Efficient Development Portfolio Design for Sub-Saharan Africa

The Report by the Commission on the Measurement of Economic Performance and Social Progress (Stiglitz et al., 2009) published in September 2009 has brought back to the attention of policy makers and researchers that measuring a country’s development solely on the basis of GDP or GDP per capita is not sufficient. An early attempt at multidimensional measurement is the Human Development Index (HDI) developed by the United Nations Development Program in 1990. This measure consists of three components: a health index, an education index, and a standard of living index. Even though it was and still is subject to criticism, it is the only multidimensional measure that has been around for almost 20 years. Using the HDI we present an approach to designing development policies that takes into account the intrinsic uncertainties surrounding the impact of individual development policy instruments on the development goals to be achieved. The policy instruments under consideration are government expenditures on different spending categories associated with the HDI-components. The policy goal to be achieved is the maximization of the HDI of individual Sub-Saharan African countries as a direct measure of the level of development of these countries, through directed government spending of a given government budget. Obviously, maximization implies efficient spending in this case. Thus we obtain a benchmark for assessing the efficiency of actual spending. References Stiglitz, J.E., A. Sen and J.-P. Fitoussi (2009). Report by the Commission on the Measurement of Economic Performance and Social Progress. http://www.stiglitz-sen-fitoussi.fr.The approach consists of two stages. The first stage is concerned with the econometric estimation of a linear model that links variation in the policy instruments to the corresponding variation in the individual components of the HDI in a given general environment implicitly defined by a set of exogenous variables, such as population structure, the HIV-rate or colonial ancestry. Using the method of Seemingly Unrelated Regression, we estimate the contribution of each instrument to each target as part of a simultaneous equations system. As a bonus, we obtain the covariance matrix of the parameter estimates. In a second stage, we use these estimation results, including the covariance matrix of the parameter estimates, to define a portfolio-selection problem, known from financial optimum portfolio analysis. In our case, however, the distribution of a given budget of government expenditures over the three HDI components constitutes the portfolio selection problem, rather than distributing funds over a portfolio of financial assets. An efficient portfolio minimizes the variance in the HDI for a given expected value of the HDI.We are able to calculate efficient HDI portfolios by varying the degree of risk-aversion over a preset range, and tracing the corresponding set of optimum portfolios which are necessarily efficient as well. This set can be interpreted as the hull of all feasible portfolios in the Variance-HDI-plane. This set turns out to be convex, as in ordinary financial portfolio applications. We also show how, as the budget increases, these efficient portfolios move through the Variance-HDI-plane in a North-Easterly direction in most cases, following convex expansion paths for a given level of risk-aversion, indicating a more than proportional increase of Variance for a given increase in HDI. In some cases we find that these expansion paths are U-shaped, suggesting that there is a double dividend in expanding a low total budget in terms of HDI gained and Variance lost, or a ‘double punishment’ for decreasing an already low budget. In most cases we find that actual HDI performance lags significantly behind the HDI range achievable through efficient spending of the actual available budget. Our approach enables us to indicate how existing budgets should then be reallocated and how much would be gained in terms of the accompanying improvement in the HDI. In most countries higher budget shares should be allocated to both health and education, leaving a smaller share for general spending, which corresponds to the standard-of-living component of the HDI measured by GDP per capita. In addition, we are able to show how much extra HDI and corresponding Variance an additional dollar spent would be able to generate, assuming that dollar would be spent efficiently.