Insure the Uninsurable by Yourself : Accounting for Consumption Insurance in a Life-Cycle Model

This paper investigates the degree of consumption insurance in a standard overlapping generations life-cycle model calibrated to the U.S. data. To directly confront the model predictions with the recent empirical evidence of Blundell, Pistaferri and Preston (2008) (BPP hereafter), I adopt BPP's measure of consumption insurance and apply the same estimation procedure proposed by BPP to the model generated data. I find that the plain-vanilla life-cycle model, where there is only self-insurance available, accounts for around 80% of the insurance for permanent shocks and almost complete insurance for transitory shocks found in the data. The validity of BPP's measure and the severity of model mis-specifications are discussed. I also find the heterogeneity of the degree of insurance in age and wealth. The partial insurance parameter for permanent shocks decreases over the life cycle and the age profile is concave, which reconfirms the puzzle of the concave shape of consumption inequality profile. Together with BPP's findings, this paper suggests that the partial insurance over and above self-insurance could be quantitatively small and decrease over the life cycle