Multiple Exchange Rates, Fiscal Deficits and Inflation Dynamics
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

The paper explores the inflationary implications of exchange rate regime reforms in a small open economy model combining the public finance view of inflation with multiple exchange markets. To account for the experience of many developing countries, the analysis focuses on transitions to multiple official exchange markets. In those countries, multiple exchange rates were often announced as temporary. The paper shows that the dynamic response of inflation to the reform markedly differ whether the announcement is credible or not. The paper also compares the response of inflation under a fixed crawl of nominal official rates and under the presence of policy rules aimed at reducing the spread between the official and parallel exchange rates.

Abstract

The paper explores the inflationary implications of exchange rate regime reforms in a small open economy model combining the public finance view of inflation with multiple exchange markets. To account for the experience of many developing countries, the analysis focuses on transitions to multiple official exchange markets. In those countries, multiple exchange rates were often announced as temporary. The paper shows that the dynamic response of inflation to the reform markedly differ whether the announcement is credible or not. The paper also compares the response of inflation under a fixed crawl of nominal official rates and under the presence of policy rules aimed at reducing the spread between the official and parallel exchange rates.

I. Introduction

The literature on multiple exchange rates is extensive. So far, most of the analytical work on multiple exchange rates has been concerned with the response of exchange rates to exchange rate unification (see, i.e. Lizondo, 1987; Agénor and Flood, 1992). By contrast, the inflationary implications of exchange rate regime reform is an issue that has only received little attention. 2/ The objective of the present paper is to address this issue.

To explore this issue, the present paper develops a simple model of a small open economy with multiple exchange rates. The model combines two important features: the public finance view of inflation, that is the central bank’s financing of government fiscal deficits; and multiple exchange markets, where a freely floating parallel exchange rate co-exists with several official exchange rates. The public finance approach to inflation implies that money creation through financing of the government budget deficit is the key convergent driving force of the economy. This feature contrasts with most earlier analyses of multiple exchange rate systems where money creation originates mainly from changes in official holdings of foreign exchange reserves. The presence of several official exchange rates, hitherto neglected in the literature, complements the fiscal dimension of inflation. 3/ In effect, in many developing countries using multiple exchange rates, central bank’s exchange losses account for a large part of the government fiscal deficit. 4/ Central bank’s exchange losses (that is, the quasi-fiscal deficit) then constitute a potential source of inflation, thereby creating a direct linkage between exchange rate regime reforms and inflation. 5/

We use this model to analyze the short- and long-run response of the economy, particularly the black market premium and inflation, to the adoption of multiple official exchange rates. It is reported by Quirk and al. (1987) that in many countries, multiple exchange rates were initially viewed as temporary. In most cases however, their elimination proved difficult, and they were maintained over an extended period of time. To reflect this experience, the analysis developed below considers the case when the adoption of multiple exchange rates is accompanied by the authorities’s announcement to return to a uniform official exchange market in the future. Both cases, when the announcement is fully credible and when it is not credible, are discussed.

We also explore the response of inflation to exchange rate reforms in the presence of a policy rule governing the rate of depreciation of the official rates. Following Kharas and Pinto (1989), we assume that the monetary authorities depreciate the official rate towards the parallel exchange rate in order to reduce the premium on foreign exchange in the black market. We show that this rule affects both the long-run and short-run reactions of domestic inflation.

The rest of the paper is organized as follows. The model is presented in section 2. In section 3, the dynamics of the model is described while the steady-state properties of the model are discussed in section 4. In section 5, the dynamic adjustment of the economy to the adoption of multiple exchange rates is analyzed, while section 6 examines the response of inflation in the presence of government’s exchange rate rules. Finally, section 7 offers some conclusions.

II. The Model

This section develops a simple continuous-time, perfect foresight model of a small open economy operating a multiple exchange rate system. The model is simplified as much as possible to keep analytical clarity without losing what is essential for the problem at hand. 6/

The model represents a small open economy operating a multiple exchange rate regime in which a freely determined parallel exchange rate (s) coexists with two official rates, one for export transactions (ex) and one for import transactions (em). The two official rates apply to current account transactions authorized by the authorities, whereas all the capital account transactions and the rest of the current account transactions are settled on the parallel market at the free exchange rate. It is further assumed that the government rations the official foreign exchange market by imposing import licenses so as to maintain the level of international reserves constant.

The economy produces a single exportable good whose domestic supply is exogenous and constant over time:

yt=y*(1)

Exporters can repatriate their foreign exchange earnings either via the official market, where they earn the rate ex, or via the parallel market, where they receive the rate s. Exports on the parallel market are assumed to be a constant fraction z of total exports, y*. Normalizing the foreign price of the exportable good to unity, the foreign currency value of exports on the parallel market and the official market are zy* and (1-z)y*, respectively. The authorities are assumed to ration the official foreign exchange market so as to maintain the level of official reserves constant, that is:

R˙t=0(2)

where R denotes the stock of official reserves, in terms of foreign currency.

As all the capital transactions are settled on the parallel market, it follows from condition (2) that the current account in the official market is balanced at all time. Export receipts surrendered on the official market are used in part to finance government purchases of goods and services, gf, the rest being affected to household’s imports of consumption goods, y*(1-z)-gf.

There are no private banks. Since the stock of official reserves remains constant over time, the change in the stock of domestic money is simply the sum of changes in central bank domestic credit and central bank’s exchange losses:

M˙t=D˙t+ELt(3)

where D denotes central bank domestic credit, and EL denotes central bank’s exchange losses. 7/

Central bank’s exchange losses are equal to: 8/

ELt=y*(1z)(etxetm)(4)

Government expenditures are composed of a foreign and a domestic component. As mentioned earlier, the foreign component consists of government purchases of goods and services, gf, which are set fixed in foreign currency. The domestic component of government expenditures consists of wages and salaries whose real value, g, in terms of the domestic price level, is assumed to be fixed, owing for instance to full indexation mechanisms; that is: gt - g*. As is the case in many developing countries, government revenues consist essentially of taxes levied on international transactions, both exports and imports. For simplicity, it is assumed that exports and imports of goods and services are taxed at a similar rate, t*. Notice that taxes collected on international transactions are converted in domestic currency at the official exchange rates. It follows that an increase in the level of official rates raises the domestic currency value of fiscal revenues, while an appreciation of the official rates has the opposite effect. Under the assumptions that domestic credit to the private sector is constant, and the government deficit is fully financed by central bank money, the change in central bank domestic credit is exactly equal to the government budget deficit:

D˙t=Ptg*+etmgf(1+t*)y*(1z)(etx+etm)t*(5)

The demand for domestic real money balances is assumed to depend solely on the domestic nominal rate of interest:

Mt/Pt=h[it];h<0(6)
h[it]=γαit(7)

Under the assumptions of perfect international capital mobility and risk-neutrality, the interest rate parity holds on the free market:

it=if+s^t(8)

where if is the foreign interest rate and is constant.

The central bank is assumed to maintain a constant spread, u, between the official exchange rate for export transactions and the official rate for import transactions. Defining e, the mid-point official exchange rate, we have :

etx=et(1+0.5u)(9)
etm=et(10.5u)(10)

where u is a positive constant. 9/ Furthermore, it is assumed that the central bank depreciates the mid-point official exchange rate at a constant rate, ê, where ê is exogenous.

According to expressions (9) and (10), the exchange rate at which the central bank purchases foreign exchange from exporters is more depreciated than the rate at which it sells foreign exchange to importers, which implies that the central bank makes losses on its foreign exchange transactions.10/

For simplicity, we assume that the domestic price level depends only on the parallel exchange rate. Normalizing the world price of the tradable good to unity, this gives: 11/

Pt=St(11)

Denoting m=(M/e), the real money stock in terms of the average official exchange rate, and d=(s/e), the black market premium, equations (6) and (8) can be rewritten as: 12/

mt/dt=h[it](12)
it=if+(d˙t/dt)+e^(13)

After straightforward substitutions, the model can be summarized in two differential equations in dt and mt:

d˙t=[(γ/α)ife^]dt(1/α)mt(14)
m˙t=dtg*+kfmte^(15)

where kf = gf(1+t*)(1-0.5u) + y*(1-z)(u-2t*) represents the deficit of the public sector, including the central bank, on its foreign exchange account.

Table 1.

List of variables

article image

III. Dynamic analysis

Linearizing equations (14) and (15) around the initial steady-state, and expressing each variable in terms of deviation from the steady-state, the dynamic model can be rewritten: 13/

d˙t=(1/α)[mtm*]+(1/α)(m*0/d*0)[dtd*](16)
m˙t=g*[dtd*]e^[mtm*](17)

where d* and m* denote the steady-state value of the black market premium and the real stock of domestic money, respectively. The real stock of domestic money is a predetermined variable, while the black market premium is a forward-looking variable.

Using matrix notation, we obtain:

[d˙tm˙t]=[(1/α)(m*0/d*0)(1/α)g*e^][dtd*mtm*](18)

The determinant of the coefficient matrix is:

det=-e^(1/α)(m*0/d*0)+(1/α)g*

whose sign is undetermined. For the system to be saddle-point stable, the determinant must be negative, a condition that will be satisfied if:

d*0g*-e^m*0<0(19)

This condition requires that, in the initial steady-state, the government revenues collected through the inflation tax exceeds domestic government expenditures on wages and salaries. In other words, the stability condition requires that the contribution of the domestic part of the budget to real money creation be negative.

The solution to the system of first-order linear differential equations described by (18) is: 14/

mtm*=A exp(λ1t)+B exp(λ2t)(20)
dtd*=A[1h[i*0]αλ1]exp(λ1t)+B[1h[i*0]αλ2]exp(λ2t)(21)

where h[i*0] = m*0/d*0 = α - γi*0, λ1 and λ2 are the negative (stable) and positive (unstable) roots, 15/ and A and B are as yet undetermined coefficients. The phase diagram of the system is depicted in figure 1. 16/

Figure 1.
Figure 1.

Phase diagram

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

Ruling out speculative bubbles require setting B = 0 in equations (20) and (21). It can be shown that, along the saddle path, the real stock of domestic money and the black market premium evolve according to:

dtd*=[1h[i*0]αλ1](mtm*)(22)

which indicates that the saddle-path is positively sloped. It is represented in figure 1 by the positively sloped SS-line. 17/

Given the assumption of perfect international capital mobility, the domestic rate of inflation, or alternatively the expected rate of nominal depreciation of the parallel exchange rate, rises and falls, point by point, with the differential between the domestic and world interest rates. Using (7), (8), and (12), we obtain that domestic inflation is determined according to:

πt=(1/α)(mt/dt)+(1/α)(γαif)(23)

where πt = ŝt denotes the domestic rate of inflation.

Linearizing expression (23), substituting expressions (20) and (21) into the resulting expression, and setting B=0, we obtain that, along the saddle path, the domestic inflation rate evolves according to:

πtπ*=A(1/α)(1/d*0)[αλ1h[i*0]αλ1]exp(λ1t)(24)

It can also easily be shown that, along the saddle-path, the relation between domestic inflation and the real stock of domestic money is given by:

πtπ*=(1/α)(1/d*0)[αλ1h[i*0]αλ1](mtm*)(25)

which indicates that as the economy converges towards its long-run equilibrium, the real stock of domestic money and inflation move in opposite directions (as λ1<0).

IV. Steady-State

Setting (dt=0) and (mt=0) in equations (14) and (15) respectively, and solving the resulting equations for d* and m*, we obtain that the steady-state values of the black market premium and the real stock of domestic money are given by the following expressions:

d*=kfg*-e^h[i*](26)
m*=-h[i*][kfg*-e^h[i*]](27)

where, as already mentioned, kf = gf(1+t*)(1-0.5u)+y*(l-z)(u-2t*).

It follows from the stability condition (19) and the assumption that kf is positive (kf>0) that: d*>0, and m*>0. Under the additional assumption that kf > êh[i*]-g*, which amounts to saying that the foreign contribution of the public sector deficit to real money creation exceeds its domestic contribution, we also obtain that d*>1.

The condition that the black market premium is constant in the long-run implies that in the stationary equilibrium the parallel exchange rate depreciates at the same rate as the average official rate. It follows that, in the stationary equilibrium, π* = ê. This latter result implies, in particular, that unless the government supplements exchange rate reforms with a modification of the rate at which the official rate depreciates, the steady-state rate of inflation is invariant to exchange market reforms.

Notice that in the steady-state, the real deficit of the consolidated public sector is financed by the inflation tax êm*.

To illustrate the properties of the model, consider now the effects of a perfectly unanticipated and permanent unification of the official exchange markets. As usual, it is assumed that the economy is initially in a steady-state with d=d* and m=m*. 18/

In the simple model described above, exchange market unification corresponds to the case where u=0. The effect of unification on mt and dt is depicted on figure 2a. The permanent reduction in u shifts the MM-locus to the left, and the steady-state equilibrium moves down from A to C. At point C, the long-run equilibrium of the real stock of domestic money has declined, as well as the stationary value of the black market premium. 19/ This result is explained as follows. The unification of official exchange markets entails a long-run reduction of the consolidated public sector deficit--as central bank’s exchange losses vanish--which must be compensated by a decline of the inflation tax, êm*. As ê is constant, the contraction of seigniorage must originate from a decline of the domestic money stock. Given that the demand for real money balances is unchanged in the long-run, there must be a proportionate reduction of the black market premium.

Figure 2a.
Figure 2a.

Exchange rate unification

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

Upon the unification of the official rates, there must be a jump of the black market premium to place the economy on the new saddle path. Upon the exchange rate unification, individuals come to understand that the black premium will drop in the future, which lead them to revise their expectations about the future path of the black market premium. As if and ê are fixed, this causes a reduction in the domestic interest rate and an increase in the demand for domestic real money balances. As the real money stock (m) is unchanged at the time of the shock, there must be an immediate drop of dt to restore the money market equilibrium. Instantaneously then, the economy is located at B on the new saddle-path, where both variables undershoot their long-run value. Over time, as the economy moves towards its stationary equilibrium, the real money stock and the black market premium are both decreasing.

The transitional dynamics of inflation is depicted in figure 2b. It is shown that inflation falls on impact. The intuitive explanation is as follows. In response to the unification of exchange rates, there is an instantaneous decline in the black market premium, and accordingly an increase of the real money stock. Due to the assumption that capital is perfectly mobile internationally, equilibrium on the domestic money market is restored through a decline of the expected rate of devaluation of the parallel exchange rate, that is the inflation rate. 20/ Until reaching its final steady-state, inflation increases steadily but at a decreasing rate, while remaining below its stationary level.

Figure 2b.
Figure 2b.

Inflation dynamics

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

V. Exchange Reform. Credibility, and the Dynamics of Inflation

This section provides further insights into the dynamics of inflation in response to exchange rate reforms.

The economy is supposed to be initially in a steady-state where a single official exchange rate co-exists with a parallel exchange rate. The policymakers then decide to replace the uniform official rate by two exchange rates, one for export transactions and one for import transactions, the two rates being set according to equations (9) and (10). At the same time, the policymakers announce a return to a uniform exchange rate on a specified future date. In the rest of the section, two cases are examined. In the first case, it is assumed that the announced return to a unified rate is fully credible. In the second case, by contrast, the public does not believe that the multiple exchange rate system will end up at the specified future date.

Case 1. Full credibility

At time t=0 (the “present”), the authorities decide to reform the existing exchange rate arrangement by introducing two official rates. At the same time, they announce a return to the initial exchange rate at a specified future date, T. The announcement is fully credible; that is, the public believes that the multiple exchange rate will be abandoned at time T. Analytically, this scenario is modeled as a temporary change in u: at time t=0, u becomes positive, then returns to zero at time T (>0).

The dynamics of mt and dt over the period preceding and following the return to a uniform exchange rate is given by the following equations:

t<=T

mtm*=A1exp(λ1t)+A2exp(λ2t)(28)
dtd*=A1[1h[i*0]αλ1]exp(λ1t)+A2[1h[i*0]αλ2]exp(λ2t)(29)

t>=T

mtm*u=B exp(λ1t)(30)
dtd*u=B[1h[i*0]αλ1]exp(λ1t)(31)

where m* and d* are the steady-state value of dt and mt, respectively, when the authorities operate multiple exchange rates, while m*u and d*u are the steady-state value when there is a uniform official exchange rate.

The arbitrary constants A1, A2, and B are determined by two conditions: first, an initial condition on the real money stock, mt; second, price continuity, which requires that the time path for mt and dt be continuous for t>0, so preventing any jump of m and d at time T. As shown in appendix 2, the solutions for the arbitrary constants are:

A1=[m*m*u][1+[λ1λ2λ1*h[i*0]αλ2h[i*0]]exp(λ2T)](32)
A2=[m*m*u][λ1λ2λ1*h[i*0]αλ2hi*0]exp(λ2T)(33)
B[m*-m*u][1exp(λ1T)exp(λ1T)]+[m*-m*u][exp(λ2T)exp(λ1T)exp(λ1T)*λ1λ2λ1*h[i*0]αλ2h[i*0]]exp(λ2T)(34)

The dynamics of mt and dt is depicted on figure 3a. In response to the unanticipated increase of u at time t=0, there is a shift of the MM-locus to the right, leading to a shift of the steady-state from A to A’. The new steady-state is however temporary as, at time T, the MM-locus returns to its initial position with m-m*u and d=d*u.

Figure 3a.
Figure 3a.

Exchange rate reform: Full credibility

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

In the short-run, the adjustment of mt and dt is as follows. Upon the introduction of the new exchange rate arrangement at time t=0, anticipations of a future increase in the black market premium drive portfolio holders out of domestic bonds in favor of foreign bonds, leading to an increase of the domestic interest rate. It follows a disequilibrium on the domestic money market, which is immediately restored by a upward jump of the black market premium. Diagrammatically, the economy jumps from A--the initial steady-state- -to B. Formally, the initial reaction of d is given by:

d|t=0d*=[1+αλ1[1exp(λ2T)]h[i*0]αλ1][d*ud*](35)

which implies that: d*u < d|t=0 < d*.

In the aftermath of the exchange reform, the economy moves in the northeast direction, with the real money stock and the black market premium both increasing. 21/ The increase in m is driven by central bank’s exchange losses jointly with the increase in the domestic government expenditures as attributable to the indexation of wages and salaries. The increase in the money stock attenuates the pressure on domestic interest rates, so reducing the depreciation of the parallel exchange rate. It follows, as shown in figure 3a, that the trajectory of the black market premium crosses the DD-locus at some point in time (let’s say t1), after which it starts decreasing while the real money stock keeps on increasing. As d diminishes, the real value of domestic government expenditures diminishes as well, while the increase of the real money stock raises government revenues through its effect on the inflation tax. Both effects contribute to reduce the monetary financing of the fiscal deficit. It follows, as shown in figure 3a, that the trajectory of the real money stock crosses the MM-locus at some point in time (let’s say t2), after which the black premium and the real money stock are both decreasing. At time T, when official rates are re-unified, the economy is located at C on the initial saddle-path. At time T, upon the abandonment of multiple exchange rates, central bank’s exchange losses vanish instantaneously, causing a sharp contraction in money creation. 22/ It follows an increase in the domestic interest rate, which in turn attenuates the anticipated appreciation of the parallel exchange rate.

The dynamics of the black market premium, the real money stock, and domestic inflation is summarized in figure 3b. At time t=0, both the black market premium and inflation jump upward, while the real money stock is unchanged. It can be shown that the larger is T, the larger is the initial rise in d and so the stronger is the immediate acceleration of inflation. The initial acceleration of inflation is however only temporary as, from time t-0, inflation is declining until time T when the economy returns to the uniform official exchange rate. The decline in inflation is required to induce individuals to hold the additional stock of money originating from central bank’s exchange losses. As seen above, the spread between the parallel and the average official exchange rates is maximal at time t1, after which it starts to decline. From time t1 then, the parallel exchange rate depreciates at a lower rate than the official rate, which implies that from t1 to the final steady-state, inflation remains below its long-run level. At time T, upon the abandonment of multiple exchange rates, the sharp contraction in money supply causes a reversal in the dynamic adjustment of inflation. The contraction of the real money stock is accompanied by an increase of the domestic interest rate, which leads individuals to anticipate a higher rate of depreciation of the parallel exchange rate and an acceleration of inflation.

Figure 3b.
Figure 3b.

Dynamics of d, m, and Π

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

Case 2. Imperfect credibility

In this case, it is assumed that the public does not believe that policymakers will decide a return to a unified exchange rate at date T; that is, the public perceives the exchange reform as being permanent instead of temporary. This case is therefore tantamount to an unanticipated and permanent increase in u. 23/

The dynamics of inflation is depicted on figure 4. Upon the reform of the exchange rate regime, there is an immediate increase in the domestic inflation rate and a depreciation of the parallel exchange rate. At that time, inflation overshoots its long-run value. Afterwards, inflation declines until it returns to its unchanged stationary level. Notice that if, contrary to individuals’ beliefs, the authorities restore an unified official exchange market at time T, inflation falls instantaneously below its long-run level and next increases until reaching its stationary level.

Figure 4.
Figure 4.

Inflation dynamics: Imperfect credibility

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

VI. Exchange Reforms. Exchange Rate Rules, and Inflation

So far, it has been assumed that the average official rate was depreciating at a constant rate, ê. Following Kharas and Pinto (1989), it is now assumed that the authorities adjust continuously the official average rate in the hope of reducing the black market premium. Formally, we have:

e˙t=θ(Stet);0θ1(36)

where θ is a constant.

Expression (36) can be rewritten as:

e^t=θ(dt1)(37)

The extended model is obtained by substituting (37) into (14) and (15), which gives:

d˙t=[(γ/α)if+θ]dt(1/α)mtθdt2(38)
m˙t=kf+g*dtθ(dt1)mt(39)

Linearizing equations (38) and (39) around the initial steady-state, and expressing each variable in terms of deviations from the steady-state, the dynamic model can be rewritten, using matrix notations:

[d˙tm˙t][(γ/α)if+θ2θd*0(1/α)g*θm*0θ(1d*0)][dtd*mtm*](40)

The determinant of the coefficient matrix is:

det =[(γ/α)if+θ2θd*0][1d*0]θ+(1/α)[g*θm*0]

For the system to be saddle-point stable, the determinant must be negative, which will be the case if:

(γ/α)if+θ2θd*0>0
g*-θm*0<0

The phase diagram of the system is depicted in figure 5. From the above conditions, the dynamic system is saddle-point stable with a unique convergent path to the equilibrium that is represented by the upward-sloping SS-line. 24/

Figure 5.
Figure 5.

Phase diagram

(Exchange rate rules)

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

Following the same procedure as in section 3, it can be shown that along the saddle-path, the real stock of money, the black market premium and the domestic rate of inflation evolve according to:

dtd*=[1h[i*0]αθd*0αλ1](mtm*)(41)
πtπ*=(1/α)(1/d*0)[αθd*0+αλ1h[i*0]αθd*0αλ1](mtm*)(42)

The steady state rate of inflation, π*, is given by:

π*=θ[d*-1](43)

which indicates that stationary inflation is positively related to the long-run level of the black market premium. Notice also that inflation is always positive.

We suppose now that the economy is initially in a steady-state with a uniform official exchange and that, at time t=0, the policymakers decide to introduce a new exchange rate arrangement with the two official markets. The exchange rate reform is unanticipated and permanent. As shown on figure 6a, the exchange rate reform shifts the MM-locus to the right. It results an increase in the long-run equilibrium value of the real money stock and the black market premium. Instantaneously, there must be a upward jump of the black premium to place the economy on the new saddle-path. In the aftermath, as shown on figure 6a, the black market premium and the real money stock are both increasing.

Figure 6a.
Figure 6a.

Dynamics of m and d

(exchange rate rule)

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

The long-run and short-run reaction of inflation is depicted on figure 6b. As figure 6b shows, inflation increases in the long-run, which means that by following the exchange rate rule (37), the authorities allow the deterioration of the public finance to translate into a permanent increase in inflation. Instantaneously, in order to equilibrate the domestic money market, inflation must rise, which is represented on figure 6b by an upward jump of π. Formally, the initial reaction of inflation is given by:

Figure 6b.
Figure 6b.

Inflation dynamics

(exchange rate rule)

Citation: IMF Working Papers 1996, 056; 10.5089/9781451968378.001.A001

π|t=0π*=(1/α)(1/d*0)[αθd*0+αλ1h[i*0]αθd*0αλ1](m*um*)

which indicates that, at time t=0, inflation can either undershoot or overshoot its long-run equilibrium, depending on the sign of αθd*0+αλ1. In the former case, the initial increase in inflation is only temporary as inflation declines after the shock. In the latter case, inflation accelerates over time until it reaches its long-run stationary level. 25/

VII. Conclusions

In this paper, we investigated the short-run and long-run effects of exchange rate regime reforms on inflation in a simple model of a small open economy combining the public finance approach of inflation with the presence of multiple exchange markets. The present paper focussed on reform measures comprising the introduction of multiple exchange rates applied to official current account transactions.

Assuming a fixed crawl of the official exchange rates, we explored in a first part how credibility issues affect the dynamic adjustment of inflation when the transition to multiple official exchange rates is announced as only temporary. In this respect, our analysis showed that the dynamics of inflation markedly differs whether the reform is perceived as permanent or temporary. In particular, we have seen that if the exchange rate reform is announced as temporary but is viewed as permanent by the public, inflation accelerates upon the reform but next declines steadily until it returns to its initial stationary level. By contrast, if the public views the reform as temporary, the adjustment of inflation is more erratic: inflation first accelerates upon the transition to multiple exchange rates, next declines sharply below its stationary level and then rebounds after the return to a unified official exchange rate. The analysis also showed that the longer multiple exchange rates are expected to remain in place, the larger will be the initial acceleration of inflation. These results suggest that the adverse inflationary effects of transitions to multiple official exchange markets will be the smaller, the stronger the authorities’s commitment to keep the multiple exchange rate arrangement temporary, and the shorter the period of time over which it will be maintained.

In a second part, the paper examined to what extent the inflationary implications of the reform are affected by adopting an exchange rate policy consisting in a continuous adjustment of the official rate in order to reduce the spread with the parallel exchange rate. Our analysis made clear that the short-term and long-term effects of the transition to multiple official exchange markets under this alternative exchange rate policy are different from those arising under a fixed crawl. In particular, we have seen that in an economy with a fixed crawl of the nominal official exchange rate, a permanent transition to multiple official exchange rates has only a temporary impact on inflation. By contrast, when the authorities adjust the official exchange rate in order to reduce the spread with the parallel exchange rate, the impact on inflation is permanent. In this latter case, the analysis also showed that the initial reaction of inflation can either undershoot or overshoot its long-run stationary level, whereas there is only overshooting in the former case.

In the presence of exchange rate rules governing the depreciation of the official exchange rates, it is important to notice that the steady-state reaction of inflation is dependent on the impact of the exchange reform on public finances. In the present analysis, we have assumed that the transition to multiple exchange rates was accompanied by a permanent increase in the consolidated public sector deficit because of higher central bank’s exchange losses. We have seen that under this assumption the economy converges to higher inflation. Conversely, it can be shown that the economy will converge to lower inflation if the exchange rate reform is accompanied by a permanent improvement of public finance--which will be the case if the exchange rate set for export transactions is less depreciated than the rate for import transactions. These results have clear-cut policy implications. They suggest that a fixed crawl will attenuate the inflationary implications of adopting multiple official exchange rates when the exchange rate reform entails a permanent deterioration of public finances. By contrast, if public finances improve permanently because of higher central bank’s revenues, a policy of adjusting the official rate to the parallel rate will allow a permanent reduction of inflation.

Appendix 1. Derivation of the dynamic equations for dt and mt.

The dynamics of the model is described by two first-order linear differential equations in dt and mt. Using matrix notations, we have:

[d˙tm˙t]=[(1/α)(m*0/d*0)(1/α)g*e^][dtd*mtm*](A1.1)

The equations of motion of dt and mt along the saddle-path are given by:

dtd*=Ax1exp(λ1t)(A1.2)
mtm*=Ax2exp(λ1t)(A1.3)

where x1, x2 are the elements of the characteristic vector associated to the stable root (λ1), and A is an arbitrary constant to be determined, whose j value depends upon the change in the steady-state, which in turns depends on the particular disturbance impinging on the economy.

The elements x1 and x2 of the characteristic vector are obtained by solving:

[(1/α)(m*0/d*0)λ1(1/α)g*e^λ1][x1x2]=[00](A1.4)

It follows from (A1.4) that x1 and x2 are such that:

[(1/α)(m*0/d*0)-λ1]x1 -(1/α)x2 = 0

Setting arbitrarily x2=1, the value of x1 is:

x1=1h[i*0]αλ1;h[i*0]=m*0/d*0

Substituting x1 and x2 into (A1.2) and (A1.3) gives:

mt - m* = A exp(λ1t)

dtd*=A[1h[i*0]αλ1]exp(λ1t)

Appendix 2. Determination of A1, A2 and B

This appendix determines the value of the arbitrary constants A1, A2, and B in equations (28) to (31), which describe the behavior of mt and dt over the period preceding and following the re-unification of exchange rates at time T. For convenience, the equations are reproduced here:

t<=T

mtm*=A1exp(λ1t)+A2exp(λ2t)(A2.1)
dtd*=A1[1h[i*0]αλ1]exp(λ1t)+A2[1h[i*0]αλ2]exp(λ2t)(A2.2)

t>=T

mtm*u=Bexp(λ1t)(A2.3)
dtd*u=B[1h[i*0]αλ1]exp(λ1t)(A2.4)

The arbitrary constants A1, A2, and B are determined by two conditions: first, an initial condition on the real money stock, mt; second, price continuity.

Condition 1.

The stock of real money balances, mt, is a predetermined variable that only change gradually over time in response to central bank’s exchange losses and government fiscal imbalance. Accordingly, at the time multiple exchange rates are introduced (t=0), mt is not allowed to jump, which implies that:

m|t=0m*=m*um*=0(A2.5)

Setting t=0 into (A2.1) and substituting into (A2.5) gives:

A1+A2=m*um*(A2.6)

Condition 2.

Condition 2 imposes price continuity, which implies that the time path for mt and dt be continuous for t>0, so preventing any jump of mt and dt at time T. Accordingly, at time t=T, the solutions for (A2.1) and (A2.3), as well as (A2.2) and (A2.4) must coincide:

m*+A1exp(λ1T)+A2exp(λ2T)=m*u+Bexp(λ1T)(A2.7)
d*+A1[1h[i*0]αλ1]exp(λ1T)+A2[1h[i*0]αλ2]exp(λ2T)=d*u+B[1h[i*0]αλ1]exp(λ1T)(A2.8)

Solving equations (A2.6), (A2.7) and (A2.8) for A1, A2, and B gives expressions (32) to (34) in the main text.

References

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1/

I am very grateful to Saúl Lizondo for his comments and suggestions on earlier drafts of the paper. The paper also benefitted from comments by Charles Kramer and Lorenzo Pérez. All remaining errors are my sole responsibility.

2/

Noticeable exceptions in this respect are the analyses of Morris (1995), Pinto (1991), and Kharas and Pinto (1989). See also Agenor and Ucer (1995).

3/

Most of the analytical works on multiple exchange rates depicts a dual exchange rate regime where a managed official exchange rate co-exists with a freely floating parallel exchange rate, so ignoring the impact of central bank’s exchange losses on the government budget deficit. For a recent analysis of exchange rate reform in the presence of multiple official exchange rates, see Goldberg (1995).

4/

For a discussion of the fiscal effects of multiple exchange rates, see Dornbusch and Kuenzler (1993) and Agenor and Ucer (1995).

5/

An illustrative case in this respect is Suriname, where central bank’s exchange losses amounted to about 11 percent of GDP in 1993.

6/

The following notational conventions are used: a dot (.) over a variable denotes a time derivative, that is x˙=dx/dt; a hat (^) denotes a percentage rate of change, that is x^=x˙/x; and a star (*) over a variable denotes a steady-state value.

7/

The consolidated public sector consists of a central government and a central bank. The central bank manages the multiple exchange rate regime decreed by the government. In doing so, it incurs exchange losses (profits) which constitute a quasi-fiscal deficit (surplus).

8/

In a multiple exchange rate system, the central bank makes exchange losses (profits) every time it buys foreign exchange from domestic exporters at a more (less) depreciated exchange rate than the rate at which it sells foreign exchange to importers.

9/

The variable u can be interpreted as a net subsidy on exports and on imports, with ex and em being the effective exchange rate on exports and on imports, respectively. Goldberg (1995) examines the case when foreign exchange surrender taxes affect the effective exchange rate on exports.

10/

This assumption is broadly consistent with the exchange rate practice prevailing in many developing countries. This is for example the case in Suriname.

11/

While imports take place on both the official and the free markets, the pricing equation is based on the argument that goods sold on the domestic market are priced at the marginal cost, which is equal to the parallel exchange rate.

12/

In what follows, m=(M/e) will be referred to as the “real money stock”.

13/

For convenience, we replace γ-α(if+ê) by (m*0/d*0). Notice that the two expressions are equivalent provided that if and ê remain constant at their initial steady-state value.

14/

The derivation of equations (20) and (21) is presented in appendix 1.

15/

It can easily be shown that:

λ12=(1/α)(g*-êh[i*0]

λ12=(1/α)h[i*0]-ê

16/
The expressions for the DD- and MM- loci are obtained by setting (d=0) and (m-0) in equations (14) and (15), respectively. This gives:
DD(d˙=0)m*/d*=γα(if+e^)
MM(m=0)d*=(e^/g*)m*(kf/g*)

In the d-m space, the two loci are positively sloped. From the stability condition (19), it follows that the slope of the DD locus is flatter than the slope of the DD locus.

17/

From equations (16) and (22), it is easy to demonstrate that the slope of the saddle-path SS is flatter than the slope of the”DD-locus.

18/

In the rest of the paper, the term “exchange rate unification” refers to the unification of the multiple exchange rates applied to transactions in the official markets.

19/

The steady-state values of dt and mt in the presence of unified official exchange rates are obtained by setting u-0 into expressions (26) and (27). Comparing the resulting expressions for d* and m with (26) and (27) respectively, it can be shown that:

d*-d*u>0

m*-m*u>0

where the “u” subscript refers to as unified exchange rates.

20/

Alternatively, one can explain the immediate reaction of the exchange rate as follows. At the time of the shock, individuals anticipate a decline of the black market premium; that is, they anticipate the exchange rate in the parallel market to depreciate at a lower rate than the exchange rate on the official market. As the authorities maintain the rate at which the official rate depreciates constant, it follows that, on impact, inflation must undershoot its long-run level.

21/

During the period preceding the return to an uniform official exchange rate, the dynamics of the system is governed by the laws of motion corresponding to A’, which is the stationary point of the system during that period. At time T, the dynamic system must hit the SS-locus, which is the convergent path corresponding to point A, the initial stationary equilibrium.

22/

Notice that, at time T, domestic government expenditures are higher than in the initial steady-state, which implies that despite the elimination of central bank’s exchange losses, the consolidated public sector deficit does not return to its initial steady-state level. It can be also shown that, at time T, government revenues through the inflation tax exceed the consolidated public sector deficit, entailing a reduction in monetary financing of the deficit as of time T.

23/

This case is therefore the opposite of the case examined in section 4.

24/
The expressions for the DD- and MM- loci are respectively:
DD(d˙=0)m*[γαif+αθ]d*+αθ(d*)2=0
MM(m˙=0)kf+g*d*+θm*[1d*]=0
where :
DD:limd>m*=γαiflimd-->1 m*=+
MM:limd-->1m*=+limd-->  m*=g*/θ
25/

From the algebra, it has been impossible to determine when inflation undershoots or overshoots its long-run equilibrium level.

Multiple Exchange Rates, Fiscal Deficits and Inflation Dynamics
Author: Mr. Vincent Bodart