How Much Insurance in Bewley Models?

The standard life-cycle incomplete-markets model, where households face idiosyncratic income shocks and trade a non-contingent asset, is a workhorse of quantitative macroeconomics. In this paper, we assess the degree of consumption insurance implicit in a plausibly calibrated version of the model, and we compare it to the data. On both actual and simulated data, we apply a technique recently developed by Blundell, Pistaferri and Preston (2006, BPP thereafter). We …nd that households in Bewley models have access to less consumption smoothing than what is measured in the data. BPP …nd that 38% of permanent income shocks are insurable (i.e., do not translate into consumption growth), while in the model this insurance coe¢ cient is 18%. Moreover, the life-cycle pattern of insurance coef…cients is sharply increasing and convex in the model, while it is roughly ‡at in the data. Taken at face value, this result would suggest that macroeconomists should develop models with more avenues of insurance than a risk-free asset. However, we also …nd that if income shocks are not not modelled to be permanent, as assumed by BPP, but (even very) persistent, the degree of consumption smoothing implicit in Bewley models largely agrees with the data. Finally, we uncover that the BPP estimator for the insurance coe¢ cient has, in general, a small downward bias. This bias though can be substantial for households near their borrowing limit, e.g., young or poor households.