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How, then, can the HSZ model produce overall averages that resemble the means of the SCF data? The answer lies in the wealth holdings of the top few percent of the distribution. The solid line in figure 2 shows, for each age group, the average ratio of wealth to permanent income for households at the 99th percentile (by age) in the HSZ model. The dashing line shows the corresponding calculation using the actual data from the 1992 and 1995 SCFs. Clearly, the richest SCF households own enormously more wealth, in relation to their permanent income, than the richest consumers in the HSZ model.

Taken together, Figures 1 and 2 show that the stochastic Life Cycle model under HSZ parameter values matches the aggregate and average data only because it makes two offsetting errors: overestimating the wealth of the typical household and underestimating the wealth of the richest households.

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These simulations indicate that even the extended Life Cycle model misses some crucial features of household behavior. However, the model’s overprediction of the wealth of the median household is easily rectified; Carroll (1992, 1997) argues that the model captures the main features of the behavior of the median household very well if consumers are assumed to be slightly more impatient than HSZ assume, and if the income process is modified to include the benefits of aggregate productivity growth (HSZ assume that households expect, and experience, zero aggregate productivity growth over their lifetimes).
If assuming that consumers are somewhat more impatient can make the stochastic Life Cycle model match the behavior of the median household, a natural question is whether assuming that consumers are somewhat more patient can make the model match the richest households. If so, then it might be possible to argue that the only modification needed to make the stochastic Life Cycle model match the facts is to assume that consumers with higher lifetime incomes are also more patient. Figure 3 examines this possibility by showing the pattern of wealth over the working life of consumers who are the same as the consumers in the baseline HSZ model except that they have a time preference rate of zero rather than the baseline HSZ time preference rate of 3 percent annually. While the age/wealth profile is certainly higher than in the standard HSZ model, it remains far below the profile for the consumers in the top 1 percent of the SCF data. Plausible modifications of other parameter values also fail to raise the model profile to the level found in the data. In other words, the richest households are saving more than can be justified even in a version of the Life Cycle model that allows for very patient consumers with a strong precautionary saving motive.