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INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL – Introduction 2

INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL - Introduction 2If the household is constrained from borrowing to finance risky investments, the solution may be a corner at which the portfolio is 100% risky assets. If labor income is risky but uncorrelated with risky financial assets, then riskless asset holdings are still crowded out but less strongly; the portfolio tilt towards risky assets is reduced (Viceira 1997). If labor income is positively correlated with risky financial assets, then risky assets can actually be crowded out, tilting the portfolio towards safe financial assets.
Under the assumption that income shocks are uncorrelated or only weakly correlated with stock returns, these results suggest that households who expect high future labor income—discounted at some appropriate rate and measured relative to financial wealth—should have the strongest desire to hold stocks. In a life-cycle model with a realistic age profile of income, the discounted value of expected future income increases relative to financial wealth in the very early part of adulthood, but peaks fairly early and then declines as workers approach retirement. This suggests that fairly young (but not the very youngest) households are the most likely to be affected by borrowing constraints that limit their equity positions. While empirical evidence on household portfolio allocation is fragmentary, a few recent empirical papers have found that household portfolios over the life cycle have hump-shaped equity positions, and U-shaped positions in safe assets, consistent with the message of the theoretical literature (Bertaut and Haliassos 1997, Heaton and Lucas 1997b, Poterba and Samwick 1997).
A complicating factor is that many households, particularly younger and poorer ones, appear to hold no equities at all. This is inconsistent with simple frictionless models of optimal portfolio choice, but may be explained if there is a fixed cost of participating in equity markets. Such a fixed cost would deter young households from buying equities, but later in the life cycle these households might find it worthwhile to begin participating if their wealth levels are high enough to justify paying the cost.
In this paper we explore the quantitative importance of these effects by solving a calibrated life-cycle model of consumption and portfolio choice with labor income uncertainty. The model is set in partial equilibrium and takes as given the stochastic properties of income and asset returns. We closely follow CGM (1998), but augment their model to allow us to explore alternative retirement savings systems and fixed costs of equity market participation.
We also ask whether heterogeneity across households is likely to have a large effect on optimal investment patterns. This issue is important for the debate over social security privatization. A privatized system can allow greater individual choice over the investment of retirement wealth, but opponents argue that some individuals may fail to invest optimally and that privatization may increase administrative costs. Whatever the merits of these arguments, it is important to understand the potential gains from individual choice in the absence of administrative costs and optimization failures. To explore this issue we compare the labor income risk of individuals working in different sectors of the economy, and study the sensitivity of optimal choices to differences in the rate of time preference and the coefficient of relative risk aversion.
The organization of the paper is as follows. Section 2 lays out our life-cycle model and calibrates the parameters. Section 3 presents benchmark results in graphical form. Section 4 explores heterogeneity across households. Section 5 conducts a welfare analysis, and Section 6 concludes.