A method to evaluate composite performance indices based on variance-covariance matrix

In this paper we compute performance indices like those from Mereuta et all. (2007) using the eigenvalues and the eigenvectors of the variance-covariance matrix of these indices. The eigenvalues are used in this paper to give natural weights to the performance indices in order to compute the weighted competitiveness indicators, and their corresponding eigenvectors are used to obtain the desired uncorrelated performance indices. In order to point out the mutual influence in the case of each pair of the considered correlated performance indices we compute also their correlation matrix. After we order the composite performance indices (non-weighted or weighted) we classify them using either the maximum entropy principle, either the maximum separation (Chow breakpoint test). A comparison between the classifications using the weighted/non-weighted classifications using the maximum entropy principle and the maximum separation are also done in the paper. As application we consider the GDP per capita, the investment share in GDP, the unemployment rate, the Gini Index of income inequality and the share of consumption of renewal energy resources (five performance indices) for the 27 countries of European Union. These performance indices are according to Indicators of Sustainable Development (www.un.org/esa/sustdev/publications/indisd-mg2001.pdf) approved by the Commission on Sustainable Development at its Third Session in 1995.