Industrial concentration, influencing as it does the competitive nature of private enterprise, has been of interest as long as the market economy itself. The normal interest has been stimulated from time to time by ascendance of various theories of history predicting that economies based on private enterprise must contain an inherent drift toward
increasing economic concentration. Marx, for example, saw not only universal monopoly but also extreme concentration of wealth and income as ultimate and inevitable results of capitalism. Similar theses have come forth from non-Marxist sources, particularly during the 1930s, when some observers discerned a steady “decline of competition” woven into the fabric of history and blamed it for many of the ills of the great depression.
The issue of economic concentration as it has emerged is essentially twofold in nature. On the one side, there is the question of industrial concentration, of the degree to which a few firms dominate the output of industries taken individually. On the other side, there is the question of inequality of wealth and income in the economy as a whole. [SeeIncome Distribution, article onsize; National Wealth, article onDistribution.] We shall be concerned here only with concentration in the first sense.
Concentration indexes. The pattern of concentration in an industry is usually shown by a concentration curve, each point of which represents the concentration ratio (the percentage of total output, employment, or similar size variable) associated with the corresponding number of firms arrayed from largest to smallest, the firms being plotted on the horizontal axis (see Figure 1). By construction the curve will rise to the right at a nonincreasing rate and generally at a decreasing rate throughout. That is, it will generally be convex upward. The more unequal the firm sizes are over any range, the more convex the curve will be. Hence the shape of a particular curve is defined by two parameters—the degree of inequality in firm size and the number of firms.
Although it is not normal practice to do so, the
concentration curve could equally well be plotted against the number of firms arrayed from smallest to largest, in which case the curve would generally rise at an increasing rate (see Figure 2). Constructed in this way, the concentration curve is easily transformed into the well-known Lorenz curve by substituting relative for absolute numbers of firms on the horizontal axis—that is, by dividing the horizontal scale by the total number of firms (see Figure 3).
If the observed size distribution of firms in an industry fits well into a standard statistical distribution, a Lorenz curve is directly derived as the relation between the cumulative distribution function and first-moment distribution function of that cumulative distribution function. In such a case, the concentration curve can be reproduced if the parameters of the distribution function are known along with the total number of firms. Observed density distributions of firm size are almost always unimodal and skewed upward: firms are clustered about a relatively limited range of sizes with a longer taper toward the larger sizes than toward the smaller ones. It is reasonable to suppose that this characteristic shape results at least in part from a stochastic growth process, and some economists have therefore tried, with varying degrees of success, to approximate observed size distributions by lognormal, Yule, Pareto, and similar distributions that can be generated by stochastic processes (Hart & Prais 1956; Hymer & Pashigian 1962; Mansfield 1962; Quandt 1966; Shepherd 1964, pp. 208-209; Simon & Bonini 1958). Even if good fits could always be obtained, it would be prohibitively expensive, in terms of both collecting and processing data, to analyze an economy of any size in this way. Moreover, a collection of curves would mean little without some theoretical framework for interpreting them. Unfortunately, no systematic theory of industrial structure has yet emerged from studies of this type to command broad agreement among professional economists. In the absence of such a theory, measures of industrial concentration are generally confined to descriptive indexes not amenable to formal statistical analysis. A standard comprehensive measure of this nature is the Herfindahl index—the summed squares of firm sizes, with the sizes expressed as proportions of the total industry size. In mathematical language,
where N is the number of firms, S is the total size of the industry (the summed sizes of the firms), Si is the size of firm i, and ś is the mean size of firm (S/N). In other words, the Herfindahl index is the squared coefficient of variation plus one, the sum divided by the number of firms. If all firms are of equal size (Σ-2 — 0), the index is the reciprocal of the number of firms, reaching its maximum value of unity under monopoly. For any given number of firms greater than one, the index increases with the coefficient of variation. Since it is generally impractical to compile all the data needed for the comprehensive Herfindahl index, a partial index is normally computed from data for some fraction of the leading firms.
Restrictions on disclosure of information about individual firms, a normal condition for most statistics collected and published by Western governments, also place limits on the kinds of indexes of concentration that can be computed. The practice followed in official sources in the United States is not to reveal data for fewer than four firms at a time. In Canada and the United Kingdom, the minimum number is three. Points on concentration curves based on officially published statistics are therefore defined at best for only every third or fourth firm. Researchers may, of course, be given access to more detailed data, but any published results must conform to standard disclosure rules.
For the various reasons discussed, it has become common practice to describe industrial concentration with a few simple indexes that summarize the concentration curve only in part. These include concentration ratios for specified numbers of firms in multiples of three or four, areas under portions of the concentration curve, partial Herfindahl indexes, and occupancy counts. The last is the inverse of a concentration ratio, giving the number of leading firms required to account for a specified concentration ratio. For example, the 80 per cent occupancy count is the number of firms, arrayed from largest to smallest, that together make up 80 per cent of the size of the industry. In studies of U.S. and Canadian manufacturing industries, it has been found that the various partial measures all yield about the same rank order of industries in terms of concentration (Universities-National Bureau Committee for Economic Research 1955, pp. 64-69).
Concentration and monopoly. Given the current state of economic theory and leaving aside problems of identifying industries, one should not expect any simple correlation between pricing behavior and degree of concentration as reflected by the described indexes, except in extreme cases. Perhaps the most that can be said is that the higher the concentration, the more likely an industry will behave monopolistically, and the lower the concentration, the more likely it will behave competitively.
There are difficulties even with this broad conclusion, depending on the index being used to measure concentration. For example, suppose two industries show the same high concentration ratio for the four leading firms but industry B has twice as many firms as industry A. The Herfindahl index may not be smaller for B than for A, since differences in inequality of firm size may counterbalance differences in number of firms. Put the other way around, even though two industries have the same Herfindahl index, the numbers of firms, partial concentration ratios, and inequalities of firm size may differ in many possible ways.
The meaning and significance of concentration indexes are affected by practical as well as conceptual problems. Foremost is the difficulty of identifying industries so that they will be relevant for economic analysis and consistent with available data. In the first place, systematic and comprehensive statistics on industrial structure are limited primarily to the areas of manufacturing, mining, and public utilities. Most studies of concentration therefore deal only with these areas and, in fact, almost exclusively with manufacturing.
In the second place, the systems of industrial classification used in basic statistical sources, especially in census-type materials, are not designed primarily for analysis of pricing behavior. Establishments and products are grouped together mainly on the basis of technological, not economic, characteristics. Moreover, the accuracy of data aside, special technical difficulties in analyzing data may arise because of the way in which data are classified into industrial categories. For example, an industry may be defined on an establishment or on a product basis, or on the first basis for some purposes and the second for others. If defined on an establishment basis, value of output and similar data represent the total for all commodities produced by establishments assigned to the industry, assignment being based on the commodity of principal value in the establishment in question. If defined on a product basis, value of output represents the value of those commodities assigned to the industry, no matter where producing establishments are assigned. For analysis of industrial concentration, statistics should generally be compiled on a product basis, but this is not always possible. A final problem exists in matching firms with industries, a procedure that normally requires access to unpublished data.
In the third place, the scope of industrial categories usually affects the height of concentration indexes. The more narrowly industries are defined, the higher concentration indexes are likely to be. Concentration indexes should not, therefore, be interpreted without regard to the general scope of industrial categories. Although elaborate industrial classification systems have been evolved in many Western countries, a given level of classification (for example, the four-digit level) need not mean a comparable scope for all included categories. Indeed, it is not at all clear what is meant by a “comparable scope,” even though the desirability of some such standardization is apparent.
In the fourth place, statistics are usually compiled on a national basis, whereas relevant market areas are sometimes smaller or larger, differing from one industry to another [see Markets and industries]. Concentration indexes computed on a national basis may or may not be meaningful from the point of view of pricing policy, depending on the circumstances for particular industries.
For all these reasons, one must take care in attributing specific degrees of monopoly, whatever that might mean, to specific concentration indexes. At the same time, both very low and very high indexes, applied to relevantly defined industries, convey useful information on likely pricing behavior. Similarly, significant differences in levels of concentration for the same industries over time or among countries at the same time provide important evidence on likely differences in pricing behavior.
Comparative levels of concentration. A number of important studies of industrial concentration have been conducted over the last three decades, covering the United States, the United Kingdom, Canada, and Japan; less extensive studies have been made for Sweden, France, Italy, and India (see bibliography and Bain 1966, pp. 183-200). These studies have focused primarily on manufacturing, measuring and analyzing concentration in a variety of ways. The findings cannot be adequately summarized here, but a few broad generalizations can be drawn from them.
In recent years, between 14 and 18 per cent of national income in the United States has originated in highly concentrated industries, high concentration being defined in general by a four-firm concentration ratio of 50 per cent or more for industries at the four-digit level of classification (Einhorn 1964, p. 13). In manufacturing alone, the fraction of income originating in highly concentrated industries is 32 to 35 per cent (ibid., p. 26). For roughly the same years and for the sector of manufacturing alone, a greater extent of concentration is clearly shown by the evidence for Canada (Rosenbluth 1957, pp. 75-93), less clearly by the evidence for the United Kingdom (Universities-National Bureau Committee for Economic Research 1955, pp. 70-77; Shepherd 1961). In the case of Japan, the degree of concentration is now generally higher than in the United States for manufacturing industries that can be matched with U.S. counterparts, but the extent of concentration is roughly the same as in the United States in both manufacturing and the economy as a whole (Rotwein 1964, pp. 275-276).
In studies of manufacturing, concentration has been found to be inversely related to size of industry: larger industries generally have smaller concentration indexes and vice versa. This relation being taken into account, concentration also shows a significant direct relation to average firm size but no significant relation one way or the other to inequality of firm size within an industry.
Trends in concentration. Although there has been considerable interest in the question of industrial concentration for many years, systematic evidence on trends in concentration has been collected and analyzed only over relatively recent years. So far, it has been possible to study long trends only in the case of the United States. Changes in concentration in British manufacturing between 1935 and 1951, a short period for most purposes, have also been examined with inconclusive results.
The safest conclusion to draw from the studies of the United States is that there has been no pronounced trend in concentration either way. When due allowance is made for all the infirmities and incomparabilities of the measurements, there appears to be a rough stability in the fraction of national income originating in highly concentrated industries throughout the economy over the period from 1899 to 1958 (Nutter 1951; Einhorn 1964; Shepherd 1964). The same conclusion holds for the manufacturing sector taken alone.
Beneath the stability lies a rapid turnover, displacement, and replacement of industries. While some industries are becoming more highly concentrated, others are becoming less highly concentrated in roughly equal measure. Stability results because young and rapidly growing industries tend to become less and less concentrated while old and slowly growing (or declining) industries tend to become more and more concentrated. Why the two forces have managed to come so close to balancing themselves is another of the many unexplained mysteries of history.
Causes of concentration. Evidence collected so far would seem to assign an important role to technological factors, determined within the existing regime of patents and similar constraints, as causes of industrial concentration. For instance, comparison of U.S. and Canadian manufacturing shows a similar ranking of industries by both degree of concentration and number of firms, indicating similar technological conditions. But Canadian industries are generally more concentrated than their U.S. counterparts, despite the fact that they are characterized by less inequality in firm size. The greater concentration, therefore, seems attributable in general to a smaller number of firms in each industry, the result of smaller markets under the given technological conditions (Rosenbluth 1957, pp. 75-93).
The dominant role of technology is further shown by the normally high negative correlation within a country between concentration and size of industry, and the normally low correlation between concentration and inequality of firm size. Moreover, when concentration in an industry is high (or low) in terms of firms, it is ordinarily also high (or low) in terms of plants.
Other factors are no doubt important in explaining industrial concentration, but they have not been clearly isolated by statistical analysis. Some suggested causal factors have been rejected: the durability of commodities and the nature of purchasers (whether businesses or households) do not have a systematic relation to degree of concentration in an industry. While it seems reasonable to suppose that legal constraints such as antitrust laws have an important effect on concentration and its trend, we do not yet have quantitative estimates of that importance.
G. warren Nutter
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