Abstract
Exchange rate reforms in developing countries have often aimed at floating the exchange rate in an attempt to unify the official and parallel markets for foreign exchange. This paper examines the short-term dynamics associated with such reforms. The analysis shows that the behavior of the parallel market premium in the periods leading to reform depends crucially on expectations about the postreform policy stance. The paper also draws the implications of the analysis for the behavior of foreign reserves, output, and the real exchange rate.
Widespread exchange and trade restrictions in developing countries have typically led to the emergence of illegal markets for goods and foreign currencies, with parallel exchange rates deviating in some cases considerably from official rates. The existence of such markets, despite some potential gains, has entailed a variety of costs (including high volatility of exchange rates and prices, and incentives to engage in rent-seeking activities and to divert export remittances or unrequited transfers from the official to the parallel market).1 The unification of foreign exchange markets has thus been an important objective of macroeconomic policy in countries with sizable parallel currency transactions.
The process of unification has as its ultimate objective to absorb and legalize the parallel market for foreign exchange, eliminating the inefficiencies and market fragmentation associated with a quasi-illegal activity. In practice, unification attempts have often taken the form of the adoption of a uniform floating exchange rate.2 The analytical work in this area has shown that the impact of such a policy shift on the short- and long-run behavior of the exchange rate and inflation can be ambiguous. In the long run, the macroeconomic effects depend on the fiscal impact of the exchange rate reform. As argued by Pinto (1991a), the parallel market premium represents an implicit tax on exports repatriated through official channels, since governments in developing countries are typically net buyers of foreign exchange from the private sector. For a given fiscal deficit, there exists a trade-off between the premium and inflation, which represents a tax on domestic currency balances. The unification process, which results in the loss of the implicit tax on exports, may therefore entail a substantial (and permanent) rise in the rate of inflation and the rate of depreciation of the exchange rate, if the authorities attempt to compensate for a fall in revenue by an increase in monetary financing of the fiscal deficit and a higher tax on domestic money holdings. 3
The short-run effects of a preannounced future adoption of a unified, flexible exchange rate arrangement have been examined by Kiguel and Lizondo (1990) in the context of a currency substitution model developed earlier by Lizondo (1987). If the unification attempt is fully anticipated, agents will—in order to avoid capital losses—adjust their portfolios toward foreign currency-denominated assets if the uniform floating exchange rate is expected to be more depreciated than the existing parallel rate, and toward domestic currency-denominated assets if it is expected to be more appreciated. As a result of this portfolio adjustment, the parallel market rate will depreciate immediately—at the moment the unification attempt is announced or when expectations are formed—toward the level asset holders expect the postunification floating rate to be. Under perfect foresight, the parallel market rate will experience an initial jump and will keep depreciating steadily toward that level at the time of unification.
Existing analytical studies of exchange market unification are subject, however, to a number of limitations. Lizondo (1987) and Pinto (1991a) assumed that the unification process occurs overnight—a particularly restrictive informational assumption, even in the context of developing countries. Kiguel and Lizondo (1990) did examine the dynamic effects of a preannounced reform, but provided only a graphical analysis of the unification process. In addition, the real effects of a unification attempt have received only scant attention in the literature.4 This paper examines the dynamic implications for output, the real exchange rate, parallel market premia, inflation, and official reserves of an exchange rate reform that consists in the adoption of a flexible exchange rate aimed at unifying exchange rates in an informal, dual exchange rate regime. The analysis assumes forward-looking agents and explicitly considers leakages between foreign exchange markets.
The rest of the paper is organized as follows. Section I provides a brief review of recent experiences with exchange market unification in developing countries. Section II presents a basic model of a dual exchange rate regime with leakages. The dynamics of the premium and foreign reserves implied by this setup in the pre- and postreform periods are examined in Section III. Section IV extends the analysis to consider real effects of anticipated reforms. Section V provides some concluding comments.5
I. Experiences with Exchange Market Unification
The experience of developing countries with exchange market unification has attracted a great deal of attention recently. Of particular interest among available studies are those discussing the experience of several sub-Saharan African countries that attempted to unify official and parallel markets for foreign exchange in the 1980s.6 Although some of these countries chose to follow a gradual path to unification, most of them opted for an “overnight” approach, consisting in floating the official exchange rate.7
The experience of this last group of countries provides important lessons regarding the behavior of official and parallel exchange rates, inflation, and budget deficits in the periods leading to, and the periods following, the implementation of exchange rate reform. First, in some countries—-particularly in Sierra Leone and Zambia, where a floating arrangement was implemented in July 1986 and September 1985. respectively—exchange rate unification led to a surge in inflation. Second, the evidence also suggests that the parallel market premium rose substantially in the months preceding the unification attempt, and fell sharply upon implementation. The unified floating exchange rate that emerged immediately after the reform took place was in some cases very close to the prereform parallel rate—implying that the drop in the premium resulted essentially from a sharp depreciation of the official exchange rate.8 However, despite a sharp drop on impact, a significant premium re-emerged subsequently in some countries—most notably Ghana, Sierra Leone, Somalia, and Zambia.
The inflationary burst observed in some cases corroborates to some extent the “public finance view” of unification described earlier, and may be viewed partly as a result of the elimination of the implicit tax on exports. In addition, however, the increase in inflation resulted from the inability of the authorities to maintain control over money growth. The increase in the premium in the periods prior to reform can be interpreted as being, in part, the result of expectations about the timing of the reform process, as well as the size and direction of movements in the official and parallel exchange rates upon implementation. Faced with a possibility of a future depreciation of the parallel exchange rate, for instance, asset holders would tend to reallocate their portfolio away from domestic-currency denominated assets—thereby causing the parallel rate to depreciate immediately and the premium to rise.
The fact that the parallel market exchange rate did not experience any “jump” at the moment the reform was implemented is consistent with the intuition that the reform was widely expected by private agents. At the time of implementation little happens, because most of the effects of the change in exchange rate regime have already been discounted by forward-looking agents.9 Finally, the re-emergence of a significant premium subsequent to reform occurred in countries where money growth was not kept under control and where inflation rose substantially.
The analytical model presented in the next section attempts to provide a formal basis for this intuitive interpretation of the empirical evidence on the short-run behavior of exchange rates and the premium during the unification process.
II. A Basic Framework
Consider a small open economy operating an informal dual exchange rate regime in which an official, pegged exchange rate coexists with a freely determined parallel rate. The official rate applies to current account transactions that are authorized by the authorities, while the parallel rate is used for capital account transactions and the remainder of current account items. Private agents are endowed with perfect foresight and hold domestic and foreign currency-denominated bonds in their portfolios. The interest parity condition, properly modified to reflect repatriation of the principal on foreign bonds at the parallel exchange rate and repatriation of interest receipts at the official rate, is assumed to hold continuously. Domestic output consists of a single exportable good sold abroad and is taken as exogenous. In each period, exporters determine the proportion of their foreign exchange earnings to surrender at the official exchange rate and the proportion to repatriate via the parallel market for foreign exchange.
Formally, the model is described by the following log-linear equations, where all parameters are defined as positive:
where mt, denotes the nominal money stock; Dt domestic credit; Rt the stock of net foreign assets held by the central bank;pt, the domestic price level; et, the official exchange rate; st, the parallel exchange rate; it, the domestic nominal interest rate, and i*, the (constant) foreign interest rate. All variables, except interest rates, are measured in logarithms.
Equation (1) describes money market equilibrium. Equation (2) depicts a modified interest parity condition, which is based on the assumption that the principal on foreign bonds is acquired and repatriated at the parallel exchange rate, but interest income—a current account item—is repatriated at the official exchange rate.10 Equation (3) is a log-linear approximation, which defines the domestic money stock as a weighted average of domestic credit and foreign reserves. Equation (4) indicates that the price level depends on the official and parallel exchange rates. This results from the assumption that some commercial transactions are settled in the parallel market, with the price of these imports reflecting the marginal cost of foreign exchange—that is, the parallel rate. The purchasing power parity assumption holds, therefore, at a composite exchange rate, and the foreign price level has been set to unity (so that its logarithm is zero) for simplicity.11 Equation (5) describes the behavior of net foreign assets,12 The negative effect of the premium—defined as the difference between the official and the parallel exchange rates—on the behavior of reserves results from its impact on the underinvoicing of exports. The higher the parallel exchange rate is relative to the official rate, the greater the incentive to falsify export invoices and to divert export proceeds to the unofficial market. Finally, equation (6) indicates that the stock of credit is assumed constant.
III. Solution and Dynamics in Anticipation of Reform
In the prereform dual exchange rate system, the forward-looking parallel rate, st, and the predetermined level of official reserves, Rt, are endogenous variables, while the official exchange rate, et,, is assumed set at ē by the authorities. In the postreform unified flexible rate regime, by contrast, st = et = ∊t, and reserves remain constant. We now examine the behavior of endogenous variables in the two regimes.
Prereform Dual-Rate Regime
Setting et, = ē, Dt = 
, and i* = 0 and solving equations (1)–(6) yields
The two eigenvalues of this system are given by
System (7) is saddlepoint stabie with one negative root (denoted by ρ1) and one positive root, ρ2. Solving for the particular solutions yields, for t < T
where A and B are as yet undetermined coefficients, and s* and R* denote the steady-state values of the parallel rate and foreign exchange reserves. The mode! is, therefore, characterized by a zero premium in the steady state.
Let us first suppose that the existing dual-rate system is expected to last forever. Stability would then require setting B = 0 in the solutions (8a) and (8b). Using an initial condition on reserves would thus allow the determination of A. The economy’s equilibrium path is the unique non-explosive path, SS (which passes through the stationary point E) depicted in Figure 1. For a positive (negative) premium, reserves are falling (increasing), as indicated by the arrows pointing west (east) in the figure.
Steady-State Equilibrium in the Dual-Rate Regime
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Steady-State Equilibrium in the Dual-Rate Regime
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Steady-State Equilibrium in the Dual-Rate Regime
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Along the saddlepath, the parallel exchange rate and foreign reserves evolve according to
which indicates that SS has a positive slope.13
However, if the authorities announce their intention to switch to a floating rate arrangement in the future, agents will anticipate the abandonment of the dual-rate system. In this context, the coefficient B will not be zero. Instead, as shown below, agents will set coefficients A and B at values that satisfy constraints imposed by a perfectly anticipated transition to the postreform regime.
Postreform Flexible Rate Regime
Let T > 0 represent the future transition date announced at period t = 0—that is, the initial instant at which the authorities intend to switch to the flexible rate regime. In the postreform flexible rate system, ∊t = et = st, a condition that yields (from equation (7)) Ṙt, = 0. Therefore, reserves remain constant beyond t ≥ T, say, at
where
Equation (9) is a linear differential equation in ∈t, whose solution is
Ruling out speculative bubbles requires setting B = 0. The exchange rate in effect at the initial instant the economy switches to a unified floating rate regime is, therefore,
Dynamics in Anticipation of Reform
We now examine how reserves and the premium will evolve when agents perfectly anticipate the transition from a dual-rate regime to a flexible system. Essentially, this requires establishing conditions that “connect” the two regimes. In the present model, there are two such requirements: an initial condition on reserves, and a price continuity condition, which prevents a jump in the parallel exchange rate at the moment the reform is implemented:14
The conditions in equation (12) allow us to determine the constants A and B in the solutions for reserves and the parallel exchange rate obtained for the dual-rate regime (equations (8a) and (8b)). These solutions are given by15
where Δ = κ2 exp(ρ1 T)—κ2, exp(κ2 T) < 0.
Substituting equations (13a) and (13b) in equations (8a)–(8d) yields the complete solutions for the parallel exchange rate and foreign reserves in the dual-rate regime. These solutions are given by
for 0 ≤; t < T.
Equations (14a) and (14b) characterize the paths of reserves and the parallel rate prior to the reform. To examine the effect of a future regime switch on these variables, let s̃, and R̃t denote the solution paths that would have prevailed in the absence of any reform announcement. As discussed above, these solutions are obtained by setting B = 0 in equations (8a)–(8d) and using the initial condition on reserves to solve for A, so that
with G = ¯R0 − R*. Using equations (8a)–(8d) and (15)
with A and B given by equations (13a) and (13b).
Equations (16a) and (16b) show how the path of the parallel exchange rate and foreign reserves—relative to a “no-change” environment—depends on the relation between the initial value of reserves, 
0, and its steady-state value in the (permanent) dual-rate regime, R*, as well as the difference between the value of the official exchange rate that would have been observed at time Tin the absence of reform, ē, and the level of the exchange rate that prevails at the moment the floating regime is implemented, 0> R*.
In such a situation, it can be shown that an announcement at t = 0 of a future reform at T would lead, if
The reason for the initial jump in the parallel exchange rate at t = 0 is as follows. If there is initially a positive premium, agents realize that the future reform will imply a depreciation of the official exchange rate, a rise in prices, and, therefore, a reduction in real money balances. Under perfect foresight, these future effects will be reflected in the expected—and actual—rate of depreciation of the parallel exchange rate, leading agents to reduce immediately their demand for domestic currency. But since the nominal money stock is constant (reserves cannot jump at t = 0), equilibrium in the money market can be maintained only if an immediate rise in prices occurs—or only if the parallel exchange rate depreciates. This result is qualitatively similar to what Kiguel and Lizondo (1990) obtained in a currency substitution framework.
The behavior of the parallel exchange rate and foreign reserves in the pre- and postreform regime under the assumptions 0> R* and
Behavior of Reserves and the Parallel Exchange Rate
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Behavior of Reserves and the Parallel Exchange Rate
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Behavior of Reserves and the Parallel Exchange Rate
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
The dynamic behavior in anticipation of reform is also illustrated in Figure 3, which extends Figure 1. As assumed above, the position of the economy before the reform announcement is such that 0 > R* (corresponding to a positive premium) and is located on a point such as F on the saddlepath SS. The steady-state equilibrium in the postunification regime is E′, corresponding to a stock of net foreign assets equal to
Dynamics upon Unification of Foreign Exchange Markets
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Dynamics upon Unification of Foreign Exchange Markets
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Dynamics upon Unification of Foreign Exchange Markets
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Having studied the economy’s path in the pre- and postreform phases, we can now briefly consider how this path is related to the length of the transition period, T. First, if the exchange rate reform is announced to occur in the very distant future—that is, for T → ∞—the announcement effect on the path of the parallel exchange rate and reserves in the transition interval is negligible. By contrast, if the reform occurs overnight—that is, for T → 0—the economy will move immediately to its postreform steady state, without temporarily following an unstable path.22 In terms of Figure 3, the parallel exchange rate would immediately jump from point F to point E″, with no change in the initial stock of reserves.
The foregoing analysis highlights the fact that the short-run behavior of the parallel exchange rate, the parallel market premium, foreign reserves, and inflation during the periods preceding an exchange rate reform depends critically on expectations about the postreform policy stance—which determines the expected, unified exchange rate. The more permissive monetary policy is expected to be in the postreform regime, the more depreciated the unified floating exchange rate will be expected to be, and the more depreciated the parallel market rate will be today. If a reform is perfectly anticipated, no abrupt changes will occur upon implementation; on the contrary, a jump will take place as soon as the reform is announced—or as soon as agents become convinced that the regime change will occur at a well-defined date. These predictions of the model are largely consistent with available evidence for developing countries discussed in Section I.
IV. Real Effects of Exchange Rate Reforms
The existing literature on exchange market unification has had, as indicated earlier, very little to say regarding the behavior of real variables in the reform process. However, sharp changes in exchange rates and prices are bound to affect output and the real exchange rate, even in the short run. This section extends the analysis of the previous sections so as to consider the real sector implications of exchange rate reforms.
An Extended Framework
To endogenize output and the real exchange rate, let us start by assuming that aggregate demand is inversely related to the real interest rate and the real exchange rate—measured as the difference between a weighted average of the official and parallel exchange rates and the price level:23
where ȳ > 0, and 0≤σ≤1.
In addition, prices are now assumed to be set as a markup on wages, ωt, and prices of imported inputs, measured in domestic currency and valued at the marginal cost of foreign exchange—that is, the parallel market exchange rate:
In addition to the parallel market premium, the behavior of reserves is now assumed to depend also on the real exchange rate and aggregate output:
The demand for money function is now given by
while equations (2), (3), and (6) remain unchanged. The last step in the description of the extended model relates to wage formation. Here we adopt the forward-looking wage scheme used by Willman (1988), which follows the overlapping contract model developed by Calvo (1983). Formally, wage formation is given by
where μ > 0 represents a discount factor. In equation (21), ωt, represents the wage rate stipulated in new contracts as well as those renewed at time t. Assuming that wage contracts are made directly between employers and individual employees, ω, defined by (22) measures the marginal labor cost of production and, hence, is the relevant price to incorporate in the markup pricing equation (18). Differentiating (19) with respect to time yields
Substituting equation (18) in (22) yields
The complete model, therefore, now consists of equations (2), (3), (6), (17)–(20), and (23).
Solution Under Alternative Regimes
Since the solution of the model follows essentially the same procedure as above, we only briefly highlight its features. In the prereform dual-rate regime, the model solves for the parallel rate, the wage rate, and official reserves. As shown in the appendix, there are no unambiguous results in the general case. However, if the real interest elasticity of aggregate demand is zero, and if the income elasticity of money demand is small enough,24 then the complete solution can be shown to be
where ρk denotes the roots of the system (with ρ1, being the only negative root), and π1, π2 are coefficients defined in the appendix. R* is given by equation (8c), and the Ak’s are as yet undetermined coefficients.
When agents expect the dual-rate regime to last forever, the stable path solution is obtained as before by setting A2 = A3 = 0 and imposing the initial condition on reserves, since there are now two jump variables. In the postreform unified flexible exchange rate regime, official reserves must remain constant. From equation (23), the steady state requires also that the wage rate be equal to the unified exchange rate in the new regime—a condition that, in turn, implies from equation (18) that the real exchange rate is zero in the postreform steady state if σ = 1. Assuming, as before, that the real interest elasticity of aggregate demand is zero and that the income elasticity of money demand is small enough implies that the condition ˙Rt, = 0 for t ≥T Talways holds. Consequently, in the flexible rate regime, equation (19) becomes irrelevant for the determination of wages and the parallel exchange rate. As shown in the appendix, the solution for these variables is given by
Model Dynamics
As shown in Section III, a preannounced exchange market unification affects the behavior of the parallel exchange rate as soon as it becomes known to the public. In addition to effects on real money balances, inflation, and foreign reserves, such changes have, in the general setting considered now, an impact on output and wages, as well as the real exchange rate.
The determination of the coefficients Ak in equations (24a)–(24c) proceeds as before. There are now three conditions: the initial condition on reserves, and the conditions on the flexible exchange rate and nominal wages beyond period T (equation (25)). These solutions are given in the appendix. In the general case, these values are fairly complicated and do not allow a clear characterization of the solution path. Suppose, however, that the initial situation is such that a positive premium prevails, the parallel exchange rate is below (that is, more appreciated than) the unified floating rate, and the reform is announced sufficiently in advance. The behavior of output, prices, wages, the real exchange rate, and the trade balance can then be characterized as in Figure 4.25 Nominal wages and the parallel exchange rate jump upwards at the moment the reform announcement is made, since agents discount back to the present the future official depreciation and increase in prices that the regime switch will entail. The domestic price level increases by more than the parallel exchange rate, leading to a real exchange rate appreciation and a fall in output—relative to its “undisturbed” path.26 Equilibrium in the money market is therefore maintained not only by a depreciation of the parallel exchange rate and a rise in prices (as before) but also by an adjustment in real activity. Prices also rise by more than nominal wages, implying a fall in real wages on impact. Finally, the trade balance may deteriorate or improve, depending on whether the positive effect of the reduction in output is less or greater than the negative effects resulting from a real exchange rate appreciation on trade flows and from the rise of the premium on the propensity to underinvoice. In Figure 4 it is assumed that the net effect on the trade balance is negative. At period T, all variables reach their new, constant steady-state values, without further jumps in wages or the parallel exchange rate.27
Behavior of Output, Prices, Wages, and the Trade Balance
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Behavior of Output, Prices, Wages, and the Trade Balance
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
Behavior of Output, Prices, Wages, and the Trade Balance
Citation: IMF Staff Papers 1992, 004; 10.5089/9781451930825.024.A007
The upshot of the foregoing analysis is that exchange market unification, in addition to effects on inflation, foreign exchange reserves, and the parallel market premium, can have quite dramatic short-run effects on the behavior of the real exchange rate, and consequently, real output. Although it is not possible to determine unambiguously the direction of these effects, the analysis shows that there exist cases in which a real exchange rate appreciation and a fall in output may materialize in the transition period between the reform announcement and the implementation date. Such effects indicate that, in addition to the inflationary cost emphasized by the “fiscal view” of unification (Pinto (1991a)), exchange market unification can also be associated with an output loss. A study of a large sample of reform episodes in developing countries would provide useful information on the magnitude of these effects.
V. Summary and Conclusions
Exchange rate reforms in developing countries have often consisted in floating the exchange rate in an attempt to unify the official and parallel markets for foreign exchange. This paper has examined the behavior of output, prices, foreign reserves, and the trade balance in anticipation of such reforms. After a brief review of recent experiences with exchange market unification in developing countries, a formal analysis was conducted in the context of a simplified model that explicitly considers leakages between foreign exchange markets. The model indicates that a future reform typically leads, at the moment the announcement is made, to an instantaneous depreciation of the parallel exchange rate and no change in the stock of foreign reserves. In the transition period, the parallel exchange rate keeps depreciating (and the premium keeps rising) while net foreign assets keep falling—-both at an accelerating rate. No jumps occur when the reform is actually implemented, and the parallel market premium drops to zero.
The reason for the jump in the parallel exchange rate upon announcement of the reform is as follows. If there is initially a positive premium, agents realize that the future reform will imply a depreciation of the official exchange rate, a rise in prices, and, therefore, a reduction in real money balances. Under perfect foresight, these future effects are reflected immediately in the expected—and actual—rate of depreciation of the parallel rate, leading agents to reduce demand for the domestic currency. But since the initial money stock is constant, equilibrium in the money market can be maintained only if an immediate rise in prices occurs—or if the parallel exchange rate depreciates. The predictions of the model were shown to be consistent with available evidence on exchange market unification in developing countries.
Extensions of the model to incorporate sticky prices and forward-looking wage contracts and to endogenize output and the real exchange rate indicated that, in the transition period, a preannounced reform may be associated with an appreciation of the real exchange rate and a fall in output. Although the direction of the real effects in the model are not in general unambiguous, the possibility of a negative impact on output suggests that the cost of exchange rate reforms may be underestimated if sufficient attention is not paid to their real sector implications.
The analysis developed in this paper can be extended in various ways. First, the date at which the reform will take place in the future may not be perfectly known by agents. Second, it may be assumed that agents are uncertain about the type of exchange rate regime the authorities would adopt following a reform attempt. For instance, instead of assuming that the authorities will adopt a unified floating exchange rate system, they could envisage a transition to a uniform fixed exchange rate regime. A likely outcome of the introduction of uncertainty about the reform date and /or the nature of the post-transition regime is that expectations of a reform would cause a jump in the parallel exchange rate at the moment the reform is implemented as well as volatile exchange rate movements prior to transition if this type of uncertainty varies over time.28 Third, it may be assumed that the domestic credit rule is stochastic. Such an extension would be particularly fruitful, since it would allow use of analytical techniques developed recently in the continuous-time literature on target zones.29
Finally, the analysis could be extended to a choice-theoretic framework, so as to capture intertemporal substitution effects associated with anticipated policy changes. Although these extensions may prove useful, the basic methodological implication of this paper is likely to remain unaltered: to understand the dynamics associated with exchange market unification in developing countries, it is critically important to understand the anticipatory behavior that parallel currency markets tend to reflect regarding the postreform regime.
APPENDIX
Solution of the Model with Real Effects
In this appendix, we present the solution of the extended model, setting for simplicity σ = 1 in equations (17) and (19). First, note that, from equations (18) and (2)
while from (18), st − pt = η(st − ωt). Substituting these relations in (17) yields, with 
= 0
Substituting equations (2), (3), (26), and (18) in (20) yields
where Ω = α +veη > 0.
Similarly, substituting (26) in (19) yields
In the prereform dual exchange rate regime, equations (27), (28), and (23) form a system of differential equations in st, Rt, and ωt, in nonnormal form. To solve this system, we postulate the solution to be of the form
where the κi,’s are not all zero. Substituting these expressions in the homogenous part of the system defined by equations (27), (28), and (23) yields
where
Assuming the conventional Marsh all-Lerner condition to hold implies that π6 is positive, so that a rise in nominal wages appreciates the real exchange rate and reduces reserves. However, this condition is not sufficient to ensure that a nominal depreciation of the parallel exchange rate raises reserves (that is, that π4 > 0): this is because such a rise increases the flow of export receipts diverted to the parallel market, despite its positive effect on the real exchange rate and export volumes. We will in what follows assume that π1 > 0, an assumption that requires the income elasticity of money demand not to be too large (v < 1/c1).
Equations (30a)–(30c) must be identically satisfied for (29) to be a solution. This requires, therefore, that all expressions in brackets be zero. To obtain nontrivial solutions for the κi,’s requires that
which gives
where
A sufficient condition for τ1 to be positive is π1 > 0, The sign of τ2 is, in general, indeterminate. Consider the case where the effect of the real interest rate on output is negligible; that is, c2→0. Then τ2 < 0. By Descartes’s rule of signs, the polynominal (31) has two roots with positive real parts and only one root with negative real part (denoted ρ1), whatever the value of τ1.30 The general solutions can be written as
where the κj(k) denote a triplet of values associated with each root, ρj. The particular solutions are given by
so that π5/(π6 - π4) = (π1 + π2- π3) = 1, for c→0. Adopting the normalization rule, K1(k) = 1, and solving equations (30a)–(30c) for successive values of ρk yields
Setting c2→0 yields equations (24a)–(24c) in the text. If the dual-rate regime is expected to last forever, so that A2 = A3 = 0
which implies that, an instant before the announcement, 
0- < 
0-
In the postreform flexible exchange rate regime, st, = et = ∊t, Rt, = 0, and Rt = R+t for t ≥ T. The simultaneous system is then formed of equations (27) and (23); that is
where
and ¯m = θ
(1 − θ), assuming, as before, that c2→0 yields a11 > 0 and a12 > 0. Under these assumptions, the system (32) will be globally unstable. Solving for the particular solution yields
To determine the coefficients Ak in equation (21), set R0 - 0, and
Solving this system yields
where, for k = 1, 2, 3
From the definitions given above, q1 > 0, while
Assume, however, that T is large enough. Then, for 0 - R* > 0 and
with |A3| > |A2|. Setting t = 0 in equations (24a)–(24c), it can be established that
REFERENCES
Agénor, Pierre-Richard, Parallel Currency Markets in Developing Countries: Theory, Evidence, and Policy Implications, Essays in International Finance, No. 188, Princeton University (Princeton, New Jersey: Princeton University Press, 1992).
Agénor, Pierre-Richard, Jagdeep S. Bhandari, and Robert P. Flood, “Speculative Attacks and Models of Balance of Payments Crises,” Staff Papers, International Monetary Fund, Vol. 39 (June 1992), pp. 357–94.
Bhandari, Jagdeep S., and Carlos A. Végh, “Dual Exchange Markets Under Incomplete Separation: An Optimizing Model,” Staff Papers, International Monetary Fund, Vol. 37 (March 1990), pp. 146–67.
Calvo, Guillermo A., “Staggered Contracts and Exchange Rate Policy,” in Exchange Rates and International Macroeconomics, ed. by Jacob A. Frenkel (Chicago: University of Chicago Press, 1983).
Calvo, Guillermo A., “Anticipated Devaluations,” International Economic Review, Vol. 30 (August 1989), pp. 587–606.
Djajic, Slobodan, “Dynamics of the Exchange Rate in Anticipation of Pegging,” Journal of International Money and Finance, Vol. 8 (December 1989), pp. 559–71.
Flood, Robert P., and Nancy P. Marion, “Exchange-Rate Regimes in Transition,” Journal of International Money and Finance, Vol. 2 (March 1983), pp. 279–94.
Froot, Kenneth A., and Maurice Obstfeld, “Exchange-Rate Dynamics Under Stochastic Regime Shifts: A Unified Approach,” Journal of International Economics, Vol. 31 (November 1991), pp. 203–29.
Gros, Daniel, “Dual Exchange Rates in the Presence of Incomplete Market Separation,” Staff Papers, International Monetary Fund, Vol. 35 (September 1988), pp. 437–60.
Kiguel, Miguel A., and J. Saúl Lizondo, “Adoption and Abandonment of Dual Exchange Rate Systems,” Revista de Analisis Económico, Vol. 5 (March 1990), pp. 3–23.
Krugman, Paul, “Target Zones and Exchange Rate Dynamics,” Quarterly Journal of Economics, Vol. 106 (August 1991), pp. 669–82.
Lizondo, J. Saól, “Unification of Dual Exchange Markets,” Journal of International Economics, Vol. 22 (February 1987), pp. 57–77.
Lizondo, J. Saól, “Alternative Dual Exchange Market Regimes,” Staff Papers, International Monetary Fund, Vol. 38 (September 1991), pp. 560–81.
Montiel, Peter J., Pierre-Richard Agénor, and Nadeem Haque, Informal Financial Markets in Developing Countries (unpublished; Washington: International Monetary Fund, June 1992); forthcoming, Oxford: Basil Blackwell.
Obstfeld, Maurice, and Alan C. Stockman, “Ex change-Rate Dynamics,” in Handbook of International Economics, Vol. II, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985).
Pinto, Brian, “Black Market Premia, Exchange Rate Unification and Inflation in Sub-Saharan Africa,” World Bank Economic Review, Vol. 3 (September 1989), pp. 321–38.
Pinto, Brian, (1991a), “Black Markets for Foreign Exchange, Real Exchange Rates and Inflation” Journal of International Economics, Vol. 30 (March), pp. 121–35.
Pinto, Brian, (1991b), “Unification of Official and Black Market Exchange Rates in Sub-Saharan Africa,” in Exchange Rate Policies in Developing and Post-Socialist Countries, ed. by Emil-Maria Claassen (San Francisco: ICS Press).
Roberts, John, “Liberalizing Foreign-Exchange Rates in Sub-Saharan Africa,” Development Policy Review, Vol. 7 (June 1989), pp. 115–42.
Willman, Alpo, “The Collapse of the Fixed Exchange Rate Regime with Sticky Wages and Imperfect Substitutability Between Domestic and Foreign Bonds,” European Economic Review, Vol. 32 (November 1988), pp. 1817–38.
Pierre-Richard Agénor is an Economist in the Developing Country Studies Division of the Research Department.
Robert P. Flood is a Senior Economist in the Capital Markets and Financial Studies Division of the Research Department. He holds graduate degrees from the University of Rochester.
The authors would like to thank Saul Lizondo and Malcolm Knight for helpful discussions and comments.
See the discussion in Montiel, Agenor, and Haque (1992).
Although, in theory unification could also take the form of the adoption of a uniform fixed rate or crawling peg regime—with changes in net foreign assets clearing the official foreign exchange market—few developing countries have adopted this approach in recent years.
Pinto’s analysis assumes that agents are subject to rationing in the officiai market for foreign exchange. Lizondo (1991) has shown, however, that Pinto’s emphasis on the trade-off between the premium and inflation in the unification process remains largely valid if the official market clears through changes in foreign reserves. The existence of a trade-off, nevertheless, hinges crucially on the assumption of a positive premium in the steady state. However, most models of dual exchange rate markets with leakages—such as Bhandari and Végh (1990), Gros (1988), as well as the one presented here—predict a zero premium in the steady state.
Pinto (1991a) focused on the inflationary impact of exchange rate unification, and Lizondo (1987) and Kiguel and Lizondo (1990) examined only exchange rate and balance of payments effects. In both analyses, output is taken as fixed at its full-employment level.
The analysis in Section II dwells, in part, on Flood and Marion (1983), who developed a model of exchange rate regimes in transition, based on the Italian two-tier foreign exchange market in 1973–74. Issues similar to those considered here were also examined by Calvo (1989), Djajic (1989), and Obstfeld and Stockman (1985).
These countries include The Gambia, Ghana, Nigeria, Sierra Leone, Somalia, Zaïre, and Zambia. These experiments were examined by Agénor (1992), Roberts (1989), and Pinto (1989, 1991b).
In Ghana, for instance, unification took the form of large, but widely spaced, devaluations over almost four years (April 1983–March 1987)—with an overnight float occurring at the last stage—and was accompanied by reductions in the fiscal deficit. By contrast, in Nigeria the currency was floated overnight in September 1986.
This was the case, most notably, in Nigeria.
Peru’s attempt in August 1990 to unify its foreign exchange markets by floating its exchange rate is also consistent with this pattern. The parallel market premium, which stood at close to 200 percent at the end of 1989, rose to more than 400 percent a month before the reform—which was widely anticipated—-was implemented. The premium fell immediately afterwards as a result of a large depreciation of the official exchange rate, and dropped below 20 percent by December 1990.
A formal derivation of equation (2) was provided by Flood and Marion (1983). Assuming that interest income is also repatriated through the parallel market would imply setting γ = 0.
The coefficient v can be viewed alternatively as an approximation to the share of transactions settled illegally in the parallel market relative to total trade transactions.
Note that, although interest receipts are assumed to be repatriated at the official exchange rate, they are not accounted for in equation (5) for simplicity.
The saddlepath SS is also flatter than ˙st = 0. An increase in the interest elasticity, α, rotates the curves ṡt, = 0 and SS clockwise. An increase in shifts the curve ṡt, = 0 to the left and moves point E horizontally to the left. A rise in the propensity to underinvoice, Φ, translates into a clockwise rotation of the saddlepath SS. Finally, a devaluation of the official exchange rate leads to an upward shift of the Ṙ, = 0 curve and a right ward (leftward) shift of the ṡt, = 0 curve, if 1—v is greater (lower) than αγ. Nevertheless, a devaluation always leads to an equiproportional depreciation of the parallel exchange rate and an increase in reserves in the steady state (equation (8c)).
The price continuity principle, which can be justified as a condition to eliminate speculative profits at the time of transition, has been used extensively in the literature on speculative attacks (see Agenor, Bhandari, and Flood (1992)). However, note that in the present framework agents do not have a direct—and costless—access to official reserves. Here, capital account transactions through the official foreign exchange market are prohibited, and agents can only deplete official reserves by illegally diverting export remittances to the parallel market—presumably at a fixed (albeit nonprohibitive) cost. Consequently, speculative attacks on official reserves cannot occur.
Setting t = 0 in equation (8b), t = T in equation (8a) and using (12) yields
For a depreciation to occur, in addition to the condition 0 − R* is “small”—that is, if the initial value of the premium is not “too high.”
In this case, the parallel exchange rate always appreciates after the announcement, since, by assumption,
For t <0, the equation driving the parallel rate is equation (15), and for 0≤t≤T, equation (14a).
Unification before the dual-rate regime reaches its steady state reduces reserve losses due to leakages; equation (14b) shows that since
Regardless of the path followed in the dual-rate regime, the economy must reach point E′ at time T. Note that point E′ is necessarily located northeast of point E, since
The condition under which the parallel exchange rate will jump to a point such as D is given by using equation (14a) and the equation of the saddlepath given above:
Setting T→∞ in equations (13a) and (13b) indicates that T→G/κ1 and B→>0, so that the solutions for st, and Rt, coincide with those for ̃st, and ̃Rt. Similarly, setting T→ 0 in equations (14a) and (14b) yields 0
As before, all coefficients are defined as positive in what follows.
Formally, these conditions are c2→0, and v ≤1/c2.
The path of reserves and the parallel exchange rate is qualitatively similar to what is shown in Figure 2 and is therefore omitted for simplicity. The real exchange rate in what follows is assumed to be measured as the difference between the parallel rate and the price level—that is, by setting σ = 1.
Note that this result does not depend on whether the real exchange rate is measured in the standard way by using the official exchange rate (σ—0) or by using the parallel exchange rate (σ = 1). In fact, in the former case the real exchange rate appreciation is more pronounced than in the general case.
If, in equation (18), the price level was assumed to depend also on the official exchange rate, prices would experience a jump at r = T as a result of the depreciation occurring in the official market.
A formal proof of this proposition can be derived by extending the procedure developed in Flood and Marion (1983).
See Kragman (1991). Following Flood and Marion (1983), Froot and Obstfeld (1991) examined the unification issue in the context of a stochastic dual-rate model in which both exchange rates are floating. However, analytical solutions for systems with two state variables of the type considered here are not so far available.
