2.1. Theoretical justifications
The HDI is based on the Sen's (1985) capabilities theory. Sen (1985) postulates that three elements are essential to human fulfillment: the capability of people to access to a good education and his capability to have a decent standard of living and his capability to lead a long and healthy life. This idea is taken into account by the UNDP in these terms: “Human development is a process of enlarging people’s choices. In principle, these choices can be infinite and change over time. But at all levels of development, the tree essential ones are for people to lead a long and healthy life, to acquire knowledge and to have access to resources needed for a decent standard of living. If these essential choices are not available, many of other opportunities remain inaccessible.”(UNDP–H DR, 1990, p.10). So, “the HDI is a summary measure of achievement in key dimensions of human development [namely] a long and healthy life, access to knowledge and a decent standard of living” (UNDP-HDR 2015).
To measure the achievement in the three key dimensions in human progress, the HDI was basically the linear mean of the scores reached in education, health and income.
However, criticisms, including those of Anand and Sen (1997), Chatterjee (2005), Foster et al., (2005), Gaertner and Xu (2006), Kovacevic, (2010) led to the reformulation of the HDI in 2010. Major changes are made: the hypothesis of perfect substitutability - which had motivated the choice of aggregation of the index by the linear mean - between the three dimensions of the HDI was strongly contested. Until 2010 - and even after the major changes - the functional specification for aggregation of the index continues to fuel debate (see Desai 1991, Palazzi and Lauri, 2013, Nathan, Mishra, and Reddy, 2012 and Ghislandi et al (2019)). For these authors, the underlying properties (constant marginal contribution for each dimension, constant marginal substitution rate between dimensions, etc.) of the perfect compensation hypothesis are not verified for dimensions of human development.
Insert Fig. 1 Here
As highlighted by Fig. 1, when considering the dimensions of the HDI two by two, (we illustrate here by considering the health index and the education index) we can observe the fundamental differences that exist between linear aggregation (old formula of the HDI) and geometric, newly adopted. Curve (a) represents the situation where the HDI is obtained by a simple linear mean. Thus, it indicates that for a given HDI level I0 (the HDI score), the same level can be maintained when the "education" index increases with a decrease in the "health" index; which is contrary to the idea of the HDI which requires constant improvement in all three dimensions. This situation is called the perfect substitution situation in which the rate (the price to be paid or opportunity cost) of substitution between the two variables remains constant throughout this curve.
In another extreme case, one can assume a situation of perfect complementarity between the dimensions (curve (b)). Also known as the functional form of Leontief, this case indicates that improving the level of the HDI requires a joint effort to improve both the level of education and the level of health (Robeyns 2005).
Between the two extreme cases presented above, there is the intermediate situation which is really the synthesis of the two extreme cases. This case corresponds to the functional specification of the HDI in 2010 (curve (c)) which seems to be the appropriate situation according to Klugman, et al. (2011). For these authors, the aggregation of the index by the geometric mean is closer to reality. Indeed, individuals with mental or physical disabilities, for example, can offset this deficit if they have significant incomes. For example, the visually impaired can partially overcome their disability through specialized education (which requires more resources in terms of costs of education) such as braille. Likewise, people with reduced mobility can partially overcome this handicap by moving in electric vehicles.
Taking these remarks into account has led to a revision of the functional form of HDI aggregation from a linear mean to a geometric mean. Since 2010, the (new) formula of the index is as follows: HDI\(\sqrt[3]{\left(ei\times hi\times ri\right)}\) (1)
Where ei is defined as the index of education, hi the index of health and ri the index of income.
Criticism in the direction of improvement of the index have mainly highlighted some shortcomings of the index. To mention some, the HDI is criticized for being too simplistic. The concealment of a significant number of relevant variables limits its ability to translate true human development. Inequalities are not taken into account in the aggregation of the original HDI. Nourry (2008), for his part, notes that one of the weaknesses of the HDI is that it has not integrated the environmental component into its elaboration. However, the human being interacts with the environment in which he evolves. It is clear that a deterioration of the environmental environment would directly affect the development of the latter.
Moreover, in the choice of variables, the HDI is criticized for not being able to capture certain dimensions such as intra and intergenerational equity, political freedoms and respect for human rights, happiness, etc. (Sagar and Najam, 1998). Nussbaum (2000) regrets that “freedom of mobility”, “social bond” and “protection against different forms of discrimination” which are fundamental to human fulfillment, are not included in the HDI.
Always in the constructive criticism, other authors have pointed out the existence of a theoretical inconsistency resulting in mixed variables choices mixing both stock variables (literacy rate) and flow variables (school enrollment rate for example) and input variables (the enrollment rate). Klugman and his co-authors point out, however, that the distinction between certain “stock” and “flow” variables is not obvious. Life expectancy can be considered as a “flow” variable or a “stock” variable according to apprehensions.
Also, the choice of replacing the “gross literacy rate’’ by the mean years of schooling was justified in Klugman et al. (2011). Indeed, if in the fairly recent past years the indicator “gross literacy rate’’ was relevant and even preponderant (which explained its weight of 2/3 in the dimensional index) in the training of the capabilities of the individuals, the spectacular performances of the last countries years in this indicator with no real impact on human development (the gross literacy rate increased from 60 to 83% between 1970 and 2010 at the global level and is 95% in most countries (Klugman et al., 2011, p.266)), imposes a relativized reading of this indicator in order to take into account the quality dimension of this index beyond its gross value.
From a practical perspective, Klugman, Rodríguez, and Choi (2011) argue that the choice of a synthetic index to measure the performance of countries in terms of human progress is mainly motivated by the need to have a simple, transparent tool, easily to communicate and understandable by a wide audience. However, is the HDI statistically justified?
2.2. Empirical validity of the HDI
Although the HDI is based on solid theoretical foundations, its statistical validity is less known. As suggested by Klugman, et al. (2011), one of the legitimate manners to support the HDI legitimacy is “to do speaking its data themselves” by using statistical techniques to generate the weights to be associated with the dimensional indexes. In other words, the use of principal component analysis (PCA) makes it possible to decide which weights to assign to each of the three dimensions of the index. To do this, we mobilize the PCA techniques using the more recent HDI data, from 2020. We postulate that human development is a latent concept imperfectly captured by three individual indices namely the income index, the health index and the knowledge index. The defined indices are connected to the components defined above.
The PCA technique consists to reduce the dimensionality of multivariate observations with minimal loss of information contained in the initial individual variables. In other words, the PCA summarizes the information contained in \(n\) variables of a given phenomenon in a reduced number of \(k\) relevant factors with\(k<n\). The first principal component, also called “the relevant factor”, is a linear combination of the original variables which gives back the largest variance; the second one captures the remaining largest variance among all linear combinations that are uncorrelated with the first principal component, and so on. By default, there are as many latent factors as initial variables. However, there are criteria to select relevant factors. OECD and JRC (2008) and Dialga and Le (2016) summarize these conditions in three criteria. The following criteria must be jointly full for the choice of relevant factors.
Criterion 1: The Eigen value associated to factor to be retained must be more than one (Eigen value ≥ 1);
Criterion 2: The variance explained by the factor must be more than 10% of the total variance of the initial variables (Variance Explained ≥ 10%);
Criterion 3: The factors retained must explain at least 60% of the total variance (cumulative variance ≥ 60%).
Table 1
Relevance of measuring human development through a synthetic index
Components | Eigen Values | Variance Explained (%) | Cumulative (%) |
Component1 | 2.891 | 96.37 | 96.37 |
Component 2 | 0.061 | 2.03 | 98.40 |
Component 3 | 0.048 | 1.60 | 100.00 |
Insert Table 1 Here
Source: Author’s calculations using the 2020 HDI data
Table 1 shows that the three dimensions of the HDI are all related to one latent factor, in this case the factor 1 since it is the only one to satisfy the first two criteria described above. From a conceptual point of view, this result indicates that the three dimensions refer to a same concept. It especially shows that all three initial dimensions namely the access to knowledge; the healthy life and the access to the decent standard of living may be replaced by a single index. This composite index returns 96.37% of the information contained in the individual dimensions of human development.
In the light of this result, we conclude that the construction of the HDI is statistically relevant, since only less than 3% of the variation in human development progress is not explained by the synthetic index compared to the individual progress of its three components.