When does an individual's expected wealth accumulation profile increase as earnings risk increases? This paper answers this question for multi-period models where earnings shocks are independent over time. Sufficient conditions are stated in terms of properties of a decision rule for savings and, alternatively, in terms of properties of preferences. Copyright 2004, Wiley-Blackwell.

We analyze the insurance provided by the U.S. social security and income tax system within a model in which agents receive idiosyncratic, wage rate shocks that are privately observed. We consider two reforms: a piecemeal reform that optimally chooses the social security benefit function and a radical reform that eliminates the entire social insurance system and replaces it with an optimal tax on lifetime earnings. The radical reform outperforms the piecemeal reform and achieves nearly all of the maximum possible welfare gain when wages differ permanently over the lifetime. When wage shocks match properties in U.S. data, the piecemeal reform outperforms the radical reform.

Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital, estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth. We find that, as of age 23, differences in initial conditions account for more of the variation in lifetime earnings, lifetime wealth, and lifetime utility than do differences in shocks received over the working lifetime. (JEL D31, D91, J24, J31)