A Stylized Model of the Devaluation-Inflation Spiral
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

CARLOS A. RODRIGUEZ *

Abstract

CARLOS A. RODRIGUEZ *

CARLOS A. RODRIGUEZ *

Devaluations, or the monetization of the resulting balance of payments surpluses, are frequently mentioned as contributing factors to an inflationary process. Aside from the direct initial inflationary effect owing to the rise in the prices of traded goods (and the repercussion on the prices of nontraded goods), a devaluation usually contributes to a (transitory) balance of payments surplus,1 the monetization of which, it may be claimed, further contributes to the sustenance or acceleration of the inflationary process.

It is thus possible to understand the reluctance to devalue in countries that, having achieved a stable domestic price level, face a persistent balance of payments deficit. Alternative corrective measures range from reducing the degree of monetization of the fiscal deficit to obtaining external loans that may help to postpone the required inflationary adjustment.

Rather than resorting to the permanent, but politically costly, fiscal correction, many countries have chosen the way of periodic devaluations, the timing of each being marked by that point at which domestic prices are “well out of line” or international reserves are “dangerously low.” The outcome of such a process is a devaluation-inflation spiral with no clear relation of causality, although the external sector is often blamed for the inflationary outcome.

In this paper, the author has constructed a simple model in which to analyze some of the basic elements of the devaluation-inflation spiral. In the context of the model developed here, the main fuel behind the spiral is the monetization of the fiscal deficit and devaluation, and the subsequent inflation is the only alternative open given the fiscal constraint. In the absence of a steady flow of foreign aid that matches the fiscal deficit, the model generates a devaluation-inflation cycle, devaluation taking place at that point where international reserves reach a minimum acceptable level even though the price level may then be stable. With the possibility of the devaluation taking place when the price level has finally stabilized, there is the temptation of blaming the resulting inflation on the devaluation, and attention may be diverted away from the more basic underlying disequilibrium, which is the fiscal deficit.

Section I of this paper describes the basic structure of the model (a variant of Salter’s (1959) traded-nontraded goods model) in the absence of a fiscal deficit; Section II incorporates the fiscal deficit and describes the devaluation-inflation spiral; Section III brings a brief discussion of flexible exchange rates; and Section IV presents the conclusions.

I. Basic Structure of Model in Absence of Fiscal Deficit

The economy that is described here is small enough in international markets that all prices of traded goods are fixed in terms of foreign exchange. Thus, all traded goods are grouped into a single composite good whose output and consumption rates are denoted by QT and CT; the price of the traded good in terms of foreign exchange is assumed to equal one. The domestic price of the traded good is then equal to the exchange rate, E (units of domestic currency per unit of foreign exchange). The economy also produces and consumes a nontraded “home good” whose output and consumption rates are QH and CH and its price, PH. Given full employment of the fixed factor endowments, the supply of QH and QT depends on the relative price between both goods, EPH =e, the real exchange rate,

QT=QT(e)QH=QH(e)(1)

and supply responses are assumed to be normal, that is,

QTe> 0QHe< 0(1)

The author has abstained from the dynamic considerations of investment and capital accumulation and has assumed that domestic money, M, is the only store of value available to domestic residents.

Demand for traded and home goods depends on the nominal prices of both goods and the nominal money stock; furthermore, the author has assumed away “money illusion,” so that demands must be homogeneous of degree zero in all nominal quantities. Choosing the nominal price of the home good as the deflator for nominal variables, demands are given by

CT=CT(e,m)CH=CH(e,m)(2)

where

m=MPH

Ch and Ct are assumed to change with e and m according to

CHe>0,CHm>0CTe<0,CTm>0(2)

The stock of international reserves held by the central bank is R, and its rate of change (in the absence of capital flows) equals the excess supply of traded goods (the balance of trade = payments surplus):

dRdt=R˙=QT(e) −CT(e,m)(3)

It follows from the signs assumed in equations (1’) and (2’) that a higher e improves the trade balance, since it increases QT and reduces CT, while a higher m deteriorates the trade balance, since as consumption increases, the export surplus is reduced.

Market equilibrium for home goods is assumed to prevail at all times; this is achieved through movements in the domestic nominal price of home goods, PH, which, given the fixed M and E at any time, imply opposite movements in e and m:

QH(e)=CH(e,m)(4)

As shown in Figure 1, a higher stock of real cash balances—m—increases CH and requires a higher relative price of home goods—a lower e—to clear the market. Thus, for the market equilibrium for home goods, e and m are inversely related. Denote the reduced form relationship between m and e so that the home goods market clears by

m=H(e)H(e)< 0(5)

Since equation (5) must prevail at all times, we can substitute it in equation (3) to obtain the change in reserves only as a function of the real exchange rate:

R˙=f(e)QT(e)CT[e,H(e)](6)

where

f(e) =QTe −CTe −CTmH(e)>0

The author has assumed that there is some value of e such that the excess supply of traded goods is zero, that is, R is not changing. Denoting ē as that value of the real exchange rate, ē must satisfy

R˙=f(e¯)=0

Associated with ē, there is a level of real cash balances, m, that guarantees market equilibrium for home goods:

m¯=H(e¯)

If the only source of money creation is reserve purchases by the central bank, it is clear that m and ē are the long-run equilibrium values for e and m, since when e equals e, the nominal money supply remains unchanged, and thus there is no reason for either PH, e, or m to change. A more detailed analysis of the dynamic adjustment of the economy follows.

In the absence of domestic credit creation, the nominal money stock increases by the value of foreign exchange purchases by the central bank:

= E Ṙ, or, using equation (6),

M˙E=f(e)(7)

Thus, M˙E will be greater or less than zero as the balance of payments is in surplus or deficit.

Figure 2 describes the dynamic behavior of the economy. The downward sloping schedule HH shows the combinations of m and e for which the home goods market is in equilibrium, as in equation (4) or (5). The vertical line at e = ē represents the only level of e for which Ṁ = Ṙ = 0.

At any instant, the nominal money stock is a predetermined variable, as is, of course, the nominal exchange rate; thus, the ratio M/E is fixed at any time, although through time it changes according to equation (7). Since M/Eme, it follows that at any instant the ratio m/e is a predetermined variable. In Figure 2, the line 0M(t0)E0 shows the prevailing m/e ratio at time t0, given the nominal money stock M(t0) and the (fixed) exchange rate E0. Short-run equilibrium is then attained at the intersection of the 0M(t0)E0 line with the HH schedule, at point a. Any point on the feasible locus 0M(t0)E0 below a would imply an excess supply of home goods that is corrected through a lower PH, increasing both m and e and thus moving the equilibrium point toward a. Corresponding to the initial ratio M(t0)E0 are the short-run equilibrium values m(t0) and e(t0). Since e(t0) is shown to be less than e, the balance of payments is in deficit, so that R and M are falling. As M falls, the M(t)E0 line rotates clockwise, and thus the short-run equilibrium position moves southeast along HH until ē is reached, at which point external balance is attained, so that the money supply remains unchanged and the motion of the M(t)E0 line stops as the system reaches its steady state equilibrium with external balance and price stability.

An alternative and more intuitive explanation of the adjustment process is as follows. Starting with an initial stock of cash balances such that the balance of payments is in deficit, the subsequent fall in M owing to reserve losses decreases the demand for home goods, thus requiring a lower nominal price of home goods to clear that market. The fall in both PH and M work toward a reduction in the balance of payments deficit, as consumption of traded goods is decreased while production increases. As long as the balance of payments remains in deficit, M and PH keep falling through time and the balance of payments keeps improving; eventually, M and PH fall to a level low enough to yield balance of payments equilibrium, at which point M, and thus PH, tends to remain stable as external balance is finally achieved.

II. Structure of Model with Fiscal Deficit and Description of Devaluation-Inflation Spiral

Assume now that the government is committed to purchase a fixed amount, g0, of traded goods per unit of time, and that those purchases are financed through central bank credit (assuming that the government purchases of home goods would not change any of the basic conclusions of the model). There are now two sources of monetary expansion: reserves, R, and credit to the government, D. The nominal money supply changes according to

M˙=ER˙+D˙(8)

Dividing equation (8) by E

M˙E=R˙+D˙E(9)

Notice that Ḋ/E is the rate of government spending on traded goods (Ḋ/E = g0), so that equation (9) becomes

M˙E=R˙+g0(10)

We must now account for the fact that the rate of change in reserves equals the private sector’s excess supply of traded goods—equation (6)—minus the rate of government purchases of traded goods (g0), so that

R˙=f(e)g0(11)

from which, it follows that for to equal zero, a real exchange rate higher than ē is required in order to induce a positive excess supply of traded goods by the private sector to match the government demand. Let ê denote that level of e for which Ṙ = f(ê) – go = 0; necessarily, ê must be larger than ē (ē being such that f (ē) = 0).

Substituting equation (11) in equation (10), we obtain the final expression for the change in the nominal money stock:

M˙E =f(e)(12)

Thus, for Ṁ/E to equal zero, e must equal ē. Therefore, the level of the real exchange rate that is consistent with a stable money stock (and thus, price stability) is smaller than the one required for external balance, ê: price stability can be achieved only at the expense of a continuous balance of payments deficit. Figure 3 describes the dynamic behavior of the economy, given a positive level of deficit-financed government spending on traded goods.

Before the introduction of the deficit-financed spending, the economy was at its steady state equilibrium at point a, for which both and were zero. With the introduction of a positive rate of government spending, g0, the = 0 line shifts to the right up to e = ê, such that f(ê)g0 = 0. Neither the market equilibrium schedule for home goods nor the = 0 schedule is affected by the new rate of government spending. At the instant of the change, nothing happens with e and m, as all of the government deficit is financed with reserve losses. (Since e = ē is now less than ê, the balance of payments is in deficit.) Thus, the introduction of government spending on traded goods does not have an instantaneous inflationary impact on the prices of home goods, as all the excess demand for traded goods is equilibrated through reserve losses.

Assume now that in the initial situation international reserves were at a level (Ra) that was judged to be an acceptable long-run average. Assume also that there is a minimum acceptable reserve level (Rm) at which the central bank has to take corrective action. Assuming that the fiscal deficit cannot be removed and that a permanent inflow of foreign aid cannot be obtained, the only corrective action left to the bank is devaluation. Furthermore, it is not sensible to assume that the devaluation will be aimed at yielding precisely external balance, because in that case reserves would be stabilized only for a moment: since the money supply keeps increasing on account of domestic credit creation, the balance of payments would turn into deficit immediately afterward and thus reserves would fall again below Rm. The author has thus assumed that the central bank would devalue sufficiently to generate a period of balance of payments surpluses that would bring the stock of reserves back to the average acceptable level, Ra.

Going back to Figure 3, after the increase in g, the system remains motionless at point a while reserves are running down; when RaRm of reserves is lost, a devaluation takes place. At the prevailing nominal price for home goods, the immediate effect of the devaluation is to increase the price of traded goods, and thus resources are shifted away from the production of home goods into that of traded goods, while the demand for home goods is increased; there is thus a potential excess demand in the home goods market that is cleared through a higher PH. The increase in the nominal price of home goods must, however, be smaller than the rise in the nominal exchange rate, so that the impact effect of the devaluation is to increase the level of the real exchange rate. To see this, assume that in response to the rise in E, the price of home goods were to increase in the same proportion, such that e remained unchanged; abstaining from any real cash balances effect, both supply of and demand for home goods would then remain at their same predevaluation levels (since e would then be the same). Real cash balances, however, must be lower, since PH has risen and thus CH must have fallen, even though e is unchanged; there must then be an excess supply of home goods calling for a lower PH. It follows that, after the devaluation, PH must rise but in a smaller proportion than the increase in E.

Following the impact effect on the prices of home goods, the higher real exchange rate induced by the devaluation is assumed to turn the balance of payments into surplus. The previously stable money supply now starts rising on account of both credit creation to finance the fiscal deficit and the monetization of the reserve inflow. As M increases through time, the demand for home goods also increases, requiring a rising nominal price of home goods to clear the market. The rising PH, in turn, implies a falling real exchange rate, and thus the initial resource shift toward the traded sector is slowly reversed. Eventually, the reduction in the real exchange rate and the accumulation of cash balances is enough to eliminate the excess supply of traded goods, and reserves stop increasing as external balance is achieved. The nominal money supply, however, is still rising owing to the domestic credit creation to finance the fiscal deficit. Thus, the nominal price of home goods continues increasing, and as the real exchange rate still falls, the balance of payments turns into deficit. For a while, the contractionary effects on the money supply of the reserve losses are not enough to offset the expansionary effects owing to domestic credit creation, so that the money supply keeps rising. However, as M and PH go on increasing, the balance of payments deficit grows larger until eventually it reaches a level for which the value of reserve losses precisely equals that of domestic credit creation, and the money supply stops rising. With M stabilized, there is no tendency for the price of home goods or the real exchange rate to change, and thus a period of price stability and falling reserves is reached.

In terms of Figure 3, the impact effect of the devaluation is to shift the ME line from M(to)Eo to M(t0)E1 instantaneously, and the real exchange rate is increased from ē to e1, which has to be larger than ê in order for the balance of payments to be in surplus. The impact effect of the devaluation is to reduce real cash balances, and this is achieved through a jump in the price of home goods; notice, however, that since e has increased, the proportional increase in PH must be less than that of the devaluation.

Following the impact effect, the money stock starts increasing, as e1 > ē, so that the M/E line shifts counterclockwise, and the equilibrium point shifts along HH from b toward c. During this transitional period, the money supply increases because of both reserve purchases and domestic credit creation. As time passes, m rises while e falls. Given the fixed nominal exchange rate E = E1, the fall in e is due to a rising price of home goods. Thus, after an initial period of price stability, the outcome of the devaluation is an instantaneous jump in the prices of home goods followed by a smooth rate of increase. Therefore, the temptation to blame the devaluation for the subsequent inflation is almost unavoidable, although careful analysis shows that the devaluation was the only corrective measure left, given the structural imbalance provided by the fiscal constraint.

If the rate of devaluation was properly chosen, reserves must have reached the target level Ra when the turning point c is reached. At c, the balance of payments turns again into deficit and the equilibrium point keeps moving along HH toward a. In the transition from c to a, the money stock keeps growing as domestic credit creation exceeds the value of reserve losses. As e keeps falling, PH must keep rising. Since m is also rising, the rate of monetary expansion must exceed that of inflation in the prices of home goods (which in turn is larger than that of the overall price level, since the prices of traded goods remain constant). Eventually e falls enough so that the balance of payments deficit equals the rate of domestic credit creation, and, as point a is reached again, the nominal money stock stabilizes, as also do m, e, and PH. If reserves then still exceed Rm, another period of price stability may ensue, although eventually a new devaluation will be necessary as reserves hit Rm and the cycle starts again.

In this devaluation-inflation cycle, the price of home goods experiences three distinct phases: (1) a stable period, as the system rests at a while decumulating reserves; (2) a jump at the moment of the devaluation, as the equilibrium point moves from a to b; (3) a positive but decelerating inflation rate, as the equilibrium shifts back from b to a along HH.

International reserves follow a cyclical pattern with the troughs being reached when devaluations take place and the peaks when the equilibrium path reaches point c along HH. The nominal money stock follows two phases: (1) a stable money supply, as the system rests at point a; (2) a positive but decelerating rate of expansion, as the equilibrium moves from b to a.

Figure 4 shows the typical path for the price level. Even though PH has periods of stability, the system has a built-in inflation rate that, on average, will equal the average rate of monetary expansion for the typical cycle. Since over the typical cycle, international reserves transactions do not contribute to the money supply (at the given exchange rate reserves are built up from Rm to Ra and then lost again), all the increase in the nominal money supply must be due to domestic credit creation; thus, on the typical cycle

g0=ΔDE =ΔME =ΔMMME

so that ΔMM =g0/mT

where mT =ME is the average value of real cash balances in terms of traded goods. The average inflation rate in the prices of home goods and of traded goods, π, equals the average rate of monetary expansion over the cycle, so that

π = g0/mT

III. Flexible Exchange Rates

As we have seen, given the fiscal constraint, the objectives of external balance and price stability are incompatible with each other under a fixed exchange rate. The result is a series of periods of balance of payments crisis and devaluations followed by rising prices. The nominal price of home goods goes through phases of stability, sudden jumps, and steady inflation, an outcome that certainly is not conducive to an orderly and efficient allocation of resources. In this circumstance, neither a stable nor a smooth path of prices is achieved under fixed rates, and a free floating or crawling peg system may be preferable. Under the floating system, the central bank abstains from intervening in the foreign exchange market, and the nominal exchange rate will adjust so that external balance is continuously achieved. Since = 0 at all times, the economy will always be at point c in Figure 3 with the real exchange rate at the level ê and inflation proceeding at the stable rate π =g0mT. An alternative to a freely floating rate is a crawling peg with periodic but small devaluations. In this case, the signal for the devaluation can still be given by the level of reserves, but in order to reduce the size of exchange rate adjustment, the minimum acceptable level Rm should be put as close as necessary to the acceptable level Ra, since the size of the exchange adjustment and the length of the typical cycle vary directly with the difference between Ra and Rm.

IV. Conclusions

In this paper, the author has developed a simple model to analyze some of the essential elements of the inflation-devaluation spiral in the presence of a real government deficit financed through credit creation by the central bank. He has shown that under those circumstances the objectives of price stability and external balance are mutually inconsistent, and that the likely outcome, as the economy moves along the stages of the typical cycle, is successive periods of price stability and external deficit, devaluation followed by inflation and external surplus, and finally decelerating inflation and external deficit. While casual observation would indicate that inflation is being preceded by devaluation and monetization of the resulting balance of payments surpluses, the conclusion that the external sector is the cause of the inflation would be inappropriate. Although it is correct that over a short period following the devaluation external sector developments lead the movement in domestic prices, over the entire typical cycle the price level follows the path of the money supply, which is determined entirely by domestic credit creation to finance the fiscal deficit. (As we saw in Section II, the external sector does not contribute at all to money creation over the whole of the typical cycle.) Once the proper time dimension is recognized, it follows clearly that the price level and the exchange rate are endogenous variables with no direct causality relations between them, both being led by developments in the monetary sector, which are in turn determined by the monetization of the internal fiscal deficit.

REFERENCES

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*

Mr. Rodriguez, associate professor at Columbia University, was on leave as a visiting scholar in the Asian Department of the Fund when this paper was prepared. He is a graduate of the University of Chicago.

1

The transitory effect of a devaluation on the balance of payments is emphasized in the recent literature on the monetary approach to the balance of payments; see, for example, Dornbusch (1973) and Frenkel and Rodriguez (1975).