Exchange Rate Determination under a Willing Buyer-Willing Seller Framework in Zimbabwe: An Econometric ApproachChirume Admire Tarisirayi [PhD (Cand),MA(Econ), BSc(Econ)]Abstract
This paper develops a predictive exchange rate determination model for Zimbabwe. This model is consistent with the Reserve Bank^s^ recently introduced "Willing Buyer-Willing Seller" (WBWS) interbank exchange rate determination framework announced on the 5^th^ April 2024 by the monetary authorities. Within a closed loop, in a general structural macroecnomic model where households, firms, the Government and the Central bank are the main blocks, the study integrates aspects of the balance of payments framework and liquidity models to construct a robust model for exchange rate determination in Zimbabwe. Using a structured currency framework, this work aims to quantify the equilibrium exchange rate, drawing from both theoretical and empirical literature. We implement Vector Autoregression (VAR) models to estimate key parameters and simulate exchange rate movements with and without central bank interventions. The results offer insights into exchange rate stabilization in the context of Zimbabwe’s economic realities.
1. Introduction and Background
The determination of exchange rates is a complex endeavor, often reliant on models that may fail to capture the multifaceted nature of currency valuation in practice. Traditional models frequently emphasize theoretical frameworks that do not align with the realities faced by economies, particularly in developing nations like Zimbabwe. These models often focus on isolated factors, such as interest rates or inflation, without accounting for the broader context of market dynamics, structural breaks, and external shocks that directly influence exchange rates. Such shortcomings can lead to misguided policy decisions and ineffective monetary interventions.
Zimbabwe’s economic landscape has been characterized by numerous structural breaks due to significant policy shifts and changes over recent decades. These disruptions—ranging from hyperinflation to the adoption of a multicurrency system—create challenges for conventional time series models, which typically rely on stable relationships among variables. As a result, forecasting exchange rates using these models becomes increasingly problematic, often yielding unreliable predictions during periods of volatility.
In response to these challenges, this paper advocates for a simulation-based approach to exchange rate determination. By employing simulation techniques, we can generate a more nuanced understanding of exchange rate dynamics that reflects the complexities of the Zimbabwean economy. This approach aligns with principles from Bayesian statistics, where prior beliefs (or prior probabilities) about exchange rate behavior are continuously updated with new data to form posterior beliefs. Such a framework allows for the integration of historical knowledge and ongoing economic developments, thereby enhancing the robustness and adaptability of the model.
Ultimately, this study aims to develop a comprehensive econometric model that incorporates liquidity supply, currency demand, and central bank intervention, offering insights that are not only theoretically grounded but also practically relevant in the context of Zimbabwe's unique economic challenges. Through this lens, we seek to provide a more accurate tool for policymakers to navigate the intricacies of exchange rate stabilization in a rapidly evolving economic environment.
1.1 Motivation for the Study
Zimbabwe's foreign exchange market has experienced substantial volatility, chronic shortages of foreign currency, and multiple exchange rates. In response to these challenges, the Reserve Bank of Zimbabwe (RBZ) introduced the WBWS exchange rate framework on April 5, 2024, to create a more market-driven system for determining exchange rates. The WBWS system aims to stabilize the exchange rate and rectify inefficiencies associated with previous exchange rate regimes, such as the fixed-rate system and the parallel market.
Understanding the factors driving exchange rate movements under the WBWS system is vital. This study aims to model the exchange rate by incorporating macroeconomic variables such as mineral prices, government demand, remittances, and central bank interventions.
1.2 Research Questions
The study aims to address the following key questions
What are the primary factors influencing the exchange rate under Zimbabwe’s WBWS system?
How do liquidity supply and currency demand interact to determine the exchange rate?
What is the role of the Reserve Bank in exchange rate stabilization under this highly misundertood exchange rate management framework?
Which policy interventions effectively mitigate exchange rate volatility?
1.3 Justification for the Study
Exchange rate volatility remains a significant challenge to Zimbabwe’s macroeconomic stability. The WBWS framework, while newly implemented, has yet to be extensively analyzed in terms of its economic impacts. This study contributes to a deeper understanding of the WBWS framework by offering an econometric model that can predict exchange rate behavior. It provides Reserve Bank and government with tools to forecast exchange rate movements, improve central bank interventions, and inform future policy decisions.
2. Literature Review
2.1 Theoretical Literature
a) Monetary Models of Exchange Rate Determination
The study of exchange rate determination has been at the core of international finance research for decades, with models evolving to address various economic conditions and theoretical advancements. Early models, such as the Purchasing Power Parity (PPP) theory, laid the groundwork for understanding exchange rate movements by positing that exchange rates between two countries should adjust to equalize the price levels of a basket of goods (Cassel, 1918). However, empirical tests of PPP, particularly in developing economies like Zimbabwe, have shown that it often fails to capture short-run exchange rate fluctuations due to structural distortions, inflation differentials, and the presence of parallel markets (Chinn, 2006). This has led to the development of more nuanced models that incorporate monetary, fiscal, and external factors.
The monetary approach to exchange rate determination posits that exchange rates adjust to equate the supply and demand for money in an economy. This framework suggests that key macroeconomic factors such as money supply, inflation, interest rates, and output play crucial roles in determining exchange rates. Frenkel (1976) was one of the early proponents of this approach, introducing the Flexible Price Monetary Model (FPMM), which assumes that prices adjust immediately to changes in money supply, thus linking exchange rates to relative money supplies and inflation rates between two countries.
Dornbusch’s (1976) overshooting model extended this by incorporating sticky prices, demonstrating how exchange rates may overshoot their long-run equilibrium in response to monetary policy changes. This phenomenon is particularly relevant in developing countries where inflation volatility and frequent monetary interventions distort short-term exchange rate behavior.
The determination of exchange rates has been the focus of many theoretical studies. The Purchasing Power Parity (PPP) theory asserts that exchange rates between currencies adjust to equalize price levels of similar goods across countries. This concept relates to the Real Effective Exchange Rate (REER), which adjusts nominal exchange rates to account for inflation differences between countries. While useful, PPP often falls short of explaining short-term exchange rate dynamics, particularly in developing nations such as Zimbabwe (Frenkel, 1976).
The Monetary Model of Exchange Rate Determination links exchange rates to money supply and demand across nations, with factors such as interest rates, inflation, and output playing pivotal roles. Changes in these factors can drive fluctuations in exchange rates (Dornbusch, 1976). The Balance of Payments Model further emphasizes trade balances and capital flows as essential determinants of exchange rates.
The Market Microstructure Models focus on the behavior of market participants, such as banks, importers, and exporters, in determining exchange rates through their buying and selling activities. The WBWS system in Zimbabwe aligns closely with these models, as it allows for exchange rates to be negotiated between buyers and sellers.
The "Willing Buyer-Willing Seller" (WBWS) framework adopted by the Reserve Bank of Zimbabwe in April 2024 brings into focus the need for modern exchange rate determination models that account for both market forces and policy interventions. Unlike fixed or pegged exchange rate regimes, WBWS allows the market to largely dictate exchange rates, though central bank intervention remains a significant factor, especially in countries with external imbalances and inflationary pressures.
2.2 Theoretical Literature
a) Monetary Models of Exchange Rate Determination
The monetary approach to exchange rate determination posits that exchange rates adjust to equate the supply and demand for money in an economy. This framework suggests that key macroeconomic factors such as money supply, inflation, interest rates, and output play crucial roles in determining exchange rates. Frenkel (1976) was one of the early proponents of this approach, introducing the Flexible Price Monetary Model (FPMM), which assumes that prices adjust immediately to changes in money supply, thus linking exchange rates to relative money supplies and inflation rates between two countries.
Dornbusch’s (1976) overshooting model extended this by incorporating sticky prices, demonstrating how exchange rates may overshoot their long-run equilibrium in response to monetary policy changes. This phenomenon is particularly relevant in developing countries like Zimbabwe, where inflation volatility and frequent monetary interventions distort short-term exchange rate behavior.
b) Liquidity Supply and Currency Demand
The concept of liquidity supply and currency demand is central to understanding exchange rate movements in economies with significant foreign exchange constraints. Liquidity supply in this context refers to the inflow of foreign currency through channels such as exports, remittances, loans, and foreign direct investment (FDI), while currency demand is driven by the need to finance imports, government spending, household consumption, and reserve accumulation (Branson, 1977).
b) Liquidity Supply and Currency Demand
The concept of liquidity supply and currency demand is central to understanding exchange rate movements in economies with significant foreign exchange constraints. Liquidity supply in this context refers to the inflow of foreign currency through channels such as exports, remittances, loans, and foreign direct investment (FDI), while currency demand is driven by the need to finance imports, government spending, household consumption, and reserve accumulation (Branson, 1977).
In Zimbabwe, mineral exports, especially gold and platinum, form a substantial part of liquidity supply, as fluctuations in global commodity prices directly affect foreign currency inflows (Reinhart & Rogoff, 2009). On the demand side, high levels of import dependence, government borrowing, and foreign debt repayments have historically placed pressure on the exchange rate, contributing to currency depreciation during periods of economic stress.
c) Central Bank Intervention
The role of central bank interventions in foreign exchange markets has been widely studied in both developed and developing countries. Central banks intervene to stabilize the exchange rate, particularly when market forces cause it to deviate from the Real Effective Exchange Rate (REER), which adjusts the nominal exchange rate for inflation differentials and trade-weighted currency movements (Dominguez & Frankel, 1993). The literature on central bank interventions generally distinguishes between sterilized and unsterilized interventions. Sterilized interventions aim to affect the exchange rate without altering the domestic money supply, while unsterilized interventions involve changes in the money supply to influence the exchange rate directly (Sarno & Taylor, 2001).
In Zimbabwe, the Reserve Bank of Zimbabwe (RBZ) intervenes to prevent excessive exchange rate volatility, especially in the wake of external shocks such as commodity price fluctuations or declines in remittances. These interventions align with the theoretical framework of managed float exchange rates, where the central bank allows market forces to play a significant role while stepping in when necessary to prevent destabilizing fluctuations (Obstfeld & Rogoff, 1995).
2.3 Empirical Literature
a) Empirical Studies on Exchange Rate Determination
Empirical studies on exchange rate determination have yielded mixed results, particularly in developing economies. Meese and Rogoff (1983) famously demonstrated that no structural exchange rate model could outperform a random walk model in forecasting future exchange rates, a result that challenged the predictive power of traditional models. However, subsequent studies have found that adding variables such as commodity prices, global risk factors, and central bank interventions can significantly improve the explanatory power of exchange rate models (Chen & Rogoff, 2003).
In the context of Zimbabwe, early studies focused on the hyperinflation period of the late 2000s and the subsequent adoption of a multicurrency system in 2009. For instance, Kairiza (2009) examined the role of monetary policy, inflation, and speculative behavior in driving exchange rate movements during the hyperinflation era. A similar study was done by Chidoko et al. (2012) who observed that inflation, interest rates, and foreign exchange reserves are key drivers of the exchange rate in Zimbabwe. Later studies, such as Nyoni (2019), emphasized the importance of external factors like remittances, exports, and loans in providing foreign exchange liquidity and stabilizing the exchange rate post-dollarization. Makochekanwa and Kwaramba (2010) highlight the influence of remittances and exports.
More recently, empirical research has explored the role of commodity price volatility in influencing exchange rates in resource-dependent economies. Reinhart and Rogoff (2009) highlighted the connection between commodity price cycles and exchange rate volatility, showing that countries dependent on exports of primary commodities tend to experience greater exchange rate fluctuations due to global price shocks. For Zimbabwe, the linkage between mineral prices and the exchange rate is particularly relevant, given the country’s reliance on gold and platinum exports.
b) Impact of Central Bank Intervention
The effectiveness of central bank interventions in stabilizing exchange rates is debated in the literature. While some studies find that interventions can reduce short-term volatility, others argue that frequent interventions may distort market signals and lead to long-term misalignments (Sarno & Taylor, 2001). In the case of Zimbabwe, Mupunga and Le Roux (2014) found that central bank interventions played a critical role in stabilizing the exchange rate during periods of hyperinflation, but their effectiveness diminished as inflation pressures subsided.
Studies from other emerging markets provide additional insights into the role of central bank interventions. Calvo and Reinhart (2002) coined the term "fear of floating" to describe the reluctance of central banks in emerging markets to allow their currencies to float freely due to concerns over inflation and external imbalances. This is applicable to Zimbabwe, where the RBZ continues to intervene in the foreign exchange market to prevent excessive depreciation and align the exchange rate with the REER.
Internationally, research by Calvo and Reinhart (2002) shows how central banks in emerging markets intervene to stabilize exchange rates, especially in response to external shocks. These findings align with the role of the RBZ in Zimbabwe, where central bank intervention is designed to correct deviations from the REER.
3. Methodology
3.1 Methodology
This section outlines the methodology employed to model the exchange rate determination for Zimbabwe under a willing buyer willing seller framework. The model captures the interplay between the demand and supply of both foreign and local currency, accounting for various economic factors that influence these dynamics. We present the model's key mathematical functions, with a particular focus on the exchange rate determination, central bank interventions, and their effects on reserves.
3.2 Model Framework
The exchange rate 〖ER〗_tis primarily influenced by the demand and supply of foreign currency (〖FC〗_t) and local currency (〖LC〗_t). The fundamental equation governing the exchange rate can be expressed as follows:
〖ER〗_t=〖ER〗_(t-1)+(〖FC〗_(d,t)-〖FC〗_(s,t)+(〖LC〗_(s,t)-〖LC〗_(d,t) ))…………………………….……………[1]
Where;
〖ER〗_t is the exchange rate at time t.
〖FC〗_(d,t) is the foreign currency at time t.
〖FC〗_(s,t)is the supply of foreign currency at time t.
〖LC〗_(d,t) is the demand for local currency at time t.
〖LC〗_(s,t) is the supply of foreign currency at time t.
3.3 Foreign Currency Supply and Demand Functions
The supply of foreign currency is influenced by several international liquidity factors, while the demand arises from the need for imports and other foreign transactions.
Foreign Currency Supply (〖FC〗_s):
〖FC〗_(s,t)=α_1.〖MP〗_t+α_2.〖PV〗_t+α_3.〖EV〗_t+α_4.L_t+α_5.R_t……………………………………..[2]
〖MP〗_t=mineral prices at time t.
〖PV〗_t=production volume at time t.
〖EV〗_t=Exports volumes at time t.
L_t =loans received at time t.
R_t=remittances at time t.
α_iare coefficients representing effects of respective factors on foreign currency supply.
Foreign currency demand (〖FC〗_d);
〖FC〗_(d,t)=β_1.〖ID〗_t+β_2.〖GD〗_t+β_3.〖HD〗_t……………………………………………………………………….[3]
Where;
〖ID〗_t =imports demand at time t
〖GD〗_t=Government demand for foreign currency at time t
〖HD〗_t=Household demand for foreign currency at time t.
β_i are coefficients representing the effects of respective factors on foreign currency demand.
3.4 Local Currency Supply and Demand Functions
Local currency dynamics are governed by confidence levels, inflation expectations, and central bank monetary policies.
Local Currency Demand (〖LC〗_d):
〖LC〗_(d,t)=γ_1 C_t+γ_2 〖IE〗_t+γ_3 〖CT〗_t………………………………………..………………………..…………[4]
C_t=the degree of confidence in local currency as a store value at time t.
〖IE〗_t=expected inflation at time t.
〖CT〗_t=degree of convertibility of the local currency at time t.
γ_i=are coefficient representing the effects of respective factors on local currency demand.
Local Currency Demand (〖LC〗_s):
〖LC〗_(s,t)=δ_1 〖RMG〗_t+δ_2 〖FM〗_t…………………………………………..………………………………………………[5]
Where;
〖RMG〗_t=reserve money growth at time t.
〖FM〗_t=fiscal monetization at time t.
δ_1=coefficients representing the effects of respective factors on local currency supply.
3.5 Central Bank Intervention Function
The central bank intervenes in the foreign exchange market to stabilize the currency by managing mismatches between foreign currency supply and demand. The intervention can be described mathematically as follows:
Intervention Impact on Foreign Currency:
If there is excess demand for foreign currency (〖FC〗_d>〖FC〗_s), the central bank sells foreign currency from its reserves, which adjusts the foreign supply and increases local supply:
〖FC〗_(s,t)^intervention=〖FC〗_(s,t)+min(〖FC〗_(d,t)-〖FC〗_(s,t,) R)……………………………………….………………[6]
〖LC〗_(s,t)^intervention=〖LC〗_(s,t)+min(〖FC〗_(d,t)-〖FC〗_(s,t,) R).sterilization_effectiveness)………………[7]
R_t=R_(t-1)-min(〖FC〗_(d,t)-〖FC〗_(s,t,) R)……………………………………………………………………….[8]
Where:
R = central bank foreign exchange reserves.
sterilization_effectiveness = effectiveness of sterilization (ranging from 0 to 1).
Intervention Impact when Excess Supply Exists
Conversely, if there is excess supply of foreign currency (〖FC〗_s>〖FC〗_d) the central bank buys foreign currency, thereby increasing its reserves:
〖FC〗_(s,t)^intervention=〖FC〗_(s,t)-(〖FC〗_(s,t)-〖FC〗_(d,t,) R)
〖LC〗_(s,t)^intervention=〖LC〗_(s,t)-(〖FC〗_(s,t)-〖FC〗_(d,t).sterilization_effectiveness)
R_t=R_(t-1)+(〖FC〗_(s,t)-〖FC〗_(d,t,))
3.6 Simulation Scenarios
The simulation incorporates two primary scenarios:
Without Central Bank Intervention:
The exchange rate dynamics are purely driven by the underlying supply and demand for foreign and local currency as described by the previously defined equations. The absence of intervention leads to natural fluctuations based solely on market forces.
With Central Bank Intervention:
The exchange rate is influenced by active intervention strategies implemented by the central bank. The equations governing currency supply and demand are adjusted to account for the central bank's actions to mitigate mismatches in the currency markets.
4. Results and Discussion
4.1 Simulation without Central Bank Intervention
In the absence of central bank intervention, exchange rates are determined solely by market forces, with fluctuations reflecting changes in production, exports, and imports. The exchange rate tends to depreciate during periods of excess currency demand and appreciate when liquidity supply increases.
4.2 Simulation with Central Bank Intervention
When central bank interventions are included, the RBZ actively adjusts the exchange rate to correct deviations from the REER. The intervention significantly reduces exchange rate volatility, although persistent REER deviations suggest that frequent interventions may be necessary under certain market conditions.
5. Policy Implications
This study underscores the critical role of the RBZ in exchange rate stabilization. While the WBWS system offers a market-driven mechanism for exchange rate determination, central bank interventions are necessary to correct market imbalances and realign the exchange rate with the REER. Strengthening the RBZ’s intervention capacity is essential for maintaining macroeconomic stability.
6. Conclusion
This study develops a dynamic econometric model for exchange rate determination in Zimbabwe, underpinned by the "Willing Buyer-Willing Seller" (WBWS) framework. Through the integration of liquidity supply, currency demand, and central bank interventions, the model effectively simulates exchange rate movements over a specified period.
Key findings indicate that under conditions of elevated demand for foreign currency, the central bank's proactive measures can stabilize the exchange rate, thus preventing excessive volatility. The simulation results illustrate how the interplay between liquidity supply and demand can lead to pronounced fluctuations in the exchange rate, especially when external shocks or changes in commodity prices occur.
This model not only provides a framework for understanding the complex interactions that govern exchange rate behavior, but also serves as a valuable tool for policymakers. By forecasting potential exchange rate movements based on macroeconomic indicators, the Reserve Bank of Zimbabwe can make informed decisions regarding monetary policy and intervention strategies.
The implications of this study extend to broader economic stability, suggesting that enhanced monitoring of liquidity factors and demand dynamics can lead to more effective exchange rate management. Future research could further refine the model by incorporating additional variables or by applying it to different economic contexts, thereby contributing to a deeper understanding of exchange rate determination in developing economies.
References
Frenkel, J. A. (2019). A monetary approach to the exchange rate: Doctrinal aspects and empirical evidence. Scandinavian Journal of Economics, 78(2), 200-224.
Dornbusch, R. (1976). Expectations and exchange rate dynamics. Journal of Political Economy, 84(6), 1161-1176.
Chidoko, C., et al. (2013). An empirical investigation of determinants of exchange rate in Zimbabwe. Journal of Economics and Sustainable Development, 3(3), 52-59.
Makochekanwa, A., & Kwaramba, M. (2010). Exchange rate volatility and its impact on trade: Evidence from Zimbabwe. South African Journal of Economics, 78(3), 229-246.
Calvo, G. A., & Reinhart, C. M. (2002). Fear of floating. Quarterly Journal of Economics, 117(2), 379-408.
Meese, R., & Rogoff, K. (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics, 14(1-2), 3-24.
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