Labor income dynamics at business-cycle frequencies: Implications for portfolio choice

https://doi.org/10.1016/j.jfineco.2011.03.005Get rights and content

Abstract

Young agents with low wealth-income ratios counter factually hold more stock than young, rich agents and old agents using the standard portfolio choice model with i.i.d. stock returns and labor income. This paper matches the countercyclical volatility and procyclical mean of U.S. labor income and finds that, consistent with U.S. data, young, poor agents now hold less stock than both young, rich agents and old agents, and no stock a large fraction of the time. Our results suggest that the predictability of labor income growth at a business-cycle frequency, particularly the countercyclical variation in volatility, plays an important role in a young agent's decision making about her portfolio's stock holding.

Introduction

A large recent literature has focused on multi-period portfolio choice with labor income, and while the models are elaborate along several dimensions, they almost all assume that the labor income and asset returns are jointly identically and independently distributed (i.i.d.).2 Calibrating this joint distribution to U.S. data, these papers obtain three results not found empirically for U.S. households: Young agents choose a higher stock allocation than old agents, young agents choose a higher stock allocation when poor than when rich, and, young agents always hold some stock.3 This paper asks whether allowing the conditional joint distribution to depend on the business cycle can allow the model to generate equity holdings that better match those of U.S. households, while keeping the unconditional distribution the same as in the data. Calibrating the first two moments of labor income growth to match the countercyclical volatility and procyclical mean found in U.S. data leads to large reductions in stock holdings by young agents with low wealth–income ratios. The countercyclical volatility is the more important of the two, inducing reductions that are so large that young, poor agents now hold less stock than both young, rich agents and old agents, and no stock a large fraction of the time. Our results suggest that the predictability of labor income growth at a business-cycle frequency, particularly the countercyclical variation in volatility, plays an important role in a young agent's decision making about her portfolio's stock holding.

Enriching labor income dynamics along this dimension can be motivated by recent evidence that the first and second moments of labor income growth are predictable at business-cycle frequencies. Storesletten, Telmer, and Yaron (2004), using household-level labor-earnings data from the Panel Study of Income Dynamics (the PSID), estimate that the standard deviation of shocks to permanent log labor income increases by around 75% as the macroeconomy moves from peak to trough. Further, economic intuition strongly suggests that labor income growth is higher in good times than in bad. We estimate the magnitude of this effect by taking the changes in log aggregate labor income and covarying this series with the lagged value of the 12-month dividend yield on the value-weighted NYSE index. When the aggregate labor income measure is either monthly earnings for the retail sales industry or the total private sector, the point estimate of this covariance is negative and strongly significant. Because dividend yield is countercyclical, this point estimate implies that the change in log aggregate labor income is pro-cyclical, which is consistent with intuition.

Both the pro-cyclical behavior of mean labor income growth (state-dependent mean channel) and the countercyclical behavior of labor income volatility (state-dependent volatility channel) can reduce stock holdings by young low wealth–income ratio agents. This result can be explained by a static diversification story, which says that positive (negative) covariance between stock returns and human capital causes the agent to hold less (more) stock. When risk aversion is greater than one, both channels produce human capital that covaries more positively with stock return than when both channels are switched off, which means that the static diversification intuition implies lower stock holdings. However, the deeper question is why, when risk aversion is greater than one, the two channels produce human capital that is more positively correlated with stock return than when both channels are switched off. The hedging-demand intuition of Merton (1973) can be used to answer this question. Merton (1973) shows that for constant relative risk aversion (CRRA) investors with risk aversion greater than one, positive correlation between return and future investment opportunities leads to reductions in stock holdings by young investors. Empirically, realized stock return is low when the probability of entering or remaining in a recession increases. But in recessions expected income growth is low and the volatility of income growth is high. So a low stock return this period means low expected income growth and high volatility of income growth in the next period and future periods. Thus, stock returns and future “labor income” opportunities are positively correlated. Therefore business-cycle variation in the first two moments of income growth causes reductions in stock holdings by young investors. Moreover, these reductions are more pronounced for poor young investors, for whom future labor income is more important. This mechanism is the flipside of the one by which return predictability increases the stock holdings of young agents with risk aversion greater than one. Young agents facing return predictability hold more stock than myopic agents because of the negative correlation between stock return and future opportunity sets induced by the predictability. Consistent with the hedging-demand intuition, when risk aversion is less than one, both channels are found to produce human capital that covaries negatively with stock return, and the young low wealth–income ratio agent is found to hold more stock when either or both channels are switched on than when both channels are switched off.

Our goal is to quantify the effects of these two labor income channels on portfolio allocations by young investors. To do so, we formulate a dynamic life-cycle portfolio choice problem and calibrate the stock return and labor income processes to U.S. data. Simple vector autoregression (VAR) dynamics are used to incorporate both mechanisms, with dividend yield, a countercyclical business-cycle variable, being used as the predictor for both labor income growth and stock return. Robustness checks indicate that the VAR does a good job of capturing both the high and low frequency income growth predictability in the data. The agent starts work at age 22 and retires at 65, receiving Social Security payments of 93.8% of her retirement permanent income until death, as reported in Cocco, Gomes, and Maenhout (2005) for college graduates. Death probabilities for the agent are taken from the 2001 U.S. Life Tables provided by the NCHS. The agent has power utility and risk aversion of six. The state-dependent mean (SDM) channel is incorporated by calibrating the covariance of labor income growth and lagged dividend yield to that for aggregate monthly wages in the retail trade industry. The state-dependent volatility (SDV) channel is incorporated by allowing the second moment to be predictable using a bifurcation of dividend yield. We bifurcate the quadrature's dividend-yield variable using a cutoff value such that the unconditional probabilities of the resulting recession state and expansion state match the unconditional probabilities in the data for the National Bureau of Economic Research (NBER)-based expansions and recessions. The ratio of the innovation volatility for permanent labor income growth in recessions relative to expansions is matched to 1.75, the value reported in Storesletten, Telmer, and Yaron using the NBER variable to determine the timing of expansions and recessions. At the same time, the unconditional volatility of permanent labor income growth itself is always matched to the 15% per annum reported in Gakidis (1997) based on PSID data for professionals and managers not self-employed under age 45. We use a third order polynomial to approximate an agent's typically hump-shaped life-cycle earnings profile, taking the parameter point estimates in Cocco, Gomes, and Maenhout (2005) for college graduates.

In this base case, the simultaneous presence of the two business-cycle channels calibrated to data causes the agent's stock allocation to drop from near the boundary of 100% to an average allocation of less than 25% for a young agent whose financial wealth is less than 30 times her monthly wage. The magnitude of the reduction is only increased by considering smaller wealth–income ratios. However, while both business-cycle channels are important, the volatility channel is definitely the more important. When financial wealth is ten times the young agent's monthly labor income, the average stock allocation decreases by an allocation of 17% when the mean channel is switched on but the volatility channel is left off and by an allocation of 68% when the volatility channel is switched on but the mean channel is left off. It is the volatility channel's presence that causes the relation between average stock allocation and wealth–income ratio to flip from the negative relation in the theoretical literature to a positive one as in the data. Turning to stock allocations as a function of age for an agent with zero financial wealth at age 22, the average stock allocation is a negative function of age from age 22 to 57 and lower at retirement than at age 22 when both channels are switched off. Switching on the two business-cycle channels causes the function to become hump-shaped from age 22 to age 54 and the average stock allocation to be much higher at retirement than at age 22, consistent with the data. Turning to the nonparticipation results, both channels switched off leads to participation in the stock market virtually all the time, irrespective of age or wealth–income ratio. Switching on the two business-cycle channels results in substantial nonparticipation by agents in their first month and the nonparticipation steadily declines as the agent gets older. For example, an agent with a wealth–income ratio of 0 in the first month decides not to participate in the stock market 79% of the time in the first month; and after ten years, this probability has declined to a fraction that is still above 26%.

The volatility channel's affect on allocations is robust to using the NBER expansion–recession variable directly to calibrate the expansion–recession state, which means that this channel is able to generate large reductions in the average stock allocations of young, poor agents without relying on the large negative contemporaneous correlation between dividend yield and stock returns. Moreover, recognizing that agents might not have sufficient information to infer the NBER expansion–recession variable at the start of each month, we use the empirical relation between dividend yield and the NBER expansion–recession variable to calculate the probability of an NBER expansion conditional on the value of the dividend yield. Taking the volatility conditional on the NBER variable as given by Storesletten, Telmer, and Yaron, this probability allows us to calculate analytically the volatility conditional on the dividend-yield value. As would be expected, the effect of the volatility channel on allocations is attenuated relative to when the agent uses the NBER expansion–recession variable directly. But it is still the same qualitatively, because the reduction in the average stock allocations of young, poor agents is sufficiently large that in combination with the state-dependent mean channel, these agents still hold less stock on average than young wealthy agents.

Our model is able to generate realistic wealth accumulation by the agent over her life. And a number of robustness checks and extensions are also performed. The ability of the two business-cycle channels to reduce the stock holdings of poor young agents is largely unaffected by whether stock returns are i.i.d. or predictable, the presence of Social Security, the introduction of a realistic probability of unemployment, a flat rather than hump-shaped labor income profile, or the presence of temporary shocks to labor income.

Positive conditional correlation between today's realized return and today's labor growth innovation can also reduce equity holdings (see Davis and Willen, 2000a, Davis and Willen, 2000b and Michaelides, 2003). This is a diversification-like channel and is available even when stock return and labor income growth are i.i.d. processes. Consequently, it is a channel that is distinct from the two we are considering. However, the contemporaneous correlation between returns and labor income growth appears to be small in the data (see Davis and Willen, 2000b; Fama and Schwert, 1977; and Botazzi, Pesenti, and Wincoop, 1996). This small unconditional correlation is an important stylized fact that restricts the ability of the return correlation channel to reduce equity holdings (see Viceira, 2001).

Benzoni, Collin-Dufresne, and Goldstein (2006) is independent work that considers a setting in which the resulting generating process for labor income has some features that are similar to the one we use. They assume that aggregate labor income and stock dividend are cointegrated to obtain their predictive variable, which is the difference between the logs of the two. This difference is a stationary variable given the assumed cointegrating relation. However, the meaningfulness of their calibration relies heavily on the cointegrating relation holding, and while there is good intuition for such a relation holding (which makes their paper interesting), the empirical evidence is weak. In contrast, we do not need to assume such a cointegrating relation to identify our predictive variable. All we need is pro-cyclical expected labor income growth, which is consistent with intuition and strongly supported by the data. The resulting reductions in stock holdings from the two calibrations, theirs and ours, are likely to be quantitatively different and in fact they are. Finally, and most importantly, their setup does not allow for income growth heteroskedasticity, which we find to be a much more important channel than our SDM channel.

Section 2 presents our formulation of the problem and describes the two channels through which we allow labor income to affect the stock holdings of young agents. Section 3 describes how the return and labor income processes are calibrated to the data. Section 4 discusses our results and Section 5 concludes.

Section snippets

Formulation and solution of the problem

This section formulates the agent's problem and describes the solution technique that we use to solve the problem.

Calibration

We use the one-month Treasury bill rate to obtain a proxy for the risk-free rate, the value-weighted return of all stocks on the NYSE, AMEX, and Nasdaq as the market return, and the 12-month dividend yield on the value-weighted NYSE index as a proxy for the predictive variable D. Aggregate labor income data are used to obtain point estimates of some moments of interest. Wage earnings data are from the Bureau of Labor Statistics website (www.bls.gov). We use either Retail Trade, which is series

Results

This section reports policy functions for the various problems described above. Simulation results are also reported.

Conclusion

This paper asks whether allowing the conditional distribution of labor income to depend on the business cycle can allow the CRRA portfolio choice model to generate equity holdings that better match those of U.S. households, while keeping the unconditional distribution the same as in the data. Calibrating the first two moments of labor income growth to match the countercyclical volatility and procyclical mean found in U.S. data leads to large reductions in stock holdings by young agents with low

References (41)

  • Calvet, L., Campbell, J., Sodini, P., 2006, Down or out: assessing the welfare costs of household investment mistakes....
  • J. Campbell et al.

    Household risk management and optimal mortgage choice

    Quarterly Journal of Economics

    (2003)
  • J. Campbell et al.

    Consumption and portfolio decisions when expected returns are time varying

    Quarterly Journal of Economics

    (1999)
  • Carroll, C., 1992. Buffer-stock theory of saving: some macroeconomic evidence. Brookings Papers on Economic Activity,...
  • Carroll, C., 1996. Buffer-stock saving: some theory. Unpublished working paper, Johns Hopkins University, Baltimore,...
  • C. Carroll

    Buffer-stock saving and the life-cycle/permanent income hypothesis

    Quarterly Journal of Economics

    (1997)
  • Chamberlain, G., Hirano, K., 1997. Predictive distributions based on longitudinal earnings data. Unpublished working...
  • J. Cocco et al.

    Consumption and portfolio choice over the life cycle

    Review of Financial Studies

    (2005)
  • Curcuru, S., Heaton, J., Lucas, D., Moore D., 2004. Heterogeneity and portfolio choice: theory and evidence. Handbook...
  • Davis, S., Willen, P., 2000a. Occupation-level income shocks and asset returns: their covariance and implications for...
  • Cited by (60)

    • Robo advisors and access to wealth management

      2024, Journal of Financial Economics
    • Hedging recessions

      2019, Journal of Economic Dynamics and Control
      Citation Excerpt :

      Our model is apparently the first to include business cycle variations in unemployment risk. Lynch and Tan (2011) add business cycle variations to the standard life-cycle model by assuming that the stock market dividend yield determines the expected growth rates of both stock prices and labor income. The human capital is therefore more stock-like so the optimal stock investment is somewhat smaller than in the standard model of Cocco et al. (2005).

    View all citing articles on Scopus

    We would like to thank an anonymous referee, Luca Benzoni, Ned Elton, Marti Gruber, Joel Hasbrouck, Robert C. Merton, Lasse Pedersen, Matt Richardson, Jessica Wachter, attendees at the Portfolio Choice session of the 2008 American Finance Association Meetings, participants in the Monday New York University Finance Seminar, the New York University Macro-finance Reading Group, the Australian Graduate School of Management Research Camp and the Hong Kong University of Science and Technology Finance Conference and seminar participants at École des Hautes Études Commerciales, Fordham University, INSEAD and University of Texas at Austin for helpful comments and suggestions. All remaining errors are our responsibility.

    1

    Tel.: +1 212 636 6118.

    View full text