Measures of industry concentration are measures used to determine the distribution of the market shares of specific firms. These measures can be most basically divided into those that account for all companies on the market, and into those which consider only few (Ginevicius and Cirba, 2007). Their overview is presented in Table 6.1.
Table 6.1: Market concentration measures
Measure Functional form
Concentration Ratio CRm = �mi=1si
Hirschman-Herfindahl Index HHI=�ni=1si2
Horwath Index HI= s1+�ni=2si2(2− si)
Entropy Index EI=-�ni=1silnsi
Exponential Concentration Index ECI=Πni=1ssi
i
Rosenbluth Index RI=1/[(2�ni=1isi)− 1]
GIN Index GI=�ns=1si/[1 + n(1− si)] m - number of largest firms, i - index of i-th largest firm, si- market share of firm i, n
- total number of firms,
Among measures which capture only part of the distribution of market shares we can find the concentration ratios (CRs), which indicate the share of industry market sales of, most commonly, 4 (CR4) or 8 (CR8) largest firms. The ratios fall in the range (0%, 100%], where 100% means the given number of largest companies are the only suppliers on the market. This of course indicates the biggest drawback of concentration ratios, namely
that they are not applicable if the number of companies is smaller than n, and that they are informative as far as the competition within the top n firms is concerned.
The other measures summarized in Table 6.1 are functions of market shares of all the companies within certain industries. This is preferential in comparison to the CRs, but as can be seen the weights attached to particular sizes of firms significantly vary and affect the value of the indices. One of the most frequently used alternative measures is the Hirschman-Herfindahl Index (HHI). The square of the companies’ shares results in grater weights given to larger firms. Thus, it can capture not only the dispersion related to the number of firms, but also the inequality of their market shares. HHI makes it possible to distinguish between three companies claiming 50%, 25% and 25% of the total sales, and three companies which all have equal market shares (∼33%). In the first case the larger company (50% share) receives a higher weight than the other two, thus the value of the index increases relatively to the case where the three companies have identical sales. The index takes values in the range (0, 1], where 1 indicates that a company is the only firm in a given industry, a monopolist. The notion that the HHI uses square terms, i.e. weights which are proportional to the market share of a company, has been contested and thus the other measures have been proposed.
The Horwath Index (HI) considers the share of the largest company as it is and for the smaller firms it weighs them proportionally to their size (square term), and additionally applies a weight which inversely proportional to the size (2− si). These operations result
in the fact that, contrary to HHI, HI tends to take values in the middle and top of the value range (0,1]. Why the largest firm has been singled out (rather than e.g. two or three largest firms) seems quite arbitrary, though. As a matter of fact the division into the discrete and cumulative parts is itself controversial (Curry and George, 1983; Ginevicius and Cirba, 2007).
Two alternative measures of industrial concentration which, similarly to the HHI, are more concise in their form are the Entropy Index, and the Exponential Concentration Index. The former relates the concept of (information) uncertainty to market outcomes. It assumes that as competition grows, the probability that a customer will provide business to a given company decreases. A monopoly would have lowest entropy, as the firm is perfectly informed, i.e. able to predict customer’s actual choices, and does not face any uncertainty. The intuition laying behind applying this measure seems quite controversial, however, as it originates in a very different field. Its properties also imply that, as opposed to all the other concentration measures, it decreases as the market structure approaches a monopoly. The ECI has been found quite similar to the HHI (Ginevicius and Cirba, 2007), the only difference being the weight assigned to small and large firms. While the HHI was found by Ginevicius and Cirba more sensitive to large firms, the ECI is more sensitive to small firms. Thus, as the authors claim, in order to estimate the ECI the whole distribution of market shares has to be known, while in order to obtain a decent approximation of HHI knowing the low end of the share distribution is not critical.
The final two measures considered in Table 6.1 are the Rosenbluth Index, and the GIN Index. Due to the product of if the i-th firm’s share and i itself in the denominator of the former, it gives different weights to companies which have identical shares. This, even intuitively, seems like a disadvantageous property. The latter measure captures both the number of firms (n), and the relative size of every firm (si) in evaluating their relative
sizes (used in the summation). As Ginevicius and Cirba (2009) claim in a later text of theirs, it underreports competition in case of e.g. a market comprising two companies, one of which has 90% of the market shares, and the other one 10%. The value of the GIN index is then 0.786 - much smaller than an expected 0.9. The HHI in this case would give the value of 0.82.
What stems from the above discussion is a conclusion, that neither measure of indus- trial concentration can be considered to perform best based on objective criteria. The discourse does not provide a recommendation for which index to use. While some of them are more suitable for very dispersed markets, others better capture competition among few large firms. Given the incomplete coverage of the concentration ratios we have rejected their applicability in the first place. The debatable features of other measures be it their theoretical grounding (in case of the Entropy Index), a large degree of arbitrariness in choosing the functional form (Horwath Index, Rosenbluth Index), or strong assumptions concerning complete market information (Exponential Concentration Index) have discour- aged us from employing them in this study. Out of the reviewed measure only the HHI and the GIN Index have been eventually considered. Since they perform in a relatively similar manner, both nevertheless facing some drawbacks, following Ockham’s Razor, HHI as the simpler (and more commonly used) one has been eventually applied.
Bearing in mind the disadvantages resulting from the functional form of the HHI, another debatable aspect of this (and any other concentration measure) should be noted, namely the attribute of a company which is to be used to compute its market share. Carlton and Perloff (2005) consider the value of sales as a default. Ginevicius and Cirba (2007) refer to “attributes” in general, without providing tests of the sensitivity of reviewed measures with respect to different characteristics. Curry and George (1983) mention that among the proxies for a firm’s size we could consider value-added, sales, employment or assets. The choice for this study was limited by data availability. As it will be described in the data section, one’s self-employment, pre-tax income has been used as the company performance measure.