Topic

1

• Topic 2 Identifying the Oligopoly Solution
  Empirical Methods with Homogeneous Products
  Fall 2003
• Bresnahan, (Economic Letters, 1982), The
  Oligopoly Solution Concept is Identified
• Porter (Bell Journal of Economics, 1983) A
  Study of Cartel Stability The Joint Executive
  Committee, 1880-1886
• Ellison (Rand Journal of Economics, 1994)
  Theories of Cartel Stability and the Joint
  Executive Committee

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• Bresnahan, 1982
• This paper shows that the oligopoly solution
  concept can be identified econometrically.
• Let demand and marginal cost (MC) be linear
• Q ?0 ?1P ?2Y ? (1), where Y (income)
  is exogenous
• MC ?0 ? 1Q ?2W? (2), where W (weather)
  is exogenous
• Supply relationship P?(-Q/ ?1) ?0 ? 1Q
  ?2W ? (3), since MRPQ/ ?1. (MRMC is supply
  relationship)
• Note that ?0 implies perfect competition, ?1
  implies monopoly, while ?1/N implies Cournot
  with N firms.
• Since both equations (1) and (3) have one
  endogenous variable, and since there is one
  excluded exogenous variable from each equation,
  both equations are identified.

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• But are we estimating PMC or MRMC?
• Rewrite (3), P?0 ? Q ?2W ? , where ? (?1
  -?/ ?1).
• We can estimate ?, since the supply equation is
  identified.
• Although ?1 can be treated as known (because we
  can estimate the demand equation), we cannot
  estimate ?1 and ?.
• In figure 1 (next slide), E1 could either be an
  equilibrium for a monopolist (or cartel) with
  marginal cost MCM, or for a perfectly competitive
  industry with cost MCC.
• Increase Y to shift the demand curve out to D2
  and both the monopolistic and competitive
  equilibria move to E2
• Unless we know marginal costs, we cannot
  distinguish between competition or monopoly (nor
  anything in between).

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Figure 1 Observational Equivalence
E1
E2
MCC
MCM
D2
D1
MR2
MR1
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• The solution to the identification problem
• Suppose demand is such that
• Q ?0 ?1P ?2Y ?3 PZ ?4 Z ? , where Z is
  another exogenous variable.
• The key issue is that Z enters interactively with
  P, so that changes in Y and Z both rotate and
  vertically shift demand.
• Z might be the price of a substitute good, which
  makes the interaction term natural.
• Supply relation becomes
• P - ? Q ?0 ?1Q ?2W ? , where QQ /(?1
  ?3Z)
• Since the demand equation is still identified, ?
  and ?1 are identified. (There are two endogenous
  variables Q,Q, and two excluded exogenous
  variables Z and W.)

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• Graphically (see figure 2 on the next slide), an
  exogenous change in the price of the substitute
  good rotates the demand curve around E1.
• If there is perfect competition, this will have
  no effect on the equilibrium price and it will
  stay at the point associated with E1.
• But, if there is monopoly power, the equilibrium
  will change (to E3 as shown in figure 2).
• This result can be generalized beyond linear
  functions and pictures!
• There are other assumptions that can generate
  identification.
• Marginal cost that does not vary with quantity
  (?10).
• Use of supply shocks (Porter, 1983).

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Figure 2 Identification
E1
E3
MCC
D3
MCM
MR3
D1
MR1
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Porter, 1983 A study of cartel stability the
Joint Executive Committee (JEC) from
1880-1886 RR cartel formed in 1879, pre-Sherman
Act (1890) so publicly acknowledged. Controlled
Eastbound freight shipments between Chicago and
East Coast (mainly grain) Worked by allocating
market shares (so price was the strategic
variable). Entry occurred twice between 1880 and
1886. JEC office kept weekly records of quantity
shipped and prices
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The Model Basic Economic model -- trigger idea, a
la Green and Porter. Dynamic, non-cooperative
equilibrium permits collusion. But price wars
will occur, although such reversions are
triggered by demand shocks (firms do not
cheat). Assumption of a homogeneous good (perhaps
due to aggregate data) Assumes that reversion is
to to static Bertrand pricing (pMC).
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Porters Estimation Strategy Demand Constant
Elasticity Demand Curve
(1)
Q is aggregate quantity shipped, p is average
price and L is a dummy for whether the Great
Lakes are open and there is more competition.
(Note that he also included 12 seasonal dummies,
each dummy corresponding to a four week period.
Data are in weeks) Constant elasticity of demand
important because it allows him to use aggregate
industry-wide data
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First order condition for profit maximization for
a given firm i pt (1 ?it/?1)MCi(qit) ?it0
under perfect competition ?itsit under Cournot
behavior ?it1 under monopoly To get industry
supply relationship, weigh the individual FOCs by
market share ?i sit pt (1 ?it/?1) ?i sit
MCi(qit) Since ?i sit1, pt (1 ?t/?1) ?i sit
MCi(qit), where ?t ?i sit ?it
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Let Ci(qit)ait qit? Fi, where ?, the constant
elasticity of variable costs with respect to
output, must exceed one in order for an
equilibrium to exist. It can be shown that given
these functional forms, the market share for each
firm depends only on the as and ?, e.g., the
shares of firms are purely a function of their
marginal costs, regardless of whether they are
colluding or not. This is important because
dont want unobserved changes in marginal cost to
drive results It can then be shown that that
industry aggregate marginal cost has the
following form
Where D is a function of the as and ?.
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Aggregate Supply Relationship Hence the aggregate
supply relationship is pt(1 ?t/?1)DQt(?-1)
(2) ?t0 under perfect competition, ?tH
under Cournot behavior ?t1 under monopoly
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The interpretation of ?t is that it is an average
of the conduct parameters of the individual firms
in the industry. Letting ? vary by firm would
result in an over-parameterized model, since only
aggregate data are available. Taking logarithm of
(2) yields log(pt)-log(1 ?t/?1)log(D) (?-1)
logQt (3). Since the elasticity of demand (?1) is
constant, if ?t was constant, (2) could be
estimated. But Porter wants ?t to vary between
collusive and non-collusive regimes.
15
Renaming parameters, and adding some exogenous
institutional variables (S) the supply
relationship becomes
(4)
It is a dummy variable equal to one in periods of
collusion and zero during price wars. ?0 log
D, ?1 ? - 1, ?3 -log(1 ?t/?1), or
If It was known, it would be simple to estimate
(4). Since It is not known, Porter assumes that
It 1 with probability ? and 0 with probability
1-?. He then estimates the system (1),(4) by
switching equation methods which also yields
estimates of the probability ? and estimates of
It, i.e., whether the regime is collusive or not.
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Results The estimate of ? under periods of
collusion (implied by estimates of ?3 and ?1
is 0.234 in the first column of Table 3, using
data from trade press on whether a price war was
taking place. 0.336 in the second column of
Table 3, (estimating whether the regime is
cooperative or in a price war). This estimate
for ? is close to what would be obtained under
Cournot. Remember, that periods of competition
were assumed to be Bertrand, so ? is equal to
zero in this case. Key result is that estimate of
? for cooperative periods greater than prices
under competition. Elasticity of demand negative,
but inelastic, so marginal revenue associated
with industry demand curve is negative. This is
not consistent with single period profit
maximization.
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The estimate of ? is not significantly different
from one under the switching regression regime.
This means that there might not be an
equilibrium. If unobserved changes in the
marginal costs are correlated with regime changes
(violating the orthogonality assumption),
estimates will be biased. Summary Hence the paper
seems to document the existence of price
wars. Why price wars start or how long they last
is not examined. Functional form really matters
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Ellison, 1994 Does three key things with Porters
data (1a) Reconsiders implications of Green and
Porter theory for this industry allows demand
to be serially correlated (following an AR(1)
process). (1b) Allows probability of price war
tomorrow to be dependent on whether there was a
price war today. (Porter assumed that the
probability of a price war was independent from
period to period.) He uses a Markov process and
assumes that the indicator of collusion (It)
evolves according to the logit model ProbIt1
1 It ,Zt e?Wt/(1e?Wt), where Wt includes It
as well as other variables. (In Porters
analysis, W is a constant independent of It.)
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(1b) alone seems to make little difference. But
(1a) and (1b) combined make a big difference.
See table 2. It would be interesting to see
whether (1a) alone makes a difference. Results
elastic demand (-1.8 for Ellison vs. 0.8 for
Porter) This also makes ? (degree of collusion)
much greater .85 vs. .34 Another key difference
is that the probability of collusion after a
collusive state is 0.975 (e3.67/(1e3.67) and
0.67 after a price war (e.067/(1e.067). (See
table 2 next slide)
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(2) Ellison considers sources of possible price
war triggers, by examining the causes of price
wars. The variable BIGSHARE1 embodies the
notion that a switch in regime to a price war is
most likely to occur when one firm obtains a
suspiciously high share. Deviations are measured
by the difference between current shares and past
shares. He also defines variants of this
variable BIGSHARE2 BIGSHAREQ. The variable
SMALLSHARE1 captures the notion that someone has
a suspiciously low market share.
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He employs logit regression that attempt to
predict the probability of the onset of a price
war. Bigger signal of cheating (larger BIGSHARE)
in period t should reduce probability of
collusion in period t1. Supportive evidence in
the case of BIGSHARE as a trigger, although not
terribly statistically significant. (see table 3)
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• (3) Compares GP to Rotemberg Saloner
• If the ratio of current demand to future demand
  is high, a cartel may choose several possible
  responses.
• higher probability of price wars if you cheat
  (more sensitive triggers).
• lower equilibrium prices
• Imprecise results on interaction term (collusion
  dummy times ratio of current to future demand) in
  supply equation, so cant reject counter or
  pro-cyclical pricing.
• No evidence that price wars are more likely to
  occur.