In this paper, we build a new test of rational expectations based on the marginal dis-tributions 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 distri-bution 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 lit-erature. Next, we go beyond testing by defining and estimating the minimal deviations from rational expectations that can be rationalized by the data. In the context of structural mod-els, we build on this concept to propose an easy-to-implement way to conduct a sensitivity analysis on the assumed form of expectations. Finally, we apply our framework to test for and quantify deviations from rational expectations about future earnings, and examine the consequences of such departures in the context of a life-cycle model of consumption.

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