The rare disaster hypothesis suggests that the extraordinarily high postwar U.S. equity premium resulted because investors ex ante demanded compensation for unlikely but calamitous risks that they happened not to incur. Although convincing in theory, empirical tests of the rare disaster explanation are scarce. We estimate a disaster-including consumption-based asset pricing model (CBM) using a combination of the simulated method of moments and bootstrapping. We consider several methodological alternatives that differ in the moment matches and the way to account for disasters in the simulated consumption growth and return series. Whichever specification is used, the estimated preference parameters are of an economically plausible size, and the estimation precision is much higher than in previous studies that use the canonical CBM. Such a combination of plausibility and accuracy has not been delivered in prior literature. Our results thus provide empirical support for the rare disaster hypothesis, and help reconcile the nexus between real economy and financial markets implied by the consumption-based asset pricing paradigm.