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INVESTMENT AND MARKET POWER
Paula R. Worthington
Working Paper Series
Macro Economic Issues
Research Department
Federal Reserve Bank of Chicago
April, 1991 (WP-91-7)
Investment and Market Power
*
Paula R. Worthington
Department of Economics
Northwestern University
2003 Sheridan Road
Evanston, Illinois 60208
(708) 491-8233
Federal Reserve Bank of Chicago
Research Department
230 South LaSalle Street
Chicago, Illinois 60614
(312) 322-5802
Abstract
This paper argues that the degree of market power within an industry
is an important determinant of interindustry differences in investment
behavior. A neoclassical investment model is analyzed to show that
market power is positively associated with capital stock flexibility.
The intuition for the result is that firms adjust their stocks and
investment plans quickly in response to new conditions so as to capture
the rents associated with their market power.
"k
I would like to thank Ellen Gaske, Bruce Meyer, Bruce Petersen, Robert
Porter, Sherrill Shaffer, Steve Strongin, and seminar participants at
several institutions for helpful comments. All errors are my own.
Abstract
This paper argues that the degree of market power within an industry
is an important determinant of interindustry differences in investment
behavior.
A neoclassical investment model is analyzed to show that
market power is positively associated with capital stock flexibility.
The intuition for the result is that firms adjust their stocks and
investment plans quickly in response to new conditions so as to capture
the rents associated with their market power.
1.
Introduction
Considerable empirical evidence suggests the existence of important
differences in fixed investment patterns across industries in the U.S.
manufacturing sector.
Some industries display highly volatile
investment series, while others display relatively stable investment
paths; some industries appear to adjust capital stocks rapidly to new
conditions, while others adjust stocks more slowly.
Researchers have
pointed to technological and financial factors as explanations, yet
substantial differences between industries remain unexplained.
This paper argues that the degree of market power within an industry
is an important determinant of these differences in investment
behavior.
I analyze a neoclassical investment model and relate
investment to an index of market power at the industry level, and I
show that market power is positively associated with capital stock
flexibility.
This general result is derived from the model in three
distinct but related ways.
First, I write the model as a partial stock
adjustment model and show that the "stickiness" parameter declines as
market power increases.
I next show that the change in investment
rates due to a change in factor prices or demand is larger the greater
the degree of market power in an industry.
Finally, I derive an
expression for the variability of investment relative to output and
show that it, too, is an increasing function of the degree of market
power.
The model analyzed here is simple, but its predictions and
inplications are powerful.
Industries with market power will display
more capital stock and investment flexibility, ceteris paribus, than
2
industries without it.
Market power creates economic rents, and firms
in industries with rents respond faster to changes in their environment
than those without the appeal of such rents.
The rest of the paper is organized as follows.
The next section
briefly reviews previous work related to the issues addressed here and
places this paper in proper perspective.
Section 3 contains the
formal model, and Section 4 discusses the results and concludes the
paper.
2.
Related Work
Perhaps the two strongest characteristics of aggregate fixed
investment spending in the United States are its cyclicality and its
high volatility relative to that of output (see Shapiro {1986]).
Studies using less aggregate data have confirmed these patterns and
have also documented interindustry differences in investment patterns
that remain unexplained after accounting for technological and
financial differences between industries.
For example, Abel and
Blanchard [1988] present evidence that investment variability and
capital stock adjustment speeds differ substantially across 2-digit
Standard Industrial Classification (SIC) manufacturing industries, and
von Furstenburg et al. [1980] find significant differences across
industries in both the level and adjustment speed of a Tobin's q
measure to a long run equilibrium value.
Petersen and Strauss [1989,
1991] analyze manufacturing sector investment at both the 2- and 4digit SIC levels over the 1962-1986 time period.
They find that
3
investment is especially volatile in durables goods industries and in
industries with volatile cash flow patterns.
The interindustry
differences in investment patterns documented in these studies no doubt
reflect many factors, including differences in financial market
constraints, production technologies, and output demand
characteristics.
Little attention has been directed to the role that
competitive factors may play in accounting for these differences.^
Many researchers have used the neoclassical investment model to
analyze the roles of technology, output demand, and factor prices in
determining investment behavior.
In its simplest form, the model
explains how these factors operate in an environment of perfectly
competitive product markets and perfect capital markets.
Recent
theoretical work, however, emphasizes the role that information
asymmetries in capital markets may play in investment and financing
decisions.^
Information problems may affect investment both
indirectly, through their influence on factor prices (cost of capital),
and directly, through some sort of credit-rationing.
Indeed, recent
empirical work suggests that financing constraints due to information
asymmetries substantially affect the investment choices of several
classes of firms.^
Another strand of the literature explores the relationships between
product market competition, capital investment, and the financing of
that investment.
Numerous authors have studied how physical capital or
financial capital structure may be used to precommit to certain types
of product market competition.^
Other researchers have examined the
process from the other direction and have analyzed how market power, or
4
product market competition, influences the cost of capital and, hence,
via the neoclassical model, investment decisions.^
This paper retains
the neoclassical framework and argues that market power also affects
investment through its influence on the perceived demand curve faced by
the industry.
Thus the model focuses exclusively on how market power
determines investment in the presence of perfect capital markets,
3.
A Linear-Quadratic Investment Model
This section of the paper uses a linear-quadratic model of
investment with adjustment costs to derive a relationship between the
degree of competition in an industry and the industry's Investment
behavior.
Entry by new firms is not considered; only expansion by
existing firms is treated.^
Assuming that all n firms within the
industry are behaviorally and technologically identical allows direct
consideration of the industry's investment problem.^
The industry's
problem is to select a sequence of industry capital stocks {Kt } t ,
1,2,...., to maximize the expected present value of its profits:
00
E0
l 0c[ptqt
t-0
c
- Ptit - -(It)2] -
(!)
2
subject to
It - Kt+i - (l-5)Kt ,
(2)
Pt ” at * M t
(3)
5
and
qt - aKt ,
(4)
given initial stock Kg, where f is a discount factor satisfying 0 < / <
i
}
1;
pt is output price; a is the industry's technological coefficient;^
p£ is the price of capital goods; It is gross investment;
is capital
stock; qt is output; 6 is the depreciation rate satisfying 0 < 8 < 1; b
and c are positive constants; {at} is an unspecified stochastic
process; and
denotes the expectations operator conditional on
information available at time t.
Following previous researchers, I
assume that convex adjustment costs are incurred for gross investment
expenditures; the third term in (1) reflects these costs.
Equation (2)
embodies the assumption that capital becomes productive one period
after its acquisition costs have been incurred.
Following Bresnahan [1982], I use a simple index of market power,
denoted A, to measure the degree of competition in the industry.
The
index ranges from 0 to 1, and its extreme values can be interpreted as
evidence of competitive and collusive behavior, respectively.
A
effectively measures the perceived degree of market power in the
industry;^ it enters the first order conditions characterizing the
industry's optimal capital stock path because it affects the industry's
perceived marginal revenue product of capital.
Since the industry is assumed to choose a capital stock sequence to
maximize (1) subject to (2), (3), and (4), its optimal capital stock
sequence satisfies the following first order conditions:
6
Et-Il-Pl-I
* c <Kt - <l-«)Kt_i) + /J{apt - Xba2Kt
+ <l-5)p| + c(l-5)<Kt+1 - (l-S)Kt)}] - 0
(5)
t - 1,2...
The industry equates expected current period marginal cost of capital
with expected discounted next period marginal revenue product of
capital plus marginal cost savings.
Following Bresnahan [1982], I call
the expression [apt - Aba^Kt ] the industry's perceived marginal revenue
product.
This expression differs from the simple product of output
price and capital's marginal product if A differs from 0, i.e., if the
industry is imperfectly competitive.
Solving this second order
difference equation yields the industry's equilibrium equation of
motion for its capital stock;
Kt+
1
Ml
•
" A*lKt + ______ 1 (&*l)S Ett0aat+s+l
c(l-«) s-0
<6)
* Pt+s + 0a-«>pS+s+i] *
where
HI +
“ c(l + 0 d - S ) 2) + 0ba2 (l + A)
"
(7a)
Pc(l-S)
and
M1M2 * I •
fi
(7b)
Equation (6) says that current capital stock depends on its lagged
value as well as the current and expected future values of the forcing
variables, at and p£.
Equations (7a) and (7b) may be solved to obtain
7
explicit expressions for Ml and M2> which depend on the model's
structural parameters, c, p, b, 6 , A, and a.
In particular, it is easy
to show that
3m1
--- < 0
and
dX
3/i2
--- > 0
(8)
d\
The remainder of this section develops three implications of the
relationship between A and the difference equation roots.
Note that
for these efforts to be meaningful, A must be considered exogenous.'
That is, the degree of competition within the industry must be treated
as fixed and determined by factors not considered in this paper.^
First, note that equation (6) may be rewritten as a partial
adjustment model as follows:
Kt +1 - Kt - ( 1 - m i ) ( k£ - Kt ) ,
(9)
where Kt is desired or optimal capital stock at time t and is defined
as the level of capital that would obtain in the industry after all
stock adjustments had been made, given all current and lagged values
of the forcing processes and knowledge of the forms of the forcing
processes themselves.
The value 1-MI may be interpreted as the speed
of adjustment, and it represents the fraction of the difference between
actual and desired levels of capital that the industry actually
invests (net) in any given period.
Since Ml, the stock "stickiness”
coefficient, falls as A rises, the model predicts faster capital stock
adjustment speeds in imperfectly competitive industries than in
perfectly competitive ones.-^
8
A second implication of the model is that the size of capital stock
(and gross and net investment) responses to exogenous demand or factor
price shocks varies with the degree of competition.
This result holds
for permanent, persistent, or transitory price shocks, which affect the
optimal capital stock sequence through their effects on the expected
future sequence of demand and cost parameters.
For example, consider
an unanticipated permanent increase in the price of capital goods at
time t.
Equation (6) may be used to derive the effect on capital stock
at time t+1 as follows:
dKt+ 1
--------- dp£
-Ml(l-0 (1 -S)>
----------------------c(l-6 )(l-^l)
<
0
( 10)
An unexpected, permanent increase in the price of capital goods,
caused by a tax rate or credit change, for example, decreases the
capital stock.
The magnitude of that decrease depends on A through
/i]/s dependence on A.
Differentiating the expression in <10) and using
(8) yields the following:
a
dKt+1
d\
dp£
>
0
(ID
Equation (11) says that the capital stock response to a factor cost
shock declines in absolute value as market power increases.
Similar
results hold for the effects of persistent or transitory shocks.
Since
the capital stock response is equivalent to the investment response via
application of (2), the capital accumulation equation, equation (11)
9
predicts larger investment responses to factor price shocks in
competitive than in collusive industries.^
Since imperfect competition results in an output reduction in the
long run in this model, this result is not surprising.
The interesting
result is that the investment response relative to the current capital
stock is greater in collusive than in competitive industries.
Consider the effect of this factor cost shock on the rate of gross
investment, defined as:
It
_
Kt
-
Kt
+ 1
- (l-«)Kt
------------
(12)
Kt
Using equations (8 ) and (10)-(12) and the chain rule, it can be shown
that an unexpected factor price increase causes the investment rate to
decrease and that the magnitude of that rate decrease rises as A
r i s e s . T h u s imperfect competition is associated with smaller units
of investment responses but larger rates of investment responses to
factor price shocks.^
Again, the degree of market power positively
affects capital stock flexibility.
Finally, this model can be used to show that market power directly
influences investment variability relative to output variability.
Recall that aggregate investment is highly procyclical and that its
variability exceeds that of aggregate output (Shapiro [1986]).
Further, Abel and Blanchard [1988] and Petersen and Strauss [1989,
1991] have measured interindustry differences in these relationships.
This model demonstrates that one potential source of these differences
is the presence of market power at the industry level.
Consider an
10
example in which the price of capital goods, p£ , is constant and the
demand intercept, at , follows the following process:
(13)
at - a* + ut ,
where ut is a first order autoregressive process with parameter p.
Substituting (13) into (6 ), using the infinite order moving average
representation of (ut), and manipulating lag operators permits
computation of the variance of investment^--*:
0H lpa
2
1 4
-
var(It)
a - s - n ) 2'
c ( l * £ ) ( l - 0fi\p )
a\
(14)
(1-M?) . U
- P2\
where o\ is the variance of the white noise process underlying {ut}.
Clearly an increase in demand variability, measured by an increase in
a\, increases investment variability; thus investment is procyclical.
To derive an expression for output variability, I use equation (A),
the production technology, and proceed along the same lines as above to
obtain
2
Pp i p
1
var(q£)
(15)
c ( i - s ) a -P n p ) .
[ l - P l\ l l
- P2\
The ratio of var(I£) to var(qt) is given by
var(It)
--------- a 2
var(qt)
[ ( 1
-
m ?)
+
( 1
- « - Ml)2]
(16)
Market power influences the ratio of var(It) to var(qt) through its
influence on
It is straightforward to compute
11
d(var(It)/var(qt))
------------------------------- - -2ct2 (3j*i/dA) (1 - 5) > 0.
(17)
ax
This value is positive since dp^/dX < 0.
Equation (17) shows that
investment variability relative to output variability is an increasing
function of market power.
Thus all three measures of capital stock
flexibility, the stock adjustment speed, investment rate response to
shocks, and the ratio of investment variability to output variability,
are increasing functions of market power.
4.
Discussion and Conclusions
This paper has used a neoclassical investment model to show that
market power influences investment behavior through its effect on
perceived market demand:
higher degrees of market power are associated
with greater capital stock flexibility.
Market power creates rents,
and this gives firms in industries with market power incentives to
respond quickly to changes in conditions, thus accounting for the
capital investment flexibility results derived here.
Future theoretical work should focus on how product and financial
market factors interact to influence investment choices, and future
empirical work to test the model's implications should aim to
disentangle several sets of relationships.
The intensity of product
market competition influences investment through both demand and factor
price channels, while investment choices themselves may feedback to
influence outcomes in the product market.
Similarly, information
12
problems in capital markets may affect investment directly, by causing
credit rationing, and/or indirectly, by raising the financing cost of
investment.
Analysis of firm level data is probably best suited to distinguish
the influences of demand strength, competition, and financial market
access on investment behavior, but industry level analysis could also
prove fruitful.
For example, Lebow [1990] studies output and
employment variability in 4-digit SIC industries and finds that highly
concentrated industries tend to exhibit higher output and employment
variability than do less concentrated industries.
If high
concentration levels are associated with high degrees of market power,
then an adapted version of this paper's model may help explain Lebow's
results.
Future empirical work should attempt to distinguish
explanations based on market power from alternatives based on capital
markets and factor prices.
13
References
Abel, A.B., and Blanchard, O.J., 1988, "Investment and Sales: Some
Empirical Evidence. In Barnett, -W.A.; E.R. Berndt; and H. White,
eds. Dynamic Economic Modeling (Cambridge University Press,
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Amihud, Y . , and Mendelson, H., 1989, "Inventory Behaviour and Market
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Blundell, R . ; Bond, S.; Devereux, M . ; and Schiantarelli, F., 1989,
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of Oligopoly," Canadian Journal of Economics. 21(2), 221-243.
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Industrial Organization. (North Holland, Amsterdam).
Bresnahan, T.F., 1982, "The Oligopoly Solution is Identified,"
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Dixon, H. , 1985, "Strategic Investment in an Industry with a
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Fazzari, S.M. and Athey, M . , 1987, "Asymmetic Information, Financing
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Fazzari, S.; Hubbard, R.G.; and Petersen, B.C., 1988, "Financing
Constraints and Corporate Investment," Brookings Papers on Economic
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Wiley, New York).
Von Furstenberg, G.M.; Malkiel, B.G.; and Watson, H.S. 1980, "The
,
Distribution of Investment Between Industries: A Microeconomic
Application of the 'q' Ratio," in von Furstenberg, G.M., ed.,
Capital. Efficiency and Growth (Ballinger, Cambridge, Massachusetts)
Gertler, M.L., 1988, "Financial Structure and Aggregate Economic
Activity," Journal of Money. Credit, and Banking. 20(3, part 2), 559
588.
14
Gertler, M.L. , and Hubbard, R.G., 1988, "Financial Factors in Business
Fluctuations," in Financial Market Volatility. Federal Reserve Bank
of Kansas City.
Hoshi, T.; Kashyap, A.; and Scharfatein, D., 1989, "Corporate
Structure, Liquidity, and Investment: Evidence from Japanese
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Hubbard, R.G., and Weiner, R.J., 1986, "Oil Supply Shocks and
International Policy Coordination," European Economic Review. 30,
91-106.
Karp, L.S. and Perloff, J.M., 1989, "Dynamic Oligopoly in the Rice
Export Market," Review of Economics and Statistics. 71(3), 462-470.
Karp, L.S. and Perloff, J.M., 1988, "Open Loop and Feedback Models in
Dynamic Oligopoly^" University of California-Berkeley, Department of
Agricultural and Resource Economics, Working Paper 472.
Lebow, D.E., 1990, "Imperfect Competition and Business Cycles: An
Empirical Investigation," Federal Reserve Board of Governors,
Economic Activity Section Working Paper 104.
Liang, J.N. and Wolken, J.D., 1989, "Systematic Risk, Market Structure,
and Entry Barriers," Federal Reserve Board of Governors Finance and
Economics Discussion Series Working Paper 68.
Nguyen, T. and Bernier, G. , 1988, "Beta and q in a Simultaneous
Framework with Pooled Data," Review of Economics and Statistics.
70(3), 520-524.
Petersen, B.C., and Strauss, W.A., 1989, "Investment Cyclicality in
Manufacturing Industries," Economic Perspectives. Federal Reserve
Bank of Chicago, November/December, 19-28.
Petersen, B.C., and Strauss, W.A. , 1991, "The Cyclicality of Cash Flow
and Investment U.S. Manufacturing," Economic Perspectives. Federal
Reserve Bank of Chicago, January/February, 9-19.
Schiantarelli, F., and D. Georgoutsos, 1990, "Monopolistic Competition
and the Q Theory of Investment," European Economic Review. 34, 10611078.
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Quarterly Journal of Economics. 51(3), 513-542.
15
Startz, R . , 1989, "Monopolistic Competition as a Foundation for
Keynesian Macroeconomic Models," Quarterly Journal of Economics.
104(4), 737-752.
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Investment: Evidence from Panel Data," Manuscript, Federal Reserve
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Variations," International Journal of Industrial Organization. 8(2),
315-328.
16
Appendix
Combining equation (6) with a lagged version of (6) yields:
Ml
It
“
0
0
+ --------
Z
C^A*l)S tEt()3Qat+s+1) - Et-.iC/Saat+s) ] + N3
;
<Al)
c(l-«) s-0
Papm
“
+ --- ---------- <ut ‘ (l-5)ut_i) + N 2
c (1-«)(1-0A»1P>
where Nj are appropriately defined functions of the model's structural
parameters.
Manipulating lag operators and simplifying yields
0<xpHl
0
0
It ---------------- l /if(ut_s - <l-«)ut.s.i) + N3
c(l-5)(1-fipip) s-0
(A2)
Since {ut } is AR(1), it has an infinite order moving average
representation: ^
0
0
Ut - X pi£t-i
i-0
•
(A3>
where {ct } is an i-i.d. white noise process with variance a\.
Substituting (A3) into (A2) and simplifying yields an expression for
gross investment as a function of current and past realizations of
f30CpH ]_
00
-------------- [
c(l-6)(l-Pmp)
Z
00
P S * t-s • (1-S-A*l)
s-0
Z
i-0
00
Z ^Sct-s-i-l)l + N3 <A4)
s-0
The variance of It is computed as
2
a-s-n)2'
1
(A5)
4-
c(l-S)a-pPlP).
This is equation (14) in the text
CM W
b
Ppipa
var(It)
<!-/*?) . 1 - P2.
17
Endnotes
1.
However, see Schiantarelli and Georgoutsos [1990] for related
empirical evidence using aggregate data on fixed investment, and
see Amihud and Mendelson [1989] for firm-level analysis of
inventory investment. The latter authors find that inventory
volatility is positively correlated with several measures of
market power.
2.
See, for example, Gertler [1988], Gertler and Hubbard [1988],
and the works cited therein.
3.
For example, see Fazzari and Athey [1987]; Fazzari et al.
[1988] ; Blundell et al. [1989]; Hoshi et al. [1989]; and Whited
[1989] . These studies find that the investment of firms likely
to face borrowing constraints displays greater sensitivity to
cash flow than does that of unconstrained firms.
4.
For example, see Dixon [1985], Brander and Lewis [1988], and the
references cited therein.
5.
See Sullivan [1978], Nguyen and Bernier [1988], and Liang and
Wolken [1989].
6.
But see footnote 11 below.
7.
An equivalent approach is to begin at the firm level and exploit
the symmetry assumptions when aggregating up to the industry level.
8.
Modelling production as a fixed coefficient technology permits
me to derive simple, closed form expressions for desired capital
stock investment but precludes consideration of input
substitutability when examining the effects of factor price
shocks later in this section.9
9.
The index can be directly related to quantity-based conjectural
variations: values of 0, 1/n, and 1 for A correspond to
quantity conjectural variations of -1, 0, and n-1, respectively
Interpreting A (or the conjecture) in a game-theoretic context
requires some care, since the current problem is a dynamic one.
A conjecture of 0 corresponds to the Cournot-Nash assumption of
taking one's opponents' actions as given. Solving the model
18
with A - 1/n (or the conjecture - 0) is thus equivalent to
solving the noncooperative game of choosing capital stocks when
only open loop strategies are permitted. This paper, then, does
not consider feedback or other closed loop strategies. See Karp
and Perloff [1988] and Worthington [1990] for further
discussions of these issues, and see Bresnahan [1982, 1989] and
Shaffer [1983] for more on the standard interpretations of the
index A .
10.
See Worthington [1990] for a treatment that endogenizes the
degree of competition.
11.
Karp and Perloff [1989] and Worthington [1989] obtain related
results in similar models. The latter paper distinguishes
between the degree of competition (price-taking, Cournot,
collusive, etc.) and the number of firms, n, in the industry.
Increases in n are shown to increase the adjustment speed. The
intuition is straightforward: increases in n mean that any
given increase in capital stock can be spread over a larger
number of firms. Since stock adjustment costs are convex, this
lowers the total cost of any given stock addition and serves to
raise the industry's adjustment speed.
12.
See Hubbard and Weiner [1986] for related results. The analysis
of demand shocks is identical to that given above, since both
demand and technology are linear in this model.
13.
Specifically, the relationship is
8
d ( I t /K t )
a
'1 '
1 ‘a
dKt+1
.
1
A
SP
8X
ax b
dpt
..
'dKt+ i | l
dKt+ 1
.A
Kt a x
n
dpk ] j
}i
dPt
Since Kt falls as A rises, this expression is positive.1
4
14.
Startz [1989] obtains qualitatively similar results in a quite
different setting. Using a model of monopolistic competition,
Startz derives Keynesian rigidities and analyzes short and long
run multipliers in a macroeconomic model. He shows that "the
greater the degree of monopolistic competition, the more that
short-run movements exceed long-run movements....[and not that]
the absolute size of movements is greater under monopolistic
competition than in a [perfectly competitive] neoclassical
economy.” Similarly, in the present model, the size of capital
responses, when measured in rates (units), is larger (smaller)
19
under imperfect competition than under competition.
15.
See the Appendix for details.
16.
See Fuller [1976, p. 36].
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