²The most important differences are, first, that this model incorporates shocks to permanent income, while the HSZ model has only transitory (but very persistent) shocks (they estimate an AR(1) coefficient greater than .90); second, this model ignores health risks; third, I assume that in every period there is a small (p = .03) and serially uncorrelated chance of unemployment; and, finally, I do not extensively model the social welfare system that applies to households at the bottom of the income distribution. (However, I assume that unemployment insurance replaces 50 percent of permanent income for unemployed consumers). HSZ found that labor income risk was far more important than health risk in determining the age profile of wealth and saving, and the details of the social welfare system are not very important in determining the behavior of the median households (much less the rich households). Hence these modelling differences should not matter much for my purposes. I have adopted HSZ’s assumptions about parameter values: time preference rate equal to the interest rate at 3 percent annually; coefficient of relative risk aversion of 3; and a similar age/income profile. The definition of ‘permanent income’ here is the annual income that a household would receive if there were no transitory shocks to income. Except for the incorporation of unemployment insurance and stochastic mortality, and the use here of HSZ parameter values, this model is the same as that in Carroll 1997; see that paper for further discussion of the model’s characteristics and implications.