Recent research analyzing capital accumulation and growth in the international economy has been increasingly grounded in the underlying intertemporal optimizing behavior of private agents.1 Most of this literature, which can be viewed as deriving from the traditional optimal growth models pioneered by Cass (1965) and Koopmans (1965), focuses on small open economies. With few exceptions, it assumes that such economies face a perfect world capital market for debt and are free to borrow or lend as much as desired at the given world rate of interest.2 These models investigate the relationship between the rate of capital accumulation, the current account, and debt, in response to various types of disturbances. In particular, the responses to various types of fiscal disturbances and exogenous relative price disturbances have now been considered quite extensively.3 With a perfect world capital market, the dynamic adjustment has a simple recursive structure. On the one hand, the dynamic adjustment within the economy is driven by the accumulation of capital and does not depend directly on the stock of foreign debt. On the other hand, the current account and the stock of debt itself mirror the stable adjustment of the capital stock.4
This paper develops an intertemporal optimizing growth model for a small open developing economy, in order to study the dynamic interaction between growth and debt in response to various exogenous shocks and policies. There is little doubt that such economies require external capital, since typically they cannot generate adequate resources domestically to achieve the growth rates that may lead to an improvement in living standards.
But the assumption that such economies face a perfectly elastic supply of debt is clearly unrealistic. Experience with external borrowing in such economies has shown that debt repayments are not always made on time. Overborrowing, resulting from inadequate perceptions of domestic growth potential, has occurred on occasion. Long gestation lags in investment projects have led to difficulties in meeting repayment com-mitments in some cases (Kharas (1983) and Kharas and Shishido (1986)). International capital markets are likely to react to their perception of a country’s ability to repay, with lenders requiring a risk premium on the rate at which they are willing to lend to such economies, as well as, in some cases, imposing credit ceilings on borrowers.5
We incorporate this idea by assuming that the developing economy faces an upward-sloping supply schedule for debt, which embodies the risk premium associated with lending to a sovereign borrower. The analysis shows the effect of such a constraint on borrowing on the interaction between the dynamics of growth and debt accumulation in a fundamental way. In particular, the simple recursive dynamic structure associated with a perfectly elastic supply of debt breaks down. This is because the marginal cost of capital facing firms, and therefore determining their investment decisions, is now dependent upon the outstanding stock of national debt. Conditions in the international capital market therefore become important in determining the growth of capital in the domestic economy.
The paper analyzes the dynamic effects of various disturbances on key macroeconomic variables. Particular attention is devoted to considering shocks associated with the debt-supply schedule confronting the small developing economy. These shocks include: an increase in the level of the exogenously given world interest rate, and an increase in the risk premium associated with the country’s debt. The former reflects a general tightening in the world credit market, and the latter describes a deterioration in the country-specific borrowing opportunities. The effects of a productivity shock, which is taken to reflect some kind of structural efficiency-enhancing measure, are also considered. Finally, since fiscal policy is an important element in growth, debt accumulation, and adjustment strategies, the model considers the impact of changes in government expenditure as well. Overall, the model thus enables us to analyze the impact of both demand management and structural policies on variables such as household consumption-saving decisions, investment decisions of the firm, and the current account, and hence, debt accumulation. The paper stresses the interdependence between the rates of accumulation of capital and debt in the course of the dynamic adjustment and the possible trade-offs between them. However, the discussion focuses primarily on the growth aspects and does not address debt strategies or debt overhang issues.
The rest of the paper is organized as follows. Section I specifies the analytical framework. Section II discusses the long-run effects and dynamics of a balanced-budget policy; debt-financing deficit policy is discussed in Section III. Section IV briefly considers alternative specifications of the debt function. The main conclusions of the paper are summarized in the final section. For convenience, all technical matters relating to the solutions are relegated to the Appendix.
APPENDIX Solution of Dynamic Systems
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Brock, Philip L., “Investment, the Current Account and the Relative Price of Nontraded Goods in a Small Open Economy,” Journal of International Economics, Vol. 24 (May 1988), pp. 235–53.
Buiter, Willem H., “Fiscal Policy in Open, Interdependent Economies,” in Economic Policy in Theory and Practice, ed. by A. Razin and E. Sadka (New York: St. Martin’s Press, 1987).
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Cass, D., “Optimum Growth in an Aggregative Model of Capital Accumulation,” Review of Economic Studies, Vol. 91 (1965), pp. 233–40.
Cooper, Richard N., and Jeffrey D. Sachs, “Borrowing Abroad: The Debtor’s Perspective,” in International Debt and the Developing Countries, ed. by Gordon W. Smith and John T. Cuddington (Washington: World Bank, March 1985), pp. 21–60.
Eaton, Jonathan, and Mark Gersovitz, “LDC Participation in the International Financial Markets: Debt and Reserves,” Journal of Development Economics, Vol. 7 (March 1980), pp. 3–21.
Eaton, Jonathan, and Mark Gersovitz, “Debt with Potential Repudiation: Theoretical and Empirical Analysis,” Review of Economic Studies, Vol. 48 (1981), pp. 289–309.
Eaton, Jonathan, and Mark Gersovitz, and Stephen J. Turnovsky, “Covered Interest Parity, Uncovered Interest Parity and Exchange Rate Dynamics,” Economic Journal, Vol. 93 (September 1983), pp. 555–75.
Edwards, Sebastian, “LDC Foreign Borrowing and Default Risk: An Empirical Investigation, 1976–80,” American Economic Review, Vol. 74 (September 1984), pp. 726–34.
Kharas, H.J., and H. Shishido, “Optimal Borrowing and Over borrowing: Some Simple Simulation Lessons” (unpublished; Washington: World Bank, January 1986).
Koopmans, T.C., “On the Concept of Optimal Growth,” in The Econometric Approach to Development Planning (Chicago: Rand-McNally, 1965), pp. 225–300.
Matsuyama,K., “Current Account Dynamics in a Finite Horizon Model,” Journal of International Economics, Vol. 23 (May 1987), 299–313.
Obstfeld, Maurice, “Aggregate Spending and the Terms of Trade: Is There a Laursen-Metzler Effect?” Quarterly Journal of Economics, Vol. 97 (May 1982), pp. 251–70.
Obstfeld, Maurice, “Fiscal Deficits and Relative Prices in a Growing World Economy,” Journal of Monetary Economics, Vol. 23 (1989), pp. 461–84.
Otani, Ichiro, and Delano Villanueva, “Theoretical Aspects of Growth in Developing Countries: External Debt Dynamics and the Role of Human Capital,” IMF Working Paper WP/88/54 (Washington: International Monetary Fund, June 1988).
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Sen, Partha, and Stephen J. Turnovsky (1989b), “Tariffs, Capital Accumulation, and the Current Account in a Small Open Economy,” International Economic Review, Vol. 30 (November, pp. 811–31.
Jagdeep S. Bhandari is an economist in the European Department and is currently on leave of absence from West Virginia University where he is a Professor of Economics. He holds a Ph.D. from Southern Methodist University. He is also an attorney and counselor-at-law, having obtained a J.D. degree from Duquesne University and an LL.M. degree from Georgetown University.
Nadeem Ul Haque, an economist in the Developing Country Studies Division of the Research Department, holds degrees from the London School of Economics and Political Science and the University of Chicago.
Stephen J. Turnovsky is a Professor of Economics at the University of Washington and a Research Associate at the National Bureau of Economic Research. He holds a Ph.D. from Harvard University.
The authors are grateful to Mohsin Khan for useful comments on an earlier draft.
An early exception is Bardhan (1967) who analyzes optimal borrowing by a small open economy that faces an upward sloping supply curve for debt of the form to be introduced in this paper. Reference should also be made to a recent paper by Otani and Villanueva (1988), which analyzes the accumulation of capital and external debt in a neoclassical economy and also assumes an imperfect market for loans. However, that paper adopts a very different approach and emphasizes different issues (that is, the role of human capital formation) from those addressed in the present paper.
For example, Buiter (1987), Brock (1988), and Obstfeld (1989) consider different fiscal shocks, including different types of disturbances in government expenditure and some forms of taxes; Matsuyama (1987) analyzes input price shocks; and Sen and Turnovsky (1989a, 1989b) discuss various types of disturbances in terms of trade and tariffs.
However, the stock of foreign debt does play an indirect role in determining the dynamics of the capital stock through the intertemporal national budget constraint. For a more detailed discussion of the dynamic structure with a perfect world capital market, see Sen and Turnovsky (1989a, 1989b).
Note that since the model is real, no prices or nominal variables need be considered.
Even though in some countries the private sector has borrowed abroad, implicit or explicit government guarantees have essentially underwritten this debt, making private debt indistinguishable from government debt, insofar as the foreign creditor is concerned.
Otani and Villanueva (1988) assume that the risk premium is a positive function of the country’s debt-to-export ratio.
For simplicity, labor is assumed to be fixed. Since in a developing country context the endogeneity of labor is not likely to be a critical issue, this assumption is not viewed as being particularly restrictive.
If b > 0, the consumers are creditors, whereas if b < 0, then they are debtors. Examination of the budget constraint shows that if consumers are creditors, then acquisition of increasingly costly debt by the government adds to disposable income, and vice versa.
Subscripts and primes (‘) denote derivatives.
This formulation assumes that the representative agent, in choosing his or her holding of debt, takes account of his or her decision on the aggregate debt of the economy and therefore on the prevailing domestic interest rate. This is possible even if the number of such agents—say, n—is large. Suppose aggregate debt holdings b = Σbi, where bi = b/n is the holding of each representative agent; the optimality condition for each such agent is
As long as n < ∞, this condition is of the form represented in equation (6), with the number of agents n being simply absorbed in the coefficient ix. We are grateful to Ed Buffie for drawing this point to our attention.
Note that the cost of debt depends on whether the consumer is a net creditor or a net debtor. In the former case, the marginal cost exceeds the interest rate; in the latter case, the opposite is true.
Note that this specification implies that in the case where disinvestment may occur, C(I) < 0 for low rates of disinvestment. This may be interpreted as reflecting the revenue obtained as capital is sold off. The possibility that all changes in capital are costly can be incorporated by introducing sufficiently large fixed costs, so that C(0) > 0. This does not alter our analysis in any substantive way.
This is ensured by an appropriate adjustment in q at each point in time.
Hereafter, the labor variable will be suppressed for convenience.
In Section III below, we shall also discuss a form of debt financing, which, in order to be sustainable in the long run, needs to be accompanied by a once-and-for-all change in lump-sum taxes.
Assuming a convex debt function of the form i = i0 + i1 zα, α > 1, this will be so if the ratio b/a > 1/α.
These results may be usefully compared with the long-run effects of an increase in the foreign interest rate under the limiting assumption where the debt-supply function is horizontal. In such a case, the domestic interest rate rises by the same amount as does the foreign interest rate, leading to a larger fall in the domestic capital stock than in the present case. The stock of external debt can be shown to decline by an amount that is proportional to the reduction in the capital stock, with the resulting effect on the long-run trade balance being ambiguous, depending upon the stock of external debt.
For example, for the constant-elasticity convex debt function i = i0 + i1zα, α ≥ 1, the quantity ω – ω’
For this case, the production function is changed to f(k, θ).
For obvious reasons we restrict our discussion to the plausible case where the increase in the foreign interest rate leads to an increase in the long-run domestic interest rate and a corresponding decline in the long-run capital stock. The perverse case, where the long-run interest rate declines can be analyzed similarly but is of little practical interest.
This contrasts with the dynamics under the limiting case of uncovered interest parity when the paths followed by z and k can both be shown to be mono-tonic, following a permanent shock; see Sen and Turnovsky (1989a, 1989b).
As discussed in the Appendix, the dynamic structure of the balanced-budget variant involves four differential equations. With debt finance, the resulting dynamics is of the fifth order; the additional source of dynamics is the evolution of the stock of government debt ȧ.
For expositional convenience we restrict our discussion to the case where the debt schedule is linear.
The impact of changes in z0-that is, changes in the stock of debt held by the country—can be used to study the dynamics of the effects of debt forgiveness schemes. In this model, interest relief schemes are equivalent to negative foreign interest rate shocks.