ECO 2901
EMPIRICAL INDUSTRIAL ORGANIZATION
Lecture 5: Models of Competition in Prices & Quantities
Victor Aguirregabiria (University of Toronto)
Toronto. Winter 2016
Victor Aguirregabiria ()
Empirical IO
Toronto. Winter 2016
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Introduction
Introduction
Main source of strategic interactions between …rms comes from …rms’
price and quantity decisions.
Models of competition where …rms choose prices or quantities are at
the core of IO.
Main motives to estimate these models:
1. Complete supply / demand equilibrium model: estimation
& counterfactuals
2. Estimation of …rms’costs
3. Identi…cation/estimation of the Nature of Competition
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Empirical IO
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Introduction
Equilibrium model of demand & supply
The answer to many economy questions in IO require the
consideration of and equilibrium model of demand and supply.
E.g., e¤ects of competition on consumer welfare and pro…ts; e¤ects of
a new policy; mergers; etc.
A common approach to answer these questions is: (a) estimate
demand and supply parameters; (b) construct counterfactual versions
of the models that can be used to measure the causal e¤ect of
interest, and obtain the counterfactual equilibrium.
E.g., Counterfactuals: (a) model without the policy change; (b)
model with an hypothetical merger.
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Empirical IO
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Introduction
Estimation of …rms’costs
In many applications, researches do not have direct information on
…rms’costs.
A common approach to estimate …rms’costs is based on the
speci…cation and estimation of a model of competition, e.g., Cournot,
Bertrand, Stackelberg, Monopolistic Competition, Collusion, ...
The model predicts that form …rm i, MRi = MCi , where the concept
of MRi depends on the assumed model of competition.
Based on a estimation of demand, we can construct estimates of MR.
Then, the FOC implies estimates of MC .
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Empirical IO
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Introduction
Estimation of …rms’costs
(2)
We use this sample of realized MCs to estimate the marginal cost
function, and in particular how the marginal cost depends on:
- output of di¤erent products (economies of scale / scope);
- capacity;
- historical cumulative output (i.e., learning by doing);
- geographic distance between the …rm’s production plants
(i.e., economies of density)
- ...
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Empirical IO
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Introduction
Estimating the "Nature of competition"
The estimation of MCs is typically based on an assumption about
competition: about the nature of competition in an industry.
This consists in an assumption about:
- is the product homogeneous or di¤erentiated?
- do …rms compete in prices or in quantities?
- what does a …rm believe about behavior of other …rms?
- is there collusion between some or all the …rms?
Example: Nash-Cournot competition
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Empirical IO
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Introduction
Estimating the "Nature of competition"
(2)
The assumptions on "beliefs" and "no collusion / collusion" may be
di¢ cult to justify.
They have important implications on our estimates of …rms’costs, on
our interpretation of competition, and on our predictions using the
model.
We would like to learn from our data about the nature of competition.
This is the purpose of the conjectural variation approach.
This approach tries to estimate simultaneously …rms’costs and a set
of parameters (i.e., conjectural variation parameters) that
represent …rms’believes and that describe the nature of competition
in the industry.
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Empirical IO
Toronto. Winter 2016
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Outline
Outline
1.
Introduction
2.
Empirical Cournot models
2.1.
3.
4.
Model
2.2.
Estimation
Empirical Bertrand models of product di¤erentiation
3.1.
Model
3.2.
Estimation
Conjectural variation approach
4.1.
Homogeneous product industry
4.2.
Di¤erentiated product industry
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Empirical IO
Toronto. Winter 2016
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Outline
Main References
Bresnahan, T. (1982): “The Oligopoly Solution Concept is
Identi…ed,” Economics Letters, 10, 87-92.
Bresnahan, T. (1987): “Competition and Collusion in the American
Automobile Market: The 1955 Price War,” Journal of Industrial
Economics, 35, 457-482.
Corts, K. (1999): “Conduct Parameters and the Measurement of
Market Power,” Journal of Econometrics 88 (2), 227-250.
Genesove, D. and W. P. Mullin (1998): Testing static oligopoly
models: Conduct and cost in the sugar industry, 1890-1914. The
Rand Journal of Economics 29 (2), 355–377.
Graddy, K. 1995. “Testing for Imperfect Competition at the Fulton
Fish Market,” Rand Journal of Economics 26(Spring): 75-92.
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Empirical IO
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Empirical Cournot models
Cournot:
Model
Model
Homogenous product such as sugar. N …rms active in the industry.
The variable pro…t of …rm i is
Πi = p Q; X D , εD
Firm i believes
qi
C (qi ; Zi , ω i )
e i
∂Q
= 0. The optimal response qi :
∂qi
MRi = MC (qi ; Zi , ω i )
where MRi
p Q; X D , εD +
∂p (Q ;X D ,εD )
qi .
∂Q
These conditions characterize the equilibrium output of each …rm as a
function of the exogenous variables (X D , εD , Zi , ω i : i = 1, 2, ...N ).
Victor Aguirregabiria ()
Empirical IO
Toronto. Winter 2016
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Empirical Cournot models
Estimation
Cournot: Estimation
The researcher has data from M markets:
n
o
Data = qim , Zim , XmD : i = 1, ..., Nm ; m = 1, ..., M
Suppose that the demand function has been estimated in a …st step,
such that there is a consistent estimate p
b(.) of the demand function,
c
D
and an estimated residual εm of the error term in each …rm-market.
The researcher can construct consistent estimates of marginal
revenues as:
d im = p
MR
b
Victor Aguirregabiria ()
D
Qm ; XmD , εc
m
+
Empirical IO
D
∂b
p Qm ; XmD , εc
m
∂Q
qim
Toronto. Winter 2016
11 / 36
Empirical Cournot models
Cournot: Estimation
Estimation
(2)
We can also write the estimated MR as:
"
#
1
q
im
d im = pm 1
MR
Qm
b
ηD
m
where b
ηD
m is the estimate of the elasticity of demand at market m.
The marginal revenue of a Cournot …rm depends on:
- Market price (positively)
- The market elasticity of demand (positively)
- The …rm’s market share (negatively)
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Empirical IO
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Empirical Cournot models
Cournot: Estimation
Estimation
(3)
Consider a power speci…cation of a …rm’s variable cost function:
C (qi ; Zi , ω i ) =
1
γ +1
q
expfZi α + ω i g
γ+1 i
γ
such that MC (qi ; Zi , ω i ) = qi expfZi α + ω i g.
The econometric model is:
d im
ln MR
= γ ln (qim ) + Zim α + ω im
We are interested in the estimation of the parameters α and γ.
γ measures the degree of diseconomies of scale (γ > 0) or economies
of scale (γ < 0).
Firms’relative e¢ ciency, Zim α + ω im , and of its sources
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Empirical IO
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Empirical Cournot models
Cournot: Estimation
Estimation
(4)
The model implies that E (ln (qim ) ω im ) < 0, so OLS will provide a
(downward) bias estimate of γ.
Under assumption E (Zjm ω im ) = 0 for any (i, j ), a natural approach
to estimate this model is using GMM based on moment conditions
that use the characteristics of other …rms as an instrument for output.
E
Zim
∑j 6=i Zjm
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h
d im
ln MR
Empirical IO
γ ln (qim )
Zim α
i
=0
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Empirical Cournot models
Cournot: Estimation
Estimation
(5)
(1 )
(2 )
An alternative speci…cation: ω im = ω m + ω im , where the market
(1 )
…xed e¤ect ω m may be correlated with the observable exogenous
variables Z , e.g., more pro…table markets may attract …rms with
di¤erent variables Z (more e¢ cient …rms).
In this model, the moment conditions shows be constructed for the
equation in deviations with respect to the market means, i.e.,
#!
"
^
Zim
eim α
d im
ln MR
γ ln^
=0
E
(qim ) Z
∑j 6=i Zjm
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Empirical IO
Toronto. Winter 2016
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Empirical Bertrand models of product di¤erentiation
Bertrand:
Model
Model
Di¤erentiated product. N …rms, each …rm sells 1 product.
The variable pro…t of …rm i is
Πi = pi qi (p, X, ξ )
Firm i believes
C (qi (p, X, ξ ); Xi , ω i )
∂p i
= 0. The optimal response pi :
∂pi
qi + pi
∂qi (p, X, ξ )
∂qi (p, X, ξ )
= MC (qi ; Xi , ω i )
∂pi
∂pi
That can be written as MRi = MCi
MRi
pi
1
1
ηD
i (p, X, ξ )
= MC (qi ; Xi , ω i )
where η D
i (p, X, ξ ) is the demand elasticity .
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Empirical IO
Toronto. Winter 2016
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Empirical Bertrand models of product di¤erentiation
Bertrand:
Model
Model
(2)
The F.O.C. can be also written as:
pi = MCi + mi (p, X, ξ )
where mi (p, X, ξ ) is the equilibrium price-cost margin for …rm i,
that is equal to:
pi
mi (p, X, ξ ) = D
η i (p, X, ξ )
Note that the (actual) equilibrium price cost margin can be calculated
given the demand, without knowing the cost parameters.
Victor Aguirregabiria ()
Empirical IO
Toronto. Winter 2016
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Empirical Bertrand models of product di¤erentiation
Estimation
Bertrand: Estimation
The researcher has data from J products (alternatively, there may be
also M markets):
Data = fpi , Xi : i = 1, ..., J g
Suppose that the demand function has been estimated in a …st step,
such that there is a consistent estimate qbi (.) of the demand system,
and estimated residuals ξbi of the unobserved product characteristics
in demand.
The researcher can construct consistent estimates of marginal
revenues as:
"
#
1
d i = pi 1
MR
b
b
ηD
i (p, X, ξ )
Victor Aguirregabiria ()
Empirical IO
Toronto. Winter 2016
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Empirical Bertrand models of product di¤erentiation
Bertrand: Estimation
Estimation
(2)
Consider a power speci…cation of a …rm’s variable cost function:
Ci =
1
γ +1
q
expfXi α + ω i g
γ+1 i
γ
such that MCi = qi expfXi α + ω i g.
The econometric model is:
di
ln MR
= γ ln (qi ) + Zi α + ω i
We are interested in the estimation of the parameters α and γ.
γ measures the degree of scale diseconomies (γ < 0) or economies
(γ > 0).
Firms’relative e¢ ciency, Zi α + ω i , and of its sources.
Victor Aguirregabiria ()
Empirical IO
Toronto. Winter 2016
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Empirical Bertrand models of product di¤erentiation
Bertrand: Estimation
Estimation
(3)
The model implies that E (ln (qi ) ω i ) 6= 0, so OLS will provide
(downward) bias estimates of γ.
Under assumption E (Xj ω i ) = 0 for any (i, j ), a natural approach to
estimate this model is using GMM based on moment conditions that
use the characteristics of other …rms as an instrument for output.
E
Victor Aguirregabiria ()
Xi
∑ j 6 = i Xj
h
di
ln MR
Empirical IO
γ ln (qi )
Xi α
i
=0
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Empirical Bertrand models of product di¤erentiation
Estimation
Bertrand: Multiproduct Firms
There are F …rms indexed by f . Each …rm produces a set of
di¤erentiated products, Jf .
The variable pro…t of …rm f is:
Πf =
∑ [ pj
MCj ] qj (p, X, ξ )
j 2J f
where here, for simplicity, we assume that marginal costs are constant
(CRS).
∂p f
The …rm believes that
= 0. But it takes into account the
∂pf
substitution (cannibalization) e¤ects between the products that it
sells: i.e., reducing the price of its own product j reduces the demand
of its other products k 6= j.
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Empirical IO
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Empirical Bertrand models of product di¤erentiation
Estimation
Bertrand: Multiproduct Firms
(2)
The F.O.C. for …rm f product j:
qj + ( pj
∑
( pk
MCj )
MCk )
k 2J f ; k 6 =j
∂sj
∂pj
∂sk
∂pj
+
= 0
The second term captures the cannibalization e¤ects between the own
products that the …rm internalizes when it decides its optimal prices.
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Empirical IO
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Empirical Bertrand models of product di¤erentiation
Estimation
Bertrand: Multiproduct Firms
(2)
We can write these F.O.C. as follows:
∂sf
=
[pf MCf ]0
∂pj
qj
where [pf MCf ] is the vector of price-cost margins for …rm f ,
∂s
is the vector of partial derivatives.
and
∂pj
And the vector of …rm f best response prices is:
pf = MCf +
∂sf
∂pf0
1
sf
We can construct the vector of marginal revenue as pf +
and then estimate the model:
Victor Aguirregabiria ()
dj
ln MR
∂sf
∂pf0
1
sf ,
= γ ln (qj ) + Xj α + ω j
Empirical IO
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Nevo (2001)
Nevo (2001) on Cereals
Ready-to-Eat (RTE) cereal market: highly concentrated, many similar
products, and yet price-cost margins (PCM) are apparently relatively
high.
What is the source of market power? Di¤erentiation? Multi-product
…rms? Collusion?
Nevo estimates a demand system of di¤erentiated products for this
industry, recovers marginal cost under the assumption of Bertrand
competition, and compare these PCMs with the counterfactual PCMs
with single-product …rms (no multi-product …rms) and collusion.
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Empirical IO
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Nevo (2001)
Nevo (2001): Data
A market is a city-quarter. IRI data on market shares and prices.
65 cities x 20 quarters [Q188-Q492] x 25 brands [total share is
43-62%].
Most of the price variation is cross-brand (88.4%), the remainder is
mostly cross-city, and a small amount is cross-quarter.
Relatively poor brand characteristics so model includes brand …xed
e¤ects.
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Empirical IO
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Nevo (2001)
Nevo (2001): Identi…cation of demand
Speci…cation of unobserved demand ξ jmt :
(1 )
(2 )
ξ jmt = ξ jm + ξ t
(1 )
(2 )
controls for ξ jm and ξ t
(3 )
+ ξ jmt
using …xed e¤ects.
Instrument for pjmt : average prices in other local markets in the same
region as market m (Rm ):
pj (
m )t
=
1
pjm 0 t
jRm j m 0 2Rm∑
; m 0 6 =m
Assumption: After controlling for brand-city …xed e¤ects, all the
correlation between prices at di¤erent locations comes from
correlation in costs, and not from spatial correlation in demand
shocks.
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Empirical IO
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Nevo (2001)
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Nevo (2001)
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Nevo (2001)
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Nevo (2001)
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Empirical IO
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Conjectural variation approach
Homogeneous product industry
Conjectural variation: Model
We …rst consider the CV model in an homogeneous product industry.
The variable pro…t of …rm i is
Πi = p Q; X D , εD
qi
C (qi ; Zi , ω i )
e i
∂Q
= θ i , where θ i is a parameter
∂qi
that represents the believes of …rm i.
Suppose that …rm i believes that
The "perceived" MR of …rm i is:
MRi = p Q; X D , εD +
∂p Q; X D , εD
[ 1 + θ i ] qi
∂Q
If we treat these beliefs θ i as exogenous, we can de…ne an equilibrium
where qi is a function of the exogenous variables
(X D , εD , θ i ,Zi , ω i : i = 1, 2, ...N ).
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Empirical IO
Toronto. Winter 2016
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Conjectural variation approach
Homogeneous product industry
Conjectural variation: Model
(2)
F.O.C:
MRi = MC (qi ; Zi , ω i )
where MRi = P +
∂p
∂Q
[ 1 + θ i ] qi .
The value of the parameters fθ i g are related to the "nature of
competition", i.e., Cournot, Perfect Competition, Bertrand,
Stackelberg, or Cartel (Monopoly).
PC / Bertrand no di¤:
Cournot:
θi =
1; MRi = P
θ i = 0; MRi = P +
∂p
∂Q qi
θi = n
1; MRi = P +
∂p
∂Q
n qi
Cartel all …rms: θ i = N
1; MRi = P +
∂p
∂Q
N qi
Cartel n < N …rms:
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Empirical IO
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Conjectural variation approach
CV:
Estimation
Estimation
The researcher has data from M markets:
n
o
Data = qim , Zim , XmD : i = 1, ..., Nm ; m = 1, ..., M
It may not be panel data (…rms are di¤erent in each market).
Suppose that the demand function has been estimated in a …st step,
such that there is a consistent estimate p
b(.) of the demand function,
c
D
and an estimated residual εm of the error term in each market.
The researcher can construct estimates:
b
δm =
Victor Aguirregabiria ()
D
∂b
p Qm ; XmD , εc
m
∂Q
Empirical IO
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Conjectural variation approach
CV:
Estimation
Estimation
(2)
Consider the variable cost function:
Ci =
1
γ +1
q
[α0 + Zi α1 ] + ω i
γ+1 i
γ
such that MCi = qi [α0 + Zi α1 ] + ω i .
The econometric model is:
h
i
γ
δm qim = qim [α0 + Zim α1 ] + ω im
Pm (1 + θ im ) b
We are interested in the estimation of the parameters α’s, γ, and θ im .
We need to impose some restrictions on θ im . The most common
restriction is θ im = θ at every observation (i, m ).
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Empirical IO
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Conjectural variation approach
CV:
Estimation
h
Pm
Estimation
(3)
i
h
i
γ
γ
b
δm qim = θ b
δm qim + α0 qim + α1 Zim qim + ω im
We have an additional identi…cation problem.
Firm’s output qim is regressor associated both to the CV parameter θ
and to the parameters in the MC.
To make the discussion simpler consider:
h
i
h
i
Pm b
δm qim = θ b
δm qim + α0 qim + α1 [Zim qim ] + ω im
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Conjectural variation approach
CV:
Estimation
h
Pm
Estimation
(4)
i
h
i
b
δm qim = θ b
δm qim + α0 qim + α1 [Zim qim ] + ω im
To identify the parameters in the model we need not only instruments
for qim , but we also need the following type of exclusion restrictions:
1.
The slope of the inverse demand curve b
δm cannot be
constant (no linear demand) and it should depend on exogenous
variables;
2.
The exogenous variables a¤ecting b
δm should not be
collinear with Zim or with fZjm : j 6= i g.
Example: Genesove and Mullin (RAND, 1988), seasonality in the
demand of sugar that does not a¤ect production costs.
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Empirical IO
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