Post-Merger Product Repositioning

1. Post-Merger Product Repositioning Luke Froeb, Vanderbilt University of Texas Arlington, TX April 28, 2006

2. 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

3. Talk Outline • Policy Motivation: why are we doing this? • How does this fit into economic literature? • Computing Equilibria without calculus • Model & Results

4. FTC: Man Controlling Trade

5. 1900 Laws enacted in 1900 or before

6. 1960 Laws enacted in 1960 or before Note: EU introduced antitrust law in 1957

7. 1980 Laws enacted in 1980 or before

8. 1990 Laws enacted in 1990 or before

9. 2004 Laws enacted in 2004 or before

10. Enforcement Priorities • US & EC • 1. Cartels • 2. Mergers • 3. Abuse of dominance (monopolization) • New antitrust regimes • 1. Abuse of dominance • 2. Mergers • 3. Cartels

11. 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

12. Merger Activity

13. Merger Investigations

14. FTC Merger Challenges, 96-03

15. 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?

16. 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

17. 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

18. 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 NOTincrease relative to other regions using similar type of gasoline

19. Differences-in-Differences Estimation

20. 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 other • Merged firm responds by raising prices • Non-merging firms raise price sympathetically

21. 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)

22. 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

23. 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).

24. 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

25. 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”

26. 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

27. 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?

28. Computing Equilibria • Fixed-point algorithms • Require smooth profit functions • Require good starting points • Can’t find Multiple equilibria • Stochastic response dynamic • All it needs are profit functions.

29. 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

30. 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.

31. 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.

32. 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] • 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

33. 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.

34. 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

35. Example: Cournot equil.={1/3,1/3}

36. Example, 2 equil={{5,8},{8,5}}

37. Demand Model • Consumers on Hotelling line • Indirect utility is function of price + travel cost + random shock • Resulting demand is logit

38. Supply Model • Vendors simultaneously choose price and location • Nash Equilibrium in two dimensions • Post merger, merged firm maximizes sum of vendor products

39. Pre-merger Locations

40. 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

41. Pre- (dashed) and Post- (solid) Merger Locations (outside good)

42. Net Merger Effect =Cross elasticity + Softening

43. Non Merging Firms Softening

44. Profit Changes

45. 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

46. 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