Correlation and Concordance between the CR4 Index and the Herfindahl-Hirschman Index

The Herfindahl-Hirschman Index (HHI) and the Four-firm concentration ratio (CR4) are the leading indicators for market concentration. In order to examine if the latter can be taken as a proxy for the former, we perform a correlation analysis employing the Pearson, Spearman, and Kendall correlation coefficient, and introduce a new metric, the probability of order preservation, that measures how often the two indicators move in the same direction, thereby showing both an increase or a decrease in market concentration. We employ a group of 24 datasets pertaining to a wide selection of industries and geographical areas. We find that, though the correlation indices may be quite high, the two indicators lead to opposite conclusions in as many as 41% of the cases, so that the CR4 cannot be deemed a valid replacement for the HHI.

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