«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 ...»
Human Capital and Long-Run
Federal Reserve Bank of Chicago
Labor Income Risk
Luca Benzoni and Olena Chyruk
Human Capital and Long-Run
Labor Income Risk∗
Luca Benzoni† and Olena Chyruk ‡
November 29, 2013
This review article examines the role of labor income risk in determining the value
of a person’s human capital. We draw on the existing literature to present a model that
incorporates various types of shocks to earnings. Within this framework, we highlight the implications of diﬀerent assumptions about the correlation between market returns and labor income growth for the value of human capital and its riskiness. Further, the article surveys other work that applies similar ideas to assess the value and risk of pension promises. Finally, we discuss how to enrich the environment with heterogeneity in preferences and stock market exposures; endogenous labor supply and retirement decisions; health shocks; and human capital investment.
1 Introduction We broadly think of ‘human capital’ as the set of knowledge, skills, health, and values that contribute to making people productive (e.g., Becker 1964 and Rosen 2008). In a free society, any contract written against future labor services is not strictly enforceable, and ownership of human capital is restricted to the person who embodies it (labor income is a non-traded asset). Hence, any quantitative analysis of the value of human capital is necessarily based on the present value of a person’s future labor income ﬂows. While intuitive, this deﬁnition is hardly operational without suﬃcient knowledge of the ﬂows of earnings and wages that an individual generates by ‘renting’ his services on the labor market and appropriate discount rates to translate those cash ﬂows into a present value.
∗ This article draws on work joint with Bob Goldstein and Pierre Collin-Dufresne. We are grateful to Cristina De Nardi, Eric French, Bob Goldstein, Debbie Lucas, Bhash Mazumder, and Anna Paulson for helpful comments and suggestions. Vidur Snood provided excellent research assistance. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.
† Federal Reserve Bank of Chicago, 230 S. LaSalle St., Chicago, Il 60604, 312-322-8499, firstname.lastname@example.org.
‡ Federal Reserve Bank of Chicago, 230 S. LaSalle St., Chicago, Il 60604, email@example.com.
To some extent individuals can control future earnings by adjusting labor supply. However, the ability to smooth labor income by changing working hours or moving retirement dates is limited by the presence of various shocks. For instance, deteriorating economic conditions could precipitate job loss and subsequently lower wages. Health problems could produce similar outcomes. Hence, human capital valuation typically relies on statistical models to determine the distribution of future labor income and its covariates.
Identifying appropriate discount rates for uncertain labor income ﬂows also presents a challenge. Some labor income shocks contain an aggregate component. For instance, wages and employment rates are typically lower when the economy does poorly, especially during a long recession. Similarly, health problems in aggregate tend to increase during an extended economic downturn. These risks are likely to be priced in the economy with a premium that is pinned down by traded assets. Hence, given an estimate for the aggregate component of labor income shocks one can price these shocks at market values.
However, labor income contains also a big idiosyncratic component. For example, many health shocks that are unrelated to aggregate economic conditions could force a person out of the labor force. Similarly, a promotion could raise a worker’s earnings regardless of the overall state of the economy. A person cannot fully insure such shocks. Hence, the private value of a worker’s income may diﬀer from the estimated market value of the income based on market discount rates. In other words, the market is incomplete, and to value human capital from the perspective of a worker one needs to posit the preference function being optimized, control variables, and the constraint set. In general, the set of control variables is quite rich.
The agent faces saving vs. consumption decisions; moreover, he must choose how to allocate ﬁnancial wealth across a variety of investment classes. As mentioned previously, endogenous labor supply and retirement decisions further complicate the optimization problem. Absent closed-form solutions, numerical methods generally are used to characterize optimal policies and the implied valuations.
In this review article, we discuss how the recent literature has tackled these issues. We begin by laying out a simple framework to study the implicit market value and risk of human capital. In Section 2, which draws on work by Benzoni, Collin-Dufresne, and Goldstein (2007), we sketch a model in which labor income is assumed to be an exogenous process subject to aggregate and idiosyncratic shocks. While stylized, the model is suﬃciently general to match the main properties of labor income data, both at the aggregate and at the household level. It nests previous speciﬁcations in which the contemporaneous correlation of earnings and stock market shocks is the main source of of priced dependence between the labor market and the rest of the economy. It generalizes those previous speciﬁcations in that it allows for time-varying correlations between labor income and stock returns. In particular, the correlation between the growth rate in labor income and stock returns increases with the time horizon, consistent with economic intuition and empirical evidence. In this setting, we obtain a measure of human capital and identify its exposure to market-wide and idiosyncratic risks. Along the way, we relate this setup and its implications to the recent ﬁnance literature on life-cycle portfolio choice with stochastic labor income.
In Section 3, we discuss recent work that applies similar ideas to assess the value and risk of pension fund obligations, their funding, and the allocation of pension assets across diﬀerent investment classes. Moreover, we extend the framework to incorporate various important ingredients. We touch upon heterogeneity in preferences; diﬀerences in the exposure to stock market risk across agents; endogenous labor supply and retirement decisions; health shocks;
and human capital investment. We enrich this discussion with ideas for future work.
where T is the retirement date, C denotes consumption, π is the fraction of ﬁnancial wealth invested in the risky asset while (1 − π) is the fraction held in the risk-free bond. The second term in equation (1) captures the utility of wealth available to fund consumption during retirement and any bequest. This is similar to modeling the post-retirement consumption and investment decisions under the assumption that the agent receives a ﬁxed income ﬂow like, for example, a retirement annuity.
The budget constraint for the agent is
To study the properties of human capital as deﬁned in equation (3), we need to make additional assumptions about the labor income process L and its linkage with the factors aﬀecting consumption and hence the pricing kernel.
2.1 A Model of Exogenous Long-Run Labor Income Risk Statistical evidence suggests that individual labor income can be decomposed in two main parts (e.g., Carroll & Samwick 1997, Cocco et al. 2005, Gomes & Michaelides 2005, Gourinchas & Parker 2002, Jagannathan & Kocherlakota 1996). First, an aggregate stochastic component which captures the eﬀect of economy-wide shocks on total workers’ compensation. Second, an idiosyncratic component that embeds individual-speciﬁc shocks as well as a deterministic pattern due to life-cycle predictability in wages. Along these lines, we approximate the (logarithmic) household-level labor income, ℓ, with the sum of aggregate and idiosyncratic terms, ℓ = ℓ1 + ℓ2. (4) 2.1.1 The Aggregate Labor Income Component ℓ1
where the constant ℓd is the long-run logarithmic ratio of aggregate labor income to dividends. To capture the notion of long-run dependence between aggregate labor income ﬂow and dividends, we assume that the y(t) process is mean-reverting,
where z1 is a standard Brownian motion independent from z3. The coeﬃcient κ measures the speed of mean reversion for the process y. Benzoni et al. (2007) provide evidence that ˆ κ 0, i.e., y is stationary, so that ℓ1 and d are co-integrated. This result is economically intuitive. For instance, a model with a Cobb-Douglas production function predicts that returns to physical and human capital are perfectly correlated even in the short run (e.g., Baxter & Jermann 1997).1 2.1.2 The Idiosyncratic Labor Income Component ℓ2 We assume that the idiosyncratic labor income component is subject to permanent shocks (e.g., Carroll & Samwick 1997, Cocco et al. 2005, Gomes & Michaelides 2005, and Gourinchas & Parker 2002):2 ( 2) ν2 dℓ2 (t) = α(t) − dt + ν2 dz2,i (t), (9) where z2,i is a standard Brownian motion independent from both z1 and z3, and the ν2 coeﬃcient determines the standard deviation of the idiosyncratic shock. The subscript (i) denotes that this shock pertains to the i-th agent process. Further, we specify the timedependent drift term α(t) = α0 + α1 t, with coeﬃcients α0 and α1 calibrated to match the hump-shape of earnings over the life cycle (e.g., Cocco et al. 2005).
Second, co-integration generates non-zero long-run correlations between labor income and risky asset returns.
Previous research on life-cycle portfolio choice mainly focused on the ﬁrst type of correlation (e.g., Campbell et al. 2001, Cocco et al. 2005, Davis & Willen 2000, Gomes & Michaelides Other previous studies have advocated speciﬁcations that produce high long-run correlations between labor income and stock returns, e.g., Baxter & Jerman (1997), Campbell (1996), Huggett & Kaplan (2013), Lucas & Zeldes (2006), and Santos & Veronesi (2006). For a dissenting voice, see, e.g., Lustig and Van Nieuwerburgh (2006); their results, however, are not robust to the presence of stochastic macroeconomic volatility, e.g., Bansal et al. (2013).
It is straightforward to extend the model to include transient labor income shocks. We know however that such shocks do not aﬀect the consumption-investment decision problem of the agent (e.g., Cocco et al.
2005). Hence we ignore them here for sake of parsimony.
2005, Haliassos & Michaelides 2003, and Viceira 2001). For instance, it is straightforward to show that the labor income dynamics of Campbell et al. (2001) are identical to those in equation (10) in the limit when the mean reversion parameter κ → 0 (e.g., Benzoni & Chyruk 2009). In that case, the eﬀect of co-integration is absent and the only source of correlation between labor income and stock returns is the contemporaneous correlation in their shocks.
This channel, however, has limited support as most empirical studies have shown this correlation to be small or even zero. In contrast, in our more general setting labor income is contemporaneously uncorrelated with the stock market return when (σ − ν3 ) = 0, consistent with empirical evidence. Yet, co-integration generates non-zero long-run correlations between labor income and risky asset returns. Even though these two models are extremely diﬃcult to distinguish econometrically for ‘small’ values of κ, Benzoni et al. (2007) show that they have substantially diﬀerent predictions for the optimal portfolio choice of young agents.
Moreover, co-integration has important implications for the analysis of human capital, as we discuss in more detail below.
This analysis is also useful to clarify the link with labor income models that allow for time varying idiosyncratic shocks. For instance, Storesletten et al. (2004) estimate that idiosyncratic risk is strongly counter-cyclical, and Storesletten et al. (2007) show that, due to this property, human capital acquires stock-like features and the life-cycle risky asset holding is hump shaped. In the context of this framework, ﬂuctuations in the ν2 coeﬃcients over the business cycle would capture this feature. Lynch & Tan (2008) extend this work by showing that the conditional mean of the labor income ﬂow also ﬂuctuates at business cycle frequencies.
2.3 The Sources of Human Capital Risk In the model, the expression for the agent’s human capital Vt in equation (3) depends on three state variables, namely, y, L, and W. Hence, we can identify the sources of human capital risk in the stochastic component of dV as
Since there are no traded securities that correlate with the z1 and z2,i shocks, we follow Benzoni et al. (2007) and introduce two “pseudo-securities” Xj, j = 1 and 2, such that
The coeﬃcients λj (t), j = 1 and 2, are the risk premia on these pseudo-securities. If these claims were traded, then markets would be complete and these risk premia would be determined by the observable price processes. In our case the pseudo securities are not traded. Still, the portfolio problem can be characterized by a complete markets problem in a
2.4 A Numerical Illustration To illustrate the model properties, we calibrate the coeﬃcients to the baseline values of Benzoni et al. (2007).3 Figure 1, Panel A, shows the typical wealth, consumption, and labor income proﬁles averaged across model simulations. By design, the calibration produces realistic wealth accumulation as well as consumption and labor income patterns (e.g., Cocco et al. 2005, Cagetti 2003). Further, Panel B shows risky asset holdings that are hump shaped over the life cycle of the agent. This is also consistent with empirical evidence, which shows that most young investors hold very little ﬁnancial wealth in stocks, they progressively increase their holdings during their middle age, and reduce their exposure to stock market risk as they approach retirement (e.g., Campbell 2006, Ameriks & Zeldes 2004, Benzoni & Chyruk 2009).