Composite indicators are built by combining input variables within a mathematical model. The mathematical model can be thought of as made up of all treatments applied to the data as well as of their combination in the index (OECD, 2008). Each variable in the index is customarily attached a weight purportedly meant to appreciate the 'importance' of that variable. By far the most common strategy to aggregate variables seen in existing composite indicators is by a weighted arithmetic average of normalized variables, whereby the composite index Y is derived from a set of k normalized variables.
Weights are attached by the developers on the basis of different strategies, be those statistical, such as e.g. factor analysis, or based on expert evaluation, such as e.g. analytic hierarchy process (OECD, 2008). Weights represents a form of judgement of the relative importance of the different variables, including the case of equal weights where all variables are (in theory) equally important.
Using methods derived from global sensitivity analysis we show that important discrepancies exist in most composite indicators between declared weights and effective importance of variables or pillars.
Biography: Andrea Saltelli has worked on physical chemistry, environmental sciences and applied statistics. His main disciplinary focus is on sensitivity analysis of model output. A second focus is the construction of composite indicators or indices. Presently leads the Econometric and Applied Statistics Unit at the Joint Research Centre in Ispra. The Unit develops econometric and statistic applications in support to the services of the European Commission.