & John Rehbeck, 2023. "Computing revealed preference goodness-of-fit measures with integer programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1175-1195, November.
    • Handle: RePEc:spr:joecth:v:76:y:2023:i:4:d:10.1007_s00199-023-01489-x
    DOI: 10.1007/s00199-023-01489-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-023-01489-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-023-01489-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Syngjoo Choi & Shachar Kariv & Wieland M?ller & Dan Silverman, 2014. "Who Is (More) Rational?," American Economic Review, American Economic Association, vol. 104(6), pages 1518-1550, June.
    2. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
    3. Fleissig, Adrian R. & Whitney, Gerald A., 2005. "Testing for the Significance of Violations of Afriat's Inequalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 355-362, July.
    4. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    5. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    6. 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.
    7. Federico Echenique & Taisuke Imai & Kota Saito, 2023. "Approximate Expected Utility Rationalization," Journal of the European Economic Association, European Economic Association, vol. 21(5), pages 1821-1864.
    8. Heufer, Jan & Hjertstrand, Per, 2015. "Consistent subsets: Computationally feasible methods to compute the Houtman–Maks-index," Economics Letters, Elsevier, vol. 128(C), pages 87-89.
    9. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Laurens Cherchye & Frederic Vermeulen, 2008. "Nonparametric Analysis of Household Labor Supply: Goodness of Fit and Power of the Unitary and the Collective Model," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 267-274, May.
    11. 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.
    12. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    13. Raymond Fisman & Shachar Kariv & Daniel Markovits, 2007. "Individual Preferences for Giving," American Economic Review, American Economic Association, vol. 97(5), pages 1858-1876, December.
    14. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    15. Roy Allen & John Rehbeck, 2019. "Assessing Misspecification and Aggregation for Structured Preferences," University of Western Ontario, Departmental Research Report Series 20194, University of Western Ontario, Department of Economics.
    16. 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.
    17. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2009. "Opening the Black Box of Intrahousehold Decision Making: Theory and Nonparametric Empirical Tests of General Collective Consumption Models," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1074-1104, December.
    18. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, March.
    19. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    20. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    21. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
    22. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
    23. 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.
    24. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency and Heterogeneity of Individual Behavior under Uncertainty," American Economic Review, American Economic Association, vol. 97(5), pages 1921-1938, December.
    25. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 176-198.
    26. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
    27. repec:dau:papers:123456789/4099 is not listed on IDEAS
    28. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
    29. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    30. Aguiar, Victor H. & Serrano, Roberto, 2017. "Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality," Journal of Economic Theory, Elsevier, vol. 172(C), pages 163-201.
    31. Abi Adams, 2020. "Mutually Consistent Revealed Preference Demand Predictions," American Economic Journal: Microeconomics, American Economic Association, vol. 12(1), pages 42-74, February.
    32. 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.
    33. Castillo, Marco & Freer, Mikhail, 2018. "Revealed differences," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 202-217.
    34. Francoise Forges & Enrico Minelli, 2009. "Afriat's theorem for generalized budget sets," Post-Print hal-00360726, HAL.
    35. Famulari, Melissa, 1995. "A Household-Based, Nonparametric Test of Demand Theory," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 372-382, May.
    36. Carvajal, Andrés & Song, Xinxi, 2018. "Testing Pareto efficiency and competitive equilibrium in economies with public goods," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 19-30.
    37. Jan Heufer & Per Hjertstrand, 2019. "Homothetic Efficiency: Theory and Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 235-247, April.
    38. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    39. Geoffroy de Clippel & Kareen Rozen, 2018. "Consumer Theory with Misperceived Tastes," Working Papers 2018-10, Brown University, Department of Economics.
    40. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
    41. 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.
    42. Fare, Rolf & Grosskopf, Shawna, 1995. "Nonparametric tests of regularity, Farrell efficiency, and goodness-of-fit," Journal of Econometrics, Elsevier, vol. 69(2), pages 415-425, October.
    43. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mir Adnan Mahmood & John Rehbeck, 2022. "Correcting for Random Budgets in Revealed Preference Experiments," Games, MDPI, vol. 13(2), pages 1-14, April.
    2. Zachary Breig & Paul Feldman, 2024. "Revealing risky mistakes through revisions," Journal of Risk and Uncertainty, Springer, vol. 68(3), pages 227-254, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    2. Roy Allen & John Rehbeck, 2021. "Measuring rationality: percentages vs expenditures," Theory and Decision, Springer, vol. 91(2), pages 265-277, September.
    3. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    4. Pawel Dziewulski, 2021. "A comprehensive revealed preference approach to approximate utility maximisation," Working Paper Series 0621, Department of Economics, University of Sussex Business School.
    5. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    6. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    7. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    8. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.
    9. Sam Cosaert & Veerle Hennebel, 2023. "Parental Childcare with Process Benefits," Economica, London School of Economics and Political Science, vol. 90(357), pages 339-371, January.
    10. Yoram Halevy & Dotan Persitz & Lanny Zrill, 2018. "Parametric Recoverability of Preferences," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1558-1593.
    11. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Joshua Lanier, 2020. "Are Consumers Rational ?Shifting the Burden of Proof," Working Papers ECARES 2020-19, ULB -- Universite Libre de Bruxelles.
    12. Laurens Cherchye & Sam Cosaert & Thomas Demuynck & Bram De Rock, 2020. "Group Consumption with Caring Individuals," The Economic Journal, Royal Economic Society, vol. 130(627), pages 587-622.
    13. Dieter Saelens, 2022. "Unitary or collective households? A nonparametric rationality and separability test using detailed data on consumption expenditures and time use," Empirical Economics, Springer, vol. 62(2), pages 637-677, February.
    14. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Khushboo Surana, 2020. "Revealed Preference Analysis with Normal Goods: Application to Cost-of-Living Indices," American Economic Journal: Microeconomics, American Economic Association, vol. 12(3), pages 165-188, August.
    15. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    16. Avner Seror, 2022. "The Priced Survey Methodology," AMSE Working Papers 2224, Aix-Marseille School of Economics, France.
    17. Sam Cosaert & Alexandros Theloudis & Bertrand Verheyden, 2023. "Togetherness in the Household," American Economic Journal: Microeconomics, American Economic Association, vol. 15(1), pages 529-579, February.
    18. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2015. "Is utility transferable? a revealed preference analysis," Theoretical Economics, Econometric Society, vol. 10(1), January.
    19. Sabrina Bruyneel & Laurens Cherchye & Bram De Rock, 2012. "Collective consumption models with restricted bargaining weights: an empirical assessment based on experimental data," Review of Economics of the Household, Springer, vol. 10(3), pages 395-421, September.
    20. 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.

    More about this item

    Keywords

    Revealed preference; Choice consistency; Computation;
    All these keywords.

    JEL classification:

    • D1 - Microeconomics - - Household Behavior

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:76:y:2023:i:4:d:10.1007_s00199-023-01489-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.