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Tractable Estimation of the Money Pump Index: A Comment

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  • Gavin Kader

Abstract

The Money Pump Index (MPI) of Echenique et al. (2011) measures the severity of consumer irrationality, but computing the exact mean and median MPI over all revealed preference cycles is NP-hard (Smeulders et al., 2013). Existing solutions rely on heuristic proxies, such as evaluating only shorter cycles or bounding the MPI. By framing revealed preferences as a directed graph, this paper projects choice violations onto fundamental cycle bases, which are minimal sets of linearly independent cycles that span the graph's entire cycle space. This yields computationally tractable estimators for the mean and median MPI that are asymptotically equivalent to the original MPI. Applying this methodology to the scanner dataset analyzed by Echenique et al. (2011) and Smeulders et al., (2013), the proposed estimators compute quickly and with negligible small-sample bias.

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  • Gavin Kader, 2026. "Tractable Estimation of the Money Pump Index: A Comment," Papers 2609.16086, arXiv.org.
    • Handle: RePEc:arx:papers:2609.16086
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    References listed on IDEAS

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    1. 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.
    2. Bart Smeulders & Laurens Cherchye & Bram De Rock & Frits C. R. Spieksma, 2013. "The Money Pump as a Measure of Revealed Preference Violations: A Comment," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1248-1258.
    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. 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.
    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. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
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