In this paper, we build a new test of rational expectations in the frequent context where realizations and subjective beliefs are observed in two different datasets that cannot be matched. Using results from the risk theory literature, we show that whether we can rationalize rational expectations is equivalent to the distribution of realizations being a mean-preserving spread of the distribution of beliefs. Our null hypothesis can then be rewritten as a system of many moment inequalities, which can be tested using the procedure of \cite{andrews2016inference}. Using recent tools from optimal transport theory, we define and estimate the minimal deviations from rational expectations than can be rationalized by the data. We apply our method to test for rational expectations about future earnings, work-time and lifetime. These applications illustrate the ability of our test to detect violations of rational expectations in situations where previous tests would fail to do so. Finally, we show that in the context of structural models, our method provides a natural and easy-to-implement way to conduct a sensitivity test on the assumed form of expectations.

Co-authored with Christophe Gaillac and Arnaud Maurel