1. PCAIDS Merger Simulation with Nests: A New Framework for Unilateral Effects Analysis By Roy J. Epstein Adjunct Professor of Finance, Carroll School of Management, Boston College rje@royepstein.com Daniel L. Rubinfeld Robert L. Bridges Professor of Law and Professor of Economics at the University of California, Berkeley rubinfeld@law.berkeley.edu Presented at International Industrial Organization Conference Northeastern University April 5, 2003

2. 2 Merger Review Mergers and asset acquisitions are reviewed by the DOJ and the FTC. –Over 4,000 reviews/year (pre-2002 average) Main question: is the transaction anticompetitive, i.e., will it raise prices? The agencies can sue to block or restructure the transaction.

3. 3 Unilateral Price Effects Unilateral effect: the incentive for the newly merged firm to raise its prices (absent any collusive behavior). Arises when brand sales that previously would have been lost after a price increase can be retained because brand was acquired through the merger.

4. 4 Merger Simulation Has become a standard economic tool to evaluate unilateral effects in the U.S. FTC includes merger simulation among the past decade’s “remarkable developments in the quantitative analysis of horizontal mergers.” Goal is to quantify price changes due to the merger.

5. 5 Bertrand Pricing Assumption Typical basis for merger simulation. Each firm sets prices to maximize profits, taking account of non-collusive interactions with competitors. Bertrand equilibrium: no firm can increase profits by unilaterally changing the prices of its brands

6. 6 Notation For the ith brand: p i = price c i = incremental cost (assumed constant) s i = market share µ i = profit margin (p i – c i )/ p i  ij = elasticity of brand i w.r.t. price of brand j

7. 7 Pre- and Post-Merger Equilibria Pre-merger (A and B are single-brand firms) s 1  11 s 1 µ 1 A’s FOC: s 1 +  11 s 1 µ 1 = 0 s 2  22 s 2 µ 2 B’s FOC: s 2 +  22 s 2 µ 2 = 0 FOCs after merger of A and B s 1  11 s 1 µ 1  21 s 2 µ 2 s 1 +  11 s 1 µ 1 +  21 s 2 µ 2 = 0 s 2  22 s 1 µ 1  22 s 2 µ 2 s 2 +  22 s 1 µ 1 +  22 s 2 µ 2 = 0 Newco sets different prices because it takes account of cross-price elasticities that were not relevant before the merger.

8. 8 The Demand Model A general merger simulation analysis requires a demand model: –Calibration of the demand model yields the pre-merger own and cross-price elasticities. –The demand model generates the new elasticities and market shares consistent with post-merger market equilibrium.

9. 9 Finding the Pre-Merger Elasticities How to calibrate the demand model? –N brands imply N 2 own and cross elasticities. 200 brands of RTE cereal, for example, imply 40,000 elasticities! Needed: a large dataset, and/or structural assumptions that reduce the number of independent parameters.

10. 10 Econometric Approach Panels of scanner data can be used to estimate demand models (e.g., log-linear, logit, AIDS) econometrically. Potential limitations of scanner data: –Data cover only consumer goods sold in large outlets (e.g., supermarkets) –Data sources do not report wholesale prices relevant for mergers of producers –Limited availability outside the U.S.

11. 11 Proportionality-Calibrated Almost Ideal Demand System (PCAIDS) Approximation to the widely used Almost Ideal Demand System. Uses structural assumptions to reduce the dimensionality of the demand system. Introduced in Epstein & Rubinfeld, “Merger Simulation: A Simplified Approach with New Applications,” Antitrust Law Journal 69 (2002), pp. 883-919.

12. 12 The AIDS Framework AIDS (Deaton & Muelbauer, AER, 1980) predicts market shares in terms of prices, e.g., s 1 = a 1 + b 11 ln(p 1 ) + b 12 ln(p 2 ) + b 13 ln(p 3 ) s 2 = a 2 + b 21 ln(p 1 ) + b 22 ln(p 2 ) + b 23 ln(p 3 ) s 3 = a 3 + b 31 ln(p 1 ) + b 32 ln(p 2 ) + b 33 ln(p 3 ) (expenditure terms suppressed) Here there are 3 brands and 12 unknown parameters BUT…

13. 13 PCAIDS Restrictions Adding-up: the shares must sum to 100% (implies the last equation is redundant). Homogeneity: shares not affected by a uniform percentage price increase for all brands (implies the last brand is redundant). Slutsky-symmetry: the off-diagonal b’s are symmetric. Proportionality: share lost as a result of a price increase is allocated to the other brands in proportion to their respective shares. –Also called “Independence of Irrelevant Alternatives” or IIA

14. 14 PCAIDS with “Strict” Proportionality The restrictions imply: b 21 = –s 2 /(s 2 +s 3 )b 11 b 12 = –s 1 /(s 1 +s 3 )b 22 = b 21 b 22 = s 2 (1–s 2 )/[s 1 (1–s 1 )]b 11 Only 1 unknown parameter (b 11 ).

15. 15 PCAIDS Elasticities The b coefficients yield own and cross-price elasticities:  jj = b ii / s i – 1(Eq. 1)  ji = b ji / s j (Assumes the industry elasticity equals –1, more general formulas are also available; see Epstein & Rubinfeld, p. 916). Elasticities constrained to have proper sign. A single elasticity, e.g.,  11, can calibrate the entire system. A single elasticity, e.g.,  11, can calibrate the entire system after inverting Eq.1.

16. 16 A Simple Example Three single-brand firms (A, B, C) with shares of 20%, 30%, 50%. Industry elasticity = -1;  11 = -3. The unique PCAIDS coefficient matrix B is –0.400 0.150 0.250 –0.400 0.150 0.250 0.150–0.525 0.375 0.150–0.525 0.375 0.250 0.375–0.625 0.250 0.375–0.625 Satisfies adding-up, homogeneity, symmetry.

17. 17 Effect of Proportionality Proportionality with shares of 20%, 30%, 50% implies relative share diversion of 30/50, 20/50, and 20/30. The matrix of share parameters satisfies proportionality:.15 /.25 = 30 / 50.150 /.375 = 20 / 50.25 /.375 = 20 / 30

18. 18 Pre-Merger Information Summary Elasticity Matrix Elasticity Matrix ABC A – 3.000.75 1.25 B 0.50 – 2.75 1.25 C 0.50 0.75 – 2.25 Firm ShareMargin A 20% 33.3% A 20% 33.3% B 30% 36.4% B 30% 36.4% C 50% 44.4% C 50% 44.4%

19. 19 The Unilateral Effects Assume A and B merge. Comparison of pre- and post-merger equilibrium profit margins yields implied unilateral price increases for each firm A: 13.8% B: 10.8%

20. 20 Mitigations A complete analysis can take account of other relevant factors: –Merger-related efficiencies (reductions in marginal cost). –Restructuring (divestiture) –Credible threat of new entry

21. 21 Deviations from Proportionality What if proportionality is not a good assumption? PCAIDS is extended to non-proportionality by constructing separate “nests” of brands. –Diversion within a nest satisfies proportionality. –Share diverted to a brand in a different nest deviates from proportionality. Brands within a nest are relatively closer substitutes than brands outside the nest.

22. 22 Nesting Parameters “Nesting parameters” define deviation from proportionality –Parameter multiplies relative share diversion under proportionality by a scaling factor on the interval (0,1]. For brands within a nest, the nesting parameter equals 1. –Brands within a nest are closer substitutes than brands outside the nest.

23. 23 Share Diversion with Nests If brand B is in a different nest from brands A and C, it gains relatively less share following price increases for A or C. Suppose the nesting parameter is 0.5, so that B is “half as good” a substitute. The relative share diversion away from A would fall to 15/50, compared to 30/50 from before.

24. 24 Using Brand-Level Profit Margins to Infer Nesting Parameters Suppose margins and shares are known. –Should be available in an actual transaction –Accounting data may need adjustment Can use FOCs to solve for nesting parameters that yield elasticities consistent with pre-merger Bertrand equilibrium. See Eq. 16 in paper.

25. 25 Nesting Parameter Identification Number of parameters = w(w-1)/2, where w is number of nests. Identified using profit margin data and constraint that parameters lie in (0,1]. –Exactly identified in some cases –Can still provide useful bounds on parameters even when not fully identified or overidentified

26. 26 Nesting Parameter Example Three single-brand firms, shares of 20%, 30%, 50%. Firms A and B merge. Assume Firm A margin is 33.3% and Firm B margin is 48.1%. Suppose Firm B belongs in a separate nest from A and C. – –Higher margin for B (compared to 36.4% from before) indicates less competition than implied by proportionality.

27. 27 Nesting Parameter Example (cont.) 2-margin, 2-nest case exactly identified (see Eq. 16 in paper) Nesting parameter must equal 0.5 to satisfy pre-merger FOCs with the observed shares, margins, and the structural assumptions about proportionality.

28. 28 PCAIDS Coefficients — Nests and No Nests B Matrix With Separate Brand B Nest A B C A –0.4000.092 0.308 B 0.092 –0.323 0.231 C 0.308 0.231 –0.538 Nesting parameter = 0.5. B Matrix w/ Proportionality ABC A –0.400 0.150 0.250 B 0.150 –0.525 0.375 C 0.250 0.375 –0.625

29. 29 Elasticities — Nests and No Nests Elasticities With Brand B Nest A B C A –3.000.46 1.54 B 0.31 –2.08 0.77 C 0.62 0.46 –2.08 FOCs for calibration:.2 -3(.2).333 = 0.3 – 2.08(.3).481 = 0 Elasticities Under Proportionality ABC A –3.00 0.75 1.25 B 0.50 –2.75 1.25 C 0.50 0.75 –2.25 FOCs for calibration:.2 -3(.2).333 = 0.3 – 2.75(.3).364 = 0

30. 30 Nest Effects: Summary Generalization of PCAIDS Greater variation in the pattern of all elasticities. –Closer approximation to unconstrained AIDS model. Can be calibrated empirically using margin data and shares in the FOCs.

31. 31 Conclusions Merger simulation is ready to be used as a routine tool to evaluate unilateral effects. PCAIDS with nests offers advantages in many applications. –Nests can be calibrated empirically –Minimal data requirements –Provides a set of testable restrictions when econometric estimation of demand system is feasible Merger simulation is a fertile area for continued research and applications.