Foreign Borrowing and Export Promotion Policies

Daniel Citrin

doi:10.5089/9781451930757.024.A006

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Foreign Borrowing and Export Promotion Policies

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Mr. Daniel Citrin

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Publication Date:: 01 Jan 1989

eISBN:: 9781451930757

Language:: English

Keywords:: SP; debt; interest payment guarantee; credit ceiling; utility function; decentralized economy; credit-ceiling function; credit constraint; Credit ceilings; Credit; Imports

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The problem of allocation of investment is an important issue for a debtor country facing a ceiling on the amount of foreign debt it can accumulate. The optimal solution is for the debtor country to create a more open economy by favoring investment in the export sector over investment in the import-competing sector. The reason is that a more open economy is more sensitive to trade sanctions and is therefore more creditworthy in international markets. Because international creditworthiness is basically an externality, policy can play a role in providing higher returns to export-producing activities.

Abstract

SINCE 1982 A NUMBER of major debtor countries have faced weakened prospects for repayment of their debts and, consequently, very restricted access to foreign borrowing. The adjustment to that situation has brought about major changes in their economies, in particular, sharp drops in investment and large real depreciations of the exchange rates. The formal framework developed here analyzes one particular aspect of the optimal debtor response to this situation—namely, that of determining the optimal level of productive investment and its composition in the face of external financing difficulties.

When a debtor country faces a credit constraint, it needs to lower investment, raise domestic savings (or generate a smaller excess of investment over savings), or both, to obtain the required improvement in its trade account. In the absence of policy intervention, the adjustment in savings and investment would take place without consideration of the feedback of actions onto the credit constraint, because individual agents treat the credit constraint as exogenous. Results available in the debt literature are that the market response to the credit constraint would involve an excessive reduction in investment (see, for example, Aizenman (1987b), Cohen and Sachs (1986), and Krugman (1988)). However, there is another reason why investment may have a strong effect on the credit ceiling. The allocation of investment between export-producing and import-competing industries will affect the creditworthiness of the debtor country. The policy dilemma facing the authorities is: Is it advisable to promote investment in the production of importables that would be valuable in the event of a default, or is it preferable to invest in the production of exportables, which would help increase the availability of foreign financing? Our analysis shows that investment in export-producing activities contributes toward relaxing the foreign borrowing constraint, whereas investment in import-competing activities tightens the foreign borrowing constraint. Therefore, at least when the terms of trade are exogenous to the debtor country, policy should be directed toward promoting investment in the export-producing sector.¹

The framework of international credit markets we have adopted is similar to the one developed by Eaton and Gersovitz (1981a), and Cohen and Sachs (1986). In this framework, debtor countries may choose to repudiate their debts, even in situations in which they have enough resources to repay them.² There are, of course, costs associated with debt repudiation. At every point in time, a social planner computes the costs and benefits from the repayment and the repudiation alternatives, and decides which route to take. This option to repudiate foreign debt substantially alters the allocation decisions to be made about consumption, savings, and resources, even if the country never actually repudiates its debts.

The sanctions that a debtor country may expect to be subjected to in case of repudiation are a critical factor in this framework. When a country repudiates its debt, it is obtaining debt relief at the cost of financial and economic sanctions. The exact penalties that a repudiating country would face are not explicit, and very difficult to determine. Although there has been some historical experience, it cannot be easily extrapolated, but given the critical role of sanctions in any debt model, we discuss the issue in detail below. We conclude that sanctions consist of a permanent exclusion from foreign borrowing and some traderelated measures that reduce the advantages of international trade for the debtor country.

We consider here the case of an economy producing two goods—an import and an export good. Then, in addition to the balance between savings and investment, the adjustment to the more stringent foreign borrowing conditions implies a current account adjustment that usually requires large real exchange rate changes. This paper suggests that the optimal response, because it implies the need to promote export production relative to import-competing production, cannot be achieved through exchange rate policy alone. An increase in the production of exports helps to increase the amount of foreign borrowing available to the country. Consequently, the country needs to shift the pattern of investment toward the export sector.³ Although the country invests less in the export sector than it would in the absence of a credit ceiling, it will invest more than a decentralized economy. It is noteworthy that this policy response implies an increase in the returns to the production of exports relative to that of imports, and that an exchange rate policy is not a good instrument for that purpose.

The plan of the paper is as follows. Section I discusses the issue of costs and benefits of default, and justifies the assumptions adopted in this paper. Section II develops a two-period framework, in which precise results can be obtained. Section III considers the infinite-horizon case, which enables us to consider issues such as the cost resulting from exclusion from future borrowing. Section IV summarizes the results and considers their possible policy implications. Appendix I details the derivation of the results in Section II, and Appendix II gives the specifications of the model used in Section III and the numerical solution method applied in simulating it.

I. Debt Repudiation: Possible Sanctions

A key determinant of the implications of any debt model is the assumption about the resolution of a default situation. In this paper we assume that a country defaults whenever the expected benefits from default exceed the expected costs. This seems a more relevant criterion than determining the default decision by the country’s ability to pay. Few countries are physically unable to meet their obligations (indeed, sovereign lending was considered safe since true insolvency of a country is virtually impossible), but the costs of doing so may far exceed the benefits.⁴

Although the benefit to the debtor from debt repudiation is obvious—the avoidance of debt service—the costs of that action are difficult even to identify, let alone estimate. Although there is a growing literature on this topic,⁵ a number of issues are unresolved, and some legal issues remain to be tested in the courts. Unlike an ordinary commercial borrower, a debtor country is protected from legal sanctions under the broad concept of “sovereign immunity.” Since a foreign borrower cannot be brought to bankruptcy court, private creditors have limited recourse to legal sanctions.

The legal base empowering creditors to obtain compensation for unpaid sovereign debt is doubtful. One frequently cited line of defense is based on the Foreign Sovereign Immunities Act (FSIA) (1976) in the United States (and the corresponding legislation in the United Kingdom). However, the effectiveness of the FSIA is limited, first, because sovereign borrowers explicitly waive their immunities in loan contracts, and second, the commercial activity exception included in the FSIA prevents its application when a commercial activity is involved. Another, potentially more effective line of defense is based on the “act of state doctrine,” which originally applied to expropriation, but has recently been applied to foreign exchange controls as well. Although the act of state doctrine would not apply in the case of default on a specific contract, it could apply if, for example, a debtor country were to impose exchange controls that made it impossible to service foreign debts in foreign currency (see Zamora (1987)). The experience of private creditors (mainly bond holders until the 1970s) attempting to attach assets belonging to the defaulting country has been varied, and, especially in the last century, none too successful.⁶

It therefore appears likely that the main penalties for default will consist of nonjudicial sanctions. The most commonly cited penalty is the country’s exclusion from further participation in the capital markets.⁷ Of course, a borrower contemplating default will be unlikely to obtain much long-term credit from the capital markets in any case, which means that a future exclusion from borrowing will not represent a severe cost. Kindleberger (1982) argues that several defaults during the 1920s were prompted by the perception that financial markets were collapsing, so that the reputation of being a “good” borrower became less valuable and default became more attractive. More conclusively, in a recent paper Bulow and Rogoff (1988) show that if the country can hold foreign assets after default, it will always choose default on its debt at some point in time, and reputation thus becomes an empty concept in international borrowing.⁸

A more important direct penalty is that the defaulting country is liable to lose its short-term trade financing and the trade intermediation services provided by international banks that go along with it. Export credit flows themselves have grown rapidly in recent years, and constitute a major proportion of developing countries’ external finance. In addition to the financial component, bank intermediation provides a number of ancillary services that may greatly facilitate international transactions for debtor countries. Should a country lose access to these lines of credit and the availability of attached services, the cost of international transactions may rise considerably. Enders and Mattione (1984) estimate that the rise in import costs, per unit of exports, could be on the order of 5 percent to 10 percent. The loss of such credits and international bank services constitutes perhaps the most severe penalty creditor banks may impose on a defaulting country.

Ultimately, the penalties for default will depend upon a complex interaction of political and bargaining issues. Commercial banks will also have to consider the effects of their response to a default by one borrower on their reputations vis à vis all their other borrowers.⁹ Obviously, a formal model cannot capture all, or indeed most, of these complex considerations. At a minimum, the model should incorporate the exclusion from future borrowing (which we term the “indirect” penalty) and some form of traderelated measures, or “direct” penalty. The latter is intended to capture the increased costs of trade without trade financing, and to a lesser degree, the possible seizure of the debtor’s goods in transit.¹⁰

Typical trade sanctions associated with default would include withholding of access to commercial credit and bank trade intermediation, trade embargoes from some creditor countries—which could be avoided by trading through a third country—and the possibility of seizure of shipments of merchandise on international transport. It is not unreasonable to assume that all these actions would involve a cost that is proportionate to the dollar value of trade, and can therefore be represented as an increase in the unit cost of imports and a reduction in the unit return to exports—that is, simply a deterioration in the terms of trade. They could also be thought of as increasing “transportation costs” or “transaction costs,” which reduce export f.o.b. prices and increase import c.i.f. prices. Indeed, in their study Enders and Mattione (1984, p. 49) assume that “trade in both exports and imports is disrupted, and the costs of disruptions can be modeled as an X percent decrease in unit export earnings and an equivalent percentage increase in unit import costs; these costs are due to foreign suppliers’ attempts to insure themselves against new defaults, to creditors’ attempts to attach goods and payments, and to the inefficiencies of administering such a scheme.” Accordingly, we model the direct penalty for default as a permanent change in the country’s terms of trade. In addition, we assume the existence of an indirect penalty of perennial exclusion from the capital markets.

II. Debt and Investment in a Two-Period Model

We consider an economy with a two-period time horizon, producing one exportable and one importable good. The production of each good requires sector-specific capital. In this framework, three important results obtain. (1) The ceiling on foreign borrowing faced by this economy is an increasing function of the stock of capital in the export sector and a decreasing function of the stock of capital in the import sector. (2) The optimal response to the imposition of the credit ceiling is to reduce investment in both productive sectors (relative to the case of no risk of debt repudiation). (3) The optimal amount of investment in the export sector is higher than the amount that would obtain in a decentralized economy. This means that the credit-rationed economy should follow an “export promotion” policy.

In the two-period case, the penalties for lack of repayment cannot include exclusion from future borrowing. Thus, penalties will consist entirely of trade sanctions. Consistently with the discussion in the previous section, we assume that the effect of trade sanctions is equivalent to a permanent terms of trade deterioration for the debtor country. Specifically, in the event of external debt repudiation, a fraction ρ of exports is lost and the cost of imports rises by an equivalent proportion. Therefore, if the price of exports was unity, the net return to exports will become 1 – ρ after default, and if the price of imports was P, the total cost of imports will become P/(1 – ρ) after default.¹¹ The terms of trade—the relative price of imports in terms of exports—will therefore shift from P to θP, where θ = (1 – ρ)^-2.

As is amply documented in the literature on this type of framework, creditor banks will set a ceiling on lending to sovereign countries in order to prevent them from repudiating their obligations (see the survey by Eaton, Gersovitz, and Stiglitz (1986)). This is because as foreign debt increases, the rewards from a repudiation of foreign debt also increase.¹² Consequently, creditor banks will never increase lending past the point at which repudiation becomes more attractive than repayment.

To find out how the credit ceiling function is affected by investment in each productive sector, first obtain the credit ceiling function as of the beginning of the second period. For this purpose, it is convenient to use the indirect utility functions that correspond to the repayment and default regimes. An indirect utility function gives the maximum utility obtained by the representative consumer as a function of relative prices and income. In the case of repayment of foreign debt, the indirect utility function, V^R (the superscript R stands for repayment) will be obtained from

V^{R} [P, y^{*} + P y - (1 + r) D] = \max U (c^{*}, c), (1)

subject to

y^{*} - c^{*} + P (y - c) - D (1 + r) \geq 0,

where P is the exogenous relative price of imports; y* and y represent the supply of the exportable and importable good, respectively; c* and c represent consumption of each of the two goods; and D represents the level of foreign debt carried over from the previous period, which carries a (world) interest rate r. For the exportable and importable goods, production functions are given by

y^{*} = f (k^{*})

and

y = f (k),

where k* and k represent the capital stocks specific to the respective sector.

Let V^D represent the indirect utility function in case of repudiation (where the superscript stands for default); V^D is obtained from

V^{D} (θ P, y^{*} + θ P y) = \max U (c^{*}, c), (2)

subject to

y^{*} - c^{*} + θ P (y - c) \geq 0,

where θP represents the (net) international terms of trade received by the debtor country as a consequence of trade sanctions. The credit ceiling is the maximum amount of debt that debtors can owe and still prefer the repayment option. Since V^R is a decreasing function of D, the credit ceiling is a quantity $\bar{D}$ , such that

V^{R} [P, y^{*} + P y - (1 + r) \bar{D}] = V^{D} (θ P, y^{*} + θ P y) . (3)

Note that this implies that the credit ceiling $\bar{D}$ is the equivalent variation in income that compensates for a terms of trade deterioration in proportion θ. In terms of expenditure functions, $\bar{D}$ can be obtained as

\bar{D} = e (θ P, V^{D}) - e (P, V^{D}),

where e(•) is the expenditure function, and V^D is the indirect utility function under default defined in equation (2). The determination of the credit ceiling is illustrated in Figure 1. Point E represents the combined output of the two goods (y, y*). At the default terms of trade (θP), consumption would be at point D. At the undisturbed (free trade) terms of trade (P), the same utility level could be achieved by consuming at point R. It can be seen that if the resources of the country were reduced by an amount $\bar{D}$ (1 + r) (in export good units), the country would be indifferent between repaying or defaulting on its foreign debt, thus implying that the credit ceiling is equal to $\bar{D}$ .

Differentiating equation (3), we can investigate the dependency of the credit ceiling on the variables of interest. We first compute

\frac{d \bar{D}}{d y^{*}} = \frac{V_{I}^{R} - V_{I}^{D}}{(1 + r) V_{I}^{R}} = \frac{U_{c *}^{D} - U_{c *}^{D}}{(1 + r) U_{c *}^{R}}, (4)

where V_I represents the derivative of the indirect utility function with respect to income (its second argument). The second equality follows from a well-known envelope theorem that equates marginal utility of income to marginal utility of consumption at the optimal point.¹³ Thus

\frac{d \bar{D}}{d y} = \frac{P V_{I}^{R} - θ P V_{I}^{D}}{(1 + r) P V_{I}^{R}} = \frac{U_{c}^{D} - U_{c}^{D}}{(1 + r) U_{c}^{R}}, (5)

where the superscripts R and D in the utility function indicate that the derivatives are computed at the consumption bundles corresponding to the repayment and default situations, respectively; and where subscripts indicate partial derivatives with respect to the variable in the subscript. In obtaining the second equality, we have also used the conditions that, at an optimal point, $U_{c}^{R} = P U_{c *}^{R}$ , and $U_{c}^{R} = θ P U_{c *}^{D}$ .

Figure 1.

The Two-Period Model

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A006

Note: D is default consumption; R is repay consumption (when debt = debt ceiling); E is the endowment point (y, y*); and

\bar{D} = h (k^{*}, k) .

is the debt ceiling.

\frac{d \bar{D}}{d y} = \frac{{P V}_{I}^{R} - {θ P V}_{I}^{D}}{(1 + r) {P V}_{I}^{R}} = \frac{U_{c}^{R} - U_{c}^{D}}{(1 + r) U_{c}^{R}} (5)

For fixed terms of trade, the credit ceiling can be expressed as a function only of the capital stock in each productive sector— $\bar{D} = h (k^{*}, k) .$ = h(k*, k).¹⁴ Since the marginal product of capital is the same in either the repayment or the default case because capital is predetermined, and because there is no further use for capital after period 1, the derivatives of h(•) can be expressed simply as

h_{k}^{' *} = \frac{U_{c *}^{R} - U_{c *}^{D}}{(1 + r) U_{c *}^{R}} f_{k *} = \frac{f_{k *}}{1 + r} (1 - \frac{U_{c *}^{D}}{U_{c *}^{R}}) > 0. (6)

The sign of this derivative follows from $U_{c}^{R} > U_{c *}^{D}$ , which is proved in Appendix I. The inequality means that the export good has a higher marginal utility under repayment than under default, when evaluated at the point at which the country is indifferent between repaying or defaulting. This is because when the country defaults, the export good becomes relatively cheaper (the terms of trade deteriorates by a factor of θ), and the marginal utility of the export good decreases as its relative price falls and the utility level is kept constant.

The derivative of the credit-ceiling function with respect to capital installed in the import good industry is

h_{k}^{' *} = \frac{U_{c}^{R} - U_{c}^{D}}{(1 + r) U_{c}^{R}} f_{k} = \frac{f_{k}}{1 + r} (1 - \frac{U_{c}^{D}}{U_{c}^{R}}) < 0. (7)

Similarly, the sign of equation (7) is determined by the fact that $U_{c}^{D} > U_{c}^{R}$ , which is also proved in Appendix I. In other words, the marginal utility of the import good increases as its relative price goes up and the utility level is kept constant.

Consider now the problem of the optimal composition of investment in the debtor country, given its foreign borrowing constraints. The social planner of the debtor economy must decide how much to allocate to consumption and investment in each industry, given the credit ceiling function h(•). That decision is reached by solving

V^{P} (y_{0}^{*}, y_{0}) = \max U (c_{0}^{*}, c_{0}) + β U (c_{1}^{*}, c_{1}), (8)

subject to

y_{0}^{*} - c_{0}^{*} - I^{*} + P (y_{0} - c_{0} - I) + \frac{1}{1 + r} {f (I^{*}) - c_{1}^{*} + P [f (I) - c_{1}]} \geq 0

and

h (I^{*}, I) \geq (c_{0}^{*} + I^{*} - y_{0}^{*}) + P (c_{0} + I - y_{0}),

where we have assumed a 100 percent depreciation rate—that is, k₁ = I in both sectors—and that there is no initial debt. The first-order conditions for this problem are

U_{c *} = λ + μ (9 a)

U_{c 0} = P (λ + μ) (9 b)

β U_{c *} = \frac{λ}{1 + r} (9 c)

β U_{c_{1}} = P \frac{λ}{1 + r} (9 d)

λ (\frac{f_{k *}}{1 + r} - 1) = - μ (h_{k *} - 1) (9 e)

λ P (\frac{f_{k}}{1 + r} - 1) = - μ (h_{k *} - P) (9 f)

where λ and μ are the Lagrange multipliers associated with the constraints in equation (8). Investment in the export sector is implicitly given by (9f). Using equation (6), one obtains

\frac{f_{k *_{1}}}{1 + r} = \frac{λ + μ}{λ + μ (1 - \frac{U_{c_{1} *}^{D}}{U_{c_{1 *}}^{R}})} > 1. (10)

Equation (10) says that investment in the export sector will be less than the level that would obtain if the country did not have the option to repudiate its debt. With no risk of repudiation, the domestic interest rate would be equal to the world interest rate r, and the marginal product of capital would be equal to both. The existence of risk of debt repudiation and the consequent credit ceiling increase the actual cost of borrowing for the debtor country; the optimal domestic interest rate (the one that generates the optimal amount of investment) exceeds the world interest rate by a factor—in the right-hand side of (10)—that expresses how the choice between default or repayment is affected by additional units of capital in the export sector. Investment in the import sector can be obtained using (7) and (9f):

\frac{f_{k *_{1}}}{1 + r} = \frac{λ + μ}{λ + μ (1 - \frac{U_{c_{1}}^{D}}{U_{c_{1}}^{R}})} > 1. (11)

Thus, investment in the import sector also declines relative to the level that would prevail if there were no option to repudiate foreign debt. The decline in investment in the import sector is larger than the decline in the export sector, in the sense that the optimal domestic cost of capital for the import sector is larger than for the export sector, as is clear from equations (6) and (7).

The reason for the differential effect on investment in the two sectors is that investment in the export sector has a beneficial effect on the credit ceiling. Because the relative price of exports falls in the event of repudiation, investment in the export sector makes repudiation more costly to the debtor country and permits a higher safe limit of indebtedness, easing the credit constraint. Therefore, the response to the existence of a credit constraint by an optimal planner should be a generalized reduction in investment, but with a change in its composition into export production (relative to the levels prevailing in the absence of the repudiation option).

For policy purposes, however, the relevant comparison is between the decisions of the social planner and those that would be made in a (partially) decentralized economy, because this comparison indicates the precise nature of intervention in the form of taxes or subsidies that is needed to achieve the social optimum. In this context, an economy can only be partially decentralized, because the decision to repudiate foreign debt must be a coordinated one. In such an economy, there is a central authority whose main function is to decide, at each point in time, if the country should repudiate its foreign debt. In addition, the central authority is a financial intermediary between foreign lenders and domestic borrowers. The central authority is assumed to conduct this function in such a way as to allow domestic prices and interest rates to be determined in competitive markets, and to refund to the private sector, in a lump sum, all profits resulting from this intermediation activity.

Such a decentralized economy will face exactly the same credit ceiling function as does the socially planned economy, because the aggregate costs and benefits of repudiation are the same. In the case of repudiation, the decentralized economy will face the same implicit deterioration in the terms of trade, and will benefit from the same full debt relief as the planned economy. Thus, from the point of view of a representative consumer, the point at which default becomes optimal is the same for the two economies. This is a special feature of the two-period model; in a multiperiod setup, the change in the domestic interest rate following default would be different in the two economies, and this factor alone would make the value of the repudiation option different.

In the decentralized economy a central authority does all foreign borrowing and repayments, and the foreign resources thus obtained are passed on to the public at a market-clearing interest rate. If the country is credit-constrained, the domestic interest rate will exceed the international interest rate, and the central authority will make a profit, which we assume is returned to the private sector as a lump-sum payment at the beginning of the second period.

Private sector behavior in the decentralized economy will be determined by the solution to the following optimization problem (where the superscript c identifies the decentralized economy problem):

V^{C} (y_{0}^{*}, y_{0}) = \max U (c_{0}^{*}, c_{0}) + β U (c_{1}^{*}, c_{1}), (12)

subject to

\begin{matrix} y_{0}^{*} - c_{0}^{*} - I * + P (y_{0} - c_{0} - I) \\ + \frac{1}{1 + r^{D}} {f (I *) - c_{1}^{*} + P [f (I) - c_{1}]} + \frac{r^{D} - r}{1 + r^{D}} h (I *, I) \geq 0, \end{matrix}

where r^D is the domestic interest rate. The term [(r^D – r)/(1 + r^D)]h ( $(I_{0}^{*}, I_{0})$ , I₀ represents profits made by the central authority by borrowing abroad at the rate r, and competitively allocating those funds among domestic borrowers at rate r^D. If the country is credit-constrained, profits will always be positive. Although profits are immediately reimbursed to the private sector, agents know that their individual actions have an insignificant impact on the central authority’s profit distribution and correspondingly ignore any such repercussion. In consequence, the first-order conditions for the private sector’s problem are

U_{c * 0} = λ (13 a)

U_{c 0} = P λ (13 b)

β U_{c * 1} = \frac{λ}{1 + r^{D}} (13 c)

β U_{c 1} = P \frac{λ}{1 + r^{D}} (13 d)

\frac{f_{k *}}{1 + r^{D}} = 1 (13 e)

\frac{f_{k}}{1 + r^{D}} = 1. (13 f)

These first-order conditions are quite standard. Rates of growth of marginal utility and marginal products of capital in each sector are equalized to the domestic interest rate r^D. The two market-clearing conditions, which, assuming that the economy is credit-constrained, are given by

h (I *, I) = c_{0}^{*} + I * - y * + P (c_{0} + I - y) (14)

(1 + r) h (I *, I) = f (I *) - c_{1}^{*} + P [f (I) - c_{1}] . (15)

These two conditions represent the current account balance in periods 1 and 2. Of course, one of these conditions is made redundant by the application of the budget constraints.

To compare the planned economy and the decentralized economy we obtain the effect on utility of a representative consumer resulting from a marginal increase in investment in each sector—dV^c/dI* and dV^c/dI. Since we know that the planned economy achieves maximum utility, it follows that if dV^c/dI* > 0, the planned economy invests more in the export sector than the decentralized economy, and if dV^c/dI < 0, the planned economy invests less in the import sector than the decentralized economy:

\begin{matrix} \frac{d V^{c}}{d I *} & = & U_{c *} {- 1 + \frac{f_{k *}}{1 + r^{D}} + \frac{r^{D} - r}{1 + r^{D}} h_{k}^{' *} + \frac{h}{1 + r^{D}} \frac{d r^{D}}{d I *} \\ - \frac{1}{(1 + r^{D})^{2}} [h (1 + r) + (r^{D} - r) h] \frac{d r^{D}}{d I *}} . \end{matrix}

Applying first-order and equilibrium conditions, the expression reduces to

\frac{d V^{c}}{d I *} = U_{c *} \frac{r^{D} - r}{1 + r^{D}} h_{k}^{' *} > 0, (16)

because $h_{k}^{'}$ > 0. The effect on utility of the change in the domestic interest rate vanishes because the private sector is in a balanced position with respect to r^D with any increase in the cost of borrowing refunded by the central authority. Symmetrically,

\frac{d V^{c}}{d I *} = U_{c 0} \frac{r^{D} - r}{1 + r^{D}} h_{k}^{' *} < 0. (17)

In summary, in the two-period horizon case, the optimal policy response involves a subsidy for investment in the export sector and a tax on investment in the import-competing sector. This result will now be extended to the infinite-horizon model.

III. Debt and Investment in an Infinite-Horizon Model

The addition of the indirect penalty in the infinite-horizon model does not alter the results of the previous section in a significant way. Although we have been unable to show that the optimal policy involves a subsidy to investment in the export-producing sector and a tax on investment in the import-competing sector at every point in time, there is a strong presumption that this is in fact the case. If the derivatives of the credit-ceiling function have the same signs—as we conjecture—investment in the export sector will be subsidized in the steady-state position. With adjustment costs to investment, it then seems natural that investment in the export sector will always be subsidized. Furthermore, we provide a numerical example that is in accordance with this argument.

As before, the credit-ceiling function faced by this economy is obtained from a comparison of the value functions under the default and repayment alternatives. The determination of the credit ceiling in this model is extremely complicated. As has been noted, one of the benefits of repayment is the continued access to capital markets; the more the country will use capital markets in the future, the greater are its incentives to repay today. Therefore, the higher the credit ceiling the country expects tomorrow is, the larger are the debts it can safely owe today. But the credit ceiling tomorrow will be an increasing function of the credit ceiling in the period after as well. Clearly, the credit ceiling is infinitely recursive. This suggests that the credit-ceiling function can be solved for by using dynamic programming techniques to compute the utility value for the debtor country of the repayment and default alternatives.

Let V^D(k, k*) denote the present discounted utility (that is, the value function) if the country decides to default. This value function is computed from

V^{D} (k_{t}^{*}, k_{t}) = \max U (c_{t}^{*}, c_{t}) + β V^{D} (k_{t + 1}^{*}, k_{t + 1}), (18)

subject to

\begin{matrix} k_{t + 1}^{*} = (1 - δ) k_{t}^{*} + I_{t}^{*} \\ k_{t + 1} = (1 - δ) k_{t} + I_{t} \\ f (k_{t + 1}^{*}) - c_{t}^{*} - I_{t}^{*} = θ P_{t} [c_{t} + I_{t} - f (k_{t})], \end{matrix}

where δ is the depreciation rate of capital.

Let V^R(k, k*, D) denote the value function under repayment. This value function is computed from

V^{R} (k_{t}^{*}, k_{t}, D_{t}) = \max U (c_{t}^{*}, c_{t}) + β V^{R} (k_{t + 1}^{*}, k_{t + 1}, D_{t + 1}), (19)

subject to

\begin{matrix} k_{t + 1}^{*} = (1 - δ) k_{t}^{*} + I_{t}^{*} \\ k_{t + 1} = (1 - δ) k_{t} + I_{t} \\ D_{t + 1} = D_{t} (1 + r) + c_{t}^{*} + I_{t}^{*} - f (k_{t}^{*}) + P_{t} [c_{t} + I_{t} - f (k_{t})] \\ D_{t + 1} \leq {\bar{D}}_{t + 1}, \end{matrix}

where $\bar{D}$ represents the ceiling on foreign debt faced by the country. As before, the credit ceiling is obtained from

V^{R} (k, k *) = V^{R} (k, k *, \bar{D}) \Leftrightarrow \bar{D} h (k, k *) . (20)

From equations (18)–(20) we can compute the effects that capital accumulation in each sector has on the country’s credit ceiling. These effects are given by

h_{k}^{' *} = \frac{V_{K}^{R} - V_{K}^{D}}{{- V}_{D}^{R}} (21)

and

h_{k}^{'} = \frac{V_{k}^{R} - V_{k}^{D}}{- V_{D}^{R}} . (22)

Note that V_k* and V_k are the marginal utility values of a unit of capital in the corresponding productive sector.¹⁵ In each sector, therefore, the credit ceiling will be an increasing function of the capital stock if and only if the marginal value of capital is larger under the repayment option than under the default option. (Note that $V_{D}^{R}$ is negative.) In other words, creditors will be more willing to extend credit if the country invests in projects that make the repayment alternative more valuable than the default alternative.

An analytical derivation of the signs of the derivatives of the credit-ceiling function is, in fact, quite complex. The relative sizes of investment q s are compared in two different optimization problems (repayment and default), which display different interest rates (marginal rates of substitution in consumption). However, there is a strong presumption that—as in the two-period case—the credit ceiling is an increasing function of capital in the export sector and a decreasing function of capital in the import-competing sector. Consider the effect of an additional unit of investment in the import-competing sector. In the event of default the country is assumed to suffer a terms of trade deterioration; therefore, the value (measured in terms of the true consumer price index) of its capital stock in the import-competing sector rises by a discrete jump, θ. If the country repays, however, the value of its import-competing capital remains constant. This suggests that the gain from an additional unit of capital in the import-competing sector is larger in the case of default than it is under repayment. Exactly the opposite holds for capital in the export sector. The larger the export sector is, the larger is the loss resulting from the terms of trade deterioration should the country default. Hence, the utility value of export capital is greater under repayment than it is under default. Thus, if

V_{k}^{D} (k, k *) > V_{k}^{R} (k, k *, D)

and

V_{k *}^{R} (k, k *, D) > V_{k *}^{D} (k, k *), (23)

the credit-ceiling function is

h_{k *} (k, k *) > 0

and

h_{k} (k, k *) < 0;

that is, the credit ceiling is an increasing function of capital in the export sector, but a decreasing function of capital in the import-competing sector.

Once again, debt repudiation will never take place in this framework. This is because rational creditors foresee the debtor country’s incentives to repudiate its foreign debt and restrict credit in such a way that the debtor country always finds repayment preferable to default. Consider now the optimal plan for the debtor economy given the existence of the credit-ceiling function h(•) described above. The first-order conditions for that problem are given by

U_{c *_{t}} = - β V_{D_{t + 1}}^{R} (24 a)

U_{c_{t}} / P_{t} = - β V_{D_{t + 1}}^{R} (24 b)

V_{k *_{t + 1}}^{R} = - V_{D_{t + 1}}^{R} (24 c)

V_{k_{t + 1}}^{R} / P_{t} = - V_{D_{t + 1}}^{R}, (24 d)

where V_{D_I+1} is shorthand for $V_{D}^{R} (k_{t + 1}^{*}, k_{t + 1}, D_{t + 1}),$ etc. Also, the following envelope theorems can be proved:

V_{{k *}_{t + 1}}^{R} = U_{c *_{t + 1}} [f_{k *_{t + 1}} + (1 - δ)] + μ_{t + 1} h_{k *_{t + 1}} (24 e)

V_{k_{t + 1}}^{R} = U_{c *_{t + 1}} [f_{k_{t + 1}} + (1 - δ)] + μ_{t + 1} h_{k_{t + 1}} (24 f)

V_{D_{t + 1}}^{R} = U_{c *_{t + 1}} (1 + r) - μ_{t + 1}, (24 g)

where μ is the Lagrange multiplier on the external credit ceiling for the economy. When the credit ceiling is not binding, μ is equal to zero, and the above conditions imply the standard optimal rules for consumption and investment:

U_{c *_{t}} = β (1 + r) U_{c *_{t + 1}} (25 a)

U_{c_{t}} = β (1 + r) \frac{P_{t}}{P_{t + 1}} U_{c_{t +!}} (25 b)

f_{k *_{t + 1}} = r + δ (25 c)

f_{k_{t + 1}} = r + δ . (25 d)

The marginal utility of consumption grows at a rate inverse to the world interest rate, and the marginal product of capital equals the interest plus depreciation rates in each sector.

Once the credit constraint is binding, however, μ is positive, and the optimal policies must be modified:

U_{{c *}_{t}} = β (1 + r) U_{c *_{t + 1}} + β μ_{t + 1} (26 a)

U_{c_{t}} = β (1 + r) \frac{P_{t}}{P_{t + 1}} U_{c_{t + 1}} + β μ_{t + 1} (26 b)

f_{{k *}_{t + 1}} = (1 - h_{k *_{t + 1}}) S_{t} + h_{k *_{t + 1}} (1 + r) - 1 + δ (26 c)

f_{k_{t + 1}} = (1 - h_{k_{t + 1}}) S_{t} + h_{k_{t + 1}} (1 + r) - 1 + δ, (26 d)

where S_t is equal to U_c*/βU_{c*_t+1}, which we will refer to as the implicit domestic interest rate. Therefore, when the credit constraint is binding, the marginal product of capital in each sector is set equal to a weighted average of the implicit domestic interest rate and the international interest rate, with weights $h_{k}^{*}$ and h_k, respectively. It can be shown that this policy implies a subsidy to investment in the export sector relative to the import-substitution sector:

f_{{k *}_{t + 1}} - f_{k_{t + 1}} = [S_{t} - (1 + r)] (h_{k_{t + 1}} - h_{k *_{t + 1}}) . (27)

Since the interest rate in the credit-constrained economy must be greater than the international interest rate, the first term on the right-hand side in square brackets is positive, and since h_k* > 0 and h_k < 0, the last term on the right-hand side is negative. These signs imply that there is a bias toward greater investment in the export sector relative to the import sector. The reason is, once again, that altering the investment mix of the economy can relax the credit ceiling, which increases welfare in a credit-constrained country.

The Decentralized Economy

The decentralized economy is organized in the same way as the decentralized economy in the previous section. The actions of consumers and firms will be equivalent to those that result from maximizing utility in the following problem:

V^{C} (k_{t}^{*}, k_{t}, D_{t}) = \max \sum_{t = 0}^{\infty} β^{t} U (c_{t}^{*}, c_{t}) (28)

V^{C} (k_{t}^{*}, k_{t}, D_{t}) = \max U (c_{t}^{*}, c_{t}) + β V^{c} (k_{t + 1}^{*}, k_{t + 1}, D_{t + 1}),

subject to

k_{t + 1}^{*} = (1 - δ) k_{t}^{*} + I_{t}^{*}

k_{t + 1} = (1 - δ) k_{t} + I_{t} D_{t + 1} = D_{t} (1 + r^{D}) + c_{t}^{*} + I_{t}^{*} - f (k_{t}^{*}) + P_{t} [c_{t} + I_{t} - f (k_{t})] - (r^{D} - r) D_{t} D_{t + 1} \leq {\bar{D}}_{t + 1} .

As before, the constraint $\bar{D}$ and the lump-sum rebate of financial intermediation profits are exogenous to the atomistic agent, whose decisions are made according to the domestic interest rate r^D. Therefore, the consumption and investment rules in the decentralized economy are standard:

U_{c *_{t}} = β (1 + r^{D}) U_{c *_{t + 1}} (29 a)

U_{c_{t}} = β (1 + r^{D}) \frac{P_{t}}{P_{t + 1}} U_{c_{t + 1}} (29 b)

f_{k *_{t + 1}} = r^{D} + δ (29 c)

f_{k_{t + 1}} = r^{D} + δ . (29 d)

It is evident that the decentralized economy does not bias investment toward the export sector and away from the import-competing sector.

Comparing the investment rules of the planned economy to those of the decentralized economy is difficult, because the implicit domestic interest rates (which we have defined as being equal to the intertemporal marginal rates of substitution of consumption) are different.¹⁶ However, in the steady state, the implicit domestic interest rate is equal to β for both economies, which makes the comparison easier. In a steady-state position, investment in the planned economy will be carried out according to

f_{k *}^{R} = (1 - h_{k *}) β^{- 1} + h_{k *} (1 + r) - 1 + δ (30)

and in the decentralized economy,

f_{k *}^{C} = β^{- 1} - 1 + δ, (31)

which means that

f_{k *}^{R} - f_{k *}^{C} = (1 + r - β^{- 1}) h_{k *} < 0

h_{k *} > 0, (32)

and symmetrically,

f_{k}^{R} - f_{k}^{C} = (1 + r - β^{- 1}) h_{k} > 0

h_{k} < 0. (33)

The decentralized economy fails to take into account the effects of investment policies on the country’s credit ceiling. Accordingly, it fails to recognize the additional benefits of investment in the export sector and the negative externalities of investment in the import-competing sector, and it undertakes too little investment in the export sector and too much in the import-substitution sector.

Simulation Results

In order to confirm that the credit ceiling is indeed an increasing function of capital in the export sector but a decreasing function of capital in the import-competing sector, we undertook some numerical simulations. In essence, the simulation algorithm follows the steps outlined in Appendix II. Starting with the steady-state value functions, the repay and default value functions are recursively computed until stationary investment and borrowing rules are obtained. These policy rules are calculated as functions of the inherited state variables—that is, on a grid of possible (k*, k, D) combinations. The numerical grid used consisted of 8,000 (20 x 20 x 20) points, and 5 iterations were performed to obtain convergence of the functions. In total, therefore, some 8,000 nonlinear optimization problems had to be solved for each iteration. Given initial capital stocks and debt level (and assuming that the initial debt is not so high that the country defaults immediately) the stationary policy rules trace the dynamic path of the economy.

The parameterization of the model was done in the following way. Production functions were taken to be Cobb-Douglas; the utility function was chosen to be logarithmic; investment was assumed to be subject to quadratic costs of adjustment (see Abel (1979) and Hayashi (1982)), so that I units of investment cost I[1 + ψ/2(I/k)] units of the good. (See Appendix II for specifications of the model and parameter values.)

Figure 2 shows the time path of capital stock in both the planner’s economy and the decentralized economy. As is evident, the latter undertakes too much investment in the import-competing sector and too little in the export sector. Figure 3 graphs the credit ceiling h(•) as a function of the capital stock in each sector; it is an increasing function of the

Figure 2.

Capital Stock in Two-Sector Economy

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A006

export sector capital, k, and a decreasing function of the import sector capital, k*.¹⁷

It is remarkable that the difference between the optimal capital stocks and those chosen by the decentralized economy is substantial despite the fact that the default penalty involves only a 20 percent deterioration in the terms of trade. The capital stock in the export sector of the optimally planned economy is 50 percent higher than the capital stock in the import-competing sector; in contrast, the decentralized economy chooses the same capital stock in each sector.¹⁸ As a result, steady-state gross domestic product (GDP) is almost 17 percent higher for the optimally planned economy, and the maximum debt level is 20 percent greater. The simulation of the two-sector model thus shows that the optimal policy intervention requires a subsidy to investment in the export sector and a tax on investment in the import-competing sector.

Figure 3.

Credit Ceiling

(As a function of import and export sector capital)

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A006

IV. Conclusions

In this paper we have considered the choice of allocation of investment for a debtor country facing a ceiling on the amount of foreign debt it can accumulate. This ceiling, which is imposed by creditors to prevent default, is the highest level of foreign debt at which the debtor country prefers to repay its obligations rather than commit default and suffer the ensuing economic sanctions. We have showed, in a two-period framework, that it is optimal for the debtor country to create a more open economy by favoring investment in the export sector over investment in the import-competing sector. The reason is that a more open economy is more sensitive to trade sanctions and therefore less likely to default on its foreign debt. Rational creditors recognize this fact, which leads to a higher credit ceiling for the country, providing an additional return to the reallocation of investment toward export-producing activities.

This basic result was extended to an infinite-horizon model. Although the conclusions arising from this exercise are based only on a plausible conjecture and a numerical simulation, there does not appear to be any obstacle to the extension of the basic result to infinite-horizon cases.

Some fairly direct policy implications can be extracted from the above result. Given that country risk (in terms of the credit supply available to the country) is basically an externality, individual investors would not benefit from contributing to a more open economy. Therefore, they would undertake investment in such a way as to equalize marginal returns in both productive sectors, but such behavior would impose an overly stringent credit constraint on the country. Policy should therefore be directed toward expanding the export sector, because lower returns to it are compensated by a larger credit availability. This objective could be achieved either by subsidizing capital in the export sector or taxing capital in the import-competing sector and providing the corresponding lump-sum compensations.

Another implication arising from this study is related to a longstanding debate within development economics concerning the relative merits of export-promotion and import-substitution policies—that is, those policies directed toward the outward or inward orientation of a developing economy. The foreign debt problem adds a new dimension to that debate—one that strengthens the case for a more open economy. We have shown that investment in the export sector generates a higher limit on the amount of foreign financing that rational creditors will be willing to extend to a developing country. This result, therefore, lends support to an export-promotion strategy, because such a strategy fosters higher growth and makes it less likely that foreign credit availability will be a constraint on the country’s well-being.

APPENDIX I Proof of the Relevant Inequalities in Section II

In this Appendix we prove the two inequalities introduced in Section II: $U_{c}^{D} > U_{c}^{R}$ and $U_{c}^{D} > U_{c}^{R}$ . We start by noting that the derivatives in the above inequalities are evaluated at the credit-ceiling function, which means that the utility level is the same for the repay and the default programs. Therefore, we can pose the problem as that of comparing the marginal utility of a good at two points on the same indifference curve (in a two-good world). Consumption of the export good is higher under default, and consumption of the import good is lower under default. We next show that in both cases marginal utility is always lower at the point with higher consumption of the good.

The situation is represented in Figure 4. where the relative price of imports in terms of exports is equal to P under repayment and is equal to θP under default.

Along an indifference curve u (c*, c) = ū, it must be true that

u_{c *} (c *, c) d c * = - u_{c} (c *, c) d c (34)

\frac{d c}{d c *} = - \frac{u_{c}^{*} (c *, c)}{u_{c} (c *, c)} . (35)

Using the above equation, we can write the marginal utility of the export good as a function of its consumption level f(c*) along the indifference curve. The derivative of f(c*) is equal to

\frac{d f}{d c *} = u_{c * c *} - u_{c * c} \frac{U_{c *}}{u_{c}} . (36)

Equation (36) is negative as long as the import-competing good is not an inferior good, which is always the case in a two-good world. Consider the firstorder conditions for the two-good consumer problem:

u_{c} = λ P (37)

u_{c *} = P (38)

c * + P c = I, (39)

where λ is the Lagrange multiplier associated with the budget constraint, and I is the level of income and expenditure. Differentiation of (37)-(39) produces

[\begin{matrix} u_{c c} & u_{c c *} & - P \\ u_{c * c} & u_{c * c *} & - 1 \\ P & 1 & 0 \end{matrix}] [\begin{matrix} \begin{matrix} d c \\ d c * \end{matrix} \\ d λ \end{matrix}] = [\begin{matrix} \begin{matrix} 0 \\ 0 \end{matrix} \\ d I \end{matrix}] . (40)

Figure 4.

Comparison of Default and Repay Utilities

Citation: IMF Staff Papers 1989, 004; 10.5089/9781451930757.024.A006

From equation (40) we can compute dc/dy. which we know is positive:

\frac{d c}{d y} = P (- u_{c c *} + P u_{c * c *}) > 0 \Rightarrow - \frac{u_{c *}}{u_{c}} u_{c c *} + u_{c * c *} > 0, (41)

which implies that (36) is negative. The proof that $U_{c}^{D} > U_{c}^{R}$ follows from the noninferiority of the export good and is entirely symmetrical.

APPENDIX II The Infinite-Horizon Model: Definitions and Results

This Appendix provides a description of the infinite-horizon model and the numerical simulation algorithm.

Specifications of the Simulation Model

The infinite-horizon model developed in Section III had the following specifications: utility function,

\sum_{t = 0}^{\infty} β^{t} [α \ln (c_{t}) + (1 - α) \ln (c_{t}^{*})];

production functions.

f (k) = a K^{γ} g (k *) = a * k^{* γ^{*}};

costs of investment installation,

I [1 + Ψ / 2 (I / k)] I * [1 + Ψ / 2 (I * / k *)];

direct penalty for default,

repay terms of trade P

default terms of trade θP;

world interest rate,

(1+r)

The parameter values were as follows:

\begin{matrix} β = 0.87 & γ = 0.85 & a * = 0.5 \\ Ψ = 2.0 & δ = 0.05 & δ * = 0.05 \\ γ * = 0.85 & Ψ * = 2.0 & P = 0.1 \end{matrix} \begin{matrix} r = 0.05 & α = 0.5 \\ a = 0.5 & θ = 1.2 \end{matrix}

The initial conditions were as follows:

d⁰ = 0

k⁰ = 4.00

= 4.00.

Numerical Simulation Algorithm

In this section we describe how dynamic programming may be used to solve for the time-consistent sequence of borrowing and investment in each sector.¹⁹ Only the solution of the optimally planned economy is described in detail, since the decentralized economy is simply a special case of the planner’s problem. Normal dynamic optimization cannot be used to solve the model because there is a simultaneity problem: the credit ceiling is determined by equating the repay-value function, V^R(•), to the default value function, V^D(•), but to compute the repay-value function, the credit ceiling must be known.

The infinite-horizon model is solved by first considering its finite period analog and then letting the length of the time horizon, T, go to infinity. Suppose, therefore, that the economy has attained its steady-state capital and debt stocks by period T:

k_{T + i} = k_{T} k *_{T + i} = k *_{T} D_{T + i} = D_{T} \forall i \geq 0.

Since the investment decisions are trivial (consisting only of investment to cover depreciation), the value function and the associated investment rules, should the country decide to default, are

i_{T}^{*^{D}} (k_{T}, k_{T}^{*}) = δ k_{T}^{*} i_{T}^{D} (k_{T}, k_{T}^{*}) = δ k_{T} (42)

and

V^{D} (k_{T}, k_{T}^{*}) = \max u (c, c *) / (1 - β), (43)

subject to

f (k_{T}^{*}) + θ P f (k_{T}) - δ k_{T}^{*} - δ θ P k_{T} = c_{T}^{*} + θ P c_{T},

which is a purely static optimization problem. In contrast, if the country decides to service its debts, its stationary policies are to replace capital stocks, to make interest payments on its constant external debt, and to choose consumption optimally:

i_{T}^{* R} (k_{T}, k_{T}^{*}, D_{T}) = δ k_{T}^{*} i_{T}^{R} (k_{T}, k_{T}^{*}, D_{T}) = δ k_{T} D_{+ 1 T}^{R} (k_{T}, k_{T}^{*}, D_{T}) = r D_{T} (44)

and

V^{R} (k_{T}, k_{T}^{*}, D_{T}) = \max u (c, c *) / (1 - β) (45)

subject to

f (k_{T}^{*}) + P f (k_{T}) - r D_{T} - δ k_{T}^{*} - P δ k_{T} = c_{T}^{*} + P c_{T} .

Equating the two value functions determines the credit ceiling for T:

V_{T}^{R} [k_{T}, k_{T}^{*}, h_{r} (k_{T}, k_{T}^{*})] = V_{T}^{D} (k_{T}, k_{T}^{*}) . (46)

Therefore, if and only if D_T exceeds h_T(k_T $k_{T}^{*}$ ) will the country default. It is simple to prove, using standard revealed preference arguments (and the assumption that u(•) is strictly increasing), that V^R(•) is always strictly monotonically decreasing in D. Hence, the repay value function can always be inverted to obtain the credit ceiling.

Now consider a hypothetical period T – 1. The default optimization problem is

V_{T - 1}^{D} (k_{T - 1}, k_{T - 1}^{*}) = \max u (c_{T - 1}, c_{T - 1}^{*}) + β V_{T}^{D} (k_{T}, k_{T}^{*}), (47)

subject to

k_{T} = (1 - δ) k_{T - 1} + i_{T - 1} k_{T}^{*} = (1 - δ) k_{T}^{*} + i_{T - 1}^{*} c_{T - 1}^{*} + θ P c_{T - 1} + i_{T - 1}^{*} + θ P i_{T - 1} = f (k_{T - 1}^{*}) + θ P f (k_{T - 1}) .

The repay case is given by

V_{T - 1}^{R} (k_{T - 1}, k_{T - 1}^{*}, d_{T - 1}) = \max u (c_{T - 1}, c_{T - 1}^{*}) + β V_{T}^{R} (k_{T}, k_{T}^{*}, d_{T}), (48)

subject to

k_{T} = (1 - δ) k_{T - 1} + i_{T - 1} k_{T}^{*} = (1 - δ) k_{T - 1}^{*} + i_{T - 1}^{*} D_{T} = (1 + r) D_{T - 1} + c_{T - 1}^{*} + P c_{T - 1} + i_{T - 1}^{*} + P i_{T - 1} - f (k_{T - 1}^{*}) + P f (k_{T - 1}) D_{T} \leq h_{T} (k_{T}, k_{T}^{*}) .

The crucial constraint is the last one, the country’s credit ceiling. Since the capital market imposes this ceiling, the country’s inherited debt is always low enough to make repayment the preferred alternative, and the country never defaults.

The value functions for period T – 1 are then equated to obtain the credit ceiling that is imposed on borrowing in period T – 2:

V_{T - 1}^{R} [k_{T - 1}, k_{T - 1}^{*}, h_{T - 1} (k_{T - 1}, k_{T - 1}^{*})] = V_{T - 1}^{D} (k_{T - 1}, k_{T - 1}^{*}) . (49)

The process is repeated recursively for periods T – 2, T – 3,..., until the value functions and optimal policy functions converge to stationary functions:²⁰

[V^{D} (\cdot), V^{R} (\cdot), i^{D} (\cdot), i^{* D} (\cdot), i^{R} (\cdot), i^{* R} (\cdot), D_{+ 1}^{R} (\cdot), h (\cdot)] .

These stationary functions are then used to determine the investment and debt policies that solve the infinite-horizon model.

The algorithm we used obtains a numerical solution for the stationary functions being sought. The functions need to be calculated over a two-dimensional grid in the default case (k, k*), and over a three-dimensional grid in the repay case (k, k*, D). For each point on these grids the nonlinear optimization problem of choosing the next period’s capital stocks and level of debt, k₊₁, , d₊₁, must be solved. The maximization was done using a simple numerical search technique. The grid sizes chosen in the simulation were 20 units per dimension, so that in the repay case some 8.000 optimization problems had to be solved for each iteration T, T–1,..., until convergence.

After the policy functions are obtained via backward recursion, the time path of the economy is simulated forward using these converged policy functions to generate the dynamics. Consider the repay case. Given initial capital and debt k₀, , and D₀, the first-period dynamics of the economy are

k_{1} = (1 - δ) k_{0} + i^{R} (k_{0}, k_{0}^{*}, D_{0}) k_{1}^{*} = (1 - δ) k_{0}^{*} + i^{* R} (k_{0}, k_{0}^{*}, D_{0}) D_{1} = D_{+ 1}^{R} (k_{0}, k_{0}^{*}, D_{0}) .

The values for k₁, $k_{t}^{*}$ D₁ are then fed back into the policy functions to obtain

k_{2} = (1 - δ) k_{1} + i^{R} (k_{1}, k_{1}^{*}, D_{1}) k_{2}^{*} = (1 - δ) k_{1}^{*} + i^{* R} (k_{1}, k_{1}^{*}, D_{1}) D_{2} = D_{+ 1}^{R} (k_{1}, k_{1}^{*}, D_{1}) .

In this manner the entire time series path (k₁, $k_{t}^{*}$ , D₁) is generated; this is the optima) path that the economy will follow and it is plotted in Figure 2. By construction, since the appropriate credit ceiling has been imposed, the default-value function never exceeds the repay-value function. In equilibrium the only possibility for default occurs if the initial debt stock D₀ exceeds the credit ceiling h(k₀, $k_{0}^{*}$ ), in which case the country would default in the first period.

The dynamics of the decentralized economy are obtained in a similar manner, except that the credit ceiling is taken to be a fixed number while the optimization is being performed. Since agents have rational expectations about the level of the credit ceiling in the decentralized economy, the fixed credit ceiling must represent the maximum debt allowable at the optimally chosen investments. In practice, this was done by first conjecturing a credit ceiling ${\bar{h}}_{τ + 1}$ (in period τ), and then solving for the optimal investment choices and checking that

V_{τ + 1}^{D} (k_{τ + 1}, k_{τ + 1}^{*}) = V_{τ + 1}^{R} (k_{τ + 1}, k_{τ + 1}^{*}, {\bar{h}}_{τ + 1}) .

If the implied credit ceiling at the optimal policies differed from ${\bar{h}}_{τ + 1}$ , then the conjectured credit ceiling was revised and the optimization problem was solved again. The process is repeated until the actual and conjectured credit ceilings coincide.

REFERENCES

Abel, Andrew, Investment and the Value of Capital (New York: Garland, 1979).
- Search Google Scholar
- Export Citation
Aizenman, Joshua (1987a), “Country Risk and Contingencies,” NBER Working Paper 2236 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Search Google Scholar
- Export Citation
Aizenman, Joshua (1987b), “Investment, Openness and Country Risk,” IMF Working Paper 87/72 (Washington: International Monetary Fund).
- Search Google Scholar
- Export Citation
Aizenman, Joshua, and Eduardo Borensztein, “Debt and Conditionality Under Endogenous Terms of Trade,” Staff Papers, International Monetary Fund, Vol. 35 (December 1988).
- Search Google Scholar
- Export Citation
Bellman, Richard, Dynamic Programming (New Jersey: Princeton University Press, 1957).
- Search Google Scholar
- Export Citation
Bertsekas, Dimitri, Dynamic Programming and Stochastic Control (New York: Academic Press, 1976).
- Search Google Scholar
- Export Citation
Blackwell, David, “Discounted Dynamic Programming,” Annals of Mathematics and Statistics, Vol. 36 (1965).
- Search Google Scholar
- Export Citation
Bulow, Jeremy, and Kenneth Rogoff, “A Constant Recontracting Model of Sovereign Debt,” NBER Working Paper 2088 (Cambridge, Massachusetts: National Bureau of Economic Research, 1986).
- Search Google Scholar
- Export Citation
Bulow, Jeremy, and Kenneth Rogoff, “Sovereign Debt: Is to Forgive to Forget?” NBER Working Paper 2623 (Cambridge, Massachusetts: National Bureau of Economic Research, 1988).
- Search Google Scholar
- Export Citation
Cohen, Daniel, and Jeffrey Sachs, “Growth and External Debt Under Risk of Debt Repudiation,” European Economic Review, Vol. 30 (June 1986).
- Search Google Scholar
- Export Citation
Dooley, Michael P., “Buy-Backs and Market Valuation of External Debt,” Staff Papers, International Monetary Fund, Vol. 35 (June 1988).
- Search Google Scholar
- Export Citation
Eaton, Jonathan, and Mark Gersovitz (1981a), “Debt with Potential Repudiation: Theoretical and Empirical Analysis,” Review of Economic Studies, Vol. 48 (April 1981).
- Search Google Scholar
- Export Citation
Eaton, Jonathan, and Mark Gersovitz (1981b), “Poor Country Borrowing in Private Financial Markets and the Repudiation Issue,” Princeton Studies in International Finance, No. 47 (Princeton, New Jersey: Princeton University Press).
- Search Google Scholar
- Export Citation
Eaton, Jonathan, and Mark Gersovitz, and Joseph Stiglitz, “The Pure Theory of Country Risk,” European Economic Review, Vol. 30 (June 1986).
- Search Google Scholar
- Export Citation
Eichengreen, Barry, and Richard Portes, “Debt and Default in the 1930s,” European Economic Review, Vol. 30 (June 1986).
- Search Google Scholar
- Export Citation
Enders, Thomas O., and Richard P. Mattione, Latin America: The Crisis of Debt and Growth (Washington: The Brookings Institution, 1984).
- Search Google Scholar
- Export Citation
Ghosh, Atish R., “Dynamic Reputational Equilibria in International Capital Markets” (mimeographed: Cambridge, Massachusetts: Harvard University (1985)).
- Search Google Scholar
- Export Citation
Hayashi, Fumio, “Tobin’s Marginal Q and Average Q: A Neoclassical Interpretation,” Econometrica, Vol. 50 (January 1982).
- Search Google Scholar
- Export Citation
Kaletsky, Anatole, The Costs of Default (New York: Priority Press, 1985).
- Search Google Scholar
- Export Citation
Kindleberger, Charles P., International Economics (Homewood, Illinois: Irwin Press, 1982).
- Search Google Scholar
- Export Citation
Kreps, David, and Robert Wilson, “Reputation and Imperfect Information,” Journal of Economic Theory, Vol. 27 (August 1982).
- Search Google Scholar
- Export Citation
Krugman, Paul, “Financing vs. Forgiving a Debt Overhang: Some Analytical Notes,” NBER Working Paper 2486 (Cambridge, Massachusetts: National Bureau of Economic Research, 1988).
- Search Google Scholar
- Export Citation
Lever, H., and C. Huhne, Debt and Danger (London: Penguin Press, 1985).
- Search Google Scholar
- Export Citation
Lindert, Peter, and Peter Morton, “How Sovereign Debt Has Worked,” in Developing Country Debt and the World Economy, ed. by Jeffrey Sachs (Chicago: University of Chicago Press, 1989).
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Solow, Robert M., “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, Vol. 70 (February 1956).
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Zamora, Stephen, “Recognition of Foreign Exchange Controls in International Creditors’ Rights Cases: The State of the Art,” The International Lawyer, Vol. 21 (Fall 1987).
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Mr. Borensztein, an economist in the Research Department of the Fund, received his doctorate from the Massachusetts Institute of Technology.

Mr. Ghosh, Assistant Professor at Princeton University, received his doctorate from Harvard University. This paper was partly written during his visit to the Research Department.

The consideration of endogenous terms of trade changes may modify the above recommendation. For a debt model with endogenous terms of trade, see Aizenman and Borensztein (1988).

By contrast, in another popular framework—adopted, for example, by Dooley (1988) and Krugman (1988)—the debtor countries pay back as much as they can afford, given available resources.

This result is consistent with Aizenman’s (1987b) findings. In that paper, investment in the productive sectors with a higher component of imported inputs is favored because it helps improve borrowing conditions.

Walter Wriston, who headed Citibank in the 1970s, is associated with the development of the theory of “sovereign-risk hypothesis.” Speaking in Lausanne in 1981, Wriston is quoted as saying, “Any country, however badly off, will ‘own’ more than it ‘owes’” (Lever and Huhne (1985, p. 53)).

See, in particular, Eaton and Gersovitz (1981b), Enders and Mattione (1984). Kaletsky (1985), and Lever and Huhne (1985).

See Eichengreen and Portes (1986), for example, for a discussion of the sanctions for default in the 1930s.

However, the historical evidence indicates a very long exclusion from international borrowing for defaulting countries. See Eichengreen and Portes (1986) and Lindert and Morton (1987).

The reason is that there is always a way to obtain the same risk diversification through holding assets instead of debts, so that the inability to borrow (because of a past default) does not entail any real cost.

Ghosh (1985) develops a model in which creditors maintain a reputation for being “tough,” à la Kreps and Wilson (1982).

This latter sanction is emphasized by Bulow and Rogoff (1986).

These prices are given in terms of an arbitrary common unit.

It is conceivable that the costs of repudiation also increase with foreign debt (creditors will spend more energy trying to collect or imposing sanctions). However, the only case that makes sense is the one in which the rewards from repudiation increase more than costs; otherwise, the more indebted a country was, the safer a debtor it would become.

Note that the exportable good is being used as numeraire.

At this point, we are abstracting from temporal inconsistencies or monitoring problems that may arise in the borrowing and investment process. In our model, foreign borrowing and investment take place essentially at the same time, although in practice there is some lag between the loan and the execution of investment that might be problematic because the debtor country would have incentives to change the investment plan after drawing the loan.

In the numerical simulations, adjustment costs are introduced to investment, and V_k* and V_k will be equal to Tobin qs, measured in units of marginal utility of the respective good.

However, because the planned economy will be less credit-constrained, its implicit domestic interest rate should be lower.

The different gradients along k and k* reflect the relative price of the two goods, with the price of k*, P, being much lower than that of k, the numeraire. However, a unit of investment in k* costs only P units of k, so that $1 of investment in the export sector tends to increase the credit ceiling by approximately the same amount that $1 of investment in the import-competing sector decreases the credit ceiling.

This is a consequence of the symmetry in the production functions. Since the capital stocks in the planner economy relative to those in the decentralized economy define the targets for optimal policies, the assumption of complete symmetry contributes to expositional clarity.

This algorithm is a straightforward extension of that developed for the onesector nonlinear models of Cohen and Sachs (1986) and Ghosh (1985), which in turn are based on Bellman (1957) and Bertsekas (1976).

Conditions for convergence of this algorithm are given, for example, in Blackwell (1965).

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IMF Staff papers: Volume 36 No. 4

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1989: Issue 004

Publisher:: International Monetary Fund

ISBN:: 9781451930757

ISSN:: 1020-7635

Pages:: 240

DOI:: https://doi.org/10.5089/9781451930757.024

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Figure 1.

The Two-Period Model

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Figure 2.

Capital Stock in Two-Sector Economy

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Figure 3.

Credit Ceiling

(As a function of import and export sector capital)

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Figure 4.

Comparison of Default and Repay Utilities

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Abstract

I. Debt Repudiation: Possible Sanctions

II. Debt and Investment in a Two-Period Model

III. Debt and Investment in an Infinite-Horizon Model

The Decentralized Economy

Simulation Results

IV. Conclusions

APPENDIX I Proof of the Relevant Inequalities in Section II

APPENDIX II The Infinite-Horizon Model: Definitions and Results

Specifications of the Simulation Model

Numerical Simulation Algorithm

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