Robust Distribution-Based Winsorization in Composite Indicators Construction

Abstract

Composite indicators are widely used to determine the ranking of countries, organizations or individuals in terms of overall performance on multiple criteria. Their calculation requires standardization of the individual statistical criteria and aggregation of the standardized indicators. These operations introduce a potential propagation effect of extreme values on the calculation of the composite indicator of all entities. In this paper, we propose robust composite indicators for which this propagation effect is limited. The approach uses winsorization based on a robust estimate of the distribution of the sub-indicators. It is designed such that the winsorization affects only the composite indicator rank but has no effect on the entities ranking in each sub-indicator. The simulation study documents the benefits of distribution-based winsorization in the presence of outliers. It leads to a ranking that is closer to the clean data ranking when compared to the ranking obtained using either no winsorization or the traditional winsorization based on empirical quantiles. In the empirical application, we illustrate the use of winsorization for ranking countries based on the United Nations Industrial Development Organization’s Competitive Industrial Performance index. We show that even though the sub-indicator ranking does not change, the robust winsorization approach has a material impact on the ranking of the composite indicator for countries with large discrepancies in the scores of the sub-indicators.