Empirical Industrial Organization
Empirical Industrial Organization
Topic 1: Static Models of Differentiated Products
Michelle Sovinsky
University of Zürich
January 31, 2013
Empirical Industrial Organization
Discrete-Choice Utility
Discrete Choice Model
I
Utility of consumer i for product j
uij = U(xj , pj , vi )
I
I
I
I
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
I
I
xj is the location of the product along the line
vi is the location of the consumer
Empirical Industrial Organization
Discrete-Choice Utility
Discrete Choice Model
I
Utility of consumer i for product j
uij = U(xj , pj , vi )
I
I
I
I
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
I
I
xj is the location of the product along the line
vi is the location of the consumer
Empirical Industrial Organization
Discrete-Choice Utility
I
Vertical Model Example: (Shaked and Sutton, Bresnahan 97)
uij = vi xj − pj
I
I
xj is the quality of the product
vi is the consumer’s taste for quality (ie willingness to pay)
I
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
I
There are J alternatives in market, indexed by j = 1, ..., 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.t.pj + pz z = yi
I
j,z
Empirical Industrial Organization
Discrete-Choice Utility
I
Vertical Model Example: (Shaked and Sutton, Bresnahan 97)
uij = vi xj − pj
I
I
xj is the quality of the product
vi is the consumer’s taste for quality (ie willingness to pay)
I
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
I
There are J alternatives in market, indexed by j = 1, ..., 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.t.pj + pz z = yi
I
j,z
Empirical Industrial Organization
Discrete-Choice Utility
I
Vertical Model Example: (Shaked and Sutton, Bresnahan 97)
uij = vi xj − pj
I
I
xj is the quality of the product
vi is the consumer’s taste for quality (ie willingness to pay)
I
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
I
There are J alternatives in market, indexed by j = 1, ..., 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.t.pj + pz z = yi
I
j,z
Empirical Industrial Organization
Discrete-Choice Utility
I
Substitute in the budget constraint (ie z =
conditional indirect utility
Uij∗ (xj , pj , pz , y ) = Ui (xj ,
I
I
to derive
yi − pj
)
pz
if buy outside good
∗
Ui0
(pz , y ) = Ui (0,
I
yi −pj
pz )
yi − pj
)
pz
the consumer buys product that gives highest conditional
indirect utility maxj Uij∗ (xj , pj , pz , yi )
Why is it important to allow for outside option?
I
market wide increase in price will cause many consumers to
not buy
Empirical Industrial Organization
Discrete-Choice Utility
I
Substitute in the budget constraint (ie z =
conditional indirect utility
Uij∗ (xj , pj , pz , y ) = Ui (xj ,
I
I
to derive
yi − pj
)
pz
if buy outside good
∗
Ui0
(pz , y ) = Ui (0,
I
yi −pj
pz )
yi − pj
)
pz
the consumer buys product that gives highest conditional
indirect utility maxj Uij∗ (xj , pj , pz , yi )
Why is it important to allow for outside option?
I
market wide increase in price will cause many consumers to
not buy
Empirical Industrial Organization
Discrete-Choice Utility
I
Substitute in the budget constraint (ie z =
conditional indirect utility
Uij∗ (xj , pj , pz , y ) = Ui (xj ,
I
I
to derive
yi − pj
)
pz
if buy outside good
∗
Ui0
(pz , y ) = Ui (0,
I
yi −pj
pz )
yi − pj
)
pz
the consumer buys product that gives highest conditional
indirect utility maxj Uij∗ (xj , pj , pz , yi )
Why is it important to allow for outside option?
I
market wide increase in price will cause many consumers to
not buy
Empirical Industrial Organization
Discrete-Choice Utility
I
Substitute in the budget constraint (ie z =
conditional indirect utility
Uij∗ (xj , pj , pz , y ) = Ui (xj ,
I
I
to derive
yi − pj
)
pz
if buy outside good
∗
Ui0
(pz , y ) = Ui (0,
I
yi −pj
pz )
yi − pj
)
pz
the consumer buys product that gives highest conditional
indirect utility maxj Uij∗ (xj , pj , pz , yi )
Why is it important to allow for outside option?
I
market wide increase in price will cause many consumers to
not buy
Empirical Industrial Organization
Discrete-Choice Utility
I
Substitute in the budget constraint (ie z =
conditional indirect utility
Uij∗ (xj , pj , pz , y ) = Ui (xj ,
I
I
to derive
yi − pj
)
pz
if buy outside good
∗
Ui0
(pz , y ) = Ui (0,
I
yi −pj
pz )
yi − pj
)
pz
the consumer buys product that gives highest conditional
indirect utility maxj Uij∗ (xj , pj , pz , yi )
Why is it important to allow for outside option?
I
market wide increase in price will cause many consumers to
not buy
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Random Utility Model (RUM)(McFadden)
I
Uij∗ usually specified as a sum of two parts
Uij∗ (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij
I
I
What does it mean for tastes to be represented by product
and consumer specific random terms?
I
I
I
I
εij i.i.d. across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)
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 , ...pj , pz , yi ) = Pr ob εi0 , ..., εij : Uij∗ > Uik∗ , for j 6= k
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Random Utility Model (RUM)(McFadden)
I
Uij∗ usually specified as a sum of two parts
Uij∗ (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij
I
I
What does it mean for tastes to be represented by product
and consumer specific random terms?
I
I
I
I
εij i.i.d. across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)
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 , ...pj , pz , yi ) = Pr ob εi0 , ..., εij : Uij∗ > Uik∗ , for j 6= k
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Random Utility Model (RUM)(McFadden)
I
Uij∗ usually specified as a sum of two parts
Uij∗ (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij
I
I
What does it mean for tastes to be represented by product
and consumer specific random terms?
I
I
I
I
εij i.i.d. across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)
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 , ...pj , pz , yi ) = Pr ob εi0 , ..., εij : Uij∗ > Uik∗ , for j 6= k
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Random Utility Model (RUM)(McFadden)
I
Uij∗ usually specified as a sum of two parts
Uij∗ (xj , pj , pz , yi ) = Vij (xj , pj , pz , yi ) + εij
I
I
What does it mean for tastes to be represented by product
and consumer specific random terms?
I
I
I
I
εij i.i.d. across products and consumers; represents consumer
tastes (observed by consumer but not by the researcher)
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 , ...pj , pz , yi ) = Pr ob εi0 , ..., εij : Uij∗ > Uik∗ , for j 6= k
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
One Product Example
I
Buy good 1 (and not outside good j = 0) if
Vi0 + εi0 ≤ Vi1 + εi1 ⇐⇒ Vi0 − Vi1 ≤ εi1 − εi0
I
I
Conditional Probit: errors distributed N(0, 1)
where probability good 1 is purchased conditional on
covariates
Pr(εi1 − εi0 ≥ Vi0 − Vi1 = 1 − Φ(Vi0 − Vi1 )
I
Conditional Logit: errors distributed EV (double exponential)
F (ε) = e −e
I
−ε
with market share
si1 =
exp(Vi1 )
exp(Vi0 ) + exp(Vi1 )
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
One Product Example
I
Buy good 1 (and not outside good j = 0) if
Vi0 + εi0 ≤ Vi1 + εi1 ⇐⇒ Vi0 − Vi1 ≤ εi1 − εi0
I
I
Conditional Probit: errors distributed N(0, 1)
where probability good 1 is purchased conditional on
covariates
Pr(εi1 − εi0 ≥ Vi0 − Vi1 = 1 − Φ(Vi0 − Vi1 )
I
Conditional Logit: errors distributed EV (double exponential)
F (ε) = e −e
I
−ε
with market share
si1 =
exp(Vi1 )
exp(Vi0 ) + exp(Vi1 )
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
One Product Example
I
Buy good 1 (and not outside good j = 0) if
Vi0 + εi0 ≤ Vi1 + εi1 ⇐⇒ Vi0 − Vi1 ≤ εi1 − εi0
I
I
Conditional Probit: errors distributed N(0, 1)
where probability good 1 is purchased conditional on
covariates
Pr(εi1 − εi0 ≥ Vi0 − Vi1 = 1 − Φ(Vi0 − Vi1 )
I
Conditional Logit: errors distributed EV (double exponential)
F (ε) = e −e
I
−ε
with market share
si1 =
exp(Vi1 )
exp(Vi0 ) + exp(Vi1 )
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Multinomial Logit (MNL)
I
Attractive feature of logit is that the choice probabilities scale
up easily when we increase the number of products
sij =
exp(Vij )
J
P
exp(Vik )
k=0
I
If we add an outside good with Vij = 0
sij =
exp(Vij )
J
P
1+
exp(Vik )
k=1
I
I
I
MNL often used in discrete-choice settings
with individual level data can estimate this model using MLE
While the MNL market share is easy to calculate, the model
has unintuitive properties
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Multinomial Logit (MNL)
I
Attractive feature of logit is that the choice probabilities scale
up easily when we increase the number of products
sij =
exp(Vij )
J
P
exp(Vik )
k=0
I
If we add an outside good with Vij = 0
sij =
exp(Vij )
J
P
1+
exp(Vik )
k=1
I
I
I
MNL often used in discrete-choice settings
with individual level data can estimate this model using MLE
While the MNL market share is easy to calculate, the model
has unintuitive properties
Empirical Industrial Organization
Estimation of Random Utility Discrete Choice Models
Multinomial Logit (MNL)
I
Attractive feature of logit is that the choice probabilities scale
up easily when we increase the number of products
sij =
exp(Vij )
J
P
exp(Vik )
k=0
I
If we add an outside good with Vij = 0
sij =
exp(Vij )
J
P
1+
exp(Vik )
k=1
I
I
I
MNL often used in discrete-choice settings
with individual level data can estimate this model using MLE
While the MNL market share is easy to calculate, the model
has unintuitive properties
Empirical Industrial Organization
Implications of Assumptions on Error Term
Independence of Irrelevant Alternatives (IIA)
I
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin0
exp(Vin0 )
I
Red bus/blue bus problem: Walk or take red bus
I
I
If consumer walks half the time then siW = siRB = 0.5
odds ratio walk/RB=1
I
Introduce a red bus
I
But buses are perfect substitutes
I
I
I
I
odds ratio between walk/BB is 1
new choice prob should be siW = 0.5; siRB = siBB = 0.25
new odds ratio should be walk/RB=2
IIA is especially troubling if want to predict penetration of
new products
Empirical Industrial Organization
Implications of Assumptions on Error Term
Independence of Irrelevant Alternatives (IIA)
I
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin0
exp(Vin0 )
I
Red bus/blue bus problem: Walk or take red bus
I
I
If consumer walks half the time then siW = siRB = 0.5
odds ratio walk/RB=1
I
Introduce a red bus
I
But buses are perfect substitutes
I
I
I
I
odds ratio between walk/BB is 1
new choice prob should be siW = 0.5; siRB = siBB = 0.25
new odds ratio should be walk/RB=2
IIA is especially troubling if want to predict penetration of
new products
Empirical Industrial Organization
Implications of Assumptions on Error Term
Independence of Irrelevant Alternatives (IIA)
I
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin0
exp(Vin0 )
I
Red bus/blue bus problem: Walk or take red bus
I
I
If consumer walks half the time then siW = siRB = 0.5
odds ratio walk/RB=1
I
Introduce a red bus
I
But buses are perfect substitutes
I
I
I
I
odds ratio between walk/BB is 1
new choice prob should be siW = 0.5; siRB = siBB = 0.25
new odds ratio should be walk/RB=2
IIA is especially troubling if want to predict penetration of
new products
Empirical Industrial Organization
Implications of Assumptions on Error Term
Independence of Irrelevant Alternatives (IIA)
I
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin0
exp(Vin0 )
I
Red bus/blue bus problem: Walk or take red bus
I
I
If consumer walks half the time then siW = siRB = 0.5
odds ratio walk/RB=1
I
Introduce a red bus
I
But buses are perfect substitutes
I
I
I
I
odds ratio between walk/BB is 1
new choice prob should be siW = 0.5; siRB = siBB = 0.25
new odds ratio should be walk/RB=2
IIA is especially troubling if want to predict penetration of
new products
Empirical Industrial Organization
Implications of Assumptions on Error Term
Independence of Irrelevant Alternatives (IIA)
I
ratio of choice prob (odds ratio) does not depend on the
number of alternatives available
exp(Vij )
sij
=
sin0
exp(Vin0 )
I
Red bus/blue bus problem: Walk or take red bus
I
I
If consumer walks half the time then siW = siRB = 0.5
odds ratio walk/RB=1
I
Introduce a red bus
I
But buses are perfect substitutes
I
I
I
I
odds ratio between walk/BB is 1
new choice prob should be siW = 0.5; siRB = siBB = 0.25
new odds ratio should be walk/RB=2
IIA is especially troubling if want to predict penetration of
new products
Empirical Industrial Organization
Implications of Assumptions on Error Term
Price Elasticities of Demand
I
Let Vij = αpj + xj β
I
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk
= −αsij (1 − sij )
= αsij sik
I
Is it concerning that they depend only on the market shares of
the products?
I
Yes, do not depend on the degree to which products have
similar characteristics
Empirical Industrial Organization
Implications of Assumptions on Error Term
Price Elasticities of Demand
I
Let Vij = αpj + xj β
I
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk
= −αsij (1 − sij )
= αsij sik
I
Is it concerning that they depend only on the market shares of
the products?
I
Yes, do not depend on the degree to which products have
similar characteristics
Empirical Industrial Organization
Implications of Assumptions on Error Term
Price Elasticities of Demand
I
Let Vij = αpj + xj β
I
then own and cross-price elasticity of demand between two
products
∂sij
∂pj
∂sij
∂pk
= −αsij (1 − sij )
= αsij sik
I
Is it concerning that they depend only on the market shares of
the products?
I
Yes, do not depend on the degree to which products have
similar characteristics
Empirical Industrial Organization
Implications of Assumptions on Error Term
Counter-intuitive substitution patterns:
I
Not only from the distributional logit assumption
I
Due to assumption that the only variance in consumer tastes
comes through the i.i.d. product-specific terms εij
I
Since i.i.d., there is no source of correlation in consumer
tastes across similar products
I
Changes to allow for more intuitive substitution patterns
I
I
I
I
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 Industrial Organization
Implications of Assumptions on Error Term
Counter-intuitive substitution patterns:
I
Not only from the distributional logit assumption
I
Due to assumption that the only variance in consumer tastes
comes through the i.i.d. product-specific terms εij
I
Since i.i.d., there is no source of correlation in consumer
tastes across similar products
I
Changes to allow for more intuitive substitution patterns
I
I
I
I
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 Industrial Organization
Implications of Assumptions on Error Term
Counter-intuitive substitution patterns:
I
Not only from the distributional logit assumption
I
Due to assumption that the only variance in consumer tastes
comes through the i.i.d. product-specific terms εij
I
Since i.i.d., there is no source of correlation in consumer
tastes across similar products
I
Changes to allow for more intuitive substitution patterns
I
I
I
I
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 Industrial Organization
Implications of Assumptions on Error Term
Counter-intuitive substitution patterns:
I
Not only from the distributional logit assumption
I
Due to assumption that the only variance in consumer tastes
comes through the i.i.d. product-specific terms εij
I
Since i.i.d., there is no source of correlation in consumer
tastes across similar products
I
Changes to allow for more intuitive substitution patterns
I
I
I
I
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 Industrial Organization
Implications of Assumptions on Error Term
Counter-intuitive substitution patterns:
I
Not only from the distributional logit assumption
I
Due to assumption that the only variance in consumer tastes
comes through the i.i.d. product-specific terms εij
I
Since i.i.d., there is no source of correlation in consumer
tastes across similar products
I
Changes to allow for more intuitive substitution patterns
I
I
I
I
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 Industrial Organization
Models with Correlations Across Consumer Tastes
Generalized EV models (McFadden 1978, 1981)
I
Allows for correlations over alternatives
I
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
I
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
I
I
I
I
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 Industrial Organization
Models with Correlations Across Consumer Tastes
Generalized EV models (McFadden 1978, 1981)
I
Allows for correlations over alternatives
I
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
I
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
I
I
I
I
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 Industrial Organization
Models with Correlations Across Consumer Tastes
Generalized EV models (McFadden 1978, 1981)
I
Allows for correlations over alternatives
I
When all correlations are zero the GEV distribution becomes
the product of EV distributions and GEV becomes standard
logit model
I
Advantage that choice probabilities usually take a closed form,
so they can be estimated without simulation
Most widely used is Nested Logit Model
I
I
I
I
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 Industrial Organization
Models with Correlations Across Consumer Tastes
Nested Logit Model
I
I
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
I
Define the inclusive value of nest g as:
X
uij
sig =
exp
1−σ
j∈g
I
I
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)
I
need to compute a high dimensional integral and this is tough
Empirical Industrial Organization
Models with Correlations Across Consumer Tastes
Nested Logit Model
I
I
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
I
Define the inclusive value of nest g as:
X
uij
sig =
exp
1−σ
j∈g
I
I
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)
I
need to compute a high dimensional integral and this is tough
Empirical Industrial Organization
Models with Correlations Across Consumer Tastes
Nested Logit Model
I
I
Within-group correlation parameter is σg
Across nests, parameter σ (within (0,1)) describes correlation
between nests
uij = xj β − αpj + σg vig + εij
I
Define the inclusive value of nest g as:
X
uij
sig =
exp
1−σ
j∈g
I
I
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)
I
need to compute a high dimensional integral and this is tough
Empirical Industrial Organization
BLP
Berry, Levinsohn, Pakes (BLP) 1995 ECMA
I
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
I
endogenous prices and random coefficients.
I
consistent estimation even with imperfect competition
I
To motivate framework consider Berry (RAND, 1994)
I
I
K observed product characteristics: Xjt = (xj,1,t , ..., xj,K ,t )0
I
I
There are i = 1, ..., I = ∞ agents in t = 1, ..., T markets who
choose among j = 1, ..., J mutually exclusive alternatives
Product characteristics/choice sets may evolve over markets
one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
I
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j
Empirical Industrial Organization
BLP
Berry, Levinsohn, Pakes (BLP) 1995 ECMA
I
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
I
endogenous prices and random coefficients.
I
consistent estimation even with imperfect competition
I
To motivate framework consider Berry (RAND, 1994)
I
I
K observed product characteristics: Xjt = (xj,1,t , ..., xj,K ,t )0
I
I
There are i = 1, ..., I = ∞ agents in t = 1, ..., T markets who
choose among j = 1, ..., J mutually exclusive alternatives
Product characteristics/choice sets may evolve over markets
one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
I
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j
Empirical Industrial Organization
BLP
Berry, Levinsohn, Pakes (BLP) 1995 ECMA
I
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
I
endogenous prices and random coefficients.
I
consistent estimation even with imperfect competition
I
To motivate framework consider Berry (RAND, 1994)
I
I
K observed product characteristics: Xjt = (xj,1,t , ..., xj,K ,t )0
I
I
There are i = 1, ..., I = ∞ agents in t = 1, ..., T markets who
choose among j = 1, ..., J mutually exclusive alternatives
Product characteristics/choice sets may evolve over markets
one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
I
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j
Empirical Industrial Organization
BLP
Berry, Levinsohn, Pakes (BLP) 1995 ECMA
I
Method for estimating demand in differentiated product
markets using aggregate data (ie only data on market shares
not individual choices)
I
endogenous prices and random coefficients.
I
consistent estimation even with imperfect competition
I
To motivate framework consider Berry (RAND, 1994)
I
I
K observed product characteristics: Xjt = (xj,1,t , ..., xj,K ,t )0
I
I
There are i = 1, ..., I = ∞ agents in t = 1, ..., T markets who
choose among j = 1, ..., J mutually exclusive alternatives
Product characteristics/choice sets may evolve over markets
one unobserved product characteristics: ξjt = ξj + ξt + ∆ξjt
I
ξj is a permanent component for j; ξt is a common shock and
∆ξjt is a product/time specific shock for j
Empirical Industrial Organization
BLP
I
Consumer i’s indirect utility is given by
Uijt = Xjt0 β − αpjt + ξjt +εijt
|
{z
}
≡ δjt
I
Derive market-level (aggregate) share expression from
individual model of discrete-choice
I
εijt are iid EV so the probability i chooses j is given by
sijt =
exp(δjt )
P
1 + exp(δkt )
k
I
Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =
exp(δjt )
1
P
[Msijt ] =
M
1 + exp(δkt )
k
Empirical Industrial Organization
BLP
I
Consumer i’s indirect utility is given by
Uijt = Xjt0 β − αpjt + ξjt +εijt
|
{z
}
≡ δjt
I
Derive market-level (aggregate) share expression from
individual model of discrete-choice
I
εijt are iid EV so the probability i chooses j is given by
sijt =
exp(δjt )
P
1 + exp(δkt )
k
I
Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =
exp(δjt )
1
P
[Msijt ] =
M
1 + exp(δkt )
k
Empirical Industrial Organization
BLP
I
Consumer i’s indirect utility is given by
Uijt = Xjt0 β − αpjt + ξjt +εijt
|
{z
}
≡ δjt
I
Derive market-level (aggregate) share expression from
individual model of discrete-choice
I
εijt are iid EV so the probability i chooses j is given by
sijt =
exp(δjt )
P
1 + exp(δkt )
k
I
Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =
exp(δjt )
1
P
[Msijt ] =
M
1 + exp(δkt )
k
Empirical Industrial Organization
BLP
I
Consumer i’s indirect utility is given by
Uijt = Xjt0 β − αpjt + ξjt +εijt
|
{z
}
≡ δjt
I
Derive market-level (aggregate) share expression from
individual model of discrete-choice
I
εijt are iid EV so the probability i chooses j is given by
sijt =
exp(δjt )
P
1 + exp(δkt )
k
I
Aggregate market shares for product j are (weighted) sum of
individual choice probabilities (M is the market size)
sjt =
exp(δjt )
1
P
[Msijt ] =
M
1 + exp(δkt )
k
Empirical Industrial Organization
BLP
I
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
I
This is why I = ∞ is important
I
Model differs from standard conditional logit in two ways:
I
First, unobserved demand shock ξ
I
I
I
I
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 Industrial Organization
BLP
I
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
I
This is why I = ∞ is important
I
Model differs from standard conditional logit in two ways:
I
First, unobserved demand shock ξ
I
I
I
I
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 Industrial Organization
BLP
I
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
I
This is why I = ∞ is important
I
Model differs from standard conditional logit in two ways:
I
First, unobserved demand shock ξ
I
I
I
I
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 Industrial Organization
BLP
I
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
I
This is why I = ∞ is important
I
Model differs from standard conditional logit in two ways:
I
First, unobserved demand shock ξ
I
I
I
I
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 Industrial Organization
BLP
I
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
I
This is why I = ∞ is important
I
Model differs from standard conditional logit in two ways:
I
First, unobserved demand shock ξ
I
I
I
I
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 Industrial Organization
BLP
Naive Estimation
I
We observe market shares in the data; and model yields
predicted shares from previous slide (denote b
sjt )
I
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
I
Minimize squared distance between Sjt and b
sjt
I
What is the problem with this?
I
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
I
Berry (1994) suggests a clever IV based estimation approach
Empirical Industrial Organization
BLP
Naive Estimation
I
We observe market shares in the data; and model yields
predicted shares from previous slide (denote b
sjt )
I
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
I
Minimize squared distance between Sjt and b
sjt
I
What is the problem with this?
I
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
I
Berry (1994) suggests a clever IV based estimation approach
Empirical Industrial Organization
BLP
Naive Estimation
I
We observe market shares in the data; and model yields
predicted shares from previous slide (denote b
sjt )
I
Estimate parameters (α, β) by finding value of parameters
which match observed shares to predicted shares
I
Minimize squared distance between Sjt and b
sjt
I
What is the problem with this?
I
Problem: ξj enters market shares in a highly non-linear
fashion and is correlated with prices (at least)
I
Berry (1994) suggests a clever IV based estimation approach
Empirical Industrial Organization
BLP
Berry Inversion: First Step
I
At the true value of the parameters
Sjt = b
sjt (δ, α, β)
I
For each market, this gives us a system of J + 1 nonlinear
equations in the J + 1 unknowns ξ0t , ..., ξJt
I
S0t
= b
s0t (δ0t , ..., δJt )
S1t
= b
s1t (δ0t , ..., δJt )
..
.
SJt
= b
sJt (δ0t , ..., δJt )
Note: Since 1 =
J
P
sjt by construction, the equations are
j=0
linearly dependent so need to normalize δ0t = 0 and use only J
equations
Empirical Industrial Organization
BLP
Second Step
I
For each market can invert this system to solve for δ as a
function of the observed markets shares and parameters
Sj. = b
sj. (δ, α, β)
δ =b
s −1 (S, α, β)
I
I
I
After inversion have J numbers δbjt ≡ δjt (S0t , S1t , ..., SJt )
Recall that δjt = xjt β − αpjt + ξjt hence ξjt = δbjt − 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 Industrial Organization
BLP
Second Step
I
For each market can invert this system to solve for δ as a
function of the observed markets shares and parameters
Sj. = b
sj. (δ, α, β)
δ =b
s −1 (S, α, β)
I
I
I
After inversion have J numbers δbjt ≡ δjt (S0t , S1t , ..., SJt )
Recall that δjt = xjt β − αpjt + ξjt hence ξjt = δbjt − 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 Industrial Organization
BLP
Inversion Example: Berry Logit
I
Simple example of the inversion step: MNL shares
b
sjt (δ) =
exp(δjt )
J
P
exp(δkt )
1+
k=1
log b
sjt = δjt − log 1 +
J
X
!
exp(δkt )
k=1
I
but notice for outside good
log b
s0t = 0 − log 1 +
J
X
k=1
I
so δjt = log b
sjt − log b
s0t
!
exp(δkt )
Empirical Industrial Organization
BLP
Inversion Example: Berry Logit
I
Simple example of the inversion step: MNL shares
b
sjt (δ) =
exp(δjt )
J
P
exp(δkt )
1+
k=1
log b
sjt = δjt − log 1 +
J
X
!
exp(δkt )
k=1
I
but notice for outside good
log b
s0t = 0 − log 1 +
J
X
k=1
I
so δjt = log b
sjt − log b
s0t
!
exp(δkt )
Empirical Industrial Organization
BLP
Inversion Example: Berry Logit
I
Simple example of the inversion step: MNL shares
b
sjt (δ) =
exp(δjt )
J
P
exp(δkt )
1+
k=1
log b
sjt = δjt − log 1 +
J
X
!
exp(δkt )
k=1
I
but notice for outside good
log b
s0t = 0 − log 1 +
J
X
k=1
I
so δjt = log b
sjt − log b
s0t
!
exp(δkt )
Empirical Industrial Organization
BLP
I
This implies
(log Sjt − log S0t ) = δjt = Xjt β − αpjt + ξjt
I
I
Can be estimated by OLS
I
I
I
I
where S0t is the share of the outside good
dependent variable log Sjt − log S0t
covariates Xjt , pjt , and error term: ξjt
When there is not a closed form solution for the market share
then solve for ξ structural error and construct moment
condition
Restrict the model predictions for product j’s market share to
match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − Xjt0 β − αpjt
Empirical Industrial Organization
BLP
I
This implies
(log Sjt − log S0t ) = δjt = Xjt β − αpjt + ξjt
I
I
Can be estimated by OLS
I
I
I
I
where S0t is the share of the outside good
dependent variable log Sjt − log S0t
covariates Xjt , pjt , and error term: ξjt
When there is not a closed form solution for the market share
then solve for ξ structural error and construct moment
condition
Restrict the model predictions for product j’s market share to
match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − Xjt0 β − αpjt
Empirical Industrial Organization
BLP
I
This implies
(log Sjt − log S0t ) = δjt = Xjt β − αpjt + ξjt
I
I
Can be estimated by OLS
I
I
I
I
where S0t is the share of the outside good
dependent variable log Sjt − log S0t
covariates Xjt , pjt , and error term: ξjt
When there is not a closed form solution for the market share
then solve for ξ structural error and construct moment
condition
Restrict the model predictions for product j’s market share to
match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − Xjt0 β − αpjt
Empirical Industrial Organization
BLP
I
This implies
(log Sjt − log S0t ) = δjt = Xjt β − αpjt + ξjt
I
I
Can be estimated by OLS
I
I
I
I
where S0t is the share of the outside good
dependent variable log Sjt − log S0t
covariates Xjt , pjt , and error term: ξjt
When there is not a closed form solution for the market share
then solve for ξ structural error and construct moment
condition
Restrict the model predictions for product j’s market share to
match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − Xjt0 β − αpjt
Empirical Industrial Organization
BLP
I
construct the moment condition
J
1X
E [(δjt (S) − Xjt β + αpjt )Z ] ≡ Qjt (α, β)
J
j=1
I
Can estimate α and β by minimizing
min Qjt (α, β)2
α,β
I
Why does this work?
I
As J gets large, by the law of large numbers Qjt (α, β)
converges to E [(δjt − Xjt β + αpjt )Z ]
I
If there exist appropriate instruments Z then at the true
values of the parameters this expectation is equal to zero
I
Hence, the (α, β) that minimizes Qjt (α, β)2 should be close to
the true parameter values
Empirical Industrial Organization
BLP
I
construct the moment condition
J
1X
E [(δjt (S) − Xjt β + αpjt )Z ] ≡ Qjt (α, β)
J
j=1
I
Can estimate α and β by minimizing
min Qjt (α, β)2
α,β
I
Why does this work?
I
As J gets large, by the law of large numbers Qjt (α, β)
converges to E [(δjt − Xjt β + αpjt )Z ]
I
If there exist appropriate instruments Z then at the true
values of the parameters this expectation is equal to zero
I
Hence, the (α, β) that minimizes Qjt (α, β)2 should be close to
the true parameter values
Empirical Industrial Organization
BLP
I
construct the moment condition
J
1X
E [(δjt (S) − Xjt β + αpjt )Z ] ≡ Qjt (α, β)
J
j=1
I
Can estimate α and β by minimizing
min Qjt (α, β)2
α,β
I
Why does this work?
I
As J gets large, by the law of large numbers Qjt (α, β)
converges to E [(δjt − Xjt β + αpjt )Z ]
I
If there exist appropriate instruments Z then at the true
values of the parameters this expectation is equal to zero
I
Hence, the (α, β) that minimizes Qjt (α, β)2 should be close to
the true parameter values
Empirical Industrial Organization
Instruments
What are appropriate instruments?
I
IV for j should be correlated with pj but not with structural
error ξj
I
Usual demand case: cost shifters
I
but we have cross-sectional (across products) data, so we
require IV to vary across products within a market
I
Example: cars, one natural cost shifter are wages in Michigan
I
Here doesn’t work because its the same across all products
I
if ran 2SLS with wages in Michigan as IV, first stage regression
of price on wage would yield the same predicted price for all
products
Empirical Industrial Organization
Instruments
What are appropriate instruments?
I
IV for j should be correlated with pj but not with structural
error ξj
I
Usual demand case: cost shifters
I
but we have cross-sectional (across products) data, so we
require IV to vary across products within a market
I
Example: cars, one natural cost shifter are wages in Michigan
I
Here doesn’t work because its the same across all products
I
if ran 2SLS with wages in Michigan as IV, first stage regression
of price on wage would yield the same predicted price for all
products
Empirical Industrial Organization
Instruments
What are appropriate instruments?
I
IV for j should be correlated with pj but not with structural
error ξj
I
Usual demand case: cost shifters
I
but we have cross-sectional (across products) data, so we
require IV to vary across products within a market
I
Example: cars, one natural cost shifter are wages in Michigan
I
Here doesn’t work because its the same across all products
I
if ran 2SLS with wages in Michigan as IV, first stage regression
of price on wage would yield the same predicted price for all
products
Empirical Industrial Organization
Instruments
What are appropriate instruments?
I
IV for j should be correlated with pj but not with structural
error ξj
I
Usual demand case: cost shifters
I
but we have cross-sectional (across products) data, so we
require IV to vary across products within a market
I
Example: cars, one natural cost shifter are wages in Michigan
I
Here doesn’t work because its the same across all products
I
if ran 2SLS with wages in Michigan as IV, first stage regression
of price on wage would yield the same predicted price for all
products
Empirical Industrial Organization
Instruments
BLP instruments
I
BLP impose mean independence assumption: assume that ξ
ar uncorrelated with product characteristics (equivalent to
saying product characteristics are exogenous or at least
pre-determined)
I
I
I
I
I
I
exploit competition within market to derive IV
oligopolistic competition makes firm j set price pj as a function
of characteristics of all cars produced
Example: GM’s price for Hum-Vee will depend on how closely
substitutable a Jeep is with a Hum-Vee)
However, characteristics of rival cars should not affect
households valuation of firm j’s car
that is Xk are correlated with pj but aren’t correlated with ξ
so BLP instruments are functions of rival product
characteristics
Empirical Industrial Organization
Instruments
BLP instruments
I
BLP impose mean independence assumption: assume that ξ
ar uncorrelated with product characteristics (equivalent to
saying product characteristics are exogenous or at least
pre-determined)
I
I
I
I
I
I
exploit competition within market to derive IV
oligopolistic competition makes firm j set price pj as a function
of characteristics of all cars produced
Example: GM’s price for Hum-Vee will depend on how closely
substitutable a Jeep is with a Hum-Vee)
However, characteristics of rival cars should not affect
households valuation of firm j’s car
that is Xk are correlated with pj but aren’t correlated with ξ
so BLP instruments are functions of rival product
characteristics
Empirical Industrial Organization
Instruments
BLP instruments
I
BLP impose mean independence assumption: assume that ξ
ar uncorrelated with product characteristics (equivalent to
saying product characteristics are exogenous or at least
pre-determined)
I
I
I
I
I
I
exploit competition within market to derive IV
oligopolistic competition makes firm j set price pj as a function
of characteristics of all cars produced
Example: GM’s price for Hum-Vee will depend on how closely
substitutable a Jeep is with a Hum-Vee)
However, characteristics of rival cars should not affect
households valuation of firm j’s car
that is Xk are correlated with pj but aren’t correlated with ξ
so BLP instruments are functions of rival product
characteristics
Empirical Industrial Organization
Instruments
BLP instruments
I
BLP impose mean independence assumption: assume that ξ
ar uncorrelated with product characteristics (equivalent to
saying product characteristics are exogenous or at least
pre-determined)
I
I
I
I
I
I
exploit competition within market to derive IV
oligopolistic competition makes firm j set price pj as a function
of characteristics of all cars produced
Example: GM’s price for Hum-Vee will depend on how closely
substitutable a Jeep is with a Hum-Vee)
However, characteristics of rival cars should not affect
households valuation of firm j’s car
that is Xk are correlated with pj but aren’t correlated with ξ
so BLP instruments are functions of rival product
characteristics
Empirical Industrial Organization
Instruments
BLP instruments
I
BLP impose mean independence assumption: assume that ξ
ar uncorrelated with product characteristics (equivalent to
saying product characteristics are exogenous or at least
pre-determined)
I
I
I
I
I
I
exploit competition within market to derive IV
oligopolistic competition makes firm j set price pj as a function
of characteristics of all cars produced
Example: GM’s price for Hum-Vee will depend on how closely
substitutable a Jeep is with a Hum-Vee)
However, characteristics of rival cars should not affect
households valuation of firm j’s car
that is Xk are correlated with pj but aren’t correlated with ξ
so BLP instruments are functions of rival product
characteristics
Empirical Industrial Organization
Instruments
Random Coefficient Logit
I
A well-known solution to problems with logit is to interact
product and consumer characteristics (second contribution of
BLP)
I
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
I
I
I
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 Industrial Organization
Instruments
Random Coefficient Logit
I
A well-known solution to problems with logit is to interact
product and consumer characteristics (second contribution of
BLP)
I
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
I
I
I
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 Industrial Organization
Instruments
Random Coefficient Logit
I
A well-known solution to problems with logit is to interact
product and consumer characteristics (second contribution of
BLP)
I
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
I
I
I
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 Industrial Organization
Instruments
I
One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
I
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
I
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj
I
So we can rewrite indirect utility as
uij = δj + µij + εij
Empirical Industrial Organization
Instruments
I
One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
I
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
I
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj
I
So we can rewrite indirect utility as
uij = δj + µij + εij
Empirical Industrial Organization
Instruments
I
One commonly used specification is the logit model with
random (normal) coefficients
Uij = Xj βi − αpj + ξj + εij
I
The K random coefficients (one for each product
characteristic) are
βik = βk + σk vik
vik ∼ N(0, 1), iid
I
it is useful to decompose utility into two parts
µij = Σk σk Xjk vik
δj = Xj βk − αpj + ξj
I
So we can rewrite indirect utility as
uij = δj + µij + εij
Empirical Industrial Organization
Instruments
I
Consumer-level choice probability:
sij =
exp(δj + µij )
P
1 + exp(δk + µij )
k
I
Then aggregate market share is
Z
sj (δ, σ) =
exp(δj + µij )
P
dF (v )
1 + exp(δk + µij )
k
I
In practice the integral is computed using simulation
I
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion
Empirical Industrial Organization
Instruments
I
Consumer-level choice probability:
sij =
exp(δj + µij )
P
1 + exp(δk + µij )
k
I
Then aggregate market share is
Z
sj (δ, σ) =
exp(δj + µij )
P
dF (v )
1 + exp(δk + µij )
k
I
In practice the integral is computed using simulation
I
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion
Empirical Industrial Organization
Instruments
I
Consumer-level choice probability:
sij =
exp(δj + µij )
P
1 + exp(δk + µij )
k
I
Then aggregate market share is
Z
sj (δ, σ) =
exp(δj + µij )
P
dF (v )
1 + exp(δk + µij )
k
I
In practice the integral is computed using simulation
I
Once have predicted (simulated) market share, find the δ that
matches the observed market shares given σ using the Berry
inversion
Empirical Industrial Organization
Instruments
I
Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj0 βi + ξj + εij
I
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
I
0
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj0 (ΠDi + νi )
I
Then aggregate market share is
Z
exp(δj + µij )
P
dFy ,D (y , D)dFν (ν)
sj =
α
yi + r exp(δr + µir )
Empirical Industrial Organization
Instruments
I
Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj0 βi + ξj + εij
I
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
I
0
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj0 (ΠDi + νi )
I
Then aggregate market share is
Z
exp(δj + µij )
P
sj =
dFy ,D (y , D)dFν (ν)
α
yi + r exp(δr + µir )
Empirical Industrial Organization
Instruments
I
Common to also have interactions of observed product
characteristics and ”observed” consumer characteristics,
denoted Di
uij = α ln(yi − pj ) + xj0 βi + ξj + εij
I
where
βi = β + ΠDi + Σνi
νi ∼ N(0, Ik )
I
0
with δj = xj β + ξj and
µij = α ln(yi − pj ) + xj0 (ΠDi + νi )
I
Then aggregate market share is
Z
exp(δj + µij )
P
sj =
dFy ,D (y , D)dFν (ν)
α
yi + r exp(δr + µir )
Empirical Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Intuition of the Estimation Algorithm
I
I
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
I
I
I
I
I
I
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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
GMM (Generalized Method of Moments) Estimation Algorithm
Overview GMM Estimation Algorithm
I
Guess a parameter vector θ
I
Solve for δ and therefore ξ
I
Interact ξ and instruments Z these are the moment
conditions Q(θ)
I
Calculate the objective function f (θ)= Q 0 AQ for some
positive definite A how far is Q(θ) from zero?
I
I
I
Guess a new parameter and try to minimize f
Variance of θb 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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Steps for Simulation
I
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 Industrial Organization
Simulation of Market Shares
Calculating the market share via simulation:
I
More detail on step 1:
I
Condition on vi , yi – this is a logit and get closed form
I
Take draws on vi , yi and average over the implied logit shares:
ns
X
i=1
I
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 Industrial Organization
Simulation of Market Shares
Calculating the market share via simulation:
I
More detail on step 1:
I
Condition on vi , yi – this is a logit and get closed form
I
Take draws on vi , yi and average over the implied logit shares:
ns
X
i=1
I
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 Industrial Organization
Simulation of Market Shares
Calculating the market share via simulation:
I
More detail on step 1:
I
Condition on vi , yi – this is a logit and get closed form
I
Take draws on vi , yi and average over the implied logit shares:
ns
X
i=1
I
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 Industrial Organization
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:
I
Estimation of supply side parameters
I
Incorporating multi-product firms
I
Simultaneously estimating supply and demand
I
How to estimate degree of market power or presence of
collusion
Empirical Industrial Organization
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:
I
Estimation of supply side parameters
I
Incorporating multi-product firms
I
Simultaneously estimating supply and demand
I
How to estimate degree of market power or presence of
collusion
Empirical Industrial Organization
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:
I
Estimation of supply side parameters
I
Incorporating multi-product firms
I
Simultaneously estimating supply and demand
I
How to estimate degree of market power or presence of
collusion
Empirical Industrial Organization
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:
I
Estimation of supply side parameters
I
Incorporating multi-product firms
I
Simultaneously estimating supply and demand
I
How to estimate degree of market power or presence of
collusion
Empirical Industrial Organization
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:
I
Estimation of supply side parameters
I
Incorporating multi-product firms
I
Simultaneously estimating supply and demand
I
How to estimate degree of market power or presence of
collusion
Empirical Industrial Organization
Estimation of Supply Side
Supply Side
I
I
I
I
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.
The usual assumption is Nash-in-prices.
Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
I
The first order condition is
qj + (pj − mcj )
I
∂q
=0
∂pj
We can rewrite as pj = mcj + bj (p)
Empirical Industrial Organization
Estimation of Supply Side
Supply Side
I
I
I
I
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.
The usual assumption is Nash-in-prices.
Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
I
The first order condition is
qj + (pj − mcj )
I
∂q
=0
∂pj
We can rewrite as pj = mcj + bj (p)
Empirical Industrial Organization
Estimation of Supply Side
Supply Side
I
I
I
I
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.
The usual assumption is Nash-in-prices.
Profits of firm j are given by
πj (p) = pj qj (p) − Cj (qj (p))
I
The first order condition is
qj + (pj − mcj )
I
∂q
=0
∂pj
We can rewrite as pj = mcj + bj (p)
Empirical Industrial Organization
Estimation of Supply Side
I
where the price-cost markup is
qj
bj (p) = ∂q
∂pj I
Assume that marginal cost is
mcj = wj η + λqj + ωj
I
I
I
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
I
I
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 Industrial Organization
Estimation of Supply Side
I
where the price-cost markup is
qj
bj (p) = ∂q
∂pj I
Assume that marginal cost is
mcj = wj η + λqj + ωj
I
I
I
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
I
I
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 Industrial Organization
Estimation of Supply Side
I
where the price-cost markup is
qj
bj (p) = ∂q
∂pj I
Assume that marginal cost is
mcj = wj η + λqj + ωj
I
I
I
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
I
I
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 Industrial Organization
Estimation of Supply Side
I
where the price-cost markup is
qj
bj (p) = ∂q
∂pj I
Assume that marginal cost is
mcj = wj η + λqj + ωj
I
I
I
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
I
I
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 Industrial Organization
Firm Behavior with Multi-Product Firms
Multi-Product Firms
I
I
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
X
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf
I
I
I
where M is market size
sj is the simulated aggregate market share
Marginal costs
mcj = wj0 η + ωj
I
Any product must have prices that satisfy
X
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf
I
Given demand can solve for marginal costs and for ωj
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Multi-Product Firms
I
I
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
X
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf
I
I
I
where M is market size
sj is the simulated aggregate market share
Marginal costs
mcj = wj0 η + ωj
I
Any product must have prices that satisfy
X
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf
I
Given demand can solve for marginal costs and for ωj
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Multi-Product Firms
I
I
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
X
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf
I
I
I
where M is market size
sj is the simulated aggregate market share
Marginal costs
mcj = wj0 η + ωj
I
Any product must have prices that satisfy
X
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf
I
Given demand can solve for marginal costs and for ωj
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Multi-Product Firms
I
I
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
X
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf
I
I
I
where M is market size
sj is the simulated aggregate market share
Marginal costs
mcj = wj0 η + ωj
I
Any product must have prices that satisfy
X
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf
I
Given demand can solve for marginal costs and for ωj
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Multi-Product Firms
I
I
Non-cooperative oligopolistic Bertrand competition
Firm f produces a subset j ∈ Jf of the products: Profits
X
(pj − mcj )Msj (p, X , ξ; θ)
j∈Jf
I
I
I
where M is market size
sj is the simulated aggregate market share
Marginal costs
mcj = wj0 η + ωj
I
Any product must have prices that satisfy
X
∂sr (p, a)
sj (p, a) +
(pr − mcr )
=0
∂pj
r ∈Jf
I
Given demand can solve for marginal costs and for ωj
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
I
In vector form, the J FOC are
s − Ω(p − mc) = 0
I
I
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
I
I
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) = wj0 η + ωj
I
Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
I
In vector form, the J FOC are
s − Ω(p − mc) = 0
I
I
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
I
I
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) = wj0 η + ωj
I
Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
I
In vector form, the J FOC are
s − Ω(p − mc) = 0
I
I
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
I
I
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) = wj0 η + ωj
I
Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
I
In vector form, the J FOC are
s − Ω(p − mc) = 0
I
I
Notice this implies a markup equation p − mc = Ω−1 s
Ω is called the ownership matrix (of dimension JxJ)
I
I
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) = wj0 η + ωj
I
Just as in estimating demand, estimates of the parameters η
can be obtained from orthogonality conditions between ω and
appropriate instruments
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Estimation of Supply and Demand Side
I
Demand side moment: Restrict the model predictions for
product j’s market share to match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − xj0 β
I
I
Cost side moment:
Rearranging price FOC’s yields
mc = p − Ω−1 s
I
combined with marginal costs yields cost side unobservable
ω = ln(p − Ω−1 s) − w 0 η
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Estimation of Supply and Demand Side
I
Demand side moment: Restrict the model predictions for
product j’s market share to match the observed market shares
Stobs − st (δ, θ) = 0
I
then solve for the demand side unobservable
ξjt = δjt (S, θ) − xj0 β
I
I
Cost side moment:
Rearranging price FOC’s yields
mc = p − Ω−1 s
I
combined with marginal costs yields cost side unobservable
ω = ln(p − Ω−1 s) − w 0 η
Empirical Industrial Organization
Firm Behavior with Multi-Product Firms
Estimation of Supply and Demand Side
I
Use GMM estimation to find the parameters that minimize
the objective function
Λ0 ZA−1 Z 0 Λ
I
where A is an appropriate weighting matrix
I
Z are instruments orthogonal to the composite error term
#
"
1 PJ
Zξ,j ξj (δ, β)
0
j=1
J
Z Λ = 1 PJ
j=1 Zω,j ωj (δ, θ, η)
J
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Nevo: Measuring Market Power in the RTE Cereal Industry
I
The ready-to-eat (RTE) cereal industry is characterized by
high price-to-cost margins (PCM) and high concentrations
I
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:
I
1 that due to product differentiation
2 that due to multiproduct form pricing and
3 that due to price collusion
I
Overview of methodology:
I
I
I
use the BLP framework to estimate brand-level demand.
use demand estimates and different pricing rules to back out
PCMs.
compare PCMs against crude measures of actual PCM to
separate the different sources of the markup
Empirical Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
Model and Data
I
Indirect utility is
uijt = αi pjt + Xj βi + ξj + ∆ξjt + εijt
I
I
I
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
I
I
I
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
IVs with brand dummies
I
I
I
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.
I
I
I
I
prices of brand j in two cities correlated due to the common mc
but due to the independence assumption will be uncorrelated
with market specific valuation.
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 Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Identifying Collusive Behavior
I
Recall the markup is given by
p − mc = Ω−1 s
I
I
I
I
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 the ownership matrix will be diagonal
With multi-product firms, firms set the prices of all their
products jointly. 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 have no zeros
Nevo estimates parameters under different definitions of the
ownership matrix
Empirical Industrial Organization
Nevo, ECMA (2001)
Results
I
Compares predicted PCM under all three situations to the
observed PCM calculated using accounting data for costs
I
Finds that the first two effects explain most of the observed
price-cost margins
I
Prices in the industry are consistent with noncollusive pricing
behavior, despite the high price-cost margins.
Empirical Industrial Organization
Nevo, ECMA (2001)
Results
I
Compares predicted PCM under all three situations to the
observed PCM calculated using accounting data for costs
I
Finds that the first two effects explain most of the observed
price-cost margins
I
Prices in the industry are consistent with noncollusive pricing
behavior, despite the high price-cost margins.
Empirical Industrial Organization
Nevo, ECMA (2001)
Results
I
Compares predicted PCM under all three situations to the
observed PCM calculated using accounting data for costs
I
Finds that the first two effects explain most of the observed
price-cost margins
I
Prices in the industry are consistent with noncollusive pricing
behavior, despite the high price-cost margins.