Efficiency in human development: a data envelopment analysis.

• Author: Vierstraete, Valerie
• Position: Statistical data

1. Introduction

   In 1990, the first Human Development Report, published by the UNDP (United Nations Development Programme), introduced a new development indicator developed by a task force working under the guidance of Mahbub ul Haq. For many years, the only available measure of development had been per capita GDP, so the UNDP proposed the human development index (HDI) to rank the nations of the world with respect to the state of their human, not only economic, development. The UNDP has published this indicator, along with the associated country rankings, every year since 1990. While it has been subject to some criticism, its computational simplicity has given it a wide following. However, since the 2010 Human Development report, the UNDP has adopted a new methodology for measuring the HDI as well as new indicators of development (for example, the Multidimensional Poverty Index, MPI).

   Nonetheless, we may ask why some countries that seem similar, especially in terms of their economies, and that have comparable GDP or per capita GDP results, post divergent HDIs. For example, while Chile and Gabon are, respectively, 50th and 49th globally in terms of per capita GDP, in 2009, Chile was ranked 44th overall with respect to the HDI while Gabon languished in 108th position. This may suggest that some countries devote little or no expenditures specifically to human development. Conversely, they may be investing resources in education and healthcare, but in a fashion that is inefficient or wasteful and thus not yielding the desired results: a more educated and healthier population. This is what we want to verify in this article. Using classical and bootstrapped Data Envelopment Analysis (DEA) models, we will seek to determine whether past or current expenditure levels in these countries are yielding an optimal HDI--i.e. the "best" possible HDI in light of the resources invested. In an economic downturn, it seems reasonable to verify the efficiency of countries in achieving their objectives. In this paper, it is the objective of human development that we analyze.

   The remainder of this paper is structured as follows. In the second part we review the definition of the human development index and briefly examine the literature. In Part 3, we present the DEA method and, in Part 4, the data. Part 5 contains our results and is followed by the conclusion.

2. The Human Development Index

   According to the UNDP, personal incomes represent one indicator of a country's level of human development. However, it is not the only one. Thus, a country with high incomes, as might be generated by resource extraction, for example, will not have a very strong growth potential if these revenues are primarily devoted to expenditures on consumption and imports (2). Conversely, this potential may exist if there is investment in individuals. This might, for instance, take the shape of investing in citizens' education or health. For this reason, the HDI is a composite indicator consisting of two elements in addition to gross national income (GNI). Human health is measured by individuals' ability to live long lives in good health. The first element in the HDI is thus life expectancy at birth. The second component of the HDI captures populations' knowledge. This indicator is decomposed into a measure of mean- and expected- years of schooling. Finally, the log of per capita GNI is the third component of the HDI, measuring the ability to access resources, in particular healthcare and education. Thus, the HDI is measured as the geometric mean of these three indicators: health, education, and income. The value of the HDI falls between zero (0) and one (1), where one indicates the maximal value of human development and zero a deplorable lack thereof. In 2011, the HDI ranged from 0.286 (Democratic Republic of the Congo) to 0.943 (Norway).

   The UNDP also computes a non-income HDI that only accounts for the health and education indicators. By publishing this indicator in its 2010 report, the UNDP wanted to reaffirm that development is more than GNP and establish the important role of education and health in development. In 2011, the non-income HDI ranged from 0.311 (Niger) to 0.979 (Australia).

   Since its inception, numerous studies have examined the HDI. Some of these addressed the methodological rationale for this indicator, suggesting that other factors should be included in the index (Sagar and Najam, 1998; Dar, 2004), or criticizing the arbitrary weighting of the three elements in the indicator, or their aggregation (Chowdhury and Squire, 2006; Noorbakhsh, 1998; Chatterjee, 2005; Cherchye et al., 2008). They argue that changes to how the HDI is calculated would result in a re-ranking of countries (3). Moreover, Srinivasan (1994) and Cahill (2005) suggest that the HDI might be redundant, as income is correlated with education and healthcare. In light of these criticisms, other authors have questioned whether alternative weights could be applied or whether there might be better indicators of countries' performances. Thus, Mahlberg and Obersteiner (2001), Despostis (2005a, 2005b), Lee et al. (2006), and

   Lozano and Gutierrez (2008) use a DEA methodology to compute the appropriate weight for each component of the HDI. In addition, the HDI could be viewed as an inappropriate indicator of countries' performance. Malul et al. (2009) measure this performance by per capita GDP and the inverse of the Gini index; Nardo et al. (2005) suggest using a composite index with components identified by principal components analysis or cluster analysis and weighted by DEA; Rotberg (2004) emphasizes the importance of ranking countries by the quality of their governance, which can be assessed using different proxy indicators or sub-indicators; and Afonso et al. (2010) and Afonso and St Aubyn (2011) evaluate the efficiency with which public expenditures contribute to attaining the individual objectives of education, health, or social protection. As for Arcelus et al. (2005), they measure countries' performance in reaching a high HDI as a function of the resources they devote to it.

   We base our research on this last study. Using DEA, we verify the countries' efficiency of reaching a high level of human development, compare this efficiency by regions and use a bootstrapped method to confirm these efficiency results. After reviewing the DEA method in the next section, we will describe the variables we retained for this study.

3. The DEA Method

   In order to assess countries' efficiency in achieving a certain value of the HDI, we will perform inter-country comparisons and hold their results up to a target. The DEA method allows us to determine this target, which is defined by the best performers in the sample. Since we are measuring the efficiency of various countries against each other, this is a relative measure. If other countries were included in the study, the efficiency of some of those present would change.

   An alternative approach to measuring efficiency would be a parametric method, stochastic frontier analysis (SFA) developed by Aigner et al. (1977) and Meeusen and van den Broeck (1977). DEA and SFA present their own advantages and drawbacks. As an econometric method, SFA allows for some noise while DEA assumes all deviations from the frontier are basically due to inefficiency. However, DEA doesn't require any assumptions other than free disposal and convexity (4) and accommodates several inputs and outputs. Furthermore, no explicit functional form is needed for the production frontier with DEA. Another disadvantage of DEA is that the results of efficiency are sensitive to changes to the sample. The frontier can only be composed by the units in the sample. These units could thus be efficient relative to the others in the sample but inefficient compared to units outside the sample. Bootstrap techniques have been developed to solve this sampling problem. As we appreciate the flexibility that allows the DEA method, we chose to measure the countries' efficiency by this method.

   Technical efficiency ascertains whether a country is operating on its production frontier. The Banker, Charnes and Cooper (1984) (BCC) DEA model uses linear programming methodology to compute technical efficiency. The goal is to maximize the quantity of output a country is able to generate so as to arrive at the production frontier. In this study, we suppose countries use several inputs in order to maximise their development level. Although we could propose different objective functions, we assume countries promote human development to go with economic development. Our assumption is that economic development is mainly supported by human capital in the long run (Lucas, 1988; Romer, 1990). We thus assume countries maximise their Human Development Index. An input-oriented approach could have been used. Nonetheless, we retain an output-oriented approach because it appeared plausible to us that countries would prefer maximizing the HDI for a given level of resource investment over minimizing the inputs, or resources, for a given level of HDI.

   Thus, we consider N countries^ (n = 1 ... N). Each country uses R variable inputs [x.sub.r,n] (r = 1 ... R) to produce M outputs [y.sub.m,n] (m = 1 ... M). National technologies are approximated by Farrell's method (1957). The model is resolved n times (each country is designated unit 0, the reference unit, in turn) using the following linear program:

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