Demand and
supply of
differentiated
products
Paul Schrimpf
Demand and supply of differentiated
products
Paul Schrimpf
UBC
Economics 565
January 19, 2017
Demand and
supply of
differentiated
products
Paul Schrimpf
1 Introduction
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
2 Demand in product space
3 Demand in characteristic space
Early work
Model
Estimation and identification
Aggregate product data
Estimation steps
Pricing equation
Micro data
Limitations
Demand and
supply of
differentiated
products
References
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Reviews:
• Ackerberg et al. (2007) section 1 (these slides use their
notation)
• Aguirregabiria (2017) chapter 2
• Reiss and Wolak (2007) sections 1-7, especially 7
• Classic papers:
• Berry (1994)
• Berry, Levinsohn, and Pakes (1995)
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Section 1
Introduction
Demand and
supply of
differentiated
products
Introduction
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Typical market for consumer goods has many
differentiated, but similar products, e.g.
• Cars
• Cereal
• Differentiated products are a source of market power
• Having many products can result in many parameters
creating estimation difficulties and requiring
departures from textbook demand and supply models
Demand and
supply of
differentiated
products
Motivation
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Counterfactuals that do not change production
technology
• Mergers
• Tax changes
• Effects of new goods
• Cost-of-living indices
• Product differentiation and market power
• Cross-price elasticities
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Section 2
Demand in product space
Demand and
supply of
differentiated
products
Demand in product space I
Paul Schrimpf
• J products, each treated as separate good
Introduction
• Classical demand,
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
q1 =D1 (p1 , ..., pJ , z1 , η1 ; β1 )
.. ..
.=.
qJ =DJ (p1 , ..., pJ , zJ , ηJ ; βJ ),
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
and supply (firms’ first-order conditions for prices):
p1 =g1 (q1 , ..., qJ , w1 , ν1 ; θ1 )
.. ..
.=.
pdJ =gJ (q1 , ..., qJ , wJ , νJ ; θJ ),
Demand and
supply of
differentiated
products
Demand in product space II
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
where
•
•
•
•
•
•
•
•
pj = price
qj = quantity
zj = observed demand shifter
ηj = unobserved demand shock
βj = demand parameters
wj = observed supply shifter
νj = unobserved supply shock
θj = supply parameters
• Dj typically parametrically specified, e.g.
ln qj = βj0 + βj1 p1 + · · · + βjJ pJ + βjy ln y + Z1 γ + νj
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Demand in product space III
• Use reduced form to find instruments
q
q1 =Π1 (Z, W, ν, η; β, θ)
.. ..
. =.
q
qJ =ΠJ (Z, W, ν, η; β, θ)
p
p1 =Π1 (Z, W, ν, η; β, θ)
.. ..
. =.
p
pJ =ΠJ (Z, W, ν, η; β, θ)
• Cost shifters of product j excluded from demand and
supply of product k, but in reduced form
• Cost data often not available
• If available, unlikely to be product specific
• Attributes of other products
Demand and
supply of
differentiated
products
Demand in product space IV
• Hausman (1996) uses prices of other products
• Hard to justify, especially with prices
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
• Advantages of product space:
• Flexible substitution patterns
• Does not require detailed product attribute data
• Problems with product space:
1 Representative agent and aggregation issues
• With heterogeneous preferences, aggregate market
demand need not meet restrictions on individual
demand derived from economic theory
• Cannot use restrictions easily to improve estimates
• Can use simulation to aggregate (Pakes, 1986)
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
2
Too many parameters, O(J2 )
• Can limit by restricting cross-price elasticities, e.g.
Pinkse, Slade, and Brett (2002)
3
4
Too many instruments needed, J
Cannot analyze new goods
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Section 3
Demand in characteristic space
Demand and
supply of
differentiated
products
Demand in characteristic space
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
• Motivation:
• Why do firms differentiate products?
• Because consumers have heterogeneous tastes for
product characteristics
• E.g. cars: tastes for size, safety, fuel efficiency, etc
• Main idea: model consumer preferences for
characteristics and treat products as bundles of
characteristics
Limitations
• Early work: Lancaster (1971), McFadden (1973)
• Key extension to early work: Berry, Levinsohn, and
Pakes (1995)
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Early work in characteristic
space
• Consumer chooses one or none of J products
• Utility of consumer i from product j
uij = xj β + εij
with εij iid across i and j (usually Type I extreme value)
• Implies aggregate demand (for logit)
exp(xj β)
qj =
∑J
1 + k=1 exp(xk β)
Micro data
Limitations
• Problem: restrictive substitution “independence of
irrelevant alternatives”
• Two goods with the same shares have the same cross
price elasticities with any third good (think about a
luxury and bargain good with equal shares)
• Goods with same shares should have same markups
• Solution: add heterogeneity in β, allow correlation
across j in εij
Demand and
supply of
differentiated
products
Model I
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
• Consumers i, goods j, markets t
• Utility: (include good 0 = buy nothing)
Early work
unobserved
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
uijt = U( x̃jt ,
|{z}
z}|{
ξjt ,
observed
unobserved
zit ,
|{z}
z}|{
νit ,
observed
Micro data
Limitations
• xjt = (x̃jt , pjt )) ∈ RK , zit ∈ RR , νit ∈ RL
• Choose j if uijt > uikt ∀k ̸= j
pjt ; θ)
|{z}
observed
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Model II
• Usually U(·) linear:
1×K
z}|{ z
uijt = xjt
K×1
}|
θit
|{z}
{
1×1
z}|{
+ ξjt +εijt
=θ̄+θ o zit +θ u νit
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
for j = 1...J and normalize ui0t = 0
• Assume εijt i.i.d. double exponential
• Assume νit ∼ fν (·; θ), e.g. independent normal
• Write as product specific + observed interactions +
unobserved interactions
uijt =
δj +xjt |{z}
θ o zit + xjt |{z}
θ u νit + εijt
|{z}
=xjt θ̄+ξjt
K×R
K×L
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Endogeneity
• Usually assume E[νit |xjt , zit ] = 0 and E[εijt |xjt , zit ] = 0
• Not interested in counterfactuals with respect to
changes in zit , so can treat as residual, i.e.
νit = θit − E[θit |zit ]
• Market average νit or εijt plausibly correlated with pjt or
other product characteristics, but this correlation
absorbed into ξjt and/or market fixed effects
• Problem is ξjt
• Prices and other flexible product characteristics must
be correlated with ξjt
• If ξjt serially correlated, then likely also correlated with
inflexible product characteristics
• Need instrument, wjt such that E[ξjt |wjt ] = 0
• Cost shifters
• Characteristics of other products
Demand and
supply of
differentiated
products
Estimation and identification
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Depends on data:
• Aggregate product market shares and characteristics
• Individual characteristics and choices
• Additional assumptions:
• Use supply and equilibrium assumptions to get a
pricing equation
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Aggregate data I
• Often only have data on product characteristics and
market shares
• Maybe also distribution of some individual
characteristics for each market (e.g. income and
education from CPS or census)
• Instrument w such that E[ξj |w] = 0
• Distribution of ν ∼ fν (·; θν )
• Combination of estimated market level distribution of
observed individual characteristics and parametric
distributions of unobserved individual characteristics
• e.g. νit = (educit , incomeit , eit )
(
)
e − θνµ
Fν,t (s, y, e; θν ) =
F̂t (s, y)
Φ
| {z }
θνσ
empirical distribution
F̂t (s, y) estimated from CPS or other similar data set
Demand and
supply of
differentiated
products
Aggregate data II
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Assume εijt ∼ double exponential (aka Gumbel or type I
extreme value) as in logit
• Computationally convenient, but other distributions
feasible too
Demand and
supply of
differentiated
products
Estimation outline
Paul Schrimpf
Introduction
Demand in
product space
1
Estimate ξ̂jt = ξ(·; θ)1
1
Demand in
characteristic
space
2
Early work
Compute shares given θ, σ (·; θ, δ)
Find δ(·; θ) such that observed shares, sjt = model
shares, σ (·; θ, δ), then
Model
Estimation and
identification
ξ(·; θ) = δ(·; θ) − xjt θ̄
Aggregate product
data
Estimation steps
Pricing equation
2
Estimate θ from moment condition
Micro data
Limitations
E[ξ(·; θ)|w] = 0
1
In this slide · means the data. I will leave the · out of the notation in
subsequent slides. I will also leave out t subscripts.
Demand and
supply of
differentiated
products
Paul Schrimpf
Computing model shares
• Integrate over ν
∫
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
σj (θ, δ) =
• Integral typically has no closed form, so compute
numerically, usually by Monte Carlo integration
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
exp(δj + xj θ u ν)
dFν (ν)
∑j
1 + k=1 exp(δk + xk θ u ν)
Ns
∑
σj (θ, δ) =
r=1
exp(δj + xj θ u νr )
∑j
1 + k=1 exp(δk + xk θ u νr )
where νr are Ns random draws from fν
• Issues about how best to compute integral — simulation
vs quadrature, type of simulation (Skrainka and Judd,
2011)
• Simulation (more generally approximation) of integral
affects distribution of estimator
Demand and
supply of
differentiated
products
Solving for δ and ξ
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
• Want δ s.t. σj (θ, δ) = ŝj
• Berry, Levinsohn, and Pakes (1995) show
T(δ) = δ + log(ŝj ) − log(σj (θ, δ))
is a contraction
• Unique fixed point δ such that
δ = δ + log(ŝj ) − log(σj (θ, δ)), i.e. ŝj = σj (θ, δ)
• Can compute δ(θ) by repeatedly applying contraction
(in theory and practice often faster to use other
method)
• ξj (θ) = δj (θ) − xj θ̄
• Important identifying assumption: only θ s.t.
ξj (θ) = ξj0 is true θ0
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Estimating θ
• Conditional moment restriction E[ξj (θ)|w] = 0
• Empirical unconditional moments:
J
Demand in
product space
GJ,T,N,Ns =
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
T
1 ∑∑
ξjt (θ)f(wt )
JT
t=1
j=1
where
f(w) = vector of function of w
J = number of products
T = number of markets
N = number of observations in each market underlying
ŝj
• Ns = number of simulations
•
•
•
•
• Asymptotic properties (consistency, distribution),
depend on which of J, T, N, and Ns are →∞, see Berry,
Linton, and Pakes (2004)
• Reynaert and Verboven (2014): using optimal
instruments greatly improves efficiency and stability
Demand and
supply of
differentiated
products
Pricing equation I
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
• More moments give more precise estimates
• Assumption about form of equilibrium allows use of
firm first order condition (pricing equation) as
additional moment
Early work
Model
Estimation and
identification
Aggregate product
data
• Nash equilibrium in prices
• Log linear marginal cost
Estimation steps
Pricing equation
Micro data
Limitations
log mcj = rj θ k + ωj
• rj = observed product characteristics, input prices,
maybe quantity, etc
• ωj = unobserved productivity, possibly endogenous
Demand and
supply of
differentiated
products
Paul Schrimpf
Pricing equation II
• Firm f producing set of product Jf ,
max
Introduction
pj :j∈Jf
Demand in
product space
Demand in
characteristic
space
∑
Estimation and
identification
l∈Jf
Aggregate product
data
Micro data
Limitations
j∈Jf
σj (·) +
Model
Pricing equation
)
pj − Cj (·) Msj (·, p)
• First order condition:
Early work
Estimation steps
∑(
(pl − mcl )
∂σl (·)
=0
∂pj
• Collect as
s + (p − mc)∆ = 0
• Rearrange and use log linear marginal cost
log(p − ∆−1 σ ) − rθ c = ω(θ)
• Conditional moment restriction E[ω(θ)|w] = 0
∑
• Add empirical moments to G, JT1
jt ωjt (θ)f(wt )
Demand and
supply of
differentiated
products
Paul Schrimpf
Introduction
Demand in
product space
Demand in
characteristic
space
Early work
Model
Estimation and
identification
Aggregate product
data
Estimation steps
Pricing equation
Micro data
Limitations
Micro data
• Berry, Levinsohn, and Pakes (2004)
• Data on individual choices and characteristics
uijt =
δj +xjt |{z}
θ o zit + xjt |{z}
θ u νit + εijt
|{z}
=xjt θ̄+ξjt
K×R
K×L
• Random coefficients discrete choice model, so can
identify and estimate δ, θ o , and θ u without
assumptions about ξ and x
• Ichimura and Thompson (1998) give conditions for
nonparametric identification of random coefficients
binary choice models
• Estimate by MLE or (usually) GMM
• Still need θ̄ for price elasticities, etc
δj = xjt θ̄ + ξjt
• Use IV
• Use IV with a pricing equation
Demand and
supply of
differentiated
products
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
Part II
Implementation
Demand and
supply of
differentiated
products
Computational issues
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
• Non-convex optimization problems are almost always
difficult to solve, this is no exception
• Nested iteration can be problematic
• Solve for δ(theta):
while norm(T(delta) - delta) > tolerance1 { delta = T
• Minimize
while norm(theta - thetaOld) > tolTheta && norm(f - f
thetaOld = theta
fold = f
// update theta by e.g. newton's method, set f = f(t
}
• Error in δ can lead to error in minimization
• Error in δ is not a continuous with respect to θ (where
changing θ changes number of iterations)
Demand and
supply of
differentiated
products
Nevo
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
• Popular code provided by Nevo (2000)
• Requires: Matlab, optimization toolbox
• Nevo’s code does not run in current version of Matlab,
but Rasmusen (2006) update does
• Code runs in Octave after changing fminsearch to
another optimization routine
• Worked on by three people
• Used by at least six other papers (see Knittel and
Metaxoglou (2014) footnote 5 for list)
• Fast for data provided
Demand and
supply of
differentiated
products
Nevo - issues
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
• Minimization difficult and not robust
• Starting value
• Algorithm
• Tolerance for finding δ (Dubé, Fox, and Su (2012b) show
loose tolerance affects estimates)
• Knittel and Metaxoglou (2014) algorithms often stop at
point where first and/or second order conditions fail
• Knittel and Metaxoglou (2014) differences among
convergence points economically significant
Demand and
supply of
differentiated
products
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
Dubé, Fox, and Su (2012b) I
• Fixed point iteration to compute δ messes up GMM
minimization; also is not best method for finding δ
• Table 1: shows problem is too large a tolerance. NFP
gives good estimates when tolerances are tight
• Can recast problem as constrained minimization
2
J ∑
T
∑
1
ξjt (θ, δ)fℓ (wt )
JT
t=1

min
θ,δ
∑
ℓ
j=1
subject to
ŝ = σ (·; θ, δ)
• Su and Judd (2012): “mathematical programming with
equilibrium constraints” (MPEC)
• Use state of the art algorithm to solve constrained
minimization
Demand and
supply of
differentiated
products
Dubé, Fox, and Su (2012b) II
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
• Solvers work best with accurate (i.e. not finite
difference) derivatives—supplying 1st and 2nd order
derivatives makes algorithm take approximately 1/3 as
long as with just 1st order (Dubé, Fox, and Su, 2012a)
• Gains from exploiting sparsity of Jacobian of
constraints and Hessian of objective function
Demand and
supply of
differentiated
products
Dubé, Fox, and Su (2012b) code
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
• Code requires: Matlab, KNITRO
• KNITRO proprietary, free version limited to 300
variables & constraints
• KNITRO can be replaced with other optimization
algorithm, but others do not seem to work as well:
• IPOPT uses similar algorithm, but I had trouble
installing
• NLOPT has no interior point algorithm, its algorithms
do not seem to deal with nonlinear constraints very well
• Skrainka (2012) uses SNOPT, which is similar algorithm
to NLOPT’s SLSQP
• Runs in Octave with KNITRO replaced by NLOPT
Demand and
supply of
differentiated
products
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
Observations
• High quality commercial solver appears necessary; my
attempts with NLOPT fail and take longer
• Skrainka (2012) uses SNOPT instead of KNITRO
• KNITRO and SNOPT not perfect
• Still sensitive to starting values
• MPEC replaces a contraction — a problem we know we
can solve — with constraints that may make the
optimization harder
• Reynaerts, Varadhan, and Nash (2012) give method to
improve accuracy and speed of computing δ
• Dubé, Fox, and Su (2012a) using nested fixed point
requires fewer solver iterations than MPEC, but takes as
long or longer because of time spend solving for δ (can
be much longer if contraction mapping is slow)
• Reynaert and Verboven (2014): using optimal
instruments makes optimization more robust
Demand and
supply of
differentiated
products
Paul Schrimpf
Nevo
Dubé, Fox, and Su
(2012b)
References about
implementation
• Overviews
• Nevo (2000)
• Dubé, Fox, and Su (2012b), Dubé, Fox, and Su (2012a)
• Knittel and Metaxoglou (2014)
• Skrainka (2012)
• Particular issues
• Skrainka and Judd (2011): integration
• Reynaerts, Varadhan, and Nash (2012): solving for δ
• Course on discrete choice models with simulation by
Kenneth Train http:
//elsa.berkeley.edu/users/train/distant.html
• Bayesian: Jiang, Manchanda, and Rossi (2009),
Brian Viard, Gron, and Polson (2014), Sun and Ishihara
(2013)
• Overview of optimization methods and software Leyffer
and Mahajan (2010)
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Part III
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Applications and extensions
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 4
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Identification
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Review paper: Berry and Haile (2015) — summarizes
Berry and Haile (2009), Berry and Haile (2014), and
Berry, Gandhi, and Haile (2013)
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Market level data: Berry and
Haile (2014)
Demand and
supply of
differentiated
products
Model
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Market characteristics χt = (xt , pt , ξt ), xt exogenous, pt
endogenous
• Random utilities with distribution Fv (vi1t , ..., viJt |χt )
• Shares
sjt = σj (χt ) = P(arg max vikt = j|χt )
k
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Rationale for setup
• Parametric models:
• Logit random utility:
Market level data:
Berry and Haile
(2014)
uijt = xjt β − αpjt + ξjt + εijt
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
implies
(1)
xjt + ξ̃jt =
• BLP implies:
(1)
xjt + ξ̃jt =
Merger simulation
References
References
1
α
1 (−1)
(ln(sjt − ln(s0t )) + (1) pjt − (1) xjt β (−1)
(1)
β
β
β
1 (
θ̄ (1)
(−1)
δj (st , pt , θ) − xjt θ̄ (−1)
• In each case:
(1)
(−1)
xjt + ξjt = function ofst , pt , xt
)
Demand and
supply of
differentiated
products
Paul Schrimpf
Assumptions
1
(1)
(2)
Index restriction: partition xjt = (xjt , xjt ), define
Identification
(1)
Market level data:
Berry and Haile
(2014)
δjt = xjt + ξjt
Micro data: Berry
and Haile (2009)
then
Other identification
results
(2)
Fv (·|χt ) = Fv (·|δt , xt , pt )
Goolsbee and
Petrin (2004)
Fan (2013)
2
Gandhi, Lu,
and Shi (2014)
Connected substitutes: (see Berry, Gandhi, and Haile
(2013))
(2)
σk (δt , pt , xt ) is nonincreasing in δjt and −pjt for k ̸= j
2 Among any subset K ⊆ J , ∃j, k ∈ K and j ̸∈ K s.t.
(2)
σk (δt , pt , xt ) is decreasing in δjt and −pjt
1
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
3
IV exogeneity E[ξjt |zt , xt ] = 0
References
4
Rank condition / completeness: ∀B(st , pt ) if
E[B(st , pt )|zt , xt ] = 0 a.s., then B(st , pt ) = 0 a.s.
Demand and
supply of
differentiated
products
Identification of demand I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
• If 1-4, then ξjt and σj (χt ) are identified [Theorem 1]
• Connected substitute (1) ⇒ demand invertible
Goolsbee and
Petrin (2004)
δjt = σ −1 (st , pt )
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• IV & rank condition:
(1)
E[xt − σ −1 (st , pt )|z, x] = 0
Demand and
supply of
differentiated
products
Implications for instruments I
Paul Schrimpf
• 2J endogenous variables (s, p), so need at least 2J
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
instruments
• J instruments from exogenous characteristic x(1)
• Need J instruments that shift price and are excluded
from demand
• Need variation in price and variation in share
conditional on price
• Types of instruments that have been used:
• “BLP instruments” = characteristics of competing
products
• Needed, but not sufficient (without more restrictions)
• Cost shifters:
• “Hausman instruments” = price of same good in other
markets
• Consumer characteristics in nearby markets (e.g. Fan
(2013))
Demand and
supply of
differentiated
products
Implications for instruments II
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Functional form restrictions can reduce needed number
of instruments, e.g. if
(1)
δjt = xjt − αpjt + ξjt
then only need 1 instrument for price
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Marginal costs
• More assumptions:
1 σj (δt , pt ) continuously differentiable wrt pt
2
Known form of competition so know ψj such that
mcjt = ψj (st , Mt , {
∂σ
}, pt )
∂p
• Then mcjt is identified [Theorem 3]
• If want to do counterfactuals that change quantities,
need to know marginal cost function, not just mcjt =
marginal cost at observed quantity
• If mcjt = c̃j (Qjt , wjt ) + ωjt and have instruments yjt such
that E[ω|w, y] = 0, then cj and ωjt identified [Theorem 4]
• If ψj is unknown, then with stronger assumptions
about marginal cost function and cost instruments, can
still identify ωjt [Theorem 5]
• Can then test for different forms of ψj [Theorem 9]
• Require index restriction on cj ,
(1)
(2)
mcjt = cj (Qjt , wjt γj + ωjt , wjt )
Demand and
supply of
differentiated
products
Simultaneous equations
approach I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
• Use demand and supply equations together and can
replace completeness conditions with regularity
conditions about demand and supply equations
• Will need no external instruments (but do need
exclusions)
• Index assumptions imply
xjt + ξjt =σ −1 (st , pt )
| {z }
(1)
=δjt
Merger simulation
References
References
wjt + ωjt =π −1 (st , pt )
| {z }
=κjt
• Assume x, w ⊥
⊥ ξ, ω and supp(x, w) = R2J
(2)
Demand and
supply of
differentiated
products
Simultaneous equations
approach II
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
• Assume conditions (including for each δ, κ there is
unique s, p) such that can make change of variables so
fs,p (st , pt |xt , wt ) =
(
)
= fξ,ω σ −1 (st , pt ) − xt , π −1 (st , pt ) − wt |J (st , pt )|
(3)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
where J (s, p) = Jacobian wrt s, p of (1) and (2)
• Then can identify ξ, σ , ω [Theorems 6 and 7]
• Integrating (3) wrt x, w identifies |J (s, p)|, then dividing
gives fξ,ω
• Integrating fξ,ω give Fξ
• Location normalization: assume σ −1 (s0 , p0 ) − x0 ) = 0,
then know Fξ (0)
Demand and
supply of
differentiated
products
Paul Schrimpf
Simultaneous equations
approach III
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• For other s, p, can find x∗ such that
Fξ (σ −1 (s, p) − x∗ ) = Fξ (0), i.e. σ −1 (s, p) = x∗ , so σ −1
identified
• (1) identifies ξjt
• Same argument for ω
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Micro data: Berry and Haile
(2009)
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
Model I
• Consumer i, markets t, products j ∈ Jt
• Consumer observations zit = (zi1t , ..., ziJt t )
• Observed product characteristics xt = (x1t , ..., xJt t )
(includes prices, may include product dummies)
• Scalar product unobservable ξjt (zit )
• Random utility function uit : X→R
• Formally, there’s a probability space, (Ω, F , P) and
vijt = uit (xjt , ξjt (zit ), zijt ) = u(xjt , ξjt (zit ), zijt , ωit )
where ωit ∈ Ω and u is measurable in ωit with
ωit ⊥
⊥ (xjt , zit , ξjt (zit ))
• E.g. random coefficients
References
u(xjt , ξjt (zit ), zijt , ωit ) = xjt θit + zijt γ + ξjt + εijt
ωit = (θit , εi1t , ..., εiJt t )
Demand and
supply of
differentiated
products
Paul Schrimpf
Model II
• Allows distribution of θ and ε to depend on z, x, ξ
(1)
Identification
• Special regressor: zijt ∈ R s.t.
Market level data:
Berry and Haile
(2014)
(
)
(1)
(2)
(2)
vijt = ϕ(ωit )zijt + µ̃ xjt , ξjt (zit ), zijt , ωit
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Restrictions:
(1)
invariance of ξjt (zit ) to zit
2 Additive separability
3 µ̃ monotonic in ξjt
1
Identifies mapping from choice probabilities to utilities
(2)
• Henceforth, all argument conditional on zit , so leave
out of notation
• Normalizations
• ξjt ∼ U(0, 1)
• Location of utilities
vi0t = 0
Demand and
supply of
differentiated
products
Model III
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Scale of utilities ϕit = 1,
(1)
(2)
(2)
vijt = zijt + µ(xjt , ξjt (zit ), zijt , ωit )
|
{z
}
≡µj (xjt ,ξjt ,ωit )
Demand and
supply of
differentiated
products
Identification definition I
Paul Schrimpf
• Data: (t, yit , {xjt , w̃jt , zijt }j∈Jt )
Identification
• Conditional choice probabilities
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
(
)
pijt = P yit = j|t, {xkt , w̃kt , zikt }k∈Jt
• Full identification of random utility model: means that
for any given conditional choice probabilities there is a
(2)
unique distribution of ξjt (given zijt ) and a conditional
distribution of utilities {vijt }j∈Jt given {xjt , w̃jt , zijt }j∈Jt
that generates the given choice probabilities
• Identification of demand: for any conditional choice
probabilities there is a unique distribution of ξjt (given
(2)
zijt ) and unique structural choice probabilities
)
(
)
(
ρj {xjt , ξjt , zijt }j∈Jt = P yit = j|{xkt , ξkt , zikt }k∈Jt
that match the choice probabilities
Demand and
supply of
differentiated
products
Assumptions
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
1
Large support: supp{zijt }j∈Jt |{xjt }j∈Jt = R|Jt |−1
2
Independence of instruments: ξjt ⊥
⊥ (wjt , zijt )∀j, t
3
Rank condition: the quantile version of bounded
completeness from Chernozhukov and Hansen (2005)
applies to Dj (xjt , ξjt )
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Identification proof I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
(2)
• Large support:
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
(2)
• µijt = µ(xjt , ξjt (zit ), zijt , ωit )
(1)
lim
)
(
P yit = j|t, {xkt , w̃kt , zikt }k∈Jt =
zikt →−∞∀k̸=j


zijt + µijt ≥ zikt + µikt ∀k ̸= j∩

∩zijt + µijt ≥ 0|
=
lim
P
(1)
zikt →−∞∀k̸=j
|t, {xkt , w̃kt , zikt }k∈Jt
(
)
=P zijt + µijt ≥ 0|t, {xkt , w̃kt , zikt }k∈Jt
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Identification proof II
• Independence of zijt and (ξjt , ωit )
(
)
(
)
P zijt + µijt ≥ 0|t, {xkt , zikt }k∈Jt =P zijt + µijt ≥ 0|t, xjt , zijt
=1 − Fµijt |t (−zijt |xjt , t)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
averaging over xjt identifies Fµijt |t , and so identifies
conditional quantiles, e.g.
Fan (2013)
δjt ≡median[µj (xjt , ξjt , ωit )|t]
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Define
Results
median[µj (xjt , ξjt , ωit )|xjt , ξjt ] = Dj (xjt , ξjt )
Merger simulation
References
References
• Independence of wjt and ξjt , and ξjt ∼ U(0, 1) implies
that
(
)
P δjt ≤ Dj (xjt , τ)|wjt = τ
Demand and
supply of
differentiated
products
Identification proof III
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Nonparametric IV quantile regression of Chernozhukov
and Hansen (2005) shows that with the bounded
completeness condition Dj is unique identified, and so
is ξjt = D−1
j (xjt , δjt )
• Joint distribution of µ from
pi0t = P(zijt + µijt ≤ 0∀j ̸= 0|t, zit )
• Fµ|t = Fµ|xt ,zit ,ξt
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Further remarks
• To summarize if (1)-(3) then the random utility model is
identified
• If large support fails, then can still identify demand
• Identifying random utility model is not exactly the
same as identifying random coefficients
vijt = xjt θit + zijt γ + ξjt + εijt
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• This paper identifies Fv|x,z,ξ , further conditions needed
for distribution of θ, ε
• Given results in this paper, we can treat vijt as observed
and use standard results to identify distribution of
coefficients (see conclusion of Berry and Haile (2009) for
references)
• Most economic quantities that we might care about
depend on the random utility model not the random
coefficients
Demand and
supply of
differentiated
products
Other identification references
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Berry, Gandhi, and Haile (2013) show connected
substitutes is sufficient for invertibility of demand
• Fox and Gandhi (2011) identification of demand for any
dimension ξ
• Chiappori and Komunjer (2009) identification through
conditional independence instead of special regressor
• Fox et al. (2012) shows random coefficients logit
(without endogeneity) is identified
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 5
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Goolsbee and Petrin (2004)
Demand and
supply of
differentiated
products
Goolsbee and Petrin (2004)
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• In U.S. in 1996 cable television deregulated
• Hope was that multiple cable operators would enter
each area and compete
• Did not happen, but direct broadcast satellite (DBS)
companies did enter
• Questions:
• How much did competition from DBS lower cable
prices?
• How much did consumers gain from DBS?
Demand and
supply of
differentiated
products
Model
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
• Consumers n, products j, markets m
• Utility:
Other identification
results
Goolsbee and
Petrin (2004)
Unj =α0 pmj +
g=2
|
Fan (2013)
Results
Results
αg pmj dgn +β x xmj + zn βjz + (ξmj + εnj )
{z
}
income effects
5
∑
Gandhi, Lu,
and Shi (2014)
Gaynor and
Vogt (2003)
5
∑
=
δmj
|{z}
=α0 pmj β x xmj +ξmj
+
αg pmj dgn + zn βjz + εnj
g=2
Merger simulation
References
References
• εn ∼ multivariate normal with unrestricted covariance
across j (avoids IIA problem)
Demand and
supply of
differentiated
products
Estimation
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Similar to micro-BLP
• Use micro data to estimate δmj , β z
• Use estimated δ, instruments for price to estimate α0 ,
βx
• Uses local tax on cable revenues as instrument for price
• Effect of entry, need to know price as function of model
primitives
• Could fully specify costs and form of competition
• Instead estimate reduced form pricing equation,
pmj = f(observables)
• Use pricing equation to predict prices without DBS,
calculate compensating variation as measure of
consumer welfare
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Results: demographics and
demand
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Results: demand elasticities
Demand and
supply of
differentiated
products
Results: welfare
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• No DBS would increase cable prices by $4.17 per month
• Monthly consumer gains from DBS:
• $10.57 in consumer surplus for DBS subscribers
• $4.17 per month for cable subscribers from lower prices
• $1 per month for cable subscribers from increased
quality
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 6
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Fan (2013)
Demand and
supply of
differentiated
products
Fan (2013)
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Question: effect of mergers on product characteristics
• Merged firm will generally produce different product(s)
than two separate firms
• Need to endogenize choice of product characteristics
• Setting: U.S. daily newspapers
Demand and
supply of
differentiated
products
Model I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
• BLP style demand with endogenous price and other
product characteristics, xjt = quality index, local news
ratio (share of local news staff), news variety (HHI of
staff shares across sections)
• Demand for advertising:
log ajt = η + λ0 log Hjt + λ1 log qjt +
| {z } | {z }
λ2 log rj t
| {z }
market size
advertising price
circulation
+ιjt
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
Note: no cross price elasticities, i.e. no competition
• Variable profits:
References
References
(q)
(a)
πjII = (pj qj − acj qj ) + (rj aj − mcj aj ) + (µ1 qj + µ2 /2q2j )
where
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
(q)
Model II
• acj
is average cost of producing quantity q and has
some parametric form
(q)
• mcj is marginal cost of advertising sales and has some
parametric form
• Definition of market:
• Newspapers compete in many overlapping local
markets, so local paper in Portland, Maine potentially
competes with local paper in Portland, Oregon
• Define market for newspaper j as the counties where
85% of circulation for newspaper j is contained
• Equilibrium: solving backward
3 Given Qjt , advertising rate chosen to equalize marginal
cost and marginal revenue of advertising
• No competition in advertising rates
2 Given characteristics, prices chosen in simultaneous
Nash equilibrium
1 Characteristics chosen simultaneous Nash equilibrium
Demand and
supply of
differentiated
products
Data I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• 1997-2005, market level data on newspaper quantity,
price, and characteristics, and advertising quantity and
price
• County demographics (education, age, income,
urbanization)
• 5843 newspaper-year observations of newspaper
characteristics and prices
• 11203 newspaper-county-year observations of quantity
• 422 newspaper-year also with advertising information
Demand and
supply of
differentiated
products
Estimation I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Moment conditions
• Consumer demand: E[ξjt |wjt ] = 0
• Advertiser demand: E[ιjt |wjt ] = 0
• Advertising first order condition: E[ζjt |wjt ] = 0
• Price first order condition: E[ωjt |wjt ] = 0
• Characteristics first order condition: E[νjt |wjt ] = 0
• Instruments from overlapping markets
• Suppose newspaper A is only in county 1, but
newspaper B is in counties 1 and 2
• Demographics in county 2 affect prices and
characteristics of newspaper B, which in turns affects
newspaper A’s price and characteristics
• Use demographics in county 2 to instrument for
newspaper A’s price
Demand and
supply of
differentiated
products
Results I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
• Parameter estimates
• Simulation of merger of Minneapolis Star Tribune and St.
Paul Pioneer
• In reality: owner of Pioneer bought Star, DOJ filed
antitrust complaint 3 months later, owner of Pioneer
sold Star 2 months later
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Simulate with and without characteristic adjustment,
compare results
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 7
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Gandhi, Lu, and Shi (2014)
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
“Demand Estimation with
Scanner Data: Revisiting the
Loss-Leader Hypothesis”
gandhi2014 I
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Motivation:
• Frequent price discounts (sales) in scanner data
• Chevalier, Kashyap, and Rossi (2003): loss-leader model
implies prices can fall when demand increases because
of promotional effect; evidence that prices fall during
seasonal peak demand (e.g. tuna during Lent)
• Nevo and Hatzitaskos (2006): prices could also fall
during high demand because elasticity of demand could
increase (if buying more quantity, makes more sense to
search for lower price)
• Methodology: estimate BLP demand model, see if
demand elasticity is different during seasonal peak
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
“Demand Estimation with
Scanner Data: Revisiting the
Loss-Leader Hypothesis”
gandhi2014 II
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Data: Dominick’s scanner data (grocery store)
• Difficulty: many product categories have hundreds of
products, so many products have 0 observed share in
some markets
• Solution: optimally shift observed shares away from 0
Demand and
supply of
differentiated
products
Data
Paul Schrimpf
Identification
• Dominick’s scanner data (grocery store)
Market level data:
Berry and Haile
(2014)
• Estimate separately for each product category
Micro data: Berry
and Haile (2009)
• Market = store × week (all stores in Chicago,
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
1989-1997, gives ≈ 400, 000 markets)
• Many products in each category (Table 4) — 283 cheese,
537 soft drinks, 820 shampoos, 118 canned tuna, etc
• Sales concentrated among top 20% of products in each
category (Table 4) — approximately 80%
• High percent (20-80) of products with 0 sales (Table 4) —
35% for canned tuna
References
• Distribution of sales approximately follows Zipf’s law —
References
kth most popular product has sales proportional to 1/ks
for some s > 1
Demand and
supply of
differentiated
products
Model and zero share problem I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• BLP setup (but empirical results are without random
coefficients)
• Zero share problem, 0 = σ (δ) implies δ = −∞
• Cannot just drop goods with 0 share because that
creates selection (0 share implies low ξ)
• Laplace: when observe zero share, add 1 sale to each
product
sLjt S =
nt sjt + 1
nt + Jt + 1
Optimal Bayes estimator under uniform prior
• Could use Laplace transformation here, but what is
optimal for estimating shares might not be optimal for
estimating demand
Demand and
supply of
differentiated
products
Model and zero share problem II
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
• Choose transformation π ∗ (st , nt ) that minimizes
asymptotic (slowly growing nt ) MSE
( [
])
π ∗ (st , nt ) = σ E σ −1 (πt )|st , nt
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Fπt |st ,nt unknown, show that if assume Zipf’s law, can
estimate it
• Use estimated Fπt |st ,nt to estimate optimal
transformation
• Estimate rest of model using BLP with transformed
shares
Demand and
supply of
differentiated
products
Paul Schrimpf
Zero share correction reduces
bias
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Table: Table 6: Average Bias for a Repeated Simulation
Fraction of Zeros
16.48% 36.90% 49.19% 63.70%
Using Empirical Share .3833
.6589
.7965
.9424
Using Laplace Rule
.2546
.5394
.6978
.8476
Inverse Demand EB
-.0798
-.0924
-.0066
.0362
Note: T = 500, n = 10, 000, Number of Repetitions = 1, 000.
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 8
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Gaynor and Vogt (2003)
Demand and
supply of
differentiated
products
Gaynor and Vogt (2003)
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• California hospitals
• Structural model of demand & pricing
• Merger simulation
Demand and
supply of
differentiated
products
Motivation
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Many hospital mergers, 900 from 1994-2000 (among
6100 hospitals)
• Profit vs non-profit plays role in antitrust decisions
1
Source.
Demand and
supply of
differentiated
products
Continued relevance
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• “Regulators Tamp Down on Mergers of Hospitals”
NYTimes Dec 18, 2015
• “The Future of Health Care Mergers Under Trump”
NYTimes Nov 20, 2016
Demand and
supply of
differentiated
products
Model I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
• Utility of consumer i from hospital j
Vij = −αiP pj
qi +v(qi ,
|{z} |{z}
Ri
|{z}
• Aggregate to get demand, Dj (p)
• Hospital profits:
πj = pj Dj (p) − C(Dj (p); Zj , ζj , W)
Results
Merger simulation
References
• For-profit pricing: maxpj πj
References
pj =
Sj
|{z}
consumer characteristics hospital characte
price quantity
Results
Gaynor and
Vogt (2003)
,
∂Cj
Dj
−
∂Dj ∂Dj /∂pj
Demand and
supply of
differentiated
products
Model II
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
• Non-profit pricing: maxpj Uj (πj , Dj )s.t.πj ≥ πL
Goolsbee and
Petrin (2004)
pj =
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
∂Cj
∂Uj /∂Dj
Dj
+
−
∂Dj ∂Uj /∂πj + µj ∂Dj /∂pj
• Merged hospital systems maximize sum of profits or
utility
Demand and
supply of
differentiated
products
Data
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• California OSHPD https:
//www.oshpd.ca.gov/HID/Find-Hospital-Data.html
• annual discharge, annual financial, & quarterly
financial data for 1995
• 913,660 discharges (i) and 374 hospitals
Demand and
supply of
differentiated
products
Econometric model I
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
• Micro-BLP
Step 1 : use individual choice data to estimate δj
• Specification of Vij
2
Vij = − α̃iP pj E[qi ] + α̃id di→j + α̃id d2i→j +
∑
Zjk α̃ik + ξj + εij
k
where
qi = exp
(
∑
)
Xiℓ βℓ + νi
(
α̃iP
= exp
ℓ
α̃id
∑
=ρ +
2
α̃id
Xiℓ ρℓX
ℓ
2
α0P
∑
=ρ +
∑
+
ℓ
Xiℓ ρℓ2X
ℓ
References
∑
α̃ik =α0 +
ℓ
Xiℓ αℓk + ρkZ di→j + ρk2Z d2i→j
)
p
Xiℓ αℓ
Demand and
supply of
differentiated
products
Econometric model II
Paul Schrimpf
• Rearrange as hospital mean, δj , plus deviations
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Vij =
K
∑
k=0
|
Zjk ᾱk + ξj +(Xi − X̄)αZj + quadratic distance + εij
{z
}
=δj
• Estimate by MLE with individual choice data – gives
estimates of δ̂j
Step 2: estimate ᾱ (include α p ) by 2SLS
Gaynor and
Vogt (2003)
Results
Merger simulation
δj = Zj ᾱ + ξj
References
References
• Instruments: wages, exogenous product characteristics,
consumer characteristics
Demand and
supply of
differentiated
products
Paul Schrimpf
Econometric model III
• Functional form of instruments: from FOC,
Identification
pj =
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
use estimate of Dj and
∂Cj
Dj
−
∂Dj
∂Dj /∂pj
Dj
∂Dj /∂pj
• Dj depends on α p , ξj , first assume 0, get initial estimates,
then redo to get final estimates
Step 3 : estimate marginal cost function by 2SLS
(
∂D
P− Θ·×
∂p
)−1
D = ω0 + DωD + WωW + ZωZ + ζ
Merger simulation
References
References
• D endogenous, same instruments as step 2
• Steps 2 & 3 often combined for efficiency, but not
necessary for consistency
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Results as expected
• What are the
asymptotics?
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Average elasticity
-4.85 (2.03)
• First stage F-stat
4.91
Demand and
supply of
differentiated
products
Paul Schrimpf
• For-profit prices
$248 (187) higher
• Behavioral
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
marginal cost
$592 (329)
higher
• Markup 1183
(587) for profit,
948 (345)
non-profit
• First-stage F-stat
p-value < 0.01
• What is being
assumed about
dependence of ξj
when calculating
standard errors?
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Cross-price elasticities
Demand and
supply of
differentiated
products
Merge simulation
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Tenet & Ornda merged in 1997
• FTC required Tenet divest French Hospital (bought by
Vista)
• Simulate assuming:
• No divestiture of French
• With divestiture of French
• No divestiture, but assuming non-profit
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Merger simulation
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Merger simulation
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Merger simulation
Demand and
supply of
differentiated
products
Related papers
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
• Gowrisankaran, Nevo, and Town (2015): BLP model of
hospital demand, but hospital prices set through
negotiations with MCOs
• Bundorf, Levin, and Mahoney (2012), Starc (2014): BLP
model of insurance demand
• Goto and Iizuka (2016): BLP model of flu vaccine
demand
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 9
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Gowrisankaran, Nevo, and Town (2015)
Demand and
supply of
differentiated
products
Paul Schrimpf
Gowrisankaran, Nevo, and
Town (2015)
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Slides:
http://www.u.arizona.edu/~gowrisan/pdf_papers/
hospital_merger_negotiated_prices_slides.pdf
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
Gowrisankaran, Nevo, and
Town (2015)
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Section 10
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
References
Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
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Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
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Results
Gaynor and
Vogt (2003)
Results
Merger simulation
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
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Results
Gaynor and
Vogt (2003)
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Merger simulation
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supply of
differentiated
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
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Merger simulation
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supply of
differentiated
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
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Results
Gaynor and
Vogt (2003)
Results
Merger simulation
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differentiated
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
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Gaynor and
Vogt (2003)
Results
Merger simulation
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products
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Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
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supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
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Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
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Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
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Demand and
supply of
differentiated
products
Paul Schrimpf
Identification
Market level data:
Berry and Haile
(2014)
Micro data: Berry
and Haile (2009)
Other identification
results
Goolsbee and
Petrin (2004)
Fan (2013)
Gandhi, Lu,
and Shi (2014)
Results
Gaynor and
Vogt (2003)
Results
Merger simulation
References
References
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