V. Estimating The Short Run Equilibrium Exchange Rate41
52. The Zimbabwean dollar appears to be overvalued despite a recent depreciation of the official exchange rate in mid-May 2005. The exchange rate at the heavily managed tenders was allowed to depreciate to nearly Z$ 10,000/US$ following the Monetary Policy Statement on May 19. However, both consumer price inflation and parallel market activity have also picked up during this period, and the parallel exchange rate has depreciated rapidly while less than a tenth of bids submitted at the official foreign exchange tender have been met (Figure 1). This raises the question of what would be an appropriate value for the Zimbabwean dollar if it were allowed to be freely determined by demand and supply.
Figure 1.Zimbabwe: Exchange Rates (Z$/US$) and CPI
53. This paper attempts to address this question by taking a first cut at estimating the exchange rate that would prevail under a unified exchange rate regime, assuming unchanged monetary and fiscal policies, over the immediate short term. The approach to modeling the exchange rate uses trade equations to compute the real exchange rate that would be consistent with the external sector being in balance under a unified exchange rate regime.42 The extent of overvaluation (undervaluation) of the official exchange rate under the current exchange regime is estimated as the depreciation (appreciation) of the prevailing official exchange rate that would be required for the external sector to be in balance.
54. Trade equations have been used in a number of previous studies to model external sector balance, most notably in the “macroeconomic balance” or fundamental equilibrium exchange rate (FEER) literature (Williamson (1994) and Isard and others (2001)). In this literature, empirical trade equations are used to derive a real exchange rate that is consistent with both internal balance (economy operating at potential output) and a medium-term sustainable current account. However, Zimbabwe has a dual exchange rate system—with a heavily managed official foreign exchange rate and an active parallel market—which complicates the task of estimating the medium-run equilibrium for real economic variables with any reasonable degree of precision.43 Further, external official and private capital flows that can potentially finance the current account have shrunk considerably over the last few years, making the concept of a sustainable medium-term current account interest of secondary interest. In view of these factors, this paper develops a simpler short run partial-equilibrium approach to modeling the real exchange rate in a unified exchange rate regime under current policies.
55. Based on this approach, the Zimbabwean dollar appears to be significantly overvalued relative to its short-run equilibrium. The estimates show that the Zimbabwean dollar has become progressively overvalued over the recent past, with the extent of overvaluation increasing sharply during the first two quarters of 2005. However, as with any model-based estimation, given parameter uncertainty and sensitivity to underlying assumptions, the results should be considered as providing a general sense of the extent of overvaluation under the prevailing exchange rate regime compared to that under a unified regime, rather than any specific level of the equilibrium exchange rate.
56. The equation for the trade balance is modeled as a function of domestic and foreign demand and the relevant real exchange rates for exports and imports. Export demand X is assumed to depend on the real exchange rate for exports (RERx), expressed as the relative price of domestic goods in terms of foreign goods, and foreign GDP (Yf); and import demand M is assumed to depend on the real exchange rate for imports (RERm) and domestic GDP (Yd).44
More specifically, following the empirical trade literature, the import and export demand functions are modeled as:
where is the -γx and γm are the price elasticities of export and import demand with respect to the real exchange rate, ηx is the elasticity of exports with respect to foreign output and ηm is the elasticity of imports to domestic output.45 While in this methodology, exports have been modeled as depending on the official real exchange rate for simplicity, in reality they may also depend on the parallel market exchange rate due to the diversion of some exports to the parallel market (e.g. through under-invoicing or smuggling) as the parallel market premium rises.
57. In the official market for foreign exchange, the foreign exchange available for imports is given by the sum of exports and the external financing of the trade deficit. Exports are assumed to be a function of the official exchange rate and foreign demand.46 The equation for recorded or official level of imports (MO) is given by:
where RERO is the real exchange rate based on the effective official exchange rate, and the trade deficit financing (TDF) is assumed to be independent of the real exchange rate.
The level of imports MO is related to the import demand function through the parallel market exchange rate RERP.
For a given domestic GDP, the parallel market exchange rate is assumed to equilibrate the demand for imports with the amount of imports allowed through the official foreign exchange market. Combining equations (4) and (5) gives an equation that relates export and import demand functions under the prevailing exchange rate system.
58. Under a unified system, the official and parallel market real exchange rates converge to an equilibrium real exchange rate. The equilibrium with a unified exchange rate RERe = RERP = RERO is given by:
Taking the difference of equations (6) and (7), under the current exchange rate regime and the unified regime respectively, gives:
Expressing the above equation in terms of percentage changes of M, X and TDF,
where M-1, X-1, Y-1 and TDF-1 are imports, exports, output and trade deficit financing under the prevailing exchange rate regime, and Δ indicates the difference of these variables across the current and unified exchange rate regimes.
Rewriting percentage changes of the variables in logs, the above expression becomes:
Substituting the import and export demand functions in equations (2) and (3), under the prevailing and unified exchange rate regimes, into equation (8) gives
59. Assuming no change in external financing (ΔTDF = 0), the equilibrium real exchange rate can be solved in terms of the official and parallel real exchange rates, price and output elasticities of exports and imports, and output changes. The equation for the short run real exchange rate in the unified exchange rate regime is given by solving equation (9):
Assuming unchanged foreign and domestic demand, the real exchange rate under the unified regime can be expressed as a weighted average of the official and parallel market real exchange rates. Assuming that foreign and domestic real GDP are unchanged across the current and a unified exchange rate regime gives the short run equilibrium exchange rate as:47
where the weights λ and (1-λ) are functions of the elasticities of import and export demand functions and the level of imports and exports under the current exchange rate regime.
B. Data and Results
60. The estimates for the real exchange rate consistent with a unified exchange regime in the immediate run are derived for Zimbabwe for the period 1999-2005. There are three key steps. The first step is to obtain real exchange rates for both the official and parallel markets for the relevant period. The second step is to use equation (11) to estimate the real exchange rate that would prevail under a unified regime under current conditions. The final step involves backing out the nominal exchange rate (in terms of Z$/US$) from the short run equilibrium real exchange rate.
61. Data on exchange rates and trade volumes were obtained from both official and market sources. Official real exchange rates were obtained from the IMF’s Information Notice System (INS), which uses data on nominal exchange rates and relative prices provided by national authorities for Zimbabwe and its major trading partners. A similar procedure was used to arrive at the real parallel market exchange rate using data on nominal parallel market rates from private sector sources. Trade volumes were obtained from the national authorities. The real exchange rate for current transactions is estimated under certain assumptions for trade price elasticities relative to the relevant real exchange rates for export and import demand. The trade price elasticities—1.1 for import price elasticity and 0.5 for export price elasticity—are in the range of empirically derived price elasticities.48 The nominal equilibrium exchange rate (in Z$/US$) is backed out from the equilibrium short run real exchange rate assuming stable cross-exchange rates between the U.S. dollar and other major trading partner currencies. The results are presented in Table 1.
|Nominal exchange rates (Z$/US$)|
|Official exchange rate||38.1||55.0||55.0||55.0||824.0||4,968.8||9,922.6 1/|
|Parallel exchange rate||46.0||70.0||315.0||1,681.5||6,235.4||8,695.5||23,000.0|
|Real exchange rate (mult. trade weighted)|
|Official exchange rate||71.5||81.6||179.3||464.7||181.8||60.3||45.2|
|Parallel exchange rate||59.3||64.2||31.3||16.0||24.0||36.1||17.8|
|Short-run equilibrium RER||63.5||70.2||73.6||127.7||64.4||42.7||25.3|
|Equilibrium nominal exchange rate (Z$/US$)||43.0||64.0||134.1||210.3||2,323.0||7,350.9||16,187.8|
|Overvaluation in percent 2/||12.6||16.3||143.7||282.4||181.9||47.9||63.1|
Official tender exchange rate on June 13, 2005.
Equilibrium nominal exchange rate as percent of the official exchange rate.
Official tender exchange rate on June 13, 2005.
Equilibrium nominal exchange rate as percent of the official exchange rate.
62. The percentage deviation of the official exchange rate from the short run equilibrium seems to have picked up in the first half of 2005 (Figure 2). The Zimbabwean dollar was fixed first at Z$55/US$ till February 2003 and then at Z$824 till December 2003. The introduction of a foreign exchange tender in early 2004 and the gradual reduction of surrender requirements for exporters resulted in a de facto depreciation, which reduced the degree of misalignment. The model based estimates are consistent with a decrease in the extent of overvaluation from 180.1 percent of the official exchange rate in the fourth quarter of 2003 to 28.1 percent in the first quarter of 2004 as foreign exchange shortages eased and the parallel market rate appreciated (See figure below). However, during the remainder of 2004, the official exchange rate became progressively overvalued—with the extent of overvaluation increasing to around 44.6 percent by year end—as the tender exchange rate was not allowed to depreciate in line with inflation. With the parallel market rate at around Z$25,000/US$ in the second quarter of 2005, the average deviation of the official exchange rate from equilibrium almost doubled to 87.4 percent by May 2005. The devaluation of the official exchange rate to around Z$10,000 in early June, and a consequential small appreciation of the parallel market rate, helped to reduce the extent of overvaluation to around 63.1 percent.
Figure 2.Zimbabwe: Percentage Deviation from Short Run Equilibrium 1/
1/ Equilibrium nominal exchange rate as percent of the official exchange rate.
63. These model-based estimates are however sensitive to the underlying assumptions and should therefore be treated with caution. For instance, if a different set of empirical trade elasticities, for instance those of South Africa (0.19 for exports and 1.04 for imports) the short-run equilibrium exchange rate increases to over Z$19,000 in June 2005. Further, the actual responses of exports and import demands may differ from empirically derived elasticities—which are based on past time-series data—when large changes in exchange rates and substantial movement in other macroeconomic variables (e.g. money supply, fiscal deficits) are involved. In view of these factors, the estimates provide only a broad sense of the extent of overvaluation of the official exchange rate and should be regarded as illustrative.
64. The approach used for estimating the short run real exchange rate is subject to several caveats. The estimation of the real exchange rate assumes unchanged policies and is based on a very short run partial-equilibrium approach.49 Further, external financing is assumed not to change across the prevailing and unified exchange rate regimes. In addition, exports are assumed to be a function of only the official exchange rate rather than both the parallel and official rates. Finally, as with any model-based estimation, the results are sensitive to the choice of the model and underlying assumptions. On the other hand, this approach has its advantages. It requires prices and not quantities transacted in the official and parallel markets (where data would be impossible to obtain). Nor does it require much knowledge of macroeconomic policies, nor makes assumptions such as output being at potential.
65. Subject to the caveats above, the paper has used a simple methodology to obtain a broad sense of the degree of overvaluation of the Zimbabwean dollar. Overvaluation is shown to have increased sharply in 2001-03 and then to have declined in 2004 before picking up again in the first half of 2005.
IsardPeterHamidFaruqeeG. RussellKinkaid andMartinFetherston (2001) “Methodology for Current Account and Exchange Rate Assessments” IMF Occasional Papers No. 209International Monetary FundWashington.
SenhadjiAbdelhak S. (1998) “Time Series Estimation of Structural Import Demand Equations: A Cross-Country Analysis” IMF Staff Papers vol.45 no. 2International Monetary FundWashington.
SenhadjiAbdelhakS. andClaudioE.Montenegro (1999) “Time Series Analysis of Export Demand Equations: A Cross-Country Analysis” IMF Staff Papers vol.46 no. 3International Monetary FundWashington.
Prepared by Sanket Mohapatra (AFR).
The current levels of external financing are assumed to persist under the unified exchange regime.
For instance, estimating potential output is fraught with considerable difficulty for an economy that has faced extremely high inflation and large concurrent output shocks, which in addition may have affected the long-run supply of physical and human capital.
This formulation explicitly recognizes that the real exchange rate relevant for export and import demands can differ when there is a constrained foreign exchange market with multiple exchange rates.
The income elasticity of imports ηm is sometimes estimated relative to domestic output net of exports, i.e. total domestic production, rather than real GDP (For instance, see Senhadji (1998)). However, this difference is not consequential for purposes of the short run analysis of this paper.
The financing items for the trade deficit include net official and private inflows, humanitarian aid, worker remittances, trade credit, arrears and other items.
Reflecting the partial equilibrium and short run nature of the model, the response of aggregate GDP to a devaluation (and other second-order effects) are assumed not to be felt immediately but only over the medium run.
Empirical import price elasticities have been estimated for Cameroon (0.80), Malawi (1.63), South Africa (1.04), and Zambia (1.22); and export price elasticities for Cameroon (0.17), Malawi (0.11) and South Africa (0.19) (See Senhadji (1998) and Senhadji and Montenegro (1999)). The assumed export price elasticity of 0.5 is higher than neighboring countries as there may be excess capacity that can be used to expand exports as the country moves from a constrained to an unconstrained system.
For instance, this would preclude situations where the central bank increases the rate of money growth or the fiscal deficit widens further, both of which could put additional pressure on the real exchange rate.