Are the Choices of People Stochastically Rational? A Stochastic Test of the Number of Revealed Preference Violations

Revealed preference tests are frequently used to check data on the behavior of agents for consistency with economic theory. Unfortunately these tests lack a stochastic element and thus one violation of revealed preference causes a rejection of the behavior being tested. To remedy this lack of a stochastic element in revealed preference analysis, we suggest a general, simple, and intuitive statistical procedure to test whether the observed number of violations is more consistent with a pre-specified type of non-degenerate behavior than with rational behavior. We illustrate this general procedure with an example using uniform random behavior that allows researchers to test whether the actual number of violations of revealed preference is more consistent with uniform random behavior than rational behavior. This statistical test takes advantage of the fact that nonparametric revealed preference tests involve known prices and expenditures. Our illustrative example is accompanied by some Monte Carlo exercises showing that the uniform test performs very well. We implement our test using datasets from two well-known economic experiments. One is a dataset on altruistic choices from Andreoni and Miller (Econometrica 70:737–753, 2002). The second is a dataset on the choices made by subjects who act within a token economy from Battalio et al. (West Econ J 11:411–428, 1973) and Cox (Econ J 107:1054–1078, 1997). We find that for a majority of subjects in one altruistic behavior sub-experiment uniform random behavior can be rejected in favor of rational behavior at the 10 % level of significance. For all but one subject, living in the token economy, uniform random behavior cannot be rejected. For that one subject in the token experiment uniform random behavior is rejected in favor of perverse economic behavior.