Industry
Empirical Studies
Differentiated Products Structural
Models
Based on the lectures of
Dr Christos Genakos (University of Cambridge)
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)
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
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
Why is Demand so central?
Assume we observe J differentiated products and each has
aggregate demand:
Q j  D( p1 ,..., p j , Y j ,  )
Suppose there are F firms, each producing a subset Ff of the J
different brands. The profits for each firm f are
f 
( p
jF f
j
 mc j (W j ,  ))Q j  C f
Assuming that a pure-strategy equilibrium in prices exist, then
the price pj of any product j produced by firm f must satisfy:
Qr ( p)
Q j ( p)   ( pr  mcr )
0
p j
rF f
The set of J such equations imply price-cost margins for each
good
Why is Demand so central?
To solve for the mark-ups, define:
S jr
Qr

p j
and  jr
1,  j , r  F f

and  jr   jr  S jr
 0, otherwise
So we can write the FOC in vector notation
Q( p )  ( p  mc)  0
Which gives us the pricing equation
p  mc  1Q( p)
The markup vector depends only on the parameters of demand
and the equilibrium price vector
Why is Demand so central?
Different competition models can be nested within this framework
Assume two firms with two products each:
S
jr
 S11
S
   21
 S 31

 S 41
S12
S 22
S13
S 23
S 32
S 42
S 33
S 43
Single product Nash Bertrand
Multiproduct Nash Bertrand
Tacit Collusion
S14 
S 24 

S 34 

S 44 
1
0
  
0

0
0
1
0
0
0
1
0
0
1
1
  
0

0
1
1
  
1

1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0

0

1
0
0

1

1
1
1

1

1
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)
Estimation Challenges
The most intuitive way to model demand for products
j=1,...,J is to specify a system of demand equations:
q  f ( p, z)
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:
1.Dimensionality problem - curse of dimensionality
2.Multicollinearity of prices and price endogeneity
3.Consumer heterogeneity
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)
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 multistage 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.
Multilevel Demand Models
income
Breakfast Cereals
Food
Shelter
Meat
Beer
Entertainment
Kellogg
Crunchy Nuts
Apple-Cinnamon Cheerios
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
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
An Almost Ideal Demand System (AIDS) for
Differentiated products
The actual application involves a three stage system:
1. the top level corresponds to overall demand for the product
(beer or ready-to-eat cereal, in their applications)
2. the middle level involves demand for different market
segments (for example, family, kids and adults cereal)
3. 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.
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)
Hausman (1996): valuation of new goods
Ready-to-eat cereal industry
Very concentrated industry: C4>94%, 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!!!)
Empirical Framework
•
Estimate demand system AFTER introduction of new good
•
Recover expenditure function: e  e( p1 ,..., pn1 , pn , u)
•
Let pn* be the virtual price defined implicitly by the solution
to the equation:
*
qn ( p1 ,..., pn1 , pn )  0
•
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
en  e( p1 ,..., pn1 , pn , u)
*
•
*
Then e*/e are the benefits from the new good
Demand Specification
Demand model in three steps:
1.Lowest level: demand for brand j within segment g in city c
at quarter t is
s jct   jc   j log( ygct / Pgct )  k 1  jk log pkct   jct
J
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 :
log qgct   gc   g log yRct  k 1 k log  kct   gct
G
where qgct is the quantity of the gth segment in city c at quarter t, yRct is
the total cereal expenditure and πkct are the segment price indexes for
each city
Demand Specification
3.Top level: demand for the product itself is specified as
log qt   0  1 log yt   2 log  t  Z t   t
where qt is the overall consumption of cereal at quarter t, yt is
disposable real income, πt 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
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)
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
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)
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.
Random Utility Demand Models
Products' characteristics play two separate roles:
1. they are used to describe the mean utility level across
heterogeneous consumers
2. 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).
Random Utility Demand Models
•
Each individual i faces the following problem:
U ij  max U ( x j , p j , vi ; )
where xj denote the vector of product characteristics for j=0,1,2,...,J, pj
denote the price of that good, vi represents consumer
preferences and θ determines the impact of those preferences on
utility.
•
Individual i chooses product j if and only if:
U ( x j , p j , vi ; )  U ( xr , pr , vi ; ), for r  0,1,..., J
•
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.
Random Utility Demand Models
Hence for a given preferences θ, Aj is the set that lead to the
choice of good j:
A j ( )  v : U ij  U ir  for r  0,1,..., J
Let f(v) be the distribution of preferences in the population, then
the market share of good j is:
s j ( x, p; )  
vA j ( )
f (v)d (v)
where (x,p) denote the vector of characteristics of all products
in the market. Total demand will be given by Msj(x,p;θ),
where M is the total number of consumers.
Example: Multinomial Logit Model
Assume that individual's preferences differ only by an additive
term
U ij   j   ij
In other words, consumer's type is now:
i  ( i1 ,...,  iJ )
MNL (McFadden, 1973) assumes that εi 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!
sj 
exp(  j )

J
r 1
exp(  r )
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
U ij   j   ij  x j   p j   j   ij
where xj is the vector of observed product characteristics and ξj 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:
S j  s j ( x, p ,  ;  )
•
This is a system of J-1 equations and J-1 unknowns
(outside good and J inside goods).
Unobserved product characteristics: Berry (1994)
•
For each θ there is only one ξ that makes the predicted
shares equal to the observed shares
•
Therefore, conditional on the true values of δ, the model
should fit the data exactly: "invert" the demand model to find
ξ as a function of the parameter vector
S j  s j ( )    s 1 (S )
•
Precisely how we do this depends on the functional form of
the demand model
•
But once we have ξ(θ), 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
Multinomial Logit (revisited)
Remember from our MNL the market share for each good is
s j  exp( j )

J
r 0
exp( r )
With the mean utility of the outside good normalized to zero
s0  1 1  r 1 exp( r )
J
Then
ln( s j )  ln( s0 )   j  x j   p j   j
So δj 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
Problem with simple Logit model
For the own and cross price elasticities we get:
 jk
 p j (1  s j ) if j  k

 pk sk otherwise
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).
Problem with simple Logit model
Example: If the price of a Lexus (price=40, mkt share=.05) goes up,
then the impact on demand for BMW (price=55, mkt share=.01)
and Yugo (price=8, mkt share=.01) are the same! Our
elasticities are determined by the structure of the model (α=2) and not the data!
s1
s2
s3
s1
s2
s3
-76
4
4
1.1
0.16
-108.9 0.16
1.1 -15.84
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
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)
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
uij ( )  x j  i   i p j   j   ij
where α and β have now a common across consumers
component and an individual consumer component that is
based on demographics and unobserved preferences
Key Hypotheses and Data
Markups are given by:
1
p  mc   Q( p)
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
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?
Differentiated Products Structural Models:
References
*Berry, S (1994) “Estimating Discrete-Choice Models of Product
Differentiation”, Rand Journal of Economics, 25:242-262.
*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, 69:307-342.
*Nevo (2000) “A Practitioner’s Guide to Estimation of RandomCoefficients Logit Models of Demand”, Journal of Economics and
Management Strategy, 9:513-548.
Berry, S., Levinsohn J. and Pakes, A. (1995) “Automobile Prices
in Market Equilibrium”, Econometrica, 63:841-890.
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, 27:240-268
*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, 31:395-421.
Genakos, C. (2004) “Differential Merger Effects: The Case of the
Personal Computer Industry”, LBS mimeo and STICERD wp No.
EI/39.
Nevo (2001) Table VI
Nevo (2001) Table VII
Nevo (2001) Table VIII