Index-Building in a System of Interdependent Variables: The Penalty for Bottleneck

Abstract

While the importance and the popularity of indices able to capture complex categories and the multidimensional nature of a particular phenomenon have been increasing, most approaches are still not able to provide plausible policy recommendations. The Penalty for Bottleneck (PFB) methodology is based on the assumption that the performance of the system depends on the weakest link, i.e., the variable that has the lowest value. This approach deviates from the most frequently applied method of calculating the arithmetic averages of the variables, which explicitly assumes perfect substitutability and, hence, provides potentially false policy implications. The resulting PFB-based policy recommendation is clear: the bottleneck should be improved first because it has a magnifying effect on the other indicators in the system. The PFB methodology is applied to the Heritage Foundation Index of Economic Freedom data. We show how the original methodology and the PFB methodology differ from each other by using a conservative logarithmic penalty function.