Stochastic Ranking and the Volatility "Croissant": A Sensitivity Analysis of Economic Rankings

Rankings of countries are calculated using I indicator variables. Clearly, any ranking based on an index depends on the weights used, and therefore we conduct a sensitivity analysis on the weights of the index to obtain a measure for the volatility of the performance rankings. The weights are simulated from uniform and beta distributions on the simplex. As a result we observe a volatility "croissant": Countries in the top and the bottom of the ranking are less volatile than in the middle of the ranking. The methodology is shown for the standardized performance ranking (SPR) and the rank performance ranking (RPR).