سرمایه گذاری در سرمایه انسانی، عدم اطمینان از دستمزد، و سیاست های عمومی

The importance of risk characteristics of human capital for the design of tax and education policy is explored. Wages are uncertain and education, while increasing the expected wage, may increase or decrease wage variance. The government has strong reasons to encourage human capital formation in the latter case, partly due to the insurance effect of human capital, and partly due to the way the individuals—under a plausible restriction on ‘prudence’—respond to changes in risk. The analysis is illustrated using two models of education: one where education helps the individuals make better occupational choices, and a standard risk-augmented Becker-type model.

Individuals face, over the course of their lifetimes, considerable uncertainty regarding earnings. One indication of this is the large residual variance typically remaining in empirical work attempting to explain wages by schooling, experience and other explanatory variables.1 By investing in education an individual can shift the wage distribution and achieve a higher expected wage. A feature that distinguishes investments in education from other risky investments is the non-existence of a risk-free option—not even a worker who abstains from investing in education can be certain about her future earnings. Indeed, an interesting question from the point of view of investment behavior is whether an increase in human capital increases or decreases wage risk (Levhari and Weiss, 1974). The conventional wisdom, dating back to Mincer (1974), is that, from looking at the unexplained wage variation, education seems to be associated with increased wage variability. Against this evidence stands a host of other indicators that point towards the conclusion that investments in human capital may rather reduce earnings variation. Remaining within the empirical earnings literature, a typical observation is that educated workers are more likely to receive further training; training in turn generates specific human capital which tends to create employment stability and hence stable earnings (see e.g. Chapman, 1993). Relatedly it is frequently argued that more educated individuals are likely to face less uncertainty regarding match-quality when contracting with employers by the fact that more information about them is available. More generally, the time unit over which variability is measured may be critical since an individual’s wage changes over time. One branch of the literature considers the risk of being ‘low-paid’; indeed, recent evidence would suggest that education can be instrumental in helping an individual to avoid becoming low-paid and also to ‘escape’ from low-paid jobs (Stewart and Swaffield, 1999). However, there are also other sources of earnings variation which human capital can be expected to affect. These include lost earnings due to unemployment, sickness, disability, etc. Looking at unemployment risk for example, one of the most firmly established facts is that more highly educated people are unemployed to a smaller extent. Hence education reduces unemployment risk.2 The same seems to apply to other sources of earnings losses such as occupational injury risks.3 Thus although the evidence regarding the impact of human capital on wage and earnings risk is conflicting, it appears reasonable to conjecture that education can reduce earnings risk, in particular if one adopts a broad definition of earnings uncertainty. Moreover, the risk characteristics of human capital matter from a policy point of view. Governments are engaged in providing insurance against earnings uncertainty through complex systems of taxation and social insurance, while at the same time adopting policies to encourage human capital formation. Whenever only partial insurance and/or redistribution can be achieved, there is an interaction between the two tiers of government policy for which the risk characteristics of human capital are important. The purpose of this paper is to consider the simultaneous design of an income tax policy and an education policy with a particular focus on the role played by the risk-properties of human capital. To do this, we use a familiar model where workers face a labour–leisure trade-off with an uncertain wage, and where the government has sufficient instruments to control education and uses a linear income tax for social insurance/redistribution purposes. If human capital reduces earnings risk, encouraging education would seem to mitigate the insurance/redistribution problem; intuitively, human capital would seem to have a direct insurance effect that would need to be taken into account when jointly designing education and tax policy. Conversely, if human capital increases wage uncertainty, there would seem to be case for restricting education in order not to aggravate the insurance problem. Simple intuitions may be misleading in second-best settings however; in particular, one must take into account the agents’ reactions to policy changes. Since human capital affects wage risk, this will call for an analysis of the agents’ response to changes in risk, a response that will depend on preference properties such as risk aversion and ‘prudence.’ There will thus be risk effects on tax revenue, which, as the analysis will demonstrate, often tend to reinforce the direct insurance effect in the sense of moving optimal policy in the same direction. Finally, by increasing expected wages human capital will always tend to increase (compensated) labour supply leading to a positive revenue effect. The insight is thus that if education moderates wage uncertainty, a second-best policy should, rather unambiguously, encourage the formation of human capital (relative to the first-best), while if education exacerbates wage uncertainty the overall conclusion is ambiguous. As an illustration we explore policy design in two different models of human capital. In the first model education provides the agents with information about their own talents which helps them avoid occupational mismatches. In this setting education naturally reduces wage variance. The second model is a standard risk-augmented Becker model in which human capital is associated with larger wage variance. In numerical simulations we then show that the optimal policies are radically different in the two settings; in particular, it is optimal to encourage education to a large extent in the occupational-matching model while the insurance and revenue effects more or less cancel out in the Becker model. There is a substantial literature on income taxation and education, most of which, however, does not deal with wage uncertainty.4 Contributions that do consider wage uncertainty include Eaton and Rosen (1980b) who consider a two-period model with human-capital investment; they focus on the comparative statics of labour supply with respect to the tax rate, and perform only a rough analysis of optimal taxes showing that the optimal linear tax is strictly positive. Hamilton (1987) considers the simultaneous design of education policy and tax policy (including a capital-income tax) in an environment where human-capital investments are uncertain; he does not consider variation in the riskiness of the human-capital investment. Recently, Wilson (1999) has considered how publicly provided education can alleviate a moral-hazard problem when investments are unobservable. Judd (1998) provides a general discussion of the issues arising when risky human capital is included in optimum-tax models. Poutvaara (2000) considers risky investments in education where an income tax is subsequently chosen by majority rule. None of these papers deals with variation in wage risk. The paper is organized as follows. Section 2 sets up the general model. Section 3 illustrates the model by contrasting two models of education, and Section 4 concludes. All proofs are gathered in an Appendix (available on request).

The starting point of the paper was the simple insight that whether education increases or decreases wage variability is likely to be important when education policy and tax policy are jointly determined in a second-best environment. If e.g. education reduces wage variability it has a direct insurance effect which justifies encouraging human capital formation since it mitigates the tax problem. However, as usual, the simple intuition needs to be supplemented since the agents are likely to react to the change in the level of education. There we noted that—beyond a standard substitution effect—the agents’ reactions are also determined by the risk-properties of human capital. In particular, we found that, under plausible conditions, these risk-effects unambiguously reinforce the policy conclusions derived from the direct insurance effect. The last part of the paper compared two different education technologies that have different implications for the riskiness of wages but are otherwise similar. The comparison provides an example that, arguably, indicates that the effects can be important in practice. The analysis has focused entirely on the case where wage uncertainty is not resolved until after the workers commit to labour supplies; an alternative that may be more appropriate if uncertainty arises primarily in the education technology is to assume that a worker learns about her earning capacity prior to choosing labour supply (see Hamilton, 1987). If the wage realization is not observed by the government a standard optimal taxation problem obtains. By affecting human capital formation the government can then affect the severity of the tax problem. It can be shown that the same type of arguments apply: if human capital moderates (exacerbates) wage variability it has a direct insurance effect which calls for education to be over-provided (under-provided). Of course, in this case labour supplies are determined by actual wage outcomes (as opposed to risk) but the aggregate labour supply can still be related to the variability in wages and risk preferences. Hence, the aggregate compensated labour supply response can again be disaggregated into a substitution effect and a risk-effect; moreover, as for the case presented in the paper, the risk-effect tends to reinforce the direct insurance effect under plausible conditions on risk-aversion and prudence. The paper points to several directions for future research. One is to further investigate and disentangle the effect of human capital on wage and earnings risk. In general, several sources of earnings uncertainty will co-exist and human capital can be expected to affect these sources differently. Whereas we have adopted the approach of aggregating all sources of uncertainty and assumed that one tax system exists to provide insurance, this is clearly unrealistic. In reality several programmes exist to cover specific sources of earnings losses such as unemployment. Hence if multiple sources of uncertainty can be identified it would also seem desirable to combine models of general taxation with models of more specific social insurance programmes.