Consumption-Based Asset Pricing with Higher Cumulants

I extend the Epstein-Zin-lognormal consumption-based asset-pricing model to allow for general i.i.d. consumption growth. Information about the higher moments--equivalently, cumulants--of consumption growth is encoded in the cumulant-generating function. I apply the framework to economies with rare disasters, and argue that the importance of such disasters is a double-edged sword: parameters that govern the frequency and sizes of rare disasters are critically important for asset pricing, but extremely hard to calibrate. I show how to sidestep this issue by using observable asset prices to make inferences that are robust to the details of the underlying consumption process.