An increase in government spending must be financed by an increase in taxes. The optimal choice between tax finance and debt finance is really a choice about the timing of those taxes. A permanent increase in government spending must be matched by at least an equally large permanent increase in taxes unless taxes are increased by even more in the short run … [T]here is no way to choose between a permanently higher level of taxes and a permanently higher level of debt (Feldstein (1985, p. 244)).
IN THE VOLUMINOUS literature on economic growth and capital accumulation, no result has richer and more enduring positive and normative implications than the “golden rule” of savings (hereafter referred to as the golden rule)1 as a guide for the conduct of fiscal policy. In addition to being the rule that governs the steady-state, welfare-maximizing level of capital intensity in the economy, it has also become the crucial benchmark against which to assess the role government debt plays in the steady state. This latter point was made particularly clear in the exchange between Barro (1976) and Feldstein (1976) on Barm’s (1974) earlier restatement of the Ricardian equivalence principle, which had assumed a stationary economy. The basic point was that in a growing economy a positive level of government debt in the steady state could be either a net burden on or a net addition to private wealth, depending on whether the steady-state growth rate is, respectively, less than or greater than the interest rate.2
The possibility that government debt could be regarded as net wealth by bond holders in the steady state is intriguing. The prevailing view in the public finance and growth literature, however, is that a steady-state equilibrium characterized by a rate of growth that exceeds the interest rate is somehow inconsistent with rational behavior, although it has long been recognized that in a competitive economy there is really no reason, on pure theoretical grounds, to presume that the steady-state level of capital intensity is necessarily below that implied by the golden rule.3 If one agrees with the prevailing view, then the conclusion reached by Feldstein (1985), quoted at the beginning of this paper, is inescapable. In a steady state where the level of per capital debt is constant, the total amount of debt must be increasing at the same rate as the labor force. But if the interest rate exceeds this rate, taxes must be raised in order to service the debt. The choice between debt and taxes as a source of financing the government budget is therefore illusory in the long run under these circumstances.
In writing off the government’s ability to reduce taxes in the long run simply by further increasing its borrowing,4 the literature has apparently overlooked the fact that steady states with an interest rate greater than the growth rate could be incompatible with stability, if the level of debt is positive. This observation is superficially obvious under the simplifying assumption that the interest rate can be treated as a constant. For under such circumstances, either per capita taxes must be forever increasing to keep the level of per capita debt constant, or with constant taxes per capita debt would rise without limit. Although these consequences do not immediately follow in a more complete model in which the interest rate, or equivalently the stock of capital, is allowed to vary, the dynamic properties of a model whose path of evolution is government by simultaneous adjustments in debt and capital deserve more than the rather scant attention they have received so far.5
The necessary and sufficient conditions for stability are studied here based on an intertemporal optimizing model in which both capital and government debt are endogenous, driven by the utility- and profit-maximizing behavior of private agents and tax and expenditure policies of the government. In such a model, it turns out that a necessary (but not sufficient) condition for stability in the neighborhood of a steady-state equilibrium with a constant positive per capita debt is that the growth rate of the economy be greater than the interest rate.6 Under very general assumptions regarding utility and production functions, an operational rule expressed purely in terms of familiar economic parameters for the determination of the critical level of debt above which it cannot be sustained is also derived. Because the model, though simple, is sufficiently rich in economic structure, the sustainability rule can be conveniently used to ascertain in a meaningful way the margin between an economy’s existing and sustainable debt levels, given unchanged existing economic conditions.
An important implication of the above sustainability analysis is that, if one restricts one’s attention only to stable equilibria (as is customary), then debt could be considered as a legitimate source of revenue for the government to finance its budget. Assuming lump-sum taxes are not available under realistic economic settings, the choice between debt and (distortionary) tax financing by the public sector therefore has substantive economic content and provides the motivation for the analysis of the optimal level of government debt.
In this paper, the government’s optimization calculus is defined in terms of its objective to maximize the steady-state utility level of the representative individual, subject to its budget constraint as well as the technological and behavioral constraints of the private sector. Three different policy experiments are analyzed: (1) the determination of the optimal level of expenditures for a given tax rate, (2) the determination of the optimal tax rate for a given level of expenditures, and (3) the simultaneous determination of the optimal levels of expenditures and the tax rate. In all cases, taxation is taken to be in the form of a general income tax at a constant ad valorem rate. Formulating the government’s problem in this way implies that the optimal debt level is a derived concept (as it should be) through the government budget constraint.
In each of the policy experiments described above, the impact of a given government action is transmitted to the private sector by its effect on the latter’s level of capital intensity. The long-run incidence effects of taxing incomes from productive factors are the subject of a large body of economic literature (see, for example, Diamond (1970) and Feldstein (1974a, 1974b)), and it is also generally recognized that variations in the level of debt can produce incidence (interest rate) effects (unless private savings behavior responds to negate them, such as under complete Ricardian equivalence). Seen in this light, debt and taxes are essentially fiscal tools by which the government alters the path of private capital accumulation to achieve its objective.7
In a decentralized economy in which the government has no direct control over the economy’s resources, and the optimal conduct of fiscal policy necessitates the use of debt or distortionary taxes or both, the optimal level of capital intensity in the steady state no longer always coincides with that implied by the golden rule.8 To see the possible negation of the golden rule as an optimality condition requires a basic understanding of the implication of the rule for fiscal policy. When the rate of growth of the labor force is positive, the maintenance of a steady-state capital stock of any given size requires the sacrifice of some consumption. Hence, even though a higher capital stock would necessarily produce more output, steady-state consumption is maximized only if the marginal product of capital is equated with the marginal unit of foregone consumption. However, in a life-cycle model such as the one employed in this paper (see Section I), not only the steady-state level of consumption matters but also its distribution between the young and the old. Hence, the optimality of the golden rule in this context is implicitly predicated on the ability of the government to peg the interest rate to the rate of population growth and then clear the capital market by varying the level of government debt. (No taxes and subsidies would be required, however, if there were no autonomous government expenditures.)9 This is the fundamental reason why the golden rule can be characterized, paradoxically, entirely by the given rate of population growth alone, with other parameters in the production and utility functions playing no role in the optimality condition.
Now suppose the government can increase or decrease the economy’s capital intensity only by changing the level of its outstanding debt through discretionary tax or expenditure or both.10 In such circumstances, the constraint imposed by the capital market equilibrium condition of a decentralized system becomes binding, and one would expect that the optimal level of capital intensity could either exceed or fall short of that implied by the golden rule. Since variations in capital intensity produce changes in the ratio of wages to interest rates, which in turn would alter the lifetime income profile of the representative individual, the exact location of the optimum relative to the golden rule should now depend, among other things, on the nature of both the utility and the production functions—and it does. This paper derives and interprets the optimality condition in the presence of government debt resulting from the optimization of the level of government expenditures for a given tax rate (the first policy experiment stated above) as the rational rule of savings. It turns out that, under fairly mild restrictions, the rational rule can be characterized in a relatively simple way.11 Hence, it can conveniently be used as an operational optimality rule for the determination of government debt.
Two important implications follow from the above optimality analysis. First, if the level of capital intensity dictated by the rational rule is below that corresponding to the golden rule, a positive level of government debt (in order to reduce the capital intensity) is required, resulting in an interest rate in the steady state that is greater than the rate of growth. The relationship is exactly reversed should the rational rule dictate a level of capital intensity that exceeds that implied by the golden rule. In either case, therefore, a nonzero optimal debt level gives rise to an item of outlay in the government’s budget constraint in the steady state. This means that when the government’s budget is optimally conceived, debt issuance in itself cannot be a source of revenue, and therefore, sufficient positive resources at the disposal of the government are required to attain the optimum. Furthermore, it can be seen from the earlier sustainability analysis, that the optimal level of government debt, should it be positive, is necessarily incompatible with a stable steady-state equilibrium.
The second important implication is that, if the government has the freedom to choose the optimal level of expenditures and the tax rate simultaneously, then government debt plays no role in its optimization calculus. The reason is simply that since the optimal level of capital intensity is always achievable through an appropriately chosen level of expenditures (and therefore of debt), there is never a reason to use the income tax as a tool for this purpose because it necessarily entails an excess burden.12 However, to conduct an expenditure or debt policy without positive tax revenues is infeasible, unless the government has access to other nontax revenues. Hence, the third policy experiment stated above is essentially an experiment to determine the optimal tax rate, not the optimal level of government debt. The optimality condition in this case, which simply balances the benefits to be gained by moving a competitive economy toward the golden rule with the cost of the excess burden of the tax, is also derived here as the taxation rule.
The paper reaches two basic conclusions. First, in order for any (arbitrarily given) amount of positive debt to be sustainable, the rate of economic growth must be greater than the net-of-tax interest rate in the steady state. It follows that a sustainable positive debt must also be a source of revenue in the government’s budget. Second, the optimal amount of debt, determined from a maximization of the steady-state utility of a representative consumer, depends on the nature of both the utility and production functions. It is positive (negative) if the optimal level of the economy’s capital intensity is below (above) that implied by the golden rule of savings. Hence, under no circumstances can such debt, when optimally derived, be a source of revenue for the government.
The present analysis of the sustainability and optimality of government debt has been carried out within the context of a closed economy. In view of the large external imbalances experienced by most countries recently, the impact of a change in the level of government debt on an economy’s external position is clearly of importance.13 The theoretical framework employed in this paper has already been extended to an open-economy setting by Persson (1985) for a one-good model, and by Zee (1987) for a two-good world. The open-economy implications of the issues analyzed here are therefore clearly on the agenda for future research.
Barro, Robert J., “Are Government Bonds Net Wealth?” Journal of Political Economy (Chicago), Vol. 82 (November/December 1974), pp. 1095–117.
Barro, Robert J., “On the Determination of the Public Debt,” Journal of Political Economy (Chicago), Vol. 87 (Part 1, January 1979), pp. 940–71.
Blanchard, Olivier J., “Debt, Deficits, and Finite Horizons,” Journal of Political Economy (Chicago), Vol. 93 (April 1985), pp. 223–47.
Blinder, Alan S., and Robert M. Solow, “Does Fiscal Policy Matter?” Journal of Public Economics (Amsterdam), Vol. 2 (November 1973), pp. 319–37.
Blinder, Alan S., and Robert M. Solow, “Analytical Foundations of Fiscal Policy,” in The Economics of Public Finance (Washington: The Brookings Institution, 1974).
Blinder, Alan S., and Robert M. Solow, “Does Fiscal Policy Matter? A Correction,” Journal of Public Economics (Amsterdam), Vol. 5 (January-February, 1976), pp. 183–84.
Buiter, Willem, “Government Finance in an Overlapping Generations Model with Gifts and Bequests,” in Social Security Versus Private Savings, ed. by George M. von Furstenberg (Cambridge: Ballinger, 1979), pp. 395–429.
Buiter, Willem, “The Theory of Optimum Deficits and Debt,” NBER Working Paper 1232 (Cambridge, Massachusetts: National Bureau of Economic Research, November 1983).
Carmichael, Jeffrey, “On Barro’s Theorem of Debt Neutrality: The Irrelevance of Net Wealth,” American Economic Review (Nashville, Tennessee), Vol. 72 (March 1982), pp. 202–13.
Diamond, Peter A., “Incidence of an Interest Income Tax,” Journal of Economic Theory (New York), Vol. 2 (September 1970), pp. 211–24.
Feldstein, Martin (1974a), “Incidence of a Capital Income Tax in a Growing Economy with Variable Savings Rates,” Review of Economic Studies (Edinburgh), Vol. 41 (October), pp. 505–13.
Feldstein, Martin (1974b), “Tax Incidence in a Growing Economy with Variable Factor Supply,” Quarterly Journal of Economics (Cambridge), Vol. 88 (November), pp. 551–73.
Feldstein, Martin “Perceived Wealth in Bonds and Social Security: A Comment,” Journal of Political Economy (Chicago), Vol. 84 (April 1976), pp. 331–36.
Feldstein, Martin “Debt and Taxes in the Theory of Public Finance,” Journal of Public Economics (Amsterdam), Vol. 28 (November 1985), pp. 233–45.
Frenkel, Jacob A., and Assaf Razin, Fiscal Policies and the World Economy: An Intertemporal Approach (Cambridge: MIT Press, 1987).
Masson, Paul R., “The Sustainability of Fiscal Deficits,” Staff Papers, International Monetary Fund (Washington), Vol. 32 (December 1985), pp. 577–605.
Persson, Torsten, “Deficits and Intergenerational Welfare in Open Economies,” Journal of International Economics (Amsterdam), Vol. 19 (August 1985), pp. 67–84.
Zee, Howell H., “Government Debt, Capital Accumulation, and the Terms of Trade in a Model of Interdependent Economies,” Economic Inquiry (Long Beach, California), Vol. 25 (October 1987), pp. 599–618.
Mr. Zee, an economist in the Special Fiscal Studies Division of the Fiscal Affairs Department, was in the External Adjustment Division of the Research Department when an initial draft of this paper was prepared. He is a graduate of St. John’s University, Collegeville, Minnesota, and the University of Maryland, College Park.
For helpful comments and discussions, the author thanks Joshua Aizenman, Martin J. Bailey, Atish R. Ghosh, and his colleagues in the Fund.
It turns out that, as was shown later by Carmichael (1982), the validity of the Ricardian equivalence principle, at least within the theoretical framework employed by Barro (1974), is not affected by these complications.
It is worth noting, however, that both Buiter (1979) and Carmichael (1982) have shown that in an overlapping-generations model with operative transfers from children to parents (the gift motive), the steady-state equilibrium is necessarily one in which the growth rate exceeds the interest rate.
Notable exceptions are studies by Blinder and Solow (1973, 1974, 1976), which explicitly recognized stability complications arising from the presence of government debt. Their major focus of attention, however, revolved around the wealth effects of debt in a traditional IS-LM-type macroeconomic model, a concern that has certainly faded in importance in the last decade.
Masson (1985) also discussed this condition under a different model setup and with the utility function restricted to the Cobb-Douglas form.
This observation is in striking contrast to the framework used by Barro (1979), where under complete Ricardian equivalence debt serves only the function of tax smoothing.
If interest income is taxed, as it would be under a general income tax, the proper definition of the golden rule must be modified to one that equates the growth rate of the economy with the net-of-tax interest rate faced by the consumer.
When the rates of interest and population growth are equal, any level of per capita debt is self-sustaining. A more detailed discussion on this and other issues relating to the golden rule is provided in Section IV.
In an analysis of optimal fiscal policy, there is, of course, no reason why the level of government debt has to be exclusively positive.
In contrast, the optimality condition under the second policy experiment—that is, the determination of the optimal tax rate for a given level of expenditures—cannot be characterized in a simple manner, due to the excess burden of the tax, as will be shown later in Section IV.
The present analysis excludes from consideration the public goods or productivity aspects of government expenditures.
A comprehensive study of the international effects of fiscal policies can be found in Frenkel and Razin (1987).
Available empirical evidence suggests that the uncompensated elasticity of labor supply is on the whole quite small (see Killings worth (1983)).
It can easily be shown that the elasticity of substitution (kt) between capital and labor in the production function is related to φt, and
The stipulated sign for γ2t holds even if δt < 0, as long as its absolute value is not large enough for the second term in γ2t to overwhelm the first. Available empirical evidence on savings behavior does not support large and negative interest elasticity of savings, however.
This follows from the fact that the weighted average of income elasticities of consumption (current and future) must add to unity, the weights being the relative shares of each period’s consumption in total net wealth.
The per capita debt level is not well-defined if n = r (1 – τ) in the steady state.
If the utility function (equation (2)) takes the Cobb-Douglas form, then δ = 0 and η = 1, which simplifies equation (22) to
Stability conditions are, of course, highly model-specific. Policy implications derived from them should therefore always be interpreted with caution.
In contrast, the incidence of a change in government expenditures, given the tax rate, is unambiguously positive. It can be shown that the derivative dr/dg has the same denominator as that of equation (29), but its numerator is [ – (1 + n)r]. Hence, an increase in g necessarily reduces the capital intensity of the economy, as expected.
Note again that the calculation of this critical value only involves terms whose numerical magnitudes are usually readily obtainable.
This is not the only possible form of the objective function of the government. An alternative but much less tractable formulation would be to include in the function the sum of utilities of all generations along the path of transition from one steady state to another.
The slope of the individual’s budget constraint is –(1 + r*)-1 with respect to the horizontal axis. Hence, in general it will be different from the slope of line IBJ. To reduce clutter in the diagram, it has been assumed, without loss of generality, that the two lines coincide at the interest rate r*. This would occur, of course, only if r*≈0.62.
It is possible for LFSS (τ > 0) to intersect LFSS (τ = 0) along the positively sloped portion of the latter.
Alternatively, this could be interpreted as a way to return part of the tax revenues to the private sector.
This shift corresponds to the fact that wages (measured along the horizontal axis) are now lower, and the sum of interest income and capital (measured along the vertical axis) is now higher, than before the injection of debt.
For b<0, the condition [n > r (1 – τ)] is neither necessary nor sufficient for stability.
The foregoing analysis on the determination of the optimal level of government expenditures could be criticized as incomplete, since such expenditures are assumed to yield neither utility nor productivity. Although this criticism is strictly valid and extensions to the model in that direction are well worth taking, it should be pointed out that the focus of the analysis here is not on the formulation of a complete normative theory of government expenditures, but rather on their consequences on the economy’s capital intensity by altering the amount of available resources to the private sector. Nevertheless, the inclusion of g in the individual’s utility function, for example, would result in an extra term (relating to the marginal utility of g) in equation (36) and a more complicated expression for the rational rule of savings. A more substantive consequence of not ascribing an intrinsic value to g is discussed below in connection with the third policy experiment.
Substituting equation (37) into equation (27) and setting τ = 0 yields g = –(n – r)2k/(1 + n)<0. A negative g is equivalent to a government subsidy. When the optimal capital intensity is less than that of the golden rule, the subsidy is used to service and maintain a positive amount of debt. When the optimal capital intensity is greater than that of the golden rule, the subsidy increases the private capital stock through a negative amount of debt. In either case, the achievement of the rational rule of savings, when it deviates from the golden rule, requires that the government have sufficient resources at its disposal.