Download Chapter 2 - Yale Economics

Chapter 2:
Classic Empirical Models of Static Equilbrium∗
Steven Berry
Yale Univ.
Ariel Pakes
Harvard Univ.
September 18, 2003
1
Introduction
In this chapter, we begin with the classic models of partial equilibrium markets. We review the theory, which should be familiar to readers, with a
special emphasis on points that are of relevance to an empirical researcher.
We emphasize methods for uncovering the parameters of market primitives
(demand and cost) that a policy-maker would want to use to analyze alternative policies.
The ratio of econometrics to theory in this chapter is especially high.
Since the the theory ought to be perfectly familiar to anyone reading the
book, we have a simple context in which to introduce empirical ideas and
methods than will reoccur thoughout the notes.
We begin with the classic problem of estimating the supply and demand
curves in a perfectly competitive market. This leads us to review the empirical problem of endogeneity. In an important methodological aside, we
consider “method of moments” as a motivating principle for estimation techniques; the problem of endogeneity and solutions suggested by method of
moments will reoccur throughout the text. As noted in Chapter 1, however, we often that think that perfect competition is a poor approximation
to the world. We then turn to the most classic oligopoly model, Cournot,
∗
This is very much a work-in-progress. Corrections Welcome. Copyright by Steven
Berry and Ariel Pakes.
1
and consider how to estimate models under this alternative model of market
equilibrium. We highlight the literature that discusses whether one can distinguish oligopoly (Cournot) from perfect competition and from monopoly
(or a “perfect Cartel”).
We then briefly discuss theoretical critiques and extensions of Cournot,
from Bertrand to Kreps and Scheinkman (1983), again focusing on lessons
for empirical researchers. We could with an introduction to product differentiation, which looks forward to Chapter 4.
2
Supply and Demand on a Cross Section of
Markets
The simplest empirical market model is traditional supply and demand analysis on market level data.
In an empirical model of supply and demand, we can start with some set
of assumptions on the aggregate demand system. One common assumption
is that demand takes a constant elasticity form. For example, demand in
market i might be given by
ln(Qi ) = xi β − αln(pi ) + i
(1)
where Qi is quantity demanded in market i, pi is price and represents
unobserved (by us) terms that effect demand. The vector x contains marketlevel “demand shifters” such as income and the prices of substitutes and
complements. We don’t mean to emphasize the specific functional form, but
to emphasize that we want to at least carefully describe the variables and
the economic process by which they are generated.
The supply side might be similarly modeled at the market level. Say that
market marginal cost is given by
mci = wi γ + λQi + ωi
(2)
Here, w is a vector of cost shifters such as input prices and measures of
technology, while the term ω represents cost shifters that affect supply but
are not observed by the econometrician. Once again, the exact functional
form is not important.
In the traditional supply and demand framework, we assume that market
participants have perfect information about the demand and cost shifters.
2
Note that the empirical model adds a distinction between what we (the economic analysts) observe and what we don’t. It is unreasonable to assume
that our woefully incomplete datasets contain all the information available to
the market participants, and so we include the variables (, ω) that represent
unobserved cost and demand shifters. In the absence of such unobservables,
there would be no need for any statistical analysis, as we could obtain a deterministic fit to the equations given even a small number of observations. Once
we include unobservables, however, we will have to make some assumption
about their distribution. These assumptions will then drive the statistical
analysis.
In the (partial equilibrium) theory, the cost and demand shifters are exogenous, while Q and P are determined within the model via an equilibrium
assumption. The easiest statistical assumption for us to make on the exogenous variable is that their joint distribution is i.i.d. across markets (of
course, this assumption is particularly unlikely to hold with time-series data,
where we would want to modify it to incorporate correlation over time.)
The traditional supply and demand model assumes marginal cost pricing,
so, given our functional form assumption,
pi = wi γ + λQi + ωi
(3)
Let us take the demand shifters (xn and n ) and cost shifters (wn and ωn ) as
the “primitives” of the model and assume for now that they are distributed
i.i.d. across markets.
The temptation for early researchers was to estimate the demand equation
by OLS, regressing a time series of log output quantity on log prices and other
demand shifters. The results were disappointing and, in retrospect, pretty
obvious. The pitfalls of using OLS to estimate demand are recounted in an
entertaining way in Christ’s account ((Christ 1985)) of the early history of
economic statistics. For example, Henry J. Moore, known as the “father of
economic statistics”, was an early advocate of data collection and explicit
statistical methods. Seeking to learn about demand, he collected data on
prices and quantities in a variety of industries. In the market for corn, he
regressed price on quantity and found a seemingly reasonable estimate for the
demand elasticity of about -1 ((Moore 1914)). However, the results where
more puzzling in his study of pig-iron, where Here, he found an upwardsloping demand. As Christ notes, Moore therefore concluded that “he had
discovered a new type of demand curve with a positive slope.”
3
Moore’s conclusion was quickly criticized by Philip Wright and was throughly
exposed as incorrect in Working (1927). Working noted that in markets with
a lot of supply variation but less demand variation (e.g. agricultural markets), the data mostly traced out something that looked like a demand curve.
Manufactured goods markets, on the other hand, experience large shifts in
demand across the business cycle. The positive relationship between price
and quantity in such markets reflects a demand curve shifting around a relatively stationary supply curve. Moore’s “new” demand curve was closer to
a old supply curve.
What goes wrong here? Recall that for OLS to provide consistent estimates of β and α in (1), the demand error must be uncorrelated with (x,p).
(This uncorrelatedness assumption is sometimes replaced by the slightly
stronger mean independence assumption that E( | x, p) = 0.) We might
be willing to except that and x are uncorrelated; this says that the unobserved demand shifter consists of those factors which are orthogonal to the
observed shifters. However, when the unobserved component of demand is
high, we expect price to be high and therefore from theory alone we expect
p and to be correlated with each other. Note that this correlation might be
non-zero even if q does not enter the supply equation; that is, the problem of
endogenous prices is more general than the problem of “simultaneity” (the
fact that p determines q and vice-versa.)
The well-known solution to this problem is to employ instrumental variable methods. The idea is to find some set of variables that are correlated
with x and p but that are exogenous in the sense that they are uncorrelated with . Instrumental variables (IV) estimators (such as two-stage least
squares) can be derived from the mean independence assumption
E( | w, x) = 0.
The uncorrelatedness of with observed supply shifters then replaces the
theoretically untenable assumption of uncorrelatedness with price. However,
OLS is no longer consistent.
Two stage least squares (2SLS) is so named because the method can be
described as taking place in two steps. In the first step, the endogenous
variable ln(p) is regressed on the vector of instruments (x,w). A fitted value
ˆ is obtained from the results of this OLS regression. The fitted value is
ln(p)
then put into the demand equation in place of ln(p). Consistent estimates
of the demand parameters can then be found from the regression of ln(Q)
4
ˆ
on x and ln(p).
The intuitive notion is that we are estimating the demand
equation using only the variation in p that is “due to” exogenous shifts in w
and not the variation that comes from the error term (which, for OLS, must
be uncorrelated with the right hand side variables.)
Note that there must be some element of w that is not found in x, othˆ and x would be perfectly correlated and the coefficient α could
erwise ln(p)
not be estimated. Also, intuitively we will get better estimates if w is highly
correlated with with prices. Therefore, we guess (correctly) that a good
instrument must be uncorrelated with the error, but correlated with the
right-hand side endogenous variables.
The “two-stage” description of instrumental variables methods, while intuitive, does not carry over non-linear estimation methods. A more general
intuition for instrumental variables methods is provided in the next subsection, on the Method of Moments.
Another way to think of instrumental variables and the problem of simultaneity is to think of the reduced-form of the model. The theoretical
reduced-form solves for the endogenous variables, Q and p, as a function
of the exogenous shifters, x and w. The question arises as to whether the
reduced form parameters, once estimated, can be used to uncover the “behavioral” or structural parameters of the supply and demand curves. The
conditions for this, in the linear model, are the similar to the condition for
2SLS and are reviewed in any standard econometrics text, e.g. Goldberger
(1991). We prefer the IV (or more generally, method of moments) appoarch
because it is far easier to extend to non-linear models.
2.1
Example of Applications and Instruments.
[in progress]
It is easy to say that all we need is an instrumental variable, but it
can be harder to find one. In agricultural markets, one aclassic supply side
instrument is weather. For example, a study of the Fulton fish market in
New York city .... [cite] uses the weather at deep sea fishing locations to
shift the supply of fish at the market, but not the demand for fish in the city.
On the demand side, instruments might be constructed from changes in
income and/or the prices and availability of complementary goods. For example, in his classic study of a nineteenth century railroad cartel for the
shipment of grain from Chicago to the east coast of the US, Porter (1983)
needs a instrument that shifts demand but not supply. He uses the seasonal
5
availability of shipping on the Great Lakes. When the lakes are closed because of ice, the demand for railroad transportation increases, but the supply
of railroad transportation does not change.
2.2
Lessons from Supply and Demand.
What general lessons do we learn about modelling markets from the supply
and demand model? One important point is that we have to think about what
is in our error term. Early work that regressed manufacturing quantities on
prices and “proved” that demand slopes up is an important example of this.
Another point is that a fully “structual” model need be no more complicated
that the very first models we teach to undergraduates.
However, the Supply and Demand model is clearly not the best model for
the majority of markets that are best described as imperfectly competitive.
3
Cournot
The Cournot model of oligopoly is a good model to begin a discussion of
imperfect competition. The model is simple and many of the estimation
ideas discussed here will carry over to more complicated models of oligopoly.
In this chapter we review some very simple theory, with an emphasis on
firm heterogeneity, on connections to the S-C-P literature and to the types
of empirical predictions that are implied by the Cournot model. Then, we
turn to the question of estimation conditional on a Cournot assumption.
Finally, we discuss how to “test” the Cournot model versus the model of
perfect competition. This last topic relates to the traditional literature on
estimating the “conjectural variations” parameter. As background reading, it
might be useful to start with Tirole’s textbook treatment of Cournot theory,
perhaps supplemented by the more sympathetic treatment of Cournot in
Friedman (1983) and the more detailed and modern treatment in Vives.
Bresnahan’s Handbook of IO chapter (Bresnahan 1989) is good background
for the empirics.
6
3.1
Review of Theory
Basics
In the Cournot model, we begin as in the S&D model with a market-level
demand curve. However, now we presume that a finite number of firms set
quantities in a Nash equilibrium. To set out the theory, consider the general
market demand curve for a homogeneous good, Q(p). The inverse demand
curve is then p(Q). Each firm has its own total cost function Cj (qj ) and
marginal cost function, mcj (qj ).
The profit of firm j as a function of own and rival output is then
πj (qj ) = p(Q)qj − Cj (qj ),
with Q =
this firm is:
P
j
(4)
qj . Assuming differentiability, the first-order condition for
∂p
− mcj = 0.
∂Q
One can re-write this last equation in interesting ways. For example, it
is clear that firm marginal revenue equals marginal cost. Firm marginal
revenue is less than price (the MR of the perfectly competitive firm) but
∂p
greater than market marginal revenue (p + Q ∂Q
), so that the Cournot firm
partially internalizes the effect of output increases on market revenue. This
implies that Cournot falls between the Monopoly and Perfectly Competitive
models in terms of price.
However, the Cournot model behaves somewhat differently with respect
to industry costs. Remember that data on firms shows substantial heterogeneity in firm sizes, qj . Looking that the right hand side of (3.1), we see that
p and ∂p/∂Q are constant across firms. Across firms within the same market,
higher qj must be associated with lower marginal cost. Thus, the Cournot
model provides a partial explanation – cost differences – for the distribution
of firm sizes, but does not explain why costs are different. An important
implication of the Cournot first-order condition is that industry costs are not
minimized given the industry output level. Larger firms have lower marginal
cost, and so it would be cost-reducing to shift output from smaller to larger
firms. In the Cournot model, from the pure cost perspective, large firms are
not large enough.
Note that in the industry cost comparison, the Cournot model does not
fall in between Monopoly and Competition, for in both of those models industry cost in minimized (by profit maximization in the case of Monopoly
p(Q) + qj
7
and by the equality of marginal cost across firms in the case of perfect competition.) This result is consistent with the empirical findings of Olley and
Pakes (1996), who find that moving from monopoly to oligopoly results in an
inefficient allocation of output across existing plants (even while increasing
average productivity by allowing for the entry of productive new firms.)
We can decompose price as marginal cost plus a markup,
p(Q) = mcj + bj (qj , Q, p),
∂p
|. The markup is larger when the inverse demand
with the markup bj = qj | ∂Q
curve is steeply sloped and, within a market, is larger for large firms. Now,
divide through by p and then multiply the markup by Q/Q to obtain
Lj ≡
(p − mcj )
sj
= ,
p
η
where L is the Lerner index, sj is the market share of firm j and η is the
elasticity of demand.
In the case of monopoly, sj = 1, (3.1) gives the familiar inverse elasticity
rule for pricing, while in the case of very small firms (sj ≈ 0) it gives marginal
cost pricing. The Cournot value of L is then intermediate to monopoly and
competition. By taking the output weighted sum of the firm Lerner indices
within a market, one obtains
L≡
(p − m̄c)
H
= ,
p
η
where H is the Herfindahl index and m̄c is the weighted average marginal cost
(Cowling and Waterson 1976). Note that (3.1) looks alot like the traditional
S-C-P relationship between concentration and markups, while (3.1) looks
like the Demsetz critique of S-C-P that relates market shares to markups.
Thus, the Cournot model implies that there is not a tension between the two
results. The question of whether the markups are “justified” in some sense
must depend on an endogenous model of entry into the market, the sort of
model that we will consider later in the course.
Note the large firms have a smaller marginal revenue than small firms
because they internalize a larger share of the price decline from increased
output. Therefore, in equilibrium, the large firms have a smaller marginal
cost than small firms. This implies that the cost of producing industry output
is not minimized, for output could be redistributed from the high to the low
8
cost firms. In terms of industry cost minimization, then, the Cournot model
is not intermediate to monopoly or perfect competition, for in both of those
cases industry costs, conditional on industry output, are minimized. This
can have odd implications; for example, the entry of a small (read high cost)
firm could reduce social welfare.
Of course the first order condition is only a necessary condition for firm
j to maximize profits given the outputs of the other firms. The second order
condition is:
∂2p
∂mcj
∂p
+ qj
−
< 0.
2
∂Q
∂Q
∂qj
A sufficient condition for the s.o.c. to hold everywhere is that market marginal
revenue slopes down everywhere and marginal cost is never declining in qj
∂p
). If
(prove this by differentiating market marginal revenue, p(Q) + Q ∂Q
the s.o.c. holds everywhere, then the f.o.c. implicitly defines a “best reply
function”, qj∗ = rj (q−j ), for all qj and rival outputs q−j . The existence of a
best reply function, of course, does not guarantee the existence of a unique
equilibrium. Empirical reseachers typically care more about uniqueness than
do theorists, because often we want to make a specific prediction instead of a
qualitative statement. For a discussion of the conditions for uniqueness, see
Friedman (1983). Note that the s.o.c. need not hold, however, and indeed an
equilibrium may not exist if marginal cost declines steeply enough or if the
inverse demand curve is sufficiently convex.
Exercise 1 Exercises with the Linear Cournot Model.
When an IO economist says something is “intuitive”, sometimes it means
that it accords with the linear Cournot model. Consider the linear (inverse)
demand function, p = a − bQ and a constant (in q) mc function.
1. Derive the expressions for equilibrium price, quantity and profits in a
symmetric N-firm Cournot equilibrium. Do firm profits increase in this
model if N is reduced from 4 to 3?
2. Consider a model of heterogeneous firms with differing (but still constant) marginal costs, mcj . Derive an expression for equilibrium prices
as a function of the linear demand parameters, own-firm cost, average
firm cost and N .
9
3. For the linear Cournot duopoly model, graph the iso-profit curves and
best-reply functions of the firms. What is the slope and intercept of the
best-reply function? What is the slope of the iso-profit curve?
Strategic Substitutes and Complements
The Cournot assumptions is restrictive, in the sense that the model implies
certain kinds of behavior that are difficult to change via simple reparametrization of the model. For example, one interesting question in an oligopoly
model is how a change in the behavior of firm 2 will affect the behavior of
firm 1. Indeed, the answers to many policy quesitons will depend on the
answer to this more fundamental question. [examples and cites].
Bulow, Geanakoplos, and Klemperer (1985) introduce the idea of strategic
substitutes and complements. In the context of the Cournot model, the
output of two firms are strategic substitutes if an exogenous increase in the
output of one firm decreases the output of the rival firm. From the previous
exercise, we know that the best-reply functions of duopolists in the linear
Cournot model slope down and therefore outputs are strategic substitutes.
An implication is that if something happens to drive up the output of firm
2 (such as a decrease in the cost of firm 2), the output of firm 1 will, in the
linear Cournot model, decrease.
We are interested in the question of strategic substitutes and complements
because later in the course we will study how equilibrium changes in response
to firm decisions such as investment. If, for example, one firm invests to lower
its cost and therefore shifts its reaction function out, how will the output of
a rival firm respond? The answer obviously depends on the slope of the
reaction function. Similarly, how firms respond to government policy (e.g. a
tariff placed on an international oligopolist), will depend on the shape of the
reaction functions.
Whether two strategies are strategic substitutes depends in general on
how the marginal profitably of an action changes with an action of a rival.
In Cournot duopoly, the optimal level of firm 1’s quantity satisfies
∂π1 (q1 , q2 )
= 0.
∂q1
By the implicit function theorem, the slope of the reaction function is then
dq1
∂ 2 π1 /∂q1 ∂q2
=− 2
dq2
∂ π1 /∂q12
10
Since by the s.o.c. ∂ 2 π1 /∂q12 < 0,
sign[
dq1
∂ 2 π1
] = sign[
].
dq2
∂q1 ∂q2
In the Cournot case,
∂ 2 π1
∂p
∂2p
=
+ q1 2 .
∂q1 ∂q2
∂Q
∂Q
The first term on the RHS is negative when demand slopes down, explaining why for many functional forms the Cournot model gives strategic substitutes. However, if the second term is sufficiently positively (sufficiently
convex demand), the Cournot model can imply strategic complements. In
the later case, an example of which is in Bulow, Geanokoplos and Klemperer
(1985,JPE), a decrease in the cost of one firm could actually lead to increased
output by the rival firm, contrary to the “intuition” from the linear model.
4
Estimating The Cournot Model.
The problem of estimating the Cournot Model is not much different from
basic supply and demand. For the moment, assume that we observe firms
within a cross-section of markets. For each market, we observe market price,
output and a set of exogenous demand shifters. For each firm within the
market, say for now that we observe firm output and a set of (possibly firmspecific) exogenous cost shifters.
Since the Cournot model assumes homogeneous goods, estimates of the
demand side can be obtained in exactly the same fashion as in the S&D
model. If inverse demand in market n is linear,
pn = xn βx − βq Q + ,
then estimates of βx and the slope of demand, βq , can be obtained by a linear
instrumental variables regression of price on demand shifters and market
quantity.
Now however, the supply curve is replaced by the Cournot first-order
condition. If marginal cost for firm j in market n is linear,
mcnj = wnj γ + λqnj + ωnj ,
11
then the Cournot first-order condition reduces to
pn − βq qnj − wnj γ − λqnj − ωnj = 0,
or
ωnj = pn − wnj γ − (βq + λ)qnj .
As with the supply equation, the parameters entering the Cournot f.o.c. can
be estimated from a restriction that
E[ωnj | znj ] = 0
for some instruments z, when ω is evaluated at the true value of the parameters. As before, instruments might include demand shifters that don’t enter
wnj . However, now we have a first order condition for each firm, so we have
more than one “pricing equation” in each market. (One might want to model
the correlation between unobserved firm costs within a market.)
An advantage of using the first-order condition for estimation is that the
f.o.c. holds as long as an equilibrium exists, whether that equilibrium is
unique or not. Thus, we can estimate the parameters of the model from
demand and the f.o.c. even if the “reduced form” of the model is not welldefined because of non-uniqueness. Given the estimated parameters of the
model, we can check second-order conditions to see if the parameters are
consistent with the existence of equilibrium. Remember that firm output qnj
varies with the cost shifters of all firms in the market, as well with own-firm
wnj and with x. This gives us more potential instruments than in the S&D
model.
Note that the supply side in this linear Cournot model will identify only
the sum θq = (βq + λ). However, we have an estimate of βq from the demand
side and so can use as our estimate λ̂ = θ̂q − β̂q . This raises an important
question of whether it is possible to distinguish the competitive and Cournot
models (see Bresnahan (1982)). One can estimate both by an IV regression of
price on cost shifters and quantity. Under p = mc, the slope of this equation
is the slope of mc, while under Cournot the estimated slope is the sum of
the slopes of demand and mc. If demand and mc are linear, then, the two
models cannot be distinguished although they have different implications.
Now consider the case of non-linear cost and demand. Some intuition
may be gained by considering a rotation of a demand curve about a given
12
P 6
H
@HH
@ H
M CC
H
@H@ HH
@HH
@H HHH E 1
H
@ @HH
•
@ @ HE2HHH
•H
@ @H
HH HH D1
@@
HH
@ @
M(C M H D2
@ (
@(
(
(
((( @ @
(((
@ @
(
M R2
M R1
-
Q
P 6
H
@HH
@ H
M CC
HH
``@
H
H
` ` H
H`
``H
E1 H@`
``
@
HH
H
E3
`
• ` •`
H
HH``
@
H
HH D3
@H
H
H D1
@ HH
HH
@
M
( MC
(
(
H
@
(
(
H
((@
((((((
M R3
(
(
@
M R1
-
Q
Figure 1: Source: Bresnahan(1982), Fig
1. Perfect competition and oligopoly models
each predict the impact of an exogenous shift
of the demand curve. We observe output and
price combinations E1 , E2 , which are consistent with either a high marginal cost competitive market, or a low marginal cost oligopoly.
Moving the intercept of the demand curve is
therefore not sufficient to allow us to distinguish between the two models.
Figure 2: Source: Bresnahan(1982), Fig 2.
The figure shows a rotation of the demand
curve about E1 . Under perfect competition,
E1 should be the equilibrium under either D1
or D3 . However, if M C M were the marginal
revenue curve, the equilibrium shifts to E3 ,
where M C M = M R3 .
point, as shown in the Figure below. If some demand shifters change the
slope of the demand curve, then the two models can be distinguished. Under
perfect competition, p = mc, the equilibrium price and quantity should not
change. In contrast, under Cournot competition, changing the slope of the
demand curve changes the markup and thereby change the equilibrium price
and quantity.
For an example, consider an inverse demand function with interactions
13
between quantity and demand shifters
pn = xn βx − βq Qn − Qn xn βqx + The f.o.c. for the Cournot model becomes:
pn − (βq + xn βqx )qnj − wnj γ − λqnj − ωnj = 0,
while the pricing equation under perfect competition does not change. In
this case, if interactions between qnj and xn are found to enter the pricing
equation with statistically significant coefficients, we can reject the marginal
cost pricing model since it does not explain why xn should enter the pricing
equation directly.
Note that it practice we may often fail to have enough market-level data
to get precise estimates of interaction terms like βqx and so may have difficulty
testing the hypothesis of competition. This suggests a further advantage of
using consumer level data to obtain more precise estimates of demand.
5
The “Conduct” Parameter
Sometimes the discussion of whether one can distinguish competitive behavior from marginal cost pricing is put in terms of identifying a “conduct
parameter”. This discussion is motivated by rewriting the Cournot first-order
condition as
∂p ∂Q
− mcj = 0.
p(Q) + qj
∂Q ∂qj
∂Q
The term ∂q
is suppose to represent firm j’s “conjecture” about how total
j
industry output changes with firm j’s own output conjectural variations approach treated quite seriously, with elaborate variations that are sometimes
difficult to reconcile with any theory. For example, some authors let the
conjectural variations parameter depend on firm outputs in a very general
way.
However, it is still possible to note that we can write a single pricing
equation that nests competition, Cournot and monopoly or joint-profit maximization:
∂p
1
p(Q) + qj
(θ1 + θ2 ) − mcj = 0.
∂Q
sj
14
where under competition (θ1 = θ2 = 0), under Cournot (θ1 = 1, θ2 = 0)
and under joint-profit maximization (θ1 = 0, θ2 = 1). Other values for the
“conduct parameters” can not be explained by a static equilibrium model
and so must be the result of either estimation error or misspecification of
the model. Despite the rather restrictive “correct” interpretation of (5),
many authors who know better will still refer to parameters like (θ1 , θ2 ) as
“conduct” or “c.v.” parameters.
6
Formal Identification
Lau (1982) provides more formal conditions under which the shape of the
marginal cost curve can be identifying without knowing the type of competitive behavior (but when the demand curve is known.) Lau assumes that we
observe p, Q, q and the functional form of demand, P (Q, x). We know that
mc = g(q, w), but don’t know the form of g(·). Further, we know that the
data satisfies the “c.v.” first-order condition,
p + θqP 0 (Q, x) = mc(q, w)
Formally, non-identification implies that there are more than one combination of θ and g(·) that can satisfy this equation for all possible combinations
of data. Lau shows that the problem is not identified if and only if x enters
demand as a single index. That is, θ and mc are not separately identified iff
P (Q, x) = P (Q, r(x)), for some r(x) : RKx → 1.
An implication of Lau’s result is that given linear demand, the slope must
depend on x and given a constant elasticity demand function the elasticity
as well as the level of demand must depend on x.
Of course, restrictions on the functional form of g(·) can also provide
identification. If mc is constant in q, then θ is always identified.
Lau’s result does not explicitly consider the role of any unobservable
factors in supply and demand. He considers data generated by moving x,
and therefore shifting the known deterministic demand function against the
unknown and fixed marginal cost function.
A more realistic identification approach would follow on the non-parametric
structural identification literature in Brown (1983), Roehrig (1988), and
Brown and Matzkin (1998). This approach is followed in Benkard and Berry
15
(in process). Benkard and Berry show that requires two separate sources
of change in the markup, either from at least two x0 s or, more subtly, from
x and from the demand error . This last observation was not available in
earlier treatments of the problem, such as Lau. The intution is that if, for example, shifts the slope of the demand curve while x shifts the level, then we
can identify the role of the Cournot markup. (Recall that given the demand
estimates, the level of is defined as a residual and is therefore “observed”
once the parameters of demand are known.)
Exercise 2 Exercises on Conduct and Identification
1. Show that the first-order condition for joint profit maximization by firms
can be derived from (5) in the case where the elasticity of firm output
with respect to market output is one.
2. Show how to rewrite (5) as
1
p + (θ1 + θ2 sj )p = mcj
η
where the η is the demand elasticity and the “c.v.” parameters θ1 , θ2
now have a different interpretation. What restrictions do the three
“modes of conduct” now impose on these parameters?
7
Aggregation and Cost Information
In some cases one may only observe market-level information and not firmlevel information. In this case the firm’s first-order conditions can be aggregated into a single market pricing equation by taking an average of firm’s
first-order conditions equations. For example, Appelbaum (1982) and Porter
(1983) aggregate their first-order conditions to the market level. Either a
simple average or else a share-weighted average could be taken, depending in
part on the data that is observed. For example, if we take the output-share
weighted average of the firm level first-order conditions, we obtain:
p+H
∂p
= m̄c,
∂Q
16
(5)
where m̄c is the average of the firms’ marginal cost functions. If, for example,
we assume that firm marginal cost is linear in firm cost shifters, then the
share-weighted average of those shifters will appear in the market-level price
∂p
relation. Also note, for better or worse, that the “coefficient” on ∂Q
can be
interpreted as the a market-level conduct parameter, with the value 0 for
competition, H for Cournot and 1 for Monopoly.
At the opposite extreme of data availability, we may observe not just firm
outputs and costs shifters, but also the input choices of firms and/or their
costs, C(qnj , wnj ), a case we return to in Chapter 3.
In this case of input demand demand, we could estimate both cost and
demand separately and then test various values of the “conduct parameters”
to see how well they fit the theory (see Genesove and Mullin (1996)), or we
could gain efficiency by jointly estimating cost, demand and “conduct” from
the demand, cost and pricing equation (or alternatively from the demand,
pricing and input demand equations.)
For example, Gollop and Roberts (1979) consider the unconditional input
demands that are generated by the Cournot model. Consider profits as a
function of inputs xj ,
p(Q)fj (xj ) − w0j xj
where wj are input prices, fj (xj ) is the production function for firm j and
P
Q = j fj (xj ) is again total market output. The first order condition is that
marginal revenue product of an input equal the input price:
[p + qj
∂p ∂fj (xj )
][
] = wjk
∂Q ∂xjk
Or,
M Rq M Pk = wjk ,
where M R is marginal revenue and M P is marginal product. There is one
such first-order condition for each input for each firm.
Gollop and Roberts (1979) use a translog production function, but don’t
model the error structure. Given some other production function, the error
structure could be modeled in the fashion of McElroy (1987), as input specific
shocks.
Exercise 3 Exercises on Aggregation and Cost Information
17
Show how you would aggregate the first-order condition from the linear
Cournot model to obtain an average first-order condition. What data
must you observe to estimate the model?
2. Suggest a way to derive Gollop’s and Roberts estimation, including a
1.
specification for the error term. What do you think of the idea of treating capital as being choosen in each period? In contrast, how do Olley
and Pakes treat capital stocks?
7.1
Applications
Many of the early papers were focused quite clearly on the question of estimating the “conjectural variations” parameter, for example Appelbaum
(1982) used Census input data a wide variety of markets to calculate CV
parameters. There are a number of problems with his approach, but he finds
sensible results in that, for example, the tobacco industry is found to be
relatively uncompetitive (behaving as if it consisted of two or three equally
sized Cournot competitiors), while the texfile industry is found to be quite
competitive.
Porter (1983) begins his empirical study of collusion (discussed later in
the course) with a simple variant of a CV model. Porter studies the late
19th century market for railroad transportation of grain from Chicago to
East Coast ports. Demand in week t is given by
ln(Qt ) = α0 + α1 ln(pt ) + α2 ln(Lt ) + ut ,
(6)
where p is price L is an indicator for whether the water transportation via
the Great Lakes is possible, or whether the water route is shut down by
winter weather. Here, the lake indicator is a nice example of an exogenous
demand shifter. Costs are given by a constant elasticity function at the firm
level, which implies a first-order condition that (with some effort) is possible
to aggregate to the market level. Changes in competitive conditions (such
as the number of railroads in operation) provide a supply-side variable that
is not in the demand function and is, under some assumptions, a possible
instrument for price in the demand function.
Sometime we might be interested in using the Cournot model to recover
marginal cost information, so that we can in turn conduct some policy experiement. Genesove and Mullin (1996) “test” the CV model by applying
18
it to a industry where they directly observe marginal cost data. In particular, they look at historical data on the sugar industry, where historical
records provide good engineering estimates of marginal cost. They estimate
the model both using and not using the marginal cost data. In the later
case, they have to “back out” marginal cost from the estimated first order
condition. For this data, they find the CV method does a pretty good job
of reproducing observed marginal costs. The CV parameter, unfortunately,
indicates a “high” level of competition which is not consistent with any static
model.
Wolfram (1999) also considers an industry, the British electricity market,
where she has independent measures of marginal cost. She considers number
of approaches, one of which is to compare the estimates of marginal cost from
a Cournot model to those defined in her data. She finds that while there are
substantial markups over marginal cost, they are not as high as those that
would be implied by Cournot model.
7.2
Qualitative Tests of Monopoly or Market Power.
A number of authors have proposed tests of monopoly or market power which
do not rely on estimates of the demand and cost parameters, but rather on
other “reduced form” features of the data. See, for example, Ashenfelter
and Sullivan (1987) who look for implications of monopoly behavior on the
“pass through” of cigarette excise taxes to consumers. There are a number
of problems with the approach, as there are few strictly monopoly industries
where the pure monopoly hypothesis is of interest. However, the general idea
of looking for implications on the reduced form of a model (i.e. a version of
the model with only exogenous data on the right-hand side) is of considerable
interest.
19
8
Alternative Static Models of price or quantity setting with homogeneous products.
9
Bertrand, Edgeworth and Kreps-Scheinkman
9.1
Bertrand
Some decades after the Cournot model, the French mathematician Bertrand
criticized the model on the grounds that quantity-setting is obviously wrong
and that firms clearly set prices. In the case of price-setting, Bertrand attacked Cournot’s equilibrium concept (essentially, Nash equilibrium) on the
grounds that it led to a ridiculous result. With homogeneous goods and constant marginal cost, the best-response to any rival’s price set above marginal
cost is to undercut the rival slightly and take the whole market. The equilbrium is at price equal marginal cost. Bertrand thought the firm’s would
more likely collude than settle for this outcome.
The “Bertrand model”1 makes an extreme use of the homogenous good
assumption (any undercutting in price leads to 100% of the market switching
to the low price firm). It is difficult to think of very many markets where the
products are this homogenous – most products differ in at least in geographic
location, reputation and terms of service. (Note that gasoline stations located
on the same corner often charge different prices, despite offering what appears
to be a homogenous goods at nearly the same location.)
It is also very difficult to know how the market ever comes to be a duopoly,
with p = mc there is no chance to recover any fixed entry cost. If the
firms cannot follow Bertrand’s advice and collude, it seems that a potential
Bertrand duopoly would almost certainly remain a monopoly.
Finally, the simple Bertrand equilibrium analysis seems to disappear when
short-run marginal cost is increasing – in that case the undercutting firm
might not want to serve the whole market at a fixed price.
For all these reasons, the homogeneous goods Bertrand model seems to
be a very bad starting point for any kind of empirical or applied theory exercise (unfortunately, the model is frequently used as a benchmark in applied
theory.)
There is still the interesting question of how firms would behave as price
setters in a realistic context. One idea is to introduce just a little product
1
An odd name for a model that Bertrand set out to ridicule.
20
differentiation – we will return to this idea below.
Another idea is to consider capacity constraints, which turn out to lead to
a connection between Bertrand-style price setting and the Cournot quantitysetting outcome.
9.2
Edgeworth
Edgeworth suggested looking at the Bertrand model with capacity constraints,
which are one simple version of upward sloping marginal cost.
As a simple example, consider an inverse demand function of
Q=1−p
(7)
with zero marginal cost and capacity, K, the same for each firm.
If if K ≥ 1, we obviously get the Bertrand equilibrium. Now suppose
that K is sufficiently small that a firm cannot necessarily serve all the demand if it undercuts its rival. Now there are two possible equilibria: either
undercutting or else serving as a monopolist against the residual demand.2
It is straightforward to show that as the rival firm’s output drops, at some
point it becomes better to serve the residual demand. For intermediate levels
of capacity (where K is above the Cournot level), Edgeworth noted that the
best-reply curves never cross. The best-reply is to undercut down to some
level (say p̂) and then jump up to a higher price (say p∗ ) on the residual demand curve. The higher price is not an equilibrium, because the best-reponse
to it is to undercut. The best-reply dynamics then form an “Edgeworth cycle” and there is no pure-strategy Nash equilibrium.
However, if capacities are below the Cournot level, then jointly setting the
monopoly price against the residual demand is a pure-strategy equilibrium;
the firms are capacity constrained and there is no point to undercutting.
This suggests that pricing in the face of capacity competition can look like
“Cournot” pricing, where the capacity is dumped on the market and the
market-clearing price is set. However, Edgeworth did not examine the problem of how capacities are choosen.
2
There is an issue of how the residual demand is formed. The easiest assumption
is “efficient rationing,” where the highest willingness-to-pay consumers are served first.
Then, the output of the other firm is just subtracted from the quantity intercept of the
demand curve to form the residual demand.
21
9.3
Kreps and Scheinkman
The capacity setting problem is considered by Kreps and Scheinkman (1983),
consider a two-stage game where K1 and K2 are choosen in the first stage and
the second stage is an Edgeworth game. For small K’s, the firms produce
K in the second stage and so the game locally looks like Cournot – a small
increase in K gives the Cournot marginal revenue. For large enough K
the pure-strategy equilibrium breaks down and Kreps-Scheinkman have to
caculate the expected profits from the mixed-strategy equilibrium. It turns
out that the firms don’t want to enter the mixed-strategy region and so stop
at the Cournot level of K1 = K2 = 13 . (See also the discussion in Tirole.)
K-S is not entirely robust to, for example, the choice of the rationing
mechanism, but the general spirit seems to survive even in dynamic versions
of the game. K-S provide an empirical rationale for something like a Cournot
model if we think that capacity constraints (or other similar constraints,
like adjustment costs) are important in an industry that is approximately
homogeneous goods.
See also the discussion of Judd and Cheong in the chapter on oligopoly
dynamics, below.
10
Differentiated Products
While Kreps and Scheinkman (1983) provide one empirically plausible response to the Bertrand Paradox, the most straightforward solution is to
introduce differentiated products.
While homogenous goods is a convenient assumption for many models,
it is frequently violated in practice. Many markets feature goods that are
not identical, they vary in quality, features, reliability, reputation and/or
geographic location. Indeed, markets of literally identical goods seem to be
relatively rare, especially once differences in seller’s locations and reputations
are taken into account.
A small amount of “smooth” product differentiation can result in a model
that is approximately Cournot, but doesn’t have all the very odd results of
the Bertrand model (which come in large part from the discontinuity in
own-firm demand caused by the extreme assumption of exact homogeneous
goods.)
22
10.1
Nash Equilibrium in Differentiated Products Oligopoly
In a differentiated products demand model, we replace the homogenous good
assumption with a demand system for each of N goods. For product 1 in
market i we might a demand function of
q1i = D(p1 , p2 , . . . , pN ).
In Chapter 4, we will consider the detailed analysis of such a demand system,
but for now we will assume that the demand system is given.
The simplest models of product differentiation would consider a set of
single product firms each producing a differentiated product. We could begin
by specifying a demand system for this set of related products, together with
cost functions and an equilibrium notion. The usual assumption is Nash in
prices. To analyze the case of equilibrium with differentiable demand, note
that the profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p)).
The first-order condition is:
qj + (pj − mcj )
∂qj
= 0.
∂pj
Note that we can rewrite this as
pj = mcj + bj (p),
where the markup is
bj (p) =
qj
|∂qj /∂pj |
Also, we can write the product Lerner index in terms of the usual “inverse
elasticity” rule.
(pj − mcj )
= 1/ηj ,
pj
where ηj is the absolute value of the product-specific elasticity.
The second order-condition is given by:
∂qj
∂ 2 qj
∂mcj
+ (pj − mcj ) 2 −
(∂qj /∂pj )2 < 0
∂pj
∂pj
∂qj
23
This is surely negative when demand slopes down and is concave and marginal
cost does not slope down. If demand is too convex, we sometimes have trouble (e.g. remember the monopoly case with constant elasticity demand, with
an elasticity less than 1.) If the second-order condition holds everywhere,
we have a sufficient (but not necessary) condition for a well-defined reaction
function.
Differentiating the first-order condition, we find that prices are strategic
complements when
∂ 2 qj
∂mcj ∂qj ∂qj
∂qj
+ (pj − mcj )
−
>0
∂pk
∂pj ∂pk
∂qj ∂pk ∂pj
(8)
This obviously holds in the linear demand case when the goods are substitutes, but need not hold in a non-linear case. This accounts for the general
intuition that prices are strategic complements in the price-setting model.
Non-differentiable Demand
Some care must be taken in assuming differentiable demand functions, because many natural specifications result in discontinuous demand functions.
For example, consider the simple Hotelling model of competition on a line,
with the transportation cost equal to the absolute value of the distance between the consumer and the firm
uij = ū − pj − kxj − νi k,
In this case it is possible for one firm to undercut . . . [AND SO FORTH]
Quantity vs. Price Setting
. In differentiated products models, one could also consider quantity setting
firms, as in the Cournot model. In this case, the first-order condition becomes
p j + qj
If
∂pj
− mcj = 0.
∂qj
∂pj
1
=
,
∂qj
(∂qj /∂pj )
(9)
then this first-order condition is the same as the price-setting f.o.c. Condition
(9) holds when a change in price changes only the own-product quantity: this
24
is just the monopoly case. However, in general, ∂pj /∂qj is the j th diagonal
element of the J by J matrix
"
#−1
∂q
,
∂p0
which is not the same as the inverse of of ∂qj /∂pj . For many examples, the
quantity-setting markup will be higher than the price setting markup.
The question of price vs. quantity setting in differentiated product models
is asked, in a Kreps-Scheinkman like way, in J. Friedman (RAND, 1988) and
I. Hendel (1994).
10.2
Estimation from the First-Order Conditions
Once again, we will leave the question of demand analysis to Chapter 4.
Assume for now that we know (from the empirical estimation of demand as
outlined in Chapter 4), the demand function and its derivatives. The demand
for good j in market i is
qji = D(p, x, , θd ),
(10)
where p is a vector of prices, a demand error (or a vector of demand errors),
x is a vector of demand shifters and θd is a parameter that is known from
the demand analysis. We assume that once θd is known, we can calculate the
derivatives of demand with respect to price and any point in the observed
data.
While the demand analysis will turn out to be more complicated than
in the Cournot or Supply and Demand case, the supply side, given Nash
pricing, is almost the same as in the Cournot case. Once again, we can write
down the first order condition, show how it reveals the error in marginal cost
as a “residual” and then build an estimator on the assumed property of the
cost error/supply residual.
Once again, say that marginal cost is
mc = wji γ + λqji + ωji .
(11)
From the first-order condition, we know that
mci = pi +
25
qi
|∂D/∂pi |
(12)
The second term on the right, the markup, is known by observing q and
knowing the derivatives of demand (via the empirical demand analysis).
Thus, our options as the same as in the estimation of Cournot. In particular, we can plug in the functional form for mc and solve for ω:
ωji = pi +
qi
− wji γ − λqji ,
|∂D/∂pi |
(13)
and we can use this equation to build a method of moments estimator as
before.
The interesting new problem with differentiated products is therefore not
the supply side but the demand side, and so we put off a through discussion of
empirical applications involving differentiated products until Chapter 4. The
applications there are typically richer than the applications we have discussed
to this point because the differentiated products framework typically allows
a richer match to real-world detail.
Exercise 4 Exercises on simple models of Product Differentiation
1. Consider a duoploy with the demand functions:
1
qj1 = a − (p1 − p2 )
t
and
1
qj2 = a − (p2 − p1 ),
t
where a and t are (strictly positive) parameters. Assume that the firm’s
marginal costs are constant at mc1 and mc2 .
(a) Graph the best reply functions of the two firms.
(b) What happens to the equilibrium price as t goes to zero?
2. Consider a differentiable demand function.
(a) Give sufficient conditions for each term of (8) to be positive.
(b) Show that the derivatives of market share in the logit model are
∂sj /∂pj = −αsj (1 − sj ) and ∂sj /∂pr = αsj sr .
26
11
Method of Moments (More Advanced Material)
This is a useful time to give an intuitive introduction to the generalized
method of moments, which we will often use to motivate estimators. Your
Applied Micro-econometrics class will provide a formal exposition. We begin
with the mean independence assumption E( | Z) = 0. Note that the demand
“error” is implicitly defined by the demand equation as a function of the
data and the parameters:
n (θ) = ln(Qn ) − xn β − αln(pn ),
where the vector of parameters is θ = (β, α). The true value of the demand
errors is then defined as this function evaluated at the true parameter values,
θ0 .
From the mean independence assumptions, we know that has zero covariance with any function of Z. This leads to the population “moment
conditions”,
G(θ0 ) ≡ E( (θ0 )H(Z) ) = 0,
(14)
for any function H(·) of Z. The “sample analogue” of this restriction on the
population of random variables (Z, ) is that the sample covariance should
equal zero.
N
1 X
GN (θ0 ) =
(θ0 )n H(Zn ) = 0.
(15)
N n=1
It might seem reasonable, then, to treat as our estimate of θ0 the value
of θ that sets this sample analog as close to zero as possible. Indeed, this
suggests a general estimation strategy, know as “method of moments”. We
posit a population moment restriction, such as the restriction that some
pairs of variables have zero covariance. We then choose as our estimator
the parameter values that satisfy the sample analogue of the population
restriction.
OLS is easy to motivate in this way. For example, consider the model
y = xβ + ,
(16)
with E(x0 ) = 0. The sample restriction is:
1 0
x = 0,
N
27
(17)
or, substituting in = y − xβ,
1 0
x (y − xβ) = 0.
N
(18)
If the matrix x has k columns, this is a system of k linear equations in the k
unknown values of β. Solving the system of equations for β gives the familiar
OLS estimator:
β̂ = (x0 x)−1 x0 y.
In cases other than OLS, the number of moment conditions (i.e. the
length of the vector G(θ)) may be greater than the the dimension of θ, and
so may be impossible to zero each of the moment conditions. In this case,
one can choose as an estimate the value of θ that minimises the quadratic
form:
Gn (θ)0 AGn (θ),
for some positive definite “weighting matrix” A.
Consider now the linear model with potentially endogenous right-hand
side variables. We still choose the functional form y = xβ + , but now we
use the moment conditions
E(z 0 ) = 0.
for some vector of “instruments” z. The sample objective function to be
minimized is then
(y − xβ)0 zAz(y − xβ).
This has first-order condition
−2x0 zAz 0 (y − xβ) = 0,
which gives the linear IV solution of
β̂ = (x0 zAz 0 x)−1 x0 zAz 0 y
(19)
Note that x0 z has to be of full rank, which says that the instruments have to
be correlated with the right-hand side variables, in addition to being uncorrelated with .
It turns out that 2SLS is equivalent to the one-stage estimator in (19),
with the weighting matrix A = (z 0 z)−1 .
We will often use non-linear instrumental variable methods, where G is
not linear in the parameters. In these cases, the objective function will have
28
to be minimized by numerical methods, but otherwise the method is the
same. The general non-linear method is called the Generalized Method of
Moments (Hansen 1982).
√
From (Hansen 1982), we find that the variance of N times the GMM
estimator θ̂ is
(Γ0 AΓ)−1 Γ0 AV ar(Gn )AΓ(Γ0 AΓ)−1 .
, where Γ = ∂G
. The method of moments literature also notes that the
∂θ
optimal choice of the weighting matrix is A = V ar(Gn )−1 and that the
optimal instrument (under regularity conditions including homoskedasticity)
is (Chamberlain, cite)
∂
H ∗ (Z) = E(
| Z)
(20)
∂θ
12
Non-parametric Identification (more advanced material)
One criticism of structural models is that they rely on too many assumptions.
The choice of functional form can often seem particularly arbitrary. One
response is to do a sensitivity analysis, varying the functional form to see
who it affects the policy conclusions.
Another idea is discuss weaker assumptions on functional form. It is
traditional to do this in two stages. The first stage considers the pure “identification” question: could the ture parameter be uniquely recovered given an
infinite amount of data (i.e. the true data generating process.) The second
stage is to discuss estimation with finite samples.
The idea is to consider more general functional forms, like a demand curve
of
q = D(p, x, , θ)
(21)
without specifying a functional form for D. We could think, in the simplest
case, of taking “flexible functional forms” as an approximation to a more
general function. In the 1970s, there was a extensive literature on such
functional forms (e.g. Fuss, McFadden, and Mundlak (1978)). For example, a
Cobb-Douglas (constant elasticity) function can be thought of as a first-order
taylor series approximation (in logs) to the true function. The parameters θ
are then just the parameters of the Cobb-Douglas. Going farther, function
which is quadratic in logs (the “translog”) can be thought of as a secondorder approximation and so forth. Alternatively, in a more modern spirit we
29
could think of a fully non-parametric case, where θ is an infinite dimensional
index of all functional forms that satisfy the assumptions of the model.
Following Brown (1983), Roehrig (1988), and Brown and Matzkin (1998),
we make the following assumptions:
• the function D is continuously differentiable in x, p and , which all
take on continuous values;
• is idependent of x;
• there is a true reduced form for the model, that generates the data
(q, p) as a function of the demand and supply shifters (x, w) and the
demand and supply errors (, ω);
• there is a “residual function” (or “link function”) – we can solve for
the demand and supply errors as a function of the parameters, the
endogenous outcomes (q, p) and the shifters.
These assumptions are discussed more formally and carefully in the cited
papers.
Under the Brown-Roehrig assumptions, a kind of instrumental variables
argument still works. The true θ is identified at some point in (q, p, x, w)
space if at that point there is a w which [i] enters the reduced-form with a
non-zero derivative and [ii] does not enter the demand function. See Benkard
and Berry (in process) for examples.
Of course, an identification result does not tell us how to estimate the
parameters in finite samples. In real life, we will still effectively have to make
some further assumptions to obtain parameter estimates, but it may be of
some comfort to know that as more data is obtained the functional form
assumptions can be relaxed.
13
More Advanced Material: Estimates FirstOrder Conditions, Uniqueness, Consistency
and Non-parametrics.
14
Empirical Examples
Very Brief Notes here:
30
The aren’t many recent examples of pure “supply and demand” estimation. Graddy (1995) has a nice example of a supply-side instrument for
demand: weather at sea as an instrument for wholesale fish prices in New
York City.
Turning to models of imperfect competition, historically:
• Rosse (1970) – first clear discussion estimation via an first-order to
uncover marginal cost (here the Monopoly first-order condition.)
• Iwata (1974) Estimates a Cournot / conjectural variations (CV) model
of the Plate glass industry.
• Gollop and Roberts (1979) use Census data and the first-order conditions from input choices, rather than output choice.
• Appelbaum (1982) uses Census industry data and an elaborate CV
approach.
• Porter (1983) uses data on railroads: instruments for demand include
the opening of the Great Lakes and instruments for supply include
changes in market structure (entry/exit).
• Two recent papers that have some marginal cost data and that see
how well the Cournot model can reproduce that data are Genesove and
Mullin (1996) (on the historical Cuban sugar industry) and Wolfram
(1999).
References
Appelbaum, E. (1982): “Estimating the Degree of Oligopoly Power,” Journal of Econometrics, 9(2), 287–299.
Ashenfelter, O., and D. Sullivan (1987): “Nonparametric Tests of
Market Structure: An Application to the Cigarette Industry,” Journal of
Industrial Economics.
Bresnahan, T. (1982): “The Oligopolistic Solution Concept is Identified,”
Economic Letters, 10, 87–92.
31
(1989): “Empirical Studies of Industries with Market Power,” in The
Handbook of Industrial Organization, ed. by R. Schamlensee, and RobertWillig, no. 10 in Handbooks in Economics. North-Holland.
Brown, B. (1983): “The Identification Problem in Systems Nonlinear in
the Variables,” Econometrica, 51(1), 175–96.
Brown, D. J., and R. L. Matzkin (1998): “Estimation of Nonparametric Functions in Simultaneous Equations Models with Application to
Consumer Demand,” Working paper, Yale Univeristy.
Bulow, J., J. Geanakoplos, and P. Klemperer (1985): “Multimarket
Oligopoly, Strategic Substitutes and Complements,” JPE, pp. 488–511.
Christ, C. F. (1985): “Early Progress in Estimating Quantitative Economic Relationships in America,” AER, 75(6), 39–52, (special oversized
number).
Cowling, and Waterson (1976): “Price Cost Margins and Market Structure,” Economic Journal, 43, 267–274.
Friedman, J. (1983): Oligopoly Theory. Cambridge Univ. Press, Cambridge.
Fuss, M., D. McFadden, and Mundlak (1978): “A Survery of Functional Forms in the Economic Analysis of Production,” in Production Economics: A Dual Approach, vol. 1. North-Holland, Amsterdam.
Genesove, D., and W. P. Mullin (1996): “Testing Static Oligopoly
Models: Conduct and Cost in the Sugar Industry, 1890-1914,” RAND,
29(2), 355–77.
Goldberger, A. (1991): A Course in Econometrics. Harvard, Cambridge
MA.
Gollop, F., and M. Roberts (1979): “Firm Interdependence in Oliopolistic Markets,” Journal of Econometrics, 10, 313–311.
Graddy, K. (1995): “Testing for Imperfect Competition in the Fulton Fish
Market,” RAND Journal of Economics, 26(1), 75–92.
32
Hansen, L. (1982): “Large Sample Properties of Generalized Method of
Moments Estimators,” Econometrica, 50, 1029–1054.
Iwata, G. (1974): “Measurement of Conjectural Variations in Oligopoly,”
Econometrica, 42, 947–966.
Kreps, D., and J. Scheinkman (1983): “”Quantity Precommittment with
Bertrand Competition,” Bell J. of Economics, 14, 326–337.
Lau, L. (1982): “On Identifying the Degree of Competitiveness from Industry Price and Output Data,” Economics Letters, 10, 93–99.
McElroy, M. B. (1987): “Additive General Error Models for Production,
Cost, and Derived Demand or Share Systems,” Journal of Political Economy, 1995(4), 737–757.
Moore, H. L. (1914): Economic Cycles: Their Law and Cause. Macmillan,
New York.
Olley, S. G., and A. Pakes (1996): “The Dynamics of Productivity in the
Telecommunications Equipment Industry,” Econometrica, 64(6), 1263–97.
Porter, R. H. (1983): “A Study of Cartel Stability: The Joint Executive
Committee, 1880-1886,” Bell Journal of Economics.
Roehrig, C. S. (1988): “Conditions for Identification in Nonparametric
and Parametic Models,” Econometrica, 56(2), 433–47.
Rosse, J. N. (1970): “Estimating Cost Function Parameters without using
Cost Function Data: An Illustrated Methodology,” Econometrica, 38(2),
256–275.
Wolfram, C. D. (1999): “Measuring Duopoly Power in the British Electricity Spot Market,” The American Economic Review, 89(4), 805–826.
Working, E. J. (1927): “”What do Statistical Demand Curvers Show”,”
QJE, 41, 212–35.
33