PCAIDS Merger Simulation with Nests: A New Framework for Unilateral Effects Analysis

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. 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. 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. 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. 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. Notation For the ith brand: pi= price ci = incremental cost (assumed constant) si = market share µi = profit margin (pi–ci)/ pi ij= elasticity of brand i w.r.t. price of brand j

7. Pre- and Post-Merger Equilibria • Pre-merger (A and B are single-brand firms) A’s FOC: s1 + 11s1µ1 = 0 B’s FOC: s2 + 22s2µ2 = 0 • FOCs after merger of A and B s1 + 11s1µ1 + 21s2µ2= 0 s2 + 22s1µ1 + 22s2µ2= 0 • Newco sets different prices because it takes account of cross-price elasticities that were not relevant before the merger.

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. Finding the Pre-Merger Elasticities • How to calibrate the demand model? • N brands imply N2 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. 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. 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. The AIDS Framework • AIDS (Deaton & Muelbauer, AER, 1980) predicts market shares in terms of prices, e.g., s1 = a1 + b11 ln(p1) + b12 ln(p2) + b13 ln(p3) s2 = a2 + b21 ln(p1) + b22 ln(p2) + b23 ln(p3) s3 = a3 + b31 ln(p1) + b32 ln(p2) + b33 ln(p3) (expenditure terms suppressed) • Here there are 3 brands and 12 unknown parameters BUT…

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. PCAIDS with “Strict” Proportionality • The restrictions imply: b21 = –s2/(s2+s3)b11 b12 = –s1/(s1+s3)b22 = b21 b22 = s2(1–s2)/[s1(1–s1)]b11 • Only 1 unknown parameter (b11).

15. PCAIDS Elasticities • The b coefficients yield own and cross-price elasticities: jj= bii / si– 1 (Eq. 1) ji= bji / sj (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 after inverting Eq.1.

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 0.150 –0.525 0.375 0.250 0.375 –0.625 • Satisfies adding-up, homogeneity, symmetry.

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. Elasticity Matrix A B C A –3.00 0.75 1.25 B 0.50 –2.75 1.25 C 0.50 0.75 –2.25 Firm Share Margin A 20% 33.3% B 30% 36.4% C 50% 44.4% Pre-Merger Information Summary

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

29. Elasticities With Brand B Nest A B C A –3.00 0.46 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 A B C 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 Elasticities — Nests and No Nests

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. 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.