Static versus dynamic measures of aggregate concentration: the case of Fortune's 500.

• Author: Deutsch, Joseph

1. Introduction

   Studies of business concentration have usually made a distinction between market concentration which "is concerned with the dominance of individual markets by the leading firms therein" [4, 182] and aggregate concentration which looks "at the degree of control exercised over a large portion of some aggregate of economic activity (assets, sales, value added) by a small absolute or relative number of firms" [17, 239]. Various indexes, such as the Concentration ratio, the Hirschman-Herfindahl, the Rosenbluth, the Hannah and Key, or the Entropy Index, have been proposed to measure such a concentration [17, 22], but the general idea has always been that a higher degree of concentration of output or sales implies a greater extent of monopoly power in a given market or industry.

   Some authors have, however, questioned the choice of such concentration indices, in particular those looking at the relative size of leading firms, as measures of market control. Demsetz [7, 3] has, for example, criticized the public policy implications which are too often derived from analyses of market structure. "If rivals seek better ways to satisfy buyers or to produce a product, and if one or a few succeed in such endeavors, then the reward for their entrepreneurial efforts is likely to be some short term monopoly power and this may be associated with increased industrial concentration. To destroy such power when it arises, may very well remove the incentive for progress. This is to be contrasted with a situation in which a high rate of return is obtained through a successful collusion to restrict output; here there is less danger to progress if the collusive agreement is penalized."

   In fact, as argued by Gott [14, 51], a high degree of concentration "may be consistent with considerable instability in the market shares of individual firms. In judging the intensity of competition in an industry, the ability of leading firms to maintain their relative position in a market, is probably more significant than the extent of concentration at a single point in time." This is why Simon and Bonini I32, 616] suggested that "a measure of mobility for firms would appear to provide a better index of what we mean by 'equality of opportunity' than do the usual measures of concentration." Such a point of view was also shared by Joskow [19, 113] when he stated "that the appearance of structural stability given by the familiar concentration measures masks a significant degree of fluidity." He proposed, therefore, to measure shifts in the relative position of firms within an industry. Such an analysis would "give weight to the obvious economic fact that changes in the identity of the firms comprising the so-called top 4, 8, 12, etc. sellers is an indicator of the workability of competition" [19, 113]. But even when a significant degree of rank change is observed, it may correspond to different situations, as Hymer and Pashigian [18, 82] have shown: "An industry with rather wild fluctuations, such that leading firms in one year drop to negligible 'size' the next year or disappear (and then perhaps return) is no industry or market at all: it has been too narrowly defined. . . . Second . . . incessant back-and-forth changes in market share and position might indicate that it was impossible to form any stable collusive understanding or agreement. . . . Third an industry might show a gradual shift in one direction or another rather than year-to-year reversals. . . . "This is why Hymer and Pashigian [18] suggested measuring changes in market shares rather than in firms ranks. But the connection between market structure and the stability of shares is also complex. "For instance, as seller concentration rises from 'moderate' to 'high', the effectiveness of collusion and hence the stability of shares should rise. However it should also rise as concentration falls from 'moderate' to 'low' so that firms' behavior approaches that under pure competition and there are no mutual understandings to be violated [3, 292]." In fact, Heggestad and Rhoades [15] think that mobility and turnover of market shares should not be considered as elements of industry structure; they rather "reflect conduct that theory would predict to arise from certain market structures [15, 444]." In their study of commercial banking in the U.S. they have shown that the lower the level of concentration in the market, the greater the mobility of dominant banks.

   It seems thus necessary to look at the concentration as well as at the stability of market shares. If high stability is associated with increasing concentration, there may be "a more serious problem from the standpoint of maintaining competition [14, 54]." Quantitative studies in the field of industrial organization attempting to measure the extent of monopoly power in a given market or industry should then be based on measures of concentration as well as of market shares instability.

   The contribution of the present paper is, precisely, to suggest an overall measure of distributional change which may be decomposed into a first component which reflects the change in concentration and a second one which measures changes in the ranking of firms. Such an approach provides, therefore, a simple link between static analyses of concentration and dynamic studies of the turnover of firms.

   The paper is organized as follows. The next section reviews the existing indices of business concentration and turnover of firms. Section III defines new indices of distributional change which are derived from the Gini Concentration Ratio and take into account both the changes in concentration and the degree of stability of market shares. Sections IV and V present an application of these indices to data on sales and assets of the 500 largest U.S. industrial firms reported by the magazine Fortune during the period 1976-1990. The empirical dynamic analysis (section V) reveals a significant level of permutations in the ranking of the firms, and no significant increase in concentration among the firms over time, whereas the static analysis of section IV would have led us to conclude that concentration increased over time. To test the robustness of these results we have used bootstrapping techniques. A summary of the main findings is presented in section VI.

2. Measuring Concentration and Turnover: The Existing Indices

   Assume that the level of economic activity in an industry is measured by the value of total assets (or sales). Let then [s.sub.i] be the share of firm i in the total assets (or sales) of the industry. The most popular measures of industry concentration are the Concentration ratio,(1) [C.sub.m], the Hirschman-Herfindahl Index H and the Entropy (or Theil) Index E, where [C.sub.m], H and E are respectively defined as

   [C.sub.m] = [summation of] [s.sub.i] where i=1 to m (1)

   [Mathematical Expression Omitted]

   E = [summation of] [s.sub.i] ln(1/[s.sub.i]) where i=1 to n. (3)

   Another possible measure of concentration, though less often used in the industrial organization literature, is Gini's Concentration Ratio [I.sub.G] which was originally proposed by Gini [13; 21] and is defined as

   [Mathematical Expression Omitted]

   where [A.sub.h] represents the sales (or assets) of firm h and [Mathematical Expression Omitted] is the arithmetic mean of [A.sub.h].

   Given that [Mathematical Expression Omitted], expression (4) may also be written as

   [Mathematical Expression Omitted]

   Note that (m/n) [less than or equal to] [C.sub.m] [less than or equal to] 1; 0 [less than or equal to] H [less than or equal to] 1; 0 [less than or equal to] E [less than or equal to] ln n; 0 [less than or equal to] [I.sub.G] [less than or equal to] 1.

   Since the upper bound of the entropy or Theil Index E is equal to ln n, it is also possible to define a standardized Theil Index (T) [33] as the ratio of the actual entropy over the maximum possible entropy for the number of outcomes considered. In other words

   T = - ([summation of] [s.sub.i] ln [s.sub.i]) where i=1 to n) / ln n (6)

   with 0 [[less than or equal to] T [less than or equal to] 1.

   The Entropy Index E has often been used because it can be decomposed into a "between sets" and a "within sets" component. Nissan and Caveny [22], for example, following an earlier study by Hexter and Snow [17], divided the data on the assets of the 500 largest industrial firms in the period 1955-1966 into five sets of 100 firms. In such a case the "between sets entropy", ignores the differences in assets size which might exist within each of these five sets while the "within sets entropy" is a weighted average of the entropies of each of the five sets so that it takes into account differences in the size of firms' assets within each of the five sets, ignoring between sets differences.

   Various measures have also been proposed to measure the turnover of firms. The simplest index is probably...