گزینه های واقعی و سرمایه گذاری سرمایه انسانی

This paper extends the standard human capital model with real options. Real options influence investment behavior when risky investments in human capital are irreversible and individuals can affect the timing of the investment. Option values make individuals more reluctant to invest in human capital and, as a result, required returns on the investment increase. Real options may help to explain a larger human capital premium for higher education, smaller responsiveness of higher educational investments to financial incentives, and larger sensitivity of higher educational investments to low-return outcomes and human capital risks. Higher tax rates (or lower subsidies) depress human capital investments, but to a lesser extent than in the standard human capital model if not all direct costs are tax-deductible. A flat income tax remains neutral if education expenditures are fully deductible.

“The long time required to collect the return on an investment in human capital reduces the knowledge available, for knowledge required is about the environment when the return is to be received. […] The desire to acquire additional knowledge about the return and about alternatives provides an incentive to postpone any risky investment […].” Becker (1964, pp. 91–92, 94). Observed returns to human capital are typically larger than the risk-free rate as Palacios-Huerta, 2004 and Palacios-Huerta, 2006 has shown in a novel finance approach. High returns are also consistently found in the empirical labor literature (Card, 1999, Ashenfelter et al., 1999 and Harmon et al., 2003). This begs the question why the private returns to education are so high. Capital markets may not make sufficient borrowing available due to enforcement and information problems (Stiglitz and Weiss, 1981). Liquidity constraints increase required returns on human capital. The empirical plausibility of liquidity constraints is controversial, however. Carneiro and Heckman (2003), Cameron and Taber (2004), Plug and Vijverberg (2004) and others find that liquidity constraints only have a slight impact on enrolment in higher education and seem to be insufficient to explain high observed rates of return to education.1 Income risk may also justify a high rate of return. Risk averse individuals want to be compensated for income risks. Indeed, Palacios-Huerta, 2004 and Palacios-Huerta, 2006 finds that human capital returns include a substantial risk premium. Many papers find evidence for risk compensation in wages, see the overview by Hartog (2005). Nevertheless, the high return on human capital is suggestive of a human capital premium puzzle, just like in the finance literature (see e.g., Mehra and Prescott, 2003). Palacios-Huerta (2006) has shown that risk alone cannot explain the difference between the real return on human capital and the risk-free interest rate. Only implausibly large coefficients of relative risk aversion, ranging from 30–60, generate a risk-premium on human capital investments that is consistent with the data. Judd (2000) argues that, if idiosyncratic income risks are so important, governments or markets would look for institutions to insure these risks. Apparently, neither is the case. Both private and public insurance are not likely to emerge if moral hazard renders the income risks endogenous rather than idiosyncratic, see also Judd (2000) and Sinn (1995). Another empirical puzzle is that the covariance between earnings or employment and the marginal investment in education appears to be negative, see also Gould et al. (2000), Hartog and Diaz-Serrano (2002), and Belzil and Hansen (2004). Also, Palacios-Huerta, 2004 and Palacios-Huerta, 2006 empirically finds that the human capital premium is lowered as workers become more educated. This suggests that, although human capital investment is risky on average, higher levels of human capital hedge against labor market risks on the margin, cf. Levhari and Weiss (1974). Rubinstein and Tsiddon (2001) show that the negative correlation between education and unemployment or earnings risk vanishes, once controls for parental education are included in the analysis. Earnings and unemployment risks could then be driven mainly by parental or even genetic transfers of skills, rather than market risks. Indeed, Cunha et al. (2005) demonstrate that a large part of risk in labor market outcomes can be traced back to non-observed heterogeneity, not to market risk. These empirical findings also substantially weaken the case for a substantial risk premium for human capital investments. This paper demonstrates that real options could provide another explanation as to why returns are high for higher educational investments. Real options are present in irreversible and risky investments in which there is a possibility to influence the timing of the investment. Human capital is generally regarded as a non-liquid asset (e.g., Friedman, 1962). It is impossible to recover forgone earnings and tuition expenses by selling the asset after the investment has been made. Investments are therefore sunk. Individuals can, however, influence the timing of the decision to invest in risky higher education. They have an option to wait for better information regarding the returns (or costs) of the investment. If they invest immediately in higher education, they give up a valuable option to wait, which must be compensated with higher returns. In equilibrium, the option value of postponing the investment drives up returns to investment in human capital, which could explain why returns are high. Moreover, high returns are an equilibrium outcome in the presence of perfect capital and insurance markets. Palacios-Huerta (2006) shows that about two-thirds of the observed human capital premium could be the result of the illiquidity of human capital if short-sale constraints would be the relevant market imperfection. These findings can, however, also suggest that option values are important. Indeed, the illiquidity of the investment is the prime reason why the real option emerges. Therefore, even with risk neutral individuals, rates of return to human capital investments would increase when investments in human capital are illiquid and subject to short-sale constraints. The option value of postponing investment is relevant whenever individuals can influence the timing of the investment. From a theoretical perspective, it would therefore apply to all types of investment in human capital. In practice, however, it is relevant mainly for higher education where, by the nature of voluntary choice, there is indeed a possibility to influence the timing of the investment. It is not likely that waiting options could explain a human capital premium for lower, compulsory levels of education. Nevertheless, there is potentially also a waiting option associated with education levels below obligatory school entrance ages when parents have the possibility to decide when to send their children to kindergarten, preschool or early childhood programs. This paper nevertheless confines the analysis to higher education only. As a side step, this paper also analyzes the effects of (progressive) income taxes and education subsidies when options in higher educational investments are important. Investment in higher education will be less elastic to taxes and subsidies when waiting options are more valuable. However, the neutrality of flat income taxes with full deductibility of investments in the standard human capital framework remains (cf. Heckman, 1976). This paper is organized as follows. Section 2 briefly describes some earlier papers and how this paper relates to the literature. Section 3 describes the model of irreversible investment in higher education. Section 4 derives the main results and performs comparative static analysis. Section 5 concludes.

This paper analyzed the consequences of real options in human capital investments. Human capital investments are both risky and largely irreversible. It is generally impossible to recover forgone labor earnings and paid tuition fees. If individuals can influence the timing of the investment, i.e., decide to go to higher education now or later, option values will influence investment behavior. This paper has shown that with perfect financial markets, the option to postpone investment could explain why returns to education are high, why investment in human capital is not very sensitive to returns, taxes and subsidies, and why students are rightly concerned with low return outcomes. These findings can be relevant in explaining various empirical findings. Options may offer an explanation as to why skill-premia for higher educated workers are high. Returns should be high because they compensate for the lost option value of waiting once individuals make the irreversible investments in education. This is an equilibrium outcome which does not require incompleteness of financial markets. This paper has shown that option values tend to make human capital investments less responsive to the net returns of the investments compared to the standard human capital model. This may help to explain findings that enrolment does not appear to be very price responsive. The empirical picture appears to be that doubling tuition costs will decrease enrolment rates with roughly 5–10%-points after controlling for selection effects, see recent estimates provided in Kane, 1994 and Kane, 1995, Hilmer (1998), Heckman et al. (1998), Card and Lemieux (2000), Cameron and Heckman (2001), and Dynarski (2003). Option values may also help to explain why returns to education are larger in countries with larger income inequality, insofar as inequality reflects labor market risk.8 In more risky labor markets, option values of postponing investments in education increase, and students need to be compensated for giving up the option to wait with higher returns. OECD (2006) data reveal that income inequality is typically larger in countries with high Mincer returns to education, as estimated by Harmon et al. (2003). Hence, the data are not inconsistent with the prediction that larger returns on education should be found in more risky labor markets. Option values can be an important reason why students wait with enrolment in higher education. However, the vast majority of high school graduates immediately enrolls in higher education. The observation that many students do not wait to enroll may is not a direct refutation of the model presented in this paper. Students will enroll immediately as long as rates of return to education are high enough to give up their valuable waiting option to enroll later. The analysis of other types of options could be relevant for future research. No research exists on the option to terminate the investment in initial education, i.e., to drop out, when the investment turns out to be unprofitable. There could also be an option to switch from initial education to OJT investments or from general education to vocational education in case the latter becomes more profitable compared to the former. There can also be compound options when there is some combination of options involved in the investment in human capital. Furthermore, the model of this paper could be cast in a continuous time framework similar to examples in Dixit and Pindyck (1994). This would allow for an empirically grounded analysis to study the potential explanatory powers of the model. One could then also allow for a variety of stochastic processes describing the returns to the investment. A more in depth treatment of cost uncertainty could also be analyzed in more detail. This paper assumed that costs were exogenous and not time-varying. Cost uncertainty is equivalent to what Levhari and Weiss (1974) call ‘input-uncertainty’, i.e., the uncertainty about individual capacities. If cost uncertainty decreases when the project is undertaken, there may be reasons to start investing immediately even if the net present value is negative. This is related to the growth options in sequential investments as discussed in Comay et al (1973) and Heckman et al. (2006). Further, the impact of options on the distribution of wages would be interesting to investigate in a general equilibrium setting in which wages of skilled and unskilled workers are endogenously determined. Finally, interactions of options in human capital investment with various types of capital and insurance market failures may be a promising avenue for future research.