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PCAIDS Merger Simulation with Nests: A New Framework for Unilateral
Effects Analysis
ByBy
Roy J. EpsteinRoy J. EpsteinAdjunct Professor of Finance, Carroll School of Management, Boston CollegeAdjunct Professor of Finance, Carroll School of Management, Boston College
[email protected]@royepstein.com
Daniel L. RubinfeldDaniel L. RubinfeldRobert L. Bridges Professor of Law and Professor of Economics at the Robert L. Bridges Professor of Law and Professor of Economics at the University of California, Berkeley University of California, Berkeley
[email protected]@law.berkeley.edu
Presented at International Industrial Organization Conference Presented at International Industrial Organization Conference Northeastern UniversityNortheastern University
April 5, 2003April 5, 2003
22
Merger ReviewMerger Review
Mergers and asset acquisitions are Mergers and asset acquisitions are reviewed by the DOJ and the FTC.reviewed by the DOJ and the FTC.
– Over 4,000 reviews/year (pre-2002 average)Over 4,000 reviews/year (pre-2002 average)
Main question: is the transaction Main question: is the transaction anticompetitive, i.e., will it raise prices?anticompetitive, i.e., will it raise prices?
The agencies can sue to block or The agencies can sue to block or restructure the transaction.restructure the transaction.
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Unilateral Price EffectsUnilateral Price Effects
Unilateral effect: the incentive for the Unilateral effect: the incentive for the newly merged firm to raise its prices newly merged firm to raise its prices (absent any collusive behavior).(absent any collusive behavior).
Arises when brand sales that previously Arises when brand sales that previously would have been lost after a price would have been lost after a price increase can be retained because brand increase can be retained because brand was acquired through the merger. was acquired through the merger.
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Merger SimulationMerger Simulation
Has become a standard economic tool to Has become a standard economic tool to evaluate unilateral effects in the U.S. evaluate unilateral effects in the U.S.
FTC includes merger simulation among FTC includes merger simulation among the past decade’s “remarkable the past decade’s “remarkable developments in the quantitative analysis developments in the quantitative analysis of horizontal mergers.”of horizontal mergers.”
Goal is to quantify price changes due to Goal is to quantify price changes due to the merger.the merger.
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Bertrand Pricing AssumptionBertrand Pricing Assumption
Typical basis for merger simulation.Typical basis for merger simulation.
Each firm sets prices to maximize profits, Each firm sets prices to maximize profits, taking account of non-collusive taking account of non-collusive interactions with competitors. interactions with competitors.
Bertrand equilibrium: no firm can increase Bertrand equilibrium: no firm can increase profits by unilaterally changing the prices profits by unilaterally changing the prices of its brands of its brands
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NotationNotation
For the ith brand:For the ith brand:
ppii= price= price
ccii = incremental cost (assumed constant) = incremental cost (assumed constant)
ssii = market share = market share
µµii = profit margin ( = profit margin (ppii – – ccii)/ )/ ppii
ijij = = elasticity of brand i w.r.t. price of elasticity of brand i w.r.t. price of
brand j brand j
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Pre- and Post-Merger EquilibriaPre- and Post-Merger Equilibria
Pre-merger (A and B are single-brand firms)Pre-merger (A and B are single-brand firms)A’s FOC: ss11 + 1111ss11µµ1 1 = 0
B’s FOC: ss22 + 2222ss22µµ2 2 = 0
FOCs after merger of A and BFOCs after merger of A and Bss11 + 1111ss11µµ1 1 + 2121ss22µµ22 = 0
ss22 + 2222ss11µµ1 1 + 2222ss22µµ22 = 0
Newco sets different prices because it takes Newco sets different prices because it takes account of cross-price elasticities that were not account of cross-price elasticities that were not relevant before the merger.relevant before the merger.
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The Demand ModelThe Demand Model
A general merger simulation analysis A general merger simulation analysis requires a demand model:requires a demand model:
– Calibration of the demand model yields the Calibration of the demand model yields the pre-merger own and cross-price elasticities.pre-merger own and cross-price elasticities.
– The demand model generates the new The demand model generates the new elasticities and market shares consistent with elasticities and market shares consistent with post-merger market equilibrium.post-merger market equilibrium.
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Finding the Pre-Merger ElasticitiesFinding the Pre-Merger Elasticities
How to calibrate the demand model?How to calibrate the demand model?
– N brands imply NN brands imply N22 own and cross elasticities. own and cross elasticities. 200 brands of RTE cereal, for example, imply 200 brands of RTE cereal, for example, imply 40,000 elasticities! 40,000 elasticities!
Needed: a large dataset, and/or structural Needed: a large dataset, and/or structural assumptions that reduce the number of assumptions that reduce the number of independent parameters.independent parameters.
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Econometric ApproachEconometric Approach
Panels of scanner data can be used to Panels of scanner data can be used to estimate demand models (e.g., log-linear, estimate demand models (e.g., log-linear, logit, AIDS) econometrically.logit, AIDS) econometrically.
Potential limitations of scanner data:Potential limitations of scanner data:– Data cover only consumer goods sold in large Data cover only consumer goods sold in large
outlets (e.g., supermarkets)outlets (e.g., supermarkets)– Data sources do not report wholesale prices Data sources do not report wholesale prices
relevant for mergers of producersrelevant for mergers of producers– Limited availability outside the U.S.Limited availability outside the U.S.
1111
Proportionality-Calibrated Almost Ideal Proportionality-Calibrated Almost Ideal Demand System (PCAIDS)Demand System (PCAIDS)
Approximation to the widely used Almost Ideal Approximation to the widely used Almost Ideal Demand System.Demand System.
Uses structural assumptions to reduce the Uses structural assumptions to reduce the dimensionality of the demand system.dimensionality of the demand system.
Introduced in Epstein & Rubinfeld, “Merger Introduced in Epstein & Rubinfeld, “Merger Simulation: A Simplified Approach with New Simulation: A Simplified Approach with New Applications,” Applications,” Antitrust Law JournalAntitrust Law Journal 69 (2002), 69 (2002), pp. 883-919.pp. 883-919.
1212
The AIDS FrameworkThe AIDS Framework
AIDS (Deaton & Muelbauer, AER, 1980) predicts AIDS (Deaton & Muelbauer, AER, 1980) predicts market shares in terms of prices, e.g.,market shares in terms of prices, e.g.,
ss11 = = aa11 + + bb1111 ln( ln(pp11) + ) + bb1212 ln( ln(pp22) + ) + bb1313 ln( ln(pp33))
ss22 = = aa22 + + bb2121 ln( ln(pp11) + ) + bb2222 ln( ln(pp22) + ) + bb2323 ln( ln(pp33))
ss33 = = aa33 + + bb3131 ln( ln(pp11) + ) + bb3232 ln( ln(pp22) + ) + bb3333 ln( ln(pp33))
(expenditure terms suppressed)(expenditure terms suppressed)
Here there are 3 brands and 12 unknown Here there are 3 brands and 12 unknown parameters BUT…parameters BUT…
1313
PCAIDS RestrictionsPCAIDS Restrictions
Adding-upAdding-up: the shares must sum to 100% (implies the : the shares must sum to 100% (implies the last equation is redundant).last equation is redundant).
HomogeneityHomogeneity: shares not affected by a uniform : shares not affected by a uniform percentage price increase for all brands (implies the last percentage price increase for all brands (implies the last brand is redundant).brand is redundant).
Slutsky-symmetrySlutsky-symmetry: the off-diagonal : the off-diagonal bb’s are symmetric.’s are symmetric.
ProportionalityProportionality: share lost as a result of a price increase : share lost as a result of a price increase is allocated to the other brands in proportion to their is allocated to the other brands in proportion to their respective shares.respective shares.– Also called “Independence of Irrelevant Alternatives” or IIAAlso called “Independence of Irrelevant Alternatives” or IIA
1414
PCAIDS with “Strict” ProportionalityPCAIDS with “Strict” Proportionality
The restrictions imply:The restrictions imply:
bb2121 = – = –ss22/(/(ss22++ss33))bb11 11
bb1212 = – = –ss11/(/(ss11++ss33))bb2222 = = bb2121
bb2222 = = ss22(1–(1–ss22)/[)/[ss11(1–(1–ss11)])]bb1111
Only 1 unknown parameter (Only 1 unknown parameter (bb1111).).
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PCAIDS ElasticitiesPCAIDS Elasticities
The The bb coefficients yield own and cross-price coefficients yield own and cross-price elasticities:elasticities:
jjjj = b= biiii / / ssii – 1– 1 (Eq. 1)(Eq. 1)
jiji = b= bjiji / / ssjj
(Assumes the industry elasticity equals (Assumes the industry elasticity equals –1,–1, more general formulas are also more general formulas are also available; see Epstein & Rubinfeld, p. 916).available; see Epstein & Rubinfeld, p. 916).
Elasticities constrained to have proper sign.Elasticities constrained to have proper sign.
A single elasticity, e.g., A single elasticity, e.g., 1111, can calibrate the , can calibrate the entire systementire system after inverting Eq.1..
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A Simple ExampleA Simple Example
Three single-brand firms (A, B, C) with shares of Three single-brand firms (A, B, C) with shares of 20%, 30%, 50%. Industry elasticity = -1; 20%, 30%, 50%. Industry elasticity = -1; 1111 = -3. = -3.
The unique PCAIDS coefficient matrix The unique PCAIDS coefficient matrix BB is is
––00.400.400 0.150 0.150 0.250 0.250
0.1500.150 –0–0.525.525 0.375 0.375
0.2500.250 0.375 0.375 –0–0.625.625
Satisfies adding-up, homogeneity, symmetry.Satisfies adding-up, homogeneity, symmetry.
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Effect of ProportionalityEffect of Proportionality
Proportionality with shares of 20%, 30%, Proportionality with shares of 20%, 30%, 50% implies relative share diversion of 50% implies relative share diversion of 30/50, 20/50, and 20/30.30/50, 20/50, and 20/30.
The matrix of share parameters satisfies The matrix of share parameters satisfies proportionality: proportionality:
.15 / .25 = 30 / 50.15 / .25 = 30 / 50
.150 / .375 = 20 / 50.150 / .375 = 20 / 50
.25 / .375 = 20 / 30.25 / .375 = 20 / 30
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Pre-Merger Information SummaryPre-Merger Information Summary
Elasticity MatrixElasticity Matrix
AA BB CC
AA ––3.003.00 0.750.75 1.251.25
BB 0.50 0.50 ––2.75 1.252.75 1.25
CC 0.50 0.75 0.50 0.75 ––2.252.25
Firm ShareFirm Share MarginMargin
AA 20% 33.3% 20% 33.3%
BB 30% 30% 36.4% 36.4%
CC 50% 50% 44.4% 44.4%
1919
The Unilateral EffectsThe Unilateral Effects
Assume A and B merge.Assume A and B merge.
Comparison of pre- and post-merger Comparison of pre- and post-merger equilibrium profit margins yields implied equilibrium profit margins yields implied unilateral price increases for each firmunilateral price increases for each firm
A: 13.8%A: 13.8%B: 10.8% B: 10.8%
2020
MitigationsMitigations
A complete analysis can take account of A complete analysis can take account of other relevant factors:other relevant factors:
– Merger-related efficiencies (reductions in Merger-related efficiencies (reductions in marginal cost).marginal cost).
– Restructuring (divestiture)Restructuring (divestiture)– Credible threat of new entryCredible threat of new entry
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Deviations from ProportionalityDeviations from Proportionality
What if proportionality is not a good assumption?What if proportionality is not a good assumption?
PCAIDS is extended to non-proportionality by PCAIDS is extended to non-proportionality by constructing separate “nests” of brands. constructing separate “nests” of brands. – Diversion within a nest satisfies proportionality.Diversion within a nest satisfies proportionality.– Share diverted to a brand in a different nest deviates Share diverted to a brand in a different nest deviates
from proportionality.from proportionality.
Brands within a nest are relatively closer Brands within a nest are relatively closer substitutes than brands outside the nest.substitutes than brands outside the nest.
2222
Nesting ParametersNesting Parameters
““Nesting parameters” define deviation from Nesting parameters” define deviation from proportionalityproportionality– Parameter multiplies relative share diversion Parameter multiplies relative share diversion
under proportionality by a scaling factor on under proportionality by a scaling factor on the interval (0,1]. the interval (0,1].
For brands within a nest, the nesting For brands within a nest, the nesting parameter equals 1. parameter equals 1. – Brands within a nest are closer substitutes Brands within a nest are closer substitutes
than brands outside the nest. than brands outside the nest.
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Share Diversion with NestsShare Diversion with Nests
If brand B is in a different nest from brands If brand B is in a different nest from brands A and C, it gains relatively less share A and C, it gains relatively less share following price increases for A or C. following price increases for A or C.
Suppose the nesting parameter is 0.5, so Suppose the nesting parameter is 0.5, so that B is “half as good” a substitute. The that B is “half as good” a substitute. The relative share diversion away from A relative share diversion away from A would fall to 15/50, compared to 30/50 would fall to 15/50, compared to 30/50 from before.from before.
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Using Brand-Level Profit Margins to Using Brand-Level Profit Margins to Infer Nesting ParametersInfer Nesting Parameters
Suppose margins and shares are known.
– Should be available in an actual transactionShould be available in an actual transaction– Accounting data may need adjustmentAccounting 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.
2525
Nesting Parameter IdentificationNesting Parameter Identification
Number of parameters = w(w-1)/2, where Number of parameters = w(w-1)/2, where w is number of nests.w is number of nests.
Identified using profit margin data and Identified using profit margin data and constraint that parameters lie in (0,1].constraint that parameters lie in (0,1].
– Exactly identified in some casesExactly identified in some cases– Can still provide useful bounds on parameters Can still provide useful bounds on parameters
even when not fully identified or overidentifiedeven when not fully identified or overidentified
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Nesting Parameter ExampleNesting Parameter Example
Three single-brand firms, shares of 20%, Three single-brand firms, shares of 20%, 30%, 50%. Firms A and B merge.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.
2727
Nesting Parameter Example (cont.)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.
2828
PCAIDS Coefficients — Nests and No PCAIDS Coefficients — Nests and No NestsNests
BB Matrix With Separate Brand B Matrix With Separate Brand B NestNest
AA B B C C
AA –0.400–0.400 0.0920.092 0.308 0.308
BB 0.092 0.092 –0–0.323 0.231.323 0.231
CC 0.308 0.231 0.308 0.231 –0–0.538.538
Nesting parameter = 0.5.Nesting parameter = 0.5.
BB Matrix w/ Proportionality Matrix w/ Proportionality
AA BB CC
AA –0.400–0.400 0.150 0.250 0.150 0.250
BB 0.150 0.150 –0.525–0.525 0.375 0.375
CC 0.250 0.375 0.250 0.375 –0.625–0.625
2929
Elasticities — Nests and No NestsElasticities — Nests and No Nests
Elasticities With Brand B NestElasticities With Brand B Nest
AA B B C C
AA ––3.003.00 0.460.46 1.54 1.54
BB 0.31 0.31 ––2.08 0.772.08 0.77
CC 0.62 0.46 0.62 0.46 ––2.082.08
FOCs for calibration:FOCs for calibration:
.2 -3(.2).333 = 0.2 -3(.2).333 = 0
.3 – 2.08(.3).481 = 0.3 – 2.08(.3).481 = 0
Elasticities Under ProportionalityElasticities Under Proportionality
AA BB CC
AA ––3.00 0.75 1.253.00 0.75 1.25
BB 0.50 0.50 ––2.75 1.252.75 1.25
CC 0.50 0.75 0.50 0.75 ––2.252.25
FOCs for calibration:FOCs for calibration:
.2 -3(.2).333 = 0.2 -3(.2).333 = 0
.3 – 2.75(.3).364 = 0.3 – 2.75(.3).364 = 0
3030
Nest Effects: SummaryNest Effects: Summary
Generalization of PCAIDSGeneralization of PCAIDS
Greater variation in the pattern of all Greater variation in the pattern of all elasticities. elasticities.
– Closer approximation to unconstrained AIDS Closer approximation to unconstrained AIDS model.model.
Can be calibrated empirically using margin Can be calibrated empirically using margin data and shares in the FOCs.data and shares in the FOCs.
3131
ConclusionsConclusions
Merger simulation is ready to be used as a Merger simulation is ready to be used as a routine tool to evaluate unilateral effects. routine tool to evaluate unilateral effects.
PCAIDS with nests offers advantages in many PCAIDS with nests offers advantages in many applications.applications.– Nests can be calibrated empiricallyNests can be calibrated empirically– Minimal data requirements Minimal data requirements – Provides a set of testable restrictions when Provides a set of testable restrictions when
econometric estimation of demand system is feasibleeconometric estimation of demand system is feasible
Merger simulation is a fertile area for continued Merger simulation is a fertile area for continued research and applications.research and applications.
