Recently in an interesting paper in *IMF Staff Papers*, Pierre-Richard Agénor and Robert Flood (1992) set up a theoretical model of dual exchange rates and analyzed how the economy would work given the shock of an announcement to unify dual exchange markets. Provided that the unified exchange rate under the flexible regime is greater than the official exchange rate under the dual regime, their major findings are (i) at the announcement, the domestic price of foreign currency in the parallel exchange market depreciates immediately, (ii) the parallel exchange rate keeps rising and net foreign assets keep falling during the pre-unification period, and (iii) the unified exchange rate of the post-unification regime is independent of the timing of unified implementation.

This paper is written for two purposes. First, we intend to show that the unified exchange rate of the post-reform regime is inversely related to the date of reform. Second, we attempt to extend the graphical presentation of Agénor and Flood (1992) and to trace the possible dynamic behavior of relevant variables during the unified process.^{1}

## I. The Model

The Agénor and Flood (1992) model can be described by the following log-linear equations:

With the exception of the domestic interest rate i and the foreign interest rate i^{*}, all variables are expressed in logarithms. The variables are defined as follows: *m =* nominal money supply; *p* = domestic price level; *s* = parallel exchange rate; *e* = official exchange rate; *R* = foreign reserves; and *D =* domestic credit.

Equation (1) is the standard equilibrium condition for the money market. A logarithmic approximation of the interest rate parity under dual exchange rates is given in equation (2).^{2} Equations (3) and (4) are the definition of money supply and of domestic price level, respectively. Equation (5) describes how foreign reserves change over time, while the divergence between the official and the parallel exchange rates captures the arbitrage activity between two foreign exchange markets.^{3} Finally, equation (6) depicts that domestic credit remains constant at all times.

The experiment of the Agénor and Flood (1992) study is that the foreign authorities announce the regime will switch from a dual to a unified flexible regime at a specific date *T* in the future. Because the regime switch involves dual exchange rates and flexible exchange rates, in what follows we examine the dynamic features of both regimes. For expository convenience, throughout this paper 0^{–} and 0^{+} denote the instants before and after announced unification, *T ^{–}* and

*T*

^{+}denote the instants before and after implemented unification.

### Dual Exchange Regime

Under dual exchange rates, * e* is given at the level

*e*. Letting D =

^{*}= 0, from equations (1)–(6), we have

Let ρ_{1} and ρ_{2} be the two roots of the dynamic system, we then have

Following Agénor and Flood (1992), we assume that ρ_{1}<0<ρ_{2} The general solutions for *s* and *R* during the pre-unification period are

where s^{*} and *R*^{*} are the steady-state values of *s* and *R*, and A and *B* are undetermined coefficients.

The dynamic behavior of the system can be illustrated by means of a phase diagram like Figure 1, which is similar to Figure 1 in Agénor and Flood (1992). It is clear from equation (7) that the slopes of loci *ṡ* = 0 and *Ṙ* = 0 are

Figure 1. Dynamic Behavior of Exchange Rate System Before Unification

Equipped with the information of arrow directions and with equation (8), we can see that the model has a saddlepoint solution. In the phase space plane, the stable branch SS, which is the unique trajectory that leads to the stationary equilibrium, is associated with *B =* 0 in equations (9) and (10), while the unstable branch *UU* is associated with *A* = 0. All other unstable trajectories indicated in the figure correspond to the values *A* ≠0 and *B* ≠ 0. It is clear from equations (9) and (10) that the slope of *SS* is

### Flexible Exchange Regime

As in Agénor and Flood (1992), we proceed to consider the post-unification (flexible) regime. Under flexible exchange rates, given *Ṙ* = 0 and *ε = e = s*, from equations (1)–(6), we derive

where *m=θR _{T+}+(1–θ) D*.

The general solution for equation (14) is

As the unique root of flexible exchange rates is positive, the convergent condition thus requires that the speculative bubble should be ruled out. As a consequence, substituting *C =* 0 into equation (15) gives

Two points should be noted from equation (16). First, from *T ^{+}* onward, the economy is operating under flexible exchange rates, and hence the stock of foreign reserves is frozen at the level R

_{T+}Second, the unified exchange rate ε is solely determined by the stock of foreign reserves, which in turn is crucially related to the timing of regime switch

*T*.

^{4}It should be noted that equations (9)–(16) are a restatement of the analysis in Agénor and Flood (1992).

The *AA* schedule presented in the diagrams of the next section traces the combinations of ε and *R* that satisfy equation (16). It is clear from equation (16) that the slope of *AA* is

## II. The Unification Process

We are now in a position to deal with the evolution of the economy during the unification process.^{5} As indicated in equations (13) and (17), the *A A* schedule may be either flatter or steeper than the *SS* schedule. We thus have to consider two possible situations.

Figure 2 illustrates the Agénor and Flood (1992) situation where the slope of *AA* is greater than that of 55. Following Agénor and Flood (1992), assume that initially the system is at the point Fon the saddlepath *SS*; the initial parallel exchange rate and foreign reserves are *s*_{0} and *R*_{0}, respectively.

Figure 2. Agénor and Flood’s Unification Process

Corresponding to the timing of the regime switch, the economy will display a different unification process. First, if *T* = 0, at the instant 0^{+}, the parallel exchange rate will discretely jump from *s*_{0} to ε_{0+}, while the foreign reserves remain intact at its initial level *R*_{0}. In consequence, the economy will immediately move upward from the point *F* to *E’’* on the *AA* schedule. From 0^{+} onward, the economy will remain intact at *E’’*.^{6} Second, if T→∞ (the announcement effect is negligible on the public), the parallel exchange rate will not jump, and the economy will move along the saddlepath trajectory *SS* to point *E*.

As claimed by Agénor and Flood (1992), corresponding to a specific value of *T* (namely *T*_{c} the economy will happen to jump to a point such as *D* on the *ṡ* = 0 schedule at the moment of announced unification.^{7} During the dates between 0^{+} and *DE*_{C}. At the instant *E*_{c} on the *AA* line. During the post-unification period, the economy will stay at *E*_{c}. As is evident from Figure 1, the parallel exchange rate continues to rise and foreign reserves continue to fall throughout the pre-unification period. If *T* (namely *T*_{g}) is greater than *T _{c}*, the system will follow an unstable branch

*GE*

_{g}during the time interval 0

^{+}and

*E*

_{g}. The dynamic path indicates that the parallel exchange rate will first fall then rise during the pre-switch period. However, if

*T*(namely

*T*) is less than

_{l}*T*

_{c}, the system will follow an unstable branch

*GE*

_{g}during the time interval 0

^{+}and

*E*. The dynamic path indicates that the parallel exchange rate will keep rising during the pre-switch period.

_{t}Figure 3 illustrates the situation where the *AA* schedule is flatter than the *SS* schedule. Three distinct patterns of adjustment should be recognized. One possibility is associated with *T* = 0. If this is the case, the economy will jump downward to *E’’* on the *AA* schedule and stay at that point at all times. The second possibility is associated with T→∞. If this is the case, the economy will remain at its initial position *F* at the instant of unified announcement, and then move along *SS* toward the point *E*. The last possibility is associated with *0 <T < ∞* (namely *T _{k}*). In this case, the economy will jump downward to the point

*K*on impact and then move along an unstable trajectory like

*KE*

_{k}between 0

^{+}and

*E*. Under such a situation, the economy is characterized by both a falling parallel exchange rate and falling foreign reserves during the period prior to the unification.

_{k}^{8},

^{9}

Figure 3. An Alternative Unification Process

## III. Concluding Remarks

The Agénor and Flood (1992) paper is an important addition to the literature on the dynamic adjustment of anticipated unification. In this comment, we have pointed out that some points are not fully explored in the Agénor and Flood (1992) work. Based on our analysis, given that the unified exchange rate under the flexible regime is greater than the official exchange rate under the dual regime, their conclusions should be generalized as follows: ^{10}

(i) The parallel exchange rate may either rise or fall at the instant of unified announcement;

(ii) The economy may display a variety of unified processes. In particular, both the parallel exchange rate and foreign reserves may fall throughout the pre-unification period; and

(iii) The unified exchange rate of the flexible regime is negatively related to the timing of unified implementation.

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 (June1992), pp.357–94.

Agénor, Pierre-Richard, and Robert P.Flood,“Unification of Foreign Exchange Markets,”Staff Papers,International Monetary Fund, Vol. 39 (December1992), pp.923–47.

Flood, Robert P., and Nancy P.Marion,“Exchange-Rate Regimes in Transition: Italy 1974,”Journal of International Money and Finance,Vol. 2 (December1983), pp.279–94.

Gros, Daniel,“Dual Exchange Rates in the Presence of Incomplete Market Separation,”Staff Papers,International Monetary Fund, Vol. 35 (September1988), pp.437–60.

Agénor, Bhandari, and Flood (1992) provide an excellent survey of the exchange regime reform.

For a detailed derivation, see Flood and Marion (1983).

Gros (1988) provides a good microfoundation for linking arbitrage behavior with exchange rate differentials.

Since the flexible regime is adopted after the dual regime, the stock of foreign reserves under the dual regime, denoted by *R _{T}+*, will serve as an initial condition for the dynamics under the flexible regime beyond time

*T*.

^{+}The detailed mathematical derivations behind the graphical results are available upon request.

It is clear from equation (16) that, if *T* = 0, ε_{0}+ is equal to initial money stock *m _{0}(= θR_{0}* + [1 - θ]

*AA*is steeper or flatter than

*SS*is crucially related to the size of initial money stock.

See footnote 21 of Agénor and Flood (1992).

To save space, we omit the case where *AA* is steeper than *SS* but flatter than *ṡ =* 0.

Agénor and Flood (1992, p. 933) also refer to another situation where the unified exchange rate under the flexible regime is lower than the official exchange rate under the dual regime. Under such a situation, “a reform announcement would lead to an immediate appreciation of the parallel rate and a gradual increase in the stock of net foreign reserves.”

Provided that (i) the coefficient θ is small, (ii) the *AA* curve is steeper than the *SS* curve, and (iii) the transition period is short, the following two conclusions reported in the Agénor and Flood (1992) analysis hold: the parallel exchange rate rises at the moment of unified announcement, and both the parallel exchange rate and foreign reserves fall throughout the pre-unification period. However, their third conclusion, which indicates that the unified exchange rate of the flexible regime is independent of the timing of unified implementation, does not hold.