Exploring Wider Well-Being in the EU-15 Countries: An Empirical Application of the Stiglitz Report

Abstract

We draw on the recommendations of the Stiglitz Report to select a set of economic and social variables that can be used to make cross-country comparisons of wider well-being. Using data for the EU-15 countries for 1999 and 2005, we show how three-way analysis can be used to extract synthetic information from a large data set to determine the main latent explanatory factors. In our case, we identify one dominant factor that we term the development profile, which is positively associated with the level of education outputs, technological progress and female labour market participation and negatively associated with the level of pollution. We rank the countries according to this factor and compare these rankings with simpler GDP comparisons and find that the two rankings are only weakly correlated.

Appendices

Appendix 1: Countries and Variables

See Tables 5 and 6.

Table 5 List of countries

Table 6 List of variables

Appendix 2: STATIS

STATIS (Structuration des Tableaux a Trois Indices de la Statistique)—attributed to Escoufier (1980) and L’Hermier des Plantes (1976)—allows us to analyse a dataset represented by a matrix, X, composed of a three dimensions: time (for k = 1, 2,…K time periods), variables (for j = 1,2,…J variables) and units (for i = 1,2,…I units). Thus, each matrix I × J _k of data (X _k ), defines the structure for all units in the kth time period, and this depends on their respective position as defined by the distances between each pair of units:

$$ d_{k}^{2} (i,i^{\prime } ) = \sum\limits_{j = 1}^{J} {\left( {x_{ijk} - x_{{i^{\prime } jk}} } \right)^{2} } $$

The goals of STATIS are the following: (a) to compare and analyze the relationship between the different data matrices; (b) to combine the matrices into an average structure (compromise) on which PCA is applied; (c) to project the trajectories of units and variables in a compromise space.

In order to derive the compromise structure, STATIS generates some weights that are applied to each of the data matrices. Applying PCA to the compromise structure one derives the position of the observations in the compromise space.

STATIS is composed of three main steps: the inter-structure analysis, the intra-structure one and the project the trajectories of units and variables in a compromise space. The first one involves the analysis of correlation among variables or time periods (objects). This is done by comparing the structure of K matrices, each one to the others. To do this, each matrix is considered as a unique statistical object and the variance–covariance matrix W _k —reflecting the similarities between objects within each matrix—is computed:

$$ W_{k} = X_{k} Q_{k} X_{k}^{{^{\prime } }} $$

where X ^′ _k is the transpose of data matrix X _k , and Q _k is a matrix of dimension J _k  × J _k with the diagonal elements equal to 1/J _k . In our case, as we have the same number of variables in each time period, Q _k is an identity matrix of dimension J × J.

The similarities between two variance–covariance matrices W _k and W _k’ can be computed as follows:

$$ \Upomega_{{kk^{\prime } }} = (W_{k} ,W_{{k^{\prime } }} ) = {\text{trace (}}W_{k} DW_{{k^{\prime } }} D) $$

where D is a matrix of weights. A measure of closeness between the variance–covariance matrices is provided by the RV coefficient defined as:

$$ RV(W_{k} ,W_{{k^{\prime } }} ) = \frac{{W_{k} W_{{k^{\prime } }} }}{{\sqrt {(W_{k} ,W_{k} )(W_{{k^{\prime } }} ,W_{{k^{\prime } }} )} }}. $$

The RV coefficients range from 0 to 1. If the RV coefficients are close to 1 the variance–covariance matrices are very similar. Applying PCA to the RV matrix, we can represent in the space of principal components the similarities among data matrices concerning different time periods.

The elements of the first eigenvector that come out from PCA are normalized in such way that their sum is equal to one. In the intra-structure analysis, they are used as weights (v _k ) to define the so called ‘compromise’ among k time periods, that is:

$$ W = \sum\limits_{k = 1}^{K} {v_{k} W_{k} } . $$

The compromise matrix is then analysed to explore the common structure in the data.

Finally, plotting the coordinates of the different units in the compromise space allows us to visualize the path of units across time periods.