The Money Pump as a Measure of Revealed Preference Violations: a Comment

In a recent and insightful paper, Echenique et al. [4] proposed the Money Pump Index(MPI) as an intuitive measure to evaluate the severity of violations of consumer rationality(defined in terms of revealed preference axioms). For practical applications, they suggest usingthe Mean or Median MPI. In this note, we show that computing these Median and Mean MPIis computationally hard, which makes them impractical in the case of large datasets (including"scanner" datasets as the one used by Echenique et al.). To overcome this problem, we proposeMaximum and Minimum MPIs as easy-to-apply alternatives. These MPIs preserve the intuitionof the Median and Mean MPIs and can be computed efficiently (i.e. in polynomial time). Wealso show the practical usefulness of the Maximum and Minimum MPI through an applicationto the dataset of Echenique et al..