اولویت دوم بدهی دولت با آثار جانبی سرمایه انسانی

This paper studies optimal public debt in a dynastic model with human capital externalities that cause human capital investment (fertility) to be below (above) its socially optimal level. By reducing fertility and raising human capital investment, the optimal debt can exceed 10% of output for plausible parameterizations.

This paper studies optimal public debt in a dynastic model with externalities in the form of positive spillovers from average human capital in the education sector. The spillovers lower the private rate of return to education from the social rate, and thus education investment is too low. At the same time, through the trade-off between the number and quality of children, fertility is too high. This combination of low education investment and high fertility is commonly observed in early development stages across nations. One obvious policy instrument to tackle this problem is to subsidize education. The education subsidy can be partly financed by debt to improve welfare from a competitive equilibrium, as shown in Zhang (2003). In the real world, however, many countries issue debt to finance many types of government expenditures. It is thus important to see whether public debt can improve on the competitive solution with human capital externalities in the absence of education subsidies. Intuitively, higher public debt leads to higher future tax liabilities, inducing current altruistic parents to leave more private intergenerational transfers per child in the form of bequests. The increased bequest cost of having a child tends to reduce fertility and increase human capital investment per child. As a consequence, public debt can reduce the efficiency loss originating from the externalities. If the externalities are strong enough, the optimal debt-output ratio can exceed 10% in this model. Our study differs from a large body of literature on public debt. The traditional justification of public debt is based on the Ricardian equivalence hypothesis, whereby any mix of public debt and a lump-sum tax to finance government lump-sum transfers has no real effect as demonstrated in Barro (1974). Ever since the seminal work by Barro, some realistic factors have been suggested to invalidate the debt neutrality.1 But little attention has been paid to the welfare implication of public debt and its optimal level, particularly in the presence of human capital externalities. A recent exception is Aiyagari and McGrattan (1998), who find that the optimum quantity of public debt is close to the current US level using precautionary saving motives and borrowing constraints. The remainder of the paper is organized as follows. The next section introduces the model. Section 3 characterizes the competitive equilibrium and optimal public debt. The last section concludes. Proofs of the results are relegated to appendices.

In this paper, we have derived analytically the second-best optimal debt-output ratio in a two-sector growth model with education spillovers, altruistic bequests, and endogenous fertility. The spillover in education leads to under-investment in human capital and over-reproduction of population. We have shown that as the debt-output ratio rises, altruistic parents expect higher future tax burdens on their children and respond by leaving more bequests. When the bequest cost of having a child rises, fertility falls but investment in human capital per child rises, moving closer to their first-best levels unless public debt is exceedingly high. We have also provided simulation results to see how the value of the optimal debt-output ratio varies with the degree of the spillover. We find that moderate or strong education spillovers may lead to a 10% debt-GDP ratio or higher. The results may have some useful policy implications. For countries under pressure from high public debt and low fertility, a reduction in public debt may result in welfare improvements as well as an increase in birth rates. For countries with high fertility rates and low investment in education, raising public debt may benefit from trading the number of children for their productivity.