# 程序代写代做代考 GMM data structure Lecture 1: Measuring Market Power and Collusion

Lecture 1: Measuring Market Power and Collusion

Yiyi Zhou

Department of Economics

Stony Brook University

ECO 637: Empirical IO

Overview

1 Measuring Market Power

Genesove and Mullin (1998)

Bounds on Market Power

2 Collusion and Price Wars

Porter (1983)

Ellison (1994)

Bresnahan (1987)

Estimating cost functions without using cost data

During the 1960s and 1970s, IO economists were building methods

to estimate cost functions. Why?

I Return to scale,

I Learning by doing,

I Efficient scale, etc.

At the same time, many papers tried to test the SCP paradigm

using accounting data.

For instance, cross-industry comparisons were conducted to

estimate the “causal” effect of concentration on profitability or

prices:

Profits

jt

= ↵+ �Concentration

jt

+ �X

jt

+ u

jt

Critics started pointing out that,

1 Market structure is not exogenous

2 Accounting costs 6= economic costs

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 2 / 55

Rosse (1970, Econometrica)

Combine economic theory assumptions with prices and output

data to estimate economic marginal cost functions.

One output y

j

example

p

j

= ↵0 + ↵1xj � ↵2yj + uj

mc

j

= �0 + �1zj + �2yj + vj

E(u) = E(v) = 0

E(u · v) = 0

E(x · u) = E(x · v) = 0

E(z · u) = E(z · v) = 0

The last two corresponds to “short-run” assumptions: Quality and

other sunk product characteristics are fixed in the short run.

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 3 / 55

Conduct Assumption

Problems: mc

j

is unobserved & How can we estimate the return to

scale parameter �2?

Conduct Assumption: Each local newspaper is a local monopolist

and chooses y

j

to maximize profits.

Equilibrium condition:

MR

j

�MC

j

= e

j

where e

j

is a mean-zero optimization/specification error

With linear demand and marginal-cost functions:

↵0 + ↵1xj � 2↵2yj + uj = �0 + �1zj + �2yj + vj + ej

$ p

j

= �0 + �1zj + (↵2 + �2)yj + vj + ej � uj| {z }

=w

j

where E (w

j

⇥ (x

j

, z

j

)) = 0

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 4 / 55

Identification and Estimation: GMM Set-Up

Theoretical and empirical moment conditions:

E(u

j

⇥ (x

j

⇠ z

j

)) = 0 )

1

n

X

j

u

j

⇥ (x

j

⇠ z

j

) = 0

E(w

j

⇥ (x

j

⇠ z

j

)) = 0 )

1

n

X

j

w

j

⇥ (x

j

⇠ z

j

) = 0

Identification?

Rank conditions: MC function is identified as long as z

j

contains

exogenous variables not included in x

j

to identify the demand

curve (and vice-versa).

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 5 / 55

More generally, demand and supply relations can take non-linear

forms:

y

j

= f (x

j

, p

j

, u

j

| ↵)

p

j

= g(y

j

, x

j

,w

j

| �)

Takeaway: If firms are optimizing (i.e. conduct), observed actions

reveal the implicit opportunity cost of production. This leads to a

(now) standard revealed-preference estimation strategy.

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 6 / 55

What about Oligopoly Markets?

Under a particular conduct assumption, the same insight can be

extended to markets with more than one firm.

Symmetric Cournot:

P(q

i,t , q�i,t) + P

0(q

i,t , q�i,t)qi,t = MC(qi,t)

$ P(Q

t

) = MC(Q

t

)�

1

n

t

P

0(Q

t

)Q

t

[Summing across i ]

Asymmetric Cournot:

P(q

i,t , q�i,t) + P

0(q

i,t , q�i,t)qi,t = MCi (qi,t)

$ P(Q

t

) =

1

n

t

X

i

MC

i

(q

i,t)�

1

n

t

P

0(Q

t

)Q

t

[Summing across i ]

Bertrand:

P(Q

t

) = MC(Q

t

)

Collusion:

P(Q

t

) + P 0(Q

t

)Q

t

= MC(Q

t

)

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 7 / 55

Supply Relations Estimation

MC is identified under specific conduct assumptions. What

identifies firms’ conduct?

Most oligopoly models can be nested into a general supply relation

equation:

P(Q

t

) = MC(Q

t

)� ✓P 0(Q

t

)Q

t

where ✓ 2 (0, 1) is a measure of market power (i.e. conduct

parameter)

Example:

I ✓ = 0: Bertrand

I ✓ = 1/n: Symmetric Cournot

I ✓ = 1: Monopoly

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 8 / 55

Two Justifications

1 Can be used to test particular models (e.g. H0 : ✓ = 1/n)

2 Theoretical foundation for ✓ 2 (0, 1) : Conjectural variation model

I CV Equilibrium

max

q

i

P

⇣

q

i

+

P

j 6=i Qj(qi ),X

⌘

q

i

� C

i

(q

i

,Z)

F .O.C . P(Q,X ) + q

i

P 0(Q,X )

0

@q

i

+

X

j 6=i

@Q

j

(q

i

)

@q

i

1

A

| {z }

1+r

� C

0

i

(q

i

,Z) = 0

I Averaging across firms: P

m

+ QP

0

m

(Q,X

m

)✓ � M̄C(Q

m

,Z

m

) = 0 where

✓ = (1 + r)/n

I The conduct parameter then corresponds to the “average”

conjecture in the industry:

F

Bresnahan (1989): “IF the conjectures are constant over time and

collusion breakdowns are infrequent, ✓ measures the average

collusiveness of conduct”

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 9 / 55

Identification of Market Conduct

Example: Linear demand/cost (symmetric)

P(Q

t

) = ↵

x

x

t

� ↵

q

Q

t

+ u

t

MC(Q

t

) = �

z

z

t

+ �

q

Q

t

+ v

t

Two estimating equations:

Demand : P

t

= ↵

x

x

t

� ↵

q

Q

t

+ u

t

Supply relation : P

t

= �

z

z

t

+ (�

q

+ ✓↵

q

)Q

t

+ v

t

Negative result: The industry conduct parameter is not identified,

even with all the necessary exclusion restrictions. Why?

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 10 / 55

The linearity of demand implies that the supply relation between

q

t

and p

t

is confounded with the possibility of a non-linear cost

function.

Note: This also implies that estimates of the pass-through of cost

shocks onto prices are not sufficient to test for market-power

(unless we assume a constant MC function).

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 11 / 55

Lack of Identification in a Figure

When P(q

t

) is linear, variation in x

t

induces parallel shifts:

P(q

t

) = x

t

↵

x

� ↵

q

Q

t

+ u

t

This implied change from E1 to E2 can be explained by collusion or

competition

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 12 / 55

Relevant Source of Variation

This is not the case when we can observe demand rotation.

I Example: P(q

t

) = x

t

↵

x

� ↵

q

y

t

Q

t

+ u

t

The implied change from E1 to E3 (caused by yt) can only be

explained by collusion

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 13 / 55

Genesove and Mullin (1998): Sugar Cartel

Historical notes:

I Industry organized as Trust in 1887.

I Between 1887 and 1911, the industry alternated between periods of

collusion, and price war episodes triggered by the entry and

expansion of outside firms.

I The trust was dismantled in 1911 by the US government.

Objective: Validate the conduct estimation approach by comparing

predicted and observed estimates of marginal costs, under known

conduct.

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 14 / 55

Direct Measure of Market-Power

With complete price and cost information, optimality condition

implies pricing relation:

P(c , ✓) =

�c⌘(P)

✓ � ⌘(P)

Therefore,

✓ = ⌘(P)

P � c

P

⌘ L⌘

so, conduct parameter ✓ = elasticity-adjusted Lerner index L⌘

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 15 / 55

Step 1: Technology

Linear production technology:

MC

t

= c

t

= c0 + kPraw,t

where k = 1.075 (i.e., inverse rate of transformation)

Intercept: c0 2 (0.16, 0.26) from industry documents

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 16 / 55

Step 2: Demand Estimation

Functional form:

Q

t

(P) = �

t

(↵

t

� P)�t

where �

t

, and ↵

t

or �

t

are allowed to vary by season (third quarter)

Instrument: Cuban imports (i.e., closest substitute)

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 17 / 55

Step 2: Demand Estimation

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 18 / 55

Step 3: Direct Conduct Estimates

Demand elasticity:

⌘

t

(P) = �

t

�

t

(↵

t

� P)�t�1

P

�

t

(↵

t

� P)�t

=

�

t

P

↵

t

� P

Prices:

P(c , ✓) =

�c⌘(P)

✓ � ⌘(P)

=

✓↵+ �c

� + ✓

Conduct parameter ✓ = elasticity-adjusted Lerner index L⌘

L⌘ = ✓ = ⌘(P)

P � c

P

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 19 / 55

Step 3: Direct Conduct Estimates

Mean L

n

is close to 0.10

I corresponds to static, ten-firm symmetric Cournot oligopoy

I reject both perfect competitive and monopoly pricing

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 20 / 55

NEIO Conduct Parameter Estimation

Supply relation (linear model):

P

t

=

↵

t

✓ + c

t

1 + ✓

=

↵

t

✓ + c0

1 + ✓

+

k

1 + ✓

P

raw ,t + ut

Using the Cuban imports as IV for the price of raw can sugar,

yields the following moment condition:

E [(1 + ✓)P

t

� ↵

t

✓ � c0 � kPraw ,t | Zt ] = 0

where ↵

t

= ↵

low

1(t = Low season) + ↵

high

1(t = High season)

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 21 / 55

Identification of ✓

Assumption: Unobserved changes in firms’ conduct (i.e.

u

t

= 4✓

t

+ e

t

) are independent of IVs.

This is a difficult assumption to satisfy

I E.g: Price wars during booms.

I Corts (1999): Correlation between “conduct changes” and demand

shocks invalidates standard instruments (downward bias)

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 22 / 55

Key Result: ✓ is Under-Estimated

(1): unknown c0 and k ; (2) k = 1.075 is known

NEIO underetsimates ✓, but this deviation was minimal

Still reject Monopoly (✓ = 1) and Cournot with nine or fewer firms

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 23 / 55

Alternative Approach: Bounds on Market Power

Market conduct tests a la Bresnahan suffer from (at least) two

critics:

I Requires knowledge of demand curve: Functional form assumptions

can invalidate the results

I Necessitates variation in the slope of the demand curve (somewhat

arbitrary)

Sullivan (1985) and Ashenfelter and Sullivan (1987) construct an

upper bound on the degree of market power.

I Null hypothesis: Monopoly.

I Minimal assumptions on demand and cost functions

I Exploits observed (exogenous) shocks to marginal cost

I Key requirement: Shock must be separable (e.g. tax shock)

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 24 / 55

Model Set-up

Homogenous goods: P(Q) = P

⇣P

j

q

j

⌘

and P 0(Q) < 0
Heterogenous cost functions: C
j
(q) with C
0
j
(q) � 0
Excise tax: C
j
(q) + tq where C
j
(q) is time-invariant
Profit maximization condition give tax level t
P(q(t)) + q
i
(t) P 0(q(t))
| {z }
=P0(t)/q0(t)
✓ = C
0
i
(q
i
(t)) + t
P(t)� t �mc
i
(t)
✓
+ q
i
(t)
P 0(t)
Q 0(t)
= 0
where Q(t) =
P
i
q
i
(t), Q 0(t) = dQ/dt and P 0(t) = dP(t)/dt
✓ is a market conjecture: @Q⇤/@q
i
I Cournot conjecture: ✓ = 1
I Collusion conjecture: ✓ = n
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 25 / 55
Necessary Conditions
Necessary equilibrium condition for conduct ✓:
P(t)� t � c
✓
+ q
i
(t)
P 0(t)
Q 0(t)
� 0, 8c < mc
i
(t)
Aggregating at the market level, this gives a lower bound on the
number of equivalent Cournot competitors:
n
⇤(t) =
X
i
1
✓
i
� n⇤(t, c) =
�P 0(t)Q(t)
(P(t)� t � c)Q 0(t)
8c < mc
i
(t)
Why is it useful?
I RHS depends only on observed variables P(t) and Q(t), and
reduced form pass-through rates P 0(t) and Q 0(t)
I If P 0(t) > 0 and Q 0(t) < 0 , n⇤(t, 0) provides a useful lower bound
on the industry conduct
I Allow to reject the monopoly model, but not the perfect
competition assumption.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 26 / 55
Application: Pass-through of cigarettes tax
Parametric reduced-form equations:
q
is
(t) = exp
�
1
is
+ g1t + h1(t � t̄)2
�
p
is
(t) = 2
is
+ g2t + h2(t � t̄)2
where j
is
controls for state FEs and time-trends.
OLS results:
I q0(t̄) = �2.93: consistent with the theory (i.e. tax increases
marginal cost).
I p0(t̄) = 1.089: significantly greater than 1, reject Bertrand with
constant mc (i.e. complete pass-through).
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 27 / 55
Estimated n⇤(t̄, c)
n⇤(t̄, c = 0) = 2.88: significantly different from 1, easily reject the
monopoly model.
The observed pass-through rates are consistent with a fairly
important level of competition.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 28 / 55
Overview
1 Measuring Market Power
Genesove and Mullin (1998)
Bounds on Market Power
2 Collusion and Price Wars
Porter (1983)
Ellison (1994)
Bresnahan (1987)
Collusion and Price Wars
Textbook models of tacit collusion predict stable prices, and
off-equilibrium cheating.
In most known cases of implicit or explicit collusions, we observe
alternating periods of high/low markups, price wars, cheating, etc.
Price series: two “regimes” of pricing. Can periods of low pricing
be explained as “price wars”?
Repeated game theory: view observed price series as realization of
equilibrium price process
Standard repeated games (e.g., repeated Cournot game) with
unchanging economic environment: equilibrium price path is
constant!
I Need to specify punishment strategies which support collusive
equilibrium, but punishment is never “observed” on the equilibrium
path.
I Need for model with nonconstant equilibrium price process
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 29 / 55
Two Models of Tacit Collusion
1
Demand fluctuations: Collusive prices must adjust to reflect
higher temptation to cheat when demand is high
I Rotember and Saloner (1986). Price wars during booms
2
Imperfect information: Price wars discipline cartel members
price cuts are not fully observed
I Green & Porter (1984): Price wars during recessions
These two models generate periods of low and high pricing on the
equilibrium path. But low prices are not caused by cheating;
rather they are manifestation of collusive behavior!
Price wars, or more generally, equilibrium cheating behavior are
still phenomena that we don’t understand very well (good research
topic!).
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 30 / 55
Rotemberg and Saloner (1986): Price Wars During
Booms
Empirical regularity: In many oligopolistic industries, prices or
markups are counter-cyclical
I Cement (Rotemberg and Saloner 1986), refined sugar (Genesove
and Mullin 1998), gasoline (Borenstein and Shepard 1996), Grocery
items (Chevalier et. al 2003)
Interpretation:
With i.i.d. demand fluctuations, fixed discount rate, constant
marginal production costs, collusive prices will be lower in periods
of above-average demand (“price wars during booms”)
Intuitively, cheat when (current) gains exceed (future) losses.
Current gains highest during “boom” periods; reduce incentives to
cheat by lowering collusive price.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 31 / 55
Price Wars During Booms?
Caveat 1: The model does not really predict “price-wars”, since
deviations are not observed in equilibrium.
I RS = Theory of countercyclical markups.
Caveat 2: To test the prediction in the data, we need to be careful.
Case 2 does not imply that p⇤2 < p
m
1 . The predictions is about
lowering the prices relative to the monopoly price (i.e. p⇤2 < p
m
2 .).
I Need to condition on demand/cost state variables.
Caveat 3: When demand shocks are not IID, the predictions can
be reversed.
I Important: Demand is expected to be low in the (near) future if it
is very high today.
I See Harrington and Haltiwanger (1991)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 32 / 55
Collusion With Secret Price Cuts
The idea that imperfect monitoring cause price wars dates back to
Stigler.
First formalization: Green and Porter (1984)
Same framework as RS(1986), but introduce imperfect
information - firms cannot observe the output choices of their
competitors, only observed realized market price. Prices can be
lower during periods of low demand (“price wars during
recessions”).
Note: market price can be low due to either (i) cheating; or (ii)
adverse demand shocks. Firms cannot distinguish.
Intuitively: equilibrium “trigger” strategies involve “low price”
regime when prices are low. That is, if the market price drops
below the “trigger level”, firms revert to one-shot Nash.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 33 / 55
Porter (1983)
Test the Green-Porter model: two regimes of behavior
(“cooperative” vs. “noncooperative/price war”)
I Subtle: noncooperative regime arises due to low demand, not due
to cheating
Empirical problem: don’t (or only imperfectly) observe when a
“price war” is occurring. How can you estimate this model then?
Prices should be lower in price war periods, holding the demand
function constant. Price war triggered by change in firm behavior.
Estimate simultaneous-equation switching regression model
with unobserved regimes.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 34 / 55
Brief History of the JEC
Legal and public cartel formed in 1879.
Control railroad eastbound shipments from Chicago to the East
coast.
Historical evidence that the cartel used “temporary” price cuts to
punish rumors of cheating by a member.
Firms set rates individually and privately.
Volume transported was surveyed weekly by the JEC.
Prices are monitored only imperfectly, and firms only observed
aggregate market shares.
Recurrent price war episodes were documented by economic
historians.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 35 / 55
Demand Side
Observed data are market-level output (Q
t
) and price (p
t
) for
weekly grain shipments between 1880 and 1886
N firms (railroads), each producing a homogeneous product (grain
shipments). Firm i chooses q
it
in period t.
Market demand:
logQ
t
= ↵0 + ↵1logpt + ↵2Lt + U1t ,
where Q
t
=
P
i
q
it
, L
t
is demand shifter: = 1 of Great lakes open
to navigation (availability of substitute to rail transport)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 36 / 55
Supply Side
Firm i ’s cost fxn:
C
i
(q
it
) = a
i
q�
it
+ F
i
Firm i ’s pricing equation:
p
t
(1 +
✓
it
↵1
) = MC
i
(q
it
)
where ✓
it
= 0: Bertrand pricing; ✓
it
= 1: Monopoly pricing;
✓
it
= s
it
: Cournot outcome
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 37 / 55
Aggregate Supply Equation
After some manipulation, aggregate supply relation:
logp
t
= logD � (� � 1)logQ
t
� log(1 + ✓
t
/↵1)
with empirical version
logp
t
= �0 + �1logQt + �2St + �3It + U2t ,
where I
t
= 1: cooperative regime (joint profit maximization); I
t
= 0:
noncooperative regime (one shot Bertrand or Cournot); S
t
: supply
shifters (dummies DM1, DM2, DM3, DM4 for entry by additional rail
companies)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 38 / 55
Simultaneous Equations
Demand and Supply Equations:
logQ
t
= ↵0 + ↵1logpt + ↵2Lt + U1t
logp
t
= �0 + �1logQt + �2St + �3It + U2t
Assume(U1t ,U2t)0 ⇠ N(0,⌃)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 39 / 55
Matrix Notation
By
t
= �X
t
+�I
t
+ U
t
y
t
=
logQ
t
logp
t
!
,X
t
=
0
B
@
1
L
t
S
t
1
C
A ,U
t
=
U1t
U2t
!
B =
1 �↵1
��1 1
!
,� =
0
�3
!
, � =
↵0 ↵2 0
�0 0 �2
!
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 40 / 55
Likelihood
Suppose in each period you know whether firms are in the collusive
or non-collusive regime.
Then, the likelihood conditional on I
t
:
L(Y
t
| I
t
) =| ⌃ |1/2| B | exp
⇢
�
1
2
(By
t
� �X
t
��I
t
)0⌃�1(By
t
� �X
t
��I
t
)
�
Problem: we don’t observe the regime (I
t
).
How to proceed?
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 41 / 55
Likelihood
Treat it as a “nuisance parameter” and integrate out over its
distribution: L(Y
t
) =
R
L(Y
t
| I
t
)g(I
t
)dI
t
Assume that I
t
follows a discrete, two point distribution (from
structure of GP equilibrium):
I
t
=
8
<
:
1, with prob �
0, with prob 1 � �
Treatment is “exogenous”. Endogeneity in this model arises from
simultaneity of Q
t
and p
t
.
So likelihood function:
L(Y
t
) = �L(Y
t
| I
t
= 1) + (1 � �)L(Y
t
| I
t
= 0)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 42 / 55
Key Results
Estimate of �3 is 0.545: prices ⇡50% higher when firms are in
“cooperative” regime
If we assume ✓ = 0 in non-cooperative periods, then
�3 = �log(1 + ✓/↵1) implies ✓ = 0.336 (close to Cournot) in
cooperative periods.
Prices 66% higher and quantity 33% lower in cooperative regime.
Price wars were not preceded by large negative demand residuals.
Cartel earns $11,000 (11%) more in weeks when they are
cooperating
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 43 / 55
Discussion
What if I
t
is endogenous (arising from, eg., price wars more likely
when demand is low, etc.)?
If regime observed, �3 is the “treatment effect” of It . Possible to
use other methods to estimate treatment effect?
I Data structure is not DID: there are no “control units” for which
I
t
= 0 throughout the sample period. So cannot distinguish effect of
I
t
apart from week dummies
I IV approach, with L
t
as (discrete) instrument? But need another
demand shifter, because only one IV (L
t
) for two endogenous
variables (I
t
adn Q
t
)
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 44 / 55
Ellison (1994 RAND)
Allow for variables to enter �: theory gives guidance that price
wars precipitated by “triggers”: low demand (in GP model), large
shifts in market share. Allow I
t
to be an endogenous in this fashion.
Allows unobserved I
t
’s to be serially correlated
Prob {I
t+1 | It ,Zt} =
e�Wt
1 + e�Wt
where Z
t
: set of predetermined variables at t, W
t
contains I
t
so
adds a Markov structure to the price wars (a constant independent
of I
t
in Porter (1983))
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 45 / 55
Ellison (1994 RAND)
Also treats RS (1986) model:
I alternative explanation for price wars (where serial correlation in
demand, not unobserved firm actions, drives price fluctuations).
I In equilibrium, prices lower in periods of relatively high demand,
when demand is expected to fall in the future.
Test for explicit cheating on the part of firms, which doesn’t
happen in the equilibrium of any of these models. Introduces
additional regimes to the model.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 46 / 55
Ellison (1994 RAND): Results
Find a greater degree of collusion.
Regimes are not independent of each other.
Unanticipated demand shock enters negatively in the price war
trigger probability (i.e. 6=RS).
The RS story is not supported in this data-set.
Find evidence of “two-type” of hidden regimes: (i) regular price
wars, and (ii) large unobserved demand shock (e.g secret price cut).
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 47 / 55
Bresnahan (1987): The 1955 price war in the US auto
market
Research question: Is the 1955 increase in production explained by
a deviation from collusion?
Focuses on static pricing models, among differentiated products.
Evidence that manufacturers compete in 1955, but not in
surrounding years.
Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 48 / 55
Quality Ladder Model
J vertical differentiated products: x
J
> x

J�1 > … > x1 > x0

Indirect utility given marginal utility for quality v

i

:

U(x

j

, v

i

,Y ) =

8

<
:
v
i
x
j
+ Y � P
j
, if j 6= 0
v
i
x0 + Y � E , if j = 0
Distribution assumption: v
i
⇠ U([0,V
max
]) with density �
Market shares
s
j
= D
j
(p
j
, p�j) =
8
>>><
>>>:

1

�

⇣

V

max

� PJ�PJ�1

x

J

�x

J�1

⌘

if j = J

1

�

⇣

P

j+1�Pj

x

j+1�xj

� Pj�Pj�1

x

j

�x

j�1

⌘

if 1 j < J
1
�
⇣
P1�E
x1�x0
⌘
if j = 0
Constant MC: mc(x) and mc 0(x) > 0

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 49 / 55

Conduct Assumptions

Individual product Bertrand-Nash:

s

i

+ (P

i

�mc(x

i

))

@D

i

@P

i

= 0

Multi-product Bertrand-Nash:

s

i

+

j=i+1X

j=i�1

✓

ij

(P

j

�mc(x

j

))

@D

j

@P

i

= 0

where ✓

ij

= 1 if i and j are produced by the same firm

Collusion:

s

i

+

j=i+1X

j=i�1

(P

j

�mc(x

j

))

@D

j

@P

i

= 0

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 50 / 55

Identification in a Figure

If the marginal cost function is monotonically increasing in quality,

prices should be increasing in quality independently of the presence

of closed substitutes (under collusion).

If firms are competing, prices should also be function of the

presence of close substitutes.

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 51 / 55

Empirical Model

Deterministic quality and marginal cost functions:

x

i

=

p

�0 + �0zi

mc(x) = µexp(x)

where z

i

is a vector of car char’s

Measurement errors:

p

i

= p⇤

i

(x | H, ✓) + ✏p

i

q

i

= q⇤

i

(x | H, ✓) + ✏q

i

where (✏p

i

, ✏

q

i

) ⇠ N(0,⌃)

Likelihood function:

L(P ,Q | Z , ✓,H) =

X

i

ln (f (p

i

� p⇤

i

, q

i

� q⇤

i

| ⌃))

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 52 / 55

Testing for Collusion

Non-nested hypothesis test: Likelihood ratio of H0 and H1,

evaluated under H0 (Cox statistic).

For instance, when evaluated using the parameters of the collusive

model (null), is the difference between collusion and competition

(alternative) likelihood large enough to reject the competition

model?

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 53 / 55

Conclusion: Bertrand-Nash cannot be rejected in 1955

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 54 / 55

Other Work on Collusion

Borenstein and Shepard (1996 RAND) find support for RS (1986)

theory in retail gasoline markets

Pakes and Ferschtmann (2000 RAND) examine the feasibility of

collusion in rich model of oligopolistic industry in which firms can

choose quality investment as well as price, and entry and exit can

occur.

Chevalier, Kashyap, Rossi (2003, AER ) tests RS models versus

other explanations of “price wars during booms”

Yiyi Zhou (Stony Brook) Market Power and Collusion ECO 637 55 / 55

Measuring Market Power

Genesove and Mullin (1998)

Bounds on Market Power

Collusion and Price Wars

Porter (1983)

Ellison (1994)

Bresnahan (1987)