Some dominance indices to determine market concentration

Abstract

This study intends to provide a new insight into the concentration and dominance indices as the concerns grow about the increasing concentration in the markets around the world. Most of the studies attempting to measure concentration or dominance in a market employ the popular concentration/dominance indices like Herfindahl–Hirschmann, Hannah–Kay, Rosenbluth–Hall–Tidemann and Concentration ratio. On the other hand, measures of qualitative variation are closely related to entropy, diversity and concentration/dominance measures. In this study, two normalized dominance measures that can be derived from the work of Wilcox on qualitative variation are proposed. The limiting distributions of these normalized dominance measures are formulated. By some simulations, asymptotic behaviors of these indices are analyzed under some assumptions about the market structure. In the end, by an application on the Turkish car sales in 2019, it is determined that the values of dominance indices vary in a considerably large range. Thus one of the dominance indices is determined to have the advantage of having less error in estimation, less sensitivity to smaller market shares, and less sampling variability.

Keywords:

• Herfindahl–Hirschman index
• tsallis entropy
• Shannon entropy
• dominance indices based on entropy
• dominance indices based on qualitative variation

Acknowledgments

This study is supported by TUBITAK 2211 national scholarship programme for graduate students.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Scientific and Technological Research Council of Turkey [ 2211 national scholarship programme for graduates].