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Why some industries come to be dominated worldwide by a handful of ﬁrms, even at the level of the global market, is a question that has attracted continuing interest among economists over the past 50 years—not least because it leads us to some of the most intriguing statistical regularities in the economics literature. Uncovering the forces that drive these regularities provides us with some deep insights into the workings of market mechanisms.
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The literature in this area has developed rapidly since 1980. Indeed, a fairly sharp break occurred at the end of the 1970s, with a new generation of models based on game-theoretic methods. These new models oﬀered an alternative approach to the analysis of cross-industry diﬀerences in structure and proﬁtability. Before turning to these models, it is useful to begin by looking at the earlier literature.
1. Preliminaries: Deﬁnitions and Measurement
The structure of an industry is usually described by a simple ‘k-ﬁrm concentration ratio,’ that is the combined share of industry sales revenue enjoyed by the largest k ﬁrms in the industry. Oﬃcial statistics usually report concentration ratios for several values of k, the case of k 4 being the most commonly used. (From a theoretical point of view, the case k 1 is most natural, but is rarely reported for reasons of conﬁdentiality.) A richer description of structure can be provided by reporting both these ratios and the total number of ﬁrms in the industry. If ratios are available for many values of k, we can build up a picture of the size distribution of ﬁrms, which is usually depicted in the form of a Lorenz curve. Here, ﬁrms are ranked in decreasing order of size and the curve shows for each fraction k n of the n ﬁrms in the industry, the combined market share of the largest k ﬁrms. (It is more natural in this ﬁeld to cumulate from the largest unit downwards, rather than from the smallest upwards, as is conventional elsewhere.) Certain summary measures of the size distribution are sometimes used, that of Herﬁndahl and Hirshman being the most popular (see Hirshman 1964): this is deﬁned as the sum of the squares of ﬁrms’ market shares, and its value ranges from 0 to 1. While most measures of market structure are based upon ﬁrms’ sales revenue, other measures of ﬁrm size are occasionally used, the most common choice being the level of employment.
2. The Cross-section Tradition
The beginnings of the cross-section tradition in the ﬁeld of industrial organization (IO) are associated with the pioneering work of Joe S. Bain in the 1950s and 1960s (see in particular Bain 1956 and 1966). Bain’s work rested on two ideas.
(a) If the structure of the industry is characterized by a high level of concentration, then ﬁrms’ behaviour will be conducive to a more muted degree of competition, leading to high prices and high proﬁts (or ‘performance’). This structure–conduct–performance paradigm posited a direction of causation that ran from concentration to proﬁtability. It therefore raised the question: will the high proﬁts not attract new entry, thereby eroding the high degree of concentration? This leads to Bain’s second idea.
(b) Bain attributed the appearance of high levels of concentration to certain ‘barriers to entry,’ the ﬁrst of which is the presence of scale economies in production (i.e., a falling average-cost curve). In his pioneering book Barriers to New Competition (1956), Bain reported measures of the degree of scale economies across a range of US manufacturing industries, and went on to demonstrate a clear correlation between scale economies and concentration. This correlation notwithstanding, it was clear that certain industries that did not exhibit substantial scale economies were nonetheless highly concentrated, and this led Bain and his successors to posit additional barriers to entry which included, among others, the industry’s advertising sales ratio and its R and D sales ratio. This raises a serious analytical issue however: while the degree of scale economies can be thought of as exogenously given as far as ﬁrms are concerned, the levels of advertising and R and D expenditure are the outcomes of choices made by the ﬁrms themselves, and so it is natural to think of these levels as being determined jointly with concentration and proﬁtability as part of the same equilibrium outcome (Phillips 1971, Dasgupta and Stiglitz 1980). This remark provides the key link from the Bain tradition to the modern game-theoretic literature.
2.1 The Modern (Game-theoretic) Literature
A new literature which has developed since 1980 takes a rather diﬀerent approach to that of the Bain paradigm. First, instead of treating the levels of advertising and R and D as ‘barriers to entry’ facing new ﬁrms, these emerge as the outcome of ﬁrms individual choices. The models are characterized by ‘free entry,’ but ﬁrms that fail to invest as much as rivals on such ‘sunk costs’ suﬀer a penalty in terms of their future proﬁt ﬂows. The second diﬀerence from the Bain approach is that the troublesome question of a possible ‘feedback’ from high proﬁts to subsequent entry is ﬁnessed. This is accomplished by formulating the analysis in terms of a simple (game-theoretic) model in which all ﬁrms entering the industry anticipate the consequences of their investments on future proﬁt streams.
The multistage game framework is shown in Fig. 1. Over stages 1 to T, ﬁrms make various investment decisions (construct a plant, build a brand, spend on R and D). By the end of this process, each ﬁrm’s ‘capability’ is determined by the investments it has made. In the ﬁnal stage subgame (T 1), ﬁrms compete in price, their capabilities being taken as given.
The central problem that underlies this kind of analysis is that there are many reasonable ways of formulating the entry and investment process that takes place in stages 1 to T, just as there are many ways of characterizing the nature of price competition that occurs at stage T 1. Many equally reasonable models could be written down, between which we could not hope to discriminate by reference to the kind of empirical evidence that is normally available. (Such problems are commonplace in the game-theoretic IO literature; see Fisher (1989) and Pelzman (1991) for a critique.)
For this reason, it is useful to begin, not from a single fully speciﬁed model, but rather from a ‘class of models,’ deﬁned by a few simple properties (Sutton 1998). The key innovation here lies in moving away from the idea of identifying a fully speciﬁed model within which each ﬁrm is assigned a ‘set of strategies’ (and where our aim is to identify the combination(s) of strategies that form a (perfect Nash) equilibrium). Instead, an equilibrium concept is deﬁned directly on the set of outcomes that emerge from the investment process that occurs over periods 1 to T. An outcome is described by a list of the ﬁrms’ capabilities, from which we can deduce the pattern of market shares that will emerge in the ﬁnal stage (price competition) subgame. What we aim to do it to place some restrictions on these outcomes, and so on the form of market structure. The restrictions of interest emerge from certain simple and robust properties that must hold good, independently of the detailed design of the entry and investment process. The only assumption imposed on this process is that each ﬁrm (‘potential entrant’) is assigned some ‘date of birth’ t between 1 and T, and each ﬁrm is permitted to make any (irreversible) investments it chooses either at stage t or at any subsequent stage t+1, t+2, …, T. Given the investments made by the ﬁrms (which can be represented formally by a set of points in some abstract ‘set of products’ that the ﬁrm is now capable of producing), we deﬁne a proﬁt function that summarizes the outcome of the ﬁnal stage (price competition) subgame. This speciﬁes the (‘gross’) proﬁt earned by the ﬁrm in that ﬁnal stage, as a function of the set of all ﬁrms’ capabilities. Finally, it is assumed that there are many potential entrants (in the sense that if all ﬁrms made the minimum investment required to enter the industry, then it could not be the case that all ﬁrms would earn suﬃcient proﬁts to recover their outlays). Within the (complete information) setting just described, the set of equilibrium outcomes (formally, the pure strategy perfect Nash equilibrium outcomes) will satisfy two elementary properties:
(a) ‘Viability’: The proﬁt earned by each ﬁrm in the ﬁnal stage subgame suﬃces to cover the investment costs it incurs.
Restriction (a), together with the assumption of ‘many potential entrants,’ ensures that not all ﬁrms will enter the industry. We now focus on any ﬁrm that has not entered:
(b) ‘Stability’: Given the conﬁguration of in- vestments undertaken by all the ﬁrms who have entered, then there is no investment available to a potential entrant, at time T, such that it will earn a ﬁnal stage (‘gross’) proﬁt that exceeds its cost of investment.
Outcomes that satisfy (a) and (b) are known as ‘equilibrium conﬁgurations.’
From these properties, two sets of results follow. The ﬁrst set of results pertains to the special case of industries in which neither advertizing nor R and D play a signiﬁcant role. In analyzing these industries, the only restriction placed on the ﬁnal stage (‘price competition’) subgame is that a rise in ﬁrm numbers or a fall in concentration, holding market size constant, reduces the level of prices and the gross proﬁt earned by each ﬁrm. (On this assumption, see Sect. 5 below.) The ﬁrst result relates to the way in which the level of concentration is aﬀected by the size of the market: as we increase the size of the market (by successive replications of the population of consumers) then the minimum level of concentration that can be supported as an equilibrium conﬁguration falls to zero (‘convergence’). It is important that increases in market size do not necessarily imply convergence to a fragmented market structure: this result speciﬁes only a lower bound to concentration. There will in general be many equilibrium conﬁgurations in which concentration lies above this bound.
The second result relates to the way in which, for a market of any given size, this lower bound to concentration is aﬀected by the nature of price competition. Here, the key concept is that of the ‘toughness of price competition,’ which relates to the functional relationship between market structure (number of ﬁrms, or level of concentration) and the level of prices or price-cost margins, in the industry. For the sake of illustration, suppose changes in competition law make it more diﬃcult for ﬁrms to operate a cartel, or suppose an improvement in transport networks brings into close competition a number of ﬁrms that hitherto enjoyed ‘local monopolies.’ In such cirumstances, we have an increase in the toughness of price competition in the present sense, that is for any given market structure, prices and price-cost margins are now lower. The second result states that an increase in the toughness of price competition leads to an upward shift in the lower bound to concentration (leaving unchanged its asymptotic value of zero; see Fig. 2). This result follows from the viability condition alone: the lower bound is deﬁned by the requirement that the viability condition is just satisﬁed. A rise in the toughness of price competition lowers ﬁnal stage proﬁt, at a given level of concentration. Restoring viability requires an oﬀsetting rise in concentration.
The available empirical evidence oﬀers clear support for this prediction; see Sutton (1991) and Symeonides (2000).
This simple but basic result oﬀers an interesting shift of perspective on the old idea that creating a more fragmented industry structure might oﬀer a way of generating more intense competition, and so lower prices. What it suggests, rather, is that once we treat entry decisions as endogenous then—at least in the long run—the level of concentration and the equilibrium level of prices are jointly determined by the competition policy regime: introducing tough anti-cartel laws, for example, implies inter alia a higher equilibrium level of concentration.
2.2 The Escalation Eﬀect
The second set of results relates to the diﬀerence between the industries just considered, where advertising and R and D spending are ‘low,’ and those where advertising and R and D play a signiﬁcant role. Here, we need to specify how the outlays incurred on advertising and R and D in the earlier stages of the game aﬀect the (‘gross’) proﬁt earned by the ﬁrm in the ﬁnal stage subgame. The key idea runs as follows: denote by F the ﬁxed and sunk cost incurred by the ﬁrm, and by Sπ the proﬁt it earns in the ﬁnal stage subgame. Here, S denotes market size and π is a function of the vector of products entered and so of the ﬁxed costs incurred by all ﬁrms in earlier stages. (So long as ﬁrms’ marginal cost schedules are ﬂat—an assumption maintained throughout this research paper— and market size increases by way of a replication of the population of consumers so that the pattern of consumer tastes is unaﬀected, it follows that ﬁnal stage proﬁt increases in direct proportion to market size, justifying our writing it in this form.)
The main theorem is as follows (Shaked and Sutton (1987)).
Suppose that for some constants a 0 and K 1, a ﬁrm that spends K times as much as any rival on ﬁxed outlays will earn a ﬁnal stage payoﬀ no less than aS; then there is a lower bound to concentration (as measured by the maximal market share of the largest ﬁrm), which is independent of the size of the market.
The idea is this: as market size increases, the incentives to escalate spending on ﬁxed outlays rise. Increases in market size will be associated with a rise in ﬁxed outlays by at least some ﬁrms, and this eﬀect will be suﬃciently strong to exclude an indeﬁnite fall in the level of concentration.
The lower bound to concentration depends on the degree to which an escalation of ﬁxed outlays results in proﬁts at the ﬁnal stage and so on the ratio a K. We choose the pair (a, K) which maximizes this ratio and write the maximal value of the ratio as α. The theorem says that the number α constitutes a lower bound to the (one-ﬁrm) sales concentration ratio.
In order to proceed to empirical testing, it is necessary to get around the fact that α is not easy to measure directly. So long as we have a well-deﬁned market of the classical kind (a point elaborated in Sect. 4), it is easy to develop an ancillary theorem that allows us to use the level of advertising and or R and D intensity as a suﬃcient statistic for α. Here, we obtain a simple ‘nonconvergence’ prediction, which says that no matter how large the size of the market S, the level of concentration cannot fall below some value C₁. Figure 3 illustrates the basic result for a welldeﬁned market of the classical kind.
One way of testing this prediction is to look at the same set of advertising-intensive industries across a number of countries of varying size. Since ﬁrms must spend on advertising separately in each country to develop their brand image locally, this oﬀers a valid ‘experiment’ relative to the theory. The nonconvergence property illustrated in Fig. 3 has been conﬁrmed by Sutton (1991), Robinson and Chiang (1996), and Lyons et al. (2000).
Underlying the above discussion is an important simplifying assumption relating to the deﬁnition of the market. It is tacitly assumed here, as in most of the theoretical literature, that we can think of the market as comprising a number of goods that are more or less close substitutes for each other, and that we can regard all other (‘outside’) goods as being poor substitutes for those in this group. This is the classic approach to the problem of market deﬁnition, associated with Robinson (1936): we identify the boundary of the market with a ‘break in the chain of substitutes.’
In practice, this is too simple a picture. The linkages between goods may be quite complex. Apart from the demand side, where goods may be more or less close substitutes, there may also be linkages on the supply side: goods which are independent of each other on the demand side may share some technological characteristics, for example, which imply that a ﬁrm producing both goods may enjoy some economies of scope in its R and D activities.
In order to justify the analysis of a single market in isolation from other markets (‘partial equilibrium’), it is necessary to deﬁne the market broadly enough to encompass all such linkages. Once we have widened the set of products to this point, however, we are likely to ﬁnd that there are certain clusters of products that are much more tightly linked to each other, than to products outside the cluster. In other words, the market encompasses a number of ‘submarkets.’
This complication is of particular importance in the context of R and D-intensive industries. It is often the case in these industries that the market comprises a set of submarkets containing products associated with diﬀerent technologies. The early history of many industries has been marked by competition between rival ‘technological trajectories’. Sometimes, a single ‘dominant’ trajectory emerges (Abernathy and Utterbach 1978). Sometimes, several trajectories meet the preferences of diﬀerent consumer groups, and all survive. In general, the picture of ‘escalation’ along a single R and D trajectory, which corresponds to the analysis of Sect. 3 above, needs to be extended in this more complex setting. Depending upon the interplay of technology (the eﬀectiveness of R and D along each trajectory) and tastes (the pattern of consumer preferences across products associated with each trajectory), the industry may evolve in one or other of two ways. The ﬁrst route involves ‘escalation’ along a single dominant trajectory, in the manner of Sect. 3 above. The second route involves the ‘proliferation’ of successive technological trajectories, with their associated product groups (‘submarkets’). In this setting, the predictions of the theory need to be recast in a way that is sensitive to the presence of such distinct submarkets; see Sutton (1998), Part I.
A central issue of concern in the traditional literature related to the putative link between the level of concentration of an industry, and the average level of proﬁtability enjoyed by the ﬁrms (businesses) in that industry. Here, it is necessary to distinguish two quite diﬀerent questions. The ﬁrst relates to the way in which a fall in concentration, due for example to the entry of additional ﬁrms to the market, aﬀects the level of prices and so of price-cost margins. Here, matters are uncontroversial; that a fall in concentration will lead to a fall in prices and price-cost margins is wellsupported both theoretically and empirically. (This result was embodied as an assumption in the models set out in Sect. 2 above. While theoretical counterexamples can be constructed, they are of a rather contrived kind.) To test this idea it is appropriate to look at a number of markets for the same product, which diﬀer in size (the number of consumers), so that larger markets support more sellers. It can then be checked whether prices and price-cost margins are, therefore, lower in those larger markets which support more sellers. The key body of evidence is that presented in the collection of papers edited by Weiss (1989). For a comprehensive list of relevant studies, see Schmalensee (1989) p. 987.
In terms of the basic models set out in Sect. 2 above, this ﬁrst question relates to the description of the ﬁnal stage (price competition) subgame: we are asking how the level of gross proﬁts per ﬁrm earned in the ﬁnal stage subgame relates to the level of concentration that has results from earlier investment decisions. A second, quite diﬀerent, question relates to the net proﬁt of ﬁrms (gross proﬁt minus the investment costs incurred in earlier stages). In the ‘free entry’ models described in Sect. 2, entry will occur up to the point where the gross proﬁts of the marginal entrant are just exhausted by its investment outlay. In the special setting where all ﬁrms are identical in their cost structure and in their product speciﬁcations, the net proﬁt of each ﬁrm will be (approximately) zero, whatever the level of concentration. This symmetric setup provides a useful point of reference, while suggesting a number of channels through which some relationship might appear between concentration and net proﬁts (or more conventionally, by the ﬁrm’s rate of return on its earlier investment—gross proﬁt ﬂow per annum divided by the value of the ﬁrm’s assets).
There are four channels that are worth noting. (a) Even if all ﬁrms are symmetric (whence we can express net proﬁt per ﬁrm π as a function of the number of entrants N) free entry implies zero proﬁt only in the sense that π(N)≥ 0 and π(N+1)≤ 0. When N is large, this ‘integer eﬀect’ is unimportant, but in those markets considered in Sect. 2.2, where the number of ﬁrms may be very small even if the market is large, this leaves open the possibility of ‘large’ net proﬁts for the ﬁrms that enter.
(b) If we, realistically, abandon the assumption that all ﬁrms are alike in their cost structures, then we would expect the most eﬃcient ﬁrms (those with the lowest level of average variable cost) to produce larger volumes of output at equilibrium. If we compare two hypothetical industries that are alike in all respects, except that the ﬁrms forming the pool of (potential) entrants in industry A are alike, but those in industry B diﬀer in their eﬃciency levels, then we would expect industry B to exhibit both a higher level of concentration and a higher level of (average net) proﬁtability (Demsetz 1973).
(c) Another form of asymmetry between ﬁrms may arise, not from any inherent diﬀerences in eﬃciency, but from ‘strategic asymmetries.’ In the models set out in Sects. 2 and 3, the only restriction imposed by the viability condition takes the form of a lower bound to concentration. This lower bound corresponds to a situation in which all earn ﬁrms are symmetric ex post, and all earn zero net proﬁt. Above this bound there are other, asymmetric, equilibria, where intra-marginal ﬁrms enjoy positive net proﬁt. Outcomes of this kind can arise for several reasons, such as the presence of ‘ﬁrst mover advantages.’ For example, early entrants to an advertising-intensive industry may spend heavily in advance of rival entry, in building up brand images. Later entrants may then ﬁnd it optimal to spend less on advertising than these early entrants. Under these circumstances, the ﬁrst mover may enjoy strictly positive net proﬁts.
(d) If we abandon the maintained assumption of free entry, in favour of the idea—fundamental to Bain’s approach—that high concentration levels are associated with some form of ‘barriers to entry’ that prevent (eﬃcient) ﬁrms from entering certain industries, then we would expect these concentrated industries to exhibit high levels of proﬁt, in comparison to a reference group of industries where no such ‘barriers’ were present.
These points notwithstanding, it is important to note that there is no robust theoretical prediction of the kind developed in Sects. 2.1 and 3 above which links concentration to net proﬁts.
4. Empirical Evidence
Following Bain’s early contributions, a large body of empirical work was devoted to the search for correlations, across diﬀerent manufacturing industries, between concentration and proﬁtability. While the early literature seemed broadly supportive of such a relationship, the interpretation of the results remained highly controversial, the debate being focused primarily on distinguishing between the Bain interpretation ((d) above) and the Demsetz interpretation ((b) above). A turning point in this literature was marked by the appearance of two new databases that allowed the discussion to move beyond its focus on cross industry studies based on average industry proﬁtability, towards an examination of market shares and proﬁtability of each ﬁrm within the industry: the Federal Trade Commission’s ‘Line of Business’ dataset, and the PIMS dataset. (See Scherer (1980) for an overview of the main results.)
The most authoritative review of the evidence is that of Schmalensee (1989). A key ﬁnding emerges from attempts to discriminate between the views of Bain and Demsetz by regressing the proﬁtability of a business on both the market share of that business, and the level of concentration in the industry concerned. In regressions of this kind, using datasets that span many industries, proﬁtability is strongly and positively correlated with market share, while industry concentration tends not to be positively related to proﬁtability. One important caveat is needed here, in that this ﬁnding might suggest that within each industry, ﬁrms with larger market shares enjoy higher rates of return: this is not the case. Intra-industries studies of market share versus rates of return suggest that no general relationship of this kind is present. (This, incidentally, is unsurprisingly from a theoretical standpoint: it is easy to ﬁnd standard examples in which market shares within an industry are either positively or negatively correlated with proﬁtability. In the simple ‘linear demand model,’ for instance, a ﬁrm that enters a larger number of product varieties than its rivals will enjoy a larger market share but a lower level of gross proﬁt per product (Sutton 1998, Appendix 2.1).
What appears to be driving these results, as Schmalensee notes, is the presence of a small number of industries in which there is an unusually strong positive correlation between market share and proﬁtability.
Apart from this kind of cross-sectional investigation, a quite diﬀerent but complementary perspective is provided by the study of the pattern of ﬁrms’ proﬁtability over time. Mueller (1986) examined the question of whether, at the ﬁrm level, high rates of proﬁtability were transient or persistent over long periods of time. Arguing that observed rates of return showed a substantial degree of persistence over time, Mueller drew attention inter alia to one group of industries (highly concentrated, advertising-intensive industries) as exhibiting unusually high and persistent rates of return. (Observation (c) above provides one candidate interpretation of this ﬁnding.)
The above discussion has focused heavily on the role of ‘strategic interactions’ between ﬁrms as a driver of market outcomes. It was noted in Sect. 2.3, however, that the general run of markets, as conventionally deﬁned, tend to involve a number of (more or less loosely linked) ‘submarkets.’ The presence of such (approximately) independent submarkets carries some far-reaching implications for the analysis of market structure. In particular, it implies that ‘strategic interactions’ can not in themselves tell the complete story. Any satisfactory theory of market structure must bring together the role of ‘strategic interactions’ between ﬁrms or products within each submarket, and the presence of ‘independence eﬀects’ across diﬀerent submarkets. This becomes particularly important once we begin to look for a richer characterization of market structure by examining the size distribution of ﬁrms within each industry. A full discussion of this issue is beyond the scope of this research paper; for details, the reader is referred to Sutton 1997 and (1998, Part II).
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