On weighting the components of the Human Development Index: A statistical justification - Georges Nguefack-Tsague; Stephan Klasen; Walter Zucchini (Georg-August-Universität Göttingen, Courant Research Centre - Poverty, Equity and Growth (CRC-PEG), 2010)
The Human Development Index (HDI) published in the Human Development Report (HDR) of the United Nations Development Program is calculated as a simple average of the Life Expectancy Index (LEI), the Education Index (EI) and the Gross Domestic Product Index (GDPI). This paper provides statistical support for the use of this seemingly arbitrary equal weighting of the three components by treating human development as a latent concept imperfectly captured by its three component indices. We show that a principal component analysis (PCA) based on the correlation matrix of the components leads to practically the same weights. Specifically we show that, for the period 1975 to 2005, the first principal component accounts for between 78% and 90% of the total variability in the data, and that its coefficients are positive and nearly equal. By normalizing the coefficients, the simple average weighting (1/3, 1/3, 1/3) scheme is obtained. The ranks of countries obtained using the PCA weightings are very similar to those based on the HDI. An advantage of the simple equal weighting is that one can define a simple index to measure the balance of a countryś development, given its HDI which we show below.
Keywords: I31; C43; O1; 330; Human Development Index; Human Development Report; United Nations Development Program; principal component analysis; correlation matrix