Optimal allocation of investments for a desired economic growth

The results of a study to determine the optimal distribution of investments in each sector of the Egyptian economy is presented. The main objective criterion is to attain a desired rate of growth of the gross domestic product (GDP) over the next few years. Optimal control concepts and adaptive filtering techniques are used to determine the best strategy to achieve the objectives. The Egyptian economy was divided into 13 sectors. Using the World Bank data books, we obtained the time series of investment over the period 1981–91, and the rate of growth of the Egyptian GDP over the same period. Every sector of the economy was correlated with the rate of growth, and for every sector we generated an autoregressive moving average (ARMA) model. The endogenous variable in each model is the rate of growth of the GDP, and the sectoral investment was the exogenous variable. The objective was to find the required investment in each sector to reach a predefined level of rate of growth, subject to constraints on the available funds. Other constraints included the smoothness of the investment over the years and the smoothness of the rate of growth. Another model was developed that relates the rate of growth as endogenous variable to the investment in the thirteen sectors as exogenous variables. It was used within the optimization algorithm to achieve the same objective of a fixed rate of growth. An adaptive time-varying algorithm was developed, for both models, to find the open loop (time values) of the investment to minimize the cost function subject to the different constraints. The more accurate all-sectors model showed that sectors such as construction, industry and transportation are the most profitable, and that most of the investments need to be directed towards them.