Efficient development policies in Sub-Saharan Africa: An optimum portfolio approach

Kirsten Wiebe and Adriaan van Zon, UNU MERIT

The Stiglitz Report published in September 2009 has brought attention of policy makers and researchers back to thinking that measuring a countries development solely on the basis of GDP or GDP per capita is not sufficient. An early approach for a multidimensional measure 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.
Based on the notion of the HDI we present an approach to designing development policies that takes into account the intrinsic uncertainties surrounding the impact of individual development instruments on the development goals to be achieved. The policy instruments under consideration here are government expenditures on different spending categories associated with the HDI-components. The ultimate policy goal to be achieved is the maximization of the HDI of Sub-Saharan 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.
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 the HIV-rate, colonial ancestry, and so on. 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 various HDI components constitutes the portfolio selection problem, rather than distributing funds over a portfolio of financial assets.
Here, 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 VARHDI, HDI-plane (VARHDI is the HDI variance). 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 VARHDI,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 VARHDI for a given increase in the HDI itself. 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 VARHDI 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 addition, we are able to show how much extra HDI and corresponding VARHDI an additional dollar spent would be able to generate, assuming that dollar would be spent efficiently.

Date: 20 May 2010

Time: 15:00 - 16:30  CEST