Competing Models of Firm Proﬁtability Abstract:
In this paper, I look at four models of ﬁrm proﬁtability: two taken from Industrial
Organization, one from Finance, and one from the Economics of Exhaustible Re-
sources. Only one predicts that there will be a positive relationship between ﬁrm
proﬁtability and the structure of the market in which the ﬁrm operates, and only
that one views high proﬁts as an indication of monopoly power. Nevertheless, most
antitrust authorities base their policies on a belief in those relationships. Using panel
data from 14 nonferrous–metal mining and reﬁning markets, I ﬁnd strong empirical
support only for the market–structure model. Journal of Economic Literature classiﬁcation numbers: D43, G13, L13, L71
Keywords: Firm proﬁts, market structure, market share, risk premia, resource exhaustion,
1 This paper was prepared for my Presidential Address to the members of the European Asso-
ciation for Research in Industrial Economics (EARIE) at their annual meeting in Helsinki, Finlandin August of 2003. The research was supported by a grant from the Hampton Foundation at theUniversity of British Columbia. I would like to thank Simon Anderson, Stephen Martin, and HenryThille for helpful comments and Kazuko Kano for valuable research assistance. Introduction
Virtually all branches of economics embrace the notion that ﬁrms attempt to max-
imize proﬁts. Nevertheless, although some ﬁrms are substantially more proﬁtable
than others, most earn only a competitive rate of return. Given those facts, it is
not surprising that economists from various subdisciplines have developed models
that predict which ﬁrms will earn high rates of return and how those rates can be
sustained in a world in which proﬁts attract entry.
In this paper, I summarize four such models: two that originate in the ﬁeld of
industrial organization (IO), one that comes from ﬁnancial economics, and one that
has its origins in the economics of exhaustible resources. Each singles out a diﬀerent
factor as the principal determinant of proﬁtability. In particular, the ﬁrst emphasizes
the structure of the market in which the ﬁrm operates, the second points to the ﬁrm’s
share of that market, the third focuses on the ﬁrm’s risk class, and the last emphasizes
resource scarcity and intertemporal arbitrage.
The four models of ﬁrm proﬁtability originate in traditions that view the economic
world in very diﬀerent lights. Nevertheless, although some are better characterized as
searches for empirical regularities, all can be rationalized by economic theory. Only
the ﬁrst, however, predicts a causal relationship between industry concentration and
ﬁrm proﬁtability. Furthermore, only the ﬁrst interprets the existence of high proﬁts
Nevertheless, antitrust agencies in most Western countries implicitly assume that
a proﬁts/concentration connection exists. In particular, most agencies require that
product and geographic markets be deﬁned and indices of concentration be calculated
before any monopolization or merger case can be brought forward.2 This practice is
adhered to in spite of the fact that it is not only impossible to prove unambiguously
that a causal relationship links proﬁts to concentration,3
attribute high proﬁts to superior eﬃciency, not market power.
Given an abundance of theories and predictions, it is natural to turn to data in an
attempt to disentangle and assess predicted eﬀects. This exercise is not new. Rather,
it is a very old tradition in IO that has fallen out of fashion.4 One reason for the fall
from fashion is that it is diﬃcult to move beyond mere correlation to a determination
of causality. This diﬃculty arises because most of the variables that have been used
in empirical tests are potentially endogenous.
2 Many other sorts of antitrust cases also rely heavily on concentration indices. 3 In particular, under some assumptions, one can demonstrate that no such connection exists. 4 The empirical IO literature has moved from an examination of many markets using the same
model to an emphasis on case studies that are ﬁne tuned to ﬁt particular markets and are muchmore data intensive.
Rather than attempting to determine causality, I take a descriptive approach.5 In
particular, I look at equilibrium rather than causal relationships. Those relationships
are evaluated by calculating the principal components of a matrix of endogenous
variables, interpreting the components that have the highest explanatory power, and
assessing how the original variables are related to those components. In other words,
I seek to uncover the important relationships — those that explain a large fraction
of the cross–sectional and time–series variation in the data.
This technique is applied to data from nonferrous–metal mining and reﬁning in-
dustries. Those industries produce homogeneous commodities that have well deﬁned
product and geographic markets. In particular, fourteen commodity markets are ex-
amined in the application. The data consist of an unbalanced panel of the principal
mining and reﬁning ﬁrms and include the production of each of those ﬁrms in each
The industries were chosen because they satisfy the assumptions that underlie
the theoretical models. In other words, the theories are examined in a context in
which the probability that they are valid is high. In particular, accurate market
deﬁnition is extremely important for assessing models of ﬁrm proﬁtability. Indeed,
when markets are delineated too broadly or too narrowly, statistical tests are biased
against ﬁnding relationships between proﬁts, market structure, market share, and
market risk. Fortunately, the measures of market structure and market share that
are used here are unusually accurate.
The industries were also chosen because a number of high–proﬁle mergers be-
tween mining ﬁrms have been proposed or consummated in recent years (e.g., Al-
can/Pechiney). The arguments that favor those mergers rely on alleged eﬃciencies,
moderate horizontal concentration, and the inability of achieving market power when
products are homogeneous and are traded in highly liquid commodity–futures mar-
It is therefore important to assess whether market structure matters in that
The organization of the paper is as follows. The next section describes the com-
peting models. That description is followed by a discussion of the industries, the data,
the empirical model, and the results of the principal–component analysis. Finally, I
suggest how one might interpret the ﬁndings.
5 The exercise that is performed here is most closely related to the work of Schmalensee (1985). 6 The panel is unbalanced due to mergers and acquisitions. 7 For example, Allaz and Villa (1993) show that when homogenous commodities are traded
continuously, marginal–cost pricing results regardless of market structure. Models of Firm Proﬁtability
I begin by discussing two models that have been developed by researchers in the ﬁeld
of industrial organization. I then develop the principal contenders from the ﬁelds of
ﬁnance and natural–resource economics. All four models are very simple. However,
my object is to uncover robust and stable equilibrium relationships. Models from Industrial Organization
The structure–conduct–performance (SCP) paradigm that dominated IO until the
early 1980s held that market structure (the number and size distribution of ﬁrms in
an industry) determines market conduct (the way in which the ﬁrms in that industry
interact), which in turn determines ﬁrm performance (proﬁtability). Academics from
that tradition claimed that market structure was principally inﬂuenced by technolog-
ical factors such as economies of scale and scope, and that the existence of high proﬁt
levels in an industry was evidence that the ﬁrms in that industry possessed monopoly
Researchers in the SCP tradition, which was principally an attempt to assess em-
pirical regularities, often based their assessments on cross-sectional data for “markets”
(usually Standard Industrial Classiﬁcations or SICs).8 Typically, they regressed av-
erage proﬁt rates on a number of market–wide variables such as indices of horizontal
concentration, measures of economies of scale and other barriers to entry, and R&D
and advertising intensities. I make no attempt to survey the results of the early stud-
ies but instead simply note that the relationship between market structure and ﬁrm
proﬁtability was generally found to be positive but not necessarily strong.9
That literature, which is vast, came under attack in the early 1980s on both
theoretical and empirical fronts. Among other things, empiricists pointed out that all
of the variables were potentially endogenous and that the models therefore produced
correlations that could not be given a structural or causal interpretation. In addition,
broad SICs were not really markets, either because they were deﬁned too broadly and
contained ﬁrms that operated in industries with very diﬀerent structures, or because
the ﬁrms that were assigned to each SIC had substantial operations in other SICs.
Finally, the accounting data that were typically used to measure proﬁtability were
thought to be poor proxies for economic proﬁts.
Theorists on the other hand criticized the SCP paradigm on the grounds that it
was not derived from models of optimal decision making of economic agents. More-
8 See, e.g., Bain (1951, 1956). 9 For a summary, see Weiss (1974).
over, the game–theoretic revolution that swept the ﬁeld questioned the notion that
market structure could be considered exogenous. Instead, theorists often made as-
sumptions about exogenous conduct (e.g., Cournot or Bertrand behavior) in an at-
tempt to endogenize entry and ﬁrm performance. Unfortunately, from an empiri-
cal point of view, the predictions obtained from game–theoretic models were very
sensitive to the assumptions made concerning conduct, and there were few robust
predictions from those models that could be taken to cross–sectional data.
In spite of the fact that the SCP tradition did not originate in a rigorous theory, it
is possible to build a theoretical model that yields the SCP predictions. To illustrate,
Stigler’s (1964) theory of oligopoly is based on the idea that, when ﬁrms collude either
tacitly or overtly, uncertainty inhibits detection of secret price cuts and facilitates
cartel instability. Furthermore, he showed that uncertainty in the percentage gain in
sales from undetected price cutting increases with the number of ﬁrms in the industry
and falls as the inequality of ﬁrm market shares rises.10
that, if one aggregates the variances of ﬁrms’ shares of sales, that variable is inversely
proportional to the Hirschman Herﬁdahl index (HHI) of industry concentration.
There were many later studies that attempted to remedy the ﬂaws that charac-
terized the early cross–sectional models.11
πj = αHHIi + βT xj + uj,
where πj is the proﬁt rate of ﬁrm j, HHIi is an index of concentration for the relevantmarket (i.e., ﬁrm j is in market i), and xj is a vector of other explanatory variablessuch as measures of minimum eﬃcient scale and advertising and R&D intensities.12
Nevertheless, partially as a result of the attacks, the structure–conduct–performance
literature has virtually disappeared from mainstream IO research.13 Indeed, when I
searched EconLit for SCP, although I uncovered more than 100 entries dating from
the last 15 years, most were published in books or relatively obscure journals. Fur-
thermore, unlike the earlier studies, most applications were not based on a wide range
of SICs. Instead, they were heavily concentrated in a few sectors such as agriculture
and banking. Finally, I found that, as they became less fashionable in IO, SCP mod-
els moved to other disciplines. For example, they have been applied to the public
10 The latter eﬀect is due to information pooling. In other words, a large ﬁrm is similar to several
small ﬁrms that share information.
11 For summaries, see Schmalensee (1989) and Scherer and Ross (1990). 12 Equation (1) is a cross-sectional equation. However, it extends easily to a panel. 13 In a history of thought piece, Blaug (2001, p.45) states that The structure–conduct–performanceparadigm of yesteryear . has since been superseded by game theory and transaction cost on the onehand and the Chicago School . on the other.
sector (e.g., to local governments) as well as to economies in transition or in the early
Many alternative explanations for the positive correlation between market struc-
ture and ﬁrm proﬁtability have been proposed in the IO literature, and I do not
survey them all. However, one explanation – ﬁrm market share or size – has received
more attention than any of the others. I therefore elaborate on that criticism.
In the 1970s, a number of “Chicago–school”economists criticized the SCP paradigm
on the basis that its proponents had the causality backwards.14 Indeed, SCP critics
claimed that proﬁts determine concentration rather than the other way around. Their
story runs as follows. Markets are workably competitive, but ﬁrms are not equally
productive. Eﬃcient ﬁrms grow and capture large shares of their markets, whereas
ineﬃcient ﬁrms shrink and eventually exit theirs. As a consequence, the industries in
which eﬃciency diﬀerences are greatest have the most asymmetric market structures
and the highest horizontal concentration. Moreover, since the large ﬁrms in those
industries both dominate the market and are more proﬁtable, there is a positive cor-
relation between concentration and proﬁtability. That correlation, however, does not
result from the exercise of market power. Quite the contrary, it is a sign that markets
Although the original Chicago criticism was not based on a rigorous theory, later
models embody the basic idea. For example, Jovanovic (1982) builds a theoretical
model of a competitive market in which ﬁrms, who diﬀer in their productivities, enter
the market without knowing how productive they are. As they gain experience, they
learn about their costs. When expectations are revised upwards, ﬁrms grow, whereas
when the news is unfavorable, they shrink and eventually exit. The distribution of
eﬃciencies and the maturity of the market therefore determine its structure.
The predictions of market–share and market–power models are thus very diﬀerent
from one another. At one end of the spectrum, conditional on market structure,
market share shouldn’t matter and horizontal concentration alone should determine
proﬁtability. At the other end of the spectrum, conditional on a ﬁrm’s share of the
market, the extent of horizontal concentration in that market should have no eﬀect
Nevertheless, one might expect to ﬁnd empirical support for
both theories. Indeed, the simple Cournot model of homogenous products predicts
that a ﬁrm’s price/cost margin will be directly proportional to its market share, and
14 See, e.g., Demsetz (1973) and Peltzman (1977). 15 There is an alternative model that predicts a positive relationship between market share and
proﬁtability. Bain (1956) argued that small ﬁrms might be less proﬁtable because they are unableto take full advantage of economies of scale.
that an index of industry price/cost margins will be directly proportional to the HHI
In the late 1970s and early 80s, empiricists were able to obtain more disaggregate
data that enabled them to assess the relative importance of market structure and
market share.16 A typical study was based on a regression equation of the form
πji = α1HHIi + α2SHAREji + βT xji + uji,
where πji is the proﬁt rate of ﬁrm j in market i, and SHAREji is the ﬁrm’s share ofthat market.
The results of those tests varied; some researchers found that market–structure
eﬀects were dominant, whereas others found market–share eﬀects to be more im-
Furthermore, although the issue of which eﬀect dominated was hotly
debated, it was never satisfactorily resolved.18
The diﬀerences in opinion can be illustrated by the following quotes:
Proﬁtability is positively associated with a seller’s own market share, but there is littleevidence, at least in recent richly disaggregate data, of a positive association betweenproﬁtability and indices of seller concentration independent of the proﬁt — market–share correlation. (Scherer and Ross 1990, p. 446)
Estimates supporting (the correlation between market share and proﬁtability of USﬁrms) may be dominated by a small number of industries with unusually strong pos-itive relations between share and proﬁtability. (Schmalensee 1989, pp. 984-985, text
A Financial Model
Financial economists have also attempted to explain and assess ﬁrm proﬁtability.
Like members of the Chicago school, they tend to construct models in which mar-
kets are workably competitive. Nevertheless, in their models, returns to investing in
assets such as ﬁrms vary considerably depending on the ﬁrms’ characteristics. One
characteristic that has been emphasized is systematic risk, where systematic means
16 Many tests were undertaken using the US Federal Trade Commission’s line–of–business data,
which contains statistics on ﬁrms’ operations in each of their lines of business.
17 See Schmalensee (1989) and Scherer and Ross (1990, chapter 11) for summaries of the empirical
18 Some researchers replaced ﬁrm and industry variables, such as ﬁrm market shares and industry
concentration ratios, with ﬁrm and industry ﬁxed eﬀects (see, e.g., Scott and Pascoe 1986). However,although one normally ﬁnds large diﬀerences across ﬁrms and markets, the use of ﬁxed eﬀects doesnot allow one to determine the sources of the diﬀerences.
risk that is not diversiﬁable. Speciﬁcally, an asset with higher systematic risk should
The simplest model that embodies that notion is the capital asset pricing model or
CAPM.19 According to the CAPM, investors will be willing to hold the jth asset only
if the expected return to holding that asset, rj, equals the risk–free rate of return,rf , plus an asset–speciﬁc risk premium. When the asset is a ﬁrm, the return toownership is the ﬁrm’s proﬁt, πj. Furthermore, the risk premium is a linear functionof the diﬀerence between the rate of return on the market portfolio, rm, and therisk–free rate, where the market portfolio is a portfolio of all assets in the economy. πj = rf + βj(rm − rf ) + uj,
where uj is an i.i.d. random variable that captures diversiﬁable or unsystematic risk.
Equation (3) is clearly a regression equation. The regression coeﬃcient can there-
fore be interpreted using the regression formula, βj = COV(rm, πj)/VAR(rm).20 Thisformula shows that the risk premium does not depend on the riskiness of the asset
per se, which is measured by VAR(πj). Instead it depends on the covariation of thereturn on asset j with the market portfolio. In other words, only systematic or un-
diversiﬁable risk matters. Idiosyncratic risk, uj, is irrelevant because investors caninsure against such risk by diversifying their portfolios.
The CAPM explains why highly risky assets such as gold need not command high
rates of return. Gold is a real asset whose return is not highly correlated with, for
example, the return to holding a portfolio of stocks. Indeed, when the stock market is
expected to plummet, it is not uncommon for investors to switch from ﬁnancial into
real assets. Such behavior leads to low risk premia and can even cause the return to
holding real assets to be negatively correlated with rm. When this is the case, riskpremia are negative.
The CAPM predicts that a ﬁrm’s risk class, not the structure of the market within
which it operates, determines proﬁt rates. If there is any possibility that market
structure or market share is correlated with systematic risk, it is important to use
measures of risk as conditioning variables in tests of IO models.21
interesting to assess the relationship between risk and return in its own right.
Many researchers from ﬁnance have attempted to assess the testable predictions
of the CAPM. They tend to reject the model in its simplest form but ﬁnd support for
19 See Sharpe (1964) and Lintner (1965). Unlike the early IO models, the CAPM is derived from
an equilibrium model of optimal decisions taken by economic agents.
20 It is assumed that rf is not a random variable. 21 Bothwell and Keeler (1976) is perhaps the ﬁrst study to include systematic risk in an SCP
modiﬁed versions that include additional explanatory factors.22 Most of the factors
that have been considered, however, are economy wide rather than market or ﬁrm
An Exhaustible–Resource Model
The ﬁrms that are used in my assessment of models of proﬁtability are engaged in
mining and reﬁning nonferrous metals. In other words, they operate in exhaustible–
resource markets. Natural–resource economists have also developed theories of ﬁrm
proﬁtability.23 Under the assumption that resource deposits are homogeneous, those
theories yield a number of sharp and sometimes surprising predictions. For example,
they predict that the proﬁt on the marginal unit should increase exponentially over
time, and that there should be no systematic relationship between market structure
It is possible to illustrate the two predictions using a simple stylized model. Sup-
pose that a ﬁrm owns a property that contains 100 gold nuggets that can be extracted
at zero marginal cost. In a world of certainty, market equilibrium via intertemporal
arbitrage requires that the owner be indiﬀerent between extracting a nugget today
and putting the proceeds in the bank where it will earn rf , and waiting to extractthe nugget in a future period. This can only be true if the proﬁt on that nugget (the
nugget’s price in the example) also increases at the rate of interest, rf . Speciﬁcally,
πjt = (1 + rf )πjt−1 = (1 + rf )tπj0,
where πjt is the proﬁt on the marginal unit in mine j in period t.
To understand the second prediction, consider two possibilities: With the ﬁrst
the owner of the property is a monopolist, whereas with the second, the industry
is competitive (the 100 nuggets are owned by a large number of small ﬁrms). Let
monopoly and competitive extraction be Qm and Qc, which can be plotted as functionsof time. In any equilibrium, the area under each extraction path must equal 100 (since
all nuggets must eventually be sold). This implies that the two paths must cross at
least once. Moreover, since price will adjust so that consumers are willing to purchase
the quantity that is put on the market in every period, monopoly and competitive
price paths must also cross. In particular, if the monopolist initially sets a higher
price and sells fewer units than the competitors, he will eventually set a lower price
and sell more units. Furthermore, it is possible for monopoly and competitive price
22 For a summary of more general asset–pricing models, see Brennan (1987), and for a survey of
empirical tests of more general models, see Huberman (1987).
23 In particular, see the seminal article by Hotelling (1931).
paths to coincide. For example, Stiglitz (1976) shows that, in the context of the above
simple model, when the industry price elasticity of demand is constant, the two paths
coincide. When the elasticity of demand increases (falls) over time, however, the
monopolist initially charges higher (lower) prices than the competitors.
When deposits are heterogeneous, the situation becomes more complex. In partic-
ular, it is not always the case that all ore will eventually be extracted. Nevertheless,
in periods in which there is neither rapid technical change nor large discoveries and
when exhaustion is not imminent, the proﬁt on the marginal unit should increase at
a rate that is positive but less than the rate of interest. The lower rate of increase
depends on the extent to which current extraction aﬀects future extraction costs (i.e.,
Furthermore, as with the homogeneous-deposit case, there
is no simple relationship between ﬁrm proﬁtability and the structure of the market
in which the ﬁrm operates. In particular, with heterogeneous deposits, if exhaustion
is complete, monopoly and competitive price and extraction paths must cross.25
There have been many attempts to test the implications of resource scarcity for
proﬁtability, and support for the model is limited at best. Those tests tend to be
either time–series examinations of prices and proﬁts (e.g., Heal and Barrow 1980,
Smith 1981, and Slade 1982) or more structural dynamic models (e.g., Halvorsen and
Smith 1984, Farrow 1985, Young 1992, Slade and Thille 1997, and Ellis and Halvorsen
2002).26 The structural studies, however, require much more detailed data.
There is clearly an abundance of theories of ﬁrm proﬁtability. The predicted
equilibrium relationships are summarized in table 1. In that table, rows are theories,
columns are variables that can be constructed from data, and entries indicate signs
of predicted correlations with ﬁrm proﬁts. It is useful to adopt a uniﬁed empirical
framework in which to assess the summarized predictions. I now turn to such an
The Nonferrous–Metal Industries
The production of nonferrous metals consists of several phases. In simple terms, the
exploration process produces reserves of metal ore, mining extracts that ore from the
ground, smelting and reﬁning produce metal from the extracted ore, and downstream
ﬁrms (e.g., mills) produce metal products (e.g., sheet and tube) from the output of the
reﬁneries and smelters. With the exception of the last phase, most of the large min-
24 See Levhari and Levitan (1977). 25 Exhaustion will be complete if, for example, the demand choke price is inﬁnite and if extraction
costs are multiplicatively separable in current extraction and remaining reserves.
26 The Slade and Thille paper combines a test of the theory of exhaustible resources with the
CAPM, whereas the Ellis and Halvorsen paper combines that theory with a test of market power.
ing companies are vertically integrated and are involved in all phases of production.
However, the exploration phase is much more fragmented than the others. Indeed,
many small ﬁrms engage only in exploration and sell the deposits that they discover
to mining companies. For this reason, in my empirical analysis I limit attention to
phases two and three — mining and reﬁning.27
The principal nonferrous metals are aluminum, copper, gold, lead, nickel, silver,
tin, and zinc. With the exception of aluminum companies, most large mining ﬁrms
operate in several commodity markets. Multimarket production is due to two factors.
First, many ores contain more than one metal (e.g., lead and zinc), and production
must be joint. Second, the technology of mining is similar across commodities, which
means that a ﬁrm with experience with one commodity can easily transfer that ex-
There are substantial economies of scale in mining and even more in reﬁning. As
a consequence, mining ﬁrms are included in lists of the world’s largest. However, the
markets in which they operate are also large. Indeed, nonferrous–metal markets are
worldwide. Due to their geographic size, markets for individual commodities are not
highly concentrated. Instead, they range from moderately concentrated to workably
In addition to economies of scale, entry barriers include the need to possess a
scarce resource. In particular, one cannot mine unless one owns an ore deposit.
Furthermore, it is uneconomical to enter the market if the deposit that one owns is
Technological breakthroughs revolutionized the mining industry in the late nine-
teenth and early twentieth centuries. To illustrate, the availability of cheap sources
of electricity made aluminum smelting possible, the discovery of froth ﬂotation made
recovery of metals from sulﬁde ores economical, and the advent of large earth–moving
equipment made strip mining of low–grade surface deposits inexpensive. In recent
years, however, there have been few breakthroughs. Nevertheless, there are constant
small, gradual improvements in the technology of mining.
On the production side, mineral commodities are thus similar to one another in
many respects. To reiterate, i) they are homogenous commodities that are sold in
world markets, ii) their technologies exhibit economies of scale, but minimum eﬃcient
scales are not usually large relative to market sizes, iii) they are industrial goods that
are not subject to rapid technological change, and iv) their technologies are capital
intensive with similar rates of depreciation across commodities.
On the consumption side, in contrast, the principal uses for a given commodity are
27 Henceforth, I use the word reﬁning to denote smelting and reﬁning and sometimes use the word
mining (e.g., mining ﬁrm) to denote mining, smelting, and reﬁning.
quite diﬀerent from those for the others. For example, the largest use of aluminum
is in the container and food–packaging sector, whereas the largest use of lead is in
storage batteries. This means that each commodity is sold in a diﬀerent product
market. The combination of these factors implies that both geographic and product
markets are well deﬁned. In particular, there are 16 world markets corresponding to
the eight commodities at two stages of production.
These industries are thus ideal for testing market–structure and market–share
models. Indeed, when products are homogeneous and markets are accurately deﬁned,
those models are most apt to be capable of capturing cross–sectional and time–series
variation in ﬁrm proﬁtability. Unfortunately, the industries are less well suited to
testing the relationship between risk and return. As we shall see, the problem arises
because, although the markets are highly risky, that risk is principally unsystematic.
Prices of each commodity come from the London Metal Exchange (aluminum, copper,
lead, nickel, tin, and zinc) and from COMEX (gold and silver).28
monthly averages of the daily data were used in constructing commodity-market and
The data on ﬁrms — output of each commodity, company proﬁts, and assets at
each stage of production — were obtained from the Raw Materials Group (RMG), a
consulting ﬁrm in Sweden.29 These data are somewhat unusual. Indeed, most data–
collection agencies publish commodity statistics by geographic region, and those data
contain no information on market structure. The Raw Materials Group, in contrast,
keeps track of the activities of mining companies. In particular, it tracks mergers
and other changes in the complex linkages among mining and reﬁning ﬁrms and is
consequently a unique source of information on who owns and controls whom.
RMG does not keep track of reﬁning of silver and gold. This omission is perhaps
due to the fact that ﬂows of newly reﬁned silver and gold are small relative to the
stocks of those commodities that are in circulation. In other words, silver and gold
are not discarded but remain in use or are recycled. This lack of data reduces the
total number of markets to 14, eight mining and six reﬁning markets.
Most of the data are annual for the 1994-1998 period. 1994 is the ﬁrst year for
which proﬁt data are available, and 1998 was the last year available at the time of
purchase of the data. Although 5 years is not long enough to estimate a dynamic
model, it is the approximate length of a business cycle.
28 COMEX is now part of NYMEX. 29 For more information on the Raw Materials Group, see their web page at www.rmg.se.
An observation is a ﬁrm, i, i = 1, . . . , Ij, at a stage of production j, j = 1, 2, in a
year t, t = ti, . . . , Ti. Although there is much overlap, the number and identities ofthe mining and the reﬁning ﬁrms diﬀer (thus the j subscript on I). Furthermore, due
to mergers and acquisitions, the panel is unbalanced (thus the subscript i on t).
82 mining and 54 reﬁning companies were selected for the analysis. The selection
procedure was as follows. For each commodity, year, and phase of production, the 20
All companies that made the cut for at least one
year and commodity were initially considered. However, companies were dropped if
no proﬁt data were available, which reduced the number of companies in each set. In
addition, observations were dropped from the sample if either proﬁt or output data
were incomplete, which is another reason why the panel is unbalanced. The ﬁnal
sample contains 320 observations on mining and 210 observations on reﬁning ﬁrms.
A number of variables were constructed from the raw data. First consider the
proﬁt rates. Nominal proﬁts net of taxes are recorded in $US for each ﬁrm at each
stage of production. To make nominal proﬁts comparable across companies, they
were normalized in two ways: they were divided by the ﬁrm’s total revenue and by
its assets (also in $US) and multiplied by 100. Real proﬁt rates were then created by
subtracting the annual rate of inﬂation in OECD countries from the nominal proﬁt
rates. The real proﬁt rate in percentage is denoted RP ROF ITit when divided byrevenue and AP ROF ITit when divided by assets. For ease of notation, the phase ofproduction has been suppressed here and in what follows.
Four commodity–market variables were constructed. The ﬁrst is the Hirschman
Herﬁndahl index of concentration, CHHIkt, which is the sum of the squared sharesof output of the ﬁrms that operate in commodity market k in year t, multiplied
by 10,000. The second is the four-ﬁrm concentration ratio, CCR4kt, which is thepercentage of industry output that is attributable to the four largest ﬁrms in that
industry and year. The third is the commodity beta, CBET Ak, which is calculatedas COV(rk, rm)/VAR(rm). For this calculation, rk is the rate of price appreciationfor commodity k,31
and rm is an average of the total returns (capital gains plus
dividends) to holding a number of prominent stock–market indices.32 Monthly data
for the 1990-1998 period were used in estimating the betas. The ﬁnal commodity–
market variable, CCU M EXkt, measures cumulative extraction of each commodity.
30 I limit attention to large companies because, with those companies, economies of scale are apt to
be exhausted. In other words, I want to eliminate the possibility that ﬁnding a positive relationshipbetween size and proﬁtability is due to economies of scale.
31 rk is the capital gain that is associated with holding the processed commodity. A better measure
of risk would use shadow rather than market prices (see, e.g., Slade and Thille 1997).
32 Speciﬁcally, the indices are Standard and Poors 500 (US), the Dow Jones Industrial Average
(US), FTSE 100 (UK), CAC 40 (France), Hang Seng (Hong Kong), TSE 300 (Canada), Nikkei 500(Japan), and DAX 30 (Germany). Firm variables other than proﬁt rates are weighted averages, where the weights
are revenue or output shares. In other words, wikt (Wikt) is the fraction of ﬁrm i’srevenue (output) that comes from its operations in commodity market k in year t.
The ﬁrst two ﬁrm variable are its HHI and its CR4, which are weighted averages of
The third ﬁrm variable is i’s market share, F M KT SHit, which is a weighted
average of its shares of the commodity markets in which it operates,
where SHAREikt is ﬁrm i’s share of the output of commodity market k in year t. This variable is in percentage. In addition, an alternative measure of market share,
F M AXSHit, was constructed. This measure is the largest share of any of the marketsin which a ﬁrm operates. In other words, if a ﬁrm were to produce three metals, and if
its shares of its three commodity markets were 0.5%, 10%, and 5%, the new measure
The ﬁfth ﬁrm variable, which is a weighted average of the commodity betas, is a
proxy for ﬁrm i’s risk premium,33
Finally, an exponential trend equal to exp(0.05t) was created. A 5% annual real
rate of interest was assumed in creating that variable, which is denoted T REN Dt. This variable should be correlated with proﬁts when deposits are homogeneous. In
addition, the variable CCU M EXkt that measures cumulative extraction for eachcommodity was weighted by the output weights, Wikt, to obtain cumulative extractionfor each ﬁrm, F CU M EXit. This variable is a better measure of depletion whendeposits are heterogeneous.
A number of comments on the data are in order. First, much has been written
about the relative merits of various measures of proﬁtability. My preferred measure
is RP ROF IT , which is often equated with the price/cost margin in the SCP lit-
erature. The principal drawback to using that measure is related to the fact that
33 An alternative measure of the risk premium would use company proﬁts as ri. However, there
are only ﬁve observations from which to construct that variable.
rates of depreciation and competitive rates of return diﬀer across industries (see, e.g.,
Schmalensee 1989). Within the mining sector, however, this problem is not severe.
An advantage of normalizing by sales is that data on sales are much more reliable
than data on capital stocks. More generally, however, the use of any accounting data
has its limitations, which are no more or less troubling here than in other applications.
Proﬁts are recorded by ﬁrm rather than by each market in which the ﬁrm operates.
This lack of detail is less troublesome than it might at ﬁrst appear. Indeed, it is always
diﬃcult to allocate joint costs. However, the problem is particularly acute in the
mining industry. To illustrate, when an ore is extracted, it can be diﬃcult to know apriori which metals the ore will contain. Moreover, even when the metals are known,
the grades of each can usually only be determined ex post. Furthermore, when mining
ﬁrms allocate joint costs across commodities, they often assign all joint costs to the
primary or high–revenue commodity. This procedure makes economic sense since, at
the margin, capacity expansions are usually driven by a desire to produce more of
the more proﬁtable commodity. However, for the purpose of this study, the practice
has the drawback of implying that, as the price of a metal increases, its costs can
also appear to increase, and low–value metals (byproducts) appear to be produced
at very low cost. For this reason, even if available, proﬁts by line of business would
be unreliable. Revenues, in contrast, can be accurately constructed for each market,
and those revenues are used to form the weights that enter into the construction of
In contrast to the measure of proﬁtability, the measures of market structure that
are used here are unusually accurate. Indeed, both product and geographic markets
are well deﬁned, and the raw data on ﬁrm output is recorded at the appropriate
market level. The data were collected at two phases of production. Although reﬁning
markets are clearly important, due to the prevalence of vertical integration, one might
question the relevance of mining markets. For this reason, the empirical model is
estimated for each phase of production separately.
SCP studies typically employ many other control variables. For example, it is
common to include measures of R&D and advertising intensities and dummy variables
that indicate whether the product is durable and whether it is a consumer or a
producer good. With my data, due to the similarity of the markets, there is no need
Finally, one problem with the use of a single cross section is that the relationships
of interest are apt to vary over the business cycle. Using a panel that is at least as
long as a typical business cycle, as is done here, eliminates that problem.
Table 2 gives summary statistics by phase of production for each of the four
endogenous variables that are used in the analysis. The variables have been scaled
so that they have similar means. In particular, the HHI has been divided by 100 so
that it ranges between 0 for perfect competition and 100 for monopoly, and the betas
The table shows that, at least in mining, the variation in proﬁt rates is substan-
tially greater than the variation in the other variables. Moreover, in spite of the
fact that mining and reﬁning are highly risky activities, the betas are small, which
is not unexpected. The table also shows that the largest ﬁrms in the sample (as
measured by FMKTSH) control just over 20% of the markets in which they operate.
Finally, markets vary between fairly competitive (the usual HHI = 180) to moderately
The Empirical Model
Much of the variation in the data is cross sectional, and diﬀerences across ﬁrms
are relatively stable. This means that one can interpret cross sectional variation in
the ﬁrm variables, RPROFIT, FHHI, FMKTSH, and FBETA, as long–run stable
diﬀerences. Unfortunately, this also means that all of those variables are potentially
endogenous. Moreover, without ﬁrm–level exogenous variables, such as ﬁrm–speciﬁc
factor prices, it is diﬃcult to ﬁnd instruments that could be used in a regression
analysis. For this reason, a descriptive approach is adopted. In particular, I use
principal components to analyze variations in the data.
Principal components transforms a set of variables, X, into a new set of variables,
Z, that are pairwise uncorrelated. Furthermore, the ﬁrst of the Z variables (or
components) has the maximum possible variance, the second has the maximum among
those that are uncorrelated with the ﬁrst, and so forth. If there are M variables in
the original data, x , = 1, . . . , M , and if those variables are not perfectly collinear,
it is always possible to ﬁnd M linearly–independent components, z ,
that explain all of the variation in X.34
However, it is often the case that m < M
components explain a very large fraction of the variation.
The components are linear combinations of the original variables, and it is not
always possible to give each an economic interpretation. However, sometimes one
can. Whether or not one can interpret the components, it is possible to calculate
correlation coeﬃcients between each component and each of the original variables.
One can also calculate the proportion of the variation in each x that is associated
The procedure adopted here is to consider a matrix X that consists of the four
34 For the expression “the variation in X” to make sense, the constituent vectors should be
measured in the same units. The variables in this study can be loosely interpreted as percentages.
endogenous ﬁrm variables that are shown in table 2 plus the exponential trend (M =
5). Five principal components are computed. The number m that is retained is chosen
as the smallest number of components that explains at least 95% of the variation in X.
An attempt is then made to interpret the retained components, and the correlations
between the original variables and those components are calculated. The Principal–Component Analysis
Table 3 shows the contribution of the ﬁrst 3 principal components to the total vari-
ation in X, both individually and jointly, for both phases of production. One can
see that the ﬁrst component accounts for more than 60% of the variation, the second
for about 10–30%, and the third for 4–7%. There is therefore very little variation
left for the last two components to explain. Moreover, given the rule for retention of
components, the ﬁrst two are retained for mining and the ﬁrst three are retained for
Table 4 contains correlation coeﬃcients between each variable in X and the re-
tained components for both phases of production. The ﬁrst thing to notice is that the
ﬁrst component is essentially proﬁt, RP ROF IT , the second is essentially the risk pre-
mium, F BET A, and, for reﬁning, the third is essentially market share, F M KT SH.
Indeed, the correlation between those variables and the respective components is at
least 0.95 in all ﬁve cases. In particular, this means that RP ROF IT and F M KT SH
are orthogonal to one another in reﬁning. In other words, in those industries there
is no systematic relationship between a ﬁrm’s market share and its proﬁtability, and,
within a market, smaller ﬁrms are just as proﬁtable as larger ones.
This ﬁnding is contrary to what the proponents of “market–share” models pre-
dict. In particular, even though the ﬁrms in the sample are all large, they control
between 0.1 and 21% of the markets in which they operate. Variation in F M KT SH
is therefore substantial. That variation, however, is uncorrelated with proﬁtability.
Furthermore, this ﬁnding implies that, if there is a correlation between proﬁtability
and market structure in those markets, it cannot be due to a failure to control for
the common causal factor, market share.
Since one can interpret the ﬁrst three components as proﬁt, systematic risk, and
market share respectively, it is possible to investigate how those variables are related
to the remaining variables. In particular, the correlations in table 4 reemphasize the
fact that a ﬁrm’s market share is not correlated with its proﬁtability as embodied in
Table 4 shows that the market–structure variable, F HHI, is positively correlated
with all of the retained components. Moreover, those correlations are signiﬁcant at
1%. The implications are that ﬁrms that operate in concentrated markets are more
proﬁtable and command higher risk premia, and concentrated reﬁning markets have
larger ﬁrms (in relative terms). The ﬁrst of these conclusions gives support to the
traditional structure–conduct–performance paradigm. In other words, market struc-
ture matters. The third, which is more of an accounting identity, simply implies that
if some ﬁrms control large shares of a market, that market is apt to be concentrated.
The measure of systematic risk, F BET A, which is proportional to the ﬁrm’s
risk premium, is positively correlated with proﬁts in mining but not in reﬁning. The
results are therefore mixed, and the CAPM receives only partial support. This ﬁnding,
however, might simply be due to the fact that all of the estimated betas are small,
which means that none of the ﬁrms in the sample commands a high rate of return as
Finally, proﬁts do not exhibit an upward trend. In fact, there appears to be a
downward trend in mining proﬁtability. Sensitivity Analysis
The robustness of the results was assessed in a number of ways. In particular, the
calculations were redone using proﬁt divided by assets, AP ROF IT , as an alterna-
tive measure of proﬁtability, using the four–ﬁrm concentration ratio, F CR4, as an
alternative measure of market structure, the variable, F M AXSH, as an alternative
measure of market share, and with F CU M EX as an alternative measure of scarcity.
In addition, I created a ﬁrm–speciﬁc trend that depends on the ﬁrm’s risk premium,
F BET A. Finally, the commodity risk premium, CBET A, was allowed to vary by
year. None of the alternative speciﬁcations, however, changed the qualitative nature
For the ﬁnal speciﬁcation test, I performed the calculations for each year in the
data. When I did this, I found that the relationship between proﬁts and market
structure is stronger in economic downturns. This ﬁnding might indicate that ﬁrms
in all industries do well in upturns, and in fact I ﬁnd that proﬁts are positively
related to industrial production. Firms in concentrated industries, however, might
have better methods of disciplining each other and might therefore be less likely to
suﬀer proﬁt losses in periods when demand is falling. Conclusions
Four models of ﬁrm proﬁtability were surveyed, each originating in a diﬀerent tra-
dition and each focusing on a diﬀerent determinant of proﬁtability. The ﬁrst, the
familiar structure–conduct–performance (SCP) model, predicts that the structure of
the market in which the ﬁrm operates will be the most important determinant of its
proﬁts. The second predicts that ﬁrms with large market shares will be proﬁtable and
that failure to condition on market share will bias the results of tests of SCP models.
The third singles out a ﬁrm’s risk class and predicts that ﬁrms that must bear more
systematic risk will earn higher rates of return. Finally, the fourth predicts a tempo-
ral increase in proﬁts as the ﬁrm’s reserves are depleted and scarcity rents are earned.
Although at times mutually contradictory, the predictions from all four models can
be rationalized by rigorous theories. The question of what actually determines ﬁrm
proﬁtability is therefore an empirical issue.
Using panel data from nonferrous mining and reﬁning markets, I am able to assess
each prediction. I ﬁnd strong support for the ﬁrst (SCP) model. Indeed, ﬁrms’ proﬁts
are positively and signiﬁcantly related to the structures of their markets, and this
relationship holds in all speciﬁcations that were estimated. A ﬁrm’s market share,
in contrast, is found to be uncorrelated with its proﬁtability. This means that, not
only is market share not an important determinant of proﬁtability in nonferrous–
metal markets, but also that the correlation between market structure and proﬁts
is not spurious. A ﬁrm’s risk premium, which is a measure of the systematic risk
that it must bear, is found to be positively correlated with proﬁtability in mining
but not in reﬁning. The latter ﬁnding, however, is perhaps due to the fact that in
the industries studied, there is not much variation in risk premia across ﬁrms and
time periods. Finally, there is no evidence of a temporal increase in proﬁts. These
empirical regularities are summarized in the last row of table 1 under the heading of
It is perhaps worth elaborating on the second ﬁnding. It is somewhat surprising
that market share does not aﬀect proﬁtability in these industries. In particular, since
low-cost ﬁrms should expand more in an upturn and contract less in a downturn,
most economic models predict that size, even when not the principal determinant
of proﬁtability, will be positively correlated with it. My counterintuitive ﬁnding can
be explained, however, if some ﬁrms are capacity constrained while others are not.
Under that hypothesis, output expansions will be undertaken by the unconstrained
ﬁrms, which need not be the low-marginal-cost ﬁrms. Furthermore, this is not just a
short–run phenomenon since, in exhaustible–resource industries, capacities are more
apt to be determined by reserves than by marginal costs.
I began by stating that competition authorities rely heavily on concentration in-
dices as tools for determining potential competitive harm. The issue of whether this
practice is justiﬁed is clearly not resolved. Most economists would agree, however,
that it does not work well when products are diﬀerentiated. For this reason, authori-
ties are starting to supplement the conventional analysis with merger simulations and
other more sophisticated evaluation methods. This practice, however, is also prob-
lematic. For example, the results of merger simulations are sensitive to the choice
of functional form for demand equations. Furthermore, the predictions that are ob-
tained depend heavily on the cross–price elasticities that are used. Unfortunately, the
magnitudes of estimated elasticities are sensitive to the choice of the outside good as
well as to the number of alternatives considered.35 When products are homogeneous,
shares may thus be as good indicators as simulations. It is therefore unlikely that the
traditional approach will be totally abandoned in the near future.
35 A general discussion of the alternatives is beyond the scope of this paper. Interested readers
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Table 1: Equilibrium Predictions
Table 2: Summary Statistics for Firm Variables Mining Variable Reﬁning Variable
Proﬁt rate in percentage. HHI is divided by 100. Size in percentage of market. Beta is multiplied by 100. Coeﬃcient of variation = standard deviation/mean.
Table 3: Contribution of Principal Components to Variation Mining Component Reﬁning Component
Table 4: Correlation Coeﬃcients Reﬁning
* denotes signiﬁcance at 5%. ** denotes signiﬁcance at 1%.
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Bradley Philip Stoner Personal Information: Sex: Citizenship: Address and Telephone Numbers: Division of Infectious Diseases Washington University School of Medicine Tel. 314-935-5673 FAX 314-935-8535 e-mail: [email protected] Present Position: Associate Professor of Anthropology Director, Medicine and Society Program Director, Undergraduate Minor in Public