TESTING THE DIFFERENTIAL EFFICIENCY HYPOTHESIS
by
Richard Schmalensee
SSM WP#1628-85
February 1985
Testing The Differential
Efficiency Hypothesis
Richard Schmalensee
Sloan School of Management
Massachusetts Institute of Technology
ABSTRACT
The predictions of collusion- and efficiency-based static
equilibrium explanations of inter-industry profitability
differences are developed and tested using intra-industry
data on 70 US Internal Revenue Service minor manufacturing
industries in 1963 and 1972.
The 1963 data
favor
collusion-based models, while the 1972 estimates are
Patterns
of
with
both
paradigms.
inconsistent
profitability are radically different (in complex ways
apparently unrelated to cyclical forces or the Phase II
These findings call
price controls) in these two years.
into question the value of single-year inter-industry
studies and suggest the potential importance of panel data
and dynamic disequilibrium models in industrial economics.
February 1985
_1_11_11_
I. Introduction
Since
the
positive,
pioneering
work
of Joe Bain
(1951),
the
existence
of
a
but typically weak correlation between concentration and accounting
measures
of profitability has been accepted as an important stylized fact
industrial
economics.
universally
Until
rationalized
relatively
recently,
this
by means of the Differential
fact
was
Collusion
of
almost
Hyeothesis
(DCH):
Industries differ in the effectiveness with which sellers are able
to limit competition by tacit or explicit collusion.
Collusion is
more likely to be effective, and profitability is more likely to be
above competitive levels, the higher are concentration and barriers
to entry (as defined by Bain (1956)).
This
hypothesis
has inspired a multitude of cross-section
industry-level
other
measures
factors
various
(1980,
thought
measures
ch.
of concentration,
relating
of conditions of entry,
likely to affect the effectiveness
of industry profitability.
of
and
of
collusion
to
(See Weiss (1974)
9) for overviews of this literature.)
produced results broadly consistent with the DCH,
generally
studies
and
Scherer
Most of these efforts have
with statstical
weaknesses
rationalized in terms of the difficulty of measuring key
variables
(especially conditions of entry) with great precision.
A
decade
explanation
ago,
of
the
Harold
Demsetz (1973,
positive
1974)
correlation
proposed
between
an
alternative
concentration
and
profitability, the Differential Efficiency Hypothesis (DEH):
Effective collusion is rare; effective tacit collusion is virtually
nonexistent.
Industries differ in the importance of long-lived
efficiency differences among sellers.
Where these differences are
unimportant, concentration and accounting profitability will
be
low.
Where efficiency differences are important,
the most
efficient firms will grow large relative to their rivals and will
earn
Ricardian
rents based on their
lower
costs.
Both
concentration and profitability will thus be high in such cases.
If
this
cartel
hypothesis is correct,
arrangements
seller behavior in the absence
can be analyzed using
competitive
or
of
explicit
non-cooperative
- 2 -
models,
issues
elements
of
of
entry
barriers and entry deterrence do
not
arise,
market structure central to DCH-based analysis can be
and
ignored.,
The DEH also implies that antitrust should abandon its historic, DCH-supported
concern
with
market structure and limit itself to prosecution
of
collusive
behavior.
The
present
study
examines the consistency of
these
hypotheses
Demsetz (1973,
intra-industry profitability differences in US manufacturing.
1974)
conducted
the first empirical examination of this sort.
followed by a host of subsequent authors,
Pugel
with
He has
including Carter (1978),
been
Caves and
(1980), Clarke, Davies, and Waterson (1984), Daskin (1983), Long (1982),
Porter (1979), Round (1975), Ravenscraft (1983), and Schmalensee (1985).2
strategy in much of this work,
on
the
inter-industry
parameters
share.
of
which is also employed here, has been to focus
relation between
industry-specific
(Scherer
(1980,
ch.
The
seller
concentration
and
distributions of profitability
9),
Brozen (1982),
various
and
and Daskin (1983)
market
provide
contrasting summaries of this literature.)
Most
previous
have
not
employed formal models of industry behavior under alternative hypotheses.
As
a consequence,
in
clarify
comparisons of the DEH and the
DCH
it is often unclear whether the empirical results obtained are
consistent with one,
begin
empirical
Section
both,
or neither of these hypotheses.
Accordingly,
II by analyzing simple equilibrium models that
the intra-industry and inter-industry implications of
and a hybrid hypothesis combining the key features of both.
this
analysis
is
not
to
develop a
full-blown
determinants of accounting profitability.
would
argue,
testable
more
realistic):
to
structural
serve
to
DEH,
the
the
DCH,
The goal of
model
of
the
The aim is less ambitious (and,
use simple models to
predictions of these alternative world-views.
I
identify
I
critical
I am concerned
here
- 3 -
with empirical regularities and stylized facts, not structural coefficients.
III describes the data used in this study.
Section
are examined in 1963 and 1972,
The same
two cyclically comparable years.
industries
This design
was chosen to permit both evaluation of the stability of key relationships and
analysis of industry-level changes over time.
Section IV presents the results
taking explicit account
of estimating intra-industry profitability relations,
both
the aggregation of firms into size classes
of
Revenue
data
Service)
employed
and
of
in
the
(U.S.
Internal
patterns
plausible
of
heteroscedasticity.
Section
1972
of
V
the
presents the results of inter-industry analyses for 1963
levels
of key
parameters,
industry-specific
along
with
and
an
evaluation of the consistency of the DEH and the DCH with the main features of
these
data.
Intra-industry estimates are explicitly treated as measuring the
Section VI
employs
estimation technique to describes the pattern of parameter
changes
unknown industry-level parameters of interest with error.
the
same
1963 and 1972,
between
and Section VII summarizes the main findings of
this
study and their implications for future research.
IiImEglications of Alternative- Hvotheses
Two
model
central features of the DEH,
designed
to
reveal
which should be present in any
the implications
of
that
hypothesis,
formal
are
of market shares on efficiency differences and the independence of
dependence
seller behavior and market concentration.
In contrast,
a central feature of
I also
the DCH is the dependence of seller behavior on market concentration.
take as a central feature of what I term the
relation
pure' DCH the lack of a
between market share and differential efficiency within
-_-._11^-1(--11-I-
-.-
random
shocks
are stressed as sources
general
industries.
mergers, historical accidents,
In at least some textbook versions of the DCH,
and
the
of
concentration,
rather
than
- 4 -
differential efficiency or,
(See,
for
deriving
except for very small firms,
for
that
equation.
The
I begin
simple
by
intra-
I then explore the implications of the pure
Section concludes with
of a hybrid DEH/DCH model,
implications
4).)
implications of the DEH for the parameters of a
the
industry profitability equation.
DCH
ch.
the discussion in Scherer (1980,
instance,
economies of scale.
an
in which shares
of
analysis
reflect
the
efficiency
differences and concentration facilitates collusion.
A. The Pure DEH
This relation between market share and differential efficiency under
is
DEH
basically
relation,
capacity has been expanded or modified.
implications
that
long-run
an
since
efficiency-enhancing
full impact on the innovator's market share is usually not
innovation's
until
a
of the DEH,
the
felt
To explore the inter-industry
it is thus natural to focus on long-run
reflect the presence of efficiency differences.
Moreover,
equilibria
while
one
cannot expect all industries in any data set to be in long-run equilibrium, it
seems reasonable in the absence of a suitable dynamic theory of disequilibrium
to treat deviations from long-run equilibrium as random in cross-section data.
This is,
of course,
the standard practice in the cross-section literature in
industrial economics.
I thus consider an industry in long-run equilibrium in which N firms sell
a homogeneous product.
and
hence
economies
face
have
Suppose that all have attained minimum efficient scale
constant long-run average costs.
(Most
studies
concluded that firms generally need relatively
shares to be in this position;
see Scherer (1980,
...
I co,
with at least one inequality strict,
scale
market
small
ch. 4) for a survey.)
Let
so that c
c2
is firm i's
unit
there be long-lived efficiency differences among these firms,
C
of
where c
cost.
3
Unit cost should not be interpreted in narrow process efficiency terms
here.
A
firm
with a superior product may simply be more efficient
the
production
of
market.
While
differentiation
sensibly
minor
Lancastrian characteristics it supplies
major
and
product
create
innovations
something approaching a
as simply reducing costs,
modeled
differences
that
to
an
yield
new
in
the
existing
substantial
market
cannot
be
it seems reasonable to think
of
among products in cost/efficiency terms
for
purposes
of
formal analysis of profitability.
Adoption of the DEH as a working assumption rules out collusive behavior.
But
I
do not think that as a logical matter it requires
behavior.
pure
price-taking
Firms with large shares of industry capacity or output should
not
simply be assumed to ignore the effects of their actions on market price.
It
seems
uch
more
cooperative
plausible
behavior,
to
under
begin with
which
the
equilibria,
variable.
This
assumption
each fire simply makes
profitable) response to its rivals' actions.
run
basic
its
of
non-
best
(most
As we are concerned with
long-
investment in productive capacity becomes a central decision
is in effect an output choice,
equilibria are the most relevant.
which suggests
More formally,
that
Cournot
Kreps and Scheinkman (1983)
have recently shown that non-cooperative capacity decisions,
followed by non-
cooperative (Bertrand) price competition yield Cournot outcomes.
Accordingly,
let
us
explore the implications of the DEH
Cournot equilibria with cost differences.
behavioral
identically;
assumption
that
here is that all
by
examining
(As is noted below, the fundamental
firms,
behavior need not be Cournot).
in
all
industries,
behave
The economic profit of
a
typical fire is given by
i =
P(q+4q)
where P is market price,
P(Q) is
- c]q
1,
the inverse demand function, and q
(1)
Q - q,
- 6 -
Firm i's first-order condition, with
is the total output of firm i's rivals.
rivals' output treated as exogenous, can be written as follows:
(P - c)
=
(2)
ePq1 /Q,
elasticity
E -1/[(aQ/8P)(P/Q)] is the reciprocal of the industry
where
demand.
Multiplication
If
equilibrium.
(2)
of
firm
i
by q
employs
yields firm i's
assets
worth
K*,
economic
and
if
profit
the
of
in
normal,
rate of return on invested capital relevant to the industry is p,
competitive
firm i's accounting profit is given by
ira
Finally,
its
letting
revenue/capital
=
(3)
K1 + e(q/Q) (Pq).
si
Pq±/KI
q/Q be firm i's market share and v
ratio,
can divide (3) by K
one
to
obtain
a
be
simple
equation involving the accounting rate of return on assets:
r, = A + B(sivi),
where,
under the DEH,
A =
,
(4)
the competitive rate of return, and B = e, the
reciprocal of the market elasticity of demand.
of
One can think of A as the rate
return corresponding to a zero market share.
operating
in any industry will thus generally have rates of return in
of A under the DEH.
concentration. 4
accept
investigations
While equation (4) flows directly from the DEH,
that
of
the
intra-industry
presence
variables the same units.)
Under
DEH,
excess
The size of this excess may even be positively related to
one need not
hypothesis to view (4) as a natural specification to
that
particular
The smallest firms actually
profitability
of v
gives
the
differences.
independent
and
employ
in
(Note
in
dependent
It is employed as such in what follows.
as described above,
both A and B should be positive for all
- 7 -
industries.
Further,
negatively)
with
neither parameter should be correlated (positively
seller
concentration across industries.
Under
or
the
DEH,
variations of A across industries ought mainly to reflect differences in
risk
and
in
accounting
biases,
while
variations in
elasticities.
differences
in
demand
large-firm
profitability
advantage
B
should
mainly
To obtain an alternative
that
should
be
reflect
measure
correlated
of
with
concentration,
define RA as the difference between an industry's average rate
of return,
and its intercept parameter, A.
R,
Then, using equation (4),
the
DEH implies
N
N
(E a,/E Ki) - A =
i=l
i=l
RA
where
v
(PQ/E K)
and
seller concentration.
and
it
should
H
E (s)
z
(5)
veH,
is the
Hirschman-Herfindahl
index
of
RA should be positive for all industries under the DEH,
be positively correlated with
most
concentration
measures,
especially when differences in capital intensity are controlled for.
varies across industries,
however,
Since e
one cannot expect the correlation between
RA and concentration to be particularly strong.
B. The Pure DCH
Under
what I have called the pure DCH,
by differences in efficiency.
Under this hypothesis, estimation of (4) should
still yield positive values of A.
systematically related,
have
a
mean
market shares are not determined
But,
since share and profitability are not
the distribution of B and RA across industries should
of approximately zero.
Inter-industry
differences
in
these
parameters would reflect accounting quirks and historical accidents.
There
the DCH,
is no reason why B should be correlated with
concentration
but the implications regarding A and RA are less clear.
under
On the one
-
hand,
if
barriers
industries
to
differ
-
in the importance of
mobility (Caves and Porter (1977))
barriers
entry,
but
generally
unimportant,
collusive behavior will raise the profits of all firms together.
With market
shares
A
and
positively
concentration
are
to
unrelated to efficiency
differences,
correlated with concentration in cross-section,
a
positive
correlation between RA and seller
consistent with the pure DCH.
that
small
in
On the other
concentration
is
also
To see this, suppose (following Porter (1979))
industry has two strategic groups:
and into which entry is
be
but RA (which may
be positive or negative in any particular industry) will not be.
hand,
will
free,
one in which market
shares
are
and one in which established sellers are
protected by barriers to entry and mobility.
Sellers in the first group will
earn only competitive returns, while the DCH implies that if (and only if) the
second group is concentrated,
its members will earn monopoly rents,
industry average rate of return will be supracompetitive.
If this
and
the
two-group
structure is typical, RA will be positively related to concentration in crosssection, while A will not be.
To summarize, the pure DCH predicts that
be uncorrelated with concentration,
while either A,
or RA,
will
or possibly both
will be positively correlated with concentration in cross-section.
C. A DEH/DCH Hybrid
Since
both the DEH and the DCH seem rather special,
it is important
to
investigate the implications of DEH/DCH models, in which shares are related to
differential efficiency and seller concentration facilitates collusion.
this,
I
generalize the Cournot model developed above,
using the conjectural
variation formalism to describe possible collusive equilibria.
i's conjectural derivative, 8a1 /3qi,
ri =
To do
If Xl is firm
equation (4) can written as
+ [(l+Xk)e](siv).
(6)
- 9 -
equal,
It is easy to show that all else (including rivals' total output)
the lower is firm i's output. In other words, the higher is
higher is X,
the X
X,
Under the DEH/DCH, one would
the more firm i restricts output in equilibrium.
expect
the
to be positive and to be generally larger the more concentrated
is the industry considered.
If
Xi
=
X
for
all firms in
immediately that estimation of
evH(l+X).
If,
uncorrelated
in
addition,
industry,
(4) should yield A =
equation
(6)
B = e(l+k),
,
the
implications
indistinguishable from those of the pure DEH.
this
of
and RA
and RA should be positive,
=
least
model
are
however, X
Under the DEH/DCH,
should be positively correlated with concentration across industries.
B,
implies
or at
X is constant across industries,
concentration,
with
some
Then A,
A should be independent of concentration,
and
both B and RA should be positively correlated with concentration.
There
is no strong theoretical or empirical
that the Xi are equal within industries,
have
r
version
=
(See also Long
assumption
the
Clarke and Davies (1982)
(1-s)/s1,
with a
(1982) and Clarke,
positively
Davies, and
Under this assumption, equation (6) becomes
Waterson (1984).)
This
of course.
proposed the alternative assumption X
correlated with concentration.
support for
=
Q+aevi] + [(1-c)e(sv).
(7)
of the DEH/DCH thus implies that greater
seller
concentration
should be associated with higher estimates of A and lower estimates of B.
main
rationale for the Clarke-Davies assumption appears to be that as a
The
4
1
(with rising marginal cost), the equilibrium described by (7) converges to the
maximization of total industry profit.
While total industry profit may be a plausible cartel objective
when
side
payments
are
possible,
however,
it does
not
seem
function
especially
-
when,
Moreover,
maximization
-
essentially
impossible.
of total industry profit requires small,
inefficient
such payments are
as in the U.S.,
plausible
10
firms to be the main restrictors of output,
st
Xi
and
in
imperfectly
the
and the inverse relation
Clarke-Davies assumption imposes
equilibria (i.e.,
collusive
this
OPEC,
(See
But this
those with a<l).
imperfect
Nash
within
counter
to
If, (loosely) following the
relevant cooperative and non-cooperative theory.
widely-employed
runs
Clarke-Davies assumption also
The
all
pattern
almost any recent discussion of behavioral differences
instance.5 )
for
on
pattern
seems inconsistent with most descriptions of the actual behavior of
cartels.
between
model of bargaining as a cooperative game without
side
payments, one examines the conditions for maximizing the product of the firms'
profits,
is
it
easy
show that the optimium can be
to
represented
conjectural variation equilibrium in which firms with lower costs have
thus
than
that small firms run a lower risk of detection and punishment
oligopoly
restriction.
firms if they fail to do their "fair share' of output
large
higher
it follows from Stigler's (1964) model of
On the non-cooperative side,
X's.
that a positive relation between s, and X
conclude
a
as
is
I
plausible
more
than a negative relation of the sort pos tulated by Clarke and Davies.
suppose that the DEH/DCH
To explore the implications of such a relation,
holds
for
some
industry,
so
that equation (6),
with the
addition
homoscedastic- disturbance distributed independently of the X1 and
the
correct
suppose
specification.
that v
in
employed
to
= X + Ys
so that X
the industry,
and
focus on the
Finall y,
= v for all i.
are linear in the si,
firms
To
is
concentration,
where N is the number of
1 -(1/N)],
Then if least
a bit of algebra
expectations of the estimated parameters
of
(sivi),
a
assume that the X, have mean X and
is some constant.
estimate equation (4),
influence
of
yields
the
squares
is
following
-
E(A) =
2
+ ev[YH
-E(s,)
2
E(B) = e(l+X) + eN
3
11
-
]/[NH-1],
(8a)
E(s1 )3-2NH+1]/[N(NH-1)],
(8b)
+ evH(1+X) + evY[E(s,)3 -(H/N)] - E(A),
E(RA) =
(8c)
where H = E(st) 2 , as above.
If
approximated
by
the
which is commonly treated as a workable approximation to firm size
lognormal,
it
distributions,
ch.
(1963),
of the s, can be adequately
distribution
the
2)
is
that
and
easy to show (using results from Aitcheson
expected value of E(s 1 )3
the
substitution in equations
NH 3.
is
Brown
Making
this
(8) yields
- evYH 2 ,
E(A) =
(9a)
E(B) = e(l+X) + e[YN
3 3
(9b)
H -2NH+13/[N(NH-1),
E(RA) = evH(1+X) + evYNH3 +H2 -(H/N)].
As
an
empirical matter,
concentration.
is
it
N is at best weakly
(negatively)
easy to show that the second terms on the right of (9b) and
Equations
A
though
are
is generally positive and independent
should be negijively correlated with
the
(9c)
And
/N, its lower bound.
(9) thus imply that if
concentration,
cross-section,
with
correlated
(See, for instance, Schmalensee (1977), esp. footnote 1.)
positive and increasing in H for H >
of
(9c)
correlation
may be
weak,
concentration
while
the
in
positive
correlation between concentration and both B and RA will be stronger than if
= 0.
If
is large,
A could be negative for highly concentrated industries,
but B and RA should be positive in all cases. In what follows I treat these as
the most likely outcomes under the DEH/DCH.
Equations
____·
(9) also show that negative values of
,
which I have
argued
- 12 -
are relatively implausible, will tend to induce a positive correlation between
concentration
concentration
and
and
A
and
to
weaken
the
positive
and between concentration and RA.
B
between
correlations
If
generally
is
negative and large, these latter correlations could become negative, producing
A should
be
but negative values of B and RA could be observed
in
results like those implied by equation (7).
in all cases,
positive
highly
concentrated
industries
industries.
with v and
(along
),
Since
<O is the norm,
If
e
may
vary
among
substantially
one cannot expect any of the
correlations
predicted by this hybrid DEH/DCH model to be particularly strong.
III. Data Employed
The data employed in this study cover U.S. Internal Revenue Service (IRS)
minor
which
manufacturing industries for 1963 and 1972.
Census
concentration.
of
Manufactures
data
could
be
I chose to use years
used
to
measure
for
seller
These particular Census years were selected because data
for
them were readily available, they were far enough apart in time for changes in
industry-level variables to reflect changes in their fundamental determinants,
and
because they were comparable in terms of the business cycle. 6
and 1972 were relatively prosperous years.
5.5% in both years,
Both 1963
The overall unemployment rate was
while the civilian unemployment rate was 5.7% in 1963 and
5.6%
in 1972.' Real GNP grew 4.6% during 1963 and 5.7% during 1972.
was
somewhat
higher in 1972 than in 1963:
the 6NP deflator rose
Inflation
only
1.5%
during 1963 but rose 4.9% during 1972.
Focusing on the manufacturing sector,
quite
similar.
the two years studied again appear
The Federal Reserve Board's measure of capacity
was 83.5% in both periods.
1963 and 10.4% in 1972.
utilization
Real 6NP originating in manufacturing rose 7.7% in
The corresponding implicit deflator fell 1.1% during
- 13 -
1963
and rose only 0.3% during 1972.
Almost all the inflation
that
worried
policy-makers during 1972 occurred outside the manufacturing sector.
Perhaps
operation
the
obvious
most
difference
between 1963
But there are
Phase II price controls during 1972.
of
1972
and
is
at
least
reasons for concluding that this is unimportant for the present
three
the
study.
the macroeconomic literature suggests that these controls did not have
First,
effects on the economy as a whole;
large
controls
Second, Appendix A
results of a time-series analysis indicating that the
the
reports
had
insignificant
an
effect
on
of
relation
the
This
manufacturing.
between
study,
firm
size
and
II
Third,
time-series
US
in
profitability
undertaken to test for the possibility that the
II controls were enforced mainly against leading
Phase
Phase
profits.
manufacturing
Appendix A also reports the results of a small-scale study of the
behavior
and
Dornbusch
for instance,
566-67) and the references they cite.
pp.
Fischer (1981,
see,
smaller rivals artificial competitive advantages,
firms,
their
giving
does not find 1972 to be an
outlier in any relevant sense.
Data
Revenue
by industry and by industry-specific asset size-class for
minor
Service
industries
for 1972 were mainly
obtained
Internal
from
the
Project on Industry and Company Analysis (PICA) at the Harvard Graduate School
of Business Administration. In order to reduce well-known
easurement problems
associated with very small fires and to reduce the importance of scale-related
cost
differences
(the presence of which would tend to bias
of the DEH) in the data,
favor
excluded.
industry,
In
order
to
from the sample.
broadly
defined
results
have at least four usable
2398,
2899,
size
classes
Nany of the remaining industries are
with at least some supply-side links.
for
eact
3860, and 3870) were ther
sufficiently
that they should be thought of as including several
11^_1____---.-----_~~~1.~~~-1__
In
data on fires with assets below $500,000 were
five IRS industries (2380,
dropped
our
A final industry (3990,
markets
miscellaneous
- 14 -
manufactured
dropped
except ordinance,
manufacturing not
allocable)
because the markets it included seemed unlikely to be at all
linked.
least
products,
Our final sample consisted of 70 IRS minor industries,
four
usable size classes.
was
closely
each with at
The maximum number of usable
classes
was
eight; the mean number was 6.8.
for 1963 IRS industries was provided by Allan J.
Data
from the
Daskin,
data
set assembled for use in his dissertation (Daskin (1983)).
were
aggregated
(size-class by size-class) to conform to the
These
1972
data
industry
All
following the 1968 IRS Sourcebook of Statistics of Income.
definitions,
1963 industries had between five and nine usable size classes,
with a mean of
8.3 classes per industry.
For
each size-class for each industry,
total assets,
The
ratio
I compiled the number of
pre-tax profits plus interest payments,
the
distorting
taxation.
of
and business receipts.
of total pre-tax returns (profits plus interest) to
employed was used as the accounting rate of return,
effects
of
differences in
r.
leverage
firms,
total
assets
This measure
avoids
and
effective
income
(Daskin (1983) reports that the effects in this context of the use
returns
after-tax
profitability,
r
is
are
negligible.)
inherently
Like
imprecise.
all
The
accounting
measures
inter-industry
of
equations
discussed below include controls (crude ones, to be sure) for some frequentlydiscussed accounting biases.
one
should
anything
expect
more
the
More importantly,
however, it is not clear why
most obvious infirmities of accounting
than add noise to our estimates.
In particular,
data
it
to
is
obvious why accounting biases should be correlated with concentration in
a
way
as
Similarly,
to produced biased estimates of
key
cross-section
do
not
such
coefficients.
the conglomerate merger wave of the late 1960's undoubtedly serves
to lower the quality of the 1972 data,
but it is not clear why it should bias
-
15
-
estimates of relations involving concentration.
The
following
variables were computed for each IRS minor
manufacturing
industry in 1963 and 1972:
= Ratio of pre-tax profits plus interest payments to total assets
for all firms with assets above $500,000
R
CONC = Weighted average, using value-added weights, of four-firm
concentration ratios of constituent 4-digit Census industries.
AD/K = Ratio of advertising outlays to total assets.
PQ/K = Ratio of business receipts to total assets.
DDUR = 1 - DNDR = 1 for durable goods industries, zero otherwise.
DCON = 1 - DPRO = 1 for consumer goods industries, zero otherwise.
standard deviations, and inter-year correlations of the first four
The means,
of
these
variables
are
shown in Table
1.
Those
figures
seem
generally
consistent with the presumption that 1963 and 1972 are comparable years.
They
also indicate that dramatic changes between these years were relatively rare.@
correlations between R and the corresponding industry-wide rates
The
return were above .99
in both years.
multiple markets,
including
If one thinks of IRS minor industries as
also
be computed using (net)
asset
seemed the closest readily available substitute.
The correlations between AD/K,
Thus CONC should
weights
value-added
The advertising-sales ratio,
which seems slightly preferable because it has
the same units as the other variables,
is
also
the
both
correction
__II__IDEl____1-__
and AD/PD exceeded .96 in both
more natural variable to use as a
advertising-related accounting biases;
serves
weights;
as
is often treated as a proxy for product differentiation under the DCH.
AD/PQ,
AD/K
of
observed rates of return must be thought
asset-weighted averages of rates of return in those markets.
ideally
of
rough
see Demsetz (1979).
for
correction
The variable PQ/K
to control for differences in capital intensity and as
for accounting biases in asset valuation during inflation.
_-
years.
a
rough
I
do
-
16
-
not attempt to provide structural interpretations of the coefficients of
and
PQ/K;
these
variables
are included
as controls
and
for
AD/K
descriptive
purposes.
Similarly,
in
the interests of providing an adequate description of the
it seemed desirable to examine differences between industries producing
data,
nondurable goods and between industries producing
and
durable
between
the
along with 1963 value-added weights and
digit Census industries in 1967,
1963 and 1972 IRS definitions to classify the
sample
Seventeen of the 70 industries in the
sample
along these lines.
industries
and
I used Ornstein's (1977, Appendix B) classification of four-
producer goods.
correspondence
consumer
were found to produce mainly durable goods, and 22 were classified as consumer
goods industries by this procedure.'
IV._ Intra-Industry_Estimation
In order to compare values of A,
(4)
must
be
estimated
B,
and RA across industries,
for each industry in the
sample.
This
the data are for groups of firms within asset-based size-classes.
seems
to
have
is
not
a
since (4) relates to individual firms, while
completely straightforward task,
(1983)
equation
recognized that one cannot obtain
Only Daskin
unbiased
or
even
consistent estimates by simply substituting size-class averages into equations
He dealt with the problem by estimating an intra-industry equation
like (4).
linear
in profits and assets,
bias.
Unfortunately, it is
for which there is no problem
of
aggregation
difficult to interpret the parameters of Daskin's
equation in terms of the hypotheses of interest here.
The
class
approach taken in this study is to aggregate (4) from firm to
data
explicitly
and
to
unobservable
quantities
(defined
substitute
below)
consistent
that appear as
estimates
a
size-
of
consequence
the
of
- 17 -
Suppose it
class c in some industry.
size
Consider
aggregation.
ci" denote the it h firm in class c.
firms, and let the subscript
Nc
has
Multiplying
equation (4) by the firem's total assets and adding a disturbance term yields
a,
+ BP(q,)2 + c,i.
= AK ,
(10)
by
The basic equation for size-class average rates of return is then obtained
summing over the firms in class c and dividing by total assets in the class:
r=
-
N,
N=
E a=,/S K,
i=1
i=1
a/K= = A + B(4f=9v.) + u.
(11)
The new variables in this equation are defined as follows:
N,
f,
- N,
N,
(q,)2/(
N=
q)2
N
(q,)2/(q,)z
(12a)
(12b)
-(q=/N=)/Q,
s9
vc
=
u
-
(12c)
Pqc/Kc,
Nc
(12d)
E zc,/Kc.
i=1
The unobservable quantity f
c have the same sales.
variance
of
the
equals one if and only if all firms in size class
In general f
equals one plus the ratio of the sample
qci to the square of their sample
mean.
It
thus
is
an
indicator of the importance of intra-class differences in market share.
In
order to handle the unobservability of the f,
I assume that
class differences in assets are as important as those in sales:
intra-
-
-
18
N,
N.
E (K
i=l1
) 2 /(K)
2.
(13)
This assumption is needed here because size-class boundaries relate to assets,
not
A' sufficient
sales.
satisfied
(but
not necessary) condition
is that within a given industry,
the same revenue/capital ratio.
K.,
on
Given (13),
the f
alternative
be
N.,
The procedure employed is based
density function linear in assets.
approach
to
are estimated using
assumption that assets of firms within each class are
class-specific
(13)
all firms in each size class have
and the values of size-class boundaries.
the
for
drawn
from
a
Details are given (and an
based on the lognormal distribution
is
discussed)
in
Appendix B.
A
second
problem
in
estimating
(11) with
size-class
data
aggregation may produce differences in the variances of the u.
possible
heteroscedasticity
among the u
within industries,
is
To deal with
I
employ
bounding assumptions about the distribution of the s.c in
Perhaps
most natural of these is that the standard deviation of
equal
to
aK_
for all i and c,
where
is an
Under this assumption, the variance of u
industry-specific
two
(10:).
alternative,
the
that
ec
is
constant.
is given by
N.
2(U.)
=
02
E
(K,)
2
/(Kc)
2
= a2 (f /N,).
(14)
i=1
Division
of
(11)
by (f¢/N)
1 2
'
yields what is referred to below as
the
CRS
estimating equation, because it embodies the assumption of stochastic constant
returns to scale:
r (N /f,)'
s
The variance of $g is
= A(N./f.)' 2 + B[s,v,(f,N,)'23
2
+
$,.
(15)
for all classes in a given industry if (14) holds.
-
The
section
CRS
literature
19
-
on the effects of scale on the
cross-
(K1 )-1
of
overviews
/2
(See
.
Prais (1976,
of this literature.)
e.c is generally equal to
specification
the
These studies generally find that the standard deviation
of rates of return declines with firm size,
CRS
and
variability of firms' rates of return suggests an alternative to
specification.
that
time-series
pp.
92-98) and
Daskin
than
(1983)
for
This suggests that the standard deviation
where
a(Kc~)b,
assumes
with the decline less rapid
= 1.
b
X
is as before and 1/2
Since b is unknown and
may
of
1.
The
vary
from
industry to industry and from year to year, I deal with the possibility that b
is
less than unity by exploring the implications of the alternative
assumption b = 1/2.
Under this assumption the variance of u
o 2(uC)
Division
of
(11)
bounding
is simply
= a2/K.
by
(16)
(K=) -'' 2 yields the
IRS
estimating
equation,
which
embodies the assumption of stochastic increasing returns to scale:
re(K)
The
statistics
with
given
explanatory. 1 0
estimates
1963
under
1963,
Perhaps
while
the
obtained
by
and 1972 data are
the
heading
+
(17)
c.
employing
summarized
'Sample
Those statistics indicate that
positive in both years,
both years.
+ BS9v.fc(K=) ' / 23
2 = A(Kc) 1/'
parameter
specifications
are
/
the
CRS
in
Table
Coefficients'
and
IRS
2.
The
are
essentially all estimates of A
while estimates of B and RA have both
The majority of estimates of B (59X)
signs
striking
feature of this Table is
between the 1963 and 1972 estimates.
in
and RA (56%) are positive in
negative values (66Z of B's and 69% RA's) are the rule in
most
self-
the
sharp
1972.
difference
Table 1 shows that on average R (= RA
+
A) changed little between these years, but Table 2 reveals that A rose broadly
and substantially, while B and RA generally fell.
_1_________111____1-11_--
- 20 -
are
The
first
two statistics given
the
significance levels obtained in standard X2 tests of
null hypotheses.
indicate
that
under the heading
Probability
the
Levels"
indicated
Except for estimates of B under the CRS specification, these
the null hypotheses that the underlying
parameters
or
their
1963-1972
changes are the same across industries can be confidently rejected.
That
the
is,
intra-industry estimates of the coefficients of
equation
(4)
provide information on what seem to be real inter-industry differences.
The
statistics
under
the heading
Population
Estimates"
in
Table
2
provide summary information on the importance of those differences. Following,
for instance,
Swamy (1970,
esp.
parameter, pj, for industry j,
+
bj=
==
if
Sect 5),
b
is the estimate of some true
one can write
+ v
+
(18)
Here qj is the sampling error associated with b.
can
be
treated
standard
error
population
as
of
from
It is unobservable, but it
having mean zero and standard
b5 ,
which we denote
(qj).
which the pj are drawn,
deviation
If p is
so that the v
equal
to
the
mean
of
the
the
have mean
zero,
an
unbiased estimator of the variance of the population distribution of the p
is
given by
N
¢2(v) =
M
- 6) 2/(M-1) -
E (b
j=1
where
E
Given
a2 (v),
(19)
j=1
is the sample mean of the b,
estimate of
E o2 (qj)/M,
and M is the
the precision-weighted average of the b
number
of
provides an
industries.
efficient
:
=
N
£ bj/tE
j=1
2
(v)+a 2 (qS)]}/
H
E {1/o
j=1
2
(v)+ff2(R)]}.
(20)
- 21 -
A
comparison
of
p with its
large-sample
variance,
l/E{l/o
2
(v)+
2
(q)]},
yields a large-sample X2 test of the null hypothesis that the population
of the p
mean
is zero.
The
statistics
computed
using
equations
- (20)
(18)
reinforce
impression of considerable inter-industry variation in underlying
Population
standard
deviations
especially
for RA and B.
appear large relative to
(Equation (19)
the
parameters.
population
means,
(v)
yielded a negative estimate of
for B under the CRS specification, reflecting the large standard errors of the
corresponding
from zero,
parameter
estimates.)
Population means
differ
significantly
and the changes in estimated values between 1963 and 1972 seem
to
reflect real changes in underlying population distributions.
I
the
postpone discussion of the consistency of the results in Table 2
with
models of Section II until after an examination of the key inter-industry
correlations identified by those models.
V. Inter-Industry Estimation:
In
order
efficiently,
from
to estimate cross-section relations involving
one
must
8
B,
A,
take explicit account of the fact that the
intra-industry regressions measure the true underlying
error.
and
Levels
and
RA
estimates
parameters
with
If pj is the true value of some such parameter for industry j, and Zj
are
vectors
of industry-specific explanatory
industry coefficients,
variables
and
inter-
respectively, a typical inter-industry equation can be
written as follows:
bj =
The
gj
variance
and
j,+
, = Z'6
+ (
+
).
the Aj are assumed to be independent.
2(4),21
the
(21)
If the
variance of the jth error term in
gj
have
equation
common
(21)
is
- 22 -
[a
2
2
(t)+a
Since
(j,)].
of
application
differ
the sampling variances of the b
ordinary
least
squares
to
would
(21)
in
yield
general,
inefficient
estimates of 6.
This
Saxonhouse
problem
has been treated in general terms by Hanushek
(1974)
and
(1977);
Long (1982) and Daskin (1983) have previously allowed
for
source
this
of
heteroscedasticity
of the b
errors
obtained
by
applying
division
by
the
different
can be treated as known,
of
sensitive to the estimate of
approach
to
presented
the
and because estimates of
2(t)
estimation
often
employed,
the
yield
are in
details
can
or
be
after
rather
many
I used an iterative
of that variance,
obtain
Since the
2(t).
estimates
such
Because these two regressions
2(t)
to
either as it stands
least squares to (21),
(qj).
estimates
order
, one needs a consistent estimate of
efficient estimates of
standard
In
in this context.
cases
fixed-point
of
which
are
Weighted least squares estimation was then used to
in Appendix C.
obtain efficient estimates of &.
presents weighted least squares estimates of the
3
Table
relation between concentration and A,
estimates
of
Model"
capital
terms,
labeled
in
relation
and RA.
For comparison
between between concentration
which CONC is the only independent variable,
the
and
R
are
while
in
the
variables AD/K and PQ/K are added to control for advertising
intensity
which
differences.
All equations estimated
are of little interest and hence are
'Pooled'
corresponding
Since
also
not
the
CRS
reported.
Equations
regressions
(In no case could the
and IRS parameter estimates
and
intercept
were estimated by simply stacking the weighted
to the CRS and IRS specification.
"Full
included
hypothesis of coefficient identity be rejected at any reasonable
level.)
purposes,
statistics labeled "Basic Model' refer to a simple bivariate
The
presented.
model
the
B,
cross-section
cannot
null
significance
be
considered
- 23 -
independent,
the 'Pooled" estimates have no claim to optimality.
They merely
provide convenient summary information.
The first measure of goodness of fit
the
R2
R2 -Wtd.,
presented in Table 3,
statistic of the weighted regression used to estimate
8.
A
is
second
measure, R2 -Raw, is the square of the correlation between predicted and actual
values of b.
zero
and
The second measure can be negative; the first must lie between
one.
involving
A,
differences
Chow
B,
or
tests for coefficient stability
RA
provided no evidence
of
applied
to
significant
equations
coefficient
between durable goods and nondurable goods industries or
between
consumer goods industries and producer goods industries.1 2
The
tests
Prob. Level' statistics in Table 3 are the significance levels of F-
with
intercepts
These
generally cast appreciable doubt on this
not only do the average values of A,
1972,
but
and
1972,
allowed to differ in light of the results shown in Table
statistics
That is,
and
the null hypotheses of equal slope coefficients in 1963
of
their
correlations with
B,
null
2.
hypothesis.
and RA differ between 1963
concentration
and
other
industry
characteristics (themselves relatively stable, as Table 1 indicates) appear to
differ
as
well.
The
instability detected in Table 2 is
apparently
quite
fundamental.
Coefficient
instability
is
most
clearly present in
equations involving R, industry-level profitability.
for
1963
.20
1972
there
that
inflationary
is
with
the
in
the estimated coefficients imply that an increase in
no visible
relation at all between
the
concentration
to .85 would raise R by only about one standard deviation.
consistent
data)
3
Estimates of both Models
yield the traditional weak positive relation between
and profitability;
from
Table
CONC
and
R.
CONC
But
in
This
is
eiss's (1974) observation (based on studies using pre-1970's
concentration/profitability
periods,
though
relation
tends
(as was noted in Section III)
to
the
weaken
n
inflation
- 24 -
rate
in manufacturing was only 1.3 percentage points higher in 1972
1963.
The
implications
statistics
in
of the instability revealed in the first
than
in
column
of
Table 3 for the reliability of conclusions drawn from
single-
year cross-section studies are obvious and depressing.
The remaining regressions in Table 3, none of which have such explanatory
indicate that the relations between concentration and A, B, and RA are
power,
On the other hand,
also likely to differ between the two years studied.
Basic
generally
Full Models and the CRS and IRS specifications
and
the
produce
Since the DEH and the DCH predict only the existence
very similar estimates.
of statistically weak relations (because of inter-industry variation in E),
is
appropriate
to
looser than usual
With this in mind,
of
positively
correlated with concentration in 1963.
negatively
correlated
non-zero
and
relation.
standards
hypotheses
concentration
no
apply
with
concentration,
B appears to be positive.
correlation
A
for
RA
and
In 1972,
while
the
it
null
rejecting
to
be
A appears to
be
appear
correlation
between
There is not a hint here of
between B and concentration in 1963 or between
RA
a
and
concentration in 1972.
Table 4 summarizes the implications of the DEH,
developed
in
Section II,
from Tables 2 and 3.
a
the
DCH,
concentration,
the
along with the corresponding statistical
Consider first the findings for 1963.
positive relation between A and concentration,
pure
DEH
and
is
the DCH, and the DEH/DCH
findings
The evidence for
which is predicted only
as strong as that for a similar relation between
RA
which is consistent with all three hypotheses and required
the DEH/DCH.
The DEH/DCH prediction of
a
between B and concentration receives absolutely no support.
positive
by
and
by
relation
The correlations
with concentration in 1963 thus tend to favor the DCH as against the other two
hypotheses.
- 25 -
Similarly,
RA
the DEH and the DEH/DCH both predict positive values of B and
in all industries,
but the 1963 estimates imply that these parameters are
nearly as likely to be negative as positive.
population
zero,
distributions of both parameters are significantly different
they
estimated
are
small
population
only with the DCH.
previous
While the estimates means of the
authors,
both absolutely and
relative
standard deviations.
to
the
corresponding
This pattern appears
consistent
Results similar to these have been reported by a host
including
Caves and
Pugel
(1980),
Clark,
Davies,
Waterson (1984), Comanor and Wilson (1974), Daskin (1983), Long(1982),
(1969),
and
Porter
from
(1979),
of
and
Marcus
using a variety of specifications and data sets.
It is clear from this literature as well as from Table 2 that one cannot treat
the
positive intra-industry relation between profitability and
predicted
by
manufacturing.
the
DEH
and
the
DEH/DCH
as
a
stylized
market
fact
share
in
1
While the 1963 data thus favor the DCH over the DEH and the DEH/DCH,
results
obtained
hypotheses.
US
for
Negative
1972
are
basically
inconsistent
values of B and RA are the norm;
with
the null
all
the
three
hypotheses
that the corresponding population means are zero are decisively rejected.
The
estimated population mean of B is small relative to the corresponding standard
deviation,
however,
so that the estimated distribution of B could perhaps be
described as approximately symmetric around zero and thus consistent with
DCH.
the
But the statistics for RA describe a distribution with most of its mass
below zero, and this is consistent with none of the three hypotheses.
Similarly,
concentration
would
be
the
clear
lack
of a positive correlation
between
RA
in 1972 is inconsistent with both the DEH and the DEH/DCH.
consistent
with
the
DCH
concentration were positive, but it is
if
the
negative.
correlation
between
A
and
It
and
The correlations involving A
and B are consistent with the DEH/DCH, but that hypothesis predicts a positive
-
26
relation between concentration and RA,
short,
the
-
and no such relation is
present.
In
pattern of correlations observed for 1972 is consistent with none
of the three static equilibrium hypotheses considered here.
Perhaps the most disturbing aspect of the findings summarized in Table
4
is the striking difference between the 1963 and 1972 estimates for identically
defined
implicit
single-year cross-section work
in
industrial
The
economics.
weaknesses
the static equilibrium approach on which standard versions of both the DEH
and the DCH rest.
to
in
obtained here may well signal the presence of fundamental
results
in
This difference casts doubt on the stability assumption
industries.
Except in periods of unusual stability, it may be necessary
model deviations from long-run equilibrium explicitly in order to
the
main
patterns
differences.
Panel
of
intra-industry
and
inter-industry
explain
profitability
data seem necessary to provide tests of such models with
adequate power.
VI. Inter-Industry Estimation: Chanqes
I had originally intended to estimate a variety of dynamic specifications
using
data
relations
from
1963
between
and 1972 to
changes
parameters analyzed in Table 3.
B's
1972
in
test
some
concentration
(For instance,
DEH-based
hypotheses
and
industry-specific
the
about
industries with above-average
in 1963 might be expected to have become more concentrated on average
as
reflected
leading
in
firms expanded to exploit cost
market
presented in Table 3,
share.)
The
evidence
advantages
of
not
coefficient
the dramatic changes in the distributions of
shown in Table 2,
yet
fully
instability
industry-
and the results of a few attempts
specific
parameters
estimate
dynamic models indicate that the stationarity
conditions
for such an exercise to be sensible are simply not satisfied here.
by
to
necessary
- 27 -
The pattern of changes in A,
B,
and RA across industries over the nine-
year period between 1963 and 1972 is nonetheless of some interest.
Tables
5
6 present simple descriptive estimates of the Basic and Full models using
and
parameter changes as dependent variables and average values of CONC, AD/K, and
PQ/K
as
quantities
these
experiments
clear the futility of trying to associate changes in A,
B,
or RA
relations
No
and
industries
however,
real
to
good
of
for
differences
industries
across
stability
sub-sets
consumer
between
encountered.
was
unstable between durable
be
goods
and
Surprisingly,
the
goods
nondurable
I have no supportable explanation for this basic finding or
related details discussed below;
of
goods
showed most versions of the Full Model (but not of
tests
Model)
checked
evidence
producer
Chow
industries.
were
with
The presentation follows that in Table 3.
in these three variables.)
industries.
the
indicates,
of
estimated
Basic
1
and a number
changes
All
(As Table
change little between 1963 and 1972,
generally
make
variables.
independent
I present these results in part in
for
the
hope that someone will be thereby stimulated to provide such an explanation. 3s
The
estimates
experienced
smaller
decreases in R.
Table 5 indicate that
in
than
more
average increases in
concentrated
A and
larger
industries
than
average
As the P-Levels reported at the bottom of the Table indicate,
durable/nondurable instability in the Full Model for A seems to be confined to
the intercept (CNST) and the coefficient of average PQ/K.
R
shows no significant instability of this sort;
(The Full Model for
it is estimated in the same
version as the A equations entirely for purposes of comparability.)
equal,
durable
nondurable
goods
industries
goods industries.
experienced smaller increases
Among durable goods industries,
opposite
indicates
that
effect
in
industries
the nondurables
in
A
subsampl-e.
with higher than
average
The
else
than
increases in A
while there is some evidence
are smaller the higher is capital intensity,
the
All
Full
advertising
Model
of
also
intensity
- 28 -
experienced
smaller than average increases in A,
while advertising intensity
was unrelated to changes in R.
Table
6 presents a similar analysis of changes in RA and B.
The
Basic
Model indicates a weak tendancy for more concentrated industries to experience
larger
than
in
in the Full Models for RA and B did not seem to be confined to
Instability
subset
average declines in RA and smaller than average declines
of the coefficients,
B.
a
so that separate estimates of the Full Model are
presented in Table 6 for durable and nondurable good industries.
(Recall that
there are 17 durable good industries and 53 nondurable good industries in this
sample.)
RA
and
All else equal, the intercept terms point to larger declines in both
B
for industries producing
industries,
declines
higher
concentration
nondurables.
is
Among
associated with
larger
in RA but had no significant effect changes in B.
producing nondurables the pattern is reversed:
the
durable
than
good
average
Among industries
concentration has no effect on
changes in RA, but higher concentration is associated with smaller declines in
B
among
nondurables.
Advertising
intensity has a
positive
sign
in
estimates, but coefficients and significance levels vary considerably.
all
Higher
capital intensity has a positive effect on changes in RA and B in the durables
subsample but has a negative effect on both changes among industries producing
nondurables.
There
of
may be some simple explanation for the apparently complex
changes shown in Tables 5 and 6.
But
pattern
static equilibrium versions of the
DEH and the DCH do not seem likely to produce it,
nor do plausible hypotheses
regarding the incidence of the Phase II price controls.
VII.
Conclusions and Imelications
This
essay
has derived a set of testable implications of the
DCH, and a hybrid DEH/DCH model
DEH,
the
and employed new techniques for testing those
- 30 -
To
explore
profits,
I
the impact of the Phase II price controls
estimated a variety of standard
with data for the period 1955-1970.
controls
that
on
manufacturing
acroeconometric profit equations
(I excluded 1971 because the Nixon price
began with the imposition of the Phase I price freeze in
year.
satisfactory,
Estimates
also
August
employing post-controls (1975-1982)
were
presumably at least in part because of the 1973-1974 oil
of
less
shock
and contemporaneous changes in the definitions of the manufacturing profit and
sales
series employed.)
Both manufacturing sales and real 6NP originating in
manufacturing were used as measures of activity.
were employed in these experiments,
of
Standard cyclical variables
along with trend terms and
growth of average gross hourly earnings of production and
manufacturing workers.
data
series
HE,
the rate
non-supervisory
(Unless otherwise specified, footnote 7 applies to all
introduced
in
this
outperformed those based on GNP.
Appendix.)
Equations
based
on
sales
Deletion of insignificant variables led
to
the following standard equation, which was then estimated using data for 19551970 and 1972:
wa/PQ = -.0320 - .0011 T + .1492 CU + .0004 PQ - .0031 D72
(2.34) (11.1)
(8.45)
(2.69)
(1.30)
RZ = .973,
(A1)
DW = 2.33.
Here wa/PQ is the ratio of pre-tax manufacturing profits to sales, T is a time
trend
(1954
=
1),
CU
is the Federal Reserve
utilization in manufacturing
Board
(expressed as a fraction),
increase
in manufacturing sales from the preceding year,
variable
for
1972.
Figures
in
parentheses
are
measure
of
capacity
APQ is the percentage
and D72 is a
absolute
values
dummy
of
t-
statistics.
The coefficient of D72 in equation (Al) is insignificant at usual levels,
II
- 31 -
and
its absolute value is only about a third of the standard deviation of the
dependent
data,
variable.
the
suggests
sectors
(In the best of the equations that also
coefficient
that
of
of
used
D72 had a t-statistic of -0.58.)
the Phase II controls mainly
affected
the
This
analysis
non-manufacturing
where most of the inflation in 1972
the economy,
1975-1982
occurred;
the
effects on total manufacturing profits were at any rate insignificant.
In
order
to see whether the Phase II controls produced a shift
relative
profitability
obtained
the
of
following
large and small manufacturing firms
variables
from the IRS
Statistics
in
of
in
1972,
Income
Sourcebook of Statistics of Income for the 20-year period 1958-1977,
the
I
and
which is
centered on the two years analyzed in the text:
RT = Pre-tax profits plus interest payments as a percentage of
total assets for all manufacturing firms.
RS = Pre-tax profits plus interest payments as a percentage of
total assets for manufacturing firms with assets between
$500,000 and $1,000,000.15
dR = 100x(RT - RS).
RS
gives
the profitability of the smallest firms considered in our
analysis of 1963 and 1972.
asset values below $500,000,
the
While most manufacturing firms in most years have
the aggregates used to compute RT mainly reflect
performance of firms with assets above $1,000,000.
gives
a
reasonable
detailed
indicator
of
the
average
The variable dR thus
importance
of
large-firm
profitability advantages, measured in basis points.
One
might
expect
dR to be positive in most years,
positive in 16 of the 20 years in the sample.
assumes
uch larger negative values in
1968,
in
fact
It is negative in 1972, but it
1975,
and 1977.
dR in these years are as follows: 1968 = -26.7, 1972 = -4.2,
1977 = -71.2.)
and it is
(The values of
1975 = -80.1, and
Even if 1972 is something of an outlier, these findings do not
- 32 -
point toward the Phase II price controls as the reason.
The
behavior of dR over time is illustrated in Figure 1.
seven years of the sample, the mean of dR is 201.6.
very
large
economics
fraction
relatively
The
steadily to -26.7.
first
It is worth noting that a
of the published cross-section
studies
From 1965 through
use data from this period.
In the
in
1968,
industrial
dR
declines
Thereafter its behavior is somewhat
erratic.
mean of dR in the last seven years of the sample is 4.3,
just over 2% of
its mean in the first seven years of the sample.
In
this sample,
dR is negatively correlated with the rate of growth
the implicit deflator for
and
RT.
It
originating
is
NP originating in manufacturing, a time trend,
uncorrelated
with CU and the rate of growth
in manufacturing,
of
also
6NP
standard cyclical variables with which RT
and
of these measures with RT are .62 and
equation
(Al),
HE,
real
other measures of aggregate profitability are positively correlated.
correlations
of
above.)
.27,
This suggests that the
(Simple
respectively.
correlation
See
with
RT
reflects accounting practice rather than economic reality.
The
discussed
most
in
satisfactory
the
regression
equation
involving
preceding paragraph and natural variants
the
thereof
variables
is
the
following, where figures in parentheses are absolute values of t-statistics:
dR
=
535.2
(3.90)
-
38.33
(5.33)
HE
-
22.45 RT
R2
(1.71)
DW = 2.26
The residual for 1972 from equation (A2) is negative,
for 1963.
= .644
but so is the
(A2)
residual
And 1961, 1967, and 1968 have larger negative residuals than 1972.
The residual for 1971, the year in which price controls were first imposed, is
also negative, but it is smaller in absolute value than the negative residuals
for
seven other years.
When dummy variables for 1963 and 1972 are added
to
this equation, the coefficient of the former is a tenth of its standard error,
- 33 -
the coefficient of the latter is
and
Once
1972
again,
does
equal to 1.09 times its standard
not emerge as an outlier in any way
that
error.
might
be
attributable to the operation of the Phase II price controls.
Consider a size class including N firms with assets between a and b
Let K be the assets of a typical firm
let m be reported mean assets per firm.
in
and
assumed to be a draw from the density function g(K) with mean
this class,
Taking the expectation of the second-order Taylor series expansion of the
p.
right-hand side of equation (13) about the point at which all the K
= , one
obtains the asymptotic approximation employed to estimate the f:
f* =
where
the
quantity
R,
+ (N-1)R]/N,
which
equals
(B1)
or exceeds
unity
and
reflects
the
population dispersion in g(K), is given by
R = E(K2 )/g2 .
that for N = 1,
Note
any distribution,
and
f*
(Bi)
both the true f and the approximation f* equal one
as there are no intra-class differences.
approach the population value R.
The mechanics
As N e
of
for
, both
estimating
4
the
population ratio R depend on whether b is known or unknown.
In the largest size class in each industry, the upper bound on firm size,
b,
is unknown.
function of K
it
is
I deal with this by assuming that g(K) is a linear decreasing
and reaches zero at K = b.
For such a triangular distribution
easy to show that
p = (2a + b)/3,
(B3)
- 34 E(K2 ) = (3a2 + 2ab + b2 )/6.
p
Setting
(B4)
= m in (B3) yields an estimate of b.
Substitution into (B4)
and
division by m2 then produces an estimate of R.
I assume initially that g(a) = a,
When b is known,
0,
g(b) = p, with
,p
For such a
and that g(K) is a linear function of K between these points.
trapezoidal distribution,
(85)
p = u[(2a+b) + (1-w)(a+2b)]/3,
=
where
/(a+p),
and
E(K2 ) = [6(a+b)p-(a 2 +4ab+b 2)]/6.
For
(2a+b)/3
dividing
by
preceding
<
< (a+2b)/3,
m2 .
For
m
R is estimated by setting
the triangular
< (2a+b)/3,
paragraph is employed.
triangular with g(b)
(Sb)
For m > (a+2b)/3,
= m
in
(B6)
and
o4
the
distribution
to
g(K) is assumed
> 0 and g(x) = 0 for some x > a.
experimented at some length with an alternative approach that involved
I
This
assuming a lognormal distribution of firms' assets within each industry.
approach
with
should
be more efficient than that described above
approximately lognormal size distributions.
computed
(1963, Sects. 9.2 and 9.6).
produced
class-specific
industries
estimates
were
see Aitcheson and
Brown
Exact formulae for conditional expectations then
estimates of R.
For most industries this
approach
f*'s and estimates of A and B that were very close to those produced
the method described above.
with
Parameter
for
using variants of the basic maximum likelihood method for estimating
the parameters of truncated lognormal distributions;
gave
be
In a few cases,
size distributions that seemed
approach
however,
involving
far from lognormality,
yielded implausible estimates of the f,.
The
by
industries
this alternative
technique
described
- 35 -
above was employed because of its apparently greater robustness to substantial
departures from lognoreality.
Apendix
Consider
dividing
the
estimating
consistent estimate of
where
(wj) 1
observation by
jth
v =
equation (21) in the text by
For any set
.
2(4), the unknown variance of the
M
SSR - E (
j=1
v
a
j, is given by
and SSR is the sum of squared
residuals
Interest attaches here to weights of the form
+
2(q,) ].
(C2)
deviation of these weights to their mean.
0 and s/m,
wj,
(C1)
Let D equal the coefficient of variation of the wj,
between
positive
M
(qj)/wj)]/E (l/wj),
j=1
from the weighted regression.
=
of
regression,
2
is the number of industries,
wj
2
weighted
the ratio of the standard
For weights given by (C2), D varies
where m is the mean of the
2
(hj) and s is their standard
deviation.
Now
consider
the function F,
constructively as follows.
(C2)
to
compute
w
negative.
F(DO).
O0,s/ml to the
real
line,
Pick a non-negative initial value of v,
the corresponding
calculate the initial value of D,
vector
from
DO.
vector
of
weights,
w,
and
defined
vO.
Use
directly
Run a weighted regression with weight
and use (C1) to obtain a new value of v,
which need not
be
non-
(C2) to compute new weights and a new value of D, D1
Finally, use
Iterated weighted least squares is simply a search for a fixed point
of F.
In this study it proved very efficient computationally to employ a linear
approximation
_1_1
to
the
function
__1___1_________
F.
_
OLS estimation
of
(21)
yields
F(O);
III
- 36 -
estimation
wj =
with
r2 (qj)
yields F(s/m).
the first regression,
residuals
from
residuals
from the second.
Let SSRo be tne sum of
squared
of
squared
and let SSRW be the
sum
A bit of algebra establishes that if F is
linear
and has a fixed point, the corresponding value of v is given by
(C5!
v* = (SSR./M)[(SSR./M)-1]/E(SSR./M)-l+Yl, where
n
E
n
2(q~)][E 1/a2(q,)]/N 2
j=l
j=1
(C4)
[E
Given an estimate of a2
(4)
from (C3),
a third weighted regression.
one can use (C2) to compute weights for
If a fixed point of F has been found, it follows
from (C1) and (C2) that the sum of squared residuals from this regression will
equal M.
This technique could not be applied to equations involving estimates of B
computed using the CRS specification;
relative to their standard errors,
the
because these estimates differed little
(C3) produced negative values of v*.
discussion of Table 2 in Section II of the text.)
Instead,
(See
estimates of
~2(g) derived from the IRS specification were used for all equations involving
IRS
estimates
the CRS
and
Otherwise,
the
(In equations involving estimates of A and RA,
estimates of B.
of
g2(g)
were generally nearly
identical.)
approach described above either yielded an approximate fixed point directly or
made it easy to obtain such a point with one additional iteration.
- 37 -
References
Aitcheson, J.,
and Brown, J.A.C. The Lognqoral
Cambridge University Press, 1963.
Bain,
Distribution.
Cambridge:
Joe S.
Relation of Profit Rate to Industry Concentration: American
Manufacturing,
1936-1940." Quarterly Journal of Economics, 65 (August
1951): 293-324.
.
Barriers to New Competition. Cambridge: Harvard University Press,
1956.
Brozen, Yale. Concentration
1982.
MerqgersL and Public Policy. New York: Macmillan,
Carter, John R.
Collusion, Efficiency, and
and Economics, 21 (October 1978): 435-444.
Antitrust." Journal
of
Law
Caves, Richard E., and Porter, Michael E. 'From Entry Barriers to Mobility
Barriers:
Conjectural
Decisions and Contrived Deterrence to
New
Competition." Quarterly Journal of Economics, 91 (May 1977): 241-61.
. 'The Dynamics of Changing Seller Concentration."
Industrial Economics, 29 (September 1980):1-15.
Journal
of
Caves,
Richard E., and Pugel, Thomas A. Intraindustry
Differences in
Conduct and Performance:
Viable Strategies in U.S.
Manufacturing
Industries.
New York:
New York University Graduate School of Business
Administration, Salomon Brothers Center for the Study of Financial
Institutions, 1980.
Clarke, Roger, and Davies, Stephen W. "Market Structure
Margins." Economica 49 (August 1982): 277-287.
Clarke,
Roger;
Davies,
Stephen,
W.;
and Waterson,
Profitability -- Concentration Relation:
Market Power
Journal of Industrial Economics 32 (June 1984): 435-50.
and
Price-Cost
Michael.
"The
or Efficiency?'
Comanor, William S., and Wilson, Thomas A. Advertising and Market
Cambridge: Harvard University Press, 1974.
Daskin, Alan J. 'Essays on Firm Diversification and Market
Ph.D. dissertation, M.I.T., 1983.
Demsetz, Harold. "Industry Structure, Market Rivalry,
Journal of Law and Economics 16 (April 1973): 1-10.
Power.
Concentration."
and Public Policy."
·
"Two
Systems of Belief about Monopoly.'
In
Industrial
Concentration:
The New Learning,
edited by H.J. Goldschmid, H.M. Mann,
and J.F. Weston. Boston: Little-Brown, 1974.
…________.
"Accounting for Advertising as a Barrier to Entry." Journal
Business, 52 (July 1979): 345-360.
Dornbusch,
Rudiger,
·L1-..----
-
and Fischer,
of
Stanley. Macroeconomics. 2nd Ed. New York:
- 38 -
McGraw-Hill, 1981.
Regression
Regressing
Estimators for
A.
'Efficient
Eric
Hanushek,
Coefficients." American Statistician, 28 (May 1974): 66-67.
'Selection
Jovanovic, Boyan.
50 (May 1982): 649-70.
and the Evolution of Industry.'
Econometrica
Kreps, David M., and Scheinkman, Jose A. "Quantity Precommitment and Bertrand
14
Competition Yield Cournot Outcomes.' Bell Journal of Economics,
(Autumn 1983): 326-337.
An Analysis
"Uncertain Imitability:
Lippman, S.A., and Rumelt, R.P.
Interfirm Differences in Efficiency under Competition.' Bell Journal
Economics 13 (Autumn 1982): 418-38.
of
of
Long, William F. 'Market Share, Concentration and Profits: Intra-industry and
Inter-industry Evidence."' Mimeographed, U.S. Federal Trade Commission,
October 1982.
Lustgarten, Steven. '"ains and Losses from Industrial Concentration:
Comment." Journal of Law and Economi cs, 22 (April 1979): 183-190.
A
Industrial
.
Productivity
and Prices:
The Consequences of
Concentration. Washington: American Enterprise Institute, 1984.
Some Further Evidence."
'Profitability and Size of Firm:
Marcus, Matityahu.
Review of Economics and Statistics 51 (February 1969): 104-107.
Ornstein, Stanley I. Industrial Concentration and
Washington: American Enterprise Institute, 1977.
Advertising
'The Gains and Losses from Industrial
Sam.
Peltzman,
Journal of Law and Economics 20 (October 1977): 229-63.
"The
.
Concentration:
209-211.
Intensity.
Concentration."
Industrial
of
Rising
and
Consequences
Causes
22 (April 1979):
A Reply." Journal of Law and Economics,
Companies'
E.
'The Structure Within Industries and
Michael
Porter,
214-227.
(May
1979):
61
Statistics,
and
Performance." Review of Economics
Prais, S.J. The Evolution of Giant Firms in
University Press, 1976.
Britain.
Cambridge:
Cambridge
Ravenscraft, David J. Structure-Profit Relationships at the Line of Business
65 (February
and Industry Level." RevLew of Economics and Statistics,
1983): 22-31.
Some
Round, D.K. 'Industry Structure, Market Rivalry and Public Policy:
Australian Evidence." Journal of Law and Economics, 18 (April 1975): 273-281.
Different
Having
Samples
from
R.
'Regressions
Gary
Saxonhouse,
Characteristics." Review of Economics and Statistics, 59 (May 1977): 234237.
- 39 -
Scherer,
F.M.
'The
Causes
and Consequences
of
Rising
Concentration." Journal of Law and Economics 22 (April 1979):
·
. …____
Industrial Market Structure and Economic
Chicago: Rand-McNally, 1980.
Industrial
191-208.
Performance,
2d
Ed.
Schmalensee, Richard.
Using the H-Index of Concentration with Published
Data." Review of Economics and Statistics 59 (May 1977): 186-193.
. "Do Markets Differ Much?" American Economic Review,
forthcoming.
75
(1985):
Spiller, Pablo T., and Favaro, Edgardo. The Effects of Banking Regulation on
Oligopolistic Interaction: The Uruguayan Banking Sector." Rand Journal of
Economics 15 (Summer 1984): 244-254.
Stigler,
eorge J. A Theory of Oligopoly."
(February 1964): 44-61.
Journal of Political Economy, 72
Swamy, P.A.V.B. 'Efficient Inference in a Random
Model." Econometrica, 38 (March 1970): 311-323.
Coefficient
Telser,
Lester. 'A Theory of Innovation and its Effects."
Economics 13 (Spring 1982): 69-92.
Bell
Regression
Journal
of
Weiss, Leonard
The Concentration-Profits Relationship and Antitrust."
In
Industrial Concentration:
The New Learning,
edited by H.J. Goldschmid,
H.M. Mann, and J.F. Weston. Boston: Little-Brown, 1974.
__IE·DIFY___IIJII_-
- 40 -
Footnotes
I am indebted to the National Science Foundation for financial support, to
Alan J. Daskin and the PICA project at the Harvard Graduate School of Business
(especially Michael Spence and Marilyn Shesko) for providing
Administration
most of the data used in this study, and to Steven Postrel and, especially,
I am grateful to
Ian Ayres,
Ian Ayres for excellent research assistance.
William Long, and seminar audiences at Johns Hopkins and the Federal Trade
Commission for helpful comments on earlier versions of this essay. Only I can
be held responsible for sins of omission or commission embodied in this paper,
however.
Under the DEH, one should
1. There is important common ground, however.
attempt to understand the obstacles to diffusion of knowledge that must be
Under
present if intra-industry efficiency differences are to persist.
the DCH, obstacles of this sort are a subset of what Caves and Porter
(1977) have termed barriers to mobility".
2. The interesting work of Peltzman (1977, 1979) and Lustgarten (1979, 1984)
on the relation between changes in concentration and improvements in
productivity (see also Scherer (1979)) was designed to test the DEH in a
rather different fashion.
The main finding of these studies is that large
increases or decreases in concentration are associated with above-average
While this is certainly consistent with the
increases in productivity.
DEH, it is not inconsistent with the DCH. After all, one does not expect
to see major changes in seller concentration under plausible variants of
either hypothesis except in response to major alterations in competitive
Major innovations, which are likely to be followed by an
relationships.
increase in the innovator's market share under almost any plausible
hypothesis about market behavior,
are an important source of such
alterations.
Innovations by market leaders should thus tend to be
associated with increases in both concentration and industry productivity
under either the DEH or the DCH.
Innovations by new entrants or small
firms
should
tend to lower concentration while
raising
average
productivity. Industries in which little innovation occurs are likely to
in
along with below-average
gains
exhibit
stable
concentration
productivity.
(Note also that Peltzman (1977) finds evidence in support
'of
the DCH assertion that increases in concentration lead to increases in
price -- cost margins.)
3. This model has been used by Clarke and Davies (1982) to analyze the
determinants of equilibrium concentration in the presence of efficiency
differences; see also Long (1982) and Clarke, Davies, and Waterson (1984)
The more complex DEH
for further development and empirical applications.
and Telser (1982)
models of Jovanovic (1982), Lippman and Rumelt (1982),
stress the dynamic mechanisms determining N and the c
rather than
equilibrium and do not lend themselves readily to use in empirical
analysis.
In the Cournot model in the text, the larger is N, the smaller
the differences among the c that are consistent with non-negative market
If the market demand curve is P = a - bQ, for instance, nonshares.
is the
[a + (N-1)J,]/N for all i, where
negative shares require c
average of all c's except cl.
4. To see this last point, suppose, in the spirit of the more complex DEH
models cited in footnote 3, that in order to enter any particular
- 41 -
industry, firms must spend some industry-specific amount on research and
This allows them in effect to draw a value of c from the
development.
Firms that draw a
industry-specific distribution of possible unit costs.
high c will elect not to start up production, while lucky firms with low
Depending on the
c's will enter and earn positive rents on their luck.
pattern of differences in R&D costs and distributions of possible c's
across industries, one might expect industries that attract relatively few
firms to draw costs or to enter (and are thus concentrated ex post) to
produce substantial rents to all those lucky enough to be able to operate
profitably.
5. But see Spiller and Favaro (1984) for an apparent counterexample.
6. On the necessity of using substantial inter-period gaps in the analysis of
structural change, see, for instance, the discussion of concentration
It should be noted that
changes by Caves and Porter (1980, esp. p. 9).
(1974) has argued that 1963 is an outlier that is somewhat less
Demsetz
consistent with the DEH than surrounding years, though the statistical
analysis that supports his argument is suspect because it is based on
absolute fire size rather than market share.
(See Daskin (1983) for a
general discussion of this issue.)
7. All data used in this and the next paragraph come from the 1984 Economic
Reogrt of the President. Growth rates reported for any year T are are the
This
(T-1) and (T+1).
annual rates of growth experienced between
procedure better reflects growth during the second half of each year than
the usual approach of reporting changes from the previous year.
8. To investigate the intertemporal stability of R and CONC, equations of the
form X(1972)-X(1963)] = [ - X(1963)] were estimated for each variable.
, or both were functions of
(More complex specifications, in which ,
other variables, generally did not perform noticeably better.) Estimates
of I indicate a half-life of deviations of R from the mean
(=
9.0x[ln(0.5)/ln(1-)], the equation's median lag in years) of 8.8 years,
CONC also tends to
with an asymptotic standard error of 2.1 years.
regress toward the mean in these data, but the process seems much slower;
the estimated half-life of deviations from the mean is 19.9 years, with an
asymptotic standard error of 6.6 years. It is unclear exactly how to
interpret this difference in adjustment speeds, especially in light of the
differences in patterns of profitability between the 1963 and 1972 samples
The implications of this
that are discussed in Sections IV - VI.
difference for choice between the DEH and the DCH are in any case not
obvious.
9.
__*_1__IL(·l__l_
Previous studies using IRS data from the early 1960's (e.g., Comanor and
(1974) and Porter (1979)) typically have many more consumer goods
Wilson
industries. A good deal of the difference is accounted for by aggregation
from 1963 to 1972 industries and the deletion of some of the latter.
But
a detailed comparison reveals that a number of industries generally
classified as producing mainly consumer goods in earlier studies in fact
generate the majority of their value-added in four-digit industries that
Ornstein (1977, Appendix B) classifies as producer goods industries.
Examples include IRS minor industries 2850 (Paints and allied products),
3010 (Rubber products), and 3420 (Cutlery, hand tools, and hardware).
..1__1__.-_..·..
III
- 42 -
10. Since R is known, the sampling variance of RA
the standard error of A. Similarly, since 1963
providing independent observations, sampling
parameters between these two years are sums of
standard errors.
is equal to the square of
and 1972 can be treated as
variances of changes in
the corresponding squared
11. There is, of course, no guarantee that the tj are homoscedastic in fact.
In particular, differences in the numbers and relative sizes of economic
markets
included
in
different
IRS
industries
will
induce
heteroscedasticity, as will various differences among the basic markets
themselves. As is usual in applied work, homoscedasticity is assumed here
simply because it is unclear how to obtain plausible estimates of the
pattern of heteroscedasticity.
12. The equations involving R (Table 3) and R (Table 5) showed signs of
coefficient instability between consumer and producer goods industries.
But since these equations play no direct role in our comparisons of the
DEH and the DCH, the sources of this instability were not explored.
13.
(1985)
A number of authors including Ravenscraft (1983) and Schmalensee
have found highly significant relations between share and profitability in
models in which the coefficient of share is constrained to be the same
across industries. (See Scherer (1980, ch. 9) for a discussion of earlier
work of this sort.)
The tests of coefficient equality in Table 2 indicate
that this constraint is highly suspect.
Profitability is apparently
strongly related to market share in some industries, but not in all.
14. Aggregate time series for durable and nondurable goods industries do not
reveal differences substantial enough to suggest obvious explanations
based on either standard cyclical arguments or the findings reported in
Appendix A. Real NP growth (computed as per footnote 7) in 1963 was 8.6%
for durables and 11.4% for nondurables.
The 1972 figures were 6.4% and
9.0%.
The corresponding figures for growth in the implicit 6NP deflator
were -1.2% and -0.6% for 1963 and 1.2% and -0.9% for 1972.
Rates of
growth of average hourly gross earnings per production or nonsupervisory
worker
(from Business Statistics:
1982) were 2.7% for both groups of
industries in 1963, 7.0% for durables in 1972, and 6.4% for nondurables in
1972.
(All
these series are based on more precise divisions between
durable and nondurable goods industries than could be employed with IRS
data.)
It has been suggested to me that an explanation of
the
durable/nondurable instability could be constructed out of cross-sectional
differences in the incidence of unionization, coupled with changes in
union behavior over time between 1963 and 1972.
A serious attempt to
construct such an explanation would carry me far beyond the bounds of the
present study, however.
15. Interest payments by manufacturing firms in this size class were not
published for 1962.
A quadratic fit to the ratio of interest payments by
these firms to interest payments by all manufacturing firms over the
periods 1958-1961 and 1963-1970 had an R2 of .975 and a Durbin-Watson of
by
1.76.
This
equation was used to estimate interest payments
manufacturing firms in this size class in 1962.
Table 1
Main Industry-Level Variables
Mean
1963
Std. Dev.
R
.1028
.0352
.0995
.0299
.5802
CONC
.3353
.1572
.3606
.1511
.7602
AD/K
.0270
.0326
.0197
.0226
.8302
PQ/K
1.5837
.6310
1.4086
.4502
.8764
Variable
Mean
1972
Std. Dev.
Note. -- See text for sources and definitions.
1963-1972
Correlation
III
Table 2
Summary Statistics from Intra-Industry Regressions
Coefficient/Specification
RA/CRS
RA/IRS
A/CRS
A/IRS
Statistics for 1963
Sample Coefficients
Sample Mean
Standard Deviation
Number Positive
B/CRS
B/IRS
.0910
.0322
69
.0955
.0296
70
.0118
.0416
39
.0077
.0322
40
.4823
1.7599
42
.1747
.9397
40
Mean t-Statistic
Mean Itl-Statistic
11.2
11.2
7.27
7.27
1.27
3.35
0.64
1.68
0.31
0.76
0.89
2.29
Population Estimates
Estimated Mean
Standard Deviation
.0919
.0275
.0929
.0220
.0114
.0381
.0077
.0254
*
*
.1359
.4391
Probability Levels
Coefficients = 0
Coefficients Equal
Population Mean = 0
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
.02
<.01
<.01
.03
.18
.29
*
<.01
<.01
.03
Statistics for 1972
Sample Coefficients
Sample Mean
Standard Deviation
Number Positive
.1118
.0253
70
.1079
.0273
70
-.0123
.0350
19
-.0084
.0325
24
-.3554
.8492
23
-.3532
1.0839
24
Mean t-Statistic
Mean ItI-Statistic
18.0
18.0
12.8
12.8
-2.00
4.31
-0.99
2.83
-0.32
0.83
-1.18
3.45
Estimated Mean
.1121
.1077
-.1249
-.0079
*
-.2586
Standard Deviation
.0228
.0242
.0332
.0300
*
1.0119
Probability Levels
Coefficients = 0
Coefficients Equal
Population Mean = 0
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
.04
.08
.08
*
Changes, 1963 to 1972
Sample Coefficients
Sample Mean
Standard Deviation
Number Positive
.0208
.0323
53
.0128
.0336
49
-.0241
.0372
15
-.0162
.0330
20
-.8377
1.8832
18
Mean t-Statistic
Mean ItI-Statistic
1.86
2.34
0.87
1.50
-2.06
2.04
-1.09
1.69
-0.45
0.67
Estimated Mean
.0211
.0135
-.0245
-.0170
*
-.3731
Standard Deviation
.0253
.0241
.0314
.0289
*
1.2373
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
<.01
Population Estimates
<.01
<.01
.04
-.5279
1.5400
19
-1.44
.29
Population Estimates
Probability Levels
Coefficients = 0
Coefficients Equal
Population Mean
0
.97
.99
*
*Could not be computed because estimated population variance was negative.
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<.01
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Table 5
Correlates of 1963-1972 Changes in Average and
Estimated Zero-Share Profitability*
AR
Dependent Variable
AA/Pooled
AA/CRS
AA/IRS
Basic Model
CONC
-.0905
-.0518
-.0500
-.0573
(3.96)
(2.88)
(2.02)
(2.02)
.187
.057
.068
.057
.090
.057
.049
DDUR
-.0201
(0.55)
-.0508
(1.74)
-.0517
(1.27)
-.0531
(1.26)
DNDR
.0186
(1.20)
.0445
(4.20)
.0560
(3.82)
.0325
(2.12)
CONC
-.0801
(3.15)
-.0355
(1.89)
-.0411
(1.59)
-.0270
(0.99)
AD/K
-.0429
(0.32)
-.2797
(2.89)
-.1585
(1.25)
-.4562
(3.07)
DDUR*PQ/K
.0351
(1.42)
.0615
(3.05)
.0642
(2.27)
.0607
(2.11)
DNDR*PQ/K
.0044
(0.61)
-.0046
(0.99)
-.0098
(1.54)
.0009
(0.13)
.179
.169
.190
.168
.219
.197
.03
.24
.04
.11
.40
.18
R2-Wtd.
-Raw
Full Model
R2 -Wtd.
-Raw
.217
P-Levels:
CNST & PQ/K Equal
CONC & AD/K Equal
All Coeffs Equal
.45
.17
.27
<.01
.38
<.01
*Figures in parentheses are absolute values of t-statistics.
"----^'-`"~~~"~"""1"-^~1`"1-
Table 6
Correlates of Estimated 1963-1972 Changes in
Large Firm vs. Small Firm Differentials
ARA/Pooled
ARA/CRS
Dependent Variable
ARA/IRS
AB/Pooled
AB/CRS
AB/IRS
-.0439
(1.46)
-.0472
(1.75)
.5074
(0.86)
1.078
(1.62)
Basic Model
CONC
-.0455
(2.27)
R2-Wtd.
-Raw
.036
.010
.031
-.002
.9003
(2.00)
.043
.026
.028
.009
.011
-.034
.037
.039
Full Model
Durables:
CNST
.0934
(2.74)
.0657
(1.24)
.1152
(2.34)
2.936
(2.82)
2.339
(1.33)
3.118
(2.02)
CONC
-.1394
(4.14)
-.1087
(2.07)
-.1638
(3.40)
-1.305
(1.23)
-1.059
(0.61)
-1.428
(0.90)
AD/K
1.824
(3.90)
2.026
(2.95)
1.690
(2.38)
21.40
(1.92)
20.67
(1.10)
21.92
(1.34)
PQ/K
-.0642
(3.19)
-.0579
(1.87)
-.0694
(2.38)
-2.158
(3.13)
-1.827
(1.44)
-2.245
(2.25)
R2-Wtd.
-Raw
.572
.355
.552
.328
.617
.424
.305
.286
.245
.208
.326
.327
CNST
-.0377
(2.88)
-.0492
(2.47)
-.0291
(1.68)
-1.272
(4.54)
-1.362
(3.44)
-1.257
(3.05)
CONC
-.0079
(0.31)
-.0055
(0.15)
-.0118
(0.35)
1.141
(2.33)
1.119
(1.78)
1.186
(1.60)
AD/K
.1425
(1.28)
.0032
(0.02)
.2845
(1.84)
5.377
(2.58)
4.140
(1.54)
5.943
(1.91)
PQ/K
.0105
(1.97)
.0161
(2.00)
.0062
(0.88)
.1710
(1.59)
.2262
(1.67)
.1508
(0.92)
.070
.053
.089
.053
.100
.088
.144
.042
.142
.030
.150
.063
.01
.01
.01
.01
.07
.06
.05
.03
Nondurables:
R 2 -Wtd.
-Raw
P-Level:
Slopes =
All Coeffs =
<.01
<.01
.05
<.01
*Figures in parentheses are absolute values of t-statistics.
Q)
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