# 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 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

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

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

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)

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