توسعه پایدار بدهی های عمومی، شکل گیری سرمایه های عمومی و رشد درون زا در تنظیم نسل های دارای اشتراک

Under the golden rule of public finance for public investment with a constant budget deficit/GDP ratio, we show that for the sustainability of government budget deficits there is a threshold of the initial public debt for a given stock of public capital, and that this threshold level of public debt is increasing in the stock of public capital. If the initial public debt is greater than the threshold, the government can no longer sustain budget deficits, while if it is smaller, the government can conduct a permanent deficit policy, which eventually leads to a positive public debt/GDP ratio.

Since the outstanding work by Arrow and Kurz (1970), many authors have investigated the effects of public capital formation on the performance of the economy and the optimal fiscal policy in dynamic general equilibrium models.1 In an endogenous growth setting, Futagami, Morita and Shibata (1993), among others, analyzed the growth-maximizing public investment size (the public investment/GDP ratio) assuming public capital formation rather than public flow expenditures of Barro (1990) type. In these theoretical contributions, however, they assumed that the government runs a balanced budget at any moment in time. Nonetheless, recently, an intensive debate has arisen regarding the long-term growth effects of public investment financed under various versions of the so-called golden rule of public finance (e.g. Greiner and Semmler, 2000 and Ghosh and Mourmouras, 2004). 2 The golden rule of public finance is considered the fiscal rule according to which government expenditures for public consumption, transfer payments and interest payments must be smaller than the tax revenue. Under the rule, borrowing is allowed to finance only government investment. Greiner and Semmler (2000) showed that the long-term growth effects of public capital depend on the exact budgetary regime adopted by the government, and that a less strict budgetary regime may not lead to a positive growth effect of a deficit-financed government investment. By comparing the welfare effects of allowing public borrowing under the standard dynamic government budget constraint and under the golden rule of public finance, Ghosh and Mourmouras (2004) showed that the golden rule of public finance can be an effective restriction on the composition of government expenditure and that a less strict budgetary stance may lead to a lowering of welfare. Under budget deficit policies, public debt accumulates and in turn affects the government budget. While Greiner and Semmler (2000) and Ghosh and Mourmouras (2004) did not focus their attention on accumulation of public debt, the sustainability of public debt has been examined, for example, by Hamilton and Flavin (1986) and Bohn (1998). Among others, pointing out that the transversality condition tests depend on sensitivity on the choice of discount rates and the cointegration tests generally do not adjust real levels of fiscal variables, Bohn (1998) proposed a new test that requires that primary surplus increases at least linearly with the ratio of debt to GDP at high debt-GDP ratios. In contrast, Chalk (2000) examined the sustainability of government budget deficits in an overlapping generations model of Diamond (1965) type, and showed that the present value budget balance may not be crucial to the sustainability of permanent deficits. While it is well known that permanent budget deficits can be sustainable when the dynamic resource allocation is dynamically inefficient in an overlapping generations setting (e.g. Diamond, 1965 and Tirole, 1985), Chalk (2000) also showed that, even when the growth rate is lower than the interest rate and hence the cost of debt finance is high, the government can run the primary deficits, and that the permanent deficits are sustainable only when the initial public debt is not too large. Bräuninger (2005) showed in an overlapping generations model with the AK production structure that under a fiscal rule in which the government purchase/GDP ratio and the budget deficit/GDP ratio are constant, the tax rate therefore being endogenously adjusted, there is a stable steady-growth path as long as the initial debt-capital ratio is lower than a certain level, and that an increase in the deficit rate reduces the growth rate. However, both Chalk (2000) and Bräuninger (2005), as well as most of the literature on public debt sustainability, assumed that government expenditures are public consumption. 3 Our purpose in this study is to analyze the sustainability of budget deficits, simultaneously taking into account the growth effects of a deficit-financed public investment, in an endogenous growth setting with the growth engine of public capital formation. For our purpose, we use the overlapping generations model pioneered by Diamond (1965), in which public debt can have real effects. We assume that the government not only controls the public investment/GDP ratio but also keeps the deficit finance ratio in public investment at less than one. Thus, the financing rule in this study is the mixture of the golden rule of public finance, as to the borrowing rule, and a deficit rule of keeping the budget deficits at a certain percentage of GDP, while the tax rate must be endogenously adjusted according to the government budget constraint.4 The public debt/GDP ratio is endogenously determined by the fiscal rule along the growth path. We illustrate that there can be two long-term equilibria, one locally stable and one saddle-point stable, and that there is a threshold for the initial public debt in order for budget deficits to be sustainable at each level of public capital stock. The threshold of the initial public debt is represented by a point on the stable branch to the saddle-point equilibrium, and is increasing in the stock of public capital, i.e. the so-called public assets. If the initial public debt is greater than the threshold at a level of public capital, the government can no longer sustain the fiscal deficit policy. If the initial debt is smaller than the threshold, the economy converges to the stable equilibrium and the government can run the permanent fiscal deficit and public investment policy, which eventually leads to a positive public debt/GDP ratio. We also show that decreases in the public investment/GDP ratio and/or the deficit finance ratio will raise the threshold for a given level of public capital stock, and that the decreased deficit finance ratio leads to higher balanced growth, while an increase in the public investment ratio can have a growth-enhancing effect. The remainder of the paper is organized as follows. We devote the next section to developing an overlapping generations model of Diamond (1965) type, which incorporates public capital formation. Section 3 analyzes dynamics of the economy and the long-term equilibrium. The effects of policy changes are analyzed in Section 4, while the last section presents concluding remarks.

In an endogenous growth model, populated by two-period-lived generations and with an engine of public capital formation, we have analyzed the sustainability of public debt policy, assuming that the public capital/GDP ratio and the public debt finance ratio of public investment are kept constant, and that the tax rate is adjusted so as to satisfy the government budget equation. With Cobb–Douglas production function and the log-linear utility function, we have shown that there is a threshold for the initial stock of public debt at each level of public debt in order for the public investment and deficit policy to be sustainable, and that the threshold is increasing in the stock of public capital. This contrasts with the condition of initial indebtedness of the economy given in the conventional literature without public investment in which the critical initial level of public debt is given in relation to private capital. When public debt is greater than the threshold, the economy can no longer sustain the budget deficit and hence the balanced growth. This implies that an economy which has accumulated only small public capital in the past may seriously diminish its set of feasible policy alternatives. In our study with public capital formation, the sustainable fiscal policy is also conditioned by the public investment/GDP ratio and the debt finance ratio of public investment, rather than the size of government budget deficit itself. Although the critical combination of the ratios cannot be explicitly obtained, the result is also in contrast to the literature without public capital accumulation. So far we have analyzed the sustainability of government deficit policy under the golden rule of public finance, assuming that the public investment ratio and the debt finance ratio are kept constant and that the tax rate is endogenously determined to satisfy the government budget. The problems analyzed here are rather positive models in the sense that the fiscal policy may not necessarily be optimally arranged. In a representative, infinitely-lived agent model, Ghosh and Mourmouras (2004) showed that the optimal fiscal policy depends on the budgetary regime taken by government. While many authors (e.g. Pestieau, 1974) examined the optimal public capital formation and taxation policy in decentralized economies populated by overlapping generations in which public debt can have real effects, most of them did not take into account the restriction of the golden rule of public finance. Analyzing the optimal policy under various fiscal regimes in such a setting is an interesting issue for future research.