We propose a simulation-based strategy to estimate and empirically assess a class of asset pricing models that account for rare but severe consumption contractions that can extend over multiple periods. Our approach expands the scope of prevalent calibration studies and tackles the inherent sample selection problem associated with measuring the effect of rare disaster risk on asset prices. An analysis based on postwar U.S. and historical multi-country panel data yields estimates of investor preference parameters that are economically plausible and robust with respect to alternative specifications. The estimated model withstands tests of validity; the model-implied key financial indicators and timing premium all have reasonable magnitudes. These findings suggest that the rare disaster hypothesis can help restore the nexus between the real economy and financial markets when allowing for multi-period disaster events. Our methodological contribution is a new econometric framework for empirical asset pricing with rare disaster risk.