debt sustainability and overadjustment

World Development, Vol. 17, No. 1. pp. 29-43, 1969. 0305-750x/89 $3.00 + 0.00 Printed in Great Britain. 0 19S9 Pergamon Press plc

Debt Sustainability and Overadjustment

JAIME DE PIN&S* Department of International Economic and Social Affairs, United Nations

Summary. - A simple debt accumulation model based on balance-of-payments identities is analyzed and used to project debt-to-export ratios in Latin America and Africa up to 1990. The fundamentals of debt dynamics are shown to be determined by four ratios: interest rate to export growth, import growth to export growth and the initial debt-to-export and import-to-export ratios. The relevance of the initial conditions and the importance of import growth on debt dynamics are discussed.

Sustainability of the debt in terms of keeping debt-to-export ratios on a declining trend is defined and used to quantify the associated amount of excess import restraint in debtor countries. Two tests are constructed that measure excess restraint (i.e., overadjustment) based on the fundamentals of debt dynamics. Both tests assume that interest rates exceed export growth. The first requires a substantial amount of past adjustment effort: the second does not, but places tighter restrictions on the future commitment that is needed to remain solvent. These tests are applied to Latin America and to Africa both before and after the recent downward oil price shock. Estimates of excess import restraint are reported.

1. INTRODUCTION

Developing countries have encountered severe

credit restraints since the early 1980s. As a result,

non-interest current account deficits have been reduced in both Africa and Latin America. In the case of Latin America, the non-interest current account balance has actually swung into surplus.

The sudden reappearance of credit rationing to many debtor developing countries is presumably based on a deterioration of their creditworthiness in international credit markets. Because of the large financial sums that are involved and the rudimentary state of knowledge about national debt capacity, summary measures such as the debt-to-export ratio have been heavily relied upon to assess creditworthiness.’ A debt-to- export ratio of 2, for example, has often been cited as a critical value that would reestablish creditor confidence for many debtor developing countries.*

If a debt-to-export ratio of 2 were really a threshold for new lending, there might be a good argument for dropping the ratio quickly even in the face of resource rigidities. since it would restore credit flows that have a high rate of return for the debtor. But there is no evidence that a debt-to-export ratio of 2 is a threshold for creditworthiness. Financial markets have regularly lent with much higher ratios and have cut off lending at lower ratios. The debt-to-export ratio could fall to 2 without any new lending taking place.

This is a strong argument for not dropping the debt-to-export ratio rapidly.

Thresholds for the debt-to-export ratio are arbitrary. This is due to the fact that no single number can convey much information about a country’s capacity to repay its debt. The path of the debt-to-export ratio through time. however,

does matter. If the debt-to-export ratio grows without limit. it correctly signals that both the debt, and the balance-of-payments deficits which give rise to it, are unsustainable. Conversely, if

debt-to-export ratios are on a downward trend,

the debt will be sustainable and the debtor country solvent; that is, the debtor will be able to repay its debt.’

To the extent that solvency governs creditworthiness, the fundamentals that determine the dynamics of the debt-to-export ratio will also govern creditworthiness. If a debtor country can keep its debt-to-export ratio on a declining trend,

*The author is an Economic Affairs Officer in the Office of Development Research and Policy Analysis. He would like to ihank his colleagues at DRPA/DI&A and G. Anaviotos, W. Darity, R. Devlin, V. Filatov, A. Fishlow, M. Todaro and j. ViAals for their sugges- tions and comments.. In addition, he would like to thank S. Jan for valuable computing assistance and M. Angunawela for efficient typing.

The views expressed herein are those of the author and do not necessarily reflect the views of the United Nations.

29

30 WORLD DEVELOPMENT

it will be able to repay its debt and should remain creditworthy.

Taking this approach to the problem of creditworthiness and with the advantage of hindsight, this paper suggests that international credit markets have overreacted in the last few years. The severe credit rationing which has been imposed on debtor developin g countries was not warranted by the fundamentals governing debt dynamics. These countries could have borrowed substantially more than they did in the last few years and still have remained solvent. They could have imported significantly more than they did and still have had ample capacity to repay their debt. Indeed, the excess import restraint into which debtor developing countries have been forced is the most serious threat to their ultimate capacity and willingness to repay.

Solvency, however, is not the only aspect that determines creditworthiness. In addition to being able to repay debt, sovereign countries must be willing to repay as well.’ From the latter perspective, “excess import restraint” is the counterpart of rational credit rationing resulting from the existence of repudiation risk. Under this interpreta- tion, excess import restraint implicitly measures the amount of extra credit that should be forthcoming to solvent borrowers. but is not because of the fear of repudiation.’ The reduction of repudiation risk is clearly in the interest of risk- averse creditors and, to the extent that it allevi- ates credit constraints and overadjustment, to debtors as well.

The objective of this paper is to render the concept of overadjustment operational. Excess import restraint, which is synonymous with overadjustment in this paper, is defined as the difference between actual and warranted imports.6 Warranted imports, in turn, are the maximum amount of imports that place debt-to-export ratios on a declining trend. The concept of overadjustment can be used to ask how much imports can grow while keeping the debtor solvent. Im- plicitly, it measures the amount of extra credit that a debtor country could borrow and repay.

In this paper, therefore, overadjustment will be linked to attempts at rapid reductions in debt- to-export ratios. If a rapid drop in the ratio were to restore credit flows, of course, then these attempts should not be considered to be excessive or a type of overadjustment. But since this reward is nowhere in sight, attempts at rapid reductions are considered to be excessive. They certainly are inordinate relative to the effort needed to keep an economy’s debt sustainable, that is, to keep an economy on a slowly declining debt-to-export ratio trend.

In this context, dynamic analysis entails spe-

cifying the relevant balance-of-payments identities and making assumptions about the behavior of economic agents. To keep the model as simple as possible, it will be assumed that all parameters in the identities are exogenous variables. That is, we wilt assume that economic agents will not alter their behavior once it is initially determined. It is well established, however, that certain variables do vary systematically with others. For example, variations in import demand for most developing countries can, to a large extent, be explained by variations in certain pertinent variables, such as the real exchange rate and the level of absorption. These channels of influence are suppressed here. As a result, the findings reported below should only be considered first approximations of the amount of overadjustment involved.’ More detailed analyses could easily be built on the structure provided here.

In Section 2, the fundamentals governing debt dynamics are discussed and recast into a framework that allows easy reference to imports. The stylized facts about Latin American and African debtors are then presented in Section 3 using a diagram which shows when an economy is situated on a downward or an upward debt-to-export ratio trend. Simulations of the debt-to-export ratio and estimates of excess import restraint are reported in Section 4. These estimates are formed using two tests of overadjustment. The first requires a substantial amount of past adjustment effort. The second imposes a strong future commitment on import growth to keep the debt- to-export ratio on a declining trend. Both tests are constructed under the assumption of an un- favorable external environment where interest rates exceed export growth. Some policy implications and caveats of the analysis are briefly noted in Section 5.

2. THE MODEL

Consider the following debt accumulation modeI:

D, = D,_, + CA, (1)

where D is the dollar value of net forei n debt and CA is the current account balance. P Equal tion (1) is the balance-of-payments identity where the capital account and variations in reserves have been consolidated.’ This consolida- tion follows from the fact that a reduction in gross foreign debt which is financed by reserves leaves net foreign debt unchanged.‘” Adding net interest payments to and subtracting them from equation (1) yields:

D,=(l+i,)D,_,+CA,-i,D,_, (2)

DEBT SUSTAINABILITY AND OVERADJUSTMENT 31

The current account balance is the difference between imports and exports of goods and non- interest services, and the difference between interest debits and credits:

CA, = MG, - XG, + MI, - XI, (3)

The last two terms of equation (3) are just net interest payments; thus, equation (2) can be rewrit- ten as:

D, = (1 + i,) D,_, + MC, - XG, (4)

Redefining imports exports of and non-interest MG and as M X, respectively, equation (4) X and ing the X, = + gx,) i, leaves:

(1 + *D,_,+ (1 gm,) M,-I

+ gx,) *--1 (5)

+ gx,)

or

d,=ad,_,+bv,_,-1

where d is the ratio of net debt to exports (of goods and non-interest services); a is the ratio of one plus the interest rate, i, to one plus the growth rate of exports, gx; and where b is the ratio of one plus the growth rate of imports (of goods and non-interest services), gm, to one plus the growth rate of exports; and v is the import-to- export ratio.” By definition, the import-to- export ratio is given by:

v, = b v,-, (7)

Equations (6) and (7) define a system of difference equations. Assuming that a and 6 are both positive and constant, the dynamic system is solved and analyzed in Appendix A where the debt-to-export ratio, d, is shown to be:

d I

= a’d + ” b (6’ - a’) (1 - 0’) -- 0 0 (8)

b-a l-a

Accordingly, the debt-to-export ratio depends on two parameters, a and 6, and on two pre- determined or inherited variables, do and v,. The parameters a and b determine the future evolution of the debt-to-export ratio. The inherited variables d, and v, anchor the projected path of the debt-to-export ratio to given initial conditions.

3. DIAGRAM AND STYLIZED FACTS

Equation (8) can be understood more easily with the assistance of Figure 1 which sets out the locus of points along which a equals one (where the interest rate equals export growth) and where b equals one (where import growth matches ex-

’ /

a.1

2

6-I

3

Zone I: u<I, b<l Zone 2: u>I, b<l Zone 3: u>I, b’l Zonc4: u<l,b>l

Figure 1

port growth). Figure 1 is drawn with export growth on the vertical axis and the interest rate along the horizontal. When a and b are less than one (zone 1 in Figure 1) export growth exceeds both the interest rate and import growth. As a result, the interest payments component and the non-interest current account balance, which jointly determine debt accumulation. will be growing less rapidly than exports. The debt-to- export ratio, therefore, will be placed on a declining trend.

Similarly, when both a and b exceed one (zone 3), the debt-to-export ratio will be explosive. In this case, the legacy from past adjustment efforts, represented by an initial import-to-export ratio v, less than one (i.e. an initial non-interest current account surplus), may keep debt-to-export ratios depressed for a finite period of time. But with import growth exceeding export growth (b > l), the non-interest current account balance will turn into an ever increasing deficit, thereby erasing the initial adjustment effort.

The legacy from any initial import-to-export ratio v, can only exert a continuing influence into the future when import growth matches export growth along the b equal to one locus. The condition b = 1 is a steady-state condition. On this locus the initial import-to-export ratio remains constant and a sufficiently large initial non- interest current account surplus (vO C 1) will place the debt-to-export ratio on a declining trend, even if the interest rate exceeds export

growth (a > 1). Specifically, the initial import-to- export ratio must obey the following inequality:

v, < 1 - do (a - 1) (9)

Inequality (9) is derived from equation (8) by setting the sum of capitalized and export- normalized values (i.e., those terms multiplied


by a’) to be negative.” This will ensure that the debt-to-export ratio will be on a downward trend when b = 1 and a > 1. In particular. the following condition (with b = 1) must hold to obtain inequality (9):

vob 1 d,-- + - <o

b-a 1-a

The meaning of condition (10) is simple. It states that capitalized and export-normalized export revenues (l/( 1 - a)) must be at least as large in absolute terms as the present values of the export-normalized initial debt (d,) and import expenditures (-v,bl(b - a). This will place debt-to-export ratios on a declining trend when N is greater than one.‘s Clearly. the lower the initial import-to-export ratio vn or the lower parameter b. the more likely is condition (10) to hold.

With inequality (9). an upper bound on the import-to-export ratio can be found. Any initial import-to-export ratio v, that is lower than this bound will be said to represent excessive import restraint. Inequality (9) forms the first test (test 1) of overadjustment that is considered in Section 4.

Both zones 2 and 4 of Figure 1 may appear to be areas of ambiguous effects given that parameters a and b are on the opposite side of their locus one values. Nonetheless, zone 4 is not ambiguous since any economy located within this zone would place the debt-to-export ratio on an explosive upward direction. This follows since the non-interest current account is not constant but growing into an ever increasing deficit. For- mally, the only explosive term present in zone 4 (b’) is multiplied by vJ(b - a), which is positive and hence upwardly explosive.

Zone 2 in Figure 1, however, is ambiguous. The explosive and opposite forces which are at work in condition (10) are fully operative in zone 2. In particular, export revenues tend to drive the debt-to-export ratio down, whereas the capitalized and export-normalized values of the initial debt and import revenues tend to drive it up. A sufficiently restrictive import growth rate, therefore, can be derived from condition (10) to place the debt-to-export ratio on a declining trend even if the interest rate exceeds export growth and even if the initial import-to-export ratio is greater than one (i.e. an initial non-interest current account deficit). In particular arameter b must obey the following inequality: ;9

az bc -

z - v, (11)

where z = d, + l/( 1 -a). With inequality (11). an upper bound on the trade balance parameter b can be found. Any trade balance parameter b that is lower than this bound will be said to represent excessive import restraint. Inequality (11) forms the second test (test 2) of overadjustment taken up in Section 4.

From the empirical point of view. zones 2 and 3 in Figure 1 have been the -most relevant for debtor developing countries in the last few years. Interest rates have certainly been higher than export growth during this period. thus placing countries in either zone 2 or 3. Since interest rates have exceeded export growth (a > 1). explosive pressure has been exerted on the debt- to-export ratio. But whether this fundamental external force is sufficient to place the debt-to- export ratio on an explosive upward path, which is unsustainable, depends on import growth. In particular, if import growth is sufficiently restrictive. that is, if inequality (11) holds. the debt-to- export ratio will be declining in zone 2. In fact, so long as import growth is below the rate of interest (that is, as long as b < a) and inequality (11) holds, an economy situated in zone 3 will also have a declining debt-to-export ratio. Explosive zone 3, however, is a region where the non- interest current account deficit is constantly increasing. For this reason, it will be ruled out as a viable location for a solvent economv.‘”

In 1984. Latin America was located’in zone 2 in Figure 1 and exerted downward force on the debt-to-export ratio.” This pressure was re- inforced by a past legacy of substantial adjustment effort (v, = 0.73). Africa in 1955 was also in zone 2. The fact that it did not have an initial import-to-export ratio less than one meant that import growth had to be lower than export growth to immediately place the continent on a downward debt-to-export ratio trend. Latin America in 1985, however, slipped down into zone 3. This was due to a sharp deterioration in the net energy exporters’ trade balance parameter b (b shifted from 1.05 to 1.18). Latin American net energy importers, on the other hand, remained in zone 2.

4. SIMULATIONS AND MEASUREMENT OF OVERADJUSTMENT

In this section, illustrative simulations of debt- to-export ratios and estimates of excess import restraint are reported. A more complete tabula- tion of findings is provided in Appendix B. The data used in all these exercises are found in Appendix C.

One noteworthy feature of data used in this

DEBT SUSTAINABILITY

section is that they are arranged in a way that breaks with past practices.” Traditional analyses have focused on the gross external debt to exports of goods and total services ratio. But if a model of debt accumulation is to measure accu- rately a country’s solvency, i.e., its capacity to repay debt, the appropriate concept that should be used is the net external debt to exports of goods and non-interest services. Net debt corresponds to the net interest payment obligation, which is the true burden that a country faces. Use of exports of goods and non-interest (as opposed to total) services, while not indispensable. facili- tates dynamic analysis and rids the model of an inherent bias in debt-to-export ratios.‘* The traditional measure of gross debt to exports of goods and services is recorded in the data tables of Appendix C next to the ratio of net debt to exports of goods and non-interest services analyzed in this paper.

Table 1 presents projected values of the debt- to-export ratio derived from equation (8). The first set of entries is for Latin America with start- ing values from 1984. The initial debt-to-export ratio is 2.22 and the import-to-export ratio is 0.73. Accordingly, if import growth were to match export growth (b=l). the debt-to-export ratio would be on a downward trend, even when interest rates exceed export growth by a sizable amount. This situation is confirmed in Table 1. Given the legacy from past adjustment efforts, if b were kept instead at a value of 1.05 (where import growth exceeds export growth by approximately 5% and if n were kept at a value of 1.04

AND OVERADJUSTMENT 33

(where the interest rate exceeds export growth by approximately A%, Latin America would still ex- perience falling debt-to-export ratios until 1988. At that time. however. the explosive force implied by keeping import growth above export growth (and more to the point, keeping import growth above the interest rate) would place Latin America in an increasingly unsustainable situation and render it insolvent.

Despite the significant amount of downward force exerted on debt-to-export ratios in 198-t. Table 1 also records the deterioration which occurred in Latin America following a sharp con- traction in world demand (and, therefore. in export growth) and a rapid, and unwarranted. expansion of imports in 1955. As noted. this unwarranted expansion of imports was due to net energy exporters, not to importers. The initial conditions in 1985 reflected the impact of these two shocks. In particular, the initial conditions worsened. Debt-to-export ratios jumped to 2.41 and the initial import-to-export ratio rose to 0.76. Nonetheless. Table 1 shows that if Latin America does not exceed warranted imports (uhich could be attained in this case by matching import and export growth), it would be on a declining debt- to-export ratio trend even if interest rates con- tinued to exceed export growth by as much as 6% forever. Barring an unexpected and significant shock, Latin America was clearly solvent from the vantage point of 1985.

The sensitivity to external conditions is es- pecially notable in Africa. As Table 1 shows, interest rates must be below export grovvth (a < 1)

Table 1. Debt-to-export ratios. 19S6-90

b a 1986 1987 1988 1989 1990

(Latin American projections given 1984 initial values: Cr,, = 2.22. v,, = 0.73) 1.0 1.02 1.76 1.52 1.27 1.03 0.77

1.04 1.84 1.64 1.43 1.22 0.99 1.06 1.93 1.77 1.60 1.43 1.24

1.05 1.04 1.95 1.87 1.83 1.83 1.88

(Latin American projections given 1985 initial values: n,, = 2.41, v,, = 0.76) 1.0 1.02 2.22 2.02 1.82 1.62 1.42

1.04 2.26 2.12 1.96 1.80 1.64 1.06 2.31 2.21 2.11 1.99 1.85

(African projections given 1985 initial values: d, = 1.37. v,, = 1.01) 1.0 0.99 1.37 1.36 1.35 1.35 1.34

1.00 1.38 1.39 1.39 1.40 1.41 1.01 1.39 1.41 1.4-l 1.46 1.48

0.95 1.08 1.44 1.46 1.44 1.38 1.27

Source: Projections derived from equation (8) using data reported in Appendix C.


for Africa as a whole to remain solvent when import growth matches export growth (b = 1). But if the region keeps import growth below export growth, by say 5%, it will remain solvent even when interest rates exceed export growth by as much as 8%. This is not to say that African economies should follow such a restrictive policy as implied by b = 0.95. Africa as a whole, however, followed an even more restrictive import growth policy in 1985 as b = 0.91. As a result, a substantial amount of excess import restraint was recorded in an overall solvent continent.

Turning to the measurement of overadjustment, Table 2 summarizes the findings for Latin America in 1984, 1985 and 1986 following the plunge in the price of crude oil by 40%. These Tables are based on test 1, which is derived from inequality (9). This test is constructed assuming that export growth matches import growth (b =

1). The principal conclusion that can be drawn

from this Table 2 is that Latin America has rea- lized a great deal of overadjustment. In all cases, even for net energy exporters following the 1986 oil price shock, imports could have been substantially larger than they were and still have kept debt-to-export ratios on a declining trend.lY

Table 3 reports measurements of overadjustment for Africa in 1985 and for African net energy importers in 1986.“‘This table is based on test 2 which is derived from inequality (11).

The main finding of Table 3 is that Africa has also experienced overadjustment. For example, in 1985 Africa could have imported US $5 billion more than it did and still have remained solvent. Similarly, when more reasonable rates of import growth are allowed for net energy importers in 1986 (say 9%) than those that prevailed in 1985 (-7%), the amount of excess import restraint is reduced to a small but still positive amount. The key to remaining solvent in the African case is to keep the parameter b slightly below one (and more precisely, below the critical values reported in Appendix Tables B8 and B9). That is, import

Table 2. Latin American overadjustment based on lesl I

a 1984 1985 1986 (millions of US dollars)

1.02 26,460 20.920 13,790 1.04 21,330 15,630 8,400 1.06 16,210 10.330 3,010

Source: Estimates derived using inequality (9) and data reported in Appendix C.

Table 3. African overadjustment based on test 2

a 1985 1986’ (millions of US dollars)

1.01 6,150 200 1.02 6,110 160 1.03 6.060 110 l.M 5,990 40

Source: Estimates derived using inequality (11) and data reported in Appendix C. *African net energy importers.

growth rates should be held marginally below export growth. Since Africa does not have a sizable legacy of past adjustment effort as Latin America has, however, the repercussions of a large downward oil price shock warrant a sizable reduction in import growth for African net energy exporters in 1986.

5. POLICY IMPLICATIONS AND CAVEATS

Tables 2 and 3 demonstrate that there has been a great deal of excess import restraint by both test 1 and test 2 criteria. The implication is that if additional finance were forthcoming. imports could be larger while still keeping debt-to-export ratios on a declining trend. So long as debt-to- export ratios are on a declining trend, the debtor country is solvent and will be able to repay its debt. From a pure solvency perspective, therefore, it should remain creditworthy.

To the extent that solvency is the real concern, there has been a great deal of unnecessary adjustment or overadjustment. Moreover, to the extent that imports have been less than warranted, the economic growth of debtor developing countries has, at least in part, been compromised. The future growth path of these economies is now less than what it might have been.

As noted in the introduction, however, solvency is not the only real concern. The fact that internationally concerted loans do not have the same degree of enforceability as nationally contracted debt affects credit availability. In particular, sovereign countries may be unwilling to repay, which raises the spectre of repudiation and credit rationing.

Aware of these aspects, most developing country debtors have advocated cooperative solutions to the debt problems that arose in 1982. The Cartagena process is an example of this cooperative behavior.*’ Developed country

DEBT SUSTAINABILITY AND OVER.ADJUSTMENT 35

creditors have also sought cooperative solutions. Among these, the Baker plan’s emphasis on growth reflects a basic shift in attitude away from pure belt-tightening and overadjustment. Had this plan or other more ambitious cooperative programs been operative in 1985, significant

losses to world trade could have been avoided.2’ The measurement of excess import restraint only partly reflects these losses. Based on this concept, however, Latin America and Africa could have easily expanded their imports by US $25 billion more than in 1985 and remained solvent.

A second caveat is that an Ed-posf experiment has been conducted here. But if one is to use this framework in a forward looking manner uncertainty in the parameters would have to be taken into account. As a general principle, it may not be possible to reach a target or critical import-to- export ratio v or parameter b in the presence of uncertainty. A cushion might then be needed to ensure that a debtor will remain solvent. As measured by excess import restraint, however,

the actual cushions in place in Latin America are too large. For example. even after an unexpected plunge in oil prices of 40%. net energy exporting Latin American countries remained solvent as a group. The net energy importers of Latin America are also solvent and they have been steadily increasing their excess import restraint since 1984; they have not done this voluntarily, but as a consequence of credit rationing.‘3 Over- reaction on the part of financial markets has had a natural counterpart in the overadjustment of debtor developing countries.

With uncertainty and the need for buffers, however, Africa cannot be said to demonstrate much in the way of overadjustment. Indeed, a marginal criterion (test 2) has to be employed to find evidence of overadjustment in Africa. This is a reflection of the sensitivity of Africa to external shocks and another way of showing the inappro- priateness of non concessional lending to Africa as a whole at its current level of development.

NOTES

1. See Dornbusch and Fischer (1985).

2. See Cline (1985) and Morgan Guaranty (various issues in 1983 and 1984).

3. Exports of goods and non-interest services will be used to measure developing country revenues. The possibility of repaying net debt by a sale of domestic assets that are internationally tradable is excluded due to the potentially large deterioration of terms of trade that might accompany the transfer. See Diaz Alejandro (1983).

3. See Gersovitz (1985) and Eaton, Gersovitz, and Stiglitz (1986).

5. The existence of many lenders instead of one large creditor might also give rise to liquidity constraints to recognized solvent borrowers. See Cooper and Sachs (1985).

6. Actual imports are assumed to be less than or equal to warranted imports.

7. In estimating overadjustment for each sequence of simulations, the initial values of the model were reset to the selected year of measurement, thereby minimiz- ing departures from the actual evolution of variables.

8. See Avramovic er al. (1964) and Dornbusch and Fischer (1985).

9. For most countries considered in this paper, trans- fers are small and do not significantly alter the conclu- sions. Direct foreign investment, which reduces the

debt financing requirement of a given current account deficit and is a significant, albeit depressed. component for some of the countries in the sample. is notoriously difficult to predict. Were direct foreign investment in- cluded, it could be deducted from imports of goods and non-interest services, thereby expanding the estimates of excess import restraint reported below.

10. See Virials (1985).

11. If debt is divided by exports of goods and Iornlser- vices then the debt-to-export ratio is artificially biased downward and. more importantly, b ceases to be solely a function of the growth of imports and exports. Then b becomes a function of interest rates and previous period levels of imports and exports as well. Moreover, the partial derivative of b with respect to interest rates would vary from being positive to negative as the non-interest current account shifts from surplus to deficit. These complications, which affect the dynamic analysis. can be avoided by simply dividing debt by exports of goods and non-inreresr services as is done here.

12. See Dornbusch (1985) and Simonsen (1985) for the continuous time analog of the discrete specification of inequality (9). Cohen (1985) also presents an ana- logous expression from which a solvency ratio is derived.

13. Condition (10) can be applied when both a and b are greater than one, but b is less than a (import growth less than the interest rate). This means that part of zone 3 can be constrained via equation (3) to keep the debt- to-export ratio on a declining trend. This is the

36 WORLD DEVELOPhlENT

rectangular portion bounded by the n = b and b = 1 lines and the horizontal axis.

11. See Appendix B for conditions needed to place the debt-to-export ratio on an immediate downward trend.

1.5. Clearly, b < 1 is also unsustainable in the long run since it means that the non-interest current account will turn into an ever-increasing surplus. But only a tempor- ary sacrifice may be needed to keep a debtor country solvent. Once the non-interest current account surplus is sufficiently large, that is. once inequality (9) is reached, import growth can be raised to its steady-state level equal to export growth (b = I).

16. See Appendix C for Latin American and African data.

17. See ViAals (19SS).

18. See note 11.

19. Projections for 1986 were constructed assuming growth rates of exports, imports and the interest rate of 8%. 7% and 9% for Latin American net energy importers and - 17%. 0% and 9% for Latin American net energy exporters. See Appendix Tables B6 and 87 for estimates of overadjustment for Latin American net energy importers and exporters in 1986.

20. Projections for 1956 were constructed assuming growth rates of exports, imports and the interest rate of 10%. 9% and 5% for African net energy importers.

21. See Massad (19Sj).

22. See United Nations (1986) for the Committee for Development Planning’s view of how to inject a development dimension into the Baker Plan.

23. Events in Brazil. however. might lead to revised estimates for 1986 for Latin American net energy importers. That is. there seems to be mounting evidence that Brazil exceeded the warranted growth path of imports in 1986, much like Mexico did in 1985 before the oil price decline.

21. See Domar (1950).

25. See references in note 12.

26. When n and b are less than one. it is easy to show that the country will converge to a net creditor position equal to -l/(1 - u). When a and b are both greater than one. it may still be possible to keep debt-to-export ratios on declining trend; this can happen when b is less than o and inequality (19) holds. Neither of these two situations, however, should be interpreted as an equi- librium. A steady state can only exist if b = 1.

27. Formally. the explosive exponential term (b’) is multiplied by v,bl(b - a). which under the stated conditions is positive.

28. The denominator will be negative for recent values of n, say between 1 and 1.1. and is likely to remain negative even for higher values of a. So long as v,b is less than (a - b)l(a - 1) as well as inequality (19). then debt-to-export ratios will be placed on an immediate downward trend.

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Dornbusch, Rudiger. and Stanley Fischer, “The world debt problem: Origins and prospects.” Journal of Der,elopmenr Planning. No. 16 (19Sj).

Domar. Evsey, ‘-The effects of foreign investment on the balance of payments,” American Economic Review, Vol. 40 (1950).

Eaton, Jonathan, Mark Gersovitz and Joseph Stiglitz, “The pure theory of country risk,” European Econ- omic Review, No. 30 (1986).

Economic Commission for Latin American and the Caribbean (ECLAC). Preliminary Overview of rhe Latin American Economy 1985 (Santiago: ECLAC. 1985).

Fishlow, Albert, “The debt crisis: A longer perspective,” Journal of Developmenr Planning, No. 16 (1985).

Fishlow, Albert, “Capital requirements for the developing countries in the next decade.” Journal of Development Planning. No. 17 (1986).

Gersovitz, Mark, “Banks’ international lending de- cisions: What we know and implications for future research.” in G. Smith and J. Cuddington (Eds.), Inlernarional Debt and rhe Developing Countries

DEBT SUSTAINABILITY AND OVERADJUSThlENT 37

(Washington, DC: The World Bank. 1985). Hellwig, Martin. ‘Comment.” Europeun Economic

Review, No. 30 (1986). International Monetary Fund. “African debt: Facts and

figures on the current situation” (Washington. DC: IMF, February 1986a).

International Monetary Fund, It’orkl Economic Out- look (Washington, DC: IMF. April 1986b).

International Monetary Fund, Balance of faymen~s Statistics (Washington. DC: I&IF, various vears).

International Monetary Fund. Itttrrnational Financial Statistics (Washington. DC: I&IF, various years).

Malan, Pedro, “Debt. trade and development: The crucial years ahead,” Joilrt~ai of Devrloprnent Plan- ning, No. 16 (1985).

Massad, Carlos, “The debt problem: Acute and chronic aspects,” Journal of Developmetu Planning. No. 16 (1985).

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APPENDIX A: DYNAMICS

Equations (6) and (7) define a system of difference equations. Assuming that a and b are both positive and constant, equation (7) can be solved iteratively as follows:

v, = b v_, = b (b v,_~) = b’ I’,_, v, = b’ v, (12)

Equation (12) is the definite solution of equation 7 where v, is the initial import-to-export ratio. According to equation (12). the representative economy will hold its import-to-export ratio constant in future periods when b = 1. If b > 1, that is, if the growth of imports exceeds exports. then the import-to-export ratio becomes explosive. This situation corresponds to an ever increasing non-interest current account deficit, which becomes unsustainable in the long run. If b < I, then the import-to-export ratio converges to zero. This latter situation, however, is also unsustainable since it means that the non-interest current account deficit, no matter how large it is initially, will turn into an ever increasing surplus.

Equation (6) can also be solved iteratively as follows:

d, =a d,_, + b v,-, - 1

=a (a d,-? + b v,_, - 1) + b (b Y,_?) - 1

=a’d,_, + d-’ (b v,_, - I) + + a(b”-’ v,_, - 1)

+ b’ 18 _ t I -I=

= a’d, + 2 arm’ (b’ v,> - I) = I=,

(b’ - a’) (1 - a’) d, = a’ d, + v,, b--- - ~

(b - a) (I - a) (13)

Equation (13) is the definite solution of equation (6) where d, is the initial debt-to-export ratio. To under- stand equation (13). it is useful to consider special cases. For example, if the economy is to avoid having an ever increasing non-interest current account balance

in the long run. then b must equal one. This is a necess- ary condition for the existence of a steady state. In this case, the solution of the difference equatton system is:

v, = v, (1 - a’)

d, = a’ d, + ~ (V” - 1) (14) (1 - a)

Thus. if the initial import-to-export ratio, i’,. is initially equal to one. then:

d, = a’ d,, (15)

Equation (15) is the traditional model used to analyze foreign debt.” According to equation (15). the debt-to- export ratio. d. is explosive when the interest rate exceeds the growth of exports: it is convergent otherwise.

If b = 1 and the import-to-export ratio. v,. is not initially in balance, however. interesting cases arise from equation (14). In particular. consider an initial non-interest current account surplus represented by

v, < 1. Three cases are possible. When u < 1. the economy will become a creditor in the limit. that is,

(V<, - I) li, = ~

(I - a)

If a = 1. an indeterminate form occurs in equation (14). Applying L’HBpital’s Rule, equation (l-l) becomes:

d, = d,, + t (v,, - 1) (16)

Thus, the economy will start out as a debtor. but it will steadily become an ever larger creditor. When the interest rate exceeds export growth. that is. a > 1, d will be explosive. But whether the economy becomes a large debtor or a large creditor in the limit depends on the sign of:

“0 1 d,- -i--

l-a l-a

debt sustainability and overadjustment

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