Determination of the optimal exchange rate via control of the domestic interest rate in Nigeria

We consider an economic scenario where the government seeks to achieve a favourable balance-of-payments over a fixed planning horizon through exchange rate policy and control of the domestic interest rate. We view the dynamics of such an economy as a bounded optimal control problem where the exchange rate is the state variable and the domestic interest rate is the control variable. The idea of balance-of-payments is used as a theoretical underpinning to specify the objective function. By assuming that changes in exchange rates are induced by two effects: the impact of the domestic interest rate on the exchange rate and the exchange rate system adopted by the government, we determine instances for both fixed and flexible optimal exchange rate regimes. Afterwards, we illustrate the use of our approach using data obtained from the Central Bank of Nigeria (CBN) statistical bulletin.