Goodness of Fit Measures for Revealed Preference Tests: Complexity Results and Algorithms

17 Pages Posted: 16 Nov 2012

See all articles by Bart Smeulders

Bart Smeulders

KU Leuven

L. Cherchye

KU Leuven; Erasmus Research Institute of Management (ERIM)

Bram De Rock

Katholieke Universiteit Leuven Campus Kortrijk (KULAK)

Frits Spieksma

Catholic University of Leuven (KUL)

Date Written: 2012

Abstract

We provide results on the computational complexity of goodness of t measures (i.e. Afriat's efficiency index, Varian's efficiency vector-index and the Houtman-Maks index) associated with several revealed preference axioms (i.e. WARP, SARP, GARP and HARP). These results explain the computational difficulties that have been observed in literature when computing these indices. Our NP-Hardness results are obtained by reductions from the independent set problem. We also show that this reduction can be used to prove that no constant factor approximations algorithm exists for Varian's index, nor for Houtman-Maks' index (unless P = NP). Finally, we give an exact polynomial time algorithm for finding Afriat's efficiency index.

Suggested Citation

Smeulders, Bart and Cherchye, Laurens and De Rock, Bram and Spieksma, Frits, Goodness of Fit Measures for Revealed Preference Tests: Complexity Results and Algorithms (2012). Available at SSRN: https://ssrn.com/abstract=2165766 or http://dx.doi.org/10.2139/ssrn.2165766

Bart Smeulders

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

Laurens Cherchye (Contact Author)

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Bram De Rock

Katholieke Universiteit Leuven Campus Kortrijk (KULAK) ( email )

Etienne Sabbelaan 53
Kortrijk, B-8500
Belgium

Frits Spieksma

Catholic University of Leuven (KUL) ( email )

Leuven, B-3000
Belgium

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