Socioeconomic and Environmental Performance: A Composite Index and Comparative Application to the USA and China

3. Formulation of a Composite Index for Welfare and Sustainability
We need an Index of Welfare which can measure both socioeconomic development and its sustainability. Such a metric should be designed to take into account the health of people of a region, nation or the world, of other species as well as the impact on the natural environment. We consider that the Gross Domestic Product (GDP) or the GDP per capita over time do not capture these features by themselves. Actually, Kuznets (1934), the inventor of the concept of GDP, indicated in his first report to the USA Department of Commerce, Senate document, that he disapproved the use of the GDP as a general indicator of welfare. He noted that “the welfare of a nation can scarcely be inferred from a measure of national income” (p. 7). Hicks (1946) also pointed out the practical difficulty of using GDP per capita as an objective indicator of a nation’s welfare.

There are an increasing number of scholars and institutions working hard on the search for how to go beyond the Human Development Index (HDI). This is the case of initiatives by the European Union, Club of Rome, World Academy of Art & Science, OECD, etc. Surely, the relevant indices of welfare must take into account a wider context and changes in related spheres of human knowledge. To make the required progress in this direction involves visions, values and methods. New theoretical formulations and empirical data are important to capture the dynamics, complexities and sustainability of socioeconomic development.

Fullerton & Stavins (2012, abstract, p. 3) argue that, “Economists themselves may have contributed to some misunderstandings about how they think about the environment, perhaps through enthusiasm for market solutions, perhaps by neglecting to make explicit all the necessary qualifications, and perhaps simply by the use of jargon”. We state specifically that the expansion of global output is not a reliable measure of development. This indicator may encourage a search for unbounded higher productivity and consumption. It may tend to overvalue unviable expectations of sustained higher levels over time. It obscures both current and potential ecological problems. It may somewhat stimulate the expansion of the economy but frequently degrades the environment and even the welfare of both humans as well as other species.

There is an extensive set of models dealing with the relationship between socioeconomic variables and measures of their environmental effects. Most such models are goal-oriented as their authors take their ultimate purpose to be the search for practical ways of improving human welfare. As expected we are unable to build models which can include most of the immense number of indicators or variables that shape the interaction between human behavior, institutions and the environment. From a methodological stand point, we need to set up reasonable abstractions and simplifications of reality. Conceptually, we need to express in simplified forms a number of different alternative representations of a complex whole. In this sense, although one should search for a more encompassing perspective, no doubt, any specific model represents a particular viewpoint. Therefore, the relevant conclusions will be the result of an emphasis on the set of particular factors being considered. Nevertheless, a formal approach is crucial but can be viewed as no more than providing some building blocks for a representation of the complex nexus of reality.

We will propose here a composite indicator of welfare which takes into account social, human and environmental criteria. We believe that our composite index provides insights into comparative development levels which most of the current indicators cannot. In this sense, our model provides a new alternative step to reach a desirable measure.

It is not surprising that we have witnessed numerous attempts to construct composite indices intended either to replace or to complement both GDP per capita and HDI. Some critics argue that while generally held to be politically useful, such new indices have proved to be somewhat redundant in the sense that their values have been shown to exhibit a positive and statistically significant correlation with GDP per capita. It follows that these indices may have failed to encompass what GDP per capita cannot capture.

As we mentioned in the introduction, a stimulating starting point to deal with the formulation of a model encompassing the interrelationship involved in the sustainability of development is a seminal article by Kaldor (1971), in which he considers the macroeconomics of the conflicts across national policy objectives. However, he does not deal with the environment. An extended enquiry led to the introduction by Karl Schiller, in the early 1970s, of a graphical representation of Kaldor’s original view. A glance at the resulting diagram reveals a diagnosis of comparative performance. This analytical instrument was called a “Magic Square” (MS) and soon after some economists from OECD began to use this geometric apparatus to evaluate economic policies. The “wonderland”, which was introduced by OECD, is an ideal configuration which takes into account desirable features of a system composed of a set of variables represented by the larger area of a quadrangle. It involves the calculation of norms or values postulated as idealized references for a given accounting period. To start the procedure, we need reliable information on the numerical values of the variables, and then to find the limits (bounding conditions), designated as “awful” and “desirable” for each.

A “naïve” macroeconomic representation of the MS was formulated by Bernard et al (1988). Medrano-B & Teixeira (2013) modified this approach. The original figure is conceived in its four directions (N, S, E and W) indicated by ϒ, τ, ϕ and ζ. All four variables (axes) are originally drawn at different scales expressed in percentages and the adjacent indices are joined by straight lines. The original area of such figure cannot be calculated due to the non-uniform scales of the axes. To construct a proper MS all four scales must be redefined to be uniform from 0 to b, where b is a numerical constant to be evaluated by normalizing the figure to a unit area. A new MS, with a larger area, is drawn not as a square but a diamond-shaped figure. The greek symbols indicating the superior (sup) and the inferior (inf) bounding conditions, given by expression (1). Note that the first inequality has a different sense as we explain in section 3. The respective differences, expressed by (2), lead to the illustration (Figure 1):

ϒinf ≥ ϒ ≥ ϒsup ; τinf ≤ τ ≤ τsup ; ϕinf ≤ ϕ ≤ ϕsup ; ζinf ≤ ζ ≤ ζsup. (1)

ϒsup – ϒinf = Γ; τsup – τinf = Τ; ϕsup – ϕinf = Φ; ζsup – ζinf = Ζ. (2)

Figure 1


The four new corresponding indices, indicated by primed variables, are given by expression (3):

0 ≤ ϒ’ ≤ b; 0 ≤ τ’ ≤ b; 0 ≤ ϕ’ ≤ b; 0 ≤ ζ’ ≤ b (3)

The next step is to find the transformation of the original un-primed to the primed (new) variables. Since all original variables have linear scales, the algebraic transformation constitutes an orthogonal representation leading to a square whose identical sides are obtained by expression (4):

ϒ’ = b (ϒ – ϒinf)/(ϒsup – ϒinf) = (b/Γ) (ϒ – ϒinf); τ’ = b (τ – τ inf)/(τ sup – τ inf) = (b/Τ) (τ – τ inf)

ϕ’ = b (ϕ – ϕ inf)/( ϕ sup – ϕ inf) = (b/Φ) (ϕ – ϕ inf); ζ’ = b (ζ – ζ inf)/( ζ sup – ζ inf) = (b/Ζ) (ζ – ζ inf) (4)

Now we illustrate in Figure 2 the visualization of the area of the square, rotated to 45 degrees:

Figure 2


Through a simple algebraic transformation a perfect square with uniform axes is created. Since all the original variables have linear scales, the sides of the new geometric representation are given by expression (4). A’ is given by equation (5):

A’ = ½ (ϒ’τ’ + τ’ϕ’ + ζ’ ϕ’ + ζ’ ϒ’) (5)

In the next section we will consider the meaning of the four variables involved in the performance of the USA and China. We will also include the relevant statistical data to be used as well as the construction and the result of the Index of Welfare (A’).

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