How Much Consumption Insurance Beyond Self-Insurance?

We assess the degree of consumption smoothing implicit in a calibrated life-cycle version of the standard incomplete-markets model, and we compare it to the empirical estimates of Blundell et al. (2008) (BPP hereafter). We find that households in the model have access to less consumption-smoothing against permanent earnings shocks than what is measured in the data. BPP estimate that 36% of permanent shocks are insurable (i.e., do not translate into consumption growth), whereas the model's counterpart of the BPP estimator varies between 7% and 22%, depending on the tightness of debt limits. In the model, the age profile of the insurance coefficient is sharply increasing, whereas BPP find no clear age slope in their estimate. Allowing for a plausible degree of "advance information" about future earnings does not reconcile the model-data gap. If earnings shocks display mean reversion, even with very high autocorrelation, then the average degree of consumption smoothing in the model agrees with the BPP empirical estimate, but its age profile remains steep. Finally, we show that the BPP estimator of the true insurance coefficient has, in general, a downward bias that grows as borrowing limits become tighter