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 = D and i^* = 0, from equations (1)–(6), we have

$\begin{array}{cc}\left[\begin{array}{c}\dot{s}\\ \dot{R}\end{array}\right]=\left[\begin{array}{cc}(\mathrm{\alpha }\gamma +v)\mathrm{\alpha }& -\mathrm{\theta }/\mathrm{\alpha }\\ -\mathrm{\Phi }& 0\end{array}\right]\left[\begin{array}{c}s\\ R\end{array}\right]\hfill & \\ +\left[\begin{array}{c}-(1-\mathrm{\theta })\overline{D}/\mathrm{\alpha }+(1-v-\mathrm{\alpha }\gamma )\overline{e}/\mathrm{\alpha }\\ \mathrm{\Phi }\overline{e}\end{array}\right]\mathrm{.}\hfill & \left(\begin{array}{c}7\end{array}\right)\end{array}$

Let ρ₁ and ρ₂ be the two roots of the dynamic system, we then have

$\begin{array}{cc}{\mathrm{\rho }}_1{\mathrm{\rho }}_2=-\mathrm{\Phi }\mathrm{\theta }/\alpha \mathrm{.}& \left(8\right)\end{array}$

Following Agénor and Flood (1992), we assume that ρ₁<0<ρ₂ The general solutions for s and R during the pre-unification period are

$\begin{array}{cc}s=s^{*}+A\exp \left({\rho }_{1}t\right)+B\exp \left({\rho }_{2}t\right);0^{+}\le t\le T^{-}& \left(\begin{array}{c}9\end{array}\right)\end{array}$

$\begin{array}{cc}R=R^{*}+\frac{\left[(\mathrm{\alpha }\gamma +v)-\mathrm{\alpha }{\mathrm{\rho }}_1\right]}{\mathrm{\theta }}A\exp \left({\mathrm{\rho }}_{1}t\right)\hfill & \\ +\frac{\left[(\mathrm{\alpha }\gamma +v)-\mathrm{\alpha }{\mathrm{\rho }}_2\right]}{\mathrm{\theta }}B\exp \left({\mathrm{\rho }}_{2}t\right);0^{+}\le t\le T^{-}\hfill & \left(10\right)\end{array}$

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

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Dynamic Behavior of Exchange Rate System Before Unification

Citation: IMF Staff Papers 1994, 001; 10.5089/9781451957037.024.A007

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$\begin{array}{cc}\partial s/\partial R{|}_{\dot{s}=0}=\mathrm{\theta }/(\alpha \gamma +v)>0,& \left(\begin{array}{c}11\end{array}\right)\end{array}$

$\begin{array}{cc}\partial s/\partial R{|}_{\dot{R}=0}=0.& \left(\begin{array}{c}12\end{array}\right)\end{array}$

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

$\begin{array}{cc}\partial s/\partial R{|}_{ss}=\mathrm{\theta }/[(\alpha \gamma +v)-\alpha {\mathrm{\rho }}_1]>0.& \left(\begin{array}{c}13\end{array}\right)\end{array}$

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 s₀ and R₀, respectively.

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Agénor and Flood’s Unification Process

Citation: IMF Staff Papers 1994, 001; 10.5089/9781451957037.024.A007

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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 s₀ to ε₀₊, while the foreign reserves remain intact at its initial level R₀. 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 $T_c^{-}$, the economy will move along the unstable branch DE_C. At the instant $T_c^{+}$, the exchange-rate unification comes into force, the system has reached the point 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 $T_g^{-}$. From $T_g^{+}$onwards, the economy will remain intact at the point 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_l) is less than T_c, the system will follow an unstable branch GE_g during the time interval 0⁺ and $T_l^{-}$. From $T_l^{+}$ onwards, the economy will remain intact at the point E_t. The dynamic path indicates that the parallel exchange rate will keep rising during the pre-switch period.

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 $T_k^{-}$. At time $T_k^{+}$ the exchange rate unification takes place, and thereafter the economy stays at point E_k. 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.⁸,⁹

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An Alternative Unification Process

Citation: IMF Staff Papers 1994, 001; 10.5089/9781451957037.024.A007

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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.