WPS5540
Policy Research Working Paper 5540
Sunk Costs, Market Contestability,
and the Size Distribution of Firms
Ioannis N. Kessides
Li Tang
The World Bank
Development Research Group
Environment and Energy Team
January 2011
Policy Research Working Paper 5540
Abstract
This paper offers a new economic explanation for the sizes. These findings provide support for one of the key
observed inter-industry differences in the size distribution predictions of the theory of contestable markets: that
of firms. The empirical estimates--based on three market forces under contestability would tend to render
temporal (1982, 1987, and 1992) cross-sections of the any inefficient organization of the industry unsustainable
four-digit United States manufacturing industries-- and, consequently, tighten the distribution of firms
indicate that increased market contestability, as signified around the optimum.
by low sunk costs, tends to reduce the dispersion of firm
This paper is a product of the Environment and Energy Team, Development Research Group. It is part of a larger effort by
the World Bank to provide open access to its research and make a contribution to development policy discussions around
the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be
contacted at ikessides@worldbank.org.
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issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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Produced by the Research Support Team
Sunk Costs, Market Contestability, and the Size Distribution of
Firms
Ioannis N. Kessides, The World Bank
and
Li Tang, Inter-American Development Bank
1 Introduction
This paper seeks to provide a new, economic explanation for the observed inter-
industry di¤erences in the size distribution of ...rms. Its main testable hypothesis is
that increased market contestability, as signi...ed by low sunk costs, tends to reduce
the dispersion of ...rm sizes.
Seller concentration is perhaps the most frequently quanti...ed and scrutinized
element of market structure.1 It plays a central role in evaluating market power,
especially in the context of mergers or potential anti-competitive behavior such as
collusion and predation. Concern about bigness and rising concentration has been
a recurring theme of public policy and a source of considerable debate in the United
States and elsewhere (White, 1981; 2002).
Concentration depends on two key characteristics of the size distribution of ...rms:
their number (fewness) and the inequality of their sizes (dispersion).2 Previous
0
a
This paper product of the Environment and Energy Team of the Development Research
is
Group also being published in the Review of Industrial Organization.
1
There is a vast theoretical and empirical literature on market structure and its various elements
such as the 4-...rm concentration ratios. See among others: White (1982), Scherer and Ross (1990),
Schmalensee (1989), Berry and Reiss (2007).
2
High levels of concentration may be achieved in two di¤erent ways. The number of ...rms
operating in the industry might be very small. In that case, concentration will be high, even if the
...rms' market shares are approximately equal. Alternatively, the number of ...rms may be large,
but their market shares could be very unequal, leading again to high concentration (Sutton, 1998).
1
empirical studies have focused on the technological explanation of concentration, un-
derscoring the signi...cance of the cost curve (especially the minimum e¢ cient scale
of production) and barriers to entry by new ...rms (Davies and Lyons, 1982). Im-
plicitly these studies have emphasized the numbers equivalent component of concen-
tration. This paper departs from mainstream practice by focusing on the observed
the
inter-industry di¤erences in the dispersion of ...rm sizes variance equivalent com-
ponent of concentration.
The paper invokes one of the fundamental welfare properties of contestable mar-
kets, which refers to the absence of any sort of ine¢ ciency in production in industry
equilibrium. Any unnecessary cost, like any excess pro...t, would constitute an
invitation to entry and render incumbents vulnerable to being displaced by more
e¢ cient entrants (Baumol, 1982). Thus, in contestable industries with U-shaped
average cost curves, we should observe a very low dispersion in the size distribution
of ...rms i.e., ...rms could stay in the market only if they produce at the minimum
point of the average cost curve, or its neighborhood. In markets that are not con-
testable, on the other hand, ine¢ cient industry structures characterized by a large
dispersion of ...rms around the minimum point could be sustainable even in the long
run. Moreover, the extent to which an industry is contestable depends critically
on the magnitude of sunk costs i.e., the irreversible costs that must be borne by an
s
entrant but are mostly bygone for the industry' incumbent ...rms (Martin, 1989).
We recognize that the assumption of U-shaped average cost curves is far from
being universally valid. Indeed, a widely accepted emprical fact is that the observed
average cost curves in many industries appear to be linear for a wide range of output.
However, as we argue below, although the implied e¤ect of contestability will be
at
weaker in industries with U-shaped cost curves with a bottom or L-shaped
curves, it will not entirely break down.
Our econometric model relates measures of ...rm size dispersion to proxies for
industry-speci...c sunk costs. The results of the paper, which are based on a cross-
section of four-digit US manufacturing industries, lend support for the hypothesis
that the structure of markets depends continuously on the degree to which they
exhibit imperfect contestability smaller dispersions of ...rm sizes are observed in
industries whose share of investment that is composed of sunk capital is low (i.e.,
industries exhibiting high degrees of contestability).3 The paper' empirical ...ndings
s
are robust to reasonable changes in model speci...cation as well as to variations in
the measures of ...rm size dispersion and sunk costs.
3
The ...nding that sunk costs in uence the size distribution of ...rms is also consistent with
the predictions of the Stackelberg-Spence-Dixit model of entry deterrence. Sunk costs allow
early entrants to exploit their headstart and limit the scale of entry of other ...rms by strategically
investing beyond their steady-state Nash levels.
2
2 The Size Distribution of Firms Reconsidered: The Impact of Sunk
Costs
A long established feature of industrial economics is that most industries are charac-
terized by a fairly skewed size distribution of ...rms. The resilience of this empirical
regularity has motivated a vast literature on stochastic models of ...rm growth that
began with the seminal contribution of Gibrat (1931). Gibrat assumed that the
number of ...rms is ...xed and their growth rates are independent of their size i.e.,
the probability of a given proportionate change in size during a speci...ed period is
the same for all ...rms in a given industry, regardless of their size at the beginning
s
of the period ("Gibrat' Law" of proportionate e¤ect).
One of the main drawbacks of the Gibrat model is that it has no steady state;
the size distribution of ...rms approaches a lognormal with unbounded mean and
s
variance (de Wit, 2005). Subsequent work re...ned Gibrat' model by integrating
a process of entry and exit into the traditional growth-of-...rms formulation and
imposed a variety of ancillary assumptions (e.g., ...rms are born at a constant rate
as the industry evolves, there exists a minimum size of ...rms above which unit
costs are constant, ...rms cannot decline below a certain minimum size) and stability
conditions to the underlying random walk process (Kalecki, 1945; Simon, 1955, 1960;
Simon and Bonini, 1958; Ijiri and Simon, 1977; Steindl, 1965; Levy and Solomon,
1996; Sutton, 1997; Gabaix, 1999; Malcai et al., 1999). Although the assumption
that enterprise growth is a random walk con icts with economic intuition and the
most fundamental theories of the ...rm, early studies found that stochastic processes
s
adhering to Gibrat' law generate highly skewed size distributions that conform
fairly closely to real-world ones.
s
More recently, there have been several empirical tests of Gibrat' law based on
diverse data sets and employing careful statistical techniques. The results of these
studies have been rather mixed, however. Some of them ...nd that ...rms' growth
s
rates do indeed follow a random walk and therefore Gibrat' Law holds (Del Monte
and Papagni, 2003; Geroski et al., 2003). Others, however, suggest that Gibrat' s
Law is not con...rmed for new entrants, incumbent ...rms tracked over long time
periods, ...rms in speci...c industries and di¤erent countries (Lotti et al., 2009; Aslan,
2008; Ce...s et al., 2007; Oliveira and Fortunato, 2006; Chen and Lu, 2003).
As a complement to the technological explanation, the stochastic approach has
made a valuable contribution to the analysis of market structure. However, the
main weakness of the stochastic description is that it lacks economic content. The
assumptions that underlie the size-growth relationship and the role of stochastic
mechanisms as a driver of skewness are not guided by a formal economic model. In
fact, the law of proportionate e¤ect, as it has been applied in the existing models,
3
does not take into account industry-speci...c characteristics. These models, there-
fore, are not designed to explain the important inter-industry di¤erences in the
degree of inequality in the size distribution of ...rms.
In recognition of the fundamental weaknesses of the stochastic approach, a richer
class of models has been constructed in recent years. These models seek to incor-
porate fundamental economic mechanisms into the stochastic process that governs
s
the ...rm' size. However, the size distributions that are derived seem to depend
on largely unobservable features of these models, thus limiting considerably the
empirical testing of their predictions (Sutton, 1998).
This paper focuses on the e¢ ciency attributes of long-run equilibria in perfectly
contestable markets and the implications of deviations from the conditions of perfect
contestability for the size distribution of ...rms. One of the most fundamental and
novel features of the theory of contestable markets is the explicit recognition that the
structure of an industry is determined primarily by economic forces. The number
of ...rms, the dispersion in their sizes, and so on, are determined endogenously and
simultaneously with the vectors of the industry' prices and outputs.4
s
Under perfect contestability, the opportunity for costless entry and exit guar-
antees the absence of any ine¢ ciency in production in industry equilibrium; i.e., it
renders any ine¢ cient organization of the industry unsustainable. The incumbent
...rms must operate in an e¢ cient manner because any unnecessary costs, like any
excess pro...t, would simply invite entry and lead to their displacement by entrants
who can supply the same output at lower cost. Thus the incumbent ...rms must
minimize costs, and total industry output must be divided among its ...rms so as to
s
minimize the industry' total production cost (Baumol, 1982).
In the single-product case and under the assumption of a unique point of min-
imum average cost, intuition suggests, in essence correctly, that market forces will
enforce the optimal number of ...rms with approximately equal outputs.5 Firms lo-
cating to the right or left of the minimum point would exhibit higher unit costs and
be vulnerable to displacement by potential entrants. Under perfect contestability,
a market structure that is characterized by a dispersion of ...rm sizes around the
unique minimum point would not be consistent with industry equilibrium in the
long run. Thus, the role of contestability is to tighten the distribution of ...rms
around the optimum.
4
The novelty of the theory of contestable markets in explicitly recognizing the endogeneity of
market structure should not be overstated. In his excellent exposition of the theory of contestable
markets, Martin (2000) correctly points out that "the literature before contestability did not treat
market structure as exogenously given."
5
It is important to note that even in the single-product case and with a U-shaped average cost,
the optimal solution will not always involve equal outputs by all ...rms. Baumol and Fischer (1978),
and Baumol et al. (1982), chapter 5, give an example.
4
Perfect contestability, like perfect competition, is only a useful theoretical bench-
mark. In markets where the elements of contestability are not present and entry is
less than ultra free, ine¢ cient equilibrium industry structures characterized by large
dispersions in the sizes of enterprises might obtain. Our basic hypothesis, then, is
that the dispersion in the sizes of ...rms around the optimum, and consequently the
structure of a market, will depend on the degree of imperfection in its contestability.
Perfect contestability requires that: (i) all entry investment is fully reversible,
i.e., there are no sunk costs; (ii) all producers have access to the same technology;
(iii) incumbents cannot adjust their prices instantaneously, i.e., there must be a
positive price response lag; and (iv) there is no consumer goodwill, i.e., consumers
respond instantly to price di¤erentials. Clearly, alternate representations of imper-
fect contestability in real world markets could be based on violations of any of the
above conditions.
This paper focuses on condition (i) and employs the degree of sunkenness of the
entry investment as the primary criterion for contestability. The economic signi...-
cance of sunk costs has received considerable attention in the industrial organization
literature. Sunk costs lower the quasi-rents that the entrant can expect to earn by
committing resources to the market; diminish the rate at which entry responds to
positive incumbent pro...ts or to unnecessary incumbent costs; and, like entry bar-
riers, impede the establishment of new ...rms.6 By shielding ine¢ cient incumbents
from the pressures of competition, sunk costs can constrain market structure and
may allow an ine¢ cient industry con...guration, characterized by a large dispersion
of ...rm sizes around the optimum, to persist.7
Entry frequently entails irrecoverable physical capital investments that are pri-
marily determined by the underlying technological characteristics of the industry' s
production i.e., tangible sunk costs that are largely exogenous. In many indus-
tries, however, there are crucial cost components related to intangible capital that
ect
re strategic decisions by the incumbent ...rms. The two most obvious examples
of discretionary sunk cost expenditures are advertising and R&D outlays (Kwoka
and White, 2001). Indeed, there is empirical evidence that in some (primarily con-
sumer goods) industries, advertising as a sunk cost is even more important to the
total entry barrier than tangible sunk costs (Kessides, 1986). Entry and competi-
tion in knowledge-intensive industries requires large R&D expenditures. Although
6
In a recent paper, Cabral and Ross (2008) question the received wisdom that sunk costs cre-
ate a barrier to entry. They argue that by providing entrants with a commitment power, sunk
investments may soften the reaction of incumbents.
7
In a recent paper, Ghosal (2007) argues that given a level of uncertainty (sunk costs), higher
sunk costs (uncertainty) reduce the number of smaller ...rms, leave larger ...rms una¤ected, and
increase market concentration the inference being that they make the ...rm size distribution less
skewed. See also Ghosal (1996, 2003a, 2003b).
5
these investments generate valuable knowledge-based assets, such assets are largely
Brien and Folta, 2009).
intangible and highly ...rm-speci...c (O'
Intangible sunk costs could play an important role in explaining cross-industry
di¤erentials in ...rm size dispersion. Their impacts, however, are more complex and
their causal mechanism requires careful attention. Advertising, for example, consti-
tutes a sunk cost barrier to entry. For the potential entrant, the need to advertise
leads to an unrecoverable entry cost in the case of failure. Large sunk invest-
ments in advertising may allow incumbents credibly to preempt potential entrants
(Thomas, 1996). On the other hand, by providing information about the existence
of alternative products and their price-quality characteristics, advertising reduces
the search costs that are faced by consumers, thereby decreasing their loyalty and
inertia. It may also allow ...rms to operate in di¤erentiated product niches. Thus,
entrants could perceive a greater likelihood of success in markets where advertising
plays an important role. In that case, advertising may actually facilitate entry and
enhance market contestability (Martin, 2002). Similar arguments could be made for
R&D. Which of these two countervailing e¤ects dominates is clearly an empirical
question.8
The e¤ect of contestability in tightening the distribution of ...rms around the
optimum will be most pronounced in industries with average cost curves that have
a smooth U shape and are thus characterized by a unique minimum point. Clearly,
this e¤ect will be somewhat diluted in industries with U-shaped curves with a at
at
bottom (depending on the relative length of the portion of the curve). However,
it is important to note that the e¤ect will not break down even in industries with
L-shaped average cost curves. First, contestability will in uence the number of
...rms locating in the sub-optimal sector, i.e., ...rms of size less than M ES. In
the long run, under perfect contestability, the density of the suboptimal sector will
be reduced to zero. Second, the factors that a¤ect the degree of contestability
ultimately determine the probability of entry. Firm size inequality is a¤ected by
the probability of entry. The higher is the rate of entry, the smaller are size
inequalities (Simon and Bonini, 1958; Davies and Lyons, 1982). Thus, the degree
of contestability will be related to the size distribution of ...rms even when average
costs are L-shaped.
3 Measuring Dispersion of Firm Sizes
To obtain a measure of the inequality in ...rm size distribution, we ...rst focus on the
relationship between concentration and the number of ...rms. Let Cmi denote the
m-...rm concentration ratio in industry i. Then it is easy to show that
m Qmi Qi
Cmi = +m ; (1)
Ni Qi
8
We would like to thank an anonymous referee for higlighting the importance of this issue.
6
where in industry i, Ni is the number of ...rms, Qmi represents the average ...rm
output of the largest m ...rms, Qi is average ...rm output computed over all the
Qmi Qi
...rms in the industry, and Qi is total industry output. The quantity
Qi
represents the relative distance between the industry-wide mean ...rm size and that
of the largest m ...rms in the industry; i.e., it is a measure, albeit a simpli...ed one, of
...rm size dispersion. This decomposition is intuitively appealing in that it signi...es
the dependence of the single summary measure of concentration Cmi on two key
characteristics of the size distribution of ...rms: their number (fewness), represented
Qmi Qi
by Ni , and the inequality of their sizes (dispersion), represented by .
Qi
If there is no size dispersion (e.g., in the case of a U-shaped average cost curve,
all ...rms in industry i locate at the minimum point), then the second term on the
m
right hand side of (1) will be zero and Cmi = ; i.e., the m-...rm concentration
Ni
ratio depends entirely on the number of ...rms (fewness). If, on the other hand,
Qmi Qi m
there exists a dispersion in ...rm sizes, will be positive, and thus will
Qi Ni
underestimate the m-...rm concentration ratio in industry i:
Rearranging (1) we obtain
Qmi Qi 1 m
= (Cmi ) (2)
Qi m Ni
for our ...rst proposed measure of the inequality in ...rm size distribution of a given
industry that is expressed in terms of observable structural parameters.
Qmi Qi
It may be argued that the term is not an accurate measure of ...rm size
Qi
dispersion because it ignores potentially important within-group size di¤erentials
for the largest m and remaining Ni m ...rms in industry i. The basis for a more
comprehensive measure of size dispersion in industry i is provided by the variance
of market shares
N
1 Xi
Vi (s) = (sij si )2 ; (3)
Ni
j=1
where in industry i; sij is the market share of ...rm j, si is the average market share,
and as before Ni is the number of ...rms.
Noting that the Her...ndahl-Hirshman Index Hi is the sum of the squared share
values, we obtain
1 1
Vi (s) = (Hi ); (4)
Ni Ni
7
which expresses size dispersion in terms of industry structural parameters that are
observable.
Rearranging (4) leads to the decomposition
1
Hi = + Ni Vi (s); (5)
Ni
which again is intuitively appealing because it distinguishes two aspects of the single
summary measure Hi of concentration: fewness, represented by Ni , and size disper-
1
sion, represented by Vi (s). If there is no size dispersion, then Hi = ; i.e., Hi
Ni
depends entirely on the fewness of ...rms (Kelly, 2001).
4 Sunk Costs: Measurement and Correlates
Lack of detailed data on the availability of resale markets for durable inputs pre-
cludes direct evaluation of the unavoidable sunk costs that face an entrant. Such
measurement is further complicated by the fact that ...xed costs that are ...rm-speci...c
are in general more sunk than those that are just industry-speci...c. Still, readily
available measures suggested by theory permit us to construct meaningful proxies
for these costs (Kessides, 1990).
Assume that entry into industry i requires Kie units of capital that can be pur-
chased at a price of i per unit. Let e denote the portion of the capital that the
i
entrant can rent. Assume further that the entrant exercises its disinvestment option
after a period of length during which its capital depreciates by dki percent. If the
entrant can scrap its capital at the end of the period for a salvage price of i , then
the expression
SU Kie = (1 e
i )[(1 dki ) i
e
i ]Ki 0 < (1 dki ) i i <1 (6)
represents the portion of the entry investment that is irrecoverable if exit takes place
after a period of length i.e., the e¤ective sunk costs facing the entrant.
The divergence between the undepreciated portion (1 dki ) i of the original
investment and the salvage price i will depend on the characteristics of the capital
that is employed in the industry: the degree to which such capital is ...rm- rather
than industry-speci...c, its lumpiness, technological complexity, and so on. It can
be plausibly argued that the intensity of the resale market in the industry can serve
as an indicator variable for these largely unobservable capital characteristics. One
should expect an active resale market in industries in which the capital employed
is industry- rather than ...rm-speci...c. Lumpy capital, on the other hand, which is
costly to relocate becomes by default ...rm-speci...c and does not lend itself to resale
8
i
unless the ...rm is acquired. Thus, the portion of the entry investment 1
(1 dki ) i
that is sunk is assumed to be a decreasing function of the intensity of the resale
market i in the industry; i.e.,
SU Kie = (1 e
i )(1 dki ) i Kie g( i ); (7)
where g 0 ( i ) < 0: For the sake of analytic simplicity we adopt the exible functional
form g( i ) = i ; where ; > 0:
s
We assume that the entrant' capital has approximately the same composition as
RKi
that of the industry. Then e may be proxied with
i where RKi represents the
ri K i
total rental payments made for the use of capital in industry i, Ki is the industry' s
capital, and ri Ki is its maximum rental value. We also propose to use as a proxy
U Ki
for intensity of the resale market i : the portion s
of the industry' total
U Ki + N Ki
capital expenditure that consists of used plant and equipment, where U Ki and N Ki
s
are the industry' used and new capital expenditures, respectively. Then, the share
of entry investment that is composed of sunk capital (i.e., the sunkenness of the
entry investment) in industry i will be given by
SU Kie RKi U Ki
SU N Ki = e = (1 )(1 dki ) ( ) : (8)
i Ki ri K i U Ki + N K i
The above measures relate to tangible sunk costs arising from investment in
physical capital. We assume now that in addition to investment in physical capital,
e
entry into industry i requires Ae and RDi outlays in advertising and R&D respec-
i
s
tively. If the entrant' investments in advertising and R&D depreciate by dai and
dri percent during the time interval ; then the expressions
SU Ae = (1
i dai )Ae
i (9)
and
e e
SU RDi = (1 dri )RDi , (10)
provide a measure of the portion of the entry investment in advertising and R&D
that might be unrecoverable in the event of exit. In general, the assets created
by investments in advertising and R&D are intangible and highly ...rm-speci...c, with
little value outside their current applications (O'Brien and Folta, 2009; Helfat, 1994).
Thus, SU Ai e and SU RD e should be very close to the true sunk cost of advertising
i
and R&D. Still, if the exiting ...rm is taken over by one of its competitors, then these
expressions might overestimate the true sunk costs. This is because advertising and
R&D expenditures can create assets with some future value that will generally be
re s
ected in the ...rm' sale price.
9
s
We assume that the entrant' capital structure encompasses the same mix of
tangible and intangible components as that of the industry. Then, taking into
account both tangible and intangible sunk cost expenditures, our proposed measure
of sunkenness of the entry investment is modi...ed as follows:
RKi U Ki Ai RDi
SU Ni = (1 )(1 dki ) ( ) + (1 dai ) + (1 dri ) ; (11)
ri K i U Ki + N Ki i Ki i Ki
where Ai and RDi are the advertising and R&D outlays in industry i.
5 Speci...cation and Estimation Issues
Our basic hypothesis is that contestable markets, as signi...ed by low sunk costs, yield
an e¢ cient (cost-minimizing) market structure characterized by a tight distribution
of ...rms around the optimum; i.e., contestability will reduce the dispersion of ...rm
sizes. Because tangible sunk costs can be proxied more easily than can intangible
ones, we will ...rst estimate the impact of tangible sunk costs. Thus, our basic model
takes the form:
i = f (SU N Ki ) = f (RENi ; DEPi ; RESi ); (12)
RKi
where i is ...rm size dispersion and RENi = is the intensity of the rental
ri K i
U Ki
market, DEPi = dki is the rate of depreciation, and RESi = is the
U Ki + N Ki
intensity of the resale market for the capital employed in industry i: Given that our
model is not explicit as to the functional form of f , we adopt the exible form
1
i = f (SU N Ki ) = 0 SU N Ki 0; 1 > 0; (13)
which taking into account (8) reduces to
1
i = 0
1
(1 RENi ) 1 (1 DEPi ) 1 RESi : (14)
Qmi Qi
We ...rst focus on the measure of dispersion de...ned in (2). Setting
Qi
equal to i in (14) points to the estimating equation
m b
Cmi = b0 (1 RENi )b1 (1 DEPi )b2 RESi 3 eui ; (15)
Ni
where as before Cmi is the m-...rm concentration ratio and Ni is the number of op-
erating ...rms in industry i: The ui are assumed to be independently and identically
2
distributed random variables with zero mean and variance u . The multiplicative
stochastic terms speci...cation is chosen because RENi , DEPi , and RESi are mea-
sured with error and therefore a purely additive stochastic speci...cation would be
inappropriate. A comparison of (2), (14), and (15) indicates the following relation-
ships between the estimating coe¢ cients and the parameters of the model:
10
b0 = m 0
1
; b 1 = b2 = 1; and b3 = 1: (16)
Thus, with respect to (15) the hypothesis of interest is:
H01 : b1 = b2 against H11 : b1 6= b2 : (17)
In addition, it should be noted that the parameter measuring the elasticity
of sunkenness is identi...ed but not the parameter : The role of contestability in
tightening the distribution will be supported if the estimated coe¢ cients b1 and b2
are signi...cantly positive and b3 is signi...cantly negative.
The potential role of contestability in tightening the size distribution of ...rms
can be assessed more accurately by utilizing the measure of dispersion Vi (s) which
represents the variance of market shares in industry i. Thus, setting i equal to
Vi (s) in (14) points to the estimating equation
c
Vi (s) = c0 (1 RENi )c1 (1 DEPi )c2 RESi 3 e i ; (18)
where the error components i are assumed to be distributed according to N (0; 2 ).
The contestability hypothesis will be supported if c1 and c2 are signi...cantly positive
while c3 is signi...cantly negative. A comparison of (14) and (18) indicates that with
respect to (18) the hypothesis of interest is:
H02 : c1 = c2 against H12 : c1 6= c2 : (19)
To evaluate the potential impact of intangible sunk costs and taking into account
(11), (15), and (18), we adopt the parsimonious speci...cations
m a Ai RDi
Cmi = a0 + a1 (1 RENi )(1 DEPi )RESi 2 + a3 + a4 + i (20)
Ni i Ki i Ki
and
d Ai RDi
Vi (s) = d0 + d1 (1 RENi )(1 DEPi )RESi 2 + d3 + d4 + i, (21)
i Ki i Ki
where the error components i and i are assumed to be distributed according to
N (0; 2) and N (0; 2) respectively.
6 Data and Measurement Issues
Equations (15) and (18) are ...t to 1982, 1987, and 1992 Census and Annual Survey of
Manufactures (ASM) data on four-digit US manufacturing industries. After 1992,
11
the Census ceased reporting the classi...cation of capital expenditures into new and
used. Thus, after that year, proxies for the intensity of the resale market RES
could not be constructed. However, even in 1992, it is not possible to construct
RES for a large number of industries. To ensure that the three cross-sections
are comparable in terms of their sample size, the variables used for the 1992 cross-
section are averages of 1987 and 1992. Summary statistics for the key variables are
provided in the appendix.
Under rental payments, RK; manufacturing establishments are requested to re-
port payments made for the use of all items for which depreciation reserves would be
maintained if they were owned by the establishment e.g., structures and buildings,
production equipment and transportation equipment. Establishments also report:
the depreciation, DK; charged during the year against ...xed assets; their new expen-
ditures for buildings and equipment N K; the value of all used plant and equipment
U K purchased during the year; and their ...xed depreciable assets K: To facilitate
estimation, we drop r since it is just a normalization.9 We also restrict the length
of the period at the end of which the entrant exercises its disinvestment option, to
being the same across industries and set it equal to one year. Then, we can compute
RK DK UK
the following proxies: REN = ; DEP = ; and RES = :
K K UK + NK
To estimate equation (15), we set m = 4 and thus employ the four-...rm con-
centration ratio C4 . These concentration ratios were taken unadjusted from the
Census listings. For each four-digit industry, the Census also reports the values of
the truncated Her...ndahl index H, representing the sum of squared market shares
of the largest 50 ...rms in the industry or the entire universe, whichever is lower.
The census also reports the values of the 50-...rm concentration ratio C50 . From
the values of H and C50 we can derive V (s); the variance of market shares of the
largest 50 ...rms or the entire universe, whichever is lower. This will permit us to
estimate equation (18). It can be easily shown that10
9
It should be noted that dropping r leads to a change in units and could a¤ect the testing of
H01 in (17) and H02 in (19) . Moreover, established ...rms are more likely to buy their own capital,
RK
so (1 ) is likely to overstimate sunkenness.
10
rK
The variance of market shares of the largest N ...rms in an industry is given by
1X
N 2 XN
1 1 CN
V (s) = (sj s)2 = (HN + N s2 2sCN ) = (HN ) where HN = s2 ; s is the
j
N j=1 N N N j=1
X
N
average market share of the largest N ...rms, and CN = sj : If an industry contains more than 50
j=1
...rms, then we compute the variance of the market shares of the largest 50 ...rms from the values of
the truncated Her...ndahl index H50 and the 50-...rm concentration ratio C50 that are reported by
2
1 C50
the census, i.e., V (s) = (H50 ). If, on the other hand, an industry contains N ...rms where
50 50
1 1
N < 50, then CN = 1 and V (s) = (HN ):
N N
12
1 2
C50
V (s) = H50 if N 50 (22)
50 50
1 1
= HN if N < 50;
N N
N
X
where HN = s2 :
j
j=1
For advertising we employ the 1982, 1987, and 1992 input-output tables from the
Bureau of Economic Analysis (BEA). Two input industries are used to calculate
advertising: advertising, and signs and advertising displays. We supplement the
advertising data from input-output tables with data from Schonfeld & Associates.
7 Empirical Findings
We ...rst focus on assessing the impact of tangible sunk costs. Table 1 presents
the ordinary least squares (OLS) estimates of equations (15) and (18), along with
the values of the ordinary and adjusted R2 statistics. As noted above, to estimate
(15) we employ the four-...rm concentration ratio, thus setting m = 4. Separate
regressions were estimated for the census years 1982, 1987, and 1992. Overall, these
results strongly support the hypothesis that sunk costs inuence the size distribution
of ...rms.
The results of equation (15) indicate that the intensities of the rental and second-
hand markets and the rate at which capital depreciates are signi...cant determinants
Q4i Qi
of ; the di¤erence in mean size between the four largest and all ...rms in
Qi
industry i. We ...nd that the stronger is the second-hand market for the capital
employed in an industry, the faster is the rate at which such capital depreciates,
and the easier is the leasing of that capital (i.e., the lower is the sunkenness of the
capital employed in the industry), the smaller is the dispersion in ...rm size within
the industry. Moreover, the parametric restrictions implied by the model are not
rejected by these data, which provides a measure of con...dence in the model and
the measure of sunkenness proposed in (8). The likelihood ratio test indicates that
the maintained hypothesis H01 : b1 = b2 is not rejected at the 5 percent level in all
three temporal cross-sections (1982, 1987, and 1992).11
11 :95
For the 1982 cross-section, F = :07 < F1;396 = 3:87, and the probabality level at which a
:95
standard F-test rejects the restriction is .79; for 1987, F = :07 < F1;426 = 3:86 and the probabality
:95
level at which a standard F-test rejects the restriction is .78; for 1992, F = :18 < F1;425 = 3:86,
and the probability level at which the standard F-test rejects the restriction is .67.
13
Table 1 OLS Estimates of the Determinants of Dispersion in Firm Sizes
4 b
Equation (15): C4i = b0 (1 RENi )b1 (1 DEPi )b2 RESi 3 eui
Ni
Parameter Estimates b0 b1 b2 b3
1982 cross-section 56.83 6.89 7.53 -.09 R2 = :25
(1.83) (1.32) (1.50) (.02) R2 = :25
1987 cross-section 25.28 5.03 4.37 -.29 R2 = :30
(1.02) (1.10) (1.57) (.03) R2 = :29
1992 cross-section 21.76 3.83 2.93 -.32 R2 = :28
(1.06) (.82) (1.58) (.03) R2 = :27
c
Equation (18): Vi (s) = c0 (1 RENi )c1 (1 DEPi )c2 RESi 3 e i
Parameter Estimates c0 c1 c2 c3
1982 cross-section 1.17 11.74 17.19 -.24 R2 = :23
(.22) (2.84) (3.56) (.06) R2 = :22
1987 cross-section 3.00 11.61 10.67 -.72 R2 = :31
(.87) (2.63) (3.75) (.07) R2 = :30
1992 cross-section 1.93 8.55 (6.10) -.79 R2 = :29
(1.02) (1.87) (3.66) (.08) R2 = :28
Number of Observations = 400 in 1982, 430 in 1987, 429 in 1992
Standard Errors in Parentheses; p < :01; p < :05; p < :1
The signi...cance of the e¤ect of contestability in tightening the size distribution
of ...rms is also con...rmed by the analysis of a more accurate measure of dispersion
that is derived from (4). The estimates from equation (18) indicate that the factors
that determine the sunkenness of capital are also important determinants of ...rm
size dispersion, as measured by the variance of the market shares of the largest 50
...rms in each industry. We ...nd again that the lower is the sunkenness of the capital
that is employed in an industry, the smaller is the dispersion and hence, the tighter
is the distribution of ...rms around the optimum. The parametric restrictions that
are implied by the model are con...rmed by these data. Indeed, the maintained
hypothesis H02 : c1 = c2 is not rejected at the 5 percent level in all three temporal
cross-sections.12
Table 2 presents estimates of (15) and (18) using the pooled data from the
1982, 1987, and 1992 censuses. Both OLS and the asymptotically more e¢ cient
12 :95
For the 1982 cross-section, F = :07 < F1;396 = 3:87, and the probabality level at which a
:95
standard F-test rejects the restriction is .79; for 1987, F = :03 < F1;426 = 3:86; and the probabality
:95
level at which a standard F-test rejects the restriction is .87; for 1992, F = :25 < F1;425 = 3:86,
and the probabality level at which a standard F-test rejects the restriction is .62.
14
feasible generalized least squares (FGLS) were employed. The null hypothesis of
homoscedasticity is not rejected at conventional levels of signi...cance.13 However,
the test derived by Wooldridge (2002), suggests that the null hypothesis of no ...rst-
order autocorrelation is rejected in favor of AR(1).14 The inferences drawn from
the 1982, 1987, and 1992 temporal cross-sections are supported by the pooled data.
Both OLS and FGLS regressions produce statistically signi...cant parameter esti-
mates. We again ...nd that ...rm size dispersion decreases with increasing levels of
rental and resale market activity and higher rates of capital depreciation. When
(15) and (18) are estimated with OLS, the maintained hypotheses H01 : b1 = b2
and H02 : c1 = c2 are not rejected at the 5 percent level.15 However, we do note a
di¤erence in the estimated parameters when equations (15) and (18) are estimated
with OLS and when they are estimated with FGLS. This is not surprising since
OLS and FGLS are di¤erent estimation procedures; and, in any case, it is not easy
to determine whether such di¤erences are statistically signi...cant.16
13
We perform the Bickel (1978) version of the Breusch-Pagan test on (18). This tests for both
within and between heteroscedasticity. We regress the squared residuals on powers of the
predictions: for = 5; F =1:03 and P rob > F = :39: Thus for = 5, the null hypothesis of
homoscedasticity cannot be rejected at the 5% level. For = 6 to 10, we ...nd that the null
hypothesis of homoscedasticity cannot be rejected at the 10% level.
14
When we apply the Wooldridge test on (18) we obtain F = 57:31 and P rob > F = 0:00.
15 :95
For H01 , F = :73 < F1;819 = 3:85, and the probabality level at which a standard F-test rejects
:95
the restriction is .39; for H02 , F = 1:09 < F1;819 = 3:85, and the probabality level at which a
standard F-test rejects the restriction is .30.
16
In the presence of serial correlation, FGLS is preferred because it is more e¢ cient and its test
statistics are at least asymptotically valid.
15
Table 2 OLS and FGLS Estimates of the Determinants of Dispersion in Firm Sizes
(pooled 1982, 1987, and 1992 data)
4 b
Equation (15): C4i = b0 (1 RENi )b1 (1 DEPi )b2 RESi 3 eui
Ni
Parameter Estimates b0 b1 b2 b3
OLS 20.09 2.57 1.99 -.23 R2 = :20
(.54) (.41) (.45) (.02) R2 = :20
FGLS 25.53 1.63 .88 -.10
(.39) (.31) (.29) (.02)
c
Equation (18): Vi (s) = c0 (1 RENi )c1 (1 DEPi )c2 RESi 3 e i
Parameter Estimates c0 c1 c2 c3
OLS 1.77 5.86 4.21 -.55 R2 = :19
(.56) (.96) (1.05) (.05) R2 = :19
FGLS 3.19 3.72 1.67 -.23
(.35) (.73) (.68) (.04)
Number of Observations = 828
Standard Errors in Parentheses; p < :01 ; p < :05; p < :1
In assessing the impact of intangible sunk costs on ...rm size dispersion, we limit
our attention to advertising. The potential role of R&D could not be evaluated due
to insu¢ cient data. Table 3 presents the nonlinear least squares estimates of the
parameters in equations (20) and (21). We ...nd that in all temporal cross-sections,
a1 and d1 are signi...cantly positive and a2 and d2 are signi...cantly negative. These
parameter estimates once again con...rm the role of contestability, as signi...ed by low
tangible sunk costs, in tightening the distribution of ...rms. We also ...nd that a3 and
d3 are signi...cantly positive in all temporal cross-sections, with the exception of d3
in 1992. Thus, higher levels of advertising intensity are associated with increased
...rm size dispersion.
These ...ndings could be interpreted as implying that advertising gives rise to a
sunk cost barrier, and thus it augments the role of tangible sunk costs in reducing
market contestability and in allowing ine¢ cient industry con...gurations character-
ized by a large dispersion of ...rm sizes around the optimum to persist. However,
our ...nding that a3 and d3 are signi...cantly positive is also consistent with the view
that advertising may allow ...rms to operate in di¤erentiated product niches and
away from the minimum point of the average cost curve without being vulnerable
to displacement by potential entrants.
16
Table 3 Nonlinear OLS Estimates of the Determinants of Dispersion in Firm Sizes
(tangible and intangible sunk costs)
m a Ai
Equation (20): Cmi Ni = a0 + a1 (1 RENi )(1 DEPi )RESi 2 + a3 + i
i Ki
Parameter Estimates a0 a1 a2 a3
1982 cross-section -214.35 268.80 -.01 28.21
(36.38) (40.38) (.004) (9.96)
1987 cross-section -103.26 129.02 -.07 17.96
(23.23) (25.79) (.01) (8.52)
1992 cross-section -124.06 154.55 -.06 44.22
(23.75) (26.83) (.01) (12.54)
d Ai
Equation (21): Vi (s) = d0 + d1 (1 RENi )(1 DEPi )RESi 2 + d3 + i
i Ki
Parameter Estimates d0 d1 d2 d3
1982 cross-section -136.72 155.11 -.02 20.00
(33.25) (36.88) (.008) (9.10)
1987 cross-section -68.12 68.94 -.09 14.02
(15.09) (16.56) (.019) (5.54)
1992 cross-section -120.48 127.38 -.06 26.03
(33.82) (38.10) (.02) (18.47)
Number of Observations = 241 in 1982, 291 in 1987, 311 in 1992
Standard Errors in Parentheses; p < :01; p < :05; p < :1
8 Robustness Analysis
s
This paper' key testable hypothesis is that contestability tightens the distribution
of ...rms around the optimum. The extent to which costs are sunk is central to
the contestability of markets. Thus, there is an implied causal link between the
s
variables that determine the sunkenness of the industry' capital i.e., the rate of
depreciation and the intensity of the rental and resale markets and the dispersion
of ...rm sizes in the industry. However, one potential objection to our interpretation
of these results is that the variables that determine sunkenness might themselves
be a¤ected by market structure i.e., that a reverse causal link might be present in
the estimated relationships. In exploring the potential reverse causation, it will be
easier to focus on equation (15).
The available empirical evidence does not support the conjecture that there are
signi...cant di¤erences in the choice of accounting policies with respect to depreciation
17
by ...rms in concentrated and unconcentrated industries (Hagerman and Senbet,
1976; Zmijewski and Hagerman, 1981). In fact, if there is any relationship at all,
it suggests that a larger percentage of ...rms in very concentrated industries use
more frequently accelerated depreciation in comparison to ...rms in unconcentrated
industries, pointing to a probable positive correlation between concentration and
depreciation. This ...nding seems to rule out the possibility that our established
negative relationship between concentration and depreciation in equation (15) is
driven by an accounting bias.
One may plausibly argue that the intensities of the rental and resale markets
are apt to be higher in industries that are large. If concentration and industry size
are negatively correlated, then the possibility arises that the established correla-
tion between concentration and the rental and resale market variables is spurious
there may be an omitted variable (industry size) that is correlated with both the
concentration and the rental and resale market variables, and with di¤erent causal
implications. When we use industry sales as a measure of industry size, we ...nd
that the correlations between size and concentration, and also between size and
rental and resale variables, are very weak or insigni...cant. We can therefore rule
out the possibility that the correlation between the dispersion in ...rm size and the
rental and resale variables arises because industry size (as measured by industry
sales) determines the intensities of the rental and resale markets, and industry size
is strongly correlated with concentration.
Finally, one may argue that technology causes an industry to have a large num-
ber of small ...rms, many of which are undercapitalized and therefore must rent. This
possibility would again suggest that the causation runs in the opposite direction.
However, we ...nd that the correlation between the rental variable RENi and capital
intensity as measured by the capital-sales ratio is statistically insigni...cant. In addi-
tion, if the rental variable serves as a proxy for technology in equation (15), its e¤ect
should fade into insigni...cance once technology is controlled for. However, there is no
statistically signi...cant shift in the estimated coe¢ cient of the rental variable when
technology is controlled for by introducing M ES into the concentration equation.17
Hence, a potential omitted variables problem related to technology must also be
ruled out.
Sunk costs can have both industry-speci...c and ...rm-speci...c components (Ghosal,
2009). Our measure of sunkenness is based on industry-speci...c variables. We do
not have information to construct meaningful proxies for ...rm-speci...c sunk costs.
Thus, there is an implicit assumption that the capital employed by all ...rms (small
and large) in an industry and potential entrants is characterized by the same de-
gree of sunkenness. In some industries, the ...rm-speci...c component of sunk costs
17
These results are available from the authors upon request.
18
could be important, and our proxies of sunkenness are likely to contain signi...cant
measurement errors. Such mismeasurement leads to inconsistent estimates and to
potential attenuation bias.
Our model and its measure of sunkenness lead to tightly speci...ed equations (15)
and (18). Still, it would be important to assess the robustness of our empirical
...ndings to alternative functional speci...cations of the basic estimating equations.
For this we adopt a simple linear speci...cation where the dependent variable as well
as all explanatory variables appear in their natural form. For 1982, we obtain the
following parameter estimates (standard errors in parentheses):
4
C4i = 73:95 195:55 RENi 375:01 DEPi 23:84 RESi R2 = :21
Ni
(4:29) (45:40) (59:13) (9:68)
Vi (s) = 29:87 78:83 RENi 199:38 DEPi 13:07 RESi R2 = :13
(2:95) (27:81) (40:51) (6:11)
Thus, we again ...nd that there is a statistically signi...cant relationship between the
variables determining sunkenness and ...rm size dispersion.18
The main focus of this paper has been to assess the impact of tangible sunk costs
on ...rm size dispersion. We have also made an e¤ort to take into account intangible
sunk costs. Still, it would be important to ascertain whether the omission of
intangible sunk costs from our basic estimating equations gives rise to a signi...cant
bias. Overall, we do not ...nd a signi...cant di¤erence in the parameter estimates for
RENi , DEPi , and RESi when intangible (advertising) sunk costs are included in or
excluded from (15), (18), (20), and (21). When we do ...nd a di¤erence, it appears
that the statistical signi...cance and quantitative importance of the variables that
determine tangible sunk costs are actually enhanced when intangible sunk costs
are taken into account. For example, in Table 3, when advertising is omitted
from (20) and (21), we obtain the following parameter estimates (standard errors in
parentheses) for 1982:
a0 = 190:55(35:91); a1 = 245:64(40:13); a2 = :013(:005); d0 = 119:68(32:62);
d1 = 138:51(36:40); d2 = :021(:009): A comparison with the parameter estimates
in Table 3 reveals that the e¤ects of RENi , DEPi , and RESi are more pronounced
when advertising sunk costs are taken into account. Moreover, when we divide our
sample into consumer and producer goods industries, we ...nd no statistically signi...-
cant di¤erence in the e¤ects of the variables that determine sunk costs (tangible and
18
We also ...nd highly statistically signi...cant relationships in the 1987 and 1992 cross-sections.
19
intangible) across the two groups.19 Also, the inclusion of the capital/sales variable
makes no signi...cant di¤erence in the estimated coe¢ cients of RENi , DEPi , and
RESi .
We have employed in uence diagnostic techniques to identify observations that
could be considered as outliers with respect to the true underlying regression model
or observations that exert a strong in uence on the position of the ...tted regression.
Our regression diagnostics rule out the possibility that our results are driven by a
few outliers.
9 Summary
The evidence that is presented in this paper indicates that increased market con-
testability, as signi...ed by low sunk costs, tends to reduce the dispersion of ...rm
sizes.
One of the key predictions of the theory of contestable markets is that market
forces under contestability would tend to render any ine¢ cient organization of the
industry unsustainable, and consequently, tighten the distribution of ...rms around
the optimum. The extent to which an industry is contestable depends on the
sunkenness of the capital that it employs.20 Thus sunk costs should give rise to an
important non-stochastic component in the forces determining size inequalities.21
Other theoretical models also suggest that sunk costs are an important dimension
of barriers to entry and have important e¤ects on market structure. The empirical
testing of these predictions, however, has been hindered by the lack of industry-level,
and especially ...rm-level, data on sunk costs.
We employ industry-level data to construct meaningful proxies for sunkenness
and thus directly to quantify contestability. These proxies are based on reported
measures of the intensities of the second-hand and lease markets for the industry' s
capital and the rate at which that capital depreciates. We ...nd that the stronger is
the resale market for the capital employed in a given industry, the easier it is to lease
such capital; and the more rapidly that it depreciates (i.e., the lower is sunkenness),
19
We ...rst used A=S (advertising-to-sales) ratio of .01 as the cuto¤ point in separating the sample.
We subsequently employed the Chow test to test for the equality of coe¢ cients across the two sub-
samples in (15), (18), (20), and (21). For example, for the 1982 cross section with A=S included in
:95
the right-hand side of (15), the Chow F = :21 < F4;242 = 2:41; and the probability level at which
the F-test rejects the equality of coe¢ cients across the two sub-samples is .93; similarly, in (18) the
:95
Chow F = :33 < F4;242 = 2:41; and the probability level at which the F-test rejects the equality of
coe¢ cients is .85.
20
We have employed the estimated values of c1 ; c2 , and c3 in (18) to construct an index of
sunkenness for the 4-digit U.S. manufacturing industries. This ranking of sunkenness is available
from the authors upon request.
21
Cabral (1995) examines the role of sunk costs in the context of a theoretical model analyzing
the relationship between ...rm growth and ...rm size.
20
the smaller is ...rm size dispersion within the industry. These ...ndings are robust
to alternative measures of ...rm size dispersion, the time period chosen, estimation
procedures, and functional speci...cation. Both tangible and intangible sunk costs
have a statistically signi...cant inuence on the size distribution of ...rms.
This paper provides indirect support for one of the most fundamental welfare
properties of contestable markets: the absence of any sort of ine¢ ciency in produc-
tion in industry equilibrium. Incumbents whose outputs di¤er substantially from
the minimum scale of operation cannot withstand the pressure of potential entrants
who, in the presence of low sunk costs, can e¤ectively exploit the opportunities of-
fered by the presence of ine¢ ciency and waste in production through hit-and-run
entry. Thus the forces of contestability, facilitated by low sunk costs, continuously
work to weed out ine¢ cient ...rms through a process of "creative destruction". Our
...ndings provide speci...c guidance for the design of appropriate public policies to-
wards investment and changes in regulatory regimes to enhance the contestability
of markets. Accelerated depreciation policies, favorable tax treatment of leasing
operations, and the removal of regulatory restrictions on the types of capital (e.g.,
new versus used) deployed by entrants are some obvious candidates.22
Acknowledgements We are indebted to William Baumol, Christine Kessides,
Dennis Mueller, Mike Toman, two anonymous referees, and the General Editor for
their very helpful comments. Any remaining errors are our own.
Appendix
Our sample consists of all 4-digit U.S. manufacturing industries for which a complete
set of variables could be obtained. Since the estimation of our basic equation entails
a logarithmic transformation, some industries were eliminated because of zero values
of the RES variable.23 Industries were also excluded because: they were badly
de...ned; their data were not comparable to prior years due to changes in industry
classi...cation; data on DEP and RES were not available, or did not meet census
publication standards. Our ...nal sample consisted of: 400 industries in 1982, 430
in 1987, and 367 in 1992. In the pooled data, we eliminated those industries that
do not appear in all three (1982, 1987, and 1992) census years. The ...nal sample
consisted of 828 observations.
22
For example, two decades ago, entrants into ocean shipping in Peru were required to employ
new rather than used vessels if they were to be accorded a national carrier status.
23
However, under a linear speci...cation where such zero values are permitted, their exclusion does
not appear to introduce a bias.
21
Summary Statistics
1982 1987 1992
Variable Mean Std Dev Mean Std Dev Mean Std Dev
DEP :07 :02 :08 :02 :08 :02
REN :03 :02 :03 :02 :04 :03
RES :11 :11 :10 :07 :09 :05
A
:09 :11 :08 :10 :06 :09
K
V (s) 13:71 23:63 13:11 21:77 11:37 15:84
4
C4 37:86 18:39 37:27 19:03 37:03 18:06
N
Spearman Correlation
Correlation between 1982 and 1987 1987 and 1992 1982 and 1992
DEP :66 :59 :50
REN :89 :90 :84
RES :22 :43 :25
A
:90 :56 :57
K
V (s) :93 :94 :88
4
C4 :93 :95 :90
N
Number of observations=400 in 1982, 430 in 1987, 367 in 1992
A
(for : 274 in 1982, 320 in 1987, 283 in 1992)
K
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