ارزش ها و بازده های‬ ‫سرمایه انسانی: حدود ضمنی درآمد و داده های بازده دارایی ها

We provide theory for calculating bounds on both the value of an individual’s human capital and the return on an individual’s human capital, given knowledge of the process governing earnings and financial asset returns. We calculate bounds using U.S. data on male earnings and financial asset returns. The large idiosyncratic component of earnings risk implies that bounds on values and returns are quite loose. However, when aggregate shocks are the only source of earnings risk, both bounds are tight.

A long-standing problem is to provide an empirical description of the value of an individual’s human capital and the associated return on an individual’s human capital. The value of human capital is in theory simply discounted future earnings. Thus, it is key to determine how an in- dividual’s earnings and an individual’s stochastic discount factor comove. The main difficulty is that discount factor properties can only be inferred indirectly through data on financial asset returns or individual choices.One strategy for making progress on this problem is to take a structural approach and make parametric assumptions about preferences, as well as assumptions on the exact structure of an individual’s decision problem. These parameters can then be estimated, and the value and return to human capital can be characterized using the stochastic discount factor produced by a solution to an empirically-motivated specification of this decision problem. In this paper we take a different approach. We explore what can be said about individual human capital values and returns without making parametric assumptions on preferences and without solving such a decision problem. However, we assume that one knows two important things: (1) a statistical model for financial asset returns and an individual’s earnings; and (2) some key properties of an individual’s stochastic discount factor. We assume this discount factor is non-negative, satisfies an Euler equation for each financial asset and is no more variable than some specified upper bound. These assumptions will not allow one to precisely value an individual’s future earnings unless future earnings can be replicated by trade in financial assets. Nevertheless, upper and lower bounds on the value of human capital can be determined by pricing the earnings component that can be replicated by trade in financial assets and then bounding the value of the residual component of earnings. We view the two approaches as being complementary. If the bounds approach puts tight bounds on values and returns, then this tells one that all the extra assumptions and additional data used in the structural approach can only serve to slightly narrow the value and return to human capital beyond what can be determined from earnings and asset returns data. In contrast, if the bounds approach implies very loose bounds, then this tells one that the additional data and assumptions employed in the structural approach are critical for reaching conclusions about the return to human capital. We highlight one area in which an empirical understanding of the value and return to human capital is relevant. To maintain a constant fraction of overall wealth in stock holdings, an indi- vidual’s direct financial holdings of stock and bonds need to be selected with the value of human capital in mind. If human capital is like stock, then the fraction of financial wealth held in stock would need to increase over the lifetime. If human capital is like risk-free debt, then the oppo- site reasoning applies. To make progress on this argument and give practical advice, one needs to investigate this if condition empirically. To do so, it is important to adopt the human capital value and return notions used in this paper: values and returns based on an individual’s stochastic discount factor. There are three main contributions of the paper. First, we show that value bounds imply return bounds. Second, we illustrate how all the concepts work within a simple example. Third, we calculate value and return bounds using U.S. data. Value and return bounds for U.S. data are determined in two steps. We start by providing an empirical description of the joint dynamics of male earnings and stock returns. Given such a sta- tistical model, we then calculate value and return bounds using the restriction that the coefficient of variation of an individual’s stochastic discount factor is no larger than a given multiple of the conditional Sharpe ratio. If the Euler equation restriction is to hold, then this coefficient of vari- ation must, at a minimum, be at least as large as the Sharpe ratio. We find that value and return bounds are very loose even after imposing that the coefficient of variation is at most 1 . 1 times the conditional Sharpe ratio. Specifically, for this upper limit the expected lifetime return to hu- man capital must lie between − 10 and 17 percent per year. This is almost exclusively due to the large amount of idiosyncratic earnings variation that we estimate from U.S. data, consistent with findings from numerous previous empirical studies. We find that when all idiosyncratic risk is eliminated without eliminating aggregate sources of earnings risk, then value and return bounds are tight. The expected lifetime return to human capital is then between 0 . 25 and 2 . 5 percent per year, for a range of restrictions on the coefficient of variation of an individual’s stochastic discount factor. Three literatures are most closely related to the problem that we address. First, there is a literature on the value of human capital. This literature has almost exclusively focused on valu- ing highly aggregated measures of cash flows (e.g. economy-wide earnings or cohort earnings) rather than individual male earnings as examined in this paper. See Huggett and Kaplan [6] for a discussion of this literature. Second, the finance literature has put upper and lower value bounds on cash flows. Cochrane and Saa-Requejo [3] and Cochrane [2] develop theory, provide appli- cations and review this literature. The bounds literature builds on the stochastic discount factor formulation of asset pricing problems developed by Hansen and Jagannathan [5] and others. The basic idea in the value bounds literature is to value the component of cash flows that can be replicated by trade in marketed assets and bound the value of the residual component. To the best of our knowledge, we are the first to apply these ideas to calculate value and return bounds on individual-level earnings. Third, the paper is related to the literature on incomplete markets and idiosyncratic earnings risk. Specifically, market incompleteness is what generates a gap between upper and lower value bounds and is hence key to our analysis.

We have constructed bounds on the value of human capital and then used these bounds to construct bounds on the lifetime return to human capital. The bounds are derived from knowledge of the set of traded assets, the joint stochastic process for individual earnings and asset returns, as well as three assumptions about an individual’s stochastic discount factors: they are (i) nonnegative, (ii) satisfy an Euler equation for each asset and (iii) have a second moment no larger than some pre-specified upper bound. Using U.S. data, we find that value and return bounds are quite wide. Even allowing for only slightly more variation in the stochastic discount factor than is needed to price equity and debt, we find that earnings and asset returns data can only restrict the mean lifetime return on human capital to lie between − 5 percent and 17 percent per year. The vast majority of the gap is due to the idiosyncratic component of earnings risk. Absent the idiosyncratic component of earnings risk, the average lifetime return on human capital is between 0 . 25 and 2 . 5 percent per year – not far from the average risk-free rate. One of the main messages of these findings is that to learn something sharper about the return to an individual’s human capital will require a structural approach. Huggett and Kaplan [6] take up this challenge and use a fully specified structural model with idiosyncratic and aggregate sources of earnings risk to measure the value and return to human capital. We highlight two challenges to the empirical findings of this paper that might be taken up in future work. First, the statistical model of earnings analyzed in Section 4 may overstate the magnitude of persistent idiosyncratic earnings shocks. Huggett, Ventura and Yaron [7] argue that learning ability differences across individuals can account for much of the large rise in the variance of log earnings observed over the working lifetime. Thus, the role of persistent shocks may be substantially smaller than what we infer in Table 1. Second, we have assumed that the aggregate component of male earnings has a deterministic trend. Future work can investigate the possibility of stochastic trends or cointegration between the aggregate component of earnings and equity returns. These possibilities may give the aggregate component of earnings a larger role in producing higher mean returns to human capital.