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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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    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. Castillo, Marco & Freer, Mikhail, 2018. "Revealed differences," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 202-217.
    5. 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.
    6. Andreas C Drichoutis & Rodolfo M Nayga, 2020. "Economic Rationality under Cognitive Load," The Economic Journal, Royal Economic Society, vol. 130(632), pages 2382-2409.
    7. David J. Freeman & Kevin Laughren, 2024. "Task completion without commitment," Experimental Economics, Springer;Economic Science Association, vol. 27(2), pages 273-298, April.
    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. Avner Seror, 2024. "The Moral Mind(s) of Large Language Models," AMSE Working Papers 2433, Aix-Marseille School of Economics, France.
    12. Jim Engle-Warnick & Natalia Mishagina, 2014. "Insensitivity to Prices in a Dictator Game," CIRANO Working Papers 2014s-19, CIRANO.
    13. Marcos Demetry & Per Hjertstrand, 2023. "Consistent subsets: Computing the Houtman–Maks index in Stata," Stata Journal, StataCorp LLC, vol. 23(2), pages 578-588, June.

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    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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