Some patterns of market shares of brands 
within and across product categories

Rajeev Kohli and Raaj Sah

University of Chicago, Harris School of Public Policy. Working paper series 06.04. December 2005.

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ABSTRACT

This paper: (i) reports an empirical regularity in the market shares of brands; (ii) presents a theoretical framework for understanding the observed regularity; (iii) adduces additional empirical consequences of the framework, which are some counterintuitive relationships among market shares of brands across different product categories; and (iv) presents empirical evidence for these consequences, thus providing additional support for the theoretical framework. Our cross-sectional data on market shares consists of 1171 brands in 91 product categories of foods and sporting goods sold in the US. The key empirical regularity is that, in each category, the decrease in the market share between two successively ranked brands becomes smaller as one progresses from higher-ranked to lower-ranked brands. The power law represents these patterns well, in an absolute sense, and better than an alternative model, namely, the exponential form, which has been studied in the literature but without having been compared to any alternative. The latter form predicts that the ratio of the market shares of any two successively ranked brands is a constant. We present some potential implications of our findings. We also offer an interpretation of the previously known square-root relationship between market share and the order of entry of firms into an industry. The theoretical framework that we present for understanding the patterns reported here shares its foundation with that of the familiar Dirichlet-multinomial paradigm of brand purchases. This framework has some intuitive interpretations; it accommodates multiple product categories; and it allows for the entry and exit of brands over time.


Published version:

Kohli, Rajeev and Raaj Sah. “Some empirical regularities in market shares.” Management Science, Volume 52, Number 11, November 2006, pages 1792-1798.
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