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«Labor Income Risk Luca Benzoni and Olena Chyruk November 2013 WP 2013-16 Human Capital and Long-Run Labor Income Risk∗ Luca Benzoni† and Olena ...»

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Benzoni et al. (2007) use a 1929-2004 sample of data on total after-tax U.S. employee compensation and dividends on a U.S. stock index to estimate the coefficients of the co-integration relation (8). They calibrate the idiosyncratic labor income dynamics (9) to match the evidence in prior papers that have studied the properties of labor income using household-level data. The equity premium is fixed at 6% and the CRRA coefficient is 5. Further, they impose short-selling constraints on the stock and the bond and rule out any stock market entry cost.

To understand the intuition for these result, it is useful to turn to the valuation of the agent’s human capital. When the investor is young, there is sufficient time for the cointegration effect to act. Thus, the young agent’s human capital displays a high level of comovement with the stock market due to long-run labor income risk, i.e., human capital has stock-like features. Since much of a young investor’s wealth is tied up in his human capital (financial wealth is relatively small when he is young), he finds herself over-exposed to stock market risk and therefore chooses to invest his financial wealth in the risk-free asset.

This is illustrated in Figure 2, which shows the decomposition of the replicating portfolio for human capital into its various holdings of stock, pseudo-securities, and the risk-free money market.

We find the fraction of a 20-year old agent’s human capital tied up in the stock market (equation 16) to be approximately one-half, while the implicit positions in the two pseudosecurities X1 and X2 are 13.9% and 87.6%, respectively. These evidence shows that human capital is mostly equivalent to a long position in the stock market portfolio and in permanent idiosyncratic risk, which is hedged with X2.4 Moreover, the human capital of a young agent is a highly leveraged security: his implicit holding in the risk-free asset is approximately


As the agent grows older, co-integration has less time to act so that idiosyncratic shocks become the prevalent source of human capital risk. Since these latter shocks are orthogonal to stock market fluctuations, the agent has an incentive to diversify them away via a larger position in stocks. This effect generates the increasing part of the portfolio holding profile (Figure 1, Panel B). When he approaches retirement, human capital has mainly bond-like features. However, the present value of future labor income flows shrinks to zero since there are few remaining years of employment. Thus, the agent reduces his position in the stock market to buy more of the risk-free asset.

This is also evident in Figure 3, Panel A, which shows how human capital Vt evolves over the life cycle. The fraction of the agent’s labor income tied up in the risky asset is roughly constant at 50% throughout the first half of his life, and it rapidly goes to zero near retirement. Further, human capital has a hump-shaped profile. That is, although young agents face a larger stream of future labor income, they discount such cash flows more than older agents. There are three reasons for this. First, the predictable labor income component has a hump-shaped profile: Higher labor income cash flows occur at older ages, and therefore are subject to greater time discounting. Second, as the agent ages, he faces lower idiosyncratic labor income risk. Indeed we find the risk premium on the permanent idiosyncratic labor income shocks λ2 to have a downward-sloping profile. This effect is common to other models with idiosyncratic labor income risk (e.g., Campbell et al. 2001, Cocco et al. 2005, Carrol & Samwick 1997, and Gomes & Michaelides 2005). Third, in our model human capital has pronounced stock-like features, and thus commands a higher discount rate, for young agents, whereas it acquires bond-like properties, and thus is discounted at a lower rate, for older The transient idiosyncratic shocks represent only a very small fraction of the replicating portfolio. Hence we do not report them in Figure 2.

agents. Due to this third effect, which is determined by the long-run cointegration of labor income and stock market performance, the value of human capital peaks at a later point in the agent’s life compared to standard models considered in previous studies. This intuition is confirmed in Figure 3, Panel B, which shows that the correlation of stock returns and the returns to human capital remains high and basically constant over the first half of the agent’s life, and it rapidly drops as the agent approaches retirement.

3 Future Directions

3.1 The Value and Risk of Pension Funds and Social Security The methods for the valuation of human capital find direct application in the valuation of pension-plan obligations, their funding, and the allocation of pension assets across different investment classes. For instance, Lucas & Zeldes (2006) focus on the valuation and hedging of defined-benefit (DB) plans. A DB plan awards the employee deferred compensation in the form of future payments (typically a retirement annuity) linked to the length of his tenure with the firm and the salary received during the final year(s) of employment.5 From a firm’s point, a DB plan involves accrued benefit obligations (ABO) toward former and current workers, computed based on current years of employment and wages. More broadly, however, the firm’s obligations include liabilities towards all employees (former, current, and expected future workers), computed based on past and projected future years of employment and wages. Lucas & Zeldes (2006) refer to this latter measure as an ‘all-inclusive’ projected benefit obligation (PBO).

ABOs are firm’s obligations of a known amount and should be discounted and hedged accordingly. In contrast, the valuation and funding of PBOs should reflect the risk associated with these uncertain future payments. The problem is complicated by multiple factors, including taxes, the effect of the Pension Benefit Guarantee Corporation (PBGC) guarantees, accounting and tax regulations, corporate liquidity needs (funds tied up in the pension plan may not be easily redirected to other corporate needs), and other labor contracting considerations. Abstracting from some of these issues, Lucas & Zeldes (2006) argue that while the hedging of ABOs is best accomplished with a portfolio of bonds (see also Bodie 1990, 2006), the hedge portfolio for PBOs should contain a mix of stocks and bonds, with a share of stocks versus bonds that depends on firm and worker characteristics, e.g., the probability of bankruptcy, worker separation, and mortality. Moreover, the rate at which to discount uncertain PBOs is a function of similar macroeconomic, firm, and worker characteristics.

To better understand these results, consider that if wage growth correlates positively with stock returns over the long run, then future pension liabilities will also correlate positively with the performance of the stock market. Thus, stocks should be part of the hedge portfolio, and firms with a higher percentage of active workers should invest more heavily in stocks.

In spite of much recent growth in defined-contribution (DC) plans, DB plans remain popular with a number of firms still offering them in the retirement package for their employees.

Moreover, firms should discount their projected PBOs at a rate that increases with the share of active workers relative to separated and retired employees. This is consistent with the discussion above, which shows that human capital has a stock-like component that is higher for younger workers. Thus, the PBO of a firm with a higher fraction of active (i.e., younger) workers also has stock-like properties. This feature determines a higher hedge position in stocks, increases the rate at which to discount the PBO, and reduces the PBO’s present value.

Similar issues arise in the valuation of Social Security obligations. A key input to this problem is the rate at which to discount future liabilities. The traditional actuarial approach uses a risk-free rate to discount future expected cash flows. Geanakoplos & Zeldes (2010) argue that this approach underestimates the riskiness of such obligations. Social Security benefits depend on the realization of the future economy-wide wage level. If future wages and stock market performance correlate positively over the long run, then the appropriate discount rate for Social Security obligations toward active workers should exceed the riskfree rate. This risk adjustment reduces the present value of the obligation, which is relevant to assessing the projected burden of Social Security on the taxpayer. Moreover, there is much debate on the costs and benefits associated with investing a fraction of the Social Security fund in stocks (e.g., Abel 1999, 2001, Geanakoplos, Mitchell & Zeldes 1998, Heaton & Lucas 2005).6 This problem resembles optimal asset allocation in private DB pension funds. Thus, as in Lucas & Zeldes (2006) the portfolio that hedges future projected Social Security obligations contains a share of stocks that depends on macroeconomic conditions and worker characteristics.

This discussion extends to the debate about the opportunity to replace part of the existing DB U.S. Social Security system with a system of defined contributions (DC) personal accounts. If such a reform were to occur, it is possible that the private sector would take over some of the obligations that are currently guaranteed by Social Security. Geanakoplos & Zeldes (2009) offer suggestions on how to structure and trade these securities. More broadly, much work is going in computing the present value of state and municipal government pension liabilities (e.g., Novy-Marx & Raugh 2011a, b) and in understanding the risk and valuation of Federal guarantees in student loans (e.g., Lucas & Moore 2010). We point the interested reader to the review articles by Lucas (2012) and Raugh (2014) for more discussion.

3.2 Cross Sectional Heterogeneity There is a great deal of heterogeneity in stock market participation and risky asset holdings in the U.S. population (e.g., Ameriks & Zeldes 2004, Campbell 2006). Many reasons could explain this evidence, e.g., entry costs to the stock market that vary across agents due to different education levels, heterogeneity in borrowing constraints or attitude toward risk. An See also related work by Bovenberg et al. (2007) on the interaction between life-cycle portfolio choice and investment decisions by pension funds.

alternative, complementary explanation is that human capital risk varies across individuals depending on their degree of exposure to market-wide shocks. The model in Section 2 can accommodate this possibility by allowing the coefficient of cointegration κ to vary across agents. Smaller values of κ increase the correlation between labor income and stock market shocks. This raises the component of human capital implicitly tied up in the stock market and induces the agent to favor more conservative life-cycle stock holdings (Benzoni et al.


Recent empirical work by Betermier et al. (2012) suggests that this effect could be important. Using a panel data set on Swedish households that switched industries between 1999 and 2002, they conclude that households that go from an industry with low wage volatility to one with high volatility decrease their risky asset holdings. While more work is needed to better understand the sources of heterogeneity in human capital risk, the implications for optimal portfolio choice are evident. For instance, if workers in different industries are exposed to different degrees of aggregate risk, then financial advisers should tailor their recommendations accordingly (e.g., Bodie & Treussard 2007).

Moreover, this discussion has interesting implications for general equilibrium models that attempt to explain the equity premium puzzle. For instance, Basak & Cuoco (1998) take as given that a large proportion of investors do not participate in the stock market and conclude that, under this assumption, one need only attribute reasonable levels of risk aversion to those agents that invest in stocks to explain the historical equity premium.7 Benzoni et al. (2007) show that it is optimal for a large proportion of agents to not participate in the equity market. While their analysis focuses on the individual’s optimal portfolio and consumption choices taking the equity risk premium as given, their results suggest that the exogenous specification of Basak & Cuoco (1998) might be justifiable in a general equilibrium setting that considers two classes of agents that endogenously choose to participate in the stock market depending on their risk aversion and long-run exposures to aggregate risk.

3.3 Endogenous Labor Supply The discussion so far assumed that labor income is an exogenous process. In particular, most of the finance literature on life-cycle portfolio choice relies on model calibrations that strive to match the empirical properties of labor income without explicitly modeling the work-leisure behavior, nor the retirement decision. These choices are the focus of much work in labor economics. For instance, R´ ıos-Rull (1996) and Heathcote et al. (2010) propose lifecycle models of labor supply and savings in which future wages are uncertain. French (2005) augments these models to include a retirement decision and uncertain health status. French & Jones (2011) and van der Klaauw and Wolpin (2008) extend this analysis to study the effect of uncertain medical expenses and health insurance on retirement decisions (see also related work by Casanova 2010, French & Benson 2011, and Low et al. 2010). These studies fit such structural models to individual-level data and use them to conduct fiscal policy See also Mankiw & Zeldes (1991).

experiments (e.g., the effect of Medicaid or Social Security System reforms on retirement choices and life-cycle labor supply).

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