## Abstract

The possibility of reducing the real value of domestic nonindexed government debt through inflation is studied. A central result is that this kind of debt liquidation is possible even though prices are sticky and government bonds are short term. A policy implication is that short bond maturities are no safeguard against surprise devaluations intended to lower the burden of the debt. If devaluation incentives are present, nominal nonindexed bonds could give rise to situations in which devaluations are a consequence of self-fulfilling expectations cycles.

THE ACCUMULATION of public debt has recently become one of the focal points in macroeconomic policy discussions. Part of the reason is that, after the breakdown of the Bretton Woods system and the ensuing energy crises, industrialized countries have moved to higher deficit plateaus and bigger public debt. Another part is that recent anti-inflationary programs in countries such as Argentina, Bolivia, and Brazil have been associated with relatively high (ex post) real interest rates— at least during the first stages of the inflation-cutting process—which, again, contributed to debt accumulation.

In a closed economy in which wealth distribution problems are not relevant—as would be the case in an economy of identical individuals or families à la Ramsey—there is no short-run advantage in having a positive stock of government debt obligations. Positive debt in this case means that the government will have to raise taxes from the representative individual in order to pay him back in the form of interest on his public debt holdings. Thus, if taxes are distorting, a one-time total debt repudiation is optimal. In practice, of course, wealth distribution aspects are important, and there are political, administrative, and even reputation costs that may render total repudiation somewhat unattractive. The foregoing pure example, however, helps us to understand why policymakers may find it attractive to engage in some kind of *partial* debt repudiation.

Having decided to repudiate part of the outstanding debt, a government has yet to solve the problem of how to do so. Keynes (1971) was apparently sympathetic to the idea of liquidating the debt through a sudden burst of inflation. He evidently felt that debt repudiation through inflation would be more acceptable than open repudiation or special wealth taxes—a theme that he would stress later on in his *General Theory* in connection with wage stickiness.^{1} Be that as it may, the practicality of Keynes’s solution has recently been questioned by several authors (for example, Blanchard, Dornbusch, and Buiter (1985) and Spaventa (1987)), according to whom its relevance has been undermined by the sizable maturity shortening of the public debt. In the limit, with bonds of instantaneous maturity such as NOW accounts, they would argue that anything short of an unanticipated price-level jump would be ineffective. According to this point of view, anticipated inflation would tend to be incorporated in the nominal interest rate, point for point, thus offsetting the effect of inflation on the real stock of government debt. The argument of inflation ineffectiveness is completed by noting that in electronically sophisticated economies it is very difficult to bring about unanticipated jumps in the price level. In the words of Blanchard, Dornbusch, and Buiter (1985, p. 5), “inflation is no longer a way out for governments; this is because debt is now of much shorter maturity, making inflation-induced debt reduction much less effective.”^{2}

More formally, let *b* and *d* denote the stock of instant-maturity bonds and the government’s operational deficit in terms of domestic goods; moreover, let *i* and π denote the instantaneous nominal interest and inflation rates (where the inflation rate refers to the proportional rate of increase of domestic prices in terms of domestic currency). Then *b* accumulates according to the following:

The first two terms on the right-hand side of equation (1) correspond to the standard definition of the government deficit in real terms, whereas the sum of the three terms on the right-hand side is the inflation-adjusted deficit.

In a perfect-foresight equilibrium, the following Fisher equation is assumed to hold:

where *r* is the real interest rate on output-type assets that appreciate in nominal terms at the rate π (for example, domestic capital goods). Thus, combining equations (1) and (2), one gets

From equation (3) it clearly follows that changes in the rate of inflation would have no effect on debt accumulation, unless inflation has an impact on the real interest rate.^{3} In other words, in a classical world in which the real interest rate is independent of monetary policy, the above equations imply that a change in the rate of inflation will have no impact on the stock of debt. The only way *b* could be changed would be through a sudden rise in the price level. But, once again, if a jump in the price level is not a feasible alternative, neither would be liquidating the debt through inflation.

The central objective of the present paper is to show that, in a world of international capital mobility, inflation may be an effective instrument to reduce the real value of government debt, particularly for countries that are relatively small in international financial markets. This will be shown to be the case, even though all debt is of instantaneous maturity and prices are sticky. This finding does not contradict the above-mentioned formal argument because, in the example, debt reduction occurs through a decrease of the relevant real interest rate. However, by focusing on a case of considerable practical importance, the paper illustrates the likely irrelevance of the view that short-term maturities coupled with sticky prices make it difficult, if not impossible, to lower the real value of government debt through inflation. Furthermore, the paper also illustrates the importance of specifying the mechanisms that account for the negative relationship between inflation and the relevant real interest rate, since it will be shown that the level of the outstanding debt and the effect of inflation depend strongly on expectations. The same devaluation could generate very different real rates of interest, and the same fiscal deficit could result in quite different levels of debt depending on the state and dynamics of expectations.

### I. International Capital Mobility

The main (straightforward) argument is developed in this section. Consider an economy open to international capital mobility. Letting ρ denote the exogenous and (for simplicity) constant international interest rate, we have the following, familiar condition for interest rate parity:

where ε is the expected rate of devaluation. In other words, equation (4) says that in equilibrium the domestic instantaneous nominal interest rate equals its international counterpart plus the expected rate of devaluation. Equation (4) differs from (2) because here, in equilibrium, the opportunity cost of bond investors is the rate of return on foreign-currency-denominated bonds, not on domestic capital as in the earlier example.^{4}

Equation (4) is a way of characterizing international capital mobility. The exogeneity of ρ with respect to domestic policy is not strictly necessary for the ensuing argument, but it is a convenient assumption because it isolates these results from ones explored by other authors.^{5}

As a benchmark, consider the case in which international inflation, output, and population growth rates—and the expected rates of devaluation and inflation—are all equal to zero. Thus, without loss of generality, one can assume output to be unity, which is a convenient device to define stocks and flows automatically in terms of output (or gross domestic product, GDP) per unit of time. Furthermore, under the present circumstances the debt accumulation equation is given by equation (3). Thus, for a constant *d* (that is, the operational deficit as a share of GDP), one can solve equation (3) to get

Let us now change the scenario above to study the implications of a one-time devaluation at time zero, followed by the expectation of no further devaluation (see Ize and Ortiz (1987)). First, note that if the devaluation provoked a once-and-for-all increase in the price level, then, of course, debt liquidation would be possible. Furthermore, if gross devaluation (equal to unity plus the rate of devaluation) is denoted by *D*, the initial value of *b* falls to *b _{0}/D*, and equation (5) becomes

Consider instead the situation where, initially, the price level does not change, but the rate of inflation rises to a constant level π (a simple way to model price stickiness). Therefore, by equation (4), debt evolves according to

Note that the rate of interest does not change because devaluation has already occurred and is not expected to happen in the future. Inflation, however, is now larger because the price level slowly starts to catch up with the higher nominal exchange rate. Comparing equations (3) and (6), one notices that equation (6) exhibits an element of debt repudiation—that is, π*b*.

Solving equation (6) and denoting the solution by *B* obtains

To exhibit the power of inflation to repudiate debt, two special cases will be examined. In the first one, the operational deficit is zero, (d = 0). Clearly, then, by equations (5a) and (7), one has

which implies that the relative debt-repudiation power of inflation with respect to a once-and-for-all jump in the price level, at time *t*, depends on the real exchange rate at time t in comparison with its level before devaluation. A recent study by Edwards (1988) suggests that an *x* percent devaluation brings about a 0.6*x* percent price-level rise after one year, and about *x* percent rise after two years. Thus, equation (8) would imply that, with sticky prices, after one year the real value of bonds will fall by about 60 percent of what they would have fallen if prices were perfectly flexible, and that after two years the real value of bonds would be about the same irrespective of price flexibility.

The intuition behind this simple case is straightforward. A devaluation that is not followed by the expectations that the currency will be further devalued has no effect on domestic nominal interest rates. Thus, to the extent that devaluation gives rise to inflation, the real value of bonds will fall. When the operational deficit is equal to zero—that is, *d =* 0—then, by equation (5a), bonds grow at rate ρ with flexible prices and at rate (ρ – π) when prices are sticky. Hence, the ratio of the latter to the former falls at rate π. This observation, plus the fact that the above-mentioned bonds ratio at time zero is equal to the gross rate of devaluation *D*, yields equation (8).

The second case to be examined is one in which the price level keeps rising (at a constant proportional rate π) until the initial ratio of the exchange rate to the price level (that is, the real exchange rate) is restored. Therefore, this is a situation in which a devaluation brings about a real depreciation of the real exchange rate for a limited amount of time (again, this is in line with empirical findings in Edwards (1988)). Denoting by *T* the time at which inflation stops, one may now study the relative debt-repudiation power of inflation at time *T*.^{6} By definition.

Thus, according to this formulation, a relatively small value of *T* implies quick price adjustment, whereas a relatively large T corresponds to very sluggish prices.

Now compare the effect on the stock of bonds of sluggish and perfectly flexible prices. By equations (5a) and (7),

which, by equation (9), implies that

Consequently, one reaches the interesting conclusion that at the time the real exchange rate has fully recovered from the effects of a devaluation (or maxi-devaluation), if (realistically) the operational deficit is positive, then the debt will be larger with flexible than with sluggish prices. Thus, not only has the analysis been able to show that *inflation could be effective to liquidate part of the debt when prices are slow to adjust*, but also that *if there exists a positive operational budget deficit, then the debt will fall even more with sluggish than with flexible prices*. Furthermore, equation (11) implies that the larger is the operational deficit, the bigger will be the advantage of inflation over price-rise debt repudiation.

The intuition behind this case is also straightforward. By previous results, if the operational deficit is zero (that is, *d* = 0), then the stock of bonds at time *T* is the same irrespective of price flexibility. When *d* > 0, however, the new debt that is incurred to pay for *d* grows at rate ρ when prices are flexible and, recalling equation (7), at rate ρ – π when prices are sticky. This explains equation (11) and related results.

### II. Role of Expectations

This section will more closely examine the role of devaluation expectations. Suppose that, before time zero, the public anticipated that a devaluation є (per unit of time) was in the offing. Then, by equations (1) and (4), with a fixed exchange rate one has

Consequently, the larger is є, the larger will be the growth of public debt under fixed exchange rates. In the interesting case in which devaluation expectations are fueled only by the public’s realization that the government could be tempted to devalue in order to liquidate part of the debt, after a successful devaluation has occurred (from the viewpoint of debt repudiation), it is quite plausible to assume that devaluation expectations may decline sharply. Thus, a devaluation may have the double effect of helping to liquidate the debt *and* to reduce the nominal rate of interest (by lowering expected є).

However, there may be effects going in the opposite direction. As noted in Calvo (1983), rational price setters are likely to start raising prices before a devaluation actually occurs. Equation (12) would then become

where *π ^{e}* indicates the actual increase in prices that occurs in anticipation of a devaluation. Thus,

*π*tends to offset the effect of є. Conceivably, prices may have risen so much that an anticipated devaluation will not increase inflation. Thus, this extreme case has characteristics similar to the ones discussed in the introduction to this paper, since a devaluation would have no effect on real debt.

^{e}^{7}

Another factor that may detract from the success of a devaluation as a debt-liquidation device is the possibility that a devaluation brings about expectations that the currency will be further devalued in the near future (which would raise e after devaluation in equation (12)). This factor will probably be more relevant if the public perceives that the devaluation has failed to accomplish what the policymakers intended.^{8} Otherwise, experience seems to indicate that markets tend to calm down after a massive currency devaluation, and no further devaluation is expected in less than a year.^{9}

Equation (12) vividly illustrates the role of expectations. The mere fact that people expect a devaluation to occur increases the rate of accumulation of government debt, thus giving the government incentives to devalue in order to get rid of its debt (at least, partially), except possibly in the extreme case discussed at the end of the preceding paragraph.^{10} It is, therefore, conceivable that expectations play a crucial role in the determination of the final devaluation-inflation outcome. With flexible prices (implying π* ^{e}* = 0, given that fixed exchange rates are assumed), a low є, for example, determines a relatively low rate of debt accumulation, which may be self-validating because the monetary authorities may see no virtue in liquidating the debt through inflation, with its attendant costs. In contrast, a high e will give rise to a relatively high rate of debt accumulation, making the authorities more receptive to proposals to liquidate part of the debt through inflation. Thus, in the end, expectations of a high devaluation rate may turn out to be self-fulfilling.

^{11}

It is important to note that the inflation-devaluation bomb could be defused if all debt were to be indexed to the price level. This type of indexation, incidentally, should not be confused with floating-rate nominal debt, since the latter is formally equivalent to the debt instruments discussed here (and which, as shown above, could be partially liquidated through inflation). Price indexation removes *by definition* all incentives to inflate in order to get rid of the debt (unless, of course, the government plays tricks with the price index).^{12} From this point of view, debt indexation to the price level may thus provide an additional, and maybe even powerful, weapon for fighting the government’s credibility problem. It goes without saying, however, that inflation is just one of many debt-liquidation instruments. Hence, removing its sting does not ensure that the government will not resort to other, perhaps more socially painful, types of debt repudiation.^{13}

### III. Conclusions

The main message from this paper is that inflation may be an effective instrument to get rid of an unduly high level of outstanding public debt. This was shown to be the case even when the monetary authorities are unable to provoke unexpected inflation and bonds are of instant maturity. In the discussion, this result was closely linked to the existence of international capital mobility. When there is a high degree of international capital mobility, the domestic nominal interest rate is highly sensitive to devaluation expectations. Thus, for example, a once-and-for-all devaluation will give rise to inflation but will not necessarily lead to an increase of the nominal interest rate if the public perceives that no further devaluation is likely to be forthcoming in the near future. This decoupling of interest rates and inflation is the proximate reason for inflation’s debt-liquidating power.

It is interesting that the reduced forms of the present model and the one discussed by Blanchard, Dornbusch, and Buiter (1985) are quite similar. These authors assume that debt liquidation will operate through a lowering of the real interest rate. In the model discussed here, in contrast, the relevant real interest rate for the Fisher equation (that is, the international interest rate) is exogenous and, thus, is not affected by domestic inflation. However, the real interest rate in terms of domestic goods, ρ — π (the one discussed by the above authors), falls—the mechanism through which the above-mentioned decoupling works. This paper has shown, however, that in order for the domestic real interest rate to react to changes in the rate of inflation, it is not necessary to assume that the interest rate in Fisher’s equation, ρ responds to changes in domestic monetary policy.

Nevertheless, the analysis herein has also shown that the effect of a devaluation on the stock of debt can become smaller if the devaluation is anticipated by the public. This, however, should not be confused with the statement—stressed by previous authors, and not true in the present context—that the debt-repudiation mechanism would be impaired if inflation is anticipated by the public.

The bad news in the paper is that short maturities, although a possible reaction to inflationary expectations and imperfect policy credibility (see Spaventa (1987)), are not a sure way to discourage inflation as a debt-repudiation device. Therefore, the existence of a relatively large stock of nominal public debt may very well give rise to the suspicion that the government may try to use inflation to reduce the social cost of servicing the debt. Consequently, the public is likely to try to cover itself against partial repudiation by requiring an interest rate larger than under full credibility. But, as argued in the text, the higher expectations-led interest rate may actually play a key role in provoking the inflationary explosion. This conundrum is likely to acquire greater significance for countries that are trying to stabilize their monetary economies from an initial position of high inflation. The combination of expectations inertia with this rational distrust of government policies associated with large debt may prove deadly: good programs may collapse under the weight of high-inflation expectations.

An easy solution to multiple expectations-led equilibria is to index debt instruments to the price level. But for indexation to work, all the other mechanisms of debt repudiation must be disabled. Otherwise debt indexation, like the removal of a safety valve, may generate even more serious pressures within the system.

In closing, I would like to stress that this paper by no means takes the position that “maxi-devaluations” are *desirable* mechanisms for reducing the real value of the government debt. The models utilized are not fit for the task because they are not built on complete choice-theoretic foundations. Instead, the central message of the paper is that short-term maturities do not eliminate the government’s temptation to devalue because, even when prices are sticky, devaluation can be a powerful instrument for reducing the debt burden.

## REFERENCES

Blanchard, Olivier, Rudiger Dornbusch, and Willem Buiter,

(Brussels: Centre for European Policy Studies, 1985).*Public Debt and Fiscal Responsibility*, CEPS Paper 22Calvo, Guillermo A.,

*“Staggered Contracts and Exchange Rate Policy,” in*ed. by Jacob A. Frenkel (Chicago: University of Chicago Press, 1983).*Exchange Rates and International Macroeconomics*,Calvo, Guillermo A., “Fractured Liberalism: Argentina Under Martínez de Hoz,”

Vol. 34 (April 1986).*Economic Development and Cultural Change*.Calvo, Guillermo A., “Servicing the Public Debt: The Role of Expectations,”

Vol. 78 (September 1988).*American Economic Review*,Calvo, Guillermo A.,

*“Controlling Inflation: The Problem of Non-Indexed Debt,” in*ed. by Sebastian Edwards and Felipe Larrain (Oxford and New York: Basil Blackwell, 1989).*Debt, Adjustment, and Recovery: Latin America’s Prospect for Growth and Development*de Pablo, Juan C., and Alfonso Martínez, “Macroeconomic Policies, Crisis and Growth in the Long Run: Argentina Country Study” (unpublished; Buenos Aires, March 1988).

Edwards, Sebastian, “Real and Monetary Determinants of Real Exchange Rate Behavior: Theory and Evidence from Developing Countries,”

Vol. 29 (November 1988).*Journal of Development Economics*,Ize, Alain, and Guillermo Ortiz, “Fiscal Rigidities, Public Debt, and Capital Flight,”

International Monetary Fund, Vol. 34 (June 1987).*Staff Papers*,Keynes, John M.,

in Vol. 4 of*A Tract on Monetary Reform*,(London: Macmillan, 1971).*The Collected Writings of John Maynard Keynes*Organization for Economic Cooperation and Development,

(Paris: OECD, 1988).*Why Economic Policies Change Course: Eleven Case Studies*Spaventa, Luigi, “The Growth of Public Debt: Sustainabilìty, Fiscal Rules, and Monetary Rules,”

International Monetary Fund, Vol. 34 (June 1987).*Staff Papers*,

^{}*

Mr. Calvo is a Senior Advisor in the Research Department, where he is on leave from the University of Pennsylvania. He holds a doctorate from Yale University.

The author thanks Joshua Aizenman, Willem Buìter, Maury Obstfeld, Lars Svensson, and his colleagues in the Fund for their perceptive comments on earlier versions of this paper.

^{}1

Unfortunately. Keynes does not seem to have gone beyond the mere description of this money-illusion type of phenomenon.

^{}2

This point of view has received further support from Spaventa (1987). He says, for example, that for inflation to be effective, a necessary condition “is that a large share of the outstanding debt consists of fixed-coupon long-term bonds, so that real interest payments can fall roughly in proportion with the real value of the stock of debt” (p. 385).

^{}3

Blanchard, Dornbusch, and Buiter (1985) claim that inflation is negatively related to the real rate of interest, *r*, and that this is an important channel through which inflation can influence the stock of government debt obligations. Although they present some empirical evidence to that effect, however, no specific mechanism is thoroughly discussed in their paper.

^{}4

This does not rule out that bond holders invest in domestic capital. With perfect capital mobility, however, the opportunity cost of funds *at the margin* is given by the rate of return on foreign bonds, so equation (4) has to hold.

^{}5

For the analysis of this section it is irrelevant whether the devaluation has or has not been anticipated. It is more important that no *further* devaluation is expected—an approximation of the more realistic case in which a devaluation momentarily restores trust in the currency’s value. See Section II for further discussion of these issues.

^{}6

Thus, contrary to the previous case, the focus here is on a particular point in time, *T*, but the (constant) operational deficit, *d*. can be any arbitrary number.

^{}7

In the staggered-prices model studied in Calvo (1983), however, prices never rise by the full amount of the devaluation before the devaluation takes place.

^{}8

In my opinion, some clear and interesting examples of “incomplete” devaluations can be found in Argentina’s recent history. These are the Martínez de Hoz devaluation of February 1981 and the one carried out by Sìgaut in March 1981 (see Calvo (1986) and de Pablo and Martinez (1988)).

^{}9

In a study of several “crisis” episodes in various member countries of the Organization for Economic Cooperation and Development, it is shown that “in no case did a new crisis erupt within the first year or so of the measures having been taken” (OECD (1988, p. 17)).

^{}10

If a devaluation was expected and does not take place, unemployment is likely to increase. Furthermore, once the public realizes that a devaluation will not happen, prices will begin to fall, increasing the real value of debt. All of these effects are likely to give rise to further devaluation incentives.

^{}11

In Calvo (1988 and 1989). examples are given in which multiple expectations-led equilibria occur even though expectations are constrained to be fully rational.

^{}12

It is worth noting, however, that if prices rise ahead of the expected devaluation, then the monetary authority may still have incentives to inflate in order to get rid of unemployment.

^{}13

Calvo (1988) shows that open, noninflationary debt repudiation can also be fraught with multiple expectations-led equilibria.