Comparison to First-best: Quality of Education Matters

Finally, we want to address the question of direct income insurance versus insur-ance via improved quality of education. We have seen in the First-best analysis that direct income insurance is always guaranteed by equalized (ex post) marginal utilities of income and that resource investment in the educational sector only de-pends on the skill premium in utility and on resource gains for redistribution by

increasing the number of skilled households. All this changes distinctly, if the government has limited instruments available, as it cannot control private learning effort directly.

In such a Second-best setting, any direct income redistribution has negative incentive effects on learning effort and causes moral hazard, because the govern-ment cannot control, if and how time is spent at university. In case of endogenous success probabilities, taxation becomes therefore even more expensive, because not only labor supply may be distorted. Taken together, these effects weaken the case for income insurance, which provides the core intuition in risk-and-insurance papers à la Eaton and Rosen (1980a,b).

At the same time, induced distortions in learning ceteris paribus call for in-creased public spending on education, in order to dampen the moral hazard effect.

Moreover, comparing the First-best level of learning effort in equation (20) with the household’s first order condition (8), we see that the households neglect the resource increasing effect on behalf of the government, the last term in equation (20). Accordingly, there is another reason for underinvestment in effort, which has to be countered by increased public spending. This need for public spending would persist even in a setting with private investment into the quality of univer-sities.

Comparing the First-best efficient level of real investment E in equation (29) and the Second-best level, determined in equation (56), these two effects are represented by the second term in the squared bracket on the RHS of (56), p^∗·f_B·²_pe·η_eE.

Next, the skill premium, measured in utility V^H − V^L, turns positive in a Second-best optimum. This ceteris paribus increases educational investment, be-cause an additional graduate increases social welfare, now. However, the marginal costs of providingEalso increase, because nowλnot only reflects marginal utility of income, but also induced distortion costs, which ceteris paribus have a negative effect on E. Although the government most likely increases its real investment, nothing can be said on the success probability p^∗, because private learning effort is likely to decline.

Last, but not least, introducing a general tuition fee (a negative lump-sum transferT <0) decreases income and induces higher learning effort according to

equation (9). The lump-sum tax can therefore be justified by aiming to increase the success probability as well.

Collecting all the effects described above, we can state:

Proposition 7. In a Second-best world, increasing quality of education matters (compared to the First-best solution) more than providing income insurance, be-cause providing directly (full) insurance via income transfers (T > 0) is (too) expensive, and because public resource investment also corrects for inefficiencies in private learning effort in a relatively cheap manner.

This result is robust and independent of informational assumptions. It holds even if the government can implement skill-specific tuition fees via f_B. Indeed, the call for improving quality of education and the preferability over income trans-fers is at the heart of all our results.

The absence of wage taxation and part of the shift from income insurance to increased quality of education are, however, sensitive to our focus on educational risk and the absence of wage risks within one skill group. Additionally introduc-ing income risks, e.g., in the skilled sector, might lead to positive graduate taxation of the Eaton/Rosen-type in a Second-best setting, which then distorts labor sup-ply of the skilled. Nevertheless, quality of education and increasing the success probability should still play a prominent role in such a setting, and we think that it is worth wile to examine these extensions in more detail in future research.

7 Conclusions

We examine the effects of endogenous human capital risk, where the probability of getting an employment in the skilled sector is endogenously determined by in-dividuals and, consequently, depends on public policy instruments as well. We apply a model, where households first choose their learning effort and after re-alization of risk, they choose their labor supply. We show that in a Second-best world increasing quality of education, measured as success probability in gradu-ation, is preferable to providing redistributive income transfers, as the latter are (too) expensive. Thus, redistribution in an ex ante sense is more important than spending resources for ‘healing’ bad outcomes ex post, i.e., enhancing the

(Kon-rad, 2004)-‘filtering mechanism’ of the education system matters most. Therefore, our results support the Lisbon agenda of the EU.

This all holds as long as the government cannot control private learning effort and it is independent of the availability of skill-specific taxes. In case the govern-ment has access to skill-specific taxes, however, a wage tax is not used, although both tax instruments are distorting different decision margins. Thus, the standard trade-off between several distortions does not apply. The reason is that combining skill-specific taxes with increasing quality of education, i.e., public spending in the educational sector, both achieves redistribution between skilled and unskilled households and provides insurance at lower costs than a wage tax.

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