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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    6. 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.
    7. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    8. 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.
    9. 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.
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    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. Hjertstrand, Per, 2020. "Income Elasticities Without Parameters," Working Paper Series 1324, Research Institute of Industrial Economics.
    9. 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.
    10. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    11. Jim Engle-Warnick & Natalia Mishagina, 2014. "Insensitivity to Prices in a Dictator Game," CIRANO Working Papers 2014s-19, CIRANO.

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    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

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