  In this paper, we build a new test of rational expectations based on the
marginal distributions of realizations and subjective beliefs. This test is
widely applicable, including in the common situation where realizations and
beliefs are observed in two different datasets that cannot be matched. We show
that whether one can rationalize rational expectations is equivalent to the
distribution of realizations being a mean-preserving spread of the distribution
of beliefs. The null hypothesis can then be rewritten as a system of many
moment inequality and equality constraints, for which tests have been recently
developed in the literature. The test is robust to measurement errors under
some restrictions and can be extended to account for aggregate shocks. Finally,
we apply our methodology to test for rational expectations about future
earnings. While individuals tend to be right on average about their future
earnings, our test strongly rejects rational expectations.

Econometrics