The Money Pump as a Measure of Revealed Preference Violations

Abstract

We introduce a measure of the severity of violations of the revealed preference axioms, the money pump index (MPI). The MPI is the amount of money one can extract from a consumer who violates the axioms. It is also a statistical test for the hypothesis that a consumer is rational when behavior is observed with error. We present an application using a panel data set of food expenditures. The data exhibit many violations of the axioms. Mostly, the MPI for these violations is small. The MPI indicates that the hypothesis of consumer rationality cannot be rejected.

The Revealed Preference Theory of Stable and Extremal Stable Matchings

“…9 It is possible that an observed matching may fail to be rationalizable because we have imposed a too rigid structure on individual preferences. In actual empirical implementations of our test, one would need to introduce some additional flexibility (possibly in the form of measurement errors, as in Varian (1985) or Echenique, Lee, and Shum (2011) in the context of consumption behavior). Finally, allowing for too much heterogeneity in individual preferences renders the theory nontestable, so it is also possible to interpret the strong conditions we obtain in our paper as a negative result.…”

Homothetic Efficiency: Theory and Applications

“…Fleissig and Whitney (2005) showed how to statistically test violations of the Afriat inequalities. Echenique, Lee, and Shum (2011) provided a new measure based on a money pump argument, and Dean and Martin (2015) provided a new measure based on the minimum cost of breaking all cycles or money pumps. Apesteguia and Ballester (2015) provided a measure based on welfare loss.…”

Empirical Revealed Preference

“…Given a revealed preference cycle of length J with q j R 0 q j−1 the intransitivity means that the consumer would also prefer q j−1 to q j , so p j q j − p j q j−1 can be extracted at each point in the cycle and J j=1 p j q j − p j q j−1 in total. Echenique et al (2011) suggest the money pump (expressed as a proportion of the consumer's total expenditure) as an aid to interpretation when GARP fails; the more money that can be extracted from the individual in this manner, the worse the violation of RP theory. These authors also show how to address the considerable combinatorial/computational challenges involved in calculating the money pump index -as the number of potential cycles which need to be investigated can be huge even when the dataset itself is not large.…”