RECOMPUTATION OF UNDP’S HDI RANKINGS BY DATA ENVELOPMENT ANALYSIS

The HDI has played an influential role in the debate on human development. No index is perfect and so is the Human Development Index of United Nations Development Program. This paper aims to measure the performance of 182 countries in terms of performance by means of non-parametric input oriented CRS employed Data Envelopment Analysis. In addition, it elaborates on the cut-off values assigned by UNDP to categorize the countries. By means of this research, countries will be able to choose those elements by benchmarking from other countries that are applicable and most likely to develop strategy formulation processes for human development and international growth. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. This journal is published by the University Library System of the University of Pittsburgh as part of its D-Scribe Digital Publishing Program, and is cosponsored by the University of Pittsburgh Press Volume 1 (2011) | ISSN 2158-8708 (online) | DOI 10.5195/emaj.2011.10 | http://emaj.pitt.edu


I. Introduction
Today, normalised measures of life expectancy, literacy, educational attainment, and GDP per capita are considered to be the main indicators of development for countries worldwide.These three indicators are unified to give a measure of development, namely the Human Development Index (HDI).HDI has been first used in the United Nations Development Program's (UNDP) World Development Report.Since the first publication of this annual report in 1990, UNDP has been seeking to explore the concept and measurement of global human development.
The Human Development Index (HDI) computes and assigns a single, scalar value to each country of the world based on three components of human development.This simple measure has changed the global debate on development and influenced public policy around the world.Criticism and proposed alternatives abound, yet the index has managed to maintain its popularity and simplicity with only minor modifications over the years of 1991, 1994, 1995, 1999 and 2005.The HDI was developed to measure "the basic concept of human development to enlarge people's choices" (Ul Haq, 1995).It was also designed as an alternative to the use of GDP per capita alone as a measure of human development.To these ends, it must be concluded that the HDI has achieved overwhelming success.However, it is still prone to criticisms as it lacks the means to correctly measure and analyse the annual performance of countries.
Ul Haq stated that the purpose of the HDI was to measure at least a few more choices besides income and to reflect them in a methodologically sound composite index.Indeed, the HDI has included only a limited number of indicators to keep it simple and manageable.This simple HDI algorithm is still being used today and calculated from regularly available data to produce a meaningful number that can be used to compare and rank countries across the world.
Up-to-date, critics on HDI have claimed that it uses very few or the wrong indicators.Others allege that it presents an oversimplified view of human development and added that a pure economic model focusing on growth alone should set the tone on discourse regarding human development.In fact, some of these critics have developed their own novel indices or have resulted in the modification of HDI.But, collecting reliable data continues to be the major obstacle in the poorest countries (Harkness, 2004).Regarding health and longevity, Harkness notes that mortality data are most likely to be missing in countries where mortality is the highest.According to another critic, both the resources allocated throughout a country and the levels of inequality that may exist across the country are not taken into account in the HDI index (Foster, 2005;Ul Haq, 1995).In recent years, most critics have taken issue with the equal weights assigned to each of the respective indicators of the index (Mahlberg and Obersteiner, 2001; Chowdhury and Squire, 2006) but assigning differing weights have been proven to be unnecessary (Stapleton and Garrod, 2007).And yet, the HDI has been extensively criticised for its lack of desirable statistical properties.
To overcome the deficiencies of previous traditional parametric approaches and weighing problems, Data Envelopment Analysis can be employed.To measure the HDI, this analysis has

II. METHOD
Data Envelopment Analysis (DEA) is a data-oriented technique which has been proven to be an effective tool in evaluating relative efficiency.It is a nonparametric method of measuring the efficiency of a decisionmaking unit (DMU) such as a country, first introduced into Operations Research literature by Charnes, Cooper and Rhodes in 1978.Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries such as sports, logistics, hospitals, universities, cities, business firms etc.Because it requires very few assumptions, DEA has opened up possibilities for use in cases which have been resistant to other approaches because of the complex and often unknown nature of relations between the multiple inputs and multiple outputs involved in the DMUs.
Throughout the paper, we use decision making units (DMUs) to represent countries.Each DMU is assumed to have a constant input and represented by three outputs , i.e.HDI component indicators (life expectancy index (LEI), education index (EI) and GDP per capita index (GDPI)).The DEA model used assumes an input oriented radial CRS technology.
The main advantages of DEA are: (1) Multiple inputs and outputs can be used effectively, while ascertaining efficiency, and a specific production function is not required; (2) The decision maker does not need prior information about weights of inputs and outputs; and (3) For each DMU, efficiency is compared to that of an ideal operating unit, rather than to the average performance.
The HDI is based on three indicators: longevity, as measured by life expectancy at birth; educational attainment, as measured by a combination of adult literacy (two-thirds weight) and combined primary, secondary and tertiary enrollement ratios; and standard of living, as measured by real GDPI (Purchasing Power Parity in US$).To calculate the dimension indices, UNDP has assigned minimum and maximum values (goalposts) for each underlying indicators.Performance in each dimension is then calculated and expressed as a value between 0% and 100%.Then, the HDI is calculated as a simple average of the dimension indices by basic algebra.In UNDP's approach, this was followed by assigning (equal) weights to each dimension index given as follows: HDI = x.(LEI) + y. (EI) + z. (GDPI) (where x = y = z = 1/3).
Whereas, in our approach, the indices are analyzed by the use of linear programming methods to construct a non-parametric piece-wise surface over the data.The CRS surface is presented by a straight line that starts at the origin and passes through the first DMU that it meets as it approaches the observed population.The models with CRS envelopment surface assume that an increase in inputs will result in a proportional increase in outputs.Efficiency measures are then calculated relative to this surface.For the purpose of analyzing the data, Efficiency Measurement System (EMS) is used.The inherent weights for the inputs and outputs are assigned by the model itself.
The essence of the CRS model is the ratio of maximization of the ratio of weighted multiple outputs to weighted multiple inputs.Any country compared to others shold have an efficiency score of 100% or less.The efficiency score in the presence of multiple input and output indicators is defined as: Efficiency = Weighted sum of outputs / Weighted sum of inputs Assuming that there are n DMUs, each of with i inputs and j outputs, the relative efficiency score of a test DMU m is obtained by solving the following model proposed by [Charnes et. al., 1978]: The above model is run n times in identifying the relative efficiency scores of all DMUs.Each DMU selects input and output weights that maximize its efficiency score.In general, a DMU is considered to be efficient if it obtains an efficiency score of 100% and a score of less than 100% implies that it is inefficient.

III. ANALYSIS
Unlike the HDI, the DEA scores on Table 1 are relative measures.Each country is compared with the best practice countries when it assesses its composite performance on the human development indicators.As shown in Table 1, the EMS analysis has yielded differences in country rankings between the UNDP and DEA approaches.The DEA approach identified a group of 20 optimally performing countries that are defined as efficient and assigns them an efficiency score of 100%.These efficient countries are then used to create an "efficiency frontier" or "data envelope" against which all other countries are compared.In sum, countries that require relatively more weighted inputs to produce weighted outputs, or, alternatively, produce less weighted output per weighted inputs than do countries on the efficient frontier, are considered technically inefficient.They are given efficiency scores of less than 100%, but greater than 0%.We compared the DEA efficiency scores with HDI values.Pearson correlation coefficient of 0.958 shows that the two indices are highly correlated.Despite this strong correlation, there are also some notable differences between the two measurements.

Benchmarks
DEA analysis shows that Australia is the country that is the most frequently used as a reference by the inefficient countries (115 times or by the 63% of the inefficient countries).The corresponding frequencies for Denmark and Japan are 94 (52%) and 58 (32%), respectively.Therefore, both Australia and Denmark can be regarded as role model countries.

Cluster Analysis
The basis of UNDP's classification of 182 countries into 4 groups (shown in Table 2) is based on a simple leveling structure.A better method for determining the real cut-offs between countries is the cluster analysis.In a previous research, Wolff et al. (2009) have examined the consequences of data error in data series used to construct aggregate indicators and found that up to 45% of developing countries were misclassified in HDR 2008.Our analysis of corrected HDI and DEA-based cutoffs are given in Table 3. Grouping of countries by means of cluster analysis is given in Table 4.In addition, the ranking results of DEA have also been examined by cluster analysis.The countries have again been classified in four groups.However, there are substantial differences between the groupings of HDI and DE  Corrected groups of HDI has differed from the former one in many terms.Firstly, Group 1 now includes many of the recently EC-integrated countries such as Estonia, Poland, Slovakia, Hungary, Lithuania, Latvia, Bulgaria and Romania.Secondly, South and Central American countries has appeared in Group 1 for the first time.These countries include Chile, Argentina, Uruguay, Costa Rica, Venezuela, Panama and Trinidad Tobago.It should be noted that Argentina, Uruguay and Venezuela are full members of Mercosur.Thirdly, none of the African countries are categorized in Group 1. Next, Group 2 now includes the majority of Asian, Turkic and North African countries.Last, whereas Group 4 includes mostly the Central African countries.
According to the classification by DEA, all ex-USSR countries except Azerbaijan and Uzbekistan have moved to Group 1 from Group 2 due to their high adult literacy rate.In return, Bahamas and Malaysia have moved to Group 2 from Group 1 due to their relatively low EI.
Equatorial Guinea have moved to Group 1 from Group 2 due to its high GDP per capita of 30.627USD.In return, Panama has moved from Group 1 to Group 2 due to its relatively low GDP per capita.
Moving from Group 3 to Group 2 has required countries to have superiority over other countries in any of the two indicators.For instance, Pakistan has higher GDP per capita (0.537 versus 0.526) and life expectancy (0.687 versus 0. 624) indices than Yemen.Therefore, Pakistan has moved to the upper group whereas the group of Yemen has remained the same.
It should be noted that high education index is proven to be the most important criterion while grouping the countries by DEA.All countries moving from Group 4 to Group 3 such as Malawi, Zambia and Rwanda have enjoyed relatively higher adult literacy rates.It is also observed that countries with the lowest efficiency scores are mainly from the Central African countries.It is true that the HDI has brought the global community closer and inspired a united effort in the common cause of improving the human condition for those dwelling in the darkest corners of the world.It is also true that HDI is a simple and universal index.However, this index has been very subjective and not been scientifically successful in correctly categorizing the countries.To overcome this problem, cluster analysis has been used.
The proposed approach in this paper differs from the previous HDI assessments since it does not need to assign any subjective weights to EI, LEI and GDPI.It also differs from the previous DEA applications on HDI assessment by clustering countries by means of DEA-based cutoff points.

Volume 1 (
2011) | ISSN 2158-8708 (online) | DOI 10.5195/emaj.2011.10| http://emaj.pitt.edubeen firstly used by Mahlberg and Obersteiner in 2001.The following year, Lozano and Gutierrez proposed a new DEA model that computes a rangedjusted measure (RAM) of efficiency for HDI and Lee et al. (2006) made use of a fuzzy multiple objective DEA for the HDI.In 2005, the HDI of the Asian and Pacific countries were calculated by Despotis (2005).Having automatically overcome the subjectivity difficulties in weighing the component indices, this technique analyses the inherencies of the data by a different approach.

Table 2
Classification of countries according to HDR, 2009

Table 3
Corrected and DEA cutoffs classifying the 182 countries