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 3σ negative shock transmits to consumption compared to 9% of an equal-sized positive shock – and the pass-through increases as the shock worsens. Our results are consistent with surveys of consumption responses to hypothetical events and suggest that tail income risk matters substantially for consumption.