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Empirical Micro

Empirical Micro
Topic 1: Static Models of Differentiated Products

Michelle Sovinsky
University of Z¨rich
u

February 5, 2013

Empirical Micro
Discrete-Choice Utility

Discrete Choice Model
Utility of consumer i for product j
uij = U(xj , pj , vi )
xj is a vector of product characteristics
pj is the price of the product and
vi is a vector of consumer characteristics

Horizontal Model Example: Hotelling with quadratic costs
uij = u − pj − (xj − vi )2
xj is the location of the product along the line
vi is the location of the consumer

Empirical Micro
Discrete-Choice Utility

Discrete Choice Model
Utility of consumer i for product j
uij = U(xj , pj , vi )
xj is a vector of product characteristics
pj is the price of the product and
vi is a vector of consumer characteristics

Horizontal Model Example: Hotelling with quadratic costs
uij = u − pj − (xj − vi )2
xj is the location of the product along the line
vi is the location of the consumer

Empirical Micro
Discrete-Choice Utility

Vertical Model Example: (Shaked and Sutton, Bresnahan 97)
uij = vi xj − pj
xj is the quality of the product
vi is the consumer’s taste for quality (ie willingness to pay)

Rather than model utility directly as a function of price, it
might be preferable to model it as a function of expenditures
on other products and then derive the indirect utility as a
function of price
There are J alternatives in market, indexed by j = 1,
...
t
...
, J
At each purchase occasion, each consumer divides her income
on (at most) one of the alternatives, and on an outside good
z:
max Ui (xj , z)s
...
pj + pz z = yi
j,z

Empirical Micro
Discrete-Choice Utility

Vertical Model Example: (Shaked and Sutton, Bresnahan 97)
uij = vi xj − pj
xj is the quality of the product
vi is the consumer’s taste for quality (ie willingness to pay)

Rather than model utility directly as a function of price, it
might be preferable to model it as a function of expenditures
on other products and then derive the indirect utility as a
function of price
There are J alternatives in market, indexed by j = 1,
...
t
...
i
...
across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)

What does it mean for tastes to be represented by product
and consumer specific random terms?
product chosen is random from the researchers point of view
McFadden won the Nobel Prize for this in 2000
Assumptions about distribution of the εij ’s determines choice
probabilities

The probability that consumer i buys product j is
∗
∗
Dij (p1 ,
...
, εij : Uij > Uik , for j = k

Empirical Micro
Estimation of Random Utility Discrete Choice Models

Random Utility Model (RUM)(McFadden)
∗
Uij usually specified as a sum of two parts
∗
Uij (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij

εij i
...
d
...
pj , pz , yi ) = Pr ob εi0 ,
...
i
...
across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)

What does it mean for tastes to be represented by product
and consumer specific random terms?
product chosen is random from the researchers point of view
McFadden won the Nobel Prize for this in 2000
Assumptions about distribution of the εij ’s determines choice
probabilities

The probability that consumer i buys product j is
∗
∗
Dij (p1 ,
...
, εij : Uij > Uik , for j = k

Empirical Micro
Estimation of Random Utility Discrete Choice Models

Random Utility Model (RUM)(McFadden)
∗
Uij usually specified as a sum of two parts
∗
Uij (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij

εij i
...
d
...
pj , pz , yi ) = Pr ob εi0 ,
...
5
odds ratio walk/RB=1

Introduce a red bus
odds ratio between walk/BB is 1

But buses are perfect substitutes
new choice prob should be siW = 0
...
25
new odds ratio should be walk/RB=2

IIA is especially troubling if want to predict penetration of
new products

Empirical Micro
Implications of Assumptions on Error Term

Independence of Irrelevant Alternatives (IIA)
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin
exp(Vin )
Red bus/blue bus problem: Walk or take red bus
If consumer walks half the time then siW = siRB = 0
...
5; siRB = siBB = 0
...
5
odds ratio walk/RB=1

Introduce a red bus
odds ratio between walk/BB is 1

But buses are perfect substitutes
new choice prob should be siW = 0
...
25
new odds ratio should be walk/RB=2

IIA is especially troubling if want to predict penetration of
new products

Empirical Micro
Implications of Assumptions on Error Term

Independence of Irrelevant Alternatives (IIA)
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin
exp(Vin )
Red bus/blue bus problem: Walk or take red bus
If consumer walks half the time then siW = siRB = 0
...
5; siRB = siBB = 0
...
5
odds ratio walk/RB=1

Introduce a red bus
odds ratio between walk/BB is 1

But buses are perfect substitutes
new choice prob should be siW = 0
...
25
new odds ratio should be walk/RB=2

IIA is especially troubling if want to predict penetration of
new products

Empirical Micro
Implications of Assumptions on Error Term

Price Elasticities of Demand
Let Vij = αpj + xj β
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk

= −αsij (1 − sij )
= αsij sik

Is it concerning that they depend only on the market shares of
the products?
Yes, do not depend on the degree to which products have
similar characteristics

Empirical Micro
Implications of Assumptions on Error Term

Price Elasticities of Demand
Let Vij = αpj + xj β
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk

= −αsij (1 − sij )
= αsij sik

Is it concerning that they depend only on the market shares of
the products?
Yes, do not depend on the degree to which products have
similar characteristics

Empirical Micro
Implications of Assumptions on Error Term

Price Elasticities of Demand
Let Vij = αpj + xj β
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk

= −αsij (1 − sij )
= αsij sik

Is it concerning that they depend only on the market shares of
the products?
Yes, do not depend on the degree to which products have
similar characteristics

Empirical Micro
Implications of Assumptions on Error Term

Counter-intuitive substitution patterns:
Not only from the distributional logit assumption
Due to assumption that the only variance in consumer tastes
comes through the i
...
d
...
i
...
, there is no source of correlation in consumer
tastes across similar products
Changes to allow for more intuitive substitution patterns
Generalized EV models (GEV, Nested logit)
Mixtures of logits (K types of logit parameters)
Product differentiation model (Bresnahan, Stern, Trajtenberg
1997)
Random Coefficients Model of Demand (Berry, Levinsohn, and
Pakes)

Empirical Micro
Implications of Assumptions on Error Term

Counter-intuitive substitution patterns:
Not only from the distributional logit assumption
Due to assumption that the only variance in consumer tastes
comes through the i
...
d
...
i
...
, there is no source of correlation in consumer
tastes across similar products
Changes to allow for more intuitive substitution patterns
Generalized EV models (GEV, Nested logit)
Mixtures of logits (K types of logit parameters)
Product differentiation model (Bresnahan, Stern, Trajtenberg
1997)
Random Coefficients Model of Demand (Berry, Levinsohn, and
Pakes)

Empirical Micro
Implications of Assumptions on Error Term

Counter-intuitive substitution patterns:
Not only from the distributional logit assumption
Due to assumption that the only variance in consumer tastes
comes through the i
...
d
...
i
...
, there is no source of correlation in consumer
tastes across similar products
Changes to allow for more intuitive substitution patterns
Generalized EV models (GEV, Nested logit)
Mixtures of logits (K types of logit parameters)
Product differentiation model (Bresnahan, Stern, Trajtenberg
1997)
Random Coefficients Model of Demand (Berry, Levinsohn, and
Pakes)

Empirical Micro
Implications of Assumptions on Error Term

Counter-intuitive substitution patterns:
Not only from the distributional logit assumption
Due to assumption that the only variance in consumer tastes
comes through the i
...
d
...
i
...
, there is no source of correlation in consumer
tastes across similar products
Changes to allow for more intuitive substitution patterns
Generalized EV models (GEV, Nested logit)
Mixtures of logits (K types of logit parameters)
Product differentiation model (Bresnahan, Stern, Trajtenberg
1997)
Random Coefficients Model of Demand (Berry, Levinsohn, and
Pakes)

Empirical Micro
Implications of Assumptions on Error Term

Counter-intuitive substitution patterns:
Not only from the distributional logit assumption
Due to assumption that the only variance in consumer tastes
comes through the i
...
d
...
i
...
, there is no source of correlation in consumer
tastes across similar products
Changes to allow for more intuitive substitution patterns
Generalized EV models (GEV, Nested logit)
Mixtures of logits (K types of logit parameters)
Product differentiation model (Bresnahan, Stern, Trajtenberg
1997)
Random Coefficients Model of Demand (Berry, Levinsohn, and
Pakes)

Empirical Micro
Models with Correlations Across Consumer Tastes

Generalized EV models (McFadden 1978, 1981)
Allows for correlations over alternatives
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
For any two alternatives in same nest, the ratio of probabilities
is independent of the attributes of other alternatives (IIA holds
within nests)
For any two alternatives in different nests, the ratio of
probabilities can depend on attributes of alternatives in other
nests (IIA does not hold for alternatives in different nests)
So logit within groups (nests) and logit-like choices of groups
across nests

Empirical Micro
Models with Correlations Across Consumer Tastes

Generalized EV models (McFadden 1978, 1981)
Allows for correlations over alternatives
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
For any two alternatives in same nest, the ratio of probabilities
is independent of the attributes of other alternatives (IIA holds
within nests)
For any two alternatives in different nests, the ratio of
probabilities can depend on attributes of alternatives in other
nests (IIA does not hold for alternatives in different nests)
So logit within groups (nests) and logit-like choices of groups
across nests

Empirical Micro
Models with Correlations Across Consumer Tastes

Generalized EV models (McFadden 1978, 1981)
Allows for correlations over alternatives
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
For any two alternatives in same nest, the ratio of probabilities
is independent of the attributes of other alternatives (IIA holds
within nests)
For any two alternatives in different nests, the ratio of
probabilities can depend on attributes of alternatives in other
nests (IIA does not hold for alternatives in different nests)
So logit within groups (nests) and logit-like choices of groups
across nests

Empirical Micro
Models with Correlations Across Consumer Tastes

Nested Logit Model
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
Define the inclusive value of nest g as:
sig =

exp
j∈g

uij
1−σ

McFadden (1978) showed nested structure is consistent with
RUM maximization iff the coefficients of the inclusive value lie
within the unit interval
More complicated forms of cross-product correlation in tastes
do not lead to closed form expressions for shares (like Nested
Logit does)
need to compute a high dimensional integral and this is tough

Empirical Micro
Models with Correlations Across Consumer Tastes

Nested Logit Model
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
Define the inclusive value of nest g as:
sig =

exp
j∈g

uij
1−σ

McFadden (1978) showed nested structure is consistent with
RUM maximization iff the coefficients of the inclusive value lie
within the unit interval
More complicated forms of cross-product correlation in tastes
do not lead to closed form expressions for shares (like Nested
Logit does)
need to compute a high dimensional integral and this is tough

Empirical Micro
Models with Correlations Across Consumer Tastes

Nested Logit Model
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
Define the inclusive value of nest g as:
sig =

exp
j∈g

uij
1−σ

McFadden (1978) showed nested structure is consistent with
RUM maximization iff the coefficients of the inclusive value lie
within the unit interval
More complicated forms of cross-product correlation in tastes
do not lead to closed form expressions for shares (like Nested
Logit does)
need to compute a high dimensional integral and this is tough

Empirical Micro
BLP

Berry, Levinsohn, Pakes (BLP) 1995 ECMA
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
endogenous prices and random coefficients
...
, I = ∞ agents in t = 1,
...
, J mutually exclusive alternatives

K observed product characteristics: Xjt = (xj,1,t ,
...

consistent estimation even with imperfect competition
To motivate framework consider Berry (RAND, 1994)
There are i = 1,
...
, T markets who
choose among j = 1,
...
, xj,K ,t )
Product characteristics/choice sets may evolve over markets

one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j

Empirical Micro
BLP

Berry, Levinsohn, Pakes (BLP) 1995 ECMA
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
endogenous prices and random coefficients
...
, I = ∞ agents in t = 1,
...
, J mutually exclusive alternatives

K observed product characteristics: Xjt = (xj,1,t ,
...

consistent estimation even with imperfect competition
To motivate framework consider Berry (RAND, 1994)
There are i = 1,
...
, T markets who
choose among j = 1,
...
, xj,K ,t )
Product characteristics/choice sets may evolve over markets

one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j

Empirical Micro
BLP

Consumer i’s indirect utility is given by
Uijt = Xjt β − αpjt + ξjt +εijt
≡ δjt
Derive market-level (aggregate) share expression from
individual model of discrete-choice
εijt are iid EV so the probability i chooses j is given by
sijt =

exp(δjt )
1 + exp(δkt )
k

Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =

exp(δjt )
1
[Msijt ] =
M
1 + exp(δkt )
k

Empirical Micro
BLP

Consumer i’s indirect utility is given by
Uijt = Xjt β − αpjt + ξjt +εijt
≡ δjt
Derive market-level (aggregate) share expression from
individual model of discrete-choice
εijt are iid EV so the probability i chooses j is given by
sijt =

exp(δjt )
1 + exp(δkt )
k

Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =

exp(δjt )
1
[Msijt ] =
M
1 + exp(δkt )
k

Empirical Micro
BLP

Consumer i’s indirect utility is given by
Uijt = Xjt β − αpjt + ξjt +εijt
≡ δjt
Derive market-level (aggregate) share expression from
individual model of discrete-choice
εijt are iid EV so the probability i chooses j is given by
sijt =

exp(δjt )
1 + exp(δkt )
k

Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =

exp(δjt )
1
[Msijt ] =
M
1 + exp(δkt )
k

Empirical Micro
BLP

Consumer i’s indirect utility is given by
Uijt = Xjt β − αpjt + ξjt +εijt
≡ δjt
Derive market-level (aggregate) share expression from
individual model of discrete-choice
εijt are iid EV so the probability i chooses j is given by
sijt =

exp(δjt )
1 + exp(δkt )
k

Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =

exp(δjt )
1
[Msijt ] =
M
1 + exp(δkt )
k

Empirical Micro
BLP

Berry assumes we are working with aggregate data and that,
at the true parameter values, sjt (X , β, α, ξ) = Sjt , where Sjt
denotes the ”true” market share
This is why I = ∞ is important

Model differs from standard conditional logit in two ways:
First, unobserved demand shock ξ
why is it important to include this term?
note that consumers willing to pay more for products for which
ξj is high
firms know product quality, which means ξj is correlated with
price (and also potentially with characteristics Xj )
unobserved product characteristic is source of the endogeneity
problem

Empirical Micro
BLP

Berry assumes we are working with aggregate data and that,
at the true parameter values, sjt (X , β, α, ξ) = Sjt , where Sjt
denotes the ”true” market share
This is why I = ∞ is important

Model differs from standard conditional logit in two ways:
First, unobserved demand shock ξ
why is it important to include this term?
note that consumers willing to pay more for products for which
ξj is high
firms know product quality, which means ξj is correlated with
price (and also potentially with characteristics Xj )
unobserved product characteristic is source of the endogeneity
problem

Empirical Micro
BLP

Berry assumes we are working with aggregate data and that,
at the true parameter values, sjt (X , β, α, ξ) = Sjt , where Sjt
denotes the ”true” market share
This is why I = ∞ is important

Model differs from standard conditional logit in two ways:
First, unobserved demand shock ξ
why is it important to include this term?
note that consumers willing to pay more for products for which
ξj is high
firms know product quality, which means ξj is correlated with
price (and also potentially with characteristics Xj )
unobserved product characteristic is source of the endogeneity
problem

Empirical Micro
BLP

Berry assumes we are working with aggregate data and that,
at the true parameter values, sjt (X , β, α, ξ) = Sjt , where Sjt
denotes the ”true” market share
This is why I = ∞ is important

Model differs from standard conditional logit in two ways:
First, unobserved demand shock ξ
why is it important to include this term?
note that consumers willing to pay more for products for which
ξj is high
firms know product quality, which means ξj is correlated with
price (and also potentially with characteristics Xj )
unobserved product characteristic is source of the endogeneity
problem

Empirical Micro
BLP

Berry assumes we are working with aggregate data and that,
at the true parameter values, sjt (X , β, α, ξ) = Sjt , where Sjt
denotes the ”true” market share
This is why I = ∞ is important

Model differs from standard conditional logit in two ways:
First, unobserved demand shock ξ
why is it important to include this term?
note that consumers willing to pay more for products for which
ξj is high
firms know product quality, which means ξj is correlated with
price (and also potentially with characteristics Xj )
unobserved product characteristic is source of the endogeneity
problem

Empirical Micro
BLP

Naive Estimation
We observe market shares in the data; and model yields
predicted shares from previous slide (denote sjt )
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
Minimize squared distance between Sjt and sjt

What is the problem with this?
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
Berry (1994) suggests a clever IV based estimation approach

Empirical Micro
BLP

Naive Estimation
We observe market shares in the data; and model yields
predicted shares from previous slide (denote sjt )
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
Minimize squared distance between Sjt and sjt

What is the problem with this?
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
Berry (1994) suggests a clever IV based estimation approach

Empirical Micro
BLP

Naive Estimation
We observe market shares in the data; and model yields
predicted shares from previous slide (denote sjt )
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
Minimize squared distance between Sjt and sjt

What is the problem with this?
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
Berry (1994) suggests a clever IV based estimation approach

Empirical Micro
BLP

Berry Inversion: First Step
At the true value of the parameters
Sjt = sjt (δ, α, β)
For each market, this gives us a system of J + 1 nonlinear
equations in the J + 1 unknowns ξ0t ,
...
, δJt )

S1t

= s1t (δ0t ,
...


...


SJt

= sJt (δ0t ,
...
= sj
...
, SJt )
Recall that δjt = xjt β − αpjt + ξjt hence ξjt = δjt − xjt β + αpjt
Error is now linear function of price so can use standard IV to
estimate model if we have instruments Z such that E (ξZ ) = 0

Empirical Micro
BLP

Second Step
For each market can invert this system to solve for δ as a
function of the observed markets shares and parameters
Sj
...
(δ, α, β)
δ = s −1 (S, α, β)
After inversion have J numbers δjt ≡ δjt (S0t , S1t ,
...
Why?

Empirical Micro
Instruments

Random Coefficient Logit
A well-known solution to problems with logit is to interact
product and consumer characteristics (second contribution of
BLP)
ε is EV, like the logit, but βi , αi are consumer-specific random
coefficients from a parametric distribution
uij = Xj βi − αi pj + ξj + εij
Variance is added to the term α or β so substitution patterns
can become more reasonable
Assume that βi and αi are distributed across consumers
according to some parametric distribution
The own- and cross-derivatives are more flexible
...
Why?

Empirical Micro
Instruments

One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj

So we can rewrite indirect utility as
uij = δj + µij + εij

Empirical Micro
Instruments

One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj

So we can rewrite indirect utility as
uij = δj + µij + εij

Empirical Micro
Instruments

One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj

So we can rewrite indirect utility as
uij = δj + µij + εij

Empirical Micro
Instruments

Consumer-level choice probability:
sij =

exp(δj + µij )
1 + exp(δk + µij )
k

Then aggregate market share is
sj (δ, σ) =

exp(δj + µij )
dF (v )
1 + exp(δk + µij )
k

In practice the integral is computed using simulation
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion

Empirical Micro
Instruments

Consumer-level choice probability:
sij =

exp(δj + µij )
1 + exp(δk + µij )
k

Then aggregate market share is
sj (δ, σ) =

exp(δj + µij )
dF (v )
1 + exp(δk + µij )
k

In practice the integral is computed using simulation
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion

Empirical Micro
Instruments

Consumer-level choice probability:
sij =

exp(δj + µij )
1 + exp(δk + µij )
k

Then aggregate market share is
sj (δ, σ) =

exp(δj + µij )
dF (v )
1 + exp(δk + µij )
k

In practice the integral is computed using simulation
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion

Empirical Micro
Instruments

Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj βi + ξj + εij
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj (ΠDi + νi )
Then aggregate market share is
sj

=

yiα

exp(δj + µij )
dFy ,D (y , D)dFν (ν)
+ r exp(δr + µir )

Empirical Micro
Instruments

Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj βi + ξj + εij
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj (ΠDi + νi )
Then aggregate market share is
sj

=

yiα

exp(δj + µij )
dFy ,D (y , D)dFν (ν)
+ r exp(δr + µir )

Empirical Micro
Instruments

Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj βi + ξj + εij
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj (ΠDi + νi )
Then aggregate market share is
sj

=

yiα

exp(δj + µij )
dFy ,D (y , D)dFν (ν)
+ r exp(δr + µir )

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Intuition of the Estimation Algorithm
The model is one of individual behavior, yet only aggregate
data is observed
...

We can still estimate the parameters that govern the
distribution of individuals
compute predicted individual behavior and aggregate over
individuals, for a given value of the parameters,
obtain predicted market shares

We then choose the values of the parameters that minimize
the distance between these predicted shares and the actual
observed shares
The metric under which this distance is minimized is not the
straightforward sum of least squares
rather it is the metric defined by the instrumental variables
and the GMM objective function
It is this last step that somewhat complicates the estimation
procedure

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Intuition of the Estimation Algorithm
The model is one of individual behavior, yet only aggregate
data is observed
...

We can still estimate the parameters that govern the
distribution of individuals
compute predicted individual behavior and aggregate over
individuals, for a given value of the parameters,
obtain predicted market shares

We then choose the values of the parameters that minimize
the distance between these predicted shares and the actual
observed shares
The metric under which this distance is minimized is not the
straightforward sum of least squares
rather it is the metric defined by the instrumental variables
and the GMM objective function
It is this last step that somewhat complicates the estimation
procedure

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Intuition of the Estimation Algorithm
The model is one of individual behavior, yet only aggregate
data is observed
...

We can still estimate the parameters that govern the
distribution of individuals
compute predicted individual behavior and aggregate over
individuals, for a given value of the parameters,
obtain predicted market shares

We then choose the values of the parameters that minimize
the distance between these predicted shares and the actual
observed shares
The metric under which this distance is minimized is not the
straightforward sum of least squares
rather it is the metric defined by the instrumental variables
and the GMM objective function
It is this last step that somewhat complicates the estimation
procedure

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
GMM (Generalized Method of Moments) Estimation Algorithm

Overview GMM Estimation Algorithm
Guess a parameter vector θ
Solve for δ and therefore ξ
Interact ξ and instruments Z these are the moment
conditions Q(θ)
Calculate the objective function f (θ)= Q AQ for some
positive definite A how far is Q(θ) from zero?
Guess a new parameter and try to minimize f
Variance of θ includes variance in data across products and
simulation error as well as any sampling variance in the
observed market shares
Can simplify the algorithm since δ in linear in some
parameters – see NEVO (JEMS 2000) for details

Empirical Micro
Simulation of Market Shares

Steps for Simulation
There are essentially four steps (plus an initial step) to follow
in computing the estimates:
0 prepare the data including draws from the distribution of v
and D
1 for a given value of θ and δ compute the market shares
2 for a given θ, compute the vector δ that equates the market
shares computed in Step 1 to the observed shares;
3 for a given θ, compute the structural error term (as a function
of the mean valuation computed in Step 2), interact it with
the instruments, and compute the value of the objective
function;
4 search for the value of θ that minimizes the objective function
computed in Step 3
...


Empirical Micro
Simulation of Market Shares

Steps for Simulation
There are essentially four steps (plus an initial step) to follow
in computing the estimates:
0 prepare the data including draws from the distribution of v
and D
1 for a given value of θ and δ compute the market shares
2 for a given θ, compute the vector δ that equates the market
shares computed in Step 1 to the observed shares;
3 for a given θ, compute the structural error term (as a function
of the mean valuation computed in Step 2), interact it with
the instruments, and compute the value of the objective
function;
4 search for the value of θ that minimizes the objective function
computed in Step 3
...


Empirical Micro
Simulation of Market Shares

Steps for Simulation
There are essentially four steps (plus an initial step) to follow
in computing the estimates:
0 prepare the data including draws from the distribution of v
and D
1 for a given value of θ and δ compute the market shares
2 for a given θ, compute the vector δ that equates the market
shares computed in Step 1 to the observed shares;
3 for a given θ, compute the structural error term (as a function
of the mean valuation computed in Step 2), interact it with
the instruments, and compute the value of the objective
function;
4 search for the value of θ that minimizes the objective function
computed in Step 3
...


Empirical Micro
Simulation of Market Shares

Calculating the market share via simulation:

More detail on step 1:
Condition on vi , yi – this is a logit and get closed form
Take draws on vi , yi and average over the implied logit shares:
ns
i=1

exp(µij + δj )
Σk exp(µik + δk )

BLP then provide an algorithm (a contraction mapping) that
solves for δ given the parameters and a set of simulation draws

Empirical Micro
Simulation of Market Shares

Calculating the market share via simulation:

More detail on step 1:
Condition on vi , yi – this is a logit and get closed form
Take draws on vi , yi and average over the implied logit shares:
ns
i=1

exp(µij + δj )
Σk exp(µik + δk )

BLP then provide an algorithm (a contraction mapping) that
solves for δ given the parameters and a set of simulation draws

Empirical Micro
Simulation of Market Shares

Calculating the market share via simulation:

More detail on step 1:
Condition on vi , yi – this is a logit and get closed form
Take draws on vi , yi and average over the implied logit shares:
ns
i=1

exp(µij + δj )
Σk exp(µik + δk )

BLP then provide an algorithm (a contraction mapping) that
solves for δ given the parameters and a set of simulation draws

Empirical Micro
Estimation of Supply Side

Having discussed some methods of deriving demand, we now turn
to the supply side and a consideration of equilibrium by considering
in turn:
Estimation of supply side parameters
Incorporating multi-product firms
Simultaneously estimating supply and demand
How to estimate degree of market power or presence of
collusion

Empirical Micro
Estimation of Supply Side

Having discussed some methods of deriving demand, we now turn
to the supply side and a consideration of equilibrium by considering
in turn:
Estimation of supply side parameters
Incorporating multi-product firms
Simultaneously estimating supply and demand
How to estimate degree of market power or presence of
collusion

Empirical Micro
Estimation of Supply Side

Having discussed some methods of deriving demand, we now turn
to the supply side and a consideration of equilibrium by considering
in turn:
Estimation of supply side parameters
Incorporating multi-product firms
Simultaneously estimating supply and demand
How to estimate degree of market power or presence of
collusion

Empirical Micro
Estimation of Supply Side

Having discussed some methods of deriving demand, we now turn
to the supply side and a consideration of equilibrium by considering
in turn:
Estimation of supply side parameters
Incorporating multi-product firms
Simultaneously estimating supply and demand
How to estimate degree of market power or presence of
collusion

Empirical Micro
Estimation of Supply Side

Having discussed some methods of deriving demand, we now turn
to the supply side and a consideration of equilibrium by considering
in turn:
Estimation of supply side parameters
Incorporating multi-product firms
Simultaneously estimating supply and demand
How to estimate degree of market power or presence of
collusion

Empirical Micro
Estimation of Supply Side

Supply Side
Simplest models of product differentiation involve single
product firms each producing a differentiated product
We could begin by specifying a demand system for this set of
related products, together with cost functions and an
equilibrium notion
...

Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
The first order condition is
qj + (pj − mcj )

∂q
=0
∂pj

We can rewrite as pj = mcj + bj (p)

Empirical Micro
Estimation of Supply Side

Supply Side
Simplest models of product differentiation involve single
product firms each producing a differentiated product
We could begin by specifying a demand system for this set of
related products, together with cost functions and an
equilibrium notion
...

Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
The first order condition is
qj + (pj − mcj )

∂q
=0
∂pj

We can rewrite as pj = mcj + bj (p)

Empirical Micro
Estimation of Supply Side

Supply Side
Simplest models of product differentiation involve single
product firms each producing a differentiated product
We could begin by specifying a demand system for this set of
related products, together with cost functions and an
equilibrium notion
...

Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
The first order condition is
qj + (pj − mcj )

∂q
=0
∂pj

We can rewrite as pj = mcj + bj (p)

Empirical Micro
Estimation of Supply Side

where the price-cost markup is
bj (p) =

qj
∂q
∂pj

Assume that marginal cost is
mcj = wj η + λqj + ωj
where wj might consist of X and input prices and q is output
ωj is a supply shock unobserved to the econometrician

Combining, the FOC is then
pj = wj η + λqj + bj (p) + ωj
If demand parameters are known then the markup is known
and can estimate by IV methods (eg 2SLS) where IV are
demand-side variables
Alternatively mc and demand can be estimated together

Empirical Micro
Estimation of Supply Side

where the price-cost markup is
bj (p) =

qj
∂q
∂pj

Assume that marginal cost is
mcj = wj η + λqj + ωj
where wj might consist of X and input prices and q is output
ωj is a supply shock unobserved to the econometrician

Combining, the FOC is then
pj = wj η + λqj + bj (p) + ωj
If demand parameters are known then the markup is known
and can estimate by IV methods (eg 2SLS) where IV are
demand-side variables
Alternatively mc and demand can be estimated together

Empirical Micro
Estimation of Supply Side

where the price-cost markup is
bj (p) =

qj
∂q
∂pj

Assume that marginal cost is
mcj = wj η + λqj + ωj
where wj might consist of X and input prices and q is output
ωj is a supply shock unobserved to the econometrician

Combining, the FOC is then
pj = wj η + λqj + bj (p) + ωj
If demand parameters are known then the markup is known
and can estimate by IV methods (eg 2SLS) where IV are
demand-side variables
Alternatively mc and demand can be estimated together

Empirical Micro
Estimation of Supply Side

where the price-cost markup is
bj (p) =

qj
∂q
∂pj

Assume that marginal cost is
mcj = wj η + λqj + ωj
where wj might consist of X and input prices and q is output
ωj is a supply shock unobserved to the econometrician

Combining, the FOC is then
pj = wj η + λqj + bj (p) + ωj
If demand parameters are known then the markup is known
and can estimate by IV methods (eg 2SLS) where IV are
demand-side variables
Alternatively mc and demand can be estimated together

Empirical Micro
Firm Behavior with Multi-Product Firms

Multi-Product Firms
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf

where M is market size
sj is the simulated aggregate market share

Marginal costs
mcj = wj η + ωj
Any product must have prices that satisfy
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf

Given demand can solve for marginal costs and for ωj

Empirical Micro
Firm Behavior with Multi-Product Firms

Multi-Product Firms
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf

where M is market size
sj is the simulated aggregate market share

Marginal costs
mcj = wj η + ωj
Any product must have prices that satisfy
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf

Given demand can solve for marginal costs and for ωj

Empirical Micro
Firm Behavior with Multi-Product Firms

Multi-Product Firms
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf

where M is market size
sj is the simulated aggregate market share

Marginal costs
mcj = wj η + ωj
Any product must have prices that satisfy
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf

Given demand can solve for marginal costs and for ωj

Empirical Micro
Firm Behavior with Multi-Product Firms

Multi-Product Firms
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf

where M is market size
sj is the simulated aggregate market share

Marginal costs
mcj = wj η + ωj
Any product must have prices that satisfy
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf

Given demand can solve for marginal costs and for ωj

Empirical Micro
Firm Behavior with Multi-Product Firms

Multi-Product Firms
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf

where M is market size
sj is the simulated aggregate market share

Marginal costs
mcj = wj η + ωj
Any product must have prices that satisfy
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf

Given demand can solve for marginal costs and for ωj

Empirical Micro
Firm Behavior with Multi-Product Firms

In vector form, the J FOC are
s − Ω(p − mc) = 0
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
Each element takes on the value of ∂sr (p, a)/∂pj for every
product that the firm owns

To estimate the FOC think of estimating the equation
mcj = pj − bj (p, x, ξ; θ) = wj η + ωj

Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments

Empirical Micro
Firm Behavior with Multi-Product Firms

In vector form, the J FOC are
s − Ω(p − mc) = 0
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
Each element takes on the value of ∂sr (p, a)/∂pj for every
product that the firm owns

To estimate the FOC think of estimating the equation
mcj = pj − bj (p, x, ξ; θ) = wj η + ωj

Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments

Empirical Micro
Firm Behavior with Multi-Product Firms

In vector form, the J FOC are
s − Ω(p − mc) = 0
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
Each element takes on the value of ∂sr (p, a)/∂pj for every
product that the firm owns

To estimate the FOC think of estimating the equation
mcj = pj − bj (p, x, ξ; θ) = wj η + ωj

Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments

Empirical Micro
Firm Behavior with Multi-Product Firms

In vector form, the J FOC are
s − Ω(p − mc) = 0
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
Each element takes on the value of ∂sr (p, a)/∂pj for every
product that the firm owns

To estimate the FOC think of estimating the equation
mcj = pj − bj (p, x, ξ; θ) = wj η + ωj

Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments

Empirical Micro
Firm Behavior with Multi-Product Firms

Estimation of Supply and Demand Side
Demand side moment: Restrict the model predictions for
product j’s market share to match the observed market shares
Stobs − st (δ, θ) = 0
then solve for the demand side unobservable
ξjt = δjt (S, θ) − xj β

Cost side moment:
Rearranging price FOC’s yields
mc = p − Ω−1 s
combined with marginal costs yields cost side unobservable
ω = ln(p − Ω−1 s) − w η

Empirical Micro
Firm Behavior with Multi-Product Firms

Estimation of Supply and Demand Side
Demand side moment: Restrict the model predictions for
product j’s market share to match the observed market shares
Stobs − st (δ, θ) = 0
then solve for the demand side unobservable
ξjt = δjt (S, θ) − xj β

Cost side moment:
Rearranging price FOC’s yields
mc = p − Ω−1 s
combined with marginal costs yields cost side unobservable
ω = ln(p − Ω−1 s) − w η

Empirical Micro
Firm Behavior with Multi-Product Firms

Estimation of Supply and Demand Side
Use GMM estimation to find the parameters that minimize
the objective function
Λ ZA−1 Z Λ
where A is an appropriate weighting matrix
Z are instruments orthogonal to the composite error term
Z Λ=

1
J
1
J

J
j=1 Zξ,j ξj (δ, β)
J
j=1 Zω,j ωj (δ, θ, η)

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Nevo: Measuring Market Power in the RTE Cereal Industry
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
Antitrust authorities accused firms of collusive pricing behavior
Nevo tests whether this is the case by estimating the
price-cost margin (PCM) and decomposing it into 3 sources:
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion

Overview of methodology:
use the BLP framework to estimate brand-level demand
...

compare PCMs against crude measures of actual PCM to
separate the different sources of the markup

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

Model and Data
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
uses brand dummy variables (ξj ) to capture the mean
characteristics of RTE cereal
once brand dummy variables are included in the regression, the
error term is the unobserved city-quarter specific deviation
from the overall mean valuation of the brand :structural error
is the change in ξj over time (denoted ∆ξjt )

Cannot use BLP Type Instruments
there is no variation in each brand’s observed characteristics
over time and across cities
only variation in IVs from characteristics is due to changes in
choice set of available brands
proposes alternative IV to separate the exogenous variation in
prices (due to differences in mc) and endogenous variation
(due to differences in unobserved valuation)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

IVs with brand dummies
Exploit the panel structure of the data (similar to those used
by Hausman (1996))
The identifying assumption is that, controlling for brand
specific means and demographics, city-specific valuations are
independent across cities (but are allowed to be correlated
within a city)
Given this assumption, the prices of the brands in other cities
are valid IV’s
...

One could potentially use prices in all other cities and all
quarters as instruments

Independence assumption may not hold (for instance, if there
is a national demand shock related to health of cereal)

Empirical Micro
Nevo, ECMA (2001)

Identifying Collusive Behavior
Recall the markup is given by
p − mc = Ω−1 s
With single product firms the price of each brand is set by a
profit-maximizing firm that considers only the profits from
that brand
...
In this case some off diagonals will be
non-zero
With collusion, firms act as one firm which owns all products
(ie joint profit-maximization of all the brands)
...
In this case the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly
...
In this case
the ownership matrix will have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix

Empirical Micro
Nevo, ECMA (2001)

Identifying Collusive Behavior
Recall the markup is given by
p − mc = Ω−1 s
With single product firms the price of each brand is set by a
profit-maximizing firm that considers only the profits from
that brand
...
In this case some off diagonals will be
non-zero
With collusion, firms act as one firm which owns all products
(ie joint profit-maximization of all the brands)
...
In this case the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly
...
In this case
the ownership matrix will have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix

Empirical Micro
Nevo, ECMA (2001)

Identifying Collusive Behavior
Recall the markup is given by
p − mc = Ω−1 s
With single product firms the price of each brand is set by a
profit-maximizing firm that considers only the profits from
that brand
...
In this case some off diagonals will be
non-zero
With collusion, firms act as one firm which owns all products
(ie joint profit-maximization of all the brands)
...
In this case the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly
...
In this case
the ownership matrix will have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix

Empirical Micro
Nevo, ECMA (2001)

Identifying Collusive Behavior
Recall the markup is given by
p − mc = Ω−1 s
With single product firms the price of each brand is set by a
profit-maximizing firm that considers only the profits from
that brand
...
In this case some off diagonals will be
non-zero
With collusion, firms act as one firm which owns all products
(ie joint profit-maximization of all the brands)
...
In this case the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly
...
In this case
the ownership matrix will have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix

Empirical Micro
Nevo, ECMA (2001)

Results

Compares predicted PCM under all three situations to the
observed PCM calculated using accounting data for costs
Finds that the first two effects explain most of the observed
price-cost margins
Prices in the industry are consistent with noncollusive pricing
behavior, despite the high price-cost margins
...


Empirical Micro
Nevo, ECMA (2001)

Results

Compares predicted PCM under all three situations to the
observed PCM calculated using accounting data for costs
Finds that the first two effects explain most of the observed
price-cost margins
Prices in the industry are consistent with noncollusive pricing
behavior, despite the high price-cost margins

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