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The basic macroeconomics of debt swaps.

1. Introduction

The practice of using debt-equity swaps or debt-debt swaps to reduce the debt overhang of developing countries has given rise to an active controversy. Academic economists have contributed to the debate by analyzing the welfare characteristics of such swaps, their potential for reducing net capital outflows, and the degree to which they can reduce the negative incentive effects of a debt overhang. Attention has also been focused on the determination of secondary market prices for debt, and the effects that swaps can have on these prices. See, for instance, the work by Helpman (1987, 1988). Ffrench-Davis (1987), Krugman (1988a, b), Bulow and Rogoff (1988a, b), and Rodriguez (1989).

By contrast, policy-makers in developing countries have tended to evaluate the desirability of these schemes on the basis of their short-term consequences. This is not an indication of short-sightedness, but simply a confirmation that the debt crisis of the 1980s placed countries in a vulnerable situation where day-to-day concerns about prices and exchange rates took on paramount importance. Countries have considered suspending debt-conversion programs because they can be inflationary, because they put excessive pressure on the free market for foreign exchange, or because replacing foreign debt with domestic debt can be expensive.(1) The existing literature offers little systematic analysis of these potential evils or guidance for avoiding them. Exceptions are Alexander (1987a, b) and Mullin (1990).

This paper departs from the existing literature in one fundamental respect. In any debt swap the country must surrender an asset in return for having a liability extinguished. What this asset is and to whom it belongs matters very much. Consider the case of a debt equity swap in which external government debt is exchanged by a claim on the capital stock owned by the domestic private sector. For this transaction to be carried out, the government must somehow gain control of these privately owned resources-whether by confiscating them, taxing them away, or purchasing them with money or bonds.(2)

The literature thus far has sidestepped this issue by assuming that the home country is one consolidated unit (i.e. there is no private-public distinction) or that the government can freely tax away as large a portion of the private sector's assets (or the income flow they generate) as it desired.(3) By contrast, we assume (realistically) that all debt being retired is public while the internationally tradable assets being given away are private, and focus on the implications of different mechanisms for financing the necessary domestic transfer of resources to the government. As a result, swaps involve choices about monetary and fiscal policy, and these choices can have an array of macroeconomic effects. Indeed, several of the perverse effects feared by policy makers are shown to be possible: in certain circumstances swaps can induce current account deficits, a depreciation of the parallel exchange rate, increasing domestic budget deficits, or inflation.

The notion that the choice of debt versus equity financing matters may strike a skeptical chord in economists well versed in the Modigliani-Miller theorem. In the context of the segmented capital markets, external credit rationing and exchange controls that we often find in highly-indebted countries, however, the notion seems plausible indeed. Hence, central to the model employed here is the realistic assumption that the economy functions under dual exchange rates and no private capital mobility. Aside from that wrinkle, the analysis is conducted in the starkest possible setup. We consider an endowment economy where income is fixed. A representative individual maximized utility in the usual way. Expectations are rational, and anticipations of future policies play a central role.

Section 2 begin by modelling a situation in which the official exchange rate (used for commercial transactions) crawls in a predetermined fashion, while the parallel (financial) exchange rate floats freely. There we analyze the implications of the simplest of debts conversion operations: a discounted repurchase of external debt with publicly or privately held foreign assets. We show that, even in a world of perfect foresight, such a repurchase entails a positive wealth effect if the domestic interest rate is above the world rate. This wealth effect leads to an increase in consumption and a current accounts surplus in the transition to a new steady state.

In Section 3 we use this model to analyze the implications of bond versus money financing of a government repurchase of official debts. As long as domestic spending adjust to keep the budget in balance, debt-financed swaps have no real effects beyond those created by the wealth effects. Money-financed swaps, on the other hand, lead to a situation of excess liquidity, a depreciation of the parallel exchanged rate and a current account deficit. Simple numerical calculations are provided in order to assess the likelihood that this outcome will occur.

Section 4 alters the model to develop a focus on budgetary and inflationary factors. There the official rate is also assumed to float, and accumulation of domestic government debts is permitted. There are two possible problems. First, if domestic real interest rates exceed world rates such swaps can be a fiscally expensive proposition. Second, there are limits to how much home debts can be issued. If swaps lead to sustained domestic bond accumulation expectations of how the government will put an end to this process become crucial. We show, among other things, that if agents perceive that the debt will eventually be monetized, inflation will begin to rise as soon as the initial swap is carried out. Once again, numerical examples are provided to assess the plausibility of alternative outcomes.

Finally, Section 5 offers a summary and conclusions.

2. The basic model and a basic swap

An infinitely-lived representative individual, endowed with perfect foresight, maximizes an additively separable utility function

[Mathematical Expressions Omitted]

where c denotes consumption and m = (M/E) real money balances, [delta] is the subjective rate of discount, and u( ) and v( ) possess the usual properties. The economy is small and open, and the one perishable consumption good is perfectly tradable. If we assume that international prices are constant,(4) the commercial nominal exchange rate E becomes equivalent (via purchasing power parity) to the domestic price level, and we can define

[pi] = E/E = inflation rate = devaluation rate > 0 (2)

In this section the commercial exchange rate is a policy variable. It is predetermined at each instant of time, but allowed to depreciate at a constant rate [pi]; this is equivalent to setting a rate of inflation also equal to [pi]. As a result, m becomes a predetermined variable as well, and real balances can only be decumulated or accumulated through a balance of payments deficit or surplus.

Private agents can store their wealth in three domestic assets: money, indexed government bonds (b), and a fixed amount of real capital ([k.sub.o]). Since we assume no international capital mobility, these assets are held by domestic residents only. A unit of capital, whose real price is denoted by q, yields a fixed flow of [rho] units of the consumption good per unit time. Finally, domestic residents also own a fixed stock of international bonds ([f.sub.o]), which can be interpreted as the stock of foreign assets held at the time capital controls were introduced. These bonds are also assumed to have a rate of return of [rho] per unit time.(5) If we further assume that real capital and international bonds are perfect substitutes, it follows that the real price of these bonds is also q, which can therefore be also interpreted as the `parallel' or financial exchange rate.(6) And by arbitrage between international and domestic bonds, it must be true that

r = ([rho] + q])/q (3)

where r is the yield on government bonds, which can be interpreted as the domestic (endogenous) real rate of interest.

Income is exogenous and equal to y per unit time. The flow budget constraint of the representative individual is

b + m = y + rb + [rho]([f.sub.o] + [k.sub.o]) - [pi]m + g - c (4)

where g denotes real government transfers (net of taxes: g can be negative), taken as given by the private agents.

Maximization of (1) with respect to m and c, subject to (4), yields(7)

v'(m) = u'(c)(r + [rho]) (5)

It is easy to show that optimality also requires that(8)

6 = - [u'(c)/u"(c)][r - [delta] (6)

which also can be written as

[Mathematical Expressions Omitted]

Finally, combining (3) and (5) we have

[Mathematical Expressions Omitted]

Equations (4) through (8) completely describe private behavior. The government, on the other hand, can use money creation, domestic borrowing, and lump-sum taxes to finance real government transfers to the private sector and required debt service. Its flow budget constraint is therefore(9)

b = (M/E) = rb + [r*d.sub.o] + g (9)

where M is the stock of nominal money, [d.sub.o] is the stock of foreign debt, and [r.sub.*) is the international interest rate.(10) We assume that the government employs the rule (M/E) = [pi]m. That is, the government issues money only to compensate the public for the erosion of real money balances caused by inflation. With this assumption we arrive at

b = rb + [r*d.sub.o] + g - [pi]m (10)

In order to abstract from fiscal considerations, which take center stage later in the paper, in this section we also assume that g adjusts continuously to ensure that b = 0. Notice that this implies that the government has the power to

tax in order to finance debt retirement. We therefore have

[rb.sub.o] + [r*d.sub.o] + g = [pi]m (11)

Substituting this expression into (4) we obtain

m = y t [rho](f.sub.o] + [k.sub.o]) - [r*d.sub.o] - c (12)

that is to say, the economy can only accumulate real balances if it runs a current account surplus. Terms containing b and g `wash out' since they involve transactions among domestic residents only.

Expressions (7), (8), and (12) constitute a system of three differential equations in m, c, and q, analogous to that developed by Obstfeld (1981). In steady state, the economy is characterized by the following equilibrium conditions:

[Mathematical Expressions Omitted]

Notice that while steady-state equilibrium requires that the domestic rate of interest converge to the rate of discount, there are no forces that ensure equalization of world and domestic real interest rates. Arbitrage determines a relative price for foreign bonds that ensures that the whole domestically held stock [f.sub.o] is willingly held. In steady state, this relative price will be equal to the ratio of yields of domestic and foreign bonds, as equation (13b) shows. However, there is no reason to believe that this ratio ought to be equal to one. If the country is effectively rationed out of international capital markets-the most relevant case for highly-indebted Latin American economies-then the domestic real rate of interest (r) will normally exceed the world rate (r* = [rho]). This is indeed what we assume in what follows, and this realistic assumption, confirmed by the data contained in Table 2, plays a crucial role in the analysis.

Off the steady state the system displays locally stable dynamics, as shown in Appendix 1. The analysis can be conducted in terms of a simple phase diagram in c, m space, because equations (7) and (12) do not depend on q. In turn, equations (13c) and (13d) provide the c = 0 and m = 0 schedules, as they appear in Fig. 1. The upward-sloping paddle path reflects the fact that m and c move together along a perfect-foresight equilibrium path.

We are now ready to consider debt swaps. We will consider cases in which the country's external debt trades at less than par value. Why do discounts on debt occur? In a world of perfect foresight, such a discount must reflect the expectation on the part of traders in the secondary market that at some point in the future the real value of a country's outstanding debt will be reduced - either because the country will default on some portion of its obligations or because some sort of negotiated 'writedown' will be a reed u on. Assume that at some initial time (t = 0) both creditors and debtor come to expect a debt writedown, and that they all agree it will happen T periods later. At that time, a portion of the debt will simply be forgiven or defaulted upon. Clearly, if T = 0, the writedown happens immediately.

Given that the country's external debt yields [r.sub.* ] per unit time, and that this yield is equal to the international rate of interest, the international price of one unit of debt must have initially been equal to unity. That is no longer the case after the writedown is announced: for any time [tau] such that 0 [less than or equal to] [tau] [less than or equal to T, the price of one unit of debt must be below unity." Let T be the time at which a domestic agent repurchases some of this discounted external debt. Clearly, this repurchase can be anticipated or unanticipated by the domestic economy - it could be unanticipated if the government suddenly buys back its debt, or if without previous warning it authorizes previously restricted domestic residents to buy debt abroad.(12)

The different values that T and [tau] can take on give rise to several possibilities, which are summarized in the following matrix:

[TABULAR DATA OMITTED]

In what follows we concentrate in the simplest possible case, contained in the NW cell of the matrix: both the writedown and the repurchase are unanticipated. In other words, the external debt is repurchased as soon as the writedown takes place. Appendix 2 treats the NE case, in which the writedown is anticipated but the repurchase is not.(13)

Consider first the simplest type of unanticipated swap, involving an exchange of the foreign bonds owned by the private sector for government external debt; that is to say, a repurchase of official debt with private resources. Algebraically, [Mathematical Expressions Omitted] where 0 < [alpha] < 1 is the discount: the larger the [alpha], the better off the country is.[14] Notice furthermore that [phi], where 0 < [phi] 1, is the portion of the debt that is subject to a discount.(15) The second equality follows from the assumption that the country repurchases all of the available discounted debt.(16)

In Fig. 2 such a change shifts the m = 0 curve up by the distance

[Mathematical Expressions Omitted]

and leaves the c = 0 schedule unchanged. Since the discount increases the sustainable level of consumption, c jumps on impact and then continues to increase along with m (there is a current account surplus). From (8) and 13b) we know that q must also be increasing in the transition. Since its steady state level is unchanged, it follows that q must have jumped down initially: the news

causes the parallel exchange rate to appreciate, and to remain above its 'normal' level as long as the current account surplus lasts.[.sup.17] Recalling (3), it also follows that the domestic real rate of interest is above its long-run level in the transition.

These results follow from the fact that the writedown constitutes a transfer from the rest of the world to domestic economy, thus creating a positive wealth effect. The swap considered simply captures at once the present value of reduced debt payments forever. The same effects would occur if (i) the private sector surrendered real capital in exchange for the debt; (ii) there were private foreign debt outstanding and domestic residents repurchased it rather than the government's debt; or (iii) official reserves paid interest and the government used them to repurchase its own debt directly. In the absence of a discount ([alpha] = 0), on the other hand, no schedules in Fig. 2 would shift, and all that would take place is a change in the composition of the country's net foreign assets.

The situation described is obviously peculiar, in that the writedown and the swap take place simultaneously. In reality, repurchases typically take place after the debt has been trading at a discount, implying that the expectation of an eventual writedown has been widely shared for some time. In this case, why should a repurchase have any wealth effects at all? Surely, these must have materialized at the initial time t = 0 when both creditors and debtor came to expect a writedown, and not at a time 0 < t when the repurchase actually takes place.

This intuition is correct if foreign lenders and domestic agents discount future flows at the same rate, but this is not the case in the situation we are considering here. As Appendix 2 shows, an unanticipated repurchase that takes place at 0 [less than or equal to] t [less than or equal to] T also has a positive effect on wealth, which leads consumption to jump on impact. We have assumed that the domestic steady-state rate of interest is at least as large as the world rate. Furthermore, it is easily shown that (in the absence of a swap) the domestic rate of interest is above its long-run level during the whole transition between times 0 and T. Hence, domestic agents discount the future debt reduction heavily up until time [tau], and consume less than they would have if their discount rate were r*.(18) Consumption therefore has to jump up at the time of the swap.

The proof of this result is mathematically somewhat cumbersome, so we relegate it to the appendix. The important point is that swaps can have positive wealth effects under a variety of circumstances. The implications of the discussion that follows, based on the special case of t = T = 0, are therefore quite general.

3. Bond versus money-financed swaps

In the real world, domestic residents cannot (or do not wish to) hold government external debt in their portfolio. Therefore, the government will usually buy the debt from private agents and issue some other kind of asset (domestic bonds, money). Does it matter how such repurchases are financed?

Consider first the case in which the government `pays' with its own domestic bonds, so that simultaneously with the other swap we have (1 - [beta]) [delta]d.sub.0] = - [delta]m.sub.0] where 0 < [beta] < 1 is the discount received from the private sector by the government.[19] Such a swap reduces the external interest overhang, but shifts the burden to more expensive domestic debt. But under the chosen assumption that the government automatically adjusts transfers or taxes,[20] this second swap does not add any additional effects on the schedules in Fig. 2, regardless of the value of [beta].

In short, if the government retires its external debt by issuing domestic bonds - under the crucial assumption of automatic budget balancing - there are no real effects beyond those created by the initial wealth effect: the economy will display a current account surplus, accompanied by an initial appreciation of the parallel exchange rate, a bear market for stocks and higher real rates of interest. The dynamics are independent of the discount received by the government.

Consider now what happens when the government chooses to finance its repurchase of debt using money, so that we have (1 - [beta]) [delta]d.sub.0] = [delta]m.sub.0] simultancously with the swap of external debt undertaken by the private sector. In other words, the government carries out an open market operation involving its own debt, and expanding the supply of money. How will the demand for money react to the swaps? From our earlier analysis we know that the discount given to the country affects the new steady state level of consumption and, ceteris paribus, the new steady-state level of money holdings. By totally differentiating (13c) we obtain

[Mathematical Expression Omitted]

where [sigma] [equivalent] u"(c)v'(m)/u'(c)v"(m) is the steady-state elasticity of money with respect to consumption. Combining (14) and (15) we have

[Mathematical Expression Omitted]

where the superscript `d' stands for demand. On the other hand, we know what [delta]m.sub.0] = - (1 - [beta]) [delta]d.sub.0], is the initial increase in the supply of money. The dynamics of the system depend on whether one of these two quantities is larger than the other.

The two possible cases appear in Figs 3a and 3b. If the initial expansion in money supply falls short of the ultimate increase in the demand, then the transition of the system is analogous to the previous case, as shown in Fig. 3a. The real quantity of money jumps on impact (recall prices are predetermined) and so does consumption, putting the system on the saddle path. The country must `accumulate money' by running a current account surplus. This ineans that consumption must undershoot its long-run level and gradually increase along with m thereafter. As before, this elicits a temporary fall in q and an increase in consumption and domestic real interest rates.

If, on the other hand, the initial supply expansion is greater than the long run demand increase, the reverse dynamics takes place. Consumption must overshoot, giving rise to a current account deficit. Furthermore, the parallel exchange rate jumps up on impact (the local currency is devalued) and only returns gradually to its stationary level, leading domestic arbitrageurs to accept a temporary decline in domestic interest rates. This dynamic adjustment process appears in Fig. 3b.

Using (16) we see that this second scenario will occur (that is to say, [delta]m.sub.0] > [delta]m.sup.d]) if and only if

[Mathematical Expression Omitted]

which implies

[Mathematical Expression Omitted]

That is to say, a situation characterized by reserve losses and high foreign excbange prices is more likely to occur when: (i) [sigma] is small, so that money demand is relatively inelastic and does not respond vigorously to the long-run increase in consumption and national income; (ii) [alpha] and [beta] are small, so that the discounts received by the country and the government, respectively, are small; and (iii) the real world rate of interest [r.sup.*] is small, so that the net gain to the country from reducing its foreign debt is small as well.

The size of the discount captured by the government matters very much: a

larger discount means a smaller monetary expansion, and a lower likelihood that this money financing will play a destabilizing role'.[21] Table 1 presents some plausible estimates of this 'stability condition'. The calculation employs observed interest rates and the discounts obtained by four highly-indebted countries, plus some reasonable values for the consumption-elasticity of money demand. Given these parameters, it is hard to avoid the conclusion that money-financed swaps will amost always be destabilizing in the sense of creating a temporary excess supply of money and a depreciation of the parallel exchange rate. The suggested results match the fears often expressed by the authorities of debtor countries.

[TABULAR DATA OMITTED]

The excess money supply case also reveals that a money-financed swap is no different than a repurchase using international reserves. Finding themselves with `too high' a stock of real balances after the swap, agents run it down by inducing a temporary current account deficit. In the transition, reserves are lost. In the extreme case in which there were no wealth effects, so that long-run money demand remained unchanged, the stock of reserves lost would be equal to the value of debt repurchased. The swap repurchase would be financed entirely out of reserves.[22]

4. Fiscal deficits and the possibility of inflation

The analysis presented so far has two principal limitations. First, the assumptions of a predetermined commercial exchange rate and strict purchasing power parity do not permit consideration of the short-run dynamics of inflation. Second, lump-sum taxes and transfers that adjust automatically to ensure budget balance assume away the problem of fiscal disequilibrium, central to any inflationary phenomenon. This section attempts to relax these restrictive assumptions.

We suppose now that the commercial exchange rate also floats, and that therefore (keeping purchasing power parity) domestic prices are perfectly flexible in both the long and short run. While such a scenario is obviously a simplification, it enables us to focus on the dynamics of inflation in a simple way. In a regime of perfectly floating exchange rates and no capital mobility the domestic stock of foreign assets cannot change, for the Central Bank will not and the private sector cannot sell foreign assets. Therefore the current account must always be balanced, implying c = y + p([f.sub.0] + [k.sub.0]) - [r.sup.*][d.sub.0] always. Since consumption is therefore constant, we know from (6) that the domestic net rate of interest must be equal to the rate of discount at all times. This also means, by (3), that the parallel exchange rate q will be unchanged as long as the yield on foreign bonds (p) does not change. The presence of a flexible commercial exchange rate takes the burden of adjustment away from the parallel exchange rate.

The other change in the structure of the model comes on the fiscal side. We now allow the government to borrow domestically to finance shortfalls, that is, b can increase or decrease as long as the government's intertemporal solvency condition is met. The government flow budget constraint becomes

[Mathematical Expression Omitted]

where [mu] = M/M is the rate of nominal monetary expansion and g is now fixed. The individual budget constraint, on the other hand, is still (4). Combining (4) and (19), and recalling that the current account must now be continually balanced, we have

m = m([mu] - [pi]

Finally, substituting an equilibrium version of (5) into (20), we obtain

[Mathematical Expression Omitted]

A steady state obtains when

[Mathematical Expression Omitted]

Equations (19) and (21) constitute a system of two differential equations in two unknowns, m and b, depicted in Fig. 4. The m = 0 schedule depends only on m and is therefore perfectly horizontal, while the b = 0 schedule slopes up: in steady-state, higher money holdings imply higher inflation tax revenues, meaning that the government can sustain a larger stock of bonds. The system is unstable, for both roots of the linear approximation are positive and only one variable (m) can jump. Nonetheless, we can use the system to study inflation dynamics, as shown by Drazen (1984), Helpman and Drazen (1986), and Drazen and Helpman (1987).

Consider now the same two-step swap as before. First the domestic private sector exchanges its foreign assets for government external debt, so that [delta]f.sub.0] = [delta]d.sub.0] (for simplicity, in this section we set [alpha] = 0, so that there is no external discount and no wealth effects). At the same time, the government repurchases its external debt issuing domestic bonds: (1 - [beta]) [delta]d.sub.0] = [delta]b.sub.0]. This operation has two consequences. First, it shifts the intercept of the b = 0 schedule down by [r.sup.*][delta]d.sub.0]. For any level of inflation revenue, the government can now sustain a higher stock of bonds in steady-state. The m = 0 schedule, on the other hand, is unchanged. Second, it instantaneously expands the stock of bonds, moving the system horizontally and to the right along the m = 0 line. The new steady state of the system would be at b'. If the bond issue is of exactly the right size to place the economy there, then the system will be locked into the new steady state instantaneously. But if it either undershoots or overshoots this point an unstable process will be generated, with bonds decumulating or accumulating without bound, respectively. Notice this interesting result: even though the government receives a discount that will presumably ease its budgetary situation, the initial swap can produce a destabilizing budget deficit. This is because domestic financing is expensive, given our assumption that the country is rationed out of international capital markets.

What occurs depends on the slope of the b = 0 schedule, as well as on the size of [beta]. From (22d) it is easy to calculate that the steady-state sustainable stock of bonds increases by ([r.sup.*]/r)Ad[0], while initially the supply of bonds is increased through the open market operation by (l - [beta]) Ad[0]. Hence, the system overshoots its bond steady-state level if and only if (1 - [beta]) > r*/r). If the discount obtained by the government is not large enough to offset the interest differential ([r.sup.*]/r) the government will find itself in a deficit after the swap, a fact that will compel it to begin issuing growing quantities of bonds.

Table 2 provides some realistic computations of this new `stability' condition.[23] Once again, measured (ex post) domestic and world real interest rates are used, in conjunction with average discounts obtained by the governments of four highly-indebted countries. The striking fact is the high level of real interest rates in all countries, particularly those that are attempting to reduce inflation, such as Argentina, Brazil, and Mexico. Given the interest rate differential with the rest of the world, discounts obtained are not enough to make debt swaps a fiscally attractive proposition. The only case where domestic real interest rates have been low relative to regional standards is Chile, but even there the `stability' condition fails to hold.(24) To some extent these exorbitantly high rates are probably a transitional phenomenon, associated with high and variable inflation and repeated stabilization attempts.(25) If that is so, it may be prudent to conclude that - if at all - swaps should only take place after the domestic monetary situation has been stabilized.

[Tabular Data Omitted]

Consider the dynamic adjustment of only one case, that in which b > 0 initially. We assume, as is common in the literature, that there is an exogenously given upper bound to the quantity of real bonds that the public will willingly hold.[26] Therefore, if bonds begin accumulating, agents will expect that at some point in the future a corrective measure will be taken. This could involve lowering net transfers (g) or increasing the rate of money creation [mu]. In turn, agents' perceptions about what measures will eventually be taken affect the behavior of the system in the transition.(27)

Figure 4a depicts the case in which agents correctly anticipate that the fiscal imbalance will be corrected by cutting spending when bonds reach a threshold level [b.sub.*]. It is clear from (22) that changes in g affect the b= 0 locus but not the m = 0 locus. Therefore, the final equilibrium must be at the same initial level of real balances. Given the dynamics of the system, furthermore, if the system ever departs from the m = 0 it can never return to it. Therefore, to avoid this instability the economy moves horizontally until the time when [b.sub.*] is reached. At that point the authorities lower g as anticipated and lock the system into a steady-state. Along the way inflation and real balances are unchanged, as is the parallel exchange rate.

The behavior of the system is very different if agents anticipate that increased money creation will eventually be used to stop the growth of domestic debt. Inspection of (22) reveals that a higher [mu] will shift the m = 0 schedule down. The b = 0 locus will move to the right in the `normal' case in which an increase in steady-state inflation increases government revenue. This requires that the elasticity of money demand with respect to the inflation rate be smaller than one. In this `normal' case, the new intersection will be to the southeast of the original one. Substituting (22a) and (22c) into (22d), and recalling that the initial stock of foreign debt has been repurchased, we obtain

[Mathematical Expression Omitted]

which shows the combinations of m and b that place the economy in a stationary state. The locus appears as MM in Fig. 4b. Suppose the public correctly anticipates that the government will let bonds accumulate until they reach the level [b.sub.*]. At that point, it will increase [mu] as much as necessary to restore budget equilibrium. Foreseeing this, agents understand that the system must find itself on MM the moment money creation increases, in order to ensure that the steady state is attained.

With the help of a few additional observations we can determine the path of the economy in the transition.[28] Define a = b + m + q([f.sub.0 + for total assets. Notice that along a path in which q = 0 (as will be the case here), a = m + b. Adding (19) and (20), and recalling [d.sub.o] = 0, we obtain

a = rb + g - [pi]m

Hence, MM also corresponds to the a = 0 schedule. Along any path above MM the quantity of total assets must be increased, so that the slope of the path will be smaller than one in absolute value. The opposite holds for any patb below MM, where total assets must be decreasing.

The dynamics of the system between the time of the swap and that of the change in monetary policy depend on the slope of the MM schedule, which equals the elasticity of money demand with respect to the nominal interest rate. If the interest elasticity of the demand for real balances is unity, then only a path that starts on MM itself can ensure convergence. In that case the system will jump down to MM and move along that schedule until the time when b = [b.sup.*].

If the relevant elasticity is less than unity in absolute value, so that MM is fiat, then the system must initially jump to a point such as c, above MM. It will then move along a trajectory whose slope is less than one but greater than that of MM in absolute value. The magnitude of the initial downward jump will be given by the need that the path cross MM through point e at the right time. Conversely, if the interest elasticity is greater than one (MM steep), the initial jump will take the economy all the way to a point such as d below MM, starting on a southwesterly trajectory thereafter.

In all cases real balances will decrease on impact, implying a steep depreciation of the exchange rate. Inflation will also rise at the time of the swap, and will converge to its permanently higher level just as bonds reach their threshold [b.sup.*]. Real balances will be falling throughout. We conclude that if money is used to finance the budget deficit generated by the swap, there is good reason to believe the policy will have inflationary consequences.

5. Summary and conclusions

This paper provides a simple framework in which to analyze the macroeconomic effects of debt swaps. The framework combines some formal elements of recent optimizing models in international finance with some realistic institutional features of the Latin American case. Five main conclusions emerge from our analysis.

First, debt swaps enable the country to bring forward in time the discounted benefits of a future debt writedown. Equivalently, they enable an otherwise credit-constrained economy to borrow, at the world interest rate. If this rate is below the domestic interest rate, swaps may yield a positive wealth effect for the domestic country.

Second, the macroeconomic effects of swaps cannot be analyzed without specifying how the government will gain control of the domestic resources to be given to creditors in exchange for the debt. Typically the external debt being retired is public, while the domestic resources belong to the private sector. This important aspect of debt conversion schemes has, thus far, been ignored in the literature.

Third, the kind of domestic liability that the government employs to finance the swap matters very much. When the budget is continuously balanced, debt-for-bonds swaps have no impact beyond that of a private sector debt repurchase. Debt-for-money swaps, on the other hand, can have significant effects: an initial excess supply of money - which is likely to happen, according to our numerical calculations - will depreciate the parallel exchange rate and induce a transitional current account deficit.

Fourth, in the more realistic case in which the government can run sustained deficits, the fiscal side provides the key link through which swaps have macroeconomic effects. If domestic real interest rates are higher than in the rest of the world, debt-for-bonds swaps can have destabilizing fiscal effects even in the presence of a discount captured by the government. Preliminary evidence suggests this effect probably has great practical relevance.

Fifth, expectations of how any resulting fiscal disequilibrium will be financed affect the course of macroeconomic variables in the short run. Some countries have managed to avoid possible inflationary effects by relying mostly on debt-for-bonds swaps. But if this leads to an accumulation of domestic debt which the public expects will be monetized eventually, the domestic rate of inflation will immediately begin to rise.

* New York University [dagger] Pontificia Universidad Catolica de Chile

REFERENCES

Alexander, L. (1987a). `Debt-for-Equity Swaps: A Formal Analysis', mimeo, Board of Governors of the Federal Reserve, International Finance Division, Washington, D.C. Alexander, L. (1987b). `Debt Conversions: Economic Issues for Heavily indebted Developing Countries,, mimeo, Board of Governors of the Federal Reserve, International Finance Division, Washington, D.C. Bodin de Moraes, P. (1988). The Debt-Equity Conversion Program in Brazil', paper presented at the Georgetown/Ilades Conference on Debt Reduction, Santiago, Chile. Bulow, J. and Rogoff, K. (1988a). `The Debt Buyback Boondogle', paper presented at the Fall Conference of the Brookings Panel on Economic Activity, Washington, D.C. Bulow, J. and Rogoff, K. (1988b). 'Sovereign Debt Restructuring: Panacea or Pangloss?', NBER Working Paper 2637. Calvo, G. (1981). `Devaluation: Levels versus Rates', Journal of International Economics, 11, 2. Drazen, A. (1984). `Tight Money and Inflation: Further Results', Journal of Monetary Economics, 15. Drazen, A. and Helpman, E. (1987). `Stabilization with Exchange Rate Management', Quarterly Journal of Economics. Ffrench-Davis, R. (1989). `Debt Equity Swaps in Chile', Nota Tecnica 129, CIEPLAN, Santiago, Chile. Helpman, E. (1987). `The Simple Analytics of Debt-Equity Swaps and Debt Forgiveness', mimeo, International Monetary Fund, Washington, D.C. Helpman, E. (1988). `Voluntary Debt Reduction: Incentives and Welfare', NBER Working Paper 2692. Helpman, E. and Drazen, A. (1986). `Future Stabilization Policies and Inflation', in M. Kohn and S. C. Tsiang (eds), Finance Constraints, Expectations and Macroeconomics. Oxford University Press, Oxford. Kruman, P. (1988a). `Financing vs. Forgiving a Debt Overhang', NBER Working Paper 2486. Krugman, P. (1988b). `Market-based Debt-Reduction Schemes,, NBER Working Paper 2587. Larrain, F. and Velasco, A. (1990). `Can Swaps Solve the Debt Crisis? Lessons from the Chilean Experience', Princeton Studies in International Finance, 69. Liviatan, N. (1984). `Tight Money and Inflation: Further Results', Journal of monetary Economics. 13. McCallum, B. (1984). `Are Bond-Financed Deficits Inflationary?', Journal of Political Economy, 92. Mankiw, G. and Summers, L. (1986). 'Money Demand and the Effects of Fiscal Policies', Journal of Money, Credit and Banking. Mullin, J. J. (1990). `The Implications of Monetary versus Bond Financing of Debt-Peso Swaps', Research Paper 9005, Federal Reserve Bank of New York. Obstfeld, M. (1981). `Inflation, Real Interest, and the Determinacy of Equilibrium in an Optimizing Framework', NBER Working Paper 723 Obstfeld, M. (1986). `Capital Controls, the Dual Exchange Rate and Devaluation', Journal of International Economics, 20. Obstfeld M. (1988). `A Theory of Currency Depreciation and Capital Flight', mimeo, University of Pennsylvania. Rodriguez, C. (1989). `Managing Argentina's Debt: The Contribution of Debt Swaps', LAC Discussion Paper IDP 0024, The World Bank, Washington, D.C. Sargent, T. and Wallace, N. (1981). `Some Unpleasant Monetarist Arithmetic', Federal Reserve Bank of Minneapolis Quarterly Review, 5. Sangines, A. (1989). "Managing Mexico's Debt: The Contribution of Debt-Reduction Schemes', LAC Discussion Paper IDP 0029, The World Bank, Washington, D.C. Velasco, A. (1989). `Real Interests Rates and Government Debt during Stabilization', Working Paper No. 89-34, CV Starr Center for Applied Economics, New York University.

APPENDIX 1

The 3 x 3 model in c, m, and q presented in Section 2 can be expressed in matrix form as

[MATHEMATICAL EXPRESSION OMITTED]

Consequently, the system has eigenvalues given by

[MATHEMATICAL EXPRESSION OMITTED]

where [lambda][sub.i]>0, [lambda][sub.2]<0, and [lambda][sub.3]>0. Since the number of negative eigenvalues is the same as the number of predetermined variables, the system is locally stable.

APPENDIX 2

This appendix derives the exact behavior of consumption and real balances in response to an unanticipated swap that takes place at a time when external debt sells at a discount as a result of an expected writedown.

The expected writedown is of magnitude [alpha][psi]d[sub.0], where the definitions of [alpha] and [phi] are as in the text. Consider first, and in the absence of any swaps, how the debtor's economy will initially react to this expectation. The dynamics appear in Fig. A1. In the new steady state, the new steady state, the expected debt writedown shifts the m = 0 line up by the distance [Lambda]c=[r.sup.*[alpha][psi][d.sub.0]>0, and leaves the c=0 schedule unchanged. Since the discount increases the sustainable level of consumption, c jumps on impact and then continues to increase, moving according to the dynamics of the initial system until it reaches the new saddle path at time T. Between 0 and T the economy is consuming more than its current resources permit, so that we observe a current account deficit and a decrease in reserves and in real balances. This trend is reversed after the writedown becomes effective.

The parallel rate q must also be increasing after T. Since its steady-state level is unchanged, it follows that q must have jumped down initially: the news causes the parallel exchange rate to appreciate, and to remain above its `normal' level as long as the economy is out steady-state equilibrium. Recalling (3), it also follows that the domestic real rate of interest is above its long-run level throughout the transition.[sub.29] In short, the country experiences some desirable effects, which follow from the fact that anticipated future debt reduction constitutes a transfer from the rest of the world to the domestic economy.

Observing that its own external debt trades at a discount, the government of the home country might be tempted to try to repurchase it in the secondary market. Suppose that, unexpected and at some time [tau], the government induces a repurchase of its foreign obligations, by commanding(30) the private sector to swap its capital or foreign bond holdings for foreign debt.(31) Algebraically, [delta][f.sub.0]=[p.sub.t][delta][d.sub.0]=[p.sub.t][phi][d.sub.0] where the we assume, as in the text, that all debt subject to a discount is retired.

How will the domestic economy react to such a transaction? The swap is tantamount to bringing forward in time the benefits of the future debt reduction. In a world with perfect capital mobility in which real rates of interest were equalized, the swap would have no real effects. Under perfect foresight the discount captured today would simply equal the present value of the the discount available tomorrow, and consumption and the current account would be unchanged by the announcement of such an operation. However, that is no longer the case when restrictions in capital mobility drive a wedge between the steady-state rates of discount at home and abroad. The matter is further complicated by the fact that such swaps could only seem attractive while the debt sells at a discount - in the time between the announcement of the debt reduction and its realization. During that period the economy is out of steady state, and the relevant rate of interest faced by domestic agents is changing over time.

Figure A2 shows the dynamics of the system in reaction to a swap. The timing of the swap will determine the final resting position of the m = 0 schedule. From (12b) we know that the market price falls as we approach time T. Depending on the actual time of the swap, the country will get a different price for its debt, and hence will place itself on the path to an eventual steady state with a different level of sustainable consumption. Define [c.sub.[tau]] as the steady-state level of consumption a country could attain if it swapped all of its discounted debt at time [tau].[sub.32] Then for every [tau], and every corresponding [c.sub.[tau]] there will be a saddle path to which the economy will have the economy will have to jump at the time of the swap. In what follows we show that consumption will always find itself below this saddle path at [tau]. Equivalently, consumption will always jump up at the time of the swap.

To prove that result we must solve the system analytically. For simplicity we deal only with the 2 x 2 system in c and m, which can be solved independently. Excluding q, system (A1) becomes

[MATHEMATICAL EXPRESSION OMITTED]

The matrix of patrial derivatives has eigenvalues given by

[MATHEMATICAL EXPRESSION OMITTED]

where [[lambda].sub.1] 0 and [[lambda].sub.2] 0, just as before.

It is straightforward to show that the general solution of the system, for all time between 0 and T, is:

[MATHEMATICAL EXPRESSION OMITTED]

Consider now the effects of a possible debt swap effected some time before T. During the period, the secondary market price for one unit of debt, denoted by [p.sub.[tau]], must be given by

[MATHEMATICAL EXPRESSION OMITTED]

for all [tau] before time T. The market price falls as we approach T. Recall [c.sub.[tau]] denotes the steady-state level of consumption a country could attain if it swapped all of its debt at some time [tau]. It must be the case that

[MATHEMATICAL EXPRESSION OMITTED]

and, recalling (A3) and the definition of [sigma],

[MATHEMATICAL EXPRESSION OMITTED]

At that time [tau], the system would jump to the saddle path leading to the steady state characterized by (A4). Along the saddle path we must have

[MATHEMATICAL EXPRESSION OMITTED]

where the subscript `[tau] +' denotes the values taken on by the variables in the instant after the swap is announced at time [tau]. But, since m is predetermined variable, it must also be true that [m.sub.[tau].sub.+]] = [m.sub.[tau]]. Combining this fact with (A5) and (A6), we arrive at

[MATHEMATICAL EXPRESSION OMITTED]

We can use (A2), evaluated at t = [tau], to substitute for [m.sub.[tau] - m]:

[MATHEMATICAL EXPRESSION OMITTED]

This last expression yields the level to which consumption would have to jump in the instant after the swap is carried out at time [tau]. By contrast, we know from (A2) (once again evaluated at t = [tau]) that the level consumption must have found itself at [tau]. Subtracting (A2) from (A8) yields

[MATHEMATICAL EXPRESSION OMITTED]

It follows that

sgn[[c.sub.[tau]+]-[c.sub.[tau]]]=sgn[lambda][sub.1]-r*

Hence, consumption will have to jump up at the time of the swap if [[gamma].sub.1] is greater than r*. But this condition always holds if [delta] [greater than or equal to] r*,; if, as assumed, the domestic steady-state rate of interest it at least as large as the world rate.(33)

Returning to Fig. A2, consumption would have reached point b along its unstable trajectory just before the swap is announced at [tau]. Consumption must therefore jump to point a on the saddle path that leads to [c.sub.[tau]]. The distance of the jump given by equation (15) is ba.

The intuition for this fundamental result is simple. When the world rate of interest (r*) is small, creditors do not discount the future debt reduction very much. Hence, the purchase price of the debt at the time of the swap is low, and the attainable level of (post-swap) steady state consumption is high. By contrast, the domestic interest is abnormally high during the transition. This difference in interest rates accounts for the wealth effect of the swap, as discussed in the text. (1)In the late 1980s Mexico and Brazil suspended debt conversion programs, citing such reasons. (2)Of course, confiscation, taxation, and bond-finance may be hard to distinguish in a fully Ricardian world. (3)The latter assumption is employed by Helpman (1987, 1988). (4)We also normalize the international price level to equal one. (5)This assumption only simplifies the algebra. It would be straightforward to analyze the case where the fixed yields differ for the two assets. Their prices would differ as well, but the arbitrage equations would still hold. (6)In the sense that it is the relative price of foreign bonds in terms of the consumption good. It is not (at least directly) the relative price of domestic and foreign monies-the more common definition of the parallel exchange rate. (7)We must also impose the usual solvency constraint, which can be written as

[Mathematical Expression Omitted]

(8)See for instance Calvo (1981). (9)Notice that, for simplicity, international reserves are assumed not to pay interest. (10)Of course, one of the crucial features with no capital mobility such as this one is that the domestic real rate of interest is in general different from the world rate. (11) This is formally shown in Appendix 2. (12)In most Latin American countries an authorization from the Central Bank is required to buy official debt abroad or even to to prepay private external debt. (13)Notice that the SE alternative only makes sense if we.assume that agents are willing to repurchase debt even if no discount is expected. (14) Notice that in the swap the domestically held international bond is valued at its exogenous international price of [q.sup.*], normalized here for simplicity at unity. This implies, furthermore, that [r.sup.*] = [rho] always. (5) It could be the case that cts [phi] < 1 if the government has external debt owed to official creditors, on which it will never default. (16)This means that we neglect the distinction between large and small swaps and between marginal and average debt, central to the analysis of Bulow and Rogoff (1988a and b). Moreover, for the swap to be feasible it must be the case that [f.sub.o] > [d.sub.o]. Notice also that, as before, the domestically held international bond is valued at its exogenous international price of [q.sup.*], normalized here for simplicity at unity. (17)Following common usage, we say that the parallel exchange rate `appreciates' when q falls. This also means, of course, that the stock market is depressed in the transition. Given the newly acquired' resources that result from the discount, the price of already existing assets goes down. (18) Equivalently, the swap enables domestic residents to borrow from abroad at the rate [r.sup.*], which they could not do before. (19) Notice that the total discount received by the country is [alpha]. Of this, the government gets [beta] and the domestic private sector gets [alpha] - [beta]. (20) This assumption does not seem far fetched in the case of many Latin American countries. In the presence of a fiscal gain, Chile might lower taxes while Brazil increases transfers, for instance. The effect of fiscal rigidities ate central to the analysis in Section 3. (21) The phrase is in quotation marks because, technically speaking, the system is stable regardless of the magnitude of [beta]. (22) This point has been stressed by Mullin (1990). (23) Notice that an external discount (([alpha] < 1) would tend to move the m = 0 locus up for reasons discussed in Section 2. A discount would raise national feasible consumption and, ceteris paribus, equilibrium real balances. Such an additional change would therefore make it less likely that the system will overshoot its steady-state. Our computations in Table 2 may therefore overstate the possible dangers of swap operations. (24) Furthermore, real domestic interest rates have risen in Chile in the first half of 1989. (25) For a discussion of why stabilization based on 'exchange rate management' may help explain these high real rates, see Velasco (1989). (26) That assumption is equivalent to ignoring the results of McCallum (1984), who showed that the stock of domestic debt can tend to infinity without violating the government's solvency condition. That result will hold as long as all interest income received by the public can be taxed away in a lump-sum fashion. In reality, of course, there are perceived limits to such lump-sum taxation and debt accumulation. If bonds seem to be growing without bound, the public is likely to expect an attempt at stabilization in the future. This is the conjecture adopted in Sargent and Wallace's classic (1981) paper, and in Liviatan (1984) and Drazen (1984). (27) Such two-step policies have been recently analyzed by Helpman and Drazen (1986) and Drazen and Heipman (1987). (28) This analysis follows Drazen (1984). (29) This can also be inferred from (6). Since we know that c is increasing throughout, it must be the case that r[greater than][delta] throughout as well. (30) Such a command could be made palatable to private agents by promising in turn to buy the extemal debt back from them, as is done in the text. (31) The results would be the same if: (i) the govemment taxed away the private assets and used them to retire debt directly; and (ii) official reserves eamed interest and the government used them to finance the transactions. (32) This variable is defined formally in equation (A4). (33) This result, of course, depends crucially on our assumptions of no uncertainty and perfect foresight. With uncertainty about thc magnitude of the debt reduction, and different attitudes toward risk among creditors and debtor, this result need not hold. The same is true of situations in which the debtor country hopes to default, and has private information about the likelihood of this event.
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Author:Velasco, Andres; Larrain, Felipe
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Date:Apr 1, 1993
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