Abstract
Afriat’s (Int Econ Rev 14(2): 460–472, 1973) critical cost efficiency index is often used to measure the extent to which experimental choice data violate the axioms of revealed preference. Under certain conditions, the index yields a value of one—which typically signifies rational choice—when, in fact, the choice violates the axioms. We term this a cost efficient violation (CEV) of the axioms, clarify the conditions under which it arises, and find that CEVs comprise the majority of violations in three of four studies reviewed. We suggest changes in experiment design to eliminate or reduce the likelihood of CEVs.
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Notes
The choices of Andreoni and Miller’s Subject 61 and Subject 90 yield this form of violation (2002, p. 742, Table II).
Six subjects (38, 41, 47, 137, 218, and 221) in Andreoni and Miller’s study report violations consistent with this configuration. Ten subjects (3, 40, 72, 87, 104, 126, 139, 211, 223, and 234) report CEVs that fit a second, similar configuration which arose when the flatter budget line yielded the bundle at the budget line intersection, and the steeper budget line resulted in a bundle lying inside the flatter one.
In both cases, we exclude \(x_1\) from the line segment.
Some studies did not report the order of choice, so while we are able to determine the magnitude of difference between two scenarios, we cannot construct a measure of change based on comparing initial to final relative price.
These violations resulted from subjects facing three more choices than the eight faced by subjects in AM sessions one through four. All five dropped observations (violations) were a subject’s single violation and all were cost efficient ones.
Indeed, because the CCEI is based on the binary comparison of choices, in the case of experiments with three or more goods such as Sippel (1997) study, it is possible that the WARP/WGARP is never violated so that \(e_{ij}=1\) always and hence the CCEI is unity. Yet SARP/GARP could be violated when choices are considered three or more at a time.
References
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Acknowledgments
We thank Jordi Brandts, the editors, and two anonymous referees for helpful comments. We also thank Christian Vossler for comments on an earlier draft of this paper and James Andreoni and Jim Miller; Syngjoo Choi, Raymond Fisman, Douglas Gale, and Shachar Kariv; and William Harbaugh, Kate Krause, and Timothy Berry for their data.
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Murphy, J.H., Banerjee, S. A caveat for the application of the critical cost efficiency index in induced budget experiments. Exp Econ 18, 356–365 (2015). https://doi.org/10.1007/s10683-014-9407-y
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DOI: https://doi.org/10.1007/s10683-014-9407-y