Industry Empirical Studies Differentiated Products Structural Models

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IndustryEmpirical StudiesDifferentiated
Products Structural Models
Based on the lectures of Dr Christos Genakos
(University of Cambridge)
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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1996)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Product Differentiation and Demand Estimation

• In our last lecture we analyzed how to estimate
  market power using a market-level model in which
  all firms sell a homogeneous product
• Today we are going to extend these methods to
  analyze market power in multiproduct
  differentiated products markets
• Help us understand empirically the role of
  product differentiation (vertical, horizontal or
  both) in determining market power
• Use these models to examine various important
  policy questions and how factors other than
  product differentiation affect market power

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Why do we care about Demand?

• This is THE major tool for comparative static
  analysis of any change that does not have an
  immediate impact on costs
• Optimising firm level pricing and product
  "placement" decisions
• Measuring effective competition between
  products/firms (essential input into any merger
  and anti-trust analysis)
• Measuring welfare impact of introduction of new
  products or regulation (taxes, patents,
  regulatory delay)
• Consumer Price Index measures

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Why is Demand so central?
Assume we observe J differentiated products and
each has aggregate demand Suppose there are F
firms, each producing a subset Ff of the J
different brands. The profits for each firm f
are Assuming that a pure-strategy equilibrium
in prices exist, then the price pj of any product
j produced by firm f must satisfy The set of
J such equations imply price-cost margins for
each good

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Why is Demand so central?
To solve for the mark-ups, define So we can
write the FOC in vector notation Which gives
us the pricing equation The markup vector
depends only on the parameters of demand and the
equilibrium price vector

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Why is Demand so central?
Different competition models can be nested within
this framework Assume two firms with two products
each Single product Nash
Bertrand Multiproduct Nash Bertrand Tacit
Collusion

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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1996)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Estimation Challenges

• The most intuitive way to model demand for
  products j1,...,J is to specify a system of
  demand equations
• The main focus of the early demand literature was
  to specify f() in a way that was both flexible
  and consistent with economic theory
• There are three main problems applying any of
  these methods to estimate demand for
  differentiate products
• Dimensionality problem - curse of dimensionality
• Multicollinearity of prices and price endogeneity
• Consumer heterogeneity

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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1996)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Multilevel Demand Models
One approach to solving the dimensionality
problem is to divide the products into smaller
groups and allow for a flexible functional form
within each group The justification of such a
procedure relies on two closely related ideas
the separability of preferences and multi-stage
budgeting Separability of preferences If this
holds commodities can be partitioned into groups
so that preferences within each group are
independent of the quantities in other
groups Multi-stage budgeting This occurs when
the consumer can allocate total expenditure in
stages at the highest stage expenditure is
allocated to broad groups, while at lower stages
group expenditure is allocated to sub-groups,
until expenditures are allocated to individual
products.

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Multilevel Demand Models
The two notions, of weak separability and
multi-stage budgeting, are closely related
however, they are not identical, nor does one
imply the other Weak separability is necessary
and sufficient for the last stage of the
multi-stage budgeting, multi-stage budget shares
allows one to derive the price index for the
group without knowing the "income" allocated to
the group

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An Almost Ideal Demand System (AIDS) for
Differentiated products
Originally AIDS model was developed for the
estimation of broad categories of product (Deaton
and Muellbauer, 1980) - Relative
successful Hausman, Leonard and Zona (1994),
Hausman (1996) and Hausman and Leonard (2002) use
the idea of multi-stage budgeting to construct a
multi-level demand system for differentiated
products

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An Almost Ideal Demand System (AIDS) for
Differentiated products

• The actual application involves a three stage
  system
• the top level corresponds to overall demand for
  the product (beer or ready-to-eat cereal, in
  their applications)
• the middle level involves demand for different
  market segments (for example, family, kids and
  adults cereal)
• and the bottom level involves a flexible brand
  demand system corresponding to the competition
  between the different brands within each segment
• For each of these stages a flexible parametric
  functional form is assumed.

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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1996)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Hausman (1996) valuation of new goods
Ready-to-eat cereal industry Very concentrated
industry C4gt94, leading sellers made very high
profits consistently, not successful entrant last
50 years! Huge variety of new products but very
few survive Big sunk cost in advertising "store
brands" getting stronger Question Introduction
of Apple-Cinnamon Cheerios by General Mills in
1989 (vs. Cheerios and Honey-Nut Cheerios!!!)

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Empirical Framework

• Estimate demand system AFTER introduction of new
  good
• Recover expenditure function
• Let pn be the virtual price defined implicitly
  by the solution to the equation
• Taking that as the price of the new good in the
  base period, calculate the expenditure level that
  would have made the consumer indifferent between
  having or not the new good given prices of all
  other goods
• Then e/e are the benefits from the new good

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Demand Specification
Demand model in three steps 1.Lowest level
demand for brand j within segment g in city c at
quarter t is where sjct is the dollar sales
share of total segment expenditure, ygct is the
overall per capita segment expenditure, Pgct is
the price index and pkct is the price of the kth
brand in city c at quarter t. 2.Middle level
demand models the allocation between segments
where qgct is the quantity of the gth segment
in city c at quarter t, yRct is the total cereal
expenditure and pkct are the segment price
indexes for each city

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Demand Specification

• 3.Top level demand for the product itself is
  specified as
• where qt is the overall consumption of cereal at
  quarter t, yt is disposable real income, pt is
  the deflated price index for cereal and Zt are
  variables that shift demand including
  demographics and time factors
• IV prices of the same brand in other cities
  (after controlling for city and brand fixed
  effects)
• Data Scanner data aggregated over brands at the
  city level over 137 weeks

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Results and Discussion

• Demand estimates and elasticities look reasonable
  (atlhough some cross price elasticities are
  negative even within segments)
• Hausman calculates the consumer welfare to be
  32,268 per city, weekly average, or 78.1
  million!!!
• One problem with this methodology is that it
  ignores the reactions of the prices of other
  goods when the new good is not in the market
• Fundamental problem is that we are projecting
  demand where there is no information. To get the
  value of the new good we need to integrate from
  the virtual price down and typically there are no
  observations near the virtual price. (with demand
  on the characteristics space, at least there
  might be other products with some similar
  characteristics as the new good)

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AIDS for Differentiated Products - Discussion

• Advantages
• model is closely linked to the neo-classical
  demand theory
• it allows for a flexible pattern of substitution
  within each segment
• it is relatively easy to estimate
• Disadvantages
• although the demand within segments is flexible,
  the segment division is potentially very
  restrictive
• the allocation of products to different segments
  is highly subjective
• the multi-level demand system does not
  fundamentally solve the dimensionality problem
• the structure of the segments and the products
  that belong to each segment are essentially the
  same over time
• no heterogeneity-distributional aspects of changes

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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1997)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Random Utility Demand Models
Products as a bundle of characteristics
(Lancaster, 1966) Consumer preferences are
defined over the characteristics space, rather
than the products themselves ? dimensionality
problem solved! Each consumer chooses bundle
that maximizes its utility. Consumers have
different relative preferences ? heterogeneous
preferences. Aggregate demand is the sum over
all individual demands ? depends on entire
distribution of consumer preferences.

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Random Utility Demand Models

• Products' characteristics play two separate
  roles
• they are used to describe the mean utility level
  across heterogeneous consumers
• guide substitution patterns products with
  similar characteristics will be closer
  substitutes.
• In other words, discrete choice models
  operationalize the notion of "how close products
  are" with reference to the products'
  characteristics (not constrained by a-priori
  market segmentation).

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Random Utility Demand Models

• Each individual i faces the following problem
• where xj denote the vector of product
  characteristics for j0,1,2,...,J, pj denote the
  price of that good, vi represents consumer
  preferences and ? determines the impact of those
  preferences on utility.
• Individual i chooses product j if and only if
• Product 0 is the "outside" good (it is the good
  not competing with the goods in the industry and
  hence whose price and quantity is set
  exogenously). If there is no outside good we can
  not use the model to study aggregate demand.

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Random Utility Demand Models
Hence for a given preferences ?, Aj is the set
that lead to the choice of good j Let f(v)
be the distribution of preferences in the
population, then the market share of good j
is where (x,p) denote the vector of
characteristics of all products in the market.
Total demand will be given by Msj(x,p?), where M
is the total number of consumers.

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Example Multinomial Logit Model
Assume that individual's preferences differ only
by an additive term In other words, consumer's
type is now MNL (McFadden, 1973) assumes that
ei is distributed in an independent and identical
way across i and j with a "type I extreme value"
distribution The extreme value assumption has a
wonderfully nice implication integral of
aggregate demands is analytic!

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Unobserved product characteristics Berry (1994)

• One possible source of error is unobserved or
  unmeasured product characteristics.
• Berry (1994) contains the first explicit
  treatment of this. Assume utility that individual
  i gets from good j is
• where xj is the vector of observed product
  characteristics and ?j is the unobserved (to the
  econometrician) product characteristic.
• Consider a demand equation that relates observed
  market shares, Sj, to the market shares predicted
  by our model, sj
• This is a system of J-1 equations and J-1
  unknowns (outside good and J inside goods).

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Unobserved product characteristics Berry (1994)

• For each ? there is only one ? that makes the
  predicted shares equal to the observed shares
• Therefore, conditional on the true values of d,
  the model should fit the data exactly "invert"
  the demand model to find ? as a function of the
  parameter vector
• Precisely how we do this depends on the
  functional form of the demand model
• But once we have ?(?), this is our error term and
  can proceed as in a normal estimation procedure
  by minimizing the sample analog of those
  disturbances to make them as close to true as
  possible

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Multinomial Logit (revisited)
Remember from our MNL the market share for each
good is With the mean utility of the outside
good normalized to zero Then So dj is
uniquely identified directly from a simple
algebraic calculation involving market shares. So
estimating the MNL model with an "unobserved"
product characteristic boils down to just running
a nice linear regression!!! All we need is
to find some instruments for price and we can
estimate that in any standard econometric
software package

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Problem with simple Logit model
For the own and cross price elasticities we
get Problems 1.Own-price elasticities are
proportional to own price the lower the price
the lower the elasticity, which implies higher
markups for the lower priced goods. 2.Cross-price
elasticities between ANY pair of products are
entirely determined by one parameter and the
market share and price of that good consumers
substitute towards other brands in proportion to
market shares, regardless of characteristics
(also small sk, means small elasticity).

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Problem with simple Logit model
Example If the price of a Lexus (price40, mkt
share.05) goes up, then the impact on demand for
BMW (price55, mkt share.01) and Yugo (price8,
mkt share.01) are the same! Our elasticities are
determined by the structure of the model (a-2)
and not the data! Solution relax the IID
assumption, such that elasticities depend on how
close products are in the characteristics
space. A large empirical literature relaxes this
assumption and gets more realistic own-cross
price elasticities
s1 s2 s3
s1 -76 1.1 0.16
s2 4 -108.9 0.16
s3 4 1.1 -15.84

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OUTLINE

1. Product Differentiation and Demand Estimation
2. Estimation Challenges
3. Multilevel Demand Models
4. Example Hausman (1997)
5. Random Utility Demand Models
6. Example Nevo (2001)

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Nevo (2001) Measuring market power in cereals
Charecteristics of the ready-to-eat cereal
industry same as discussed before in
Hausman. Question Are the high profits and
markups observed in this industry due to product
differentiation? Portfolio effect? or
collusion? Utility for each consumer is
given where a and ß have now a common across
consumers component and an individual consumer
component that is based on demographics and
unobserved preferences

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Key Hypotheses and Data
Markups are given by By varying the ownership
matrix, Nevo can distinguish between the three
hypothesis. single product firms? product
differentiation, multiproduct firms? portfolio
effect, single monopolist?collusion Data Market
shares, prices and brand characteristics (sugar,
mushy, fiber, fat), advertising and information
on demographic characteristics Scanner
supermarket data aggregate to brand at city
level for each quarter (65 cities, 6 quarters,
top 25 brands) Instruments since he controls for
brand and demographic mean effects, city specific
valuations are independent across cities?hence
prices of the same brands in other cities are
valid IV

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Results and Discussion

• Rich dataset, good identification and interesting
  interactions (children makes you less price
  sensitive and hate fiber, income makes you less
  sensitive but at a declining rate, richer people
  hate mushy less but don't like sugar etc) (Table
  VI)
• Sensible own and cross price elasticities (Table
  VII)
• Margins and hypothesis testing (observed margin
  46) (Table VIII)
• Discussion
• exceptionally good dataset, IVs?

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Differentiated Products Structural Models
References
Berry, S (1994) Estimating Discrete-Choice
Models of Product Differentiation, Rand Journal
of Economics, 25242-262. Hausman, J. (1996)
Valuation of New Goods Under Perfect and
Imperfect Competition, in Bresnahan and Gordon
eds., The Economics of New Goods, NBER. Nevo
(2001) Measuring Market Power in the
Ready-to-Eat Cereal Industry, Econometrica,
69307-342. Nevo (2000) A Practitioners Guide
to Estimation of Random-Coefficients Logit Models
of Demand, Journal of Economics and Management
Strategy, 9513-548. Berry, S., Levinsohn J. and
Pakes, A. (1995) Automobile Prices in Market
Equilibrium, Econometrica, 63841-890.

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Next time Studies on Price Discrimination, New
Products and Mergers
Verboven, F. (1996) International Price
Discrimination in the European Car Market, Rand
Journal of Economics, 27240-268 Petrin, A.
(2002) Quantifying the benefits of New Products
The Case of Minivan, Journal of Political
Economy, 110, 705-729 Nevo, A. (2000) Mergers
with Differentiated Products The Case of the
Ready-to-eat Cereal Industry, Rand Journal of
Economics, 31395-421. Genakos, C. (2004)
Differential Merger Effects The Case of the
Personal Computer Industry, LBS mimeo and
STICERD wp No. EI/39.

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Nevo (2001) Table VI

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Nevo (2001) Table VII

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Nevo (2001) Table VIII