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This paper produces endogenous equity market non-participation in an economy with uninsurable labor income risk and heterogeneous skill levels. Prudence and impatience generate stationary household wealth levels that depend on income. Skill, and therefore labor income, heterogeneity leads to wealth heterogeneity, with high skill households accumulating high wealth and low skill households accumulating low wealth. A HARA class utility with subsistence consumption requirement generates decreasing RRA with respect to household wealth. Consequently, low skill households also have significantly higher local RRA. In addition low skill households have less human capital and therefore have lower diversification demand for stocks. Low wealth, high RRA and low diversification demand predicts that low skill households do not hold stocks in the face of a moderate ownership cost. In addition, the model predicts a humped lifecycle wealth accumulation pattern and a humped lifecycle stock allocation pattern. I also find that stockholders exhibit a greater aggregate willingness to supply risky capital during the expansion phase of a business cycle, despite the lower conditional equity premium.

Using the 1984 Panel Study of Income Dynamics (PSID) data, Mankiw and Zeldes (1991) find that only 23.2% of U.S. households hold more than $1000 in stocks directly. Blume and Zeldes (1994) and Haliassos and Bertaut (1995) find similar patterns of equity market non-participation using the Survey of Consumer Finance (SCF) data. Using the U.S. Consumer Expenditure Survey (CEX) database, Brav, Constantinides, and Geczy (2002) and Vissing-Jorgensen (2002b) find that less than 30% of the U.S. households hold stock in material dollar amounts. Attanasio, Banks, and Tanner (2002) report the similar pattern of non-participation using the U.K. Family Expenditure Survey. Even during the heydays of Internet stock trading, Bertaut and Starr-McCluer (2000) find that less than 50% of households own stocks. The high equity market non-participation rate documented is puzzling given the attractive premiums offered by stocks. Insights into this question would help us understand the equity premium puzzle. Recent papers have found that equity market non-participation helps explain the smoothness in aggregate consumption growth (empirical: Attanasio et al. (2002), Brav et al. (2002), and Vissing-Jorgensen, 2002a and Vissing-Jorgensen, 2002b; theoretical: Basak and Cuoco (1998), Constantinides, Donaldson, and Mehra (2002) and Storesletten, Telmer, and Yaron (2007)). It is then doubly important to understand the nature of non-participation and the asset-pricing implications associated with a high equity market non-participation rate. Is the perceived cost associated with equity investment the main driver of non-participation? If so, what are the impacts on asset prices from the recent decreases in trading costs and increases in investor financial savvy-ness? Or perhaps, households simply are heterogeneous in their preferences, and non-participating households are just more risk averse than the stockholding households. In this case, the measure of risk aversion implied by aggregate data might overstate the risk aversion that is appropriate for studying the equity market. Standard portfolio choice models have had tremendous difficulties delivering a high rate of equity market non-participation in the population. This has led the current literature to focus on exploring high fixed-cost of stock ownership and departures from the standard expected utility framework (see Haliassos and Bertaut (1995) for an excellent discussion on this). Hong, Kubik, and Stein (2004) believe that information cost, which is high for households not endowed with social networks, which facilitate the acquisition of financial knowledge, is responsible for non-participation. Ang, Bekaert, and Liu (2005), appealing to an alternative utility function specification, suggest that disappointment aversion, which can be high for some households, account for non-participation. Cao, Wang, and Zhang (2005), using a Knightian uncertainty approach, argue that some households are extremely uncertain about the right model for understanding equity returns and therefore use worst case scenarios to analyze investments; this leads to non-participation. The more recent literature on portfolio choice finds that incorporating labor income deepens the non-participation puzzle!1 Households endowed with (risky) labor income demand greater stock allocations in their portfolios than households without labor income to diversify their human capital. Labor income, therefore, makes the high rate of equity market non-participation all the more puzzling. Models, based on alternative preferences or non-expected utility paradigms, have not addressed this issue. In this paper, I propose a model which delivers a high rate of equity market non-participation in the economy, without appealing to large market frictions, alternative preferences or non-expected utility framework. I also refrain from assuming preference heterogeneity (which is needed in Ang et al. (2005) to deliver non-participation) or cognitive heterogeneity (which is needed in Cao et al. (2005) to deliver non-participation). In my model, a high degree of wealth heterogeneity, which arises endogenously, coupled with moderate fixed-cost, leads to severe non-participation. Heterogeneity in household wealth is not addressed or linked to portfolio choice in the aforementioned theory papers on non-participation. This seems unsatisfactory since empirical studies have documented increasing probability of stock ownership with wealth. Endogenous wealth heterogeneity plays a key role in my economy and drives many of the interesting results. Two key ingredients drive the non-participation rate in my economy. The main innovation comes from the introduction of a two-sector labor market. A fraction of the population is endowed with high skill and employed at high wage rate, while the rest of the population is endowed with low skill and employed at low wage rate. The second innovation comes from the assumption of subsistence consumption needs. This is implemented through a HARA class utility function with decreasing relative risk aversion. I show that prudence (driven by volatile labor income) and impatience (driven by high subjective discount rate) lead households to develop lifecycle wealth targets (targeted levels of buffer stock savings). Below their wealth targets, prudence dominates and households accumulate wealth to hedge against unemployment spills. Above their wealth targets, impatience dominates and households decumulate to avoid deferring too much current consumption. The wealth targets, which are key to understanding the household's portfolio choice behavior, depend, in part, on the level of the household's permanent labor income as well as the volatility of that labor income stream. High skill, and therefore high income, households endogenously choose to accumulate high wealth, while low skill (low income) households choose to accumulate low wealth; this result, while intuitive is not trivial; if labor incomes were constant and guaranteed for life, households would choose to consume their entire income each period and accumulate no wealth. Since low skill households rationally choose to also become low net worth, they also make the conscious choice to be more relatively risk averse than high net worth households. This is the mechanism through which the model generates heterogeneous relative risk aversion in the population without assuming heterogeneity in the preference parameters. The greater relative risk aversions for the low income households translate to lower stock allocations for these households. The lower demand for stocks is further depressed by low income households’ small human capital portfolio. In my model, equity returns, which are only weakly correlated with the labor income fluctuations, diversify human capital risk. As a result, low income households, who have less human capital, have lower diversification demand for stocks. The combined effect of low net worth, high local RRA and low diversification demand for stocks means that low skill households allocate trivial dollar investments to stocks. In the face of moderate stock ownership cost, these households rationally choose to not participate in the equity market. In this model, equity market non-participants are predominantly the low skill households. However, lifecycle considerations, which lead to a humped lifecycle wealth accumulation pattern and a humped lifecycle stock allocation pattern for households, further predict that a large fraction of young and retired high skill households would also not invest in stocks. Households in this economy are assumed finitely lived, which allows the characterization of lifecycle behaviors. In particular, the specification of the retirement income process has important implications for households’ wealth accumulation policy. I show that the wealth target is not constant over the lifecycle of a household. In my (partial equilibrium) economy, working (not retired) households desire wealth targets that are about two to three times their annual after-tax income to hedge against transient labor income shocks and to smooth the large decrease in retirement income. 2 Once retired, households desire a zero wealth target since they received guaranteed pension income and therefore have no precautionary savings motive. 3 Without a precautionary savings motive, impatience dominates prudence and retirees decumulate their wealth to zero. This lifecycle wealth target pattern predicts a humped lifecycle wealth accumulation pattern. A young family enters the workforce with little wealth. It must accumulate toward its desired wealth target over time. Upon reaching its desired wealth target, wealth accumulation stops and the household wealth plateaus at this level for as long as a household is exposed to unemployment risk and the impending fall in income on retirement. Upon retirement, the precautionary savings motive disappears immediately and decumulation begins. The decumulation is not instantaneous, as this household desires to smooth intertemporal consumption. These sequences of events combine to produce a humped wealth accumulation pattern over a household's lifecycle. The humped lifecycle wealth accumulation pattern predicts a humped lifecycle stock allocation pattern for stockholders. As I mentioned before, a young household starts with very little wealth. Subsistence consumption need combined with a borrowing constraint make this household very relatively risk averse and shy away from stocks. As this young household accumulates toward its wealth target, it becomes less relatively risk-averse and its stock allocation increases. However, as human capital is converted into income with age, a household's diversification demand for stocks decreases. Finally, stock allocation falls to zero in retirement after the retiree decumulates toward zero wealth. These sequences of events combine to produce a humped stock allocation over a household's lifecycle. Qualitatively, the model produces significant equity market non-participation. I calibrate the model to examine its quantitative merit and to demonstrate the quantitative importance of parameters. In particular, the income processes for the two skill groups are calibrated to reflect higher unemployment rate and duration during the recession phase of a business cycle. I find that high skill households would not invest in stocks at wealth levels as high as $100,000, which traditional portfolio choice models have not been able to produce. In addition, I find that stockholders (composed entirely of the high net worth households) allocate a greater fraction of their portfolios to stocks during expansions despite the lower expansion equity premium and allocate a smaller fraction during recessions despite the higher recession equity premium. This is because during recessions, households are faced with greater uncertainty in their labor incomes; they are more likely to become unemployed, and when unemployed they are more likely to remain unemployed. The greater aggregate willingness to supply risky capital during expansions is consistent with the empirical observation that the equity premium is counter-cyclical. The rest of the paper is organized as follows. Section 2 formulates the model and calibrates it to observed U.S. data. Section 3 characterizes the household's optimal portfolio choice problem. Section 4 examines the household's lifecycle wealth targets and portfolio allocations and discusses why non-participations arise for the low skill households. Section 5 performs comparative statics on key model parameters. Section 6 offers some directions on future research and concludes.