Consumption Partial Insurance in the Presence of Tail Income Risk

Abstract

We propose a simple framework to measure consumption insurance against income shocks that accounts for higher-order moments of the income distribution. We derive a nonlinear consumption function in which the extent of insurance varies with both the sign and magnitude of shocks. Using recent 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. These consumption transmission rates further vary by age, wealth, and along the income distribution. Our results align with survey responses to hypothetical events and suggest that tail risk matters substantially for consumption.