CHAPTER XI
MERGER SIMULATION
A. Introduction to Merger Simulation
Merger simulation is a potentially useful way to generate a
quantitative prediction of the likely unilateral price effects of a proposed
merger.1 The basic idea is to combine what can be easily observed, such
as prices and shares, with reasonable assumptions about behavior of
market participants, in a manner that allows the calculation of the
implied unilateral effects. Merger simulation can illuminate what
matters in determining the unilateral effects of a merger, how it matters,
and how much it matters. This chapter discusses the strengths and
weaknesses of merger simulation generally, and of specific models used
in merger simulation.
Merger simulation has been used mainly with differentiated
consumer products, and this chapter examines three models of consumer
demand that have been used in that context. For non-economists this
may be a somewhat technical discussion. The first four sections of this
chapter, however, provide non-technical introductions to 1) the concept
of merger simulation and its proper use, 2) unilateral merger effects with
differentiated consumer products and the role of demand elasticities, 3)
three models of consumer demand that have been used in merger
simulation with differentiated consumer products, and 4) the pros and
cons of these three models in merger simulation.
Because tractable economic modeling never fully captures real-world
competitive processes, the ultimate test for the reliability of merger
simulation is how well it predicts the effects of actual mergers.
Regrettably, little is known about that accuracy, nor about the accuracy
1.
As explained below, combining the merging firms, and hence
internalizing the competition among their merging products, may alter
profit incentives and cause the merged firm to raise prices or reduce
output without any sort of coordination with competitors.
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of any other method for predicting the competitive effects of mergers.
For now, the reliability of merger simulation must be judged on the basis
of “fit” between the model and the industry.
Merger simulation with differentiated consumer products employs
the Bertrand oligopoly model. The Bertrand model assumes competitors
interact just once, each maximizing its short-run profit, with price as the
sole dimension of competition. Bertrand equilibrium is reached when all
competitors are happy with their prices, given rivals’ prices.2 The
Bertrand model should be employed in the competitive analysis of
mergers only when its proponent is prepared to persuade the trier of fact
that the model comports reasonably well with the factual setting of the
industry.3
Assessing the “fit” between the Bertrand model and real world
economic conditions is largely a matter of evaluating how well it
explains the past. One important aspect of fit is the degree to which the
predicted price-cost margins, which characterize the intensity of
competition, correspond to observed margins. Also important is how
well the model would have predicted responses to significant cost
changes or new product introductions occurring in the recent past.
Finally, it is important to evaluate the role of non-price competition, e.g.,
advertising and product positioning, as well as the strategic behavior in
repeated competitor interaction, all of which are outside the model.
Merger simulation holds such things as product characteristics and
advertising constant, which can result in misleading predictions,
particularly if aspects of marketing strategy interact in important ways
with pricing. Merger simulation also examines only the unilateral
incentive that may exist for the merged firm to raise price.4 If some form
2.
3.
4.
For a discussion of the Bertrand model, see DENNIS W. CARLTON &
JEFFREY M. PERLOFF, MODERN INDUSTRIAL ORGANIZATION 166-72 (3d
ed. 2000).
For further discussion of when the Bertrand model fits the industry well
enough to offer useful predictions, see Gregory J. Werden, Luke M.
Froeb & David T. Scheffman, A Daubert Discipline for Merger
Simulation, ANTITRUST (forthcoming 2004).
“Unilateral effects” may occur when products produced by the merging
parties are close substitutes in consumption. The merger may create a
significant incentive to raise the prices of products that had been sold
separately, if a substantial proportion of the sales lost by one merging
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of pricing coordination (e.g., overt collusion) is likely exist before the
merger, or arise as a result of the merger, merger simulation may not
offer any useful insights to the merger’s competitive effects.
If the Bertrand model reasonably approximates competitor behavior
before and after a merger, simulation may be helpful in gaining insight
into likely post-merger price changes. Merger simulation can provide
reasonable, if rough, estimates of a differentiated products merger’s price
effects. Merger simulation is good tool to have, but it should not always
be used, and it is never the only tool required. Significant weight should
be placed on the predictions of a merger simulation only if the modeling
assumptions and the simulation predictions are consistent with the
picture of the competitive landscape painted by the totality of the
evidence. Merger simulation can usefully complement a traditional, factintensive analysis of consumers, competitors, and the institutional setting
of an industry, but cannot substitute for it.
B. Unilateral Effects Analysis and the Role of Demand Elasticities
The basic idea of unilateral effects from differentiated products
mergers is straightforward: Prior to a proposed merger, the producers of
Brands A and B presumably are happy with their prices, given the prices
of rival brands. Thus, a small price increase would reduce profits
because the revenues lost from the resulting sales reduction would
exceed the cost reduction associated with producing less. If Brands A
and B compete, and the price of either is raised, some of its customers
would switch to the other product. The merger of the producers of
Brands A and B would alter the profit-maximization calculus, because
some of the sales lost from increasing the price of either brand would be
regained by the other merging brand. The merged firm would internalize
the competition between Brands A and B and create an incentive to raise
prices for both (assuming the merger did not also reduce costs).5
The strength of the incentive to increase prices depends on the
intensity of competition between the merging brands, and between those
5.
product due to a higher price flow to a product that the merger brings
under common ownership.
Unilateral competitive effects with differentiated products are explained
by Jonathan B. Baker, Unilateral Competitive Effects Theories in Merger
Analysis, ANTITRUST, Spring 1997, at 21, 23.
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brands and other products. In a Bertrand model with differentiated
products, intensity of competitive interaction is indicated by “own and
cross elasticities of demand.”
An own elasticity of demand indicates responsiveness to a product’s
own price. The own elasticity for Brand A can be defined as the
percentage change in A’s quantity demanded resulting from a one percent
increase in A’s price.
Cross elasticities of demand indicate
responsiveness to changes in the other products’ prices. The cross
elasticity of demand for Brand A with respect to Brand B’s price can be
defined as the percentage change in the quantity demanded for A that
would result from a one percent change in the price of B. Any pair of
products has two cross elasticities, indicating the responsiveness of the
demand of each to changes in the price of the other.6 Cross elasticities
between substitutes are positive, indicating there is a sales gain from an
increase in the price of a substitute, while own elasticities are negative,
indicating that a product’s own sales fall as its price is increased.7
Holding all else constant, the larger the cross elasticities of demand
between two brands, the stronger the incentive to increase prices after the
brands are merged, because the greater will be the recapture by one
brand of sales lost by the other. Own elasticities of demand affect the
incentive for price increases less directly. They indicate the pre-merger
price-cost margins, and those margins determine the increment to profit
from gaining a unit of sales. Because the relevant demand elasticities
can never be known with certainly, merger simulation always should
consider a substantial range of elasticities and explore sensitivity to other
factors affecting the unilateral effects of a merger. A differentiated
products merger also might produce coordinated effects, yet there is no
6.
7.
The diversion ratios between pairs of products combine own and cross
elasticities of demand. The diversion ratio from Brand A to Brand B
measures the proportion of sales lost by A when its price is raised that are
captured by Brand B. See generally Carl Shapiro, Mergers with
Differentiated Products, ANTITRUST, Spring 1996, at 23, 23–30.
Cross elasticities can be negative, as with complementary goods.
Estimated cross elasticities sometimes come out negative even for
substitutes. This can be simply due to statistical variation, but sometimes
suggests a problem with the data or the model of consumer demand used
in the estimation.
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straightforward relationship between the relevant demand elasticities and
such effects.
C. Introduction to Three Demand Models for Merger Simulation
This chapter presents three models of consumer demand that have
been used in merger simulation. The Almost Ideal Demand System
(“AIDS”) imposes the weakest assumptions of the three and offers the
greatest flexibility. Each of the relevant elasticities, at the consumer
level, can be independently determined by the data with an AIDS model,
subject only to restrictions that may be imposed on the basis of economic
theory. But estimating an AIDS model for differentiated consumer
products is only feasible when data is available over a wide range of
prices and a relatively long time period. Such data were only
occasionally available prior to the mid-1980s.8 Retail scanner data is
now used to estimate brand-specific demand elasticities at the consumer
level, but there are difficult issues in that estimation.9
Aggregation across observational units (e.g., retailers) and across
time may distort price-quantity relationships. Retailer promotional
activity and consumer inventory behavior may require additional
complexities be built into the econometric model. Moreover, a host of
standard, but potentially vexing, econometric issues arise and must be
dealt with. Finally, demand elasticities at the consumer level can never
be a sufficient basis for predicting the effects of a merger at the
manufacturing level. It is also essential to model retailer behavior and
retailer-manufacturer interaction, which can substantially affect the
retail-price effects of a manufacturing merger.
8.
9.
Prior to the mid-1980’s, the available aggregate-level data (i.e., data
aggregated over individuals to the level of a city or region) typically
allowed the estimation of demand elasticities for only broad categories of
goods, i.e., food, clothing, etc. The lack of aggregate-level data on the
individual products within these broad categories generally prevented the
estimation of demand elasticities for these products (i.e., individual
brands of bread or soap). The most important exception was data on
individual decisions derived through surveys. Using such data, demand
was estimated for modes of transportation and recreational sites.
See Appendix IV for a discussion of the difficulties that arise when using
scanner data.
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The antitrust logit model (“ALM”) focuses on a set of goods called
the “inside” goods, which do not necessarily coincide with the relevant
market in the antitrust sense.10 The data requirements for the ALM are
only 1) the prices of the inside goods, 2) the shares of the inside goods,
3) the aggregate elasticity of demand for the inside goods, and 4) a price
coefficient indicating the degree of substitutability among the inside
goods. This coefficient can be estimated from the sort of data used to
estimate an AIDS model, and it also can be inferred from less systematic
evidence of consumer responses to changes in prices, as well as from
price-cost margins.
There is a single price coefficient in the ALM as a result of the
assumption that consumer choice exhibits a property known as the
Independence of Irrelevant Alternatives, or IIA. What this means as a
practical matter is that substitution away from any inside good is
distributed to the other inside goods in proportion to their shares.11 As a
result of the IIA property, changing the set of inside goods affects only
the aggregate elasticity of demand for the inside goods. This is helpful
because it means that it is not necessary to settle on a relevant market in
order to determine the inside good shares, or otherwise to simulate a
merger. Omissions from the set of inside goods affect the simulation
only because the prices of outside goods are held constant, while the
prices of inside goods are affected by the merger. The IIA property,
however, is the principle drawback of the model, since it forces all inside
goods to be equally close substitutes for each other, which may not
accurately characterize consumer demand.
Like ALM, PCAIDS (proportionately calibrated AIDS) assumes that
consumer choice is characterized by the IIA property. The two models
differ, however, in that the ALM assumes this property always holds,
while PCAIDS assumes that it holds only in the pre-merger equilibrium.
10.
11.
ALM also offers the choice of the “outside” good. For example, if the
inside goods were flights for a particular route, the outside good would be
the choice of not flying. The ALM differs from a conventional logit
model with respect to how the outside choice is incorporated into the
model. In the ALM, the outside choice is reflected in an aggregate
elasticity of demand for the inside goods.
If inside goods A, B, and C have respective shares of 10%, 30%, and
60%, and the price of C is increased, the substitution to B must be three
times the substitution to A.
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The data requirements for PCAIDS are just market shares, the aggregate
elasticity of demand for the product group as a whole, and the own
elasticity of demand for any one product. Unlike ALM, PCAIDS does
not require price information.
With both the ALM and PCAIDS, the IIA assumption can be
modified to include “nests.” Nests contain groups of products that are
particularly close substitutes. For example in estimating automobile
demand, nests might be created for luxury cars, economy cars, and
possibly several other categories of automobiles.
D. The Choice of a Demand Model for Merger Simulation
Successful estimation of an AIDS model obviates the need for strong
and untestable assumptions required by the ALM or PCAIDS. Thus, it is
always worthwhile to explore the availability of data for use in demand
estimation. However, estimation of an AIDS model is apt to be time
consuming and expensive, and the data may prove inadequate to the
formidable task of estimating the large number of independent
elasticities in an AIDS model. Moreover, the estimation cannot be
worthwhile unless the Bertrand model is a good fit for the industry.
Estimating an AIDS model imposes considerable data demands
because of the potentially large number of separate demand elasticities
that are estimated. With three products, there are three own elasticities
and six cross elasticities, for a total of nine elasticities to be estimated.
With four products that total increases to sixteen, and in general, the
number of elasticities estimated in an AIDS model is the square of the
number of products. The desirable flexibility of the AIDS model, thus,
comes at a potentially significant cost. When a large number of separate
own and cross elasticities are estimated, it is difficult to estimate them
precisely, leading to a high variance12 in the estimates. Imposing
restrictions on the elasticities, like the IIA property, reduces the variance
12.
When a regression coefficient is estimated econometrically, the estimate
is properly viewed as a random variable with an associated variance that
measures its spread or dispersion. The higher the variance, the less
precise is the estimate, or in other words, the less the data say about the
“true” value of the coefficient.
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in their estimates, but this may introduce bias.13 This variance-bias
tradeoff is discussed further in the chapter.
The greater the number of separate elasticities to be estimated, the
greater the amount of data needed to attain reliable estimates. Thus, the
choice of which model to use may revolve around the amount and quality
of data available. With a significant amount of data, reflecting a
relatively wide variance in prices, it may be possible to let the data
“speak for itself” by estimating all of the relevant demand elasticities
econometrically, as with the AIDS model. With very little data is
available, no estimation may be possible, but merger simulation is
nevertheless possible if strong restrictions are placed on the form of
demand, as with the ALM and PCAIDS.
In both the ALM and PCAIDS models, the imposition of the IIA
property means that all of the relevant demand elasticities are determined
by just two independent demand parameters, and there are
straightforward ways to infer likely values of both from very little data
and without resort to econometrics. This makes merger simulation using
the ALM or PCAIDS well suited for use in the initial evaluation of a
merger designed to see whether it plausibly would yield significant price
increases (e.g., increases not easily eliminated by modest cost savings).
On final consideration in the choice among demand models is the
inherent “curvature” properties of any particular model. While the AIDS
model allows each separate demand elasticity to be determined by the
data, how those elasticities change with changes in prices is preordained
by the model. This is no less true of any other conventional model of
demand, and PCAIDS imposes the same curvature properties as AIDS.
Other demand models, including the ALM, impose different curvature
properties with different implications. The ALM may result in
substantially lower price increase predictions than AIDS or PCAIDS as a
consequence of the differing curvature properties.14
13.
14.
A biased estimate differs systematically from the “true” value, rather than
departs from the true value only because of sampling error.
Two other demand models are 1) linear demand, in which demand for
each product is a straight-line function of each price, and 2) isoelastic
demand, in which all the own and cross elasticities of demand are
assumed to be invariant to prices. The price increase predictions with
isoelastic demand are apt to be greater than those with AIDS demand,
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E. Alternative Models for Merger Simulation
1. Logit Model
a.
Introduction
The logit model is a relatively simple demand model used to
estimate demand elasticities and simulate the effects of mergers in
differentiated products industries.15 It has relatively few parameters,
which facilitates their econometric estimation or their direct calibration
from industry data. This makes the logit model ideal for quick,
preliminary analyses of potential price effects of mergers based on very
little information. The logit model, however, is highly restrictive
regarding the pattern of substitution among goods, which has been the
source of criticism from economists. Nevertheless, these restrictions
provide a useful base case that focuses a merger investigation or trial and
generalizations of the model can ease these restrictions. Each demand
model has inherent properties that distinguish it from others in ways that
substantially affect the magnitude of the predicted price effects from
mergers. Properties of the logit model cause it to yield relatively
conservative (i.e., low) price increase predictions.
b.
Choice Models of Consumer Demand
Economists modeling consumer demand commonly employ “choice
models,” in which each consumer makes a single choice from a “choice
set” of goods. Since a consumer makes a single choice, each good in the
choice set is a substitute for all the others. The goods of primary interest
are referred to as the “inside goods.” The choice set may be limited to
those goods but usually includes a “none of the above” choice, referred
to as the “outside good.” The outside good is an aggregate incorporating
all other alternatives to which the consumer could allocate income.
15.
while the price increase predictions with linear demand are apt to be
lower than those with the ALM.
Although a variety of models are properly termed “logit models,” “the
logit model” generally refers to the simplest of logit models, and this
chapter is principally concerned with that model.
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Which goods are considered “inside goods” is more modeling art
than science. In modeling the choice of a new car, the inside goods
could be all of the various models of cars and the outside good could be
not purchasing a new car. However, if the focus were on just luxury
cars, the modeler might limit the inside goods to cars selling for more
than a specific dollar amount, while all other cars would be part of the
outside good. While similar in concept, the inside goods may be more or
less inclusive than a relevant antitrust market.
Choice models directly apply the economic theory of consumer
behavior,16 positing that each consumer selects the single product from
the choice set which yields the greatest utility. Utility is specified as a
function of product characteristics, including price. The own and cross
elasticities of demand of the inside goods are determined by their choice
probabilities and the coefficient on price in the utility function. In
addition to price, choice models normally specify that utility is a function
of observed product characteristics and a choice-specific constant that
captures utility differences among goods as perceived by the average
consumer. This constant reflects brand preference and any goods’
characteristics that are not separately included in the model. The greater
the value of the choice-specific constant for a good, or the lower its
price, the greater the utility each consumer derives from that good.
Choice models are normally “random utility models,” meaning one
determinant of utility is specified as a random variable.17 This does not
imply that consumers base their purchase decisions on a roll of the dice.
Instead, it is a way of allowing different consumers to have different
16.
17.
Linear and isoelastic demand functions, which have been used to simulate
mergers, are not derived from the economic theory of consumer behavior,
so neither can be the true demand functions for an individual consumer.
Nevertheless, the aggregate demand for a population of consumers could
be well approximated by linear or isoelastic functions.
Random utility models were formalized by Charles Manski, The Structure
of Random Utility Models, 8 THEORY & DECISION 229 (1977).
Comprehensive treatments of the theory are provided by MOSHE BENAKIVA & STEVEN R. LERMAN, DISCRETE CHOICE ANALYSIS: THEORY AND
APPLICATION TO TRAVEL DEMAND ch. 3–4 (1985); Daniel McFadden,
Econometric Models of Probabilistic Choice, in STRUCTURAL ANALYSIS
OF DISCRETE DATA WITH ECONOMETRIC APPLICATIONS 198 (Charles F.
Manski & Daniel McFadden eds., 1981).
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preferences for the same product characteristics. The model specifies the
statistical distribution of the random utility component and differing
assumptions about that distribution gives rise to different models. The
most common distributional assumption gives rise to the logit model,18
which is discussed below.
c.
The Basic Logit Model and the IIA Assumption19
The logit model derives its name from the “logistic” functional form
of the choice probabilities, which traces out an S-shaped curve. Choice
probabilities are closely related to, but different from, market shares. If
two goods are both in the relevant market, the ratio of their choice
probabilities equals the ratio of their market shares (based on quantity
sales). This is true regardless of what the relevant market may be or how
the choice set is defined. Choice probabilities can be converted into
market shares by re-scaling. The market share of any inside good is its
choice probability, divided by the sum of the choice probabilities for all
goods not in the relevant market.
The own and cross elasticities of demand in a logit model are simple
functions of price, choice probabilities, and the price coefficient in the
utility function.20 In a logit model, the cross elasticities of demand for all
18.
19.
20.
The logit model was formalized by Daniel McFadden, Conditional Logit
Analysis of Qualitative Choice Data, in FRONTIERS IN ECONOMETRICS
(Paul Zarembka ed., 1974). For another useful derivation of the model,
see SIMON P. ANDERSON, ANDRÉ DE PALMA & JACQUES-FRANÇOIS
THISSE, DISCRETE CHOICE THEORY OF PRODUCT DIFFERENTIATION 41–42
(1992). For thorough treatments of the model, see BEN-AKIVA &
LERMAN, supra note 17, ch. 5; KENNETH TRAIN, QUALITATIVE CHOICE
ANALYSIS: THEORY, ECONOMETRICS, AND AN APPLICATION TO
AUTOMOBILE DEMAND ch. 2 (1986).
See Appendix II to this book for a detailed description of the logit model
and the method of maximum likelihood that is used to estimate the model.
For a more detailed discussion of the application of the logit model, see
Gregory J. Werden, Luke M. Froeb & Timothy J. Tardiff, The Use of the
Logit Model in Applied Industrial Organization, 3 INT’L J. ECON. BUS.
83, 85–87 (1996).
Denoting the own price coefficient as β, the price of good i as pi , and the
probability that the individual will choose good i as π i, the own elasticity
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inside goods, with respect to the price of any one inside good are the
same. The cross elasticities only depend on the price and choice
probability of the good for which price is changed. This pattern of cross
elasticities is a consequence of what economists term the Independence
of Irrelevant Alternatives (IIA) property,21 a notable feature of the logit
model.
Formally, the IIA property means that the ratio of the probabilities
of any two choices is independent of the presence or absence of other
possible choices. In practical terms, this means that substitution from
any good in the choice set to all others in that set is proportionate to their
relative market shares. Suppose, for example, that the choice set consists
of goods A, B, and C, with respective shares of 60 percent, 30 percent,
and 10 percent. If the price of good C is increased, the IIA property says
that the substitution to good A must be twice that to B because the share
of A is twice that of B.
The IIA property is a way to define what it means for all goods in
the choice set to be equally close substitutes for each other. In the
preceding example, it could be argued that, if many more consumers
switched to A than to B when the price of C was increased, A must be the
closer substitute for C. However, it can also be argued that, if the
substitution away from C is proportionate to the relative shares of A and
B, then A and B are equally close substitutes for C. The latter argument
makes sense partly because the cross elasticities of demand for A and B
with respect to the price of C are exactly the same if the IIA property
holds.
Most importantly, the IIA property offers a rough approximation for
substitution patterns if they have not yet been, or cannot be estimated.22
21.
22.
of demand for good i is –βpi(1 – πi). The cross elasticity of demand for
any inside good with respect to the price of good i is βpiπi.
The logit model was originally developed by R. DUNCAN LUCE,
INDIVIDUAL CHOICE BEHAVIOR: THEORETICAL ANALYSIS (1959). Luce
was a psychologist and termed the IIA property the “choice axiom.”
Robert D. Willig, Merger Analysis, Industrial Organization Theory, and
Merger Guidelines, BROOKINGS PAPERS ON ECONOMIC ACTIVITY,
MICROECONOMICS 281, 299–305 (1991). Willig argued that the logit
model, with its IIA property, is appropriate in the benchmark case in
which the merging firms’ products are neither particularly close together
nor far apart in characteristics space. He used the logit model to motivate
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Without evidence to the contrary, substitution in proportion to shares is
seen as the most natural default assumption, which is true even if the IIA
property is not viewed as defining equally good substitutes among all
goods in the choice set. Of course, the IIA property is even more
attractive as a default assumption when viewed as defining equally close
substitutes.
The IIA property has been both a blessing and a curse. Imposing
the IIA property facilitates estimation in a variety of ways, most notably
by limiting the number of parameters to be estimated. It also permits
inferences that otherwise could not easily be made, such as the impact of
adding a hypothetical new product to the choice set. Finally, imposing
the IIA property assures that goods known to be substitutes actually have
positive estimated cross elasticities of demand.
Restricting the pattern of substitution, however, can artificially
impose a highly unrealistic pattern of substitution. For example, it can
force the substitution from a particular model of luxury car or sports car
to go predominantly to a pickup truck or minivan if either is the most
popular choice among motor vehicles. There are a variety of ways to
address this problem by varying the structure of the logit model. It is
reliance on market shares in merger analysis. Willig’s analysis appears to
be reflected in U.S. DEPARTMENT OF JUSTICE & FEDERAL TRADE
COMMISSION, HORIZONTAL MERGER GUIDELINES § 2.211, reprinted in 4
TRADE REG. REP. (CCH) ¶ 13,104 (April 2, 1992), which state in part:
The market concentration measures articulated in Section 1 [of the
Guidelines] may help assess the extent of the likely competitive effect
from a unilateral price elevation by the merged firm notwithstanding the
fact that the affected products are differentiated.
The market
concentration measures provide a measure of this effect if each product’s
market share is reflective of not only its relative appeal as a first choice to
consumers of the merging firms products but also its relative appeal as a
second choice, and hence as a competitive constraint to the first choice.
Where this circumstance holds, market concentration data fall outside the
safeharbor regions of Section 1.5, and the merging firms have a combined
market share of at least thirty-five percent, the Agency will presume that
a significant share of sales in the market are accounted for by consumers
who regard the products of the merging firms as their first and second
choices.
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always possible to limit the scope of the choice set, for example, to just
luxury cars or just sports cars.
d. The Antitrust Logit Model
The Antitrust Logit Model (ALM) is a reformulation of the
conventional logit model designed to make it more useful for antitrust
practitioners.23 Unlike conventional logit models, formulated in terms of
choice probabilities, the ALM is formulated in terms of “shares” within
the set of inside goods. These shares are similar to market shares,
although the inside goods not need constitute a relevant market.
In merger analysis, conventional logit models have conceptual
difficulties because the probability of choosing the outside good is never
considered. As an illustration, consider a choice model for airlines on a
particular route. To estimate this model, one must consider the
probability of not flying at all and identify the number of potential
passengers who choose not to fly. Although there are ways to address
these issues, the ALM avoids doing so by treating the probability of not
flying as a scaling factor determined by the aggregate elasticity of
demand for the inside goods. In this illustration, that is the elasticity of
demand for commercial air travel on the relevant route.24
If the demand for the inside goods is sufficiently elastic, mergers of
inside goods cannot significantly increase prices, because the outside
goods (e.g., other modes of transportation) are very close substitutes for
the inside goods. The aggregate elasticity of demand for the inside
23.
24.
For details, see Gregory J. Werden & Luke M. Froeb, The Antitrust Logit
Model for Predicting Unilateral Competitive Effects, 70 ANTITRUST L.J.
257 (2002); Gregory J. Werden & Luke M. Froeb, Simulation as an
Alternative to Structural Merger Policy in Differentiated Products
Industries, in THE ECONOMICS OF THE ANTITRUST PROCESS 65 (Malcolm
B. Coate & Andrew N. Kleit eds., 1996); Werden et al., supra note 19;
Gregory J. Werden & Luke M. Froeb, The Effects of Mergers in
Differentiated Products Industries: Logit Demand and Merger Policy, 10
J.L. ECON. & ORG. 407 (1994).
Denoting the share of good i as si, the average price of all inside goods as
p, and the aggregate elasticity for the inside goods as ε, the own elasticity
of demand for good i is –[βp(1 – si) + εsi]pi /p, and the cross elasticity of
the demand for good i with respect to the price of good j is sj(βp – ε)pj /p.
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goods has essentially the same role as market delineation. Given the
value of the aggregate elasticity, the price coefficient determines the
responsiveness of choices to changes in prices; the greater the value of
the price coefficient, the greater the substitutability among the inside
goods.25 If the price coefficient is very low, the merger of two inside
goods has very little effect on their prices, because the inside goods are
such distant substitutes that each is essentially a monopoly unto itself. If
the price coefficient is very high, only a merger resulting in a monopoly
of the inside goods would have much effect on their prices, because the
inside goods are very close substitutes for each other.
In the ALM, competitive interaction among inside goods is
completely characterized by the shares and prices of those goods, both of
which are routinely determined in merger investigations, and two
demand parameters. Estimating the aggregate demand elasticity can be
challenging, but that challenge is already present in traditional antitrust
analysis, because the process of market delineation requires at least
intuiting from non-quantitative evidence the value of the inside goods
aggregate elasticity.26 The value of the price coefficient can be estimated
from aggregate data on prices and quantity of actual transactions,
household level data on actual choices, or survey data. It also can be
inferred in several ways: This inference can be made from observed
patterns of diversion resulting from a natural experiment such as the
entry and exit of a brand. Under the conventional assumption—that
observed prices and shares are the product of a Bertrand equilibrium in
which firms compete on the basis of price—the value of the price
coefficient can be inferred from the price-cost margin of any major
brand.
25.
26.
What matters is the price coefficient times the average price of the inside
goods, so references to high and low values of the price coefficient, are
really references to high and low values of the coefficient multiplied by
the average price of the inside goods.
See Gregory J. Werden, Demand Elasticities in Antitrust Analysis, 66
ANTITRUST L.J. 363, 378–91 (1998). Useful experiments are suggested
by the relationship between market delineation and the aggregate
elasticity. One might assume that a collection of goods constitutes a
relevant market, compute the highest demand elasticity consistent with
that assumption, and use that as the value of the inside goods aggregate
elasticity.
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ECONOMETRICS
Since the shares in the ALM are not market shares, it is not
necessary to settle on a relevant market in order to ascertain the shares
needed to apply the ALM. All that matters in the ALM are the relative
shares of inside goods. If A and B are both inside goods, their relative
shares are invariant to inclusion or exclusion of other goods from the list
of inside goods. The impact of market delineation issues comes in only
through the inside goods aggregate elasticity and not through the shares.
Simulating a merger using the ALM is straightforward.27 The
standard assumptions for differentiated products merger simulations
(which can be relaxed) are that: (1) the only strategic competitive
variable is price, hence there can be no entry or product repositioning;
and (2) the cost of producing each good depends only on the quantity of
that good produced, and consists of a constant marginal cost and a fixed
cost that does not matter for the purposes of the simulation. Merger
simulation using the ALM predicts the price and welfare effects of
mergers in three steps. First, the price coefficient and aggregate
elasticity are estimated or merely specified. Second, the necessary
conditions for pre-merger profit-maximization are solved for the implied
marginal costs and the logit probability functions are solved for the
implied values of the remaining parameters of the demand system.28
Finally, the necessary conditions for post-merger profit-maximization are
solved for prices and outputs to predict the effects of a merger.29
27.
28.
29.
For an application to an actual proposed merger, see Gregory J. Werden,
Expert Report in United States v. Interstate Bakeries Corp. and
Continental Baking Co., 7 INT’L J. ECON. BUS. 139 (2000).
Only relative values of the demand parameters matter, so one of them is
set to an arbitrary constant and the others are then easily computed from
the logit probability functions, given the prices, shares, and demand
parameters.
For a concise statement of the process of merger simulation, see Gregory
J. Werden, Simulating Unilateral Competitive Effects from Differentiated
Products Mergers, ANTITRUST, Spring 1997, at 27. More complete
statements of the analysis are found in Philip Crooke, Luke M. Froeb,
Steven Tschantz & Gregory J. Werden, The Effects of Assumed Demand
Form on Simulated Postmerger Equilibria, 15 REV. INDUS. ORG. 205
(1999); Jerry A. Hausman & Gregory K. Leonard, Economic Analysis of
Differentiated Products Mergers Using Real World Data, 5 GEO. MASON
L. REV. 321 (1997); Gregory J. Werden, Simulating the Effects of
Differentiated Products Mergers: A Practical Alternative to Structural
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When simulating a merger, the one critical difference in the
treatment of inside versus outside goods is that the prices of the inside
goods are determined by the competition among them. Mergers affect
that competition, which causes changes in the prices of the inside goods.
The outside goods are, by assumption, outside this competition. Their
prices are taken as given before the prices of the inside goods are set, and
their prices are assumed to be unaffected by the merger. The direct
effect of narrowing the list of inside goods is to preclude price increases
for all goods that are not treated as inside goods. This indirectly affects
the prices of goods determined to be inside goods, especially the merging
goods, as their prices will increase in response to any increases in the
prices of substitutes. Both of these effects tend to be slight unless
individual excluded goods, if included, would have very large shares.
In the ALM, the prices of all inside goods increase as a result of a
merger of any two inside goods, but the magnitudes of the price
increases for different brands are different. If the merging brands have
significantly different shares, the merger has asymmetric effects on the
prices of those brands. The price of the smaller-share brand increases
more than that of the larger-share brand. In addition, the prices of the
merging brands typically increase much more than the prices of nonmerging brands. The prices of larger-share, non-merging brands increase
more than the prices of smaller-share brands. Increased concentration
among the non-merging brands increases the price effects of a merger,
but the effect is typically fairly weak.30
30.
Merger Policy, 5 GEO. MASON L. REV. 363 (1997); Gregory J. Werden,
Simulating the Effects of Differentiated Products Mergers: A
Practitioners’ Guide, in STRATEGY AND POLICY IN THE FOOD SYSTEM:
EMERGING ISSUES 95 (Julie A. Caswell & Ronald W. Cotterill eds.,
1997); Gregory J. Werden & Luke M. Froeb, Simulation as an Alternative
to Structural Merger Policy in Differentiated Products Industries, in THE
ECONOMICS OF THE ANTITRUST PROCESS 65 (Malcolm B. Coate &
Andrew N. Kleit eds., 1996).
See Gregory J. Werden & Luke M. Froeb, The Effects of Mergers in
Differentiated Products Industries: Logit Demand and Merger Policy, 10
J.L. ECON. & ORG. 407 (1994). Luke M. Froeb, Timothy J. Tardiff &
Gregory J. Werden, The Demsetz Postulate and the Welfare Effects of
Mergers in Differentiated Products Industries, in ECONOMIC INPUTS,
LEGAL OUTPUTS: THE ROLE OF ECONOMISTS IN MODERN ANTITRUST 141
(Fred S. McChesney ed., 1998), have shown that a merger may enhance
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e.
ECONOMETRICS
A Rationale for Use of the ALM
Economists have long noted that the IIA property is not likely to
hold in the real world. It is usually true that a model that does not
impose the IIA property fits a real-world industry better than the ALM.
Nevertheless, the ALM is very useful as a starting point in the analysis of
differentiated products mergers. Until reliable contrary evidence is
discovered, one can start with the assumption that the merging firms’
products are neither especially close nor especially distant substitutes,
which means that the IIA property holds.31 Indeed, the ALM provides a
screen comparable to that provided by market shares in traditional
antitrust analysis;32 however, only the ALM offers quantitative priceincrease predictions. Simple merger simulations, as with the ALM, also
permit an explicit tradeoff of efficiencies in the form of synergies that
reduce marginal cost.
(1) The Variance-Bias Trade-Off and More Flexible Functional Forms
31.
32.
total welfare in the ALM without generating synergies, and even though
consumer welfare is diminished. Welfare gains can arise because a
merger causes a shift in production from merging firms to non-merging
firms. If small- or medium-share brands merge, there is a shift in
production to larger-share brands. In the ALM, larger-share brands must
have lower marginal costs and be preferred by consumers, resulting in an
increase in total welfare. Welfare gains also arise because a merger
causes a shift in production from one merging brand to the other. The
merger of a large-share brand with a smaller-share brand causes a shift in
production from the smaller-share brand to the larger-share brand, which
has a lower marginal cost and is preferred by consumers, resulting in an
increase in total welfare.
Whether the IIA property holds between the merging and non-merging
brands tends to be unimportant to the price effects of a merger. The IIA
assumption can be used to calibrate other models, see Philip Crooke et al.,
supra note 29 (using the IIA assumption to calibrate AIDS, isoelastic, and
linear demand), as it is in the PCAIDS model discussed below.
Illustrations are provided in Chapter XIII and Gregory Werden & Luke
Froeb, Calibrated Economic Models Add Focus, Accuracy, and
Persuasiveness to Merger Analysis, in THE PROS AND CONS OF MERGER
CONTROL 63 (Swedish Competition Authority 2002).
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Estimating demand presents a tradeoff between variance and bias.
The more flexible the assumed demand form, the greater the number of
parameters to be estimated, and the more difficult it is to precisely
estimate them. Thus, the more flexible the assumed demand form, the
greater may be the variance of the estimators. Conversely, the less
flexible the assumed demand form, the more likely it is that the
functional form significantly restricts substitution patterns in unrealistic
ways. Thus, the less flexible the functional form, the greater may be the
bias in the estimator.
When abundant data present sufficient price variation,33 the choice
is clear. Using a flexible functional form allows the data to speak for
itself and to indicate how consumers substitute one product for another in
response to changes in prices. Having sufficient data eliminates the need
to make any difficult decisions. However, in many cases a tradeoff must
be considered.
Estimating a restricted demand form reduces the number of
parameters and, to some extent, imposes a substitution pattern on the
data.34 It can preclude the possibility of negative cross elasticities of
demand, and in the case of the ALM, it can force substitution to be
proportionate to market share. The problem in merger analysis is that the
33.
34.
To the extent that demand elasticities are identified in the traditional way,
from quantity changes in response to price changes, independent price
variation in each brand is needed to trace out the separate demand curves
of the individual brands throughout the entire relevant range of prices.
More recent academic work has also attempted to identify demand
elasticities on the basis of consumer responses to changes in available
brands or the characteristics of existing brands. In this work, variation in
characteristics helps to trace out the separate demand curves of the
individual brands throughout the entire relevant range of prices.
Estimating a relatively flexible demand form like the AIDS in some cases
can yield a relatively high variance due to the large number of parameters
being estimated. The problem of high variance can often manifest itself
in estimated negative cross elasticities of demand, which imply that the
goods are complements, even though they may be known to be
substitutes. In merger simulation analysis, high variance also implies
wide confidence intervals for predicted price effects that can potentially
be so wide that the exercise is useless.
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ECONOMETRICS
estimated merger effects may then be determined, to a considerable
extent, by the substitution pattern imposed on the data. For example,
when substitution is assumed to be proportionate to market shares,
mergers of larger-share brands increase price more than mergers of
smaller-share brands. The ALM does not allow for the possibility that a
merger of two large-share brands would have little effect on their prices
because they are very distant substitutes. Additionally, ALM does not
allow for the possibility that a merger of two relatively small-share
brands could cause a substantial effect on price because those two brands
occupy an important niche in product space.
In the context of merger analysis, guidance about how and when to
trade off bias and variance is provided by an examination of the
important determinants of unilateral price effects. The own elasticities of
demand of the merging brands and the cross elasticities between them
are far more important than any of the other demand elasticities. Thus, it
is most important to have flexibility with respect to these few elasticities
involving the merging brands.
As noted above, the logit model results from making a particular
assumption about the statistical distribution of the random component of
utility in the choice model. Part of the distributional assumption that
gives rise to the logit model is that the random component of utility is
independently and identically distributed across consumers. As a
practical matter, what this means is that there is no correlation in the way
different goods are valued by particular consumers. It is not possible, for
example, for some consumers to systematically place a high value on
luxury cars while others place a high value on minivans. Correlations in
preferences, however, can be introduced through several generalizations
of the basic logit model.
One such generalization is the “nested” logit model, which places
“nests” around brands that are especially close substitutes for one another
and for which preferences are correlated.35 An added parameter for each
35.
See generally ANDERSON ET AL., supra note 18, at 46–48; BEN-AKIVA &
LERMAN, supra note 17, ch. 10. For several applications, see JEFFREY A.
DUBIN, STUDIES IN CONSUMER DEMAND—ECONOMETRIC METHODS
APPLIED TO MARKET DATA ch. 6–7 (1998). The nested logit model was
introduced by Daniel McFadden, Modeling the Choice of Residential
Location, in SPATIAL INTERACTION THEORY AND PLANNING MODELS 75
(Anders Karquist et al. eds., 1978).
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nest determines both the closeness among the brands in the nest and their
distance from other brands, and can be estimated from the data. When
the price of a brand in a strong nest increases, nearly all of the
substitution is to other brands within its nest. In a nested logit model, a
merger may have much larger price effects if the merging brands are in
the same nest than if they are in separate nests.
Another way to add flexibility to a logit model is to specify
“dimensions of differentiation,” similar to adding brand or product
characteristics. Brands that share the same characteristics are closer to
one another than brands that do not. In this model, the strength of a nest
can be estimated from the data and the importance of characteristics in
differentiating brands. For example, products may be distinguished on
the basis of whether they are major brands and whether they are on the
technological frontier.36 If two binary characteristics such as these are
used, brands are then classified into one of the four categories
corresponding to the four possible combinations of these two
characteristics. A merger involving two brands sharing the same
classification would produce greater price effects than a merger
involving two brands that do not.
Another generalization of the logit model, very popular in academic
research, is the “mixed” or “random-coefficients” logit model. These
models incorporate customer heterogeneity by specifying that the
observed demand is a mixture of distinct individual demands for
consumers who have different characteristics. Suppose high-income
consumers have relatively inelastic demands, while low-income
consumers have relatively elastic demands. Observed demand then can
be modeled as the weighted average or “mixture” of two logit demands,
with the weights being the population proportions of high- and lowincome consumers. Mixed logit models can approximate any underlying
choice model, although their estimation can be challenging.37
36.
37.
See Timothy F. Bresnahan, Scott Stern & Manuel Trajtenberg, Market
Segmentation and the Sources of Rents from Innovation: Personal
Computers in the Late 1980s, 28 RAND J. ECON. S17 (1997).
See, e.g., Steven T. Berry, James Levinsohn & Ariel Pakes, Automobile
Prices in Market Equilibrium, 63 ECONOMETRICA 841 (1995); Aviv
Nevo, A Practitioner’s Guide to Estimation of Random Coefficients Logit
Models of Demand, 9 J. ECON. & MGMT. STRATEGY 513 (2000).
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ECONOMETRICS
(2) Demand Curvature and Assumed Functional Forms
A demand form is “flexible to the first order” if it can be fitted
precisely into any given set of own and cross elasticities at a particular
set of prices and quantities. First-order flexibility is desirable, although a
price must be paid for it. Higher-order flexibility is also desirable, but
none of the conventional demand forms have higher-order flexibility:
All greatly restrict how the own and cross elasticities of demand change
as prices change. The most conspicuous example is the isoelastic
demand function, which assumes all demand elasticities are invariant to
prices. Isoelastic demand is not fundamentally more restrictive than
other conventional demand forms, such as linear demand; rather, each
demand form imposes a different set of restrictions on the “curvature” of
demand and these restrictions are quite important.
The different curvature properties of AIDS and isoelastic demand
cause those demand forms to yield larger price increase predictions than
the linear and logit models.38 For any given set of prices, shares, and
demand elasticities, it is not unusual for the price increases predicted
using AIDS or isoelastic demand to be several times those predicted
using linear or logit demand. The main reason is the differing rates at
which an individual product’s demand becomes more elastic as its price
increases. The idiosyncratic behavior of cross elasticities is also relevant
to these models. An increase in the price of one product may increase,
decrease, or not change the cross elasticity of its demand with respect to
the price of another product. The properties of these four demand forms
cause them to yield very different price effects from mergers, which also
cause them to yield very different pass-through rates for marginal cost
reductions.39 The pass through rate of marginal cost reductions with
AIDS or isoelastic demand is several times that with linear or logit
demand.
Any conventional demand form has drawbacks. Assuming any
demand form, in effect, assumes to a significant extent the effects of the
merger under investigation. However, statistical testing can provide a
38.
39.
See Crooke et al., supra note 29.
See Gregory J. Werden, Luke M. Froeb & Steven Tschantz, The Effects
of Merger Synergies on Consumers of Differentiated Products
(unpublished paper 2001).
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means to choose between a set of demand forms. Since prices tend to
vary over at least some range in the typical dataset, a statistical test can
be used to identify the particular demand form that best fits the curvature
within the observed range of prices. Alternatively, one can use demand
forms with flexible curvature properties. In principle this is possible but
very rarely proves a practical solution. Adding flexible curvature
properties generally exacerbates the variance problem by trying to
estimate too many parameters. In addition, the data normally will not
allow a significant determination of curvature outside the range of
observed prices.40
A far simpler alternative is to switch to an alternative analysis
unaffected by curvature. This is the computation of the marginal cost
reductions that exactly offset the price-increasing effects of a merger.41
Because this calculation involves post-merger prices that are the same as
pre-merger, the effects of price changes on demand elasticities do not
matter. Consequently, these “compensating marginal cost reductions”
are the same no matter what the demand form.
2. Flexible Demand Specification—The AIDS Model
a. Introduction
The use of a “flexible functional form” in the analysis of competition
among differentiated products allows all of the own and cross elasticities
of demand for those products to be estimated from aggregate-level data,
such as retail scanner data. The flexible functional form most commonly
used is AIDS, and this section compares the strengths and weaknesses of
AIDS relative to other specifications and identifies issues that arise in the
estimation of an AIDS model (or other demand system).42
40.
41.
42.
Mixed logit models have potential to address the curvature issue in a
useful way. They can allow demand curvature to be determined by using
empirical distributions of relevant consumer attributes (e.g., income).
See Gregory J. Werden, A Robust Test for Consumer Welfare Enhancing
Mergers among Sellers of Differentiated Products, 44 J. INDUS. ECON.
409 (1996).
Technical details on this model and its estimation are presented in
Appendicies II and IV.
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ECONOMETRICS
b. Considerations in Choosing a Demand System Specification
A less flexible demand specification such as the ALM has fewer
parameters to estimate than a flexible demand specification and, as a
result, may lead to more precise elasticity estimates than a flexible
demand specification. However, this precision may come at a price,
namely, a less flexible specification may not fit the data well, which
could induce bias into the elasticity estimates.43 During the 1980s,
econometricians came to realize the importance of using “flexible
functional forms” that place minimal (or no) restrictions on the estimated
values of the demand elasticities.44 Unfortunately, estimating a relatively
flexible demand form, like AIDS can yield a high variance due to the
large number of parameters.45
43.
44.
45.
Another consideration, particularly when estimating the price effects of a
proposed merger, is the behavior of the demand system as prices move
away from the point of approximation. Demand systems that yield the
same elasticities at the point of approximation can predict substantially
different post-merger price changes. See, e.g., Crooke, et al., supra note
19.
Ideally, statistical tests can be used to choose among alternative demand
specifications, but traditional tests involving demand parameters (i.e., ttests or F-tests) are often not appropriate. Suppose, for example, that one
is choosing between two demand systems that have different structures.
In place of a traditional test, one would need to use a, more complex
“non-nested” test. For example, the AIDS and log-log specifications
discussed below are not nested within one another. For a definition of
flexible functional forms, see W.E. Diewert, An Application of the
Shephard Duality Theorem: A Generalized Leontief Production Function,
79 J. POL. ECON. 481 (1971); see also Angus Deaton, Demand Analysis,
in 3 HANDBOOK OF ECONOMETRICS (Zvi Griliches & Michael D.
Intriligator eds., 1986); ROBERT A. POLLAK & TERENCE J. WALES,
DEMAND SYSTEM SPECIFICATION & ESTIMATION 63 (1992).
For a discussion of the tradeoffs involved in specifying complex demand
systems, and the implications for the estimation of demand elasticities,
see Daniel Rubinfeld, Market Definition with Differentiated Products:
The Post/Nabisco Cereal Merger, 68 ANTITRUST L.J. 163 (2000).
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Under the economic theory of consumer choice, a demand system
must have a certain properties.46 Some demand specifications allow
these properties to be easily imposed and tested, while other
specifications do not. Generally, one would want to impose the
restrictions implied by these properties because certain calculations (i.e.,
consumer welfare) would not be valid if the demand system did not
satisfy the properties of consumer demand.47 Thus, the ability to both
impose and test these properties is a valuable property for a demand
system specification.
A second important theoretical consideration is whether the demand
system specification can be obtained by aggregation over individual
consumers.48 The question is whether the demand system and its
properties transfer to the aggregate-level data obtained by aggregating
over individual consumers. If that is the case, the aggregate-level
demand can be treated as the demand of a “representative consumer” and
the estimated demand system should exhibit the appropriate properties.
c. The Almost Ideal Demand System
Under AIDS, the revenue share of a product is the result of three
terms.49 The first term is a constant that differs across products, which
indicates that, everything else being equal, some products would have
higher shares as a result of different consumer preferences. The second
term is based on the “real” expenditure devoted to the category. The
46.
47.
48.
49.
These properties are: Slutsky symmetry, homogeneity of degree zero in
prices and total expenditure, and adding up. Slutsky symmetry requires
that the compensated cross price derivative of Brand A with respect to
Brand B equals the compensated cross price derivative of Brand B with
respect to Brand A. Homogeneity of degree zero in prices and
expenditure requires that demand for all products be unchanged if the
prices of the products and total expenditure all increase by the same
percentage. Finally, adding up requires that the sum of expenditures on
the individual products equals total expenditure.
However, empirical demand studies have found that the properties of
consumer demand are often rejected by statistical tests.
ANGUS DEATON & JOHN MUELLBAUER, ECONOMICS AND CONSUMER
BEHAVIOR 148–59 (1980).
See Angus Deaton & John Meullbauer, An Almost Ideal Demand System,
70 AM. ECON. REV. 312 (1980).
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ECONOMETRICS
third term is based on the prices of the various products. It is helpful in
understanding the AIDS specification to suppose that the own price
coefficient is negative and that the cross price coefficients are positive
(although neither is necessary to have a well-behaved demand system).
In that case, the revenue share of a product increases when its own price
decreases or when the price of another product increases.
AIDS has a number of desirable properties: The AIDS demand
specification is a first-order approximation to any demand system.50 This
implies that even if the true underlying demand system is not AIDS,
AIDS will nevertheless provide a reasonably accurate approximation in
the neighborhood of given point of approximation. AIDS allows for easy
imposition and testing of the properties of consumer demand.51 These
restrictions can be imposed during estimation. Alternatively, the
restrictions can be tested using standard statistical methods after
estimation of the AIDS model. The AIDS model also can be obtained
through aggregation over individual consumers and can be treated as the
demand system for a representative consumer.52 The demands and
welfare calculations for this representative consumer appropriately
reflect the aggregated demands and welfare of the individual consumers.
The downside to the flexibility of AIDS is the large number of
parameters that need to be estimated. Even after imposing restrictions
from the theory of consumer choice, AIDS estimation with N products
will involve something less than N2 parameters.53
d. Comparison to Other Demand Systems
The logit model: (1) is easy to estimate, (2) satisfies the restrictions
of consumer demand, and (3) aggregates across individual consumers.
However, logit is not very flexible. The IIA property constrains all of
the cross elasticities of demand with respect to a particular product’s
price to be equal.54 This property would not hold when an industry
50.
51.
52.
53.
54.
Id. at 312.
Deaton & Muellbauer, supra note 49, at 312.
Id.
POLLAK & WALES, supra note 44.
Jerry A. Hausman, Project Independence Report: An Appraisal of U.S.
Energy Needs Up to 1985, 6 BELL J. ECON. 517 (1975); McFadden, supra
note 35, at 222; Hausman & Leonard, supra note 29, at 322.
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consists of several “premium” brands that have large industry shares, and
several “economy” brands with smaller shares. One expects the
economy brands to compete more closely with each other than with the
branded premium brands because one expects the cross elasticities
between the economy brands to be larger than the cross elasticities
between economy and premium brands. A demand specification that
severely limits the values the cross elasticities can take, could result in
severely biased cross elasticity estimates and therefore, incorrect
conclusions concerning the extent of competition between products.
With the use of nested logit models, products within a nest are
permitted to compete more closely with each other than with products
outside the nest, thus reducing the problem of equal cross elasticities.
However, the problem is not entirely eliminated because the cross
elasticities within a nest are still constrained to be equal.
The “random effects” or “mixed” logit model assumes each
consumer has logit demand, but differs in the value weights that they
place on price and other product attributes. As a result, aggregate
demand does not exhibit the equal cross elasticity property, although the
property continues to hold for each individual. For example, people who
bought Toyota station wagons and place a good deal of weight on having
a station wagon would be more likely to switch to a Honda station wagon
than to a sports car, if the price of the Toyota station wagon were to
increase. In aggregating over individuals, the people who choose station
wagons largely determine the cross elasticities among station wagons,
while the people who choose sports cars largely determine the cross
elasticity of sports cars with respect to station wagons. Therefore, in the
aggregate, the cross elasticities among station wagons are “large” and the
cross elasticities of sports cars with respect to station wagons are
“small.”
The random effects logit requires substantially fewer parameters be
estimated than a typical flexible functional form such as AIDS.
However, the random effects logit is substantially more difficult to
estimate than AIDS in a typical application. In addition, although it is
less restrictive than the basic logit model, the random effects model may
not have the flexibility to perform as well as AIDS in many situations.
In the one direct comparison, the results for AIDS and the random effects
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ECONOMETRICS
logit were similar in some respects, but different in others.55 A topic for
future research is determining the conditions under which the random
effects logit or, alternatively, a flexible functional form would be
preferred.56
e. Empirical Implementation of the AIDS
Empirical implementation of the AIDS is often possible when retail
scanner data are available on brands for a number of cities and time
periods. For example, there may be data on 10 brands in 25 cities for
104 weeks. It is best to cast a wide net when choosing the products to
include in the demand system because the purpose of estimating the
demand system is to determine the extent of competition between
products. It is better to be over-inclusive, letting the data decide the
extent to which products compete.
The basic AIDS revenue share equation needs to be modified to
account for the fact that a product’s revenue share might differ across
time and cities for reasons other than differences in prices and
expenditure. For example, consumer preferences for the product might
grow over time or be seasonal. In addition, consumers in one geographic
area might have a greater preference for the product than the consumers
in other geographic areas. To account for time-invariant differences in
demographics or preferences across cities, separate constants are needed
for each city and brand in the specification. To account for changes in
demographics or preferences over time, time trend variables and seasonal
variables in the specification are also included.
55.
56.
Aviv Nevo, Mergers with Differentiated Products: The Case of the
Ready-to-Eat Cereal Industry, 31 RAND J. ECON. 395 (2000).
Among the alternative flexible functional demand forms is the popular
log-log (or isoelastic) demand system, which derives its name from the
fact that the logarithm of a product’s quantity is related to the logarithms
of all the products’ prices and the logarithm of category expenditure.
Taking logs can sometimes “linearize” the data, which enables it to be
analyzed more easily. Other flexible demand systems exist, i.e., the
various translog forms. See, e.g., POLLAK & WALES, supra note 44, at
53-59; Deaton, supra note 44, at 1788–93. These systems share many of
the properties of the AIDS; however, they are more difficult to estimate.
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The AIDS model describes consumer demand for a product
conditional on category expenditure. However, category expenditure
itself is determined as part of the consumer’s overall decision as to how
to allocate the total expenditure across the full range of product
categories. In other words, the consumer’s unconditional demand for a
product can be broken into two parts, or stages, from a conceptual point
of view.57 In the first stage, the consumer decides how to allocate total
expenditure among the various product categories. In the second stage,
the consumer decides how to allocate the expenditure for a given
category across the products within the category.58
Under two-stage budgeting, to determine the unconditional demand
for a given product, one must combine the demand for the product,
conditional on category expenditure, with the demand for the category as
a whole. Thus, one needs to estimate the demand for the category as a
whole. This equation is referred to as the “top-level” demand equation.
The two-stage budgeting approach can be extended to three or more
stages, which is useful if the category contains a large number of
products, rendering the estimation of a single AIDS specification,
including all of the products, unwieldy. In that case, one can divide the
category’s products into segments, perhaps according to product
characteristics or company market research. For example, the products
in the beer category might be segmented into light beers, premium beers,
and low-priced beers. A separate AIDS model can be estimated for each
segment, conditional on segment expenditure. Then a segment demand
model can be estimated, conditional on beer expenditure, and finally, a
top-level beer demand model can be estimated, conditional on total
expenditure. The three models can be combined to derive the
unconditional demand for any given product.59
57.
58.
59.
It is not necessary that the consumer actually go through this thought
process for the two-stage budgeting methodology to be an appropriate
way of modeling the consumer’s decision problem.
This two-stage budgeting approach was developed by W.M. Gorman,
Two-Stage Budgeting, in COLLECTED WORKS OF W.M. GORMAN,
VOLUME 1: SEPARABILITY AND AGGREGATION 22 (C. Blackorby & A.F.
Shorrocks eds., 1995).
Use of multi-stage budgeting does impose restrictions on the demand
system. However, these restrictions can be tested. See, e.g., Hausman &
Leonard, supra note 29.
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h. Issues in Estimation
When estimating a demand system, a potential “simultaneity”
problem arises because factors unobserved to the econometrician may
affect both consumer demand and the price setting of firms. In that case,
the prices appearing on the right-hand sides of equations would be
correlated with the error terms of these equations. Ordinary least squares
and its variants would be biased and inconsistent.
In general, the solution to the simultaneity problem is to employ an
“instrumental variables” technique, which involves finding variables (the
instruments) that are correlated with the endogenous variables (in this
case, prices), but not correlated with the error terms. The endogenous
variables are in essence replaced with the instruments, and the
simultaneity problem disappears (since the instruments are not correlated
with the error terms, as were the endogenous variables).60
In an AIDS system, the estimated cross elasticities are not
guaranteed to be positive and some may be negative, especially when the
number of products is large. Negative cross elasticities can be a cause
for concern because they are counter-intuitive and because they can lead
to odd results in consumer welfare calculations or merger simulations.
The first question to ask is whether the two products in question
might, in fact, be complements rather than substitutes, in which case the
true cross elasticities would be negative. If the products should be
substitutes, the next question to ask is whether the estimates are
statistically significantly different from zero. If not, the negative
estimated cross elasticities should be of no concern unless they unduly
affect subsequent calculations of interest, i.e., merger simulations. In
that case, the cross elasticity can be constrained to zero; however, one
must proceed carefully once restrictions from economic theory have been
imposed, because these properties link the elasticities together.
If one or more cross elasticities are estimated to be negative and
statistically significantly different from zero, then the appropriate
response depends upon the number of negative estimated cross
elasticities relative to the total number of estimated cross elasticities. If
the number of products is large, so that many cross elasticities have been
60.
For additional details, see Appendicies II and IV.
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estimated, it would not be surprising to find some negative and
statistically significant cross elasticities. However, a relatively large
number of negative cross elasticity estimates would suggest a problem
with the data or the model specification. The appropriate response would
be to examine the data for errors and try different model specifications
(i.e., add other variables to the specification or implement a different
flexible functional form).61
A common finding in consumer demand studies is the rejection of
restrictions based on economic theory. One would generally want to
impose these properties, particularly if consumer welfare calculations are
to be performed using the estimated demand system. The consumer
welfare calculations are not valid if the properties do not hold. If, on the
other hand, one is performing other types of calculations (i.e., price
increases) the properties are less important, and if the properties are
rejected, one might want to proceed without imposing them.
Generally, one should examine the reason for the rejection of the
properties. If the difference between the unrestricted model and the
restricted model is small from an economic point of view, one may
impose the restrictions even if they have been rejected by the statistical
test. If the difference between the models is economically important,
then one needs to reconsider the econometric specification. For a given
category, i.e., facial tissue, the number of individual products can be
quite large because each brand (i.e., Kleenex) might have many different
package sizes or types (i.e., stand-up versus flat) and many varieties (i.e.,
different colors). Specifying a demand system to account for all of the
individual products is not realistic. Instead, the products must in some
way be aggregated and the demand system specified for the aggregates.
The question is the proper degree of aggregation and the appropriate
aggregation method to use.
Sometimes the degree of aggregation (and the method) is
predetermined. For example, the econometrician may not have access to
disaggregated data without substantial additional cost. In this situation,
the econometrician has little control over the degree of aggregation.
When disaggregated data are available, the degree of aggregation
that should be undertaken is determined by practical considerations and
61.
Choosing an alternative demand system specification that forces all cross
price elasticities to be positive, i.e., the logit demand system, may place
restrictions that are inconsistent with the data.
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the desire not to distort the econometric estimates. A good way to
proceed is to test the effect of using different levels of aggregation within
a range dictated by the practical considerations. In some cases the
degree of aggregation does not significantly affect the results, while in
others results have proven otherwise.
Regarding the method of aggregation, economic theory dictates that an
appropriate price index, with a corresponding quantity index, be used to
aggregate products. In many circumstances this approach is feasible.
However, in a situation where one or more new varieties (i.e., package
sizes or flavors) have been introduced during the period covered by the
data, formation of appropriate price and quantity indices is more
problematic. Incorporating a new product into a price index is a complex
undertaking and correctly addressing this issue may not be desirable
when it is not the primary focus of the exercise. As an alternative
solution, a new variety’s revenue and quantity can be aggregated with
those of other products and then this aggregate can be further aggregated
with other products using economically correct price and quantity
indices.
Retail scanner data may include information on the extent of in-store
promotional and advertising activity, which would be expected to affect
consumer demand. Therefore, it might be useful to incorporate this
information into the AIDS demand system. Advertising and promotion
should work in the same fashion as prices. An increase in the advertising
and promotion for one product would both increase the demand for that
product and decrease the demand for competing products. The natural
way to incorporate this information is to make city-brand specific effects
a function of the extent of advertising and promotion of each of the
products. Similarly, in the top level, an “index” that combines the
advertising and promotional activities of all the brands could be entered
as an additional variable in the share equations. However, this approach
would add a significant number of additional parameters to be estimated.
Therefore, in some situations a modified approach might be useful. For
example, an index that combines the advertising and promotion variables
of the other products into a single variable might be used in place of the
individual advertising and promotion variables for each product.
When weekly data are used, a danger exists that the elasticity
estimates obtained from a demand system represent short-run behavior
rather than long-run behavior. Specifically, if consumers stock up on
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products when they go on sale, their short-run responsiveness to price
changes (i.e., sales) might exceed their long-run responsiveness to price
changes (i.e., permanent price changes). Consumer inventorying
behavior could lead to incorrect conclusions about the effects of a
merger.
One implication of consumer inventorying behavior is that a week
with larger than normal demand (i.e., due to a sale) may be followed by
weeks with smaller than normal demand (as consumers deplete their
inventories rather than purchasing at the full price). However, the
opposite has been observed: Larger than normal demand one week
sometimes is followed by larger than normal demand the next week.
This result is inconsistent with substantial consumer inventorying
behavior; however, other recent studies have reported finding evidence
of inventorying behavior.62
Of course, the situation differs across product categories and, thus,
the extent of inventorying behavior should be investigated in a given
situation. If it appears to be an issue, then there are two ways to account
for it. First, the dynamic behavior might be explicitly modeled and the
long-run elasticities calculated as a function of the short-run elasticities
and the parameters describing the dynamic behavior. Second, the data
could be aggregated over time (monthly) and the model re-estimated on
the time-aggregated data.63
Surveys have also been used to estimate cross-elasticities of demand.
A well-designed survey conducted on a representative sample of the
population can provide unbiased results relatively quickly and
efficiently. A survey to estimate cross elasticities of demand might ask
the respondent to rank alternatives and to describe the various
alternatives in terms of their characteristics (e.g., brand, price, taste,
size). Market outcomes can be simulated for a base case scenario and
then for an alternative scenario where an attribute is changed – for
instance the price of one product may be increased by ten percent.
While surveys may be able to generate estimates of cross elasticities
that are not otherwise available, the cost of a survey may be significant.
62.
63.
See, e.g., Igal Hendel & Aviv Nevo, Sales and Consumer Inventory
(NBER Working Paper No. w9048, July 2002).
Time-aggregation provides another test of inventorying behavior. If the
estimated elasticities are significantly lower in the time-aggregated
model, inventorying behavior might be present.
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In addition, it is difficult to avoid selecting a biased sample. If, for
instance, a surveyor wanted to determine the popularity of a film, the
easiest method would be to stand outside a theater showing that film and
survey people as they leave. However, since most people go to theaters
near their homes, there will likely be a demographic bias. The same film
in a different part of town may be received very differently. Another
example of a biased survey would be Internet surveys. Clearly, the
respondents will only be Internet users, and they are not generally
representative of the population as a whole. Telephone surveys are the
most popular interview method – over 95% of homes have a phone –
however calling during the day will bias the sample since only people
who do not work or who work from home will be reached. It is not
likely that they will be representative of the population as a whole.
While these drawbacks exist for any survey, a well-designed survey can
be extremely useful and in some instances may be the only way to get
estimates of certain parameters.
The estimated demand system is typically used to estimate the likely
effects of a merger on prices, to calculate the welfare changes induced by
changes in prices or qualities of products, or to determine the lost profit
damages resulting from patent infringement. Since the demand system
has been estimated, any calculations based on the demand system will
reflect the statistical variation inherent in the estimated demand system
parameters. Thus, it is typically desirable to calculate standard errors for
any results derived from the estimated demand system. Econometrics
offers several straightforward ways in which to do this.
3. PCAIDS
a. Introduction
PCAIDS, which is short for proportionally calibrated AIDS, is an
approximation to the AIDS model that offers advantages in many
situations.64 AIDS often yields estimated cross elasticities that have low
precision and algebraic signs that are inconsistent with economic theory.
Moreover, AIDS requires substantial data, which are typically available
64.
For details, see Roy E. Epstein & Daniel L. Rubinfeld, Merger
Simulation: A Simplified Approach with New Applications, 69 ANTITRUST
L.J. 883 (2001).
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only for retail sales tracked by check-out scanners. PCAIDS, in contrast,
uses only market shares and reasonable values for two elasticities—the
price elasticity of industry demand and the price elasticity of any one
product. Estimates of these elasticities often can be obtained from
marketing information or, when appropriate, through demand estimation.
This simplicity is achieved by placing restrictions on the structure of the
AIDS model. There are methods both to test the validity of the
restrictions and to relax them to generalize the analysis. In summary,
PCAIDS is a reasonably general method for calibrating AIDS demand
with minimal data, and for which proportionality is a useful starting
point.
PCAIDS has similarities to, and differences from, the ALM. Both
rely on the principle of proportionality, which allows them to be
implemented using only market shares, the price elasticity of industry
demand, and a single brand-level demand elasticity or other equivalent
condition. There are three main differences: First, the predicted
unilateral effects from PCAIDS tend to be larger than those from the
ALM. The two models might be viewed as providing approximate upper
and lower bounds on the likely price effects of the transaction. Second,
it appears easier to relax the assumption of proportionality for PCAIDS.
Since proportionality is a strong assumption it is important to be able to
investigate the effect of not using it, and this analysis is easily
manageable with PCAIDS. Third, PCAIDS can be used even when
information on underlying product prices is not available.
b. Estimation
A simple example with three independent firms, each owning a
single brand, helps explain the logic of PCAIDS. The AIDS model
specifies that the revenue share of each brand depends on the logarithms
of the prices of all brands. More formally, the share of each brand, as a
percent of total market revenues is a function of the weighted average of
the natural logarithms of the prices of all of the brands in the system.
The weights or coefficients, which can be used to calculate own and
cross elasticities, must be determined to simulate the effects of a
merger.65 Three “own-coefficients” specify the effect of each brand’s
65.
This discussion suppresses the aggregate expenditure terms from the
original AIDS specification.
This “homotheticity” assumption is
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own price on its share. These coefficients should have negative signs,
since an increase in a brand’s price should (all other prices held constant)
reduce its share; indeed, these coefficients are closely related to and have
the same signs as the own elasticities. The six other coefficients specify
the effects of the prices of other brands on each brand’s share. These
“cross-coefficients” are expected to be positive (assuming the three
brands are substitutes), since these terms are related to and have the same
signs as the cross elasticities.66 There are a total of nine elasticities in
this example. The number of demand elasticities grows as the square of
the number of brands, so analysis of most markets must confront the
econometric complications caused by a large number of unknown
parameters.
The restrictions imposed by PCAIDS are designed to reduce the
number of parameters that have to be estimated on the basis of a simple
assumption: The share lost as a result of a price increase is allocated to
the other firms in the relevant market in proportion to their respective
shares. This is the IIA assumption discussed above, and it reduces the
number of unknown price coefficients from nine to three. We only need
to know the three own-coefficients (and market shares) to calculate the
remaining six cross-coefficients. In fact, the proportionality assumption
reduces the information requirement of PCAIDS even further. It can be
shown that the PCAIDS model, like the ALM, can be calibrated with
only two independent pieces of information (in addition to the shares)—
the elasticity of demand for a single brand and the elasticity for all
brands in the aggregate. Thus, only the aggregate elasticity and the ownprice elasticity for Brand 1 are needed as inputs in the calculation of the
own-coefficient for Brand 1, and proportionality implies that all
remaining unknown own-coefficients can be determined as simple
multiples of the Brand 1 own-coefficient. Thus, knowledge of the own
elasticity of any one brand and the aggregate industry demand elasticity
66.
reasonable to the extent that changes in industry expenditure have no
significant effects on share.
The market shares predicted by AIDS are required to sum to 100%—the
adding-up property. PCAIDS also imposes homogeneity, the assumption
that equal proportional changes in all prices have no effect on market
share (e.g., if all prices went up by 10 percent, the market shares for the
various brands should not change). Adding-up and homogeneity reduce
by one the number of brands to be analyzed in the AIDS model.
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is sufficient to obtain estimates of all relevant demand parameters of the
PCAIDS model from the market share data.
All the information required to calibrate PCAIDS should be
available. Market shares typically are known with reasonable accuracy.
It should be feasible to infer the own elasticity of demand for at least one
brand sold by the merging parties from marketing studies in the party’s
documents (including surveys and focus groups), from econometric
analyses, or from accounting data. The industry demand elasticity of
demand typically is considerably smaller than the demand elasticity of
any one brand, since brand substitution is easier than industry
substitution.67 Absent independent information about the magnitude of
that elasticity, an aggregate elasticity of –1 may be a good starting point
for a preliminary merger simulation.
To illustrate, again consider a three-brand demand system, with
shares for the brands (each sold by a different firm) of 20 percent, 30
percent, and 50 percent. Now assume: there is a proposed merger
between sellers of Brands 1 and 2; the industry elasticity is –1; and the
own elasticity for the first brand is –3. The PCAIDS are elasticities as
shown in Table 1. The calculated own elasticities—the other negative
values on the diagonal—can be larger or smaller than the elasticity for
the brand used to calibrate the system. Reading down each column of
elasticities, the cross elasticities corresponding to the change in a given
price, are equal as expected, given proportionality. PCAIDS simulation
with these parameters predicts a unilateral post-merger price increase
(absent efficiencies) of 13.8 percent for Brand 1 and 10.8 percent for
Brand 2. The same elasticities, however, yield significantly lower price
increases using the ALM.
67.
Suppose the prices of all cereals rose by 10 percent. Since many
consumers, particularly children, are likely to continue eating the similar
quantities of cereal for breakfast (some, of course, will not and
consumption of cereal for other purposes, such as snacks, may fall),
ready-to-eat demand is not likely to be highly price sensitive. On the
other hand, a 10 percent increase for a single brand, such as corn flakes,
with no change in competitors’ prices, will be more price sensitive, since
it will likely result in substantial switching to other products within the
cereal category.
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Table 1
PCAIDS Elasticities
Brand
1
2
3
Elasticity with Respect to:
p1
p2
p3
–3.00
0.75
1.25
0.50
–2.75
1.25
0.50
0.75
–2.25
c. Deviations from Proportionality—PCAIDS with Nests
Proportionality will not always characterize the diversion of lost
sales accurately when products are highly differentiated. Fortunately, it
is straightforward to modify PCAIDS to allow a more general analysis.
In a manner analogous to the generalization of the logit model, products
that are closer substitutes for each other than consistent with
proportionality may be placed together in “nests.”
To illustrate, return to the three-brand example discussed in the
previous section. In that example, Brand 2’s market share of 30 percent
and Brand 3’s share of 50 percent implied that, when Brand 1’s price is
increased, diversion to Brand 2 would be 60 percent of diversion to
Brand 3. This can be characterized using a “nesting parameter,” which
in this case is 0.6 (i.e., 60 percent). Now suppose that Brand 2 is
relatively “farther” from Brand 1 in the sense that that fewer consumers
would choose Brand 2 in response to an increase in the price of the first
brand than would be predicted by proportionality. For example, Brand 2
may only be “half as desirable” a substitute as Brand 3 and the
appropriate nesting factor really only 0.3.
PCAIDS with nests allows a more flexible pattern of cross
elasticities, as the model is no longer fully constrained by the
proportionality assumption. Continuing with the example, we can
capture the effect of Brand 2 being a less close substitute for Brand 1
than indicated by market shares by placing Brand 2 in a nest with a
nesting parameter of 0.5. Table 2 compares the calculated elasticities for
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the nested model with those of the original model.68 The nesting
parameter rescales the cross elasticities in the right-hand panel; the cross
elasticities measuring the responses of Brands 2 and 3 to the price of
Brand 1, and those measuring the responses of Brands 1 and 2 to the
price of Brand 3 are no longer equal. With nesting, Brand 2 is a poorer
substitute for Brands 1 and 3 (as indicated by the smaller cross
elasticities of Brand 2 demand with respect to the prices of Brands 1 and
3 and of Brands 1 and 3 demand with respect to the price of Brand 2),
while Brands 1 and 3 is better substitutes for each other (as indicated by
the larger cross elasticities of Brand 1 demand with respect to the price
of Brand 3 and Brand 1 demand with respect to the price of Brand 3).
Table 2
PCAIDS Elasticities with Nests
Brand
1
2
3
Non-Nested Demand
Elasticity with Respect to:
p1
P2
p3
–3.00
0.75
1.25
0.50
–2.75
1.25
0.50
0.75
–2.25
Brand
1
2
3
Separate Brand 2 Nest,
(Nesting Parameter = 0.5)
Elasticity with Respect to:
p1
p2
p3
–3.00
0.46
1.54
0.31
–2.08
0.77
0.62
0.46
–2.08
Simulation of a merger of Brand 1 and Brand 2 using this nested
PCAIDS model predicts a unilateral price increase (without efficiencies)
of 10.1 percent for both Brand 1 and Brand 2, compared to the original
increases of 13.8 percent and 10.8 percent without nests. The unilateral
effects are smaller with the nested model because the merging brands are
less close substitutes for each other.
What remains is the difficult question of when the proportionality
assumption is inappropriate, making nests necessary for accurate merger
simulations. To this point, there has been very little empirical testing of
this question.69 Note, however, that if PCAIDS introduces the possibility
68.
69.
The calculations continue to assume an own-price elasticity of –3 for
Brand 1 and an industry elasticity of –1.
A statistical test procedure is described in Jerry A. Hausman & Daniel
McFadden, Specification Tests for the Multinomial Logit Model, 52
ECONOMETRICA 1219 (1984). One recent AIDS analysis of a grocery
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of bias, it may still provide an economically useful approximation.70
Fortunately, PCAIDS makes it easy to detect whether nesting is likely to
have economically meaningful effects through a sensitivity analysis of
the nesting parameters. A coarse grid (e.g., 0.75, 0.50, and 0.25)
covering a range of nesting factors may be adequate to assess sensitivity.
There is a potentially more useful, data-based approach to the
estimation of nesting parameters, which relies on brand-level margin
data.71 Assume, for example, that the merging firms each produce a
unique brand pre merger. It is not hard to show, in this case, that one can
use brand margin data to solve for unique nesting parameters. If one or
more merging firms had several brands, however, it is possible for the
nesting parameters to be over-identified (i.e., a range of nesting
parameters would be consistent with the margin data) or under-identified
(the data would not be sufficient to estimate all the nesting parameters).
Nevertheless, one can still develop a range of values for the nesting
parameters that is consistent with the available information, and that will
generate informative predictions.
d. Using PCAIDS
This section offers an example of the application of PCAIDS to 1992
the acquisition of Scott by Kimberly-Clark. A PCAIDS analysis of this
merger may be compared to a published simulation analysis by Hausman
and Leonard that used supermarket scanner data to estimate an AIDS
model.72 There were eight toilet tissue brands. Scott produced
ScotTissue and Cottonelle, which had pre-merger shares of 30.9 percent
70.
71.
72.
item using scanner data indicates that proportionality is reasonable but it
does not formally test the hypothesis. See David A. Weiskopf,
Assessment of the Relationship between Various Types of Estimation
Bias and the Simulated Economic Impact of Certain Anti-Competitive
Scenarios 55, Table B2 (unpublished Ph.D. dissertation, Vanderbilt
University, Department of Economics, 1999).
Coefficients estimated with the PCAIDS restrictions could have a
variance that sufficiently lower variance to offset any bias introduced.
Details are available in Roy J. Epstein & Daniel L. Rubinfeld, Merger
Simulation with Nests: Using PCAIDS with Brand-Level Margin Data,
(unpublished paper 2003).
Hausman & Leonard, supra note 29.
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and 7.5 percent. Kimberly-Clark produced only Kleenex, with a share of
6.7 percent. The PCAIDS model is calibrated using Hausman and
Leonard’s estimated demand elasticity for Scott (–2.94) and a value for
the aggregate elasticity (–1.17) that can be inferred from their analysis.
Table 3
PCAIDS and Hausman-Leonard Elasticities
Own Elasticity
ScotTissue
Cottonelle
Kleenex
Charmin
Northern
Angel
Private Label
Other
Average
PCAIDS
–2.9
–3.2
–3.1
–2.6
–3.0
–3.1
–3.1
–3.1
–3.0
HausmanLeonard
–2.9
–4.5
–3.4
–2.7
–4.2
–4.1
–2.0
–2.0
–3.2
Cross Elasticity
PCAIDS
0.36
0.14
0.16
0.66
0.26
0.19
0.16
0.20
0.27
HausmanLeonard
0.24
0.22
0.13
0.35
0.41
0.26
0.09
0.27
0.24
Table 3 compares PCAIDS price elasticities to the elasticities
estimated econometrically by Hausman and Leonard. The two methods
yield similar results brand by brand, and on average there appears to be
relatively little difference.73 This suggests that the proportionality
assumption of PCAIDS is reasonably consistent with the toilet tissue
data. Moreover, differences between the elasticities yielded by the two
methods may not be statistically significant. Hausman and Leonard
report low precision for many of the estimated cross elasticities. For
73.
Each Hausman-Leonard cross elasticity in the table is calculated as the
average of the cross elasticities with respect to the price of the brand
given in the left-most column. The Hausman and Leonard study reported
several negative cross elasticities (for non-merging goods) that we found
difficult to interpret. The average values reported in the table exclude any
negative cross elasticities.
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example, they report a Kleenex-Scott cross elasticity of 0.061 with a
standard error of 0.066; this means that their estimated cross elasticity is
within two standard errors of our calibrated PCAIDS value of 0.16.
Uncertainty about the true value of this cross elasticity is particularly
crucial to the merger simulation analysis since the magnitude of this
cross elasticity has a large effect on the price increases predicted from
the merger.
Taking into account the efficiencies assumed by Hausman-Leonard,
the two simulation methods yield predicted price changes for the
merging firms as shown in Table 4. The predicted price changes are
similar for ScotTissue and Cottonelle. There is a greater difference
between the predicted price changes for Kleenex, although even this
difference may not be statistically significant. As a sensitivity test, a nest
structure was used that lowered the PCAIDS Kleenex-Scott cross
elasticity to 0.061 and left the other cross elasticities in the model
essentially unchanged. The price increase for Kleenex predicted by this
nested PCAIDS model fell to 1.7 percent. This experiment suggests that
increasing the same cross elasticity by two standard errors in the
Hausman-Leonard simulation would produce a Kleenex price change
much closer to the PCAIDS result.
Table 4
Simulated Unilateral Effects for Toilet Tissue
ScotTissue
Cottonelle
Kleenex
NYDOCS:19868.1
Price Change (%)
HausmanPCAIDS
Leonard
–0.3
–1.1
0.7
0.5
4.3
0.2