Sample-Size Independent Measures of Concentration

Thomas M. Menino Convention & Exhibition Center 

A widely used index of market concentration is the Herfindahl-Hirschman index (HHI) for firms in an industry. Defined as the sum of the proportion of scale (i.e. outputs, inputs) in the industry for firm. As the value of HHI increases, the level of concentration increases.
This index has spawned a large and growing number of investigations in the literature. In addition to comparisons of industrial concentration, it has been used to measure the competitive balance of sporting leagues, the performance of university departments, the variations in language translations, among other applications.
To make comparisons of the value of HHI between groups (industries, sporting leagues, locations), it is necessary to construct HHIs that are based on a comparable number of individuals. Unfortunately, the direct comparisons of HHI for one group will be contaminated by differences in the sample size of each group. In this paper we examine a number of alternative methods for weighting the HHI to account for differences in sample size. Then we survey the recent applications where these transformations may influence the inferences drawn in these contributions.

Herfindahl Hirschman Index

Sample moments

Measure of sporting league competition

Measure of industrial concentration 

Business and Economic Statistics Section