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Luke Froeb, Vanderbilt

University of Texas

Arlington, TX

April 28, 2006

Post-Merger Product Repositioning

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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 in Economics”

http://math.vanderbilt.edu/~tschantz/m267/ 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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1900

Laws enacted in 1900 or before

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1960

Laws enacted in 1960 or beforeNote: 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 & EC1. Cartels2. Mergers3. Abuse of dominance (monopolization)

New antitrust regimes1. Abuse of dominance2. Mergers3. Cartels

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QUESTION: Which is best?ANSWER: Enforcement R&D

How well does enforcement work? What can we do to improve?

How should we allocate scarce enforcement resources? Cartels; Mergers; Monopolization

Merger question: how do we predict post-merger world? Market share proxies Natural experiments Structural models

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0

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Year

Num

ber o

f HSR

Tra

nsac

tions

Billable f ilings under the post January 2001 system

Merger Activity

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0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

5.00%

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Seco

nd R

eque

sts

as a

Per

cent

age

of T

otal

Fili

ngs

Merger Investigations

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FTC Merger Challenges, 96-03

0

10

20

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2 to 1 3 to 2 4 to 3 5 to 4 6 to 5 7 to 6 8+ to 7+

Significant Competitors

Nu

mb

er o

f M

arke

ts

Enforced Closed

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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 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

Good if nature has been kind Model-based analysis

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 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

Prices did NOT increase relative to other regions using similar type of gasoline

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Difference Between Louisville's Retail Price and Control Cities' Retail Price

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1/1

/1997

3/1

/1997

5/1

/1997

7/1

/1997

9/1

/1997

11/1

/1997

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/1998

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/1999

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/1999

Week

Cen

ts

Chicago Houston Virginia

Merger Date

Differences-in-Differences Estimation

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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 FOC’s (P-MC)/P =1/|elas|

Prediction: Post-merger, MR for the merging firms falls as substitute products steal share from each otherMerged 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 (Werden, US bread; Slade, UK beer)

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Backlash (cont.)

Does model leave out features that bias its predictions? Static, Price-only competition, MC constant

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, 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 price-

elastic); and “extrapolation bias” caused by assuming that post-

merger promotional activity does not change (it declines).

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What if Firms Compete in Other Dimensions? Other dimensions of competition?

4 P’s of marketing: Price, Product, Promotion, Place Repositioning in Horizontal Merger Guidelines

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

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 price-and-location games “analytically

intractable”

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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 non-

merging stations. No increase in commercials

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 else to compute policy counterfactual?

e.g., what does post-merger world look like?

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Computing Equilibria

Fixed-point algorithmsRequire smooth profit functionsRequire good starting pointsCan’t find Multiple equilibria

Stochastic response dynamicAll 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)

then accept move, and go to next player. 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

quickly reach state where no one wants to move. this is a Nash equilibria

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Why does methodology work?

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

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[U∝ i(a−I | ai) /t] The normalization does not change game.

Interpret conditional utility as conditional probability. Let t → 0. This causes the sampler to get stuck in a local

mode of g. 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(at

i|at−i)=

exp[(Ui(a′I,at−i) -Ui(at

i,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(at

i|at−i)

Else, set at+1i = at

i

Let t0

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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

Resulting demand is logit

)()(),,(

),,(

xdFe

eq N

j

e

xxpv

ixxjpjvj

iii

xp,

ijjiiiij xxdtpBv )),(*(

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Supply Model

Vendors simultaneously choose price and location

Nash Equilibrium in two dimensions

Post merger, merged firm maximizes sum of vendor products

)()( xp,iiii qcpprofit

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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 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 products separate, price competition is softened As 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 Similar to effect of capacity constraints on merger.

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

Important complement to existing estimation methods