A simple dynamic-control macro model to examine the behavior of international reserves for selected economies

The purpose of the paper is to show the construction of a simple dynamic-control macro model, using an economy-wide preference (utility) function as the objective function with two variables, national income and international reserves. National income is the control variable and reserves is the state variable. The first-order equilibrium condition at each instant of time, t, shows that the two variables optimally must grow at different rates for it to be satisfied. The model is applied to the empirical data on income and reserves by examining the behavior of the ratio of income to reserves for a selected number of mature and developing economies over the time period 1970 to 2011. For both types of economies, the model shows that there is a trade-off between income and reserves based on the utility function. However, for mature economies the trade-off is such that the ratio of income to reserves is trending upwards while for the developing economies the ratio is trending downwards. In either case, the model fits the data. The policy implications are briefly discussed within the context of the existing literature on international reserves.