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Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index

Author

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  • Kohei Shiozawa

    (Graduate School of Economics, Osaka University)

Abstract

The purpose of this paper is to show that computing the minimum cost index (MCI) for a given price-amount data set, proposed by Dean and Martin (2010, 2015) as a goodness-of-fit measure for the revealed preference test, is NP-hard. Our proof uses a polynomial reduction from the feedback arc set problem, which is a decision problem known to be NP-complete. Our result refines the NP-hardness result in Dean and Martin (2010), which is presented in a more abstract framework than our economic data setting. Thus the computation of MCI is NP-hard even if we restrict our attention to the revealed preference setting for economic data. We also discuss computational procedures for MCI and provide a way of approximating MCI in polynomial-time using approximation algorithms for the (weighted) feedback arc set problem.

Suggested Citation

  • Kohei Shiozawa, 2015. "Note on goodness-of-fit measures for the revealed preference test: The computational complexity of the minimum cost index," Economics Bulletin, AccessEcon, vol. 35(4), pages 2455-2461.
    • Handle: RePEc:ebl:ecbull:eb-15-00637
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    References listed on IDEAS

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    Cited by:

    1. Shiozawa, Kohei, 2016. "Revealed preference test and shortest path problem; graph theoretic structure of the rationalizability test," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 38-48.
    2. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev.2, Osaka University, Graduate School of Economics, revised Aug 2016.

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    More about this item

    Keywords

    Revealed preference; goodness-of-fit measure; minimum cost index; NP-hard; feedback arc set problem;
    All these keywords.

    JEL classification:

    • D0 - Microeconomics - - General
    • C0 - Mathematical and Quantitative Methods - - General

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