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

Albu, Lucian-Liviu and Ciuiu, Daniel (2009): A method to evaluate composite performance indices based on variance-covariance matrix.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Sustainable development, competitiveness indices, composite indices, weighted and non-weighted indices, Shannon entropy, Chow breakpoint test.
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O47 - Empirical Studies of Economic Growth ; Aggregate Productivity ; Cross-Country Output Convergence; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; O - Economic Development, Innovation, Technological Change, and Growth > O5 - Economywide Country Studies > O57 - Comparative Studies of Countries

References

[1] Albu, L.L. (2008), ”A Model to Estimate the Composite Index of Economic Activity in Romania—IEF-RO”, Romanian Journal of Economic Forecasting, No. 2, pp. 44-50.

[2] Chow, G.C. (Jul. 1960), ”Test Between Sets of efficients in Two Linear Regressions”, Econometrica, Vol. 28, No. 3, pp. 591-605.

[3] Ciuiu, D., (2007), ”Pattern Classification using Principal Components Regression”, Proceedings of the International Conference Trends and Challenges in Applied Mathematics, 20–23 June 2007, Technical University of Civil Engineering, Bucharest, Romania, pp. 149-152.

[4] Ciuiu, D., (2008), ”Pattern Classification using Secondary Components Perceptron and Economic Applications”, Romanian Journal of Economic Forecasting, No. 2, pp. 51-66.

[5] Jula, D., (2003), Introducere In Econometrie, Ed. Professional Consulting, Bucuresti.

[6] Mereuta, C, Albu, L.L., Iordan, M. and Chilian, M.N., (2007), ”A Model to Evaluate the Regional Competitiveness of the EU Regions”, Romanian Journal of Economic Forecasting, No. 3, pp. 81-102.

[7] Onicescu, O. and Stefanescu, V. (1979), Elemente de statistica informationala si aplicatii, Ed. Tehnica, Bucuresti.

[8] Paltineanu, G., Matei, P. and Trandafir, R., (1998), Analiza numerica, Ed. Conspress, Bucuresti.

[9] Petrica, I. and Stefanescu, V. (1982) Aspecte noi ale teoriei informatiei, Ed. Academiei, Bucuresti.

[10] Preda, V. (1992) Teoria deciziilor statistice, Ed. Academiei, Bucuresti.

[11] Saporta, G., (1990), Probabilites, Analyse des Donees et Statistique, Ed. Technip, Paris.

[12] Vaduva, I. (2004), Modele de simulare, Ed. Universitatii Bucuresti.

[13] Voineagu, V. et all, (2007), Teorie si practica econometrica, Meteor Press, Bucuresti.

[14] ”Banca Nationala a Romaniei. Raport Anual 2008”, www.bnr.ro/Publicatii-periodice-204.aspx.

[15] ”European Comission. Eurostat. Your Key to European Statistics”

[16] ”Indicators of Sustainable Development”, www.un.org/esa/sustdev/publications/indisd-mg2001.pdf.

[17] ”2007/2008 Human Development Report. CIA World Factbook”, http://hdrstats.undp.org/indicators/147.html.