Post-Merger Product Repositioning
Luke Froeb, Vanderbilt
University of Texas
Arlington, TX
April 28, 2006
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Joint Work & References

Co-authors
 Amit
Gandhi, University of Chicago & Vanderbilt
 Steven Tschantz, Math Dept., Vanderbilt
 Greg Werden, U.S. Department of Justice

Merger Modeling Tools
 Vanderbilt Math: “Mathematical Models
 http://math.vanderbilt.edu/~tschantz/m267/
in Economics”
 http://www.ersgroup.com/tools
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Talk Outline
Policy Motivation: why are we doing this?
 How does this fit into economic literature?
 Computing Equilibria without calculus
 Model & Results

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FTC: Man Controlling Trade
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4
1900
Laws enacted in 1900 or before
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1960
Laws enacted in 1960 or before
Note: EU introduced antitrust law in 1957
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1980
Laws enacted in 1980 or before
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1990
Laws enacted in 1990 or before
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2004
Laws enacted in 2004 or before
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Enforcement Priorities

US & EC
 1.
Cartels
 2. Mergers
 3. Abuse of dominance (monopolization)

New antitrust regimes
 1. Abuse
of dominance
 2. Mergers
 3. Cartels
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QUESTION: Which is best?
ANSWER: Enforcement R&D

How well does enforcement work?


How should we allocate scarce enforcement resources?


Cartels; Mergers; Monopolization
Merger question: how do we predict post-merger world?



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What can we do to improve?
Market share proxies
Natural experiments
Structural models
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Year
12
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1500
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
Number of HSR Transactions
5000
4500
Merger Activity
4000
3500
3000
2500
2000
Billable filings under the post January 2001
system
1000
500
0
5.00%
4.50%
Second Requests as a Percentage of Total Filings
Merger Investigations
4.00%
3.50%
3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
1994
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1995
1996
1997
1998
1999
Year
2000
2001
2002
2003
2004
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FTC Merger Challenges, 96-03
90
80
Number of Markets
70
60
50
40
30
20
10
0
2 to 1
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3 to 2
4 to 3
5 to 4
6 to 5
7 to 6
Significant Com petitors
Enforced
Closed
8+ to 7+
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What’s wrong with structural
proxies?
Competition does not stop at market
boundary
 Shares may be poor positions for
“locations” of firms within market.
 No mechanism for quantifying the
magnitude of the anticompetitive effect.

 Benefit-cost
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analysis?
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Merger Analysis Requires
Predictions about Counterfactual

Back-of-the-envelope merger analysis




What is motive for merger?
Are customers complaining?
What will happen to price?
Price predictions are difficult

Natural Experiments


Model-based analysis


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Good if nature has been kind
Model current competition
Predict how merger changes competition
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Natural Experiment:
Marathon/Ashland Joint Venture


Combination of marketing and refining assets of
two major refiners in Midwest
First of recent wave of petroleum mergers
 January


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1998
Not Challenged by Antitrust Agencies
Change in concentration from combination of
assets less than subsequent mergers that were
challenged by FTC
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Natural Experiment (cont.):
Marathon/Ashland Joint Venture

Examine pricing in a region with a large change
in concentration
 Change

in HHI of about 800, to 2260
Isolated region
 uses
Reformulated Gas
 Difficulty of arbitrage makes price effect possible
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Prices did NOT increase relative to other regions
using similar type of gasoline
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Differences-in-Differences Estimation
Difference Between Louisville's Retail Price and Control Cities' Retail Price
25.00
Merger Date
20.00
15.00
10.00
11/1/1999
9/1/1999
7/1/1999
5/1/1999
3/1/1999
1/1/1999
11/1/1998
9/1/1998
7/1/1998
5/1/1998
3/1/1998
1/1/1998
11/1/1997
9/1/1997
7/1/1997
5/1/1997
-5.00
3/1/1997
0.00
1/1/1997
Cents
5.00
-10.00
-15.00
-20.00
-25.00
Week
Chicago
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Houston
Virginia
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Bertrand (price-only) Merger Model


Assumptions: Differentiated products, constant
MC, Nash equilibrium in prices.
Model current competition
 Estimate demand
 Recover costs from
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FOC’s  (P-MC)/P =1/|elas|
Prediction: Post-merger, MR for the merging
firms falls as substitute products steal share
from each other
 Merged firm responds by raising prices
 Non-merging firms raise price sympathetically
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Structural Model Backlash
How reliable are model predictions?
 Test merger predictions

 Yes
(Nevo, US breakfast cereal)
 No (Peters, 3/5 US airlines; Weinberg, US
motor oil and breakfast syrup)

Test over-identifying restrictions, i.e.,
does (p-mc)/p=1/|elas| ?
 Yes
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(Werden, US bread; Slade, UK beer)
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Backlash (cont.)

Does model leave out features that bias its predictions?


Related research





Ignoring demand curvature can under- or overstate merger effect
Ignoring vertical restraints can under- or overstate merger effect
Ignoring capacity constraints likely overstates merger effect
Ignoring promotional competition likely understates merger effect
This research,

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Static, Price-only competition, MC constant
Ignoring repositioning likely overstates merger effect
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Backlash (cont.)


Tenn, Froeb, Tschantz “Mergers When Firms
Compete by Choosing both Price and
Promotion”
Ignoring promotion understates estimated
merger effect
 “estimation
bias” (estimated demand is too priceelastic); and
 “extrapolation bias” caused by assuming that postmerger promotional activity does not change (it
declines).
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What if Firms Compete in Other
Dimensions?

Other dimensions of competition?


Repositioning in Horizontal Merger Guidelines



4 P’s of marketing: Price, Product, Promotion, Place
Thought to have effect similar to entry
Non-merging brands move closer to merging brands
Our BIG finding: merging brands move


increased product variety as all brands spread out
2 Price effects

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Cross elasticity effect (merged products move apart) attenuates
merger effect
Softening price competition effect (all products spread out) amplifies
merger effect
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Related Economics Literature

Berry and Waldfogel, “Do Mergers Increase
Product Variety?”
 Radio


stations change format post-merger
Norman and Pepall, “Profitable Mergers in a
Cournot Model of Spatial Competition?”
Anderson et al., “Firm Mobility and Location
Equilibrium”
 simultaneous
intractable”
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price-and-location games “analytically
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Econ. Lit Review (cont.):
“too much rock and roll”


Andrew Sweeting (Northwestern)
Following mergers among (rock n roll) stations,
 play
lists of merged firms become more differentiated.
 Merged stations steal ratings (listeners) from nonmerging stations.
 No increase in commercials
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These findings Match our theoretical
predictions
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Why do we need to compute
Equilibria?

IO methodology now allows estimation of
game parameters without equilibrium
 Bertrand
(BLP)
 Dynamic (Bajari)
 Auctions (Vuong)

must have equilibria for benefit-cost analysis
 How

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else to compute policy counterfactual?
e.g., what does post-merger world look like?
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Computing Equilibria

Fixed-point algorithms
 Require
smooth profit functions
 Require good starting points
 Can’t find Multiple equilibria

Stochastic response dynamic
 All
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it needs are profit functions.
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How does methodology work?



Players take turns moving.
Player i picks a new action at random
If i’s new action improves Profit(i)


If i’s new action does NOT improves Profit(i)


choose new action with probability P and go to next player.
Let P tend towards zero


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then accept move, and go to next player.
quickly reach state where no one wants to move.
this is a Nash equilibria
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Why does methodology work?



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Consider RV’s X and Y w/joint pdf p(x, y).
The conditionals p( x | y ) and p( y | x ) are
enough to determine the joint p(x, y).
Let the conditionals p( x | y ) and p( y | x ) each
be unimodal. If (x∗, y∗) is a local maxima of the
joint p(x, y), then x∗ maximizes the conditional p(
x | y∗ ) in the direction of X and y∗ maximizes the
conditional p( y | x∗ ) in the direction of Y.
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Why? (cont.)

Suppose we want to generate a draw (x, y) from
the distribution of (X, Y ). Here is a recipe for
doing so:
 Start
at any initial state (x0, y0).
 Draw x1 from p( x | y0 ) and y1 from p( y | x1 ).
 Repeat
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After enough repetitions, the draws (xn, yn) can
be treated as a sample from joint distribution (X,
Y). This is the Gibbs Sampler.
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Why? (cont.)


Think of each profit function Ui(a−i, ai) as a conditional
profit Ui(a−I | ai)
Normalize conditional profit to be positive and integrate
to 1, e.g., g(ai | a−i ) ∝ exp[Ui(a−I | ai) /t]



Interpret conditional utility as conditional probability.
Let t → 0. This causes the sampler to get stuck in a local
mode of g.


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The normalization does not change game.
Multiple runs for multiple modes.
Each node is a Nash equilibria
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Why? (cont.)

Note that g(a′i|at−i)/g(ati|at−i)=

exp[(Ui(a′I,at−i) -Ui(ati,at−i))/t]

We are back to the painfully easy
algorithm.
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How do we actually make draws?
Pick action a′i uniformly at random from Ai
 Set at+1i = a′i with probability

 Max[1,
g(a′i|at−i)/g(ati|at−i)
Else, set at+1i = ati
 Let t0

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Example: Cournot equil.={1/3,1/3}
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Example, 2 equil={{5,8},{8,5}}
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Demand Model

Consumers on Hotelling line

Indirect utility is function of price +
travel cost + random shock
vij  i  B( pi  t * d ( xi, xj ))  ij

Resulting demand is logit

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qi (p, x)  
e
N
vi ( pi , xi , x )
e
j
dF ( x)
e vj ( pj, xj , x )
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Supply Model

Vendors simultaneously choose price and
location

profiti  ( pi  ci )qi (p, x)

Nash Equilibrium in two dimensions

Post merger, merged firm maximizes sum of
vendor products
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Pre-merger Locations
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Merger Decomposition

PRE-merger  LOCATION  POST-merger
 LOCATION=Pre-merger
ownership at post-merger
locations

“Softening price competition” effect
 LOCATION - PRE
 Amplify merger effect

relative to no repositioning
“Cross-elasticity” effect
 POST – LOCATION
 Attenuate merger relative
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to no repositioning
Total Effect=Softening + Cross-elasticity
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Pre- (dashed) and Post- (solid)
Merger Locations (outside good)
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Net Merger Effect =
Cross elasticity + Softening
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Non Merging Firms Softening
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Profit Changes
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Price-only models can miss a lot

Taxonomy of effects
 As
 As
products separate, price competition is softened
merged products separate, smaller incentive to
raise price
 As non-merging products spread out, smaller
sympathetic price increases.

Relative to a model with no repositioning
 Total
and consumer welfare may be higher
 Merging firms raise price
 Non-merging firms may reduce price
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What Have We Learned?

Repositioning by merged firms is more significant than
repositioning by non-merging firms






Pre-merger substitution patterns likely overstate loss of
competition.
Non merging firms can do worse following merger
Price can go up or down;
Consumers can be better or worse off
New algorithm for finding Nash equilibria
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Similar to effect of capacity constraints on merger.
Important complement to existing estimation methods
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