IDEAS home Printed from https://ideas.repec.org/p/zbw/rwirep/523.html
   My bibliography  Save this paper

Consistent Subsets – Computationally Feasible Methods to Compute the Houtman-Maks-Index

Author

Listed:
  • Heufer, Jan
  • Hjertstrand, Per

Abstract

We provide two methods to compute the largest subset of a set of observations that is consistent with the Generalised Axiom of Revealed Preference. The algorithm provided by Houtman and Maks (1985) is not comput ationally feasible for larger data sets, while our methods are not limited in that respect. The first method is a variation of Gross and Kaiser's (1996) approximate algorithm and is only applicable for two-dimensional data sets, but it is very fast and easy to implement. The second method is a mixed-integer linear programming approach that is slightly more involved but still fast and not limited by the dimension of the data set.

Suggested Citation

  • Heufer, Jan & Hjertstrand, Per, 2014. "Consistent Subsets – Computationally Feasible Methods to Compute the Houtman-Maks-Index," Ruhr Economic Papers 523, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    • Handle: RePEc:zbw:rwirep:523
    DOI: 10.4419/86788598
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/105446/1/812891376.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.4419/86788598?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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 & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    3. Jan Heufer, 2013. "Testing revealed preferences for homotheticity with two-good experiments," Experimental Economics, Springer;Economic Science Association, vol. 16(1), pages 114-124, March.
    4. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    5. 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.
    6. 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.
    7. Gross, John & Kaiser, Dan, 1996. "Two Simple Algorithms for Generating a Subset of Data Consistent with WARP and Other Binary Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 251-255, April.
    8. Samiran Banerjee & James Murphy, 2009. "A simplified test for preference rationality of two-commodity choice," Experimental Economics, Springer;Economic Science Association, vol. 12(2), pages 252-252, June.
    9. 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.
    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. 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. Jan Heufer & Per Hjertstrand, 2015. "Homothetic Efficiency and Test Power: A Non-Parametric Approach," Tinbergen Institute Discussion Papers 15-064/I, Tinbergen Institute.
    3. 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.
    4. Marcos Demetry & Per Hjertstrand, 2023. "Consistent subsets: Computing the Houtman–Maks index in Stata," Stata Journal, StataCorp LP, vol. 23(2), pages 578-588, June.
    5. Castillo, Marco & Freer, Mikhail, 2018. "Revealed differences," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 202-217.
    6. E. Cettolin & P. S. Dalton & W. J. Kop & W. Zhang, 2020. "Cortisol meets GARP: the effect of stress on economic rationality," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 554-574, June.
    7. Andreas C Drichoutis & Rodolfo M Nayga, 2020. "Economic Rationality under Cognitive Load," The Economic Journal, Royal Economic Society, vol. 130(632), pages 2382-2409.
    8. David J. Freeman & Kevin Laughren, 2024. "Task completion without commitment," Experimental Economics, Springer;Economic Science Association, vol. 27(2), pages 273-298, April.
    9. Hjertstrand, Per, 2020. "Income Elasticities Without Parameters," Working Paper Series 1324, Research Institute of Industrial Economics.
    10. Matej Opatrny, 2018. "Extent of Irrationality of the Consumer: Combining the Critical Cost Eciency and Houtman Maks Indices," Working Papers IES 2018/11, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2018.
    11. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    12. Jim Engle-Warnick & Natalia Mishagina, 2014. "Insensitivity to Prices in a Dictator Game," CIRANO Working Papers 2014s-19, CIRANO.

    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. Jan Heufer, 2014. "Generating Random Optimising Choices," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 295-305, October.
    2. Heufer, Jan & Hjertstrand, Per, 2019. "Homothetic preferences revealed," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 602-614.
    3. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    4. Marcos Demetry & Per Hjertstrand, 2023. "Consistent subsets: Computing the Houtman–Maks index in Stata," Stata Journal, StataCorp LP, vol. 23(2), pages 578-588, June.
    5. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    6. 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.
    7. Jan Heufer, 2013. "Testing revealed preferences for homotheticity with two-good experiments," Experimental Economics, Springer;Economic Science Association, vol. 16(1), pages 114-124, March.
    8. 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.
    9. Castillo, Marco & Freer, Mikhail, 2018. "Revealed differences," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 202-217.
    10. Daniel R. Burghart, 2020. "The two faces of independence: betweenness and homotheticity," Theory and Decision, Springer, vol. 88(4), pages 567-593, May.
    11. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.
    12. Joshua Lanier & Bin Miao & John K.-H. Quah & Songfa Zhong, 2024. "Intertemporal Consumption with Risk: A Revealed Preference Analysis," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1319-1333, September.
    13. 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.
    14. Uttara Balakrishnan & Johannes Haushofer & Pamela Jakiela, 2020. "How soon is now? Evidence of present bias from convex time budget experiments," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 294-321, June.
    15. E. Cettolin & P. S. Dalton & W. J. Kop & W. Zhang, 2020. "Cortisol meets GARP: the effect of stress on economic rationality," Experimental Economics, Springer;Economic Science Association, vol. 23(2), pages 554-574, June.
    16. Fisman, Raymond & Jakiela, Pamela & Kariv, Shachar, 2017. "Distributional preferences and political behavior," Journal of Public Economics, Elsevier, vol. 155(C), pages 1-10.
    17. Jim Engle-Warnick & Natalia Mishagina, 2014. "Insensitivity to Prices in a Dictator Game," CIRANO Working Papers 2014s-19, CIRANO.
    18. Heufer, Jan, 2013. "Quasiconcave preferences on the probability simplex: A nonparametric analysis," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 21-30.
    19. Brocas, Isabelle & Carrillo, Juan D. & Combs, T. Dalton & Kodaverdian, Niree, 2019. "Consistency in simple vs. complex choices by younger and older adults," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 580-601.
    20. Joshua Lanier & Bin Miao & John K.-H. Quah & Songfa Zhong, 2024. "Intertemporal Consumption with Risk: A Revealed Preference Analysis," The Review of Economics and Statistics, MIT Press, vol. 106(5), pages 1319-1333, September.

    More about this item

    Keywords

    demand theory; efficiency; nonparametric analysis; revealed preference; utility maximisation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:zbw:rwirep:523. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/rwiesde.html .

    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.