BOD – min range: A Robustness Analysis Method for Composite Indicators

Composite indicators are a useful instrument to represent in a synthetic and easy to read way a phenomenon or a specific reality. However, synthesizing indicators using aggregative approaches inevitably involves a loss of information due to the reduction in size of the original matrix. So, in composite indicators construction, the robustness analysis phase is very important to validate the synthetic construct and to attempt to recover some of the lost information. This paper aims to present an interval, useful for the robustness analysis of composite indicators, between the best and the worst performance obtainable from the synthetic construct. The two margins of the range are obtained: for the upper bound, using the Benefit Of The Doubt approach, that is an application for composite indicators construction of the linear programming technique, Data Envelopment Analysis; and, for the lower bound, it has been used the minimum between the considered elementary indicators. The obtained range will comprehend almost every other synthetic measure that can be calculated with other aggregative methods for the considered matrix of indicators, so, our methodological proposal is useful to see the distance from the best and the worst obtainable cases.