This paper develops a model with partial insurance against idiosyncratic wage shocks to quantify risk sharing, and to decompose inequality into life-cycle shocks versus initial heterogeneity in preferences and productivity. Closed-form solutions are obtained for equilibrium allocations and for moments of the joint distribution of consumption, hours, and wages. We prove identification and estimate the model with data from the CEX and the PSID over the period 1967–2006. We find that (i) 40% of permanent wage shocks pass through to consumption; (ii) the share of wage risk insured privately increased until the early 1980s and remained stable thereafter; (iii) life-cycle productivity shocks account for half of the cross-sectional variance of wages and earnings, but for much less of dispersion in consumption or hours worked.
Published in: _American Economic Review_ (Vol. 104, No. 7, July 2014, pp. 2075-2126) https://doi.org/10.1257/aer.104.7.2075.
[Technical Appendix: Consumption and Labor Supply with Partial Insurance: An Analytical Framework](http://www.jonathanheathcote.com/framework_appendix.pdf)