Consumption Partial Insurance in the Presence of Tail Income Risk

We measure the extent of consumption insurance to income shocks accounting for high-order moments of the income distribution. We derive a nonlinear consumption function, in which the extent of insurance varies with the sign and magnitude of income shocks. Using PSID data, we estimate an asymmetric pass-through of bad versus good permanent shocks -- 17% of a 3 sigma negative shock transmits to consumption compared to 9% of an equal-sized positive shock -- and the pass-through increases as the shock worsens. We find similar patterns for transitory shocks among the least wealthy. Households are willing to sacrifice more than 1/8 of lifetime consumption to eliminate tail income risk. Our results are consistent with surveys of consumption responses to hypothetical events and suggest that tail risk matters substantially for consumption.