Transcript Slide 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
[email protected]
Daniel L. Rubinfeld
Robert L. Bridges Professor of Law and Professor of Economics at the
University of California, Berkeley
[email protected]
Presented at International Industrial Organization Conference
Northeastern University
April 5, 2003
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.
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
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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…
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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
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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).
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PCAIDS Elasticities
The b coefficients yield own and cross-price
elasticities:
jj = bii / si – 1
ji = bji / sj
(Eq. 1)
(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.
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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.
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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
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Pre-Merger Information Summary
Elasticity Matrix
A
B
C
A –3.00
0.75 1.25
B
0.50 –2.75
C
0.50
1.25
Firm Share
A
B
C
20%
30%
50%
Margin
33.3%
36.4%
44.4%
0.75 –2.25
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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%
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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
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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.
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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.
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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.
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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.
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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
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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.
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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.
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PCAIDS Coefficients — Nests and No
Nests
B Matrix With Separate Brand B
Nest
A
B
C
B Matrix w/ Proportionality
A
B
C
A
–0.400
0.092
0.308
A
–0.400
0.150
0.250
B
0.092
–0.323
0.231
B
0.150
–0.525
0.375
C
0.308
0.231 –0.538
C
0.250
0.375
–0.625
Nesting parameter = 0.5.
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Elasticities — Nests and No Nests
Elasticities With Brand B Nest
A
B
C
Elasticities Under Proportionality
A
B
C
A
–3.00
0.46
1.54
A
–3.00
0.75
1.25
B
0.31
–2.08
0.77
B
0.50
–2.75
1.25
C
0.62
0.46
–2.08
C
0.50
0.75
–2.25
FOCs for calibration:
FOCs for calibration:
.2 -3(.2).333 = 0
.2 -3(.2).333 = 0
.3 – 2.08(.3).481 = 0
.3 – 2.75(.3).364 = 0
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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.
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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.
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