Identification in Differentiated Products Marketspah29/AR.pdf · one has only market-level data, as in the original Berry et al. (1995) paper. This is followed by a discussion of

EC08CH02-Haile ARI 19 July 2016 11:0

RE V I E W

S

IN

AD V A

NC

E

Identification in DifferentiatedProducts MarketsSteven Berry and Philip HaileDepartment of Economics and Cowles Foundation, Yale University, New Haven,Connecticut 06520; email: [email protected], [email protected]

Annu. Rev. Econ. 2016. 8:27–52

The Annual Review of Economics is online ateconomics.annualreviews.org

This article’s doi:10.1146/annurev-economics-080315-015050

Copyright c© 2016 by Annual Reviews.All rights reserved

JEL codes: C3, C5, C14

Keywords

nonparametric identification, instrumental variables, discrete choice,differentiated products oligopoly, demand and supply, firm conduct

Abstract

Empirical models of differentiated products demand (and often supply) arewidely used in industrial organization and other fields of economics. We re-view some recent work studying identification in a broad class of such models.This work shows that the parametric functional forms and distributional as-sumptions commonly used for estimation are not essential for identification.Rather, identification relies primarily on the standard requirement that in-struments be available for the endogenous variables—here, typically, pricesand quantities. We discuss the types of instruments that can suffice, as well ashow instrumental variables requirements can be relaxed by the availability ofindividual-level data or through restrictions on preferences. We also reviewnew results on discrimination between alternative models of oligopoly com-petition. Together, these results reveal a strong nonparametric foundationfor a broad applied literature, provide practical guidance for applied work,and may suggest new approaches to estimation and testing.

27

Review in Advance first posted online on July 27, 2016. (Changes may still occur before final publication online and in print.)

Changes may still occur before final publication online and in print

Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


1. INTRODUCTION

Over the past 20 years, there has been an explosion of empirical work using models of differentiatedproducts demand and supply that build on that in Berry et al. (1995) (henceforth referred to asthe BLP model). Initially this work focused on traditional topics in industrial organization suchas market power, mergers, or the introduction of new goods. But as Table 1 suggests, thesemodels are being applied to an increasingly broad range of markets and questions in economics.A quantitative understanding of demand or supply is essential to answering many positive andnormative questions in a wide range of markets, and most markets involve differentiated goods.Empirical models following Berry et al. (1995) are particularly attractive for such applicationsbecause they incorporate both rich heterogeneity in consumer preferences and product-levelunobservables. The former is essential for accurately capturing consumer substitution patterns(own- and cross-price demand elasticities); the latter make explicit the source of the endogeneityproblems that we know arise in even the most elementary supply and demand settings.

Until recently, however, identification of BLP-type models was not well understood. One oftenencountered informal speculation—either that the models were identified only through functionalform restrictions or that certain model parameters were identified by certain moments of the data.But there was no formal analysis applicable to this class of models. In this review, we discuss somerecent work on this topic, focusing primarily on results presented in Berry et al. (2013) and Berry &Haile (2014, 2016).1 This work considers nonparametric generalizations of the BLP modeland provides sufficient conditions for identification of demand, identification of firms’ marginalcosts and cost functions, and discrimination between alternative models of firm behavior.

Table 1 Example markets and topics

Topic Example papers

Transportation demand McFadden et al. 1977

Market power Berry et al. 1995, Nevo 2001

Mergers Nevo 2000, Capps et al. 2003, Fan 2013

Welfare from new goods Petrin 2002, Eizenberg 2014

Network effects Rysman 2004, Nair et al. 2004

Product promotions Chintagunta & Honore 1996, Allenby & Rossi 1999

Environmental policy Goldberg 1998

Vertical contracting Villas-Boas 2007, Ho 2009

Equilibrium product quality Fan 2013

Media bias Gentzkow & Shapiro 2010

Asymmetric information and insurance Cardon & Hendel 2001, Lustig 2010, Bundorf et al.2012

Trade policy Goldberg 1995, Berry et al. 1999, Goldberg &Verboven 2001

Residential sorting Bayer et al. 2007

Voting Gordon & Hartmann 2013

School choice Hastings et al. 2010, Neilson 2013

1We also make some use of a recent literature on the identification of simultaneous equations models, as represented byMatzkin (2008, 2015) and Berry & Haile (2015).

28 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Broadly speaking, these papers show that when it comes to identification, there is nothingspecial about BLP-type models. Even in a fully nonparametric specification, the primary require-ment for identification is the availability of instruments providing sufficient exogenous variationin prices and quantities. In addition, there are many sources of variation that can enable discrim-ination between alternative models of firm conduct.

We view these results as important for several reasons. First, they provide a strong nonpara-metric foundation for a large and growing empirical literature. They demonstrate that functionalforms and distributional assumptions commonly used for approximation in finite samples are notrequired for identification; rather, standard instrumental variables conditions suffice. Second, theresults point to the possibility of new estimation approaches, including nonparametric estimators,as well as new tests of firm behavior. Finally, the results yield important practical guidance forapplied researchers. They clarify which types of instruments allow identification of the most gen-eral models and point to trade-offs among the flexibility of the model (e.g., between alternativeseparability restrictions), the types of data available (e.g., market level versus individual level), andthe demands on instrumental variables.

1.1. A Starting Point: The BLP Demand Model

On the demand side, Berry et al. (1995) build on classic models of demand with endogenousprices and on the rich literature discussing discrete choice models of demand (as in McFadden1981), as well as on a few earlier pioneering empirical works on differentiated products marketsin equilibrium, especially Bresnahan (1981, 1987). One variation of this model (see Berry et al.1999) posits that consumer i ’s conditional indirect utility for good j in market t can be written as

vi j t = x jtβi t − αi t p j t + ξ j t + εi j t . (1)

Here the vector x jt represents observed exogenous product characteristics, ξ j t is an unobservedproduct/market characteristic, and p j t is the endogenous characteristic price.2

In addition to an independent and identically distributed idiosyncratic product/consumermatch value εi j t , there are two types of unobservables in Equation 1, both essential. One is thevector (βi t, αi t) of random coefficients on x jt and p j t . These random coefficients allow hetero-geneity in preferences that can explain why consumers tend to substitute among similar products[those close in (xt, pt)-space] when prices or other attributes of the choice set change. The secondis the product-/market-level unobservable ξ j t . The presence of these demand shocks not onlyis realistic (typically we do not observe all relevant attributes of a product or market), but alsogenerates the familiar problem of price endogeneity. That is, the price of a good in a given marketwill typically be correlated with the latent demand shocks (those associated with all goods) in thatmarket. Such correlation is implied, for example, by standard oligopoly models when firms knowthe realizations of these shocks or, more generally, the relevant elasticities of the demand system.It is this combination of rich consumer heterogeneity through latent taste shocks and endogeneitythrough explicitly modeled product-/market-specific demand shocks that distinguishes the BLPframework, and upon which the nonparametric models of Berry & Haile (2014, 2016) build.

The parametric BLP model already raises a number of difficult questions about identification.One is how to handle the problem of price endogeneity. Instrumental variables will typically beneeded. Classic instruments for prices are exogenous cost shifters. Berry et al. (1995) made limited

2For simplicity, we discuss the usual case in which price is the (only) endogenous product attribute. The arguments extendto the case of other endogenous attributes, although when there is more than one endogenous characteristic per good, thenumber of instruments required will be greater.

www.annualreviews.org • Identification in Differentiated Products Markets 29


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


use of cost shifters, combining these with instruments (characteristics of competing products—the so-called “BLP instruments”) that economic theory tells us will shift equilibrium markups (inaddition to shifting market shares conditional on prices). Following Hausman (1996), Nevo (2001)emphasized proxies for cost shifters (prices of the same good in other markets), whereas Berryet al. (1999) added a range of cost shifters such as exchange rates. A more subtle point involvesidentification of the “substitution parameters”—those governing the distribution of the randomcoefficients. Intuition suggests that these parameters would be identified by exogenous changes inchoice sets (e.g., additions and removals of choices), as these would directly reveal the extent towhich consumers tend to substitute to similar goods. But such exogenous variation often is limitedif present at all. So can more continuous changes in choice sets—say, variation in the prices orqualities of a fixed set of goods—do the job? Are the kinds of instruments used in practice sufficientto identify these parameters without relying on distributional assumptions? What about modelswith less parametric structure on consumer preferences? Can anything be gained by combiningthe supply and demand model in a single system (see, e.g., Bresnahan 1987, Berry et al. 1995)?Do consumer-level demand data help with identification? Although many empirical papers havefollowed the modeling approach of Berry et al. (1995), these identification questions remainedwithout formal answers for many years.

1.2. Related Literatures

Above we mention some key papers that motivate the work we review, but we pause here tohighlight other related work. A huge literature on applied discrete choice demand goes backat least to McFadden (1974), with many later contributions. On the supply side, the idea ofestimating marginal costs by using first-order conditions for imperfectly competitive firms goesback to Rosse (1970), continues through the New Empirical Industrial Organization literatureof the 1980s (see Bresnahan 1989), and has become a standard tool of the empirical industrialorganization (and auctions) literatures. The literature on discriminating between different modesof oligopoly competition dates back at least to Bresnahan (1982) and Lau (1982).

There is an extensive prior literature on the identification of semi-/nonparametric discretechoice models. Perhaps surprisingly, that literature does not cover models with the key features(rich consumer heterogeneity and endogeneity through product-level unobservables) of the BLPframework. Several papers allow rich taste heterogeneity, but without endogeneity. Examplesinclude Ichimura & Thompson (1998) and Briesch et al. (2010). Other papers on the nonparametricidentification of discrete choice models without endogeneity include Manski (1985, 1987, 1988),Matzkin (1992, 1993), and Magnac & Maurin (2007). Another literature (e.g., Blundell & Powell2004) considers control function techniques for dealing with endogeneity. In general, however,control function techniques apply to triangular (or recursive) systems of equations, not to fullysimultaneous systems (see, e.g., Berry & Haile 2014, 2015, and especially Blundell & Matzkin2014). Consequently, except under strong functional form restrictions, such approaches are notapplicable to models of supply and demand.

Yet another set of papers considers endogeneity involving correlation between a choice char-acteristic and unobservables at the individual (e.g., consumer or worker) level. Lewbel (2000), forexample, considers a conditional indirect utility function of the form vi j = xi jβ + εi j , where theobservables xi j can alter the distribution F (·|xi j ) of εi j . However, typical quantities of interest ina differentiated products context (e.g., demand elasticities) involve counterfactuals that hold fixedthe market-/product-level unobservables and consumer tastes while letting the distribution of util-ities change with the value of an observed variable (e.g., a price). Defining such quantities requiresa different framework. Other papers that consider endogeneity in discrete choice models, but in

30 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


a framework different from the differentiated products framework we discuss, include Honore& Lewbel (2002), Hong & Tamer (2003), Altonji & Matzkin (2005), Lewbel (2006), Hoderlein(2009), Petrin & Gandhi (2011), and Fox & Gandhi (2011, 2016).

1.3. The Path Ahead

Looking ahead to the remainder of the article, we first review some familiar parametric demandmodels to motivate key ideas behind our approach. We then discuss identification of demand whenone has only market-level data, as in the original Berry et al. (1995) paper. This is followed by adiscussion of the gains that can be obtained from observing individual-level (micro) data. Microdata does not eliminate the endogeneity problem, but it can substantially reduce the number ofinstruments required for identification. We then turn to identification of the supply side, includingresults that demonstrate constructive joint identification of marginal costs and demand, as well asresults on discrimination between alternative static oligopoly models.

2. INSIGHTS FROM PARAMETRIC MODELS

Our approach to the nonparametric identification problem builds on insights from familiar para-metric models. Consider a standard multinomial logit model (incorporating product-specific un-observables) in which consumer i ’s conditional indirect utility from product j > 0 in market t is

vi j t = x jtβ − αp j t + ξ j t + εi j t, (2)

and the conditional indirect utility from the outside good (good 0) is vi0t = εi0t . Let

γ j t = x jtβ − αp j t + ξ j t .

Choice probabilities (or market shares) are then given by the well-known formula

s j t = eγ j t

1 + ∑k eγkt

. (3)

Each share depends on the entire vector (γ1t, . . . , γJt). The share of good j is strictly increasingin γJt and strictly decreasing in γkt for k �= j . Thus, the “mean utility” γJt can be interpreted asa quality index—one with observed and unobserved components.

As is well known, the relationship in Equation 3 can be inverted to express each index as afunction of the market share vector: γJt = ln(sJt) − ln(s0t). Remembering the definition of theindex γJt , we have

ln(s j t) − ln(s0t) = x jtβ − αpJt + ξJt .

As noted in Berry (1994), this now looks like a regression model with an endogenous covariatep j t . To identify the model parameters (α, β), one needs an excluded instrument for price. To lookeven more like what we do later, partition x jt as (x(1)

j t , x(2)j t ) where x(1)

j t is a scalar. Then conditionon x(2)

j t and rewrite the previous expression as

x(1)j t + ξ j t = 1

β

(ln(s j t) − ln(s0t)

) + α

βp j t, (4)

with ξ j t = ξ j t/β. The right-hand side of this expression is a tightly parameterized function ofshares and prices. The left-hand side is just a linear index of x(1)

j t and the (rescaled) unobservedcharacteristic.

More flexible models yield this same general form, only with less restrictive functions of sharesand prices on the right-hand side. For example, if we follow the same steps for the two-level nested



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


logit model, one can obtain (see Berry 1994) the equation

ln(s j t) − ln(s0t) = x jtβ − αp j t + (1 − λ) ln(s j |g,t) + ξ j t,

where s j |g,t denotes the share of good j within its nest (or group) g. This again looks like aregression model, but now identification requires instruments not only for p j t but also for theendogenous share s j |g,t . Loosely, the need for this extra instrument reflects the new parameter λ,which (compared to the multinomial logit) gives more flexibility to the patterns of substitutionpermitted by the model. As before, we can fix x(2)

j t and rewrite the previous equation as

x(1)j t + ξ j t = 1

β

(ln(s j t) − ln(s0t) − (1 − λ) ln(s j/g,t)

) + α

βp j t, (5)

yielding a linear index on the left and a more flexible function of price and shares on the right.Finally, consider the BLP model and assume that there is one element of the product charac-

teristic vector, x(1)j t , that does not have a random coefficient. Then the model can once again be

rewritten with a nonrandom linear index x(1)j t β

(1)0 + ξ j t for each product. Although there is no longer

a closed form for the inverse of the system of market shares, Berry et al. (1995) show that such aninverse exists (and provide a computational algorithm). To make a connection to Equations 4 and5, we can write this inverse as

x(1)j t + ξ j t = 1

β(1)0

δ j

(st, pt, x(2)

t , θ), (6)

where ξ j t = ξ j t/β(1)0 . Compared to Equations 4 and 5, the right-hand side of Equation 6 is

now a more complicated function of prices and market shares, all of which are endogenous. Foridentification of the parameters in this equation, one needs excluded instruments for prices and,in addition, excluded instruments providing sufficient independent variation in the shares st . Inthe literature, the latter set of instruments is often described loosely as instruments identifyingthe “nonlinear parameters” of the model—those determining how much the random coefficientsaffect substitution patterns.

Our discussion of each of these examples featured three key components: (a) an index of eachgood’s unobserved characteristic and an observed characteristic, (b) an inversion mapping observedmarket shares to each index, and (c) a set of instrumental variables for the prices and market sharesappearing in the inverse function. Our approach to nonparametric identification will make use ofthis same sequence of features.

3. IDENTIFICATION OF DEMAND FROM MARKET-LEVEL DATA

3.1. Demand Model

We begin by sketching the discrete choice demand model of Berry & Haile (2014). In each markett, there is a continuum of consumers. In practice, markets are typically defined by time or geog-raphy, although one can use observed consumer characteristics to define markets more narrowly.Formally, a market is defined by {Jt, χt}, where Jt denotes the number of inside goods available.The outside good—the option to purchase none of the modeled goods—is always available as welland indexed as good 0. The matrix χt describes all product and market characteristics (observedand unobserved).3 We henceforth condition on the number of goods available, setting Jt = J forall t. In each market, each consumer i chooses one good j ∈ {0, 1, . . . , J}.

3We use the terms good, product, and choice interchangeably.

32 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Following the Berry et al. (1995) notation above, x jt ∈ RK is a vector of exogenous observables

associated with good j or market t, p j t ∈ R is an endogenous observable (price), and ξ j t ∈ R

is a market-/choice-specific unobservable. We let xt = (x1t, . . . , xJt), pt = (p1t, . . . , pJt), andξt = (ξ1t, . . . , ξJt). Thus, the characteristics of the market are χt = (xt, pt, ξt) .

Demand is derived from a random utility model. Each consumer i in market t has preferencescharacterized by a vector of conditional indirect utilities (henceforth referred to as utilities) forthe available goods:

vi0t, vi1t, . . . , viJt .

Without loss, the utility vi0t of the outside good is normalized to zero for each consumer. From theeconometrician’s perspective, for each consumer i , (vi1t, . . . , viJt) is a vector of random variablesdrawn from a joint distribution Fv (·|χt).

Thus far, the model is extremely general, placing no restriction on how Fv (·|χt) depends onχt . Implicitly, we have imposed one significant assumption on the demand model by restrictingthe j t-level unobservable ξ j t to be a scalar. This is standard in practice and appears difficult torelax without data on multiple decisions (e.g., panel data, ranked data, or repeated choice data)or distinct submarkets (subpopulations of consumers) assumed to share the same demand shocks(see, e.g., Athey & Imbens 2007).

We further restrict the model with an index structure. In particular, we partition the exogenousobserved characteristics into two parts, x jt = (x(1)

j t , x(2)j t ), with x(1)

j t ∈ R. For each good j , we thendefine an index

δ j t = δ j

(x(1)

j t , ξ j t

)(7)

for some (possibly unknown) function δ j that is strictly increasing in ξ j t . We require that thejoint distribution Fv (·|χt) depend on x(1)

j t and ξ j t only through the index δ j t . That is, lettingδt = {δ1t, . . . , δJt}, we require

Fv(·|χt) = Fv(·|δt, x(2)t , pt). (8)

This is a “weak separability” condition. It places no restriction on how (δt, x(2)t , pt) together alter

the joint distribution of utilities but requires, e.g., that the marginal rate of substitution betweenx(1)

j t and ξ j t be invariant to (x(2)t , pt). The index restriction is satisfied in all of our parametric

examples. However, whereas those examples specified utilities that are separable in the index, thisis not required by Equation 8.

For the results of this section, we also assume that each δ j is linear:

δ j t = x(1)j t β j + ξ j t, (9)

with eachβ j normalized to 1 without loss (this merely defines the units of ξ j t). Berry & Haile (2014)discuss identification with a nonseparable index function, and we discuss the case of a nonlinearbut separable index function below. Henceforth, we condition on x(2)

t , suppress it in the notationwhen possible, and let x jt denote x(1)

j t . The model is then completely general in its treatment ofx(2)

t .

As usual, market-level demand is derived from the conditional (on χt) distribution of randomutilities. Each consumer chooses the product giving the highest utility, yielding choice probabilities(market shares)

s j t = σ j (χt) = σ j (δt, pt) = Pr(

arg maxj∈J

vi j t = j |δt, pt

), j = 1, . . . , J. (10)

Let st denote the vector of market shares (s1t, . . . , sJt).



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


The functions σ j fully characterize the demand system. With market-level data, we observe(st, xt, pt). If we also observed each ξ j t , we would directly observe the demand functions (σ1, . . . , σJ);i.e., identification of demand would be trivial. Thus, the main challenge to nonparametric iden-tification of demand is endogeneity arising through the unobservables ξ j t . In fact, the challengehere is more complex than in many familiar economic settings because each of the endogenousvariables p j t and s j t (price and quantity) depends on all J demand shocks (ξ1t, . . . , ξJt). Standardinstrumental variables and control function approaches cannot be applied here because pricesand quantities are determined in a fully simultaneous system. Our approach to overcoming thesechallenges builds on the index-inverse-instruments intuition developed above for the parametricexamples. We have already described the index restriction. We next discuss the inversion of marketshares.

3.2. Inversion

The goal of the inversion step is to show that, given any vector of prices and nonzero marketshares, there is a unique vector of indices δt that can rationalize this observation with the demandsystem (Equation 10). Berry et al. (2013) demonstrate this invertibility under a condition they call“connected substitutes.” This condition has two parts. The first is that all goods are weak grosssubstitutes with respect to the indices; i.e., for k �= j , σk (δt, pt) is weakly decreasing in δ j t for all(δt, pt) ∈ R

2J. This is little more than a monotonicity assumption implying that δ j t is “good” (e.g.,an index of product quality) at least on average across consumers. A sufficient condition is that,as in the parametric examples, higher values of δ j t raise the utility of good j without affecting theutilities of other goods.

The second part of the Berry et al. (2013) connected substitutes condition is “connected strictsubstitution.” This condition requires that, starting from any inside good, there be a chain ofsubstitution leading to the outside good. For example, in a multinomial logit model (or anydiscrete choice model in which additive shocks to utilities have full support), all goods strictlysubstitute directly to the outside good (all else equal, an increase in the quality of good j causesthe market share of the outside good to fall), so the condition is satisfied. In a model of pure verticaldifferentiation (e.g., Mussa & Rosen 1978, Bresnahan 1981), each good strictly substitutes onlywith its immediate neighbors in the quality hierarchy. But starting from any good j > 0, therewill be a path from one neighbor to the next that eventually links j to the outside good. Thus, inthe vertical model, the connected strict substitution requirement is again satisfied.

Formally, a good j substitutes to good k at (δt, pt) if σk (δt, pt) is strictly decreasing in δ j t . Werepresent the pattern of strict substitution with a matrix � (δt, pt) that has entries

� j+1,k+1 ={

1{good j substitutes to good k at x} j > 00 j = 0.

The second part of the connected substitutes condition is that for all (δt, pt) in their support, thedirected graph of � (δt, pt) has, from every node k �= 0, a directed path to node 0.4

Berry et al. (2013) discuss a range of examples and point out that when δ j t is a quality index, itis hard to violate the connected substitutes condition in a discrete choice setting. Weak substitutesis a direct implication of weak monotonicity in a discrete choice model, and connected strict

4One can of course define the connected substitutes condition in terms of substitution in response to changes in a productcharacteristic other than the index—for example, price.

34 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


substitution then requires only that there be no strict subset of the goods that substitute onlyamong themselves. That is to say, all the goods must belong in one demand system.

Given connected substitutes, Berry et al. (2013) prove the existence of the inverse market sharefunction. That is, for all j , there is a function σ−1

j such that

δ j t = σ−1j (st, pt) (11)

for all (st, pt) in their support.We do not discuss the proof here but point out that this result offers an alternative to the classic

invertibility results of Gale & Nikaido (1965) or Palais (1959), which can be difficult to apply todemand systems. Because Berry et al.’s (2013) result applies outside the discrete choice settingconsidered here, an interesting question is whether it can be used as the starting point for studyingidentification of demand in other settings as well.

Unlike the inversion results for the parametric examples, the invertibility result of Berry et al.(2013) provides no characterization or computational algorithm for the inverse. Nonetheless,having established that the inverse exists, we can move on to its identification using instrumentalvariables. Note that once the inverse is known, so is the value of each index δ j t and, therefore, eachdemand shock ξ j t . Thus, once we demonstrate identification of the inverse, it is as if there wereno unobservables—a situation in which (as discussed above) identification of the demand systemis trivial.

3.3. Instruments: Identifying the Inverse Demand System

The final step of the argument involves using instrumental variables to identify the inverse marketshare functions. Recalling that

δi j = x jt + ξ j t,

we can rewrite Equation 11 as

x jt = σ−1j (st, pt) − ξ j t . (12)

This equation bears close resemblance to the standard nonparametric regression model studiedby Newey & Powell (2003). They consider identification of the model

yi = (xi ) + εi , (13)

using instrumental variables wi that satisfy a standard exclusion restriction that E [εi |wi ] = 0almost surely (a.s.). They show that the analog of the classic rank condition for identification of alinear regression model is a standard completeness condition (Lehmann & Scheffe 1950, 1955),namely that if B(xi ) is a function with finite expectation satisfying E [B (xi ) |wi ] = 0 a.s., thenB (xi ) = 0 a.s. Similar to the classic rank condition, completeness requires that the instrumentsinduce “enough” variation in the endogenous variables.

Equations 12 and 13 are not quite equivalent. Whereas the endogenous variable yi appearsalone on the left-hand side in Equation 13, in Equation 12 all endogenous variables enter throughthe unknown function σ j . Furthermore, in Equation 12 the exogenous observable x jt—an essentialinstrument, as demonstrated below—is not excluded. Nonetheless, Berry & Haile (2014) showthat the proof used by Newey & Powell (2003) can be used to establish identification of σ−1

j (·)under analogous exclusion and completeness conditions. In particular, let wt now denote a setof observables and suppose that (a) E[ξ j t |xt, wt] = 0 a.s., and (b) for all functions B (st, pt) with



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


finite expectation,5 if E [B (st, pt) |xt, wt] = 0 a.s., then B (st, pt) = 0 a.s. Then each of the inversefunctions σ−1

j (·) is identified. Given Equation 12, each unobserved product characteristic ξ j t isthen identified, and identification of the demand system in Equation 10 follows immediately.

We discuss the availability of instruments below. However, it is worth pausing to observe thatthis result provides a reassuringly dull answer to the question of what ensures identification ofdemand in a BLP-type model: instruments for the endogenous variables. Because the model in-volves discrete choice, rich consumer heterogeneity, and a simultaneous system (e.g., all pricesand quantities depend on all J demand shocks), the best possible hope is that identification wouldbe obtained under the same instrumental variables conditions needed for identification of a ho-mogeneous regression model with a separable scalar error. This is what is shown by Berry & Haile(2014).

3.4. Discussion

We pause here to discuss several important issues, including (a) our focus on the demand systemrather than a joint distribution of utilities, (b) the types of observables that can serve as the requiredinstrumental variables, (c) the important and interrelated roles of the BLP instruments and theindex restriction, and (d) the ways in which additional restrictions on preferences can weaken theinstrumental variables requirements.

3.4.1. Demand versus utility. The demand functions σ j are the main features of interest onthe consumer side of the model. These functions determine all demand counterfactuals (up toextrapolation/interpolation, as usual). Demand is the input from the consumer model needed toestimate marginal costs, to test models of supply, to simulate a merger, and so forth. However,demand is not necessarily enough to identify changes in consumer welfare. As usual, valid notionsof aggregate consumer welfare changes can be obtained from market-level demand under anadditional assumption of quasilinearity. Changes in consumer welfare (consumer surplus) arethen identified whenever demand is.

Berry & Haile (2014) also show how to extend identification of demand to identificationof the joint distribution of random utilities, Fv (·|χt) under standard quasilinearity and supportconditions. However, given identification of demand and consumer surplus, there is often littlegain from identifying a particular distribution of random utilities consistent with demand.

3.4.2. Instrumental variables. Although it is encouraging that essentially all one needs for iden-tification is a suitable set of instruments, this leads to the important question of what kinds ofobservables can play the role of these instruments in practice. The analysis above reveals severalinsights. One important observation is that for the completeness condition above to hold, the in-struments must have dimension no less than 2J—i.e., instruments for all 2J endogenous variables(st, pt) are needed. This should not be surprising given the discussion of the parametric examples:Except in the most restrictive of these models, we required instruments not only for prices butfor some quantities (market shares) as well. Formally, this requirement reflects the fact that, in amultigood setting, the quantity demanded of a given good depends on the endogenous prices of allgoods, as well as the demand shocks associated with all goods.6 Inverting the demand system is a

5Other types of completeness assumptions (see, e.g., Andrews 2011) can also suffice.6Contrast this with a classical supply and demand model, in which the quantity demanded depends on only one endogenousprice and one demand shock.

36 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


valuable trick producing a system with only one structural error (demand shock) per equation (seeEquation 12). But, in general, the resulting inverted demand equations each depend on all pricesand quantities. Identification of these inverse demand functions requires independent exogenousvariation in each of these variables.

Excluded cost shifters (e.g., input prices) are the classic instruments for identifying demand.Proxies for cost shifters or for marginal costs themselves (if these proxies are properly excludedfrom demand) can of course substitute. Hausman (1996) proposes a particular type of proxyfor the marginal cost of good j in market t: the prices of good j in other markets t′ (see alsoNevo 2000). Another type of candidate instrument is an excluded shifter of firm markups. Onepossibility involves demographics of other markets falling in the same pricing zone (see, e.g.,Gentzkow & Shapiro 2010, Fan 2013). The availability and suitability of these different types ofinstruments vary across applications. Excluded cost shifters are sometimes available, either at thefirm or product level. Hausman instruments can always be constructed from a market-level dataset but have been controversial: In some applications, the exclusion restriction may be difficult todefend, and in others the instruments may have little cross-market variation. Instruments based ondemographics of other markets require at least market-level demographic data and a supply-sideconnection (like zonal pricing) between the price in one market and the demographics of another.

But even when one has suitable instruments in one or more of these classes, the analysis abovereveals something important: Such instruments cannot suffice on their own in the model above.This is because costs and markups affect the endogenous variables (st, pt) only through prices.

This point may become more clear by considering the identification problem when all pricevariation is exogenous (independent of ξt). With exogenous prices, pt can be treated as an elementof x(2)

t and held fixed for the purposes of studying identification. The inverted demand equationsthen take the form (cf. Equation 12)

x jt = σ−1j (st) − ξ j t . (14)

Each of these equations involves the J-dimensional endogenous variable st . Identification can stillbe obtained following the argument above, but this requires instruments for st . Excluded shiftersof costs or markups cannot do the job because they only alter shares through prices (which arefixed).

This raises the question of what remaining instruments, excluded from the inverse market sharefunction, can shift st in Equation 12 or 14. The exogenous product characteristics xt are the onlyavailable instruments, and they are of the correct dimension. Thus, our result on the identificationof demand requires J-dimensional instruments wt affecting prices (costs or markups), plus theproduct characteristics that enter the demand indices δ j t . Strictly speaking, we have describedsufficient conditions for identification; however, given the presence of 2J endogenous variables,it seems unlikely that one could avoid the need for exogenous variation of dimension 2J withoutadditional data or structure.

Some additional intuition about the role of the instruments xt can obtained by relating thederivatives of the market share function σ (δt, pt) = (σ1(δt, pt), . . . , σJ(δt, pt)) to the derivatives ofthe inverse mapping σ−1(st, pt) = (σ−1

1 (st, pt), . . . , σ−1J (st, pt)). Holding prices fixed (with other

instruments for prices), by the implicit function theorem, the derivative matrix ( Jacobian) of σwith respect to the indices is the inverse of the derivative matrix of σ−1 with respect to the shares.Thus, identifying the effects of shares in the inverse demand system in Equation 12 is equivalent toidentifying the effects of the indices δt on market shares in Equation 10. The xt vector directly shiftsthe indices δt , so it is not surprising that these are appropriate instruments for market shares in theinverse demand function. Furthermore, without the index structure that links the effects of ξ j t tothe effects of x jt , it is not clear how one could quantify the effects that changes in unobservables



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


have on demand. With the linear index structure, this link is particularly clear: A unit increase inξ j t has the same effects as a unit increase in x jt .

This analysis also clears up some possible confusion about the excludability of the BLP instru-ments. On one hand, it natural to ask how (whether) demand shifters could be properly excludedfrom demand. On the other hand, it is clear that characteristics of goods k �= j are excluded fromthe utility of good j , and the parametric examples suggest that perhaps this is enough. We can seein the analysis above that it is the index restriction that makes the exogenous variables xt availableas instruments [rather than being fixed like x(2)

t ] and that yields a system of inverse demand equa-tions in which each x jt appears in only one equation. Thus, both the index restriction and BLPinstruments are central to the identification result above.

Finally, we can see that the BLP instruments are not sufficient on their own in this model. Theyprovide the required independent variation in st , but something else must provide the independentexogenous variation in pt (cf. Armstrong 2015).7 This requires additional instruments for costsor markups. The importance of combining both types of variation has been recognized in muchof the applied literature. For example, Berry et al. (1995) utilize both the BLP instruments andproxies for marginal cost, and Berry et al. (1999) add further cost instruments. The importance ofhaving both types of instruments, even in a parametric setting, is supported by recent simulationsby Reynaert & Verboven (2014). The results of Berry & Haile (2014) may explain why: Both typesof instruments appear to be essential, at least without additional data or structure.

3.4.3. Functional form restrictions. We saw in the parametric examples that the instrumentalvariables requirements were milder than those for the fully nonparametric case. In fact, the para-metric structure not only reduced a completeness condition to a standard rank condition, but alsocut the number of instruments required. This suggests a potentially important role for functionalform restrictions in substituting for sources of exogenous variation. This may be a concern insome applications in which one suspects that functional form, rather than exogenous variation,is pinning down demand parameters. But this trade-off may be advantageous in other cases: Itis sometimes difficult to find J-dimensional cost shifters (or proxies) that can be excluded fromdemand, and further exploration reveals that even fairly modest restrictions on the demand systemcan yield substantial reductions in the instrumental variables requirements.

To illustrate one such possibility, consider a stronger form of the weak separability condition,requiring now that price be included in the index δ j t along with x jt [i.e., x(1)

j t ] and ξ j t :

δ j t = x jtβ − αp j t + ξ j t . (15)

Recall that x(2)t has been treated fully flexibly and that the indices δt enter demand through a fully

nonparametric nonseparable mapping σ . Thus, this more restrictive specification still substantiallygeneralizes versions of the BLP model in which, as often assumed in applied work, price and atleast one exogenous observable enter the utility function without random coefficients. Withoutloss of generality, we can choose the units of ξ j t by setting α = 1. The equations of the inversedemand system then have the form

x jtβ − p j t + ξ j t = σ−1j (st)

or

p j t = −σ−1j (st) + x jtβ − ξ j t .

7The vector xt typically will alter elasticities and therefore markups (prices). However, our formal argument relies on thedirect effect of xt on shares, holding prices fixed.

38 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


This takes the form of a classic inverse demand function with price on the left-hand side andquantities (here, shares) on the right. In this case, because shares are the only endogenous variableson the right, the BLP instruments x− j t can suffice alone: Instruments for costs or markups wouldstill be useful in practice but would not be necessary for identification.

There are many other possibilities for imposing functional form restrictions that reduce theinstrumental variables requirements. These include a variety of nonparametric restrictions suchas symmetry and various nesting structures that can often be motivated by economics or featuresof the market being studied.

4. GAINS FROM MICRO DATA

Better data can also relax the instrumental variables requirements. Here we consider micro datathat match individual choices to consumer-/choice-specific observables

zit = (zi1t, . . . , ziJt) ,

where each zi j t ∈ R.8 Often these consumer-/choice-specific variables will involve interactionsbetween consumer attributes and product attributes [x(1)

t or x(2)t in the notation of the previous sec-

tion]. For example, many applications have utilized interactions of consumer and choice locationsto create measures of distance specific to each consumer and product, e.g., to different modesof transport (McFadden et al. 1977), different hospitals (Capps et al. 2003), different schools(Hastings et al. 2010), or different retailers (Burda et al. 2015). Other examples of observables thatmight play the role of zit include exposure to product-specific advertising (Ackerberg 2003), familysize × car size (Berry et al. 1995, Goldberg 1995), consumer-newspaper political match (Gentzkow& Shapiro 2010), and household-neighborhood demographic match (Bayer & Timmins 2007).

As above, Berry & Haile (2016) start from an extremely flexible random utility model in which

(vi1t, . . . , viJt) ∼ Fv (·|χi t) , (16)

where now [dropping the distinction between x(1)t and x(2)

t ]

χi t = (zit, xt, pt, ξt) . (17)

Consumer utility maximization yields choice probabilities

σ j (χi t) = σ j (zit, xt, pt, ξt) , j = 1, . . . , J. (18)

Let σ (zit, xt, pt, ξt) = (σ1 (zit, xt, pt, ξt) , . . . , σJ (zit, xt, pt, ξt)).Within a given market, (xt, pt, ξt) are fixed, but choice probabilities vary with the value of zit .

Let Zt denote the support of zit in market t. For each z ∈ Zt , we observe the conditional choiceprobability vector st(z) = (s1t(z), . . . , sJt(z)), where each

s j t(z) = σ j (z, xt, pt, ξt)

gives the market share of good j among z-type consumers, given the true value of the vector(xt, pt, ξt) in market t. Let

St = st (Zt)

8Other consumer-level observables can be accommodated in a fully flexible way by treating these as characteristics (elementsof xt ) of distinct markets. This would permit a different vector of unobservables ξt for consumers with different observablecharacteristics. For example, an unobserved product characteristic viewed as desirable by one demographic group could beviewed as undesirable by another.



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


denote the set of all conditional choice probability vectors in market t generated by some z ∈ Zt .Of course, for every s ∈ St , there is at least one vector z∗

t (s ) ∈ Zt such that

st(z∗

t (s )) = s . (19)

The identification arguments in Berry & Haile (2016) rely heavily on the within-market vari-ation in choice probabilities that results from variation in the consumer characteristics zit . Justas in the case of market-level data, the primary challenge is uncovering the value of the latentdemand shocks ξ j t ; once the demand shocks are known, identification of demand is trivial. Berry& Haile (2016) obtain identification using two alternative approaches (applied to slightly differentmodels), each proceeding in two steps. First, within-market variation in zit is used to construct,for each j t combination, a scalar variable that is a function of prices and the scalar unobservableξ j t . Second, standard instrumental variables arguments are applied to obtain identification of thisfunction and, therefore, the value of each structural error ξ j t . Both approaches lead to resultsallowing identification of demand with weaker instrumental variables requirements than those werequired without micro data.

4.1. Identification with a Common Choice Probability

The first approach utilizes an index restriction very similar to that used in the case of market-leveldata and avoids the strongest requirements on the exogenous variation in choice probabilitiesprovided by instruments.

4.1.1. Index and inversion. Let

λi j t = g j (zi j t) + ξ j t,

where g j is an unknown strictly increasing function. Assume now that zit and ξt affect the jointdistribution of utilities only through the indices; i.e., letting λi t = (λi1t, . . . , λiJt), assume

Fv (·|χi t) = Fv (·|λi t, xt, pt) .

With this restriction, we can write the components of the demand system in Equation 18 as

σ j (λi t, xt, pt) , j = 1. . . . , J.

For the remainder of this section, we condition on xt—treating this in a completely general fashionas we did x(2)

t in the previous section—and drop it from the notation.Berry & Haile (2016) require sufficient variation in zit to generate a common choice probability

vector s . That is, they require that there be some choice probability vector s such that

s ∈ St ∀t. (20)

Because choice probabilities conditional on zit are observable, this assumption is verifiable. Fur-thermore, full support for g(zt) is not required unless the support of the unobservable ξt is itselfR

J. In many industries, unobserved tastes/product characteristics vary across markets but not toan extreme degree, so the variation in zit required need not be extreme. In particular, zit needonly move the choice probabilities to the common vector s in each market; no probability needsto be driven to zero or to 1, in contrast to the requirements of identification-at-infinity argu-ments. Indeed, such arguments typically use assumptions implying that every probability vectoris a common choice probability; here we require just one.

A key insight underlying Berry & Haile’s (2016) first approach is that variation in the valueof z∗

t (s ) (recall Equation 19) across markets can be linked precisely to variation in the vector of

40 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


demand shocks ξt . Assuming that the demand system satisfies connected substitutes (now withrespect to the indices λi j t instead of δ j t), the demand system can be inverted: For any choiceprobability vector s and any price vector pt , there is at most one vector of indices λi t such thatσ j (λi t, pt) = s j for all j . Of particular interest is the inverse at the common choice probability s .Because s ∈ St for every market t, the invertibility result of Berry et al. (2013) ensures that foreach market there is a unique z∗

t (s ) ∈ Zt such that st(z∗t (s )) = s . Thus, we may write

g j(z∗

j t(s )) + ξ j t = σ−1

j (s , pt). (21)

4.1.2. Instruments. Berry & Haile (2016) provide conditions ensuring that each function g j isidentified. For simplicity, we take this as given for the remainder of this section. This is equivalentto focusing on the case of a linear index structure

λi j t = zi j tβ j + ξ j t,

where each β j can be normalized to 1 without loss (setting the scale of the unobservable ξ j t). Thisallows us to rewrite Equation 21 as

z∗j t(s ) = σ−1

j (s , pt) − ξ j t . (22)

This equation takes exactly the form of the Newey-Powell nonparametric regression model inEquation 13, with z∗

j t(s ) playing the role of the dependent variable, σ−1j (s , pt) the unknown regres-

sion function, and ξ j t the error term correlated with the endogenous vector pt . Using this insight,and focusing now on cross-market variation, identification of each function σ−1

j (·) (and thereforeeach structural error ξ j t) follows immediately from the result of Newey & Powell (2003) discussedabove, given excluded instrumentswt for pt that satisfy the standard completeness condition. Witheach ξ j t known, identification of demand is immediate.

Here, as in the case of market-level data, we require instruments for pt . However, we no longerneed instruments for st , which is held fixed at s in Equation 22. To suggest why instrumentsfor shares are no longer needed, remember that in the case of market-level data, we relied oninstruments that provided variation in quantities (shares) even when the structural errors ξt andprices pt were held fixed. We avoid this need by exploiting within-market variation in zit . Withina market, ξt and pt are held fixed by construction, whereas variation in zit provides variation inquantities. Thus, only instruments for pt are needed when we move to arguments that rely oncross-market variation.9

Cost shifters and proxies are, as usual, important candidate instruments for pt . In addition,in this micro data context, one could also use features of the market-level distribution of zt asinstruments for price. For example, if a market as a whole features unusually many high-incomeconsumers, prices in this market may be unusually high. This type of instrument is a variant of the“characteristics of nearby markets” discussed in the case of market data, although here “nearbyconsumers” can replace “nearby markets.” Berry & Haile (2016) call these Waldfogel instruments,after the insight in Waldfogel (2003) that choice sets (including prices) naturally vary with thelocal distribution of consumer types. To see why such instruments may be excludable, recall thatwith micro data the observed choice probabilities already condition on the consumer’s own zit . Sothe exclusion restriction is a requirement that there be no demand spillovers (or sorting affects)

9Recalling the discussion in Section 3.4.2 of the relationship between derivatives of inverse shares with respect to quantities andderivatives of shares with respect to quality indices, another intuition is that variation in zt reveals the patterns of substitutionbetween goods in response to changes in goods’ quality indices.



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


that would require putting attributes of other consumers in the market in the micro-level demandsystem.

The BLP instruments are not available as instruments here because we have conditioned on xt .However, we have not imposed any condition requiring that rival characteristics x− j t be excludedfrom the shifters of vi j t . Such a restriction can restore the availability of the BLP instruments, andother functional form restrictions can reduce the number of instruments required even further.

To illustrate this, first suppose that we add pt to the index λ j t(z) so that

λi j t(z) = zi j t − αp j t + ξ j t . (23)

In this case, Equation 22 becomes

z∗j t(s ) = σ−1

j (s ) + αp j t − ξ j t . (24)

The first term σ−1j (s ) on the right-hand side is a constant; thus, we have a regression model with

just one endogenous variable. Alternatively, we could put a component of xt into the index:

λi j t(z) = zi j t + x(1)j t β + ξ j t .

This would make x(1)t available as (BLP) instruments for prices.

4.2. Utility Linear in z with Large Support

Berry & Haile (2016) consider a second approach using a slightly different specification in which(zi1t, . . . , ziJt) serve as special regressors (e.g., Lewbel 1998, 2000). This approach requires that(zi1t, . . . , ziJt) have large support, i.e., sufficient support to move choice probabilities to all pointson the simplex. This is a strong assumption, but special regressors with large support have beenused at least since Manski (1975, 1985) as a useful way to explore how far exogenous variation incovariates can go toward eliminating the need for distributional assumptions in discrete choicemodels. Berry & Haile (2016) take the same approach to explore how far variation in the demandshifters zit can go in reducing the need for excluded instruments.

In the simplest version of this second approach,10 Berry & Haile (2016) assume that utilitiestake the form

vi j t = λi j t + μi j t, j = 1, . . . , J, (25)

where

λi j t = zi j t + ξ j t (26)

as before, and the random variables (μi1t, . . . , μi1t) have a joint distribution that does not dependon λt :11

Fμ (·|χt) = Fμ (·|xt, pt) . (27)

In addition, Berry & Haile (2016) impose the standard condition that the utility from good jis unaffected by the observed characteristics of other goods. With Equation 27, this implies

Pr(μi j t < c |xt, pt, ξt) = Pr(μi j t < c |x jt, p j t). (28)

10As above, this version can be generalized to allow each zi j t to enter through an unknown monotonic function g j (·). Belowwe discuss another variation that treats ξt more flexibly.11If Fμ depended freely on λt , what appears to be an additive separability restriction in Equation 25 would actually have nocontent: The distribution of vi t could still change freely with λt .

42 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


This specification is a nonparametric generalization of standard random coefficients models, inwhich the utility from a good is a random function of its characteristics and price.12

Under the large support assumption

supp zit | (xt, pt, ξt) = RJ, (29)

identification can be shown in two simple steps. First, by standard arguments, within-marketvariation in zit traces out the joint distribution of (μi1t + ξ1t, . . . , μiJt + ξJt) separately for eachmarket. This joint distribution also reveals, for each j , the marginal distribution of μi j t + ξ j t

in each market t. The second step then treats a functional of this marginal distribution as thedependent variable in a nonparametric instrumental variables regression model. For example, byEquation 28, for a given j the mean (or any given quantile) τ j t of this marginal distribution mustsatisfy

τ j t = h j (x jt, p j t) + ξ j t (30)

for some (unknown) function h j . Once again, we can condition on x jt without loss, yielding anequation taking the form of the regression model studied by Newey & Powell (2003). Becauseτ j t can be treated as observed (by the first step), identification of the function h j (and then theresiduals ξ j t) requires instruments satisfying a standard completeness condition. Because thereis now only one price entering h j , identification can be obtained with only a single instrument.Furthermore, in this case, all the instrument types discussed above are candidates; in particular,the BLP instruments x− j t were not fixed in the derivation of Equation 30, so they are availableas instruments. In addition, because Equation 30 requires only one instrument at a time, a singlemarket-level instrument (e.g., a single Waldfogel instrument) could potentially suffice.

The model above can be generalized by dropping the requirement that utilities be separablein the demand shocks ξ j t . Consider the specification

vi j t = zi j tβ + μi j t

with the joint distribution of μi t now permitted to depend on ξt :

Fμ (·|χt) = Fμ (·|xt, pt, ξt) .

Under an appropriate monotonicity condition—for example, letμi j t be stochastically increasing inξkt when j = k but independent of ξkt otherwise—repeating the analysis above yields an equationtaking the form of a nonparametric instrumental variables regression with a nonseparable error.For example, Berry & Haile (2016) show that under appropriate assumptions the mean of themarginal distribution of μi j t would take the form

τ j t = h j (x jt, p j t, ξ j t), (31)

where h j is strictly increasing ξ j t . Chernozhukov & Hansen (2005) demonstrate identificationof such a nonseparable nonparametric regression model under modified completeness conditionsthat (at least in the case of a continuous endogenous dependent variable) are somewhat harder tointerpret than the standard completeness condition used by Newey & Powell (2003). However,whether we use the model with separable ξ j t leading to Equation 30 or the more general modelleading to Equation 31, this second class of (separable in z) models studied by Berry & Haile(2016) has the advantage of minimizing the number of instruments required while maximizingthe availability of candidate instruments.

12For example, one obtains this structure by assuming that vi j t = zi j t + ξ j t + v(x jt , p j t , θi t ) for all j , where θ j is an infinite-dimensional random parameter whose distribution does not depend on χi t .



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


5. SUPPLY

Many positive and normative questions regarding differentiated products markets require a quan-titative understanding of supply as well as demand. In a static oligopoly context, the primitives ofa supply model are marginal cost functions and a specification of oligopoly competition. Becausereliable marginal cost data are seldom available, there is a long tradition in the empirical industrialorganization literature of estimating marginal costs using firm first-order conditions.

A very early example is provided by Rosse (1970), who considers a model of monopoly news-paper publishers, and the key insight of this literature is particularly transparent in the case ofmonopoly. Marginal revenue is a function of observed quantity, observed price, and the slope ofdemand. If the slope of demand is already known, marginal cost is revealed directly as equal tomarginal revenue. Rosse (1970) considers joint estimation of demand and marginal cost parame-ters from a combination of demand equations and monopoly first-order conditions. Elements ofthis approach are carried over to oligopoly models in the New Empirical Industrial Organizationliterature (see, e.g., Bresnahan 1981, 1989). That literature also asks whether the hypothesis of aparticular form of oligopoly competition is falsifiable. The widely used approach of BLP involvescombining estimates of demand parameters with first-order conditions characterizing equilibriumin a given oligopoly model (typically multiproduct oligopoly price setting) to solve for marginalcosts and parameters of marginal cost functions.

Below we discuss nonparametric identification results that build on these earlier insights.13

We discuss identification of marginal costs, identification of marginal cost functions, and discrim-ination between particular models of oligopoly competition. For the remainder of this section,we do this treating demand as known, reflecting the results above on identification of demand.However, in Section 6, we discuss results obtained by treating demand and supply explicitly as afully simultaneous system.

5.1. Identification of Marginal Costs with a Known Oligopoly Model

When the model of oligopoly competition is known, identification of equilibrium marginal costsfollows almost immediately from identification of demand. Let mc jt denote the equilibriummarginal cost of good j in market t.14 Given the connected substitutes condition on demand(now with respect to prices), Berry & Haile (2014) point out that for a wide variety of staticoligopoly models there exists a known function ψ j such that in equilibrium

mc jt = ψ j (st,M t, Dt(st, pt), pt) , (32)

where Dt (st, pt) is the matrix of partial derivatives ∂σk/∂p�. Here M t is the scalar number ofpotential consumers in market t (market size), so the level of demand is q jt = M ts j t .

If the function ψ j is known, then mc jt is directly identified from Equation 32 once the demandderivatives Dt are identified. Because most standard oligopoly models imply a known functionalform forψ j , identification of the level of marginal cost then follows directly from the identificationof demand.

In the simple case of monopoly, ψ j is just the standard marginal revenue function. Moregenerally, the function ψ j can be interpreted as a generalized product-specific marginal revenuefunction. For example, in the case of single-product firms setting prices in a static Nash equilibrium,

13There are important questions about identification when firms make discrete supply decisions—e.g., entry or introductionof new products—as well as identification of dynamic oligopoly models. These are beyond the scope of this review.14In general, this is the marginal cost of good j in market t conditional on the observed values of all relevant quantities.

44 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


firm j ’s first-order condition can be written

mc jt = p j t + 1∂s j t/∂p j t

M ts j t . (33)

The right-hand side of Equation 33 can be interpreted as the change in revenue that results froma price decrease sufficient to increase the quantity by one unit, holding constant the prices of otherproducts. With multiproduct firms and simultaneous price setting (as in the BLP model), eachfunction ψ j is obtained by solving a simultaneous system of first-order conditions. The vector ofmarginal costs for all goods in market t is given by

mct = pt +�−1t st, (34)

where �t is a matrix with ( j, k)-entry equal to ∂skt/∂p j t when goods j and k are produced by thesame firm, and zero otherwise.

5.2. Identification of Marginal Cost Functions

When the right-hand side of Equation 32 is known, this equation immediately yields identificationof the level of market each cost mc jt . Knowledge of the equilibrium level of marginal costs issufficient to address some types of questions. But unless one assumes constant marginal costs,many counterfactuals of interest will require knowing how these costs vary with output.

Typically, one might specify a marginal cost function of the form

mc jt = c j(q jt, w j t

) + ω j t, (35)

where w j t and ω j t are observed and unobserved cost shifters, respectively. With the values ofmc jt known, Equation 35 takes the form of a standard separable nonparametric regression, as inNewey & Powell (2003). Identification of the unknown function c j requires an instrument for theendogenous variables in Equation 35. Typically, one assumes that the observed cost shifters aremean independent of ω j t . In that case, a single excluded instrument for the endogenous quantityq jt can suffice.

Natural instruments for q jt include the exogenous cost shifters w− j t of other goods. Otherpotential instruments are also likely to be available as well. Demand shifters of own and rivalproducts or firms are all possible instruments, if they are properly excluded from own-productmarginal costs. Market-level factors that influence the level of demand (e.g., total population andthe population of various demographic groups) are other possible instruments.

Given identification of demand, the problem of finding an appropriate number of instrumentsis much easier on the cost side than on the demand side. In the simplest case, there is only oneendogenous variable in the marginal cost function but possibly many available cost and demandinstruments. This availability of instruments means that richer specifications of the marginalcost functions may be accommodated. For example, in some applications, one may wish to allowproduction spillovers across goods produced by the same firm. This could introduce the entirevector Q j of a firm’s own quantities (all endogenous) as arguments of the marginal cost functionc j . In many cases, there will be excluded instruments available of dimension even larger than thatof Q j .

5.3. Identifying Cost Shocks with an Unknown Oligopoly Model

Berry & Haile (2014) show that one need not specify the oligopoly model in order to identify thelatent shocks to marginal costs, ω j t . This can be directly useful because it allows identification of



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


the reduced form for equilibrium prices, which can be used to answer some kinds of counterfactualquestions without specifying the form of oligopoly competition. Identification of the latent costshocks also leads to the most straightforward and powerful of their results on discriminationbetween alternative oligopoly models, a topic we take up in the following section.

Here we continue to assume that Equation 33 holds but allow the form of the functionψ j to beunknown. Thus, we relax the assumption of a known oligopoly model and require only that somerelation of the form of Equation 33 exist. To allow this relaxation, we require an index structureon the marginal cost function similar to one exploited previously on the demand side.15 Partitionthe cost shifters as {w(1)

j t , w(2)j t }, with w(1)

j t ∈ R, and define the cost indices

κ j t = w(1)j t γ j + ω j t, j = 1, . . . , J, (36)

where each parameter γ j may be normalized to 1 without loss. Suppose now that the cost shifterw

(1)j t and the cost shock ω j t enter marginal costs only through the index. In particular, assume that

each marginal cost function c j (q jt, w j t, ω j t) can be rewritten as

c j

(q jt, κ j t, w

(2)j t

),

where c j is strictly increasing in κ j t .Now fix w(2)

j t , treating it fully generally, and drop it from the notation. Let w j t now representw

(1)j t . Berry & Haile (2014) show that the supply-side first-order conditions can be inverted to

obtain relations of the form

κ j t = π−1j (st, pt) , (37)

where each π−1j is an unknown function.16 Rewriting this as

w j t = π−1j (st, pt) − ω j t, (38)

we obtain an equation taking exactly the form of the inverted demand equations (Equation 12)above. Identification of the functions π−1

j and, therefore, each ω j t can thus be obtained usingthe same extension of Newey & Powell (2003) relied on in Section 3.3, now with (xt, wt) as theinstruments.

Because here we have fixed not only x(2)t but also w(2)

t , the instrumental variables requirementis more demanding than that for the parallel result on identification of demand. In particular, thedemand shifters xt [i.e., x(1)

t ] must now be excluded from marginal costs. In some applications,product characteristics will vary without affecting firm costs due to technological constraints (e.g.,satellite television reception in Goolsbee & Petrin 2004) or other exogenous market-specific fac-tors (climate, topography, transportation network). In other cases, product characteristics thatshift demand may alter fixed costs rather than marginal costs—for example, quality producedthrough research and development, a product’s geographic location, or product-specific advertis-ing (e.g., Goeree 2008). Other examples of instruments that can play the role of xt here involveinteractions between market and product characteristics. For example, Berry et al. (1995) pointout that conditional on the product characteristic “miles per gallon” (which might affect marginalcost), the characteristic “miles per dollar” is a demand shifter that is properly excluded from themarginal cost function.

15This structure is also used below when we discuss identification of demand and supply within a single simultaneous system.16This function is the composition of the inverse (with respect to κ j t ) of the marginal cost function and the generalizedproduct-specific marginal revenue function ψ j appearing in the first-order condition for good j . We use the notation π−1 asa reminder that this relation is obtained by inverting the equilibrium map to express the cost index κ j t in terms of the marketoutcomes (st , pt ).

46 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Given identification of the inverted demand functions σ−1j and the functions π−1

j , total differ-entiation of the system

x jt + ξ j t = σ−1j (st, pt) ∀ j,

w j t + ω j t =π−1j (st, pt) ∀ j,

(39)

will reveal the response of quantities and prices to the exogenous shifters (xt, wt). This is trueeven when the interpretation of π−1

j is not yet established via appeal to some particular oligopolymodel. In Section 6, we return to this system of simultaneous equations to consider a differentapproach to identification.

5.4. Discrimination Between Models of Firm Conduct

An important early literature in industrial organization explored discrimination between alterna-tive models of firm conduct (see, e.g., Bresnahan 1989, and references therein). This literaturewas developed on the important insight from Bresnahan (1982) that “rotations of demand” canalter equilibrium markups differently in different models of supply. Thus, the price response tosuch rotations might be used to infer the true model. A formalization of this idea was developedby Lau (1982), although the result was limited to conjectural variations models with nonstochasticdemand and cost, homogeneous goods, and symmetric firms. Berry & Haile (2014) show thatnone of these limitations is essential, and that Bresnahan’s intuition can be generalized to pro-vide an approach for discriminating between alternative models in a much less restrictive setting.Moreover, in the differentiated products context, there are many different types of variation thatcan be exploited, not just the rotations of market demand considered by Bresnahan (1982) andLau (1982).

The most straightforward results of this type in Berry & Haile (2014) take advantage of theresults in the previous section. Suppose that we have already identified each cost index κ j t as wellas the demand derivatives in each market. Consider again the first-order condition

c j(q jt, κ j t

) = ψ j (st,M t, Dt (st, pt) , pt) , (40)

where the function ψ j is that implied by a hypothesized model of oligopoly competition. Animplication of this hypothesis is that all observations ( j t combinations) with the same values of q jt

and κ j t must have the same value for the right-hand side of Equation 40 as well. If we misspecifythe model, this restriction will often fail: Different values of marginal cost will be required torationalize the data, even though all shifters of marginal costs have be held fixed. Such a findingwill falsify a misspecified oligopoly model.

As the simplest example (and one that makes a tight connection to Bresnahan 1982), supposethat there is a single producer setting prices and quantities as a profit-maximizing monopolist. Ifwe mistakenly hypothesize that the firm prices at marginal cost, Equation 40 becomes

c j(q jt, κ j t

) = p j t ; (41)

i.e., ψ j (st,M t, Dt (st, pt) , pt) is just p j t . This hypothesis would be falsified if (for example) thereare two markets with the same (q jt, κ j t, p j t) but different demand derivatives. Berry & Haile (2014)show how this can arise when there is a nonparallel shift in demand.

However, changes in demand are just one type of variation that can reveal misspecificationof the oligopoly model though the restriction given in Equation 40. In general, a model can befalsified whenever there is variation between two markets t and t′ or products j and j ′ that (a)leaves the relation between quantities and marginal cost unchanged [i.e., c j (·, κ j t) = c j ′ (·, κ j ′t′ )], (b)yields q jt = q j ′t′ under the true model, and (c) would imply q jt �= q j ′t′ under the false model. Even if



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


preferences and market size do not change (demand is fixed), one can obtain a contradiction undera misspecified model from variation in the number of competing firms, the set of competinggoods, observed or unobserved characteristics of competing products, or observed/unobservedcost shifters of competitors. Berry & Haile (2014) provide several examples. They also show howthe insights described here can be generalized to apply without requiring identification of themarginal cost shocks and, therefore, without the cost-side index structure relied on in Section 5.3.

6. IDENTIFICATION IN A SIMULTANEOUS SYSTEM

Although the main challenge to identification in differentiated products markets is the simulta-neous determination of prices and quantities, our approach in the identification results presentedabove was sequential. We began by demonstrating identification of demand without specifying amodel of supply; then, given knowledge of demand, we showed how the primitives of supply couldbe identified. An alternative is to directly consider identification of the fully simultaneous modelof differentiated products demand and supply.

Berry & Haile (2014) explore such an approach, using the same kind of index structure (onboth the demand and cost sides) relied on in Section 5.3. In particular, they consider identificationof the system of 2J equations in Equation 39. These equations exhibit what Berry & Haile (2015)call a “residual index structure,” as each structural error enters the model through an index thatalso depends on an equation-specific observable. This class of models was introduced by Matzkin(2008) and is also studied by Matzkin (2015) and Berry & Haile (2015).17

The results in this literature show that it is possible to make trade-offs between (a) supportconditions on the instruments (here xt, wt) and (b) shape restrictions on the joint density of theunobservables (here ξt, ωt). At one extreme, Berry & Haile (2014, 2015) show identification of thesystem of Equations 39 under an assumption that the instruments have large support, but with norestriction on the density of unobservables. At the other extreme, Berry & Haile (2015) show thateven with arbitrarily small support for the instruments, failure of identification occurs only understrong restrictions on the joint density of unobservables. These results can be extended, appealingto results from Matzkin (2008) or Berry & Haile (2015), to models of the form

g j (x jt) + ξ j t = σ−1j (st, pt) ∀ j,

h j (w j t) + ω j t = π−1j (st, pt) ∀ j,

where the functions g j and h j are unknown strictly increasing functions.18

The simultaneous equations approach contrasts with the approaches in the previous sectionsthat rely on completeness conditions to establish identification. A disadvantage of identificationresults relying on completeness conditions is a lack of transparency about the kinds of assumptionson economic primitives that will generate completeness. A related point is that identification proofsrelying on completeness conditions provide little insight about how the observables uniquelydetermine the primitives; formally, identification is proved by contradiction. In contrast, theresults from the simultaneous equations literature rely on explicit conditions on the primitives ofthe supply and demand model and permit constructive identification proofs.

17Matzkin (2015) also provides conditions for identification of certain features of nonparametric simultaneous equationsmodels that partially relax the residual index structure.18Identification of this system does not require assuming a particular form of oligopoly supply, although doing so allowsidentification of firms’ marginal costs, using Equation 32. Because imposing oligopoly first-order conditions directly on thesystem of equations would introduce cross-equation restrictions, an interesting question is whether this could allow relaxationof identification conditions.

48 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


7. CONCLUSION

Above we review recent nonparametric identification results for models of discrete choice demandand oligopoly supply that are widely used in empirical economics. The primary message of theseresults is that identification holds under precisely the kinds of instrumental variables conditionsrequired for more familiar (e.g., regression) models. Most of the results exploit (a) an index restric-tion on the way structural errors enter an otherwise fully flexible model and (b) the invertibility ofthe demand system that holds under the mild connected substitutes condition. Identification thenrelies on the presence of sufficient exogenous sources of variation in prices and quantities—i.e., onthe standard requirement of adequate instruments for the endogenous variables. The results alsoshow how the standard practice of specifying a form of competition on the supply side leads tofalsifiable restrictions that can be used to discriminate between alternative models of firm conduct.

The results discussed here may suggest alternative, even nonparametric, estimation and test-ing approaches. But we believe the results are important regardless of the statistical tools usedin practice. Economists have long recognized the distinction between identifiability of a modeland properties of any particular estimator or test (e.g., Koopmans 1945, 1950; Hurwicz 1950;Koopmans & Reiersol 1950). Because every data set is finite, going beyond mere description ofthe data requires reliance on approximation techniques. Robustness to alternative specifications istherefore a concern in every application. But a nonparametric identification result demonstratesthat functional forms and distributional assumptions relied on in finite samples can correctly beviewed as tools of approximation rather than essential maintained hypotheses. Scholars and pol-icy makers should have greater confidence in the value of empirical work when it is known thatthe essential role of functional form and distributional assumptions is limited to the unavoidablejobs of approximation, extrapolation, and compensation for the gap between the exogenous vari-ation available in practice and that sufficient to distinguish between all admissible nonparametricstructures.

At a more practical level, the results discussed here provide important guidance regarding thetypes of instruments that can suffice in practice, as well as available trade-offs among the typesof data available, the flexibility of the model, and the demands on instrumental variables. Withmarket-level data, the results for the most general model require instruments for all prices andquantities: exogenous shifters of (or proxies for) costs or markups as well as the BLP instrumentsthat, besides altering markups, shift market shares directly. However, individual-level micro datacan eliminate the need for market share instruments, and some special cases require only a sin-gle exogenous price shifter to identify demand. Given identification of demand, identificationof marginal costs requires no additional instruments, and identification of firms’ marginal costfunctions can be attained with as few as one excluded instrument that shifts equilibrium quantitiesacross markets.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.

LITERATURE CITED

Ackerberg D. 2003. Advertising learning and customer choice in experience good markets: a structural em-pirical examination. Int. Econ. Rev. 44:1007–40

Allenby GM, Rossi PE. 1999. Marketing models of consumer heterogeneity. J. Econom. 89:57–78



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Altonji J, Matzkin RL. 2005. Cross-section and panel data estimators for nonseparable models with endogenousregressors. Econometrica 73:1053–102

Andrews DWK. 2011. Examples of l2 -complete and boundedly complete distributions. Discuss. Pap. 1801, CowlesFound., Yale Univ., New Haven, CT

Armstrong TB. 2015. Large market asymptotics for differentiated product demand estimators with economic modelsof supply. Work. Pap., Yale Univ., New Haven, CT

Athey S, Imbens GW. 2007. Discrete choice models with multiple unobserved choice characteristics. Int. Econ.Rev. 48:1159–92

Bayer P, Ferreira F, McMillan R. 2007. A unified framework for measuring preferences for schools andneighborhoods. J. Polit. Econ. 115:588–638

Bayer P, Timmins C. 2007. Estimating equilibrium models of sorting across locations. Econ. J. 117:353–74Berry ST. 1994. Estimating discrete choice models of product differentiation. RAND J. Econ. 23:242–62Berry ST, Gandhi A, Haile PA. 2013. Connected substitutes and invertibility of demand. Econometrica 81:2087–

111Berry ST, Haile PA. 2014. Identification in differentiated products markets using market level data.

Econometrica 82:1749–97Berry ST, Haile PA. 2015. Nonparametric identification of simultaneous equations models with a residual index

structure. Work. Pap., Yale Univ., New Haven, CTBerry ST, Haile PA. 2016. Nonparametric identification of multinomial choice demand models with heterogeneous

consumers. Work. Pap., Yale Univ., New Haven, CTBerry ST, Levinsohn J, Pakes A. 1995. Automobile prices in market equilibrium. Econometrica 60:889–917Berry ST, Levinsohn J, Pakes A. 1999. Voluntary export restraints on automobiles: evaluating a strategic trade

policy. Am. Econ. Rev. 89:189–211Blundell R, Matzkin RL. 2014. Control functions in nonseparable simultaneous equations models. Quant.

Econ. 5:271–95Blundell RW, Powell JL. 2004. Endogeneity in semiparametric binary response models. Rev. Econ. Stud.

71:655–79Bresnahan T. 1981. Departures from marginal cost pricing in the American automobile industry. J. Econom.

17:201–27Bresnahan T. 1982. The oligopoly solution concept is identified. Econ. Lett. 10:82–97Bresnahan T. 1987. Competition and collusion in the American automobile oligopoly: the 1955 price war.

J. Ind. Econ. 35:457–82Bresnahan T. 1989. Empirical studies of industries with market power. In The Handbook of Industrial Organi-

zation, Vol. 2, ed. R Schamlensee, R Willig, pp. 1011–57. Amsterdam: North-HollandBriesch RA, Chintagunta PK, Matzkin RL. 2010. Nonparametric discrete choice models with unobserved

heterogeneity. J. Bus. Econ. Stat. 28:291–307Bundorf K, Levin J, Mahoney N. 2012. Pricing and welfare in health plan choice. Am. Econ. Rev. 102:3214–48Burda M, Harding M, Hausman J. 2015. A Bayesian mixed logit-probit model for multinomial choice. J. Appl.

Econ. 30:353–76Capps C, Dranove D, Satterthwaite M. 2003. Competition and market power in option demand markets.

RAND J. Econ. 34:737–63Cardon J, Hendel I. 2001. Asymmetric information in health care and health insurance markets: evidence

from the National Medical Expenditure Survey. RAND J. Econ. 32:408–27Chernozhukov V, Hansen C. 2005. An IV model of quantile treatment effects. Econometrica 73:245–61Chintagunta PK, Honore BE. 1996. Investigating the effects of marketing variables and unobserved hetero-

geneity in a multinomial probit model. Int. J. Mark. Res. 13:1–15Eizenberg A. 2014. Upstream innovation and product variety in the United States home PC market. Rev. Econ.

Stud. 81:1003–45Fan Y. 2013. Ownership consolidation and product characteristics: a study of the U.S. daily newspaper market.

Am. Econ. Rev. 103:1598–628Fox J, Gandhi A. 2011. Identifying demand with multi-dimensional unobservables: a random functions approach.

Work. Pap., Univ. Wisconsin–Madison

50 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Fox J, Gandhi A. 2016. Nonparametric identification and estimation of random coefficients in multinomialchoice models. RAND J. Econ. 47:118–39

Gale D, Nikaido H. 1965. The Jacobian matrix and global univalence of mappings. Math. Ann. 159:81–93Gentzkow M, Shapiro J. 2010. What drives media slant? Evidence from U.S. newspapers. Econometrica 78:35–

71Goeree MS. 2008. Limited information and advertising in the US personal computer industry. Econometrica

76:1017–74Goldberg PK. 1995. Product differentiation and oligopoly in international markets: the case of the U.S.

automobile industry. Econometrica 63:891–951Goldberg PK. 1998. The effects of the corporate average fuel economy standards in the automobile industry.

J. Ind. Econ. 46:1–33Goldberg PK, Verboven F. 2001. The evolution of price dispersion in the European car market. Rev. Econ.

Stud. 68:811–48Goolsbee A, Petrin A. 2004. The consumer gains from direct broadcast satellites and the competition with

cable TV. Econometrica 72:351–81Gordon B, Hartmann WR. 2013. Advertising effects in presidential elections. Mark. Sci. 32:19–35Hastings J, Kane T, Staiger D. 2010. Heterogeneous preferences and the efficacy of public school choice. Work. Pap.,

Brown Univ., Providence, RIHausman JA. 1996. Valuation of new goods under perfect and imperfect competition. In The Economics of New

Goods, ed. TF Bresnahan, RJ Gordon, pp. 209–48. Chicago: Univ. Chicago PressHo K. 2009. Insurer-provider networks in the medical care market. Am. Econ. Rev. 99:393–430Hoderlein S. 2009. Endogenous semiparametric binary choice models with heteroskedasticity. Work. Pap. 747, Boston

Coll., Chestnut Hill, MAHong H, Tamer E. 2003. Endogenous binary choice model with median restrictions. Econ. Lett. 80:219–25Honore BE, Lewbel A. 2002. Semiparametric binary choice panel data models without strictly exogenous

regressors. Econometrica 70:2053–63Hurwicz L. 1950. Generalization of the concept of identification. See Koopmans 1950, pp. 245–57Ichimura H, Thompson TS. 1998. Maximum likelihood estimation of a binary choice model with random

coefficients of unknown distribution. J. Econom. 86:269–95Koopmans TC. 1945. Statistical estimation of simultaneous economic relations. J. Am. Stat. Assoc. 40:448–66Koopmans TC, ed. 1950. Statistical Inference in Dynamic Economic Models. New York: WileyKoopmans TC, Reiersol O. 1950. The identification of structural characteristics. Ann. Math. Stat. 21:165–81Lau L. 1982. On identifying the degree of competitiveness from industry price and output data. Econ. Lett.

10:93–99Lehmann EL, Scheffe H. 1950. Completeness, similar regions, and unbiased estimation: part I. Sankhya

10:305–40Lehmann EL, Scheffe H. 1955. Completeness, similar regions, and unbiased estimation: part II. Sankhya

15:219–36Lewbel A. 1998. Semiparametric latent variable model estimation with endogenous or mismeasured regressors.

Econometrica 66:105–21Lewbel A. 2000. Semiparametric qualitative response model estimation with unknown heteroscedasticity or

instrumental variables. J. Econom. 97:145–77Lewbel A. 2006. Simple endogenous binary choice and selection panel model estimators. Work. Pap. 613, Boston

Coll., Chestnut Hill, MALustig J. 2010. The welfare effects of adverse selection in privatized medicare. Work. Pap., Boston Univ., Boston,

MAMagnac T, Maurin E. 2007. Identification and information in monotone binary models. J. Econom. 139:76–104Manski CF. 1975. Maximum score estimation of the stochastic utility model of choice. J. Econom. 3:205–28Manski CF. 1985. Semiparametric analysis of discrete response: asymptotic properties of the maximum score

estimator. J. Econom. 27:313–33Manski CF. 1987. Semiparametric analysis of random effects linear models from binary panel data. Econometrica

55:357–62



Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.


Manski CF. 1988. Identification of binary response models. J. Am. Stat. Assoc. 83:729–38Matzkin RL. 1992. Nonparametric and distribution-free estimation of the binary choice and threshold crossing

models. Econometrica 60:239–70Matzkin RL. 1993. Nonparametric identification and estimation of polychotomous choice models. J. Econom.

58:137–68Matzkin RL. 2008. Identification in nonparametric simultaneous equations. Econometrica 76:945–78Matzkin RL. 2015. Estimation of nonparametric models with simultaneity. Econometrica 83:1–66McFadden D. 1974. Conditional logit analysis of qualitative choice behavior. In Frontiers of Econometrics, ed.

P Zarembka, pp. 105–42. New York: AcademicMcFadden D. 1981. Econometric models of probabilistic choice. In Structural Analysis of Discrete Data with

Econometric Applications, ed. C Manski, D McFadden, pp. 198–272. Cambridge, MA: MIT PressMcFadden D, Talvitie A, Cosslett S, Hasan I, Johnson M, et al. 1977. Demand model estimation and validation.

Rep. UCB-ITS-SR077-9, Inst. Transp. Stud., Berkeley, CAMussa M, Rosen S. 1978. Monopoly and product quality. J. Econ. Theory 18:301–7Nair H, Chintagunta P, Dube JP. 2004. Empirical analysis of indirect network effects in the market for personal

digital assistants. Quant. Mark. Econ. 2:23–58Neilson C. 2013. Targeted vouchers, competition among schools, and the academic achievement of poor students. Work.

Pap., Yale Univ., New Haven, CTNevo A. 2000. Mergers with differentiated products: the case of the ready-to-eat cereal industry. RAND J.

Econ. 31:395–421Nevo A. 2001. Measuring market power in the ready-to-eat cereal industry. Econometrica 69:307–42Newey WK, Powell JL. 2003. Instrumental variable estimation in nonparametric models. Econometrica

71:1565–78Palais RS. 1959. Natural operations on differential forms. Trans. Am. Math. Soc. 92:125–41Petrin A. 2002. Quantifying the benefits of new products: the case of the minivan. J. Polit. Econ. 110:705–29Petrin A, Gandhi A. 2011. Identification and estimation in discrete choice demand models when endogeneous variables

interact with the error. Work. Pap., Univ. Minn., MinneapolisReynaert M, Verboven F. 2014. Improving the performance of random coefficients demand models: the role

of optimal instruments. J. Econom. 179:83–98Rosse JN. 1970. Estimating cost function parameters without using cost function data: an illustrated method-

ology. Econometrica 38:256–75Rysman M. 2004. Competition between networks: a study of the market for yellow pages. Rev. Econ. Stud.

71:483–512Villas-Boas SB. 2007. Vertical relationships between manufacturers and retailers: inference with limited data.

Rev. Econ. Stud. 74:625–52Waldfogel J. 2003. Preference externalities: an empirical study of who benefits whom in differentiated-product

markets. RAND J. Econ. 34:557–68

52 Berry · Haile


Ann

u. R

ev. E

con.

201

6.8.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

g A

cces

s pr

ovid

ed b

y Y

ale

Uni

vers

ity -

Med

ical

Lib

rary

on

08/2

6/16

. For

per

sona

l use

onl

y.

Documents

Identification in Differentiated Products Marketspah29/AR.pdf · one has only market-level data, as in the original Berry et al. (1995) paper. This is followed by a discussion of