Consumption Partial Insurance in the Presence of Tail Income Risk

Abstract: We measure consumption insurance against income shocks accounting for high-order moments of the income distribution. We derive a nonlinear consumption function, where the extent of insurance varies with the shocks' sign and magnitude. 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 versus 9% of an equal-sized positive shock - with greater pass-through as shocks worsen. Households would sacrifice over 1/8 of lifetime consumption to eliminate tail income risk. Our results align with survey responses to hypothetical events and suggest that tail risk matters substantially for consumption.