empirical models of differentiated products

Empirical Models of Differentiated Products

Steven T. BerryYale University, Cowles Foundation and NBER

June 18-19, 2015

These slides are “as presented” in the June 18-19 Masterclass at UCL; apologies for

remaining typos and errors.

Steven T. Berry Yale University, Cowles Foundation and NBEREmpirical Models of Differentiated Products June 18-19, 2015 1 / 341

Intro and Broad Ideas

Differentiated Products: Introduction

While homogeneous goods is a convenient assumption for many models, itis frequently violated in practice. Many markets feature goods that are notidentical, they vary in quality, features, reliability, reputation and/orgeographic location. Markets of literally identical goods seem to berelatively rare, especially once differences in seller’s locations andreputations are taken into account.



Empirical modeling and estimation of differentiated products thereforeseems to be important.

We might think of differentiated products as the general case and perhapseven as the typical case.



Outline of Classes

1. Introduction, Examples and Broad Ideas (this session)

2. Identification and Estimation of Differentiated Products Demand andSupply (end of this session and then next session)

3. Models with Endogenous Product Characteristics (tomorrow)

4. Example Applications to Policy Relevant Markets: Anti-trust, Heath,Media and Education (actually, largely interspersed.)


Intro and Broad Ideas Intro Examples

Examples

I transportation demand McFadden, Talvitie, and Associates (1977)

I market power Berry, Levinsohn, and Pakes (1995), Nevo (2001))

I mergers (e.g., Nevo (2000a) Capps, Dranove, and Satterthwaite(2003))

I welfare gains from new goods/technologies Petrin (2002) Eizenberg(2011)

I network effects Rysman (2004), Nair, Chintagunta, and Dube (2004)

I product promotions Chintagunta and Honore (1996) Allenby andRossi (1999)

I environmental policy Goldberg (1998)

I vertical contracting Villas-Boas (2007), Ho (2009)



Examplescontinued

I equilibrium product quality Fan (2013)

I media bias Gentzkow and Shapiro (2010))

I asymmetric information and insuranceCardon and Hendel (2001),Bundorf, Levin, and Mahoney (2012), Lustig (2010)

I trade policy Goldberg (1995), Berry, Levinsohn, and Pakes (1999),Goldberg and Verboven (2001)

I residential sorting Bayer, Ferreira, and McMillan (2007)

I voting Gordon and Hartmann (2013)

I school choice Hastings, Kane, and Staiger (2010), Neilson (2013)



Example: Mergers

Old “classic” merger analysis involved a discussion of “concentration,”“,Herfindahl indices,” and “market definition,” which is appropriate tohomogeneous goods. But “modern” merger analysis typically involvesdifferentiated products. Key question is how close substitutes are themerging goods.

What is the level of the “diversion ratio” (of those who leave a good dueto a price rise, what fraction substitute to a given set of substitute goods)?

“Structural merger analysis” is not quite standard yet, probably correctlyso, but it an increasingly used tool.



School Choice

In the choice of universities or lower-level schools (school choice in US,Chile or France college) ), one can think of the schools as offferingdifferentiated products. Differentiation in location, quality, specialization.Demand is from students / parents. Price and/or admission policies areset in equilibrium.

What are the effects of different school choice programs? Of tuitionincreases? On student performance, student welfare?



McFadden Transportation

McFadden introduced the idea of transportation choice as a differentedproduct. Products (bus, train, car) are differentiated by price, travel timeand mode preferance. Preferences are partly “random,” but also followfrom location of home and work.



Optimal Entry

In differentiated product markets, fixed costs are often noticeably highrelative to the potential market for a given product, and so the entrydecision is an important component of market outcomes and consumerwelfare.

Oligopoly theory says that in differentiated product markets, choice ofentry on entry may not be optimal. The effect on welfare can swamp any“deadweight loss triangle” from oligopoly pricing condition on entry. Canwe measure these effects empirically?



Endogenous Quality and Location

Firms choose their characteristics as function of costs, demand andcompetition from rival firms. Can we model this decision? What are theimplications of the endogenous charateristics for empirical work? Does themarket do a “good job” of generating product variety?

To what degree does my product choice set depend on my neighbors’preferences (“preference externalities”). What are the implications of thisfor urban economics?


Intro and Broad Ideas Broad Ideas

Intro to Empirical Work

There is now a “modern” empirical literature that takes up where theolder “monopolistic competition” literature(s) left off. Consumers demandproducts differentiated by product characteristics. Fixed costs and productdifferentiation imply a limited number of products and therefore imperfectcompetition, perhaps Nash price-setting. Multi-product firms are common.

A more recent literature models how firms choose what products toproduce (in a multi-dimensional horizontal and/or vertical space.) Thisendogenizes the choice of products.



Intro to Empirical Method, cont.

The recent empirical literature looks at market-specific data, at leastdetailed models of products and firms and perhaps additional data onconsumers. The consumer data matches consumers (and their attributesor demographics) to their purchases.

The modern literature often treats unobservables as explicit latentvariables, with interpretations as demand or supply shifters. This is in the“structural modeling” tradition of supply-and-demand analysis.

The advantages of the approach are [i] explicit assumptions and [ii] theability to do detailed counter-factual policy analysis. In practice, there isoften a dependence on functional form, although there is now a literatureon non-parametric identification.



Instruments, Demand and Supply

To a large degree, the models here are the differentiated productsextension of simple homogenous goods supply and demand. As in the S &D literature, much of our discussion will be about instruments. We nowneed to learn about substitution patterns within the market, often in caseswhere the exact same products do not occur in each market. We also needto model markups on the supply side, as prices do not depend on costsalone.



Demand

On the demand side, there are difficult questions of functional form,endogeneity and identification.

I There are often many products, leading to high-dimensional demand,necessitating product aggregation and/or other ways of reducingdimension.

I There is at least price endogeneity and, realistically, endogeneity oflocations, quality and/or characteristics.

I We have to identify not just “price effects,” but also cross-productssubstitution patterns. What are good “instruments for “substitutionpatterns”?



Supply Side

The empirical differentiated products literature is often wrongly treated asbeing mostly about demand. But supply is necessary for manycounter-factuals. Furthermore, under imperfect competition, supplydecisions reflect demand elasticities and so are informative about demand.

In differentiated goods markets, there is often sufficient product varietyand fixed costs are large relative to market size and perfect competition isnot a good assumption. Positive markups are necessary to ensure at leastzero profits.



Supply Side Issues

A classic issue is that costs (especially marginal costs) are often notobserved. Therefore, they are inferred from firm behavior.

Other issues here include what is the proper model of supply (Nash inprices? quantities? dynamics?) How to handle multi-product firms? Isprice chosen simultaneously with location / quality or after?



Dynamics

Unfortunately, we will not have time to discuss dynamics, on either thefirm or consumer side. On the firm side, one could start with Ackerberg,Benkard, Berry, and Pakes (2007).


Intro and Broad Ideas Review of Theory

Review of Differentiated Products Theory

The differentiated products theory literature is largely concerned with firmbehavior, but firms’ incentives are partly driven by demand.

Two broad traditions in deriving demand.

1. A representative consumer who has a taste for consuming a variety ofproducts (much of classic “consumer theory” focuses on this)

2. Heterogeneous consumers facing products with differingcharacteristics

Representative consumer models almost always continuous demand,heterogenous consumers often discrete choice. Sometimes aggregate todiscrete choice to multiple choices or continuous demand.



Representative Consumers and a Taste for Variety

In this tradition, the demand curve is typically derived from awell-specified utility function that features decreasing marginal utility fromthe consumption of each good in the market. This provides the incentivefor the representative consumer to spread consumption across a variety ofgoods. The reason that goods are differentiated is typically buried in theparameters of the utility function, rather than being made explicit.

or . . .



Characteristics Models

This tradition locates goods in a space of product characteristics.Consumers have heterogeneous tastes and place differing utility weights onthe different product characteristics. Each consumer is often modeled asbuying at most one unit of the good, yielding a “discrete choice” model ofdemand at the consumer level. Product variety is then a response to thevariety of consumers preferences, rather than the “taste for variety” of arepresentative consumer. Aggregate (market level) demand is then foundby summing up the demands of the individual consumers.

Sometimes consumers are located in the same product space as theproducts, sometimes just have random tastes for characteristics (and/orproducts).



Examples of Representative Consumer Models

One tradition assumes a CES representative consumer model, e.g.Dixit andStiglitz (1977). Utility is a function of an aggregate of the differentiatedgoods and of money spent elsewhere. The aggregate is something like

U(Z ) = U(∑j

βjzρj ),

with ρ < 1 giving a taste for variety.

CES style models are good for the stylized treatment of equilibrium (as intrade theory), but have not been used frequently in applied IndustrialOrganization (IO). They lead naturally to constant markups and can bedifficult to reconcile with discrete purchasing patterns.



Heterogeneous CES?

As noted by Anderson, DePalma, and Thisse (1992), there is a closerelationship between the CES and the logit that we consider later. Indeed,the logit social welfare function can be considered as the utility of arepresentative agent. At the market level, both CES and logit are toorestrictive. We will add heterogeneity to the logit, but could have startedwith the CES and added heterogeneity.



Example: General Flexible Demand SystemsThe problem of too many parameters

Could use general “flexible” demand systems: e.g. constant elasticitydemand or translog demand, etc. But what are the underlying consumerpreferences? Jorgenson, et al, Jorgensen, Lau, and Stoker (1982) suggesttranslog indirect utility, for example.

A basic problem in demand estimation in product space is that to we haveto estimate many parameters from very little data. Thus for a hundredgoods (which is not a lot), an unrestricted first order approximation wouldrequire a hundred cross price elasticities and one income elasticity for eachof a hundred products. As a result a basic question is when can weaggregate goods, and still obtain a “structural” form which has all theappropriate interpretations.



Representative Consumer Example: Almost Ideal systems

How to justify demand in terms of consumer theory, but without “toomany” own- and cross-elasticities? Look for a system in which consumerscare about the “subutility” from various groups of goods and then look fora (justified) price index for the groups.

At the lowest level, model demand for a good as depending on the pricesof within group goods, conditional on group expenditure. At the next levelup, model group expenditure as depending on the group price index.

For example, Almost Ideal demand system functional form allows this (seeDeaton and Muellbauer (1980)). (Note that the CES and logit can also“nest”).



The Characteristics Approach

Products are defined by their characteristics. Consumers are defined bypreferences for characteristics.

These models are particularly useful when the nature of products changesacross markets. Less preferable when the characteristics are hard to defineand measure, but the products are stable across markets. (Hausman: whatabout champagne – the number of bubbles?)

The choice between discrete and continuous models of demand willtypically be decided by the nature of the market at hand.



Discrete Choice Models.

Many of the product differentiation models we consider are of thediscrete-choice form. An advantage of these models is that they builddemand from a well-specified utility for the characteristics of products. Anunfortunate restriction is that they usually constrain each consumer toconsider buying at most one unit of a good. This restriction can berelaxed: e.g. Hendel (1999). Examples of discrete choice models used inIO theory include the Hotelling and vertical models. Anderson, DePalmaand Thisse Anderson, DePalma, and Thisse (1992) provide a lengthydiscussion of discrete choice models as used in the theory of productdifferentiation.


Intro and Broad Ideas Theory: Discrete Choice Characteristics Models

Discrete Choice Utility

A general discrete choice model starts with by specifying the utility ofconsumer i for product j as

uij = U(xj , pj , νi ),

where xj is a vector of product characteristics, pj is the price of theproduct and νi is a vector of consumer characteristics. (Rather than modelutility directly as a function of price, it might be preferable to model it asa function of expenditures on other products and then derive the“indirect” utility U as a function of price.)



Hotelling

As example, the utility function in the Hotelling model with quadratictransportation costs is

uij = u − pj − (xj − νi )2,

where xj is the location of the product along the line and νi is the locationof the consumer.



Vertical Model

In the vertical model Shaked and Sutton (1982), Bresnahan (1987))

uij = νixj − pj

where xj is “quality”, and νi is the consumers “taste” for quality.Or, the model can be written as

uij = δj − αipj ,

We normalize the utility of the outside alternative (ui ,0) to zero.



Multiple Fixed Dimensions of Preferences

Vertical and Hotelling utility functions can be extended to multiplecharacteristics. For example, an analog of the Hotelling model, with Kcharacteristics, is

uij = u − pj −K∑

k=1

αk(xjk − νik)2,

while an extension of the vertical model is the “pure random coefficientsmodel”:

uij = [K∑

k=1

νikxjk ]− pj



Finite Dimensional Models

In models where the dimension of tastes is potentially smaller than thenumber of products, a particular product at a particular price can bestrictly dominated in preferences for all consumers. This product will havezero sales. This is maybe realistic in some markets, but the zero salescause problems for empirical work Berry and Pakes (2007).



Traditional Econometric Discrete Choice

See, e.g., McFadden (1981)A traditional econometric specification is:

uij = xjβi − αipj + εij

where the consumer “tastes” are given by

νi = (βi , αi , εi1, εi2, . . . , εiJ)

But what are the εij? Product and consumer specific random terms?



The ε’s in the traditional discrete choice model have full support and areiid (or have an iid component). Therefore every good is purchased, nomatter its price or characteristics.



Logit

In the traditional econometric specification, the εij are assumed to be i.i.d.across products and consumers. In the simplest case, there are no randomcoe fficients on the product characteristics, (βi = β and αi = α) and theεij have the “type 2 extreme value” distribution

F (ε) = e−e−ε.



Logit

This gives the traditional logit model, where the probability that good j ispurchased (i.e. the market share of product j) is

sj =eδj∑Jr=1 e

δr,

with δj = xjβ − αpj . If we add an “outside good” with δj = 0, the logitmarket share becomes:

sj =eδj

1 +∑J

r=1 eδr.



Logit Substitution

While the logit market share is easy to calculate, the model has unintuitiveproperties. In particular, cross-price effects do not depend on the degree towhich the products have similar xj ’s, but only on the values of the sum δj .In the logit,

∂sj∂pj

= −αsj(1− sj)

and∂sj∂pk

= αsjsk .



Logit Substitution

The counter-intuitive substitution patterns do not come only from thespecific distributional assumption in the logit model, but from theassumption that the only variance in consumer tastes comes through thei.i.d. product-specific terms εij . Since these terms are i.i.d., there is nosource of correlation in consumer tastes across similar products. This is instrong contrast to the finite dimensional tastes models (Hotelling, vertical,etc.)



More Flexible Substitution

When variance is added to the terms βi and/or αi , then substitutionpatterns can become more reasonable. Now, a consumer who buys a goodwith a large value of some characteristic is more likely than the averageconsumer to have as a second choice another good with a large value ofthat characteristic.



Random Coefficients Logit

Assume that ε is extreme value, like the logit, but keep (βi , αi random inutility

uij = xjβi − αipj + εij .

This is relatively easy to compute and the own- and cross-derivatives aremore flexible.



ε?

However, as long as the distribution of ε is i.i.d., there are effectively asmany product characteristics as there are products. Indeed, we can thinkof εij as the consumer taste for a product characteristic that is defined tobe equal to one for product j and zero otherwise. If the ε’s have anunbounded distribution, then all goods are strict substitutes for oneanother (e.g. ∂sj/∂pr is positive for all j and r .) Contrast this to theone-dimensional taste models (Hotelling, vertical) in which each product isa substitute with only 2 other “nearby” products.



ε’s and changes in the choice set

The ε’s are effectively product-specific tastes. When a new product isintroduced, the dimension of tastes automatically increases. With logiterrors, as J →∞, a single-product firm becomes a monopolist against the“fat tail” of consumers who care only about that good and markups go toa constant (not zero.) Also, welfare is automatically increased as theproduct spaced increases. For somewhat ad hoc ways to adjust for this,see Ackerberg and Rysman (2005).

The more important are random coefficients, the less important is thiseffect.


Intro and Broad Ideas Theory: Equilibrium and the Supply Side

Equilibrium

Having discussed some methods of deriving demand, we can turn to aconsideration of equilibrium. The simplest models of productdifferentiation would consider a set of single product firms each producinga differentiated product. We could begin by specifying a demand systemfor this set of related products, together with cost functions and anequilibrium notion.



The usual assumption is Nash-in-prices. To analyze the case of equilibriumwith differentiable demand, note that the profits of firm j are given by

πj(p) = pjqj(p)− Cj(qj(p)).

The first-order condition is:

qj + (pj −mcj)∂qj∂pj

= 0.

Note that we can rewrite this as

pj = mcj + bj(p),

where the markup is

bj(p) =qj

|∂qj/∂pj |



We can write the product Lerner index in terms of the usual “inverseelasticity” rule.

(pj −mcj)

pj= 1/ηj ,

where ηj is the absolute value of the product-specific elasticity.



Existence and Uniqueness

In a 1991 paper, Caplin and Nalebuff Caplin and Nalebuff (1991) considera broad class of discrete-choice models and provide a result on theexistence of equilibrium in such models. They also provide a partialcharacterization of the equilibrium. They require two assumptions on thedistribution of consumer utility. The first requires utility to be linear inconsumer characteristics; note that all of our examples above satisfy thisrequires (although the quadratic transport cost example requires somere-writing to see this.) The second assumption places a restriction on thedensity of consumer tastes which restricts the density to a set that isbroader than the set of log-concave densities.



Quantity vs. Price Setting

In differentiated products models, one could also consider quantity settingfirms, as in the Cournot model. In this case, the first-order conditionbecomes

pj + qj∂pj∂qj−mcj = 0.

Note that ∂pj/∂qj is the j th diagonal element of the J by J matrix[∂q

∂p′

]−1

,

which is not the same as the inverse of of ∂qj/∂pj (except in themonopoly case). For many examples, the quantity-setting markup will behigher than the price setting markup.



Complete Information in Static Models

The world isn’t actually static, so the static model must be a “metaphor”for a relatively stable situation without strong dynamic linkages.

If the situation is stable, then it is likely that the economic actors havelearned about many of the unobservables that are unobserved by us,leading to the frequent use of complete information models. In completeinformation static Nash, in equilibrium the firms only have to condition onthe actions of their rivals, not necessarily the unobserved profit shifters.

Contrast to first-price auction models, where the game is often actually“one-shot” and bidders can really suffer from ex-post regret.


Empirical Demand Models

Empirical Models

Empirical models follow the theory literature in many respects. Todescribe the data, we have to add sources of randomness. In demand,unobservables can be at the level of the consumer and the market. Onsupply, these are at the level of the firm, probably correlated across firmswithin markets.

Markets are typically separated in time and/or space. We will typicallyignore time-series correlation, but this is not good. Spatial correlation isan issue in at least some contexts.


Empirical Demand Models

Again: types of Demand Models

As in the theory, empirical demand models usually take on one of twotypes, although one can mix and match.

1. Continuous Product DemandI Utility defined directly over products (not characteristics)I continous quantity choiceI often representative consumerI problems with “too many own and cross-price elastiticies,” J2 when

number of products = J.

2. Characteristic ModelsI Utility over characteristics (helps with parsimony, counterfactual

predictions)I Usually discrete choice with heterogenous consumers

We will spend more time on characteristics models.


Empirical Demand Models Hausman and Almost Ideal demand

Continuous Demand, Representative Consumer Models

As an example, Hausman has a series of papers using Almost Idealfunctional forms to ask questions about competition and/or price indices/benefit of new goods. In Hausman (1996), he measures the benefits ofnew goods by integrating under the demand curve as price decrease fromthe “choke-price” to the observed level.



Example: Hausman ’96

Hausman (1996) studies breakfast cereals with Almost Ideal system. TheAlmost Ideal model of product demand is [i] consistent with the utility of arepresentative consumer while [ii] expressing demand in a “nested” form,which the demand for products within subgroups depending on own andcross-price elasticities and cross-group demand depending on group priceindices.

There is still a problem of “too many elasticity parameters” as the numberof products grows large. On the other hand, the same cereals are sold inmany markets and it is hard (but see Nevo (2001)) to list “characteristics”of cereal (“mushy”?). Reduce the number of coefficients by ignoring smallproducts and grouping the rest.



Price Endogeneity

The “error” in Almost Ideal models is usually “tacked on” to the end ofthe demand curve, but if we think of this as a “demand shock” there isplausibly an endogeneity problem with the coefficient on (log) price. Thisis just the usual “supply and demand” endogeneity problem—unobserveddemand shocks drive demand.

Natural instruments are cost shifters and in the Almost Ideal system thereare many prices and so we need many instruments. There are only a fewobserved cost shifters (e.g. Nevo uses price of sugar.)



“Hausman” instruments

Hausman uses the prices of goods in other markets as “cost” instruments.These are valid if price variation across market-time is driven byunobserved cost shocks, not unobserved demand shocks. Bresnahancriticized this assumption, but the Hausman instruments do provide richcross-product variation if the underlying assumption is correct.


Empirical Demand Models Aside: Hedonics

Empirical Characteristics Models

Leaving Hausman style models, we return to characteristics models wherefirms and consumers care about (pt , xt). The simplest kind of empiricalwork in this context is “descriptive hedonics,” so let’s take a brief look atthat.



Aside: Hedonics

The simplest sort of empirical work on differentiated products seeks todescriptively characterize the relationship between product characteristicsand the prices and/or quantities of each firm. A simple regression of priceson product characteristics is called a “hedonic regression.” a la GrilichesGriliches (1961). This type of regression is often used to show how the“reduced form” relationship between prices and quantities changes overtime.

In the interpretation of Griliches and Pakes 2001, the hedonic coefficientscombine the equilibrium effects of costs and demand (via markups) in acharacteristics model.



Hedonics, cont

For example, hedonic regressions are used to correct the producer priceindex for computers. The data is a panel of prices, pjt and characteristics,xjt , of products over time. Simplifying, say that in period t, price isregressed on x to obtain the parameters of

pjt = xjtβt + εt .

In period t + 1, a new set of products is on the market. It would be amistake to look at the unadjusted price of, say, a mainframe computerbecause most likely this year’s model is far better than last year’s model(i.e. the x ’s have improved.). The hedonic helps us ask how how muchtoday’s models would have cost yesterday.



Hedonics, cont

We can get a predicted price by using last year’s coefficients on this year’scharacteristics

pjt+1 = xjt+1βt .

Alternatively, we could put year dummy variables in a pooled regression oflog price on x ’s across years and treat the changes in the dummy variableas percentage changes in price, adjusted for quality.



Hedonics, cont

This hedonic technique does not generate an ideal utility-based priceindex, but Pakes (2003) discusses bounds on the difference between thehedonic and an ideal index. Consider a non-parametric regression of pt onxt generating the function pt(x). We can then construct an indexcomparing pi ,t+1 to pt(xi ,t+1) – thus asking what this product would havecost last year. By the usual price-index logic (Paache/Lespeyres) thisbounds the true index. Note that this does not deal with the welfareaffects of truly new x ′ – in that case pt(xi ,t+1) will not be defined.


Empirical Demand Models Intro to Discrete Choice Empircal Models

Intro to Discrete Choice Models.

Many of the product differentiation models we consider are of thediscrete-choice form. Advantages include

I a clearly-specified utility function for the characteristics of products

I relatively easy to handle heterogeneous consumers

I a relatively parsimonious treatment of demand for many products,since parameters are often modeled as growing in the number ofproducts, not characteristics

I handles different levels of aggregation from the consumer to themarket (although aggregation not always trivial, it is well-defined)

I easy to incorporate full or partial information on characteristics ofpurchasing consumers.


Empirical Demand Models Intro to Discrete Choice Empircal Models

Multiple Discrete Choice

An unfortunate restriction of traditional discrete choice models is that theyoften constrain each consumer to buy at most one unit of a good. Thisrestriction can be relaxed, see

I Hendel (1999) (firm demand for PCs)

I Dube (2004) and Chan (2006) (soft-drink consumption),

I Bjornstedt and Verboven (2013), a combination of logit and CES,allows for continuous choice).


Empirical Demand Models Example: Bresnahan on the 1955 Auto Price War

Example of Discrete Choice Applications on Market Data

First, look at a classic paper that combines supply and demand, not usingclassic econometric discrete choice methods. Then, turn to demand andsupply separately, and together.



Bresnahan’s Paper on the 1955 Auto Price War.

Bresnahan Bresnahan (1987) starts with a puzzle, which is the apparentdecrease in automobile prices that occured in 1955, which was aneconomic boom year, as compared to the surrounding years of 1954 and1956, when automobile prices seemed to be higher. Bresnahan wanted toknow whether differences in competition could account for the pricechange. One hypothesis is that collusive behavior collapsed in the face ofthe economics boom. The idea, then, as in the homogeneous goodsliterature on “testing the competition”, is to look for evidence on what sortof competitive regime best explains the data in each of years 1954-1956.



Bresnahan, cont

Bresnahan assumes that we observe, for each product (= car), a set ofproduct characteristics xj as well as the market outcomes of price andquantities sold, pj , qj . We observe the data only at the overall market(aggregate) level, without any information on the actions of individualhouseholds. Such data is readily available from industry-orientedpublications (such as Automotive News and Ward’s.)



Bresnahan, cont

For simplicity, Bresnahan uses the demand vertical model, so there is onlyone attribute per product. In the data, there are a number of differentcharacteristics, such as size, horsepower and luxury, so he creates an indexsay δj = xjβ. He assumes a uniform distribution of tastes for quality andderives the demand function.

qj = qj(δj , δ−j , pj , p−j). (1)

that we derived before.



Bresnahan, cont

The prices are endogenously determined by a price-setting Nashequilibrium. Note that in the automobile industry, the first-order conditionhas to be modified to account for multi-product firms. GM, for example,offers dozens of products in the market today. To solve for equilibriumprices, one must also specify a cost side of the model. Costs, particularlymarginal costs, are not typically observed so, as in the Cournot modelsabove, we often are forced to infer marginal costs with the help of theoligopoly first order condition. Bresnahan assumes that marginal costs area convex function of quality. (This helps to ensure an equilibrium withpositive shares.)



Bresnahan, cont

Bresnahan can then:

I Solve for reduced-form p and q

I Tack on errors (say they’re normal.)

I Estimate by MLE under two equilibrium assumptions: Nash in priceand collusion.

Given the estimates under the two competing equilibrium assumptions,Bresnahan does a “non-nested” hypothesis test and finds, as conjectured,that collusive pricing fits better in 1954 and 1956, but Nash pricing fitsbetter in 1955!



Bresnahan on Markups and Characteristics

Bresnahan emphasizes that under non-collusion oligopoly, markups areheavily affected by whether or not the firm faces close substitutes. Hemakes this point in the context of multi-product firms and multi-productfirst order conditions. He uses this insight to try to distinguish collusiveand non-collusive behavior, finding that collusion really did collapse in theboom.

The insight is also useful when we think about “instruments forsubstitution” patterns.



Bresnahan, cont

Critiques:

I The vertical model is way too restrictive. (Maybe better forcomputers.)

I What identifies demand elasticities when there is no within-year pricevariation? (“The model”).

I The error structure does not allow for unobservables.

So, how about traditional econometrics discrete choice models?


Empirical Demand Models Traditional Econometric Discrete Choice

Review of Econometric Discrete Choice Models

A classic probit or logit

uij = xjβ − αpj + εij ,

with ε either standard normal or else “extreme value” (double exponential,ε ∼ exp(−exp(−ε)).

I Traditional Probit

I Traditional i.i.d. Multinomial Probit

I Multinomial Probit with correlated errors and the high dimensionalityof integration.



Logit again

The i.i.d. logit solves the problem of high dimensional integration with afunction form of:

sj =exjβ−αpj∑k e

xkβ−αpk(2)

Again, note the derivatives are:

∂sj∂pj

= −αsj(1− sj)

∂sj∂pk

= αsjsk

These depend only on shares, not on x ′s.



Traditional Logit with Consumer Data

Estimating a traditional logit at the individual level within a single market:

uij = xjβ − αpj + (∑r

zirxjrγr ) + εij (3)

= δj + z ′i Γxj + εij (4)

where δj = xjβ − αpj is McFadden’s “alternative specific constant”The probability that individual i chooses good j is

Pr(i | zi , δ, Γ) =eδj+z ′i Γxj∑k e

δj+z ′i Γxj(5)



Logit MLE

We can then estimate (δj ,Γ) by MLE, where the contribution to thelog-likelihood of an individual is

ln (Pr(i | zi , δ, Γ)) = δj + z ′i Γxj + ln

(∑k

eδj+z ′i Γxj )

)

There are very standard algorithms for maximizing the log-likelihood.Note: because of the δj term, at the market level, should get an exact fitto product-market shares (integrating out across a mass of consumers.)


Empirical Demand Models McFadden Demand Example

Traditional Discrete Choice on Micro Data

Just as we gave Bresnahan as an example of traditional discrete choice onmicro data, so we can give a classic example of “econometric” discretechoice on consumer-level data.


Empirical Demand Models Example: McFadden and Transportation

Empirical Example: McFadden on BART

One classic example of discrete choice modeling with micro data is theMcFadden, Talvitie, and Associates (1977) analysis of transportation modechoice, intended to provide policy guidance for the development of masstransit systems such as the Bay Area Rapid Transit system in California.Consider a slight variation on the model of Chapter 2, Table 7 of thatstudy. In the model, each work commuter in metro area t chooses acommuter transportation mode: automobile or bus. Bus transportation isfurther divided into the choice of walking or driving to the bus, for a totalof 3 modes: auto alone, bus with walk access and bus with auto access.



The discrete choice logit utility function for person i considering mode j inmarket t is

ujt = δjt + zijtγ + εijt , (6)

where δjt is the “alternative specific constant,” zijt is a vector of consumerattributes that are potentially specific to mode j and εijt is an i.i.d.extreme value idiosyncratic shock to tastes. The functional formassumption on εijt creates the logit functional form for choice probabilities.The parameter γ is to be estimated.



McFadden Attributes

The zijt attributes are created from a survey of household attributestogether with the exact geographic location of the household andworkplace and the detailed way in which the transportation networkconnects those two household-specific locations. The list of mode-specificattributes includes, for example, transportation time in minutes, whichvaries across modes in different ways for different households. Consumersalso care about the dollar cost of the mode, which can be broken into twoparts. One part varies across consumers (for example gasoline costs varywith distance to work) and one part does not vary (the standard bus fare.)We denote the dollar cost that does not vary across consumers as pjt .



McFadden “Alternative Specific Constants”

The alternative specific δjt are estimated as parameters on dummyvariables for each mode. Note, though, that metro-area bus fare, pjt forthe bus-walk mode, is perfectly correlated with the alternative-specificdummy variable for the that mode. The authors therefore do not estimatea coefficient on bus fare but instead create a variable defined as faredivided by per-minute wage. This gives a cost, in minutes of work, thatvaries across consumers.



Alternative Specific Constants, again?

In the McFadden BART example, the characteristics are really justdummies for the alternatives, which interact with zi . Further, there is justone market, so all identification is from variation in the consumerattributes within market.

The coefficients are used to predict demand for subway service, which islike the bus, but quicker and at a different price, with a different set ofroutes.

Question for later: would the alternative-specific constant be the same insome other market?



Micro Level Nested Logit

In the micro-level logit, consumers of “type” zit will substitute to otherproducts that are predicted to be popular conditional on zit , but thesubstitution patterns do not depend directly on the characteristics of thegoods.

The nested logit model allows for tighter substitution among products whoare in a similar group (or “nest”) of products.



Nested Logit Utility

The nested logit utility function include as common “taste” for withingroup products, see Ben-Akiva (1973), McFadden (1978) and Cardell(1997). The nested logit utility function for a product in group g is

uijt = δjt + z ′itΓxjt + νig (σg ) + (1− σg )εijt . (7)

We can let the parameters βg and σg vary by group, or not.



The within group shares still follow the logit function form,

sj/g =e(δj+z ′itΓxjt)/(1−σg )

Dg(8)

where the denominator is

Dg ≡∑k∈Jg

e(δk+z ′itΓxkt)/(1−σg ). (9)

The group shares are

sg =D

(1−σg )g∑

h D(1−σh)h

(10)

This gives the market share (purchase probability) as the product of thewithin group share and the group share.



Following McFadden, we have two ways of estimating the nested logitmodel via maximum likelihood. The first method estimates the models intwo steps. At the “lower level,” we can estimate each nest separately usingthe within group shares and recover the nest-specific parameters. Then, atthe upper level we can use the group share data to recover the σ`gparameters. The second method would be to simply estimate the modelvia MLE all at once. The first method is intuitively and easier to programusing existing logit code. However, the first method will not carry over toestimation with random coefficients.



For a nested logit application see the related papers by Goldberg (1995) orGoldberg (1998).



Random Coefficient Probit or Logit

uijt = xjtβit − αitpjt + zijtγ + ξjt + εijt , (11)

where vector (βit , αit) is assumed follow a parametric distribution (normalfor the βit ’s, log-normal for the αit ’s) with parameters to be estimated andεijt is still extreme value (RCLogit) or else normal (RCProbit).



On random coefficients, see: Hausman and Wise (1978), McFadden(1989), Berry, Levinsohn, and Pakes (1995).


Empirical Demand Models Simulating Random Coefficients

Simulation

WIth random coefficients, we lose the nice logit / nested logit functionalform and are left with a high-dimensional integral. Solution: eithernumeric integration (getting a little easier) or else, traditionally, simulationmethods.

McFadden (1989), Pakes and Pollard (1989),Train (2009).



Quickest idea:

I For given parameters, draw random terms from the assumeddistribution for each individual in a sample.

I Use these draws and parms to construct simulated choices

I Average these draws across simulated individual to construct asample-average choice probability.

I Compare these simulated probabilities to the true individual choices inthe data (or to the true probabilities in the data) and/or use in anMLE method (but be careful, see below.)



Issues with Simulation and MLE

MLE takes the log of the predicted probability. This is a big problem whenshares are small – a small error in sij is a large error in ln(sij) when sharesare small, because the ln(·) function is very steep when evaluated nearzero.

With a relatively low dimension (one? three? five?) it is probably betterto use modern numeric integration.


Modern Empirical Work on Market-Level Data Intro to IO Demand and Supply

Market Level Data

In contrast to the “McFadden” tradition, there is an “IO tradition” thatfocuses on market-level data and oligopoly, as in the Bresnahan paper.After a bit we will try to put these back together.


Modern Empirical Work on Market-Level Data Discrete Choice on Market Level Data

Modern Discrete Choice on Market Level Data

The idea is to extend supply and demand empirical models to marketswith product differentiation (Berry ’94) Berry (1994) and Berry, Levinsohnand Pakes Berry, Levinsohn, and Pakes (1995).) As in the supply anddemand literature, want to account for the implications of consumer andfirm optimization together with equilibrium pricing.

First application: autos, again, with a focus on “realistic” own- andcross-price elasticities.



Data

Data are at least market-level observations on prices, quantities andcharacteristics of products. Might also have data on characteristics ofpurchasing consumers and on firm production (but this is rare.)Consumers modeled in a discrete choice framework. The utility ofconsumer i for product j depends on observed and unobserved (by us)characteristics, (y , ν), of the consumer and observed and unobserved (byus) characteristics of the product, (x , ξ). Each firm produces a given set ofproducts whose production cost depends on a vector of cost shifters w ;presumably, w includes the product characteristics, x . The equilibrium isNash in prices.



Product Choices

To derive demand, we assume that choices are all products in the marketand an outside good. The utility of a choice is determined by a parametricform for the interaction between consumer characteristics and productattributes (Lancaster Lancaster (1971), McFadden, etc.) The demandfunction is then derived by explicitly aggregating over the choices ofconsumers with different characteristics


Modern Empirical Work on Market-Level Data Berry 1994 Market Level Logit

Endogenous Prices

As in traditional homogeneous goods models, the econometric endogeneityof prices follows from the presence of unobserved characteristics.

In autos, unobserved characteristics include style, dealer quality, tradition.How to explain: prices and sales of similarly sized and powered Ford andBMW; very different sales of very similar Japanese compact cars.

Assuming no unobserved product characteristic also leads to over fittingproblem.



Unobserved Characteristics

Unobserved characteristics were usually ignored in the traditional discretechoice literature. Micro studies sometimes add product-specific intercept,but no attempt to say how this would change in a counterfactual. Productintercept is co-linear with pj , xj .

Solution (from Berry (1994)): Allow for unobserved characteristic, ξj

uij = xjβ − αpj + ξj + εij ,

= δj + εij ,

where δj = xjβ − αpj + ξj .



Unobserved Product Characteristics – cont

Problem: ξ enters sj in a highly non-linear fashion and is correlated with(at least) prices. Can solve for ξ given parameters of model. However, oneξ for every observation, need more restrictions. Following traditionaldemand literature, we assume that ξ is uncorrelated with some “demandshifters”; here these are product characteristics. Could use otherrestrictions (endogenous characteristics?)



Inverting the Market Share Function

For the true model: sj = sj(δ, θ), j = 1, . . . , J. This is Jby1 equations in Junknown δj . Note the necessity of normalizing the “outside good” (orsome good) to zero.

If possible, invert to find mean levels of utility:

δ = s−1(s, θ) (12)

Now could estimate demand parameters by IV from, e.g ., :

δj = xjβ − αpj + ξj , (13)

Alternatively, can think of solving for ξj directly. Note that the parametersare α, σ!

We will greatly generalize this later.



Instruments, again

I Cost shifters, maybe as Hausman instruments

I Changes in Rival’s x ′s over time/markets (sub-market?) This is thelogic of Bresnahan and the oligopoly supply-side. Where you are inthe characteristics space helps to determine your markups.

I Panel Data structures: (e.g. same ξ for different product in differentmarkets, or an AR(1) process with innovations that are uncorrelatedwith past observables.)

Intuition: Elasticities are “identified” by changes in the choice set overtime (including changes in price), holding preferences constant (orcontrolling for changes in preferences from observed data.)



Logit Example

Shares:sj(δ) = eδj/(1 +

∑r

eδr ), (14)

Share of outside good:

s0(δ) = 1/(1 +∑r

eδr ). (15)

⇒ ln(sj)− ln(so) = δj = xjβ − αpj + ξj . (16)

Berry (1994) also gives analytic inverse for vertical model, nested logit.More complicated models require a numerical inverse.



Example of Inversion

As in Berry (1994), in the logit case, we can estimate

yj ≡ ln(sj)− ln(so) = δj = xjβ − αpj + ξj . (17)

by 2SLS or another IV method. Note that pj is exogenous – it is likelycorrelated with the unobserved term ξj . Potential instruments includeother-firms x ′s, cost shifters – or else panel data assumptions.

Recall that the mean utility level, δj , determines all behavior includingmarket share and cross-price effects. Markups for price-setting firms varyonly with market share.



Table 3 from BLPResults with Logit Demand and Marginal Cost Pricing

2217 observations)OLS IV OLS

Logit Logit ln(price)Demand Demand on w

VariableConstant -10.068 -9.273 1.882

(0.253) (0.493) (0.119)HP/Weight ∗ -0.121 1.965 0.520

(0.277) (0.909) (0.035)Air -0.035 1.289 0.680

(0.073) (0.248) (0.019)MP$ 0.263 0.052 –

(0.043) (0.086)MPG∗ – – -0.471

(0.049)Size ∗ 2.341 2.355 0.125

(0.125) (0.247) (0.063)trend – – 0.013

(0.002)Price -0.089 -0.216 –

(0.004) (0.123)No. InelasticDemands 1494 22 n.a.(+/- 2 s.e.’s) (1429-1617) (7-101)

R2 0.387 n.a. .656



Functional Form

A well-known solution to problems with logit: Interact Product andConsumer Characteristics. Random coefficients logit or probit Hausmanand Wise (1978) example:

uij = xjβi − αpj + εij . (18)

More generally,uij = δj + µ(xj , pj , νi , θ) + εij . (19)

To get aggregate demand have to compute a complicated integral.Aggregation problem solved by simulation, as in Pakes (1986). Onsimulation see also Pakes and Pollard (1989) and McFadden (1989).


Modern Empirical Work on Market-Level Data BLP

BLP ’95

Automobile “Supply and Demand” in order to do policy counterfactuals:trade policy, environmental policy, merger policy, etc.

Data only at the market level: prices, quantities and market shares. Treattime dimension as different markets (not great: dynamics? correlation?)

Extend Berry ’94 “invert for the unobservable” to random coefficientslogit. On the supply side, solve for marginal cost via multi-product Nashpricing assumption.



Details on the Berry-Levinsohn-Pakes (BLP) UtilityFunctions

“Cobb-Douglas”

U(νi , pj , xj , ζj ; θ) = (yi − pj)αG (xj , ξj , νi )e

ε(i ,j), (20)

Taking logsuij = αlog(yi − pj) + xjβi + ξj + εij . (21)

Letβik = βk + σkνik , (22)



“Income spent elsewhere” is probably too literal for this market. Berry,Levinsohn, and Pakes (1999) put a log-normal coefficient on price andmake other improvements (while looking at trade policy.)



uij = δj + µij , with (23)

whereδj = xj β + ξj (24)

andµij = αlog(yi − pj) + Σkσkxjkνik + εij (25)



“Income” draws are assumed to be log-normal

yit = exp(yt + σνiy ), (26)

with parameters calculated from CPS distribution of income. This givessome macro effects in demand (again, not great.)



Calculating the Market Share via Simulation

Condition on νi , yi – this is a logit and get closed form. Take ns draws onνi , yi and average over the implied logit shares:

1

ns

ns∑i=1

eµij+δj∑k e

µik+δk, (27)

where µij = αlog(yi − pj) +∑

k σkxjkνik .The error in simulated shares enters linearly – not such a problem if sharesenter the estimation “linearly” so that the simulation error will averageout. (See McFadden and Pakes, 1986 on simulation.) But it is not linearhere, simulation error is a big problem (see Berry, Linton, and Pakes(2004)). BLP use “importance sampling” to reduce simulation variance.



BLP Contraction Mapping

BLP then provide an algorithm (a contraction mapping) that solves for δgiven the parameters and a set of simulation draws. Have to hold thesimulation draws fixed as the parameters chance (or incorrectly risk thatchange in objective function is due to change in simulation draws.)

Have to account for the simulation variance – the inversion means that thesimulation error does not enter linearly. The simulation error gets worse asthe shares get small – hard to accurately simulate small shares. See Berry,Linton, and Pakes (2004).



GMM Estimation of Demand-side BLP

Review of the GMM estimation algorithm for the demand-side alone. Seealso Nevo (2000b).

I Guess a parameter

I Solve for δ and therefore ξ.

I interact ξ and instruments z – these are the moment conditions G (θ).

I Calculate an objective function – how far is G (θ) from zero?f (θ) = G ′AG for some positive definite A.

I Guess a new parameter and try to minimize f .

I Variance of θ includes variance in data across products and simulationerror as well as any sampling variance in the observed market shares.

(Can simplify the algorithm since δ in linear in some parameters.)


Modern Empirical Work on Market-Level Data BLP Supply Side: Pricing

Oligopoly Supply Side

It is not at all clear that there is enough variation in the choice sets to getprecise estimates of the substitution patterns from demand-side dataalong. In an oligopoly, pricing behavior also contains information on thesubstitution patterns, via the markups. (This is also Bresnahan’s pointabout pricing in oligopoly.)



Adding the Supply Side

Adding a supply side allow us to both

I Gain additional information on demand-side substitution and

I learn marginal costs, which are necessary for many counterfactuals.

The cost is commiting to a particular model of oligopoly competition (e.g.Nash in prices). One can do robustness checks on this.



Estimating from a First Order Condition

Rosse (1970) suggests an estimation equation from an imperfectlycompetitive first order condition.

This is a direct generalization of the perfectively competitive model. Inperfect competition, the first-order condition for optimal output says to set

p = mc

If marginal costs vary with characteristics xt and an error ωt , then wewould have something like a hedonic regression

pt = xtγ + ωt

But perfect competition doesn’t make much sense given differentiatedproducts. That is why the hedonic coefficients are involve a projection onboth markups and marginal cost.



Rosse 1970Consider the single-firm monopoly case, with linear demand

qj = xjβ − αpj + ξj .

and linear marginal cost

mcj = wjγ + λqj + ωj .

The f.o.c. for optimal price gives us

qj + pj∂qj∂pj

= mc(qj)∂qj∂pj

qj − αpj = −αmcj

pj =qjα

+ mcj

pj =qjα

+ wjγ + λqj + ωj .

pj = qj(λ+1

α+ wjγ + ωj .

This gives us an estimating equation, to be estimated via IV methods (asqj is endogenous). As noted by Bresnahan, in the linear in price casesupply does not add a restriction to the demand model, but it does whenthe markup varies with data other than linearly in qj .



Firm Behavior with Multi-Product Firms

Marginal Cost:mcj = wjγ + ωj . (28)

Might also model ln(mcj), make mc a function of q, etc.Profits:

πf = Σj∈Jf (pj −mcj)M sj(p, x , ξ; θ) , (29)



First-order Condition:

sj(p, x , ξ; θ) +∑r∈Jf

(pr −mcr )∂sr (p, x , ξ; θ)

∂pj= 0. (30)

Given the demand function, it is possible to solve this for the vector ofmc’s and so for markup, bj(p, x , ξ, θ) and for ωj .In particular, write the foc as

s + ∆(p −mc) = 0, (31)

where ∆ has ∂sj/∂pj on the diagonal, ∂sr/∂pj on the off-diagonals ofjointly owned products and zeros elsewhere. MC is then:

mc = p + ∆−1s. (32)



Estimating from the FOC

Given the demand parameters, can think of estimating the equation,

mcj = pj − bj(p, x , ξ, θ) = wjγ + ωj . (33)

Just as in estimating demand, estimates of the parameters γ can beobtained from orthogonality conditions between ω and appropriateinstruments. Recall that bj can be calculated from the demand parametersalone (once again there is a problem of simulation.)Can also estimate supply and demand together. Here, we change the prioralgorithm to solve for both ω and ξ and interact these with theinstruments to form the moment conditions.



Notes:

I We do not require a unique equilibrium

I the markup depends on ξ, ω and so is econometrically endogenous

I other static equilibria are easy (e.g . qty-setting, collusion) bychanging the ∆ matrix. See Berry, Levinsohn, and Pakes (1999) forquantity setting and mixed-price and quantity setting foc’s.



Caveats:

I Nash Pricing

I no dynamics

I no production data

I no direct data on consumers



Instruments

Instruments? Again: costs (for prices) and changes in choice set. BLP usesupply-side restrictions, some cost instruments and also “BLPInstruments” (I don’t like that name), which are “characteristics of othergoods”. This is in the spirit of Bresnahan and maybe should beBresnahan-BLP instruments.

Berry, Levinsohn, and Pakes (1999) introduce better cost shifters.Intuitively, changes in the choice set identify σ and changes in cost identifythe coefficient on price. However, changes in the choice set also inprinciple change markups and can help with the price coefficient, whereasexogenous changes in price (due to costs) can help to trace outsubstitution.



Optimal Combinations of Instruments

How to approximate the optimal combination of instruments? BLP ’95tries to use a “flexible” combination of characteristics—basis functions ofa symmetric polynomial in own-product, own-firm and rival characteristics.

Linear: own x , sum (or mean of) of own-firm x , sum (or mean) of rivalfirm x .

These are not great. The sum of “other product” characteristics hardlyvaries in a market with a large number of firms. The own- andrival-product distinction helps here. We could move to a higherdimensional polynomial, but this creates a problem of too-manyinstruments and possible over-fitting.



Optimal Instruments

Berry, Levinsohn, and Pakes (1999) use Chamberlain’s result on “optimal”GMM instruments to get a better combination of x ’s. Reynaert andVerboven (2014) show in Monte Carlos and an auto application that this ismuch, much better.



Optimal Instruments

Thinking just of demand. Under some sampling assumptions, the optimalinstruments (Chamberlain or Newey (1990)) are

E

[∂ξ(θ)

∂θ|z]

Note that in the classic linear case

ε = y − xβ

the derivative of the error wrt β is just x and so the optimal instrumentwould be E [x |z ], as expected.

The question is how to implement this in the BLP example.



Implement Optimal Instruments

The Reynaert Verboven method for optimal instruments is to predict pricefrom z (regression on an exchangeable polynomial in z). For any guess atξ, say ξk , we can then predict the “true” market shares for the predicted pand the given ξ. This creates a “counterfactual” data set which definesξ(θ) and ∂ξ(θ)

∂θ for that data.

To approximate the optimal instruments, we then average over the abovecalculation for K draws on ξk from the estimated distribution of ξ (givenour demand estimates.) As in Berry, Levinsohn, and Pakes (1999), onecould alternatively use the supply side to get the prediction of p, but R &V say this doesn’t work as well.

Could use optimal instruments for demand and supply together, using

E

[∂ξ(θ)

∂θ|z],E

[∂ω(θ)

∂θ|z],



next table: some semi-price elasticities (related to single-firm markups)



Mazda Nissan Ford Chevy Honda Ford Buick Nissan Acura Lincoln Cadillac Lexus BMW323 Sentra Escort Cavalier Accord Taurus Century Maxima Legend Town Car Seville LS400 735i

323 -125.933 1.518 8.954 9.680 2.185 0.852 0.485 0.056 0.009 0.012 0.002 0.002 0.000

Sentra 0.705 -115.319 8.024 8.435 2.473 0.909 0.516 0.093 0.015 0.019 0.003 0.003 0.000

Escort 0.713 1.375 -106.497 7.570 2.298 0.708 0.445 0.082 0.015 0.015 0.003 0.003 0.000

Cavalier 0.754 1.414 7.406 -110.972 2.291 1.083 0.646 0.087 0.015 0.023 0.004 0.003 0.000

Accord 0.120 0.293 1.590 1.621 -51.637 1.532 0.463 0.310 0.095 0.169 0.034 0.030 0.005

Taurus 0.063 0.144 0.653 1.020 2.041 -43.634 0.335 0.245 0.091 0.291 0.045 0.024 0.006

Century 0.099 0.228 1.146 1.700 1.722 0.937 -66.635 0.773 0.152 0.278 0.039 0.029 0.005

Maxima 0.013 0.046 0.236 0.256 1.293 0.768 0.866 -35.378 0.271 0.579 0.116 0.115 0.020

Legend 0.004 0.014 0.083 0.084 0.736 0.532 0.318 0.506 -21.820 0.775 0.183 0.210 0.043

TownCar 0.002 0.006 0.029 0.046 0.475 0.614 0.210 0.389 0.280 -20.175 0.226 0.168 0.048

Seville 0.001 0.005 0.026 0.035 0.425 0.420 0.131 0.351 0.296 1.011 -16.313 0.263 0.068

LS400 0.001 0.003 0.018 0.019 0.302 0.185 0.079 0.280 0.274 0.606 0.212 -11.199 0.086

735i 0.000 0.002 0.009 0.012 0.203 0.176 0.050 0.190 0.223 0.685 0.215 0.336 -9.376



Direct application of BLP auto model to:

I Price Indices, Fuel Efficiency: Pakes, Berry, and Levinsohn (1993) andBerry and Pakes (1993).

I Trade: Berry, Levinsohn, and Pakes (1999).



BLP ’99Berry, Levinsohn, and Pakes (1999) add cost-side shifters in the form ofexchange rates and wages interacted with country of production. They alsouse the optimal instruments and continue to use both demand and supplyto pin down the substitution patterns. (In retrospect, maybe still too manyrandom coefficients in the specification, despite the improvements.)

How to modify foc for quota

maxpjt

∑k∈Jft

[pktMtskt(pt)− Ckt(Mtskt(pt))− Fkt ]

s.t.∑k∈Jft

Mtskt(pkt) = Qft

FOC:

sjt +∑k∈Jft

[(pkt −mckt − λft)

∂skt∂pjt

]= 0

where λft is the shadow value of the quota for firm t. In practice,constrain λft to be equal across some firms and estimate as a coeff. on adummy in “marginal cost”.Steven T. Berry Yale University, Cowles Foundation and NBEREmpirical Models of Differentiated Products June 18-19, 2015 134 / 341


Table5a.pdf



Table5b.pdf



Table5c.pdf



Table5d.pdf



On breakfast cereals (BLP crossed with Hausman): see Nevo (2001). Forthat estimation applied to mergers, Nevo (2000a).



Computation in BLP

For a introductory description of the BLP algorithm, see Nevo (2000b)and the code on Nevo’s website.

However, most importantly see the caveats and the alternative (in manycases better) computational approach Dub, Fox, and Su (2012). One keypoint: the contraction that solves for δ has to have a very tight tolerance(unlike the code on Nevo’s website) or else the “outer loop” search forparameters will behave very badly.

Dub, Fox, and Su (2012) suggest an alternative approach that usesmodern optimizers to solve for δ and θ simultaneously rather than in anested loop. In many cases this is faster and in some cases much faster.

Also, probably better to use pure modern numeric integration (or at leastdeterministic sequences for the simulation), see Skrainka and Judd (2011) .


Micro Data on Demand Micro Data: Intro

Characteristics Based Models with Micro Data.

“Micro Data” matches consumers to choices, as in the McFaddentransportation example, but we continue to worry about price endogeneityand the supply side.

Two data scenarios

1. Good market level data but limited micro data either [a] small sampleof purchases or [b] limited cross-tabs of purchases by consumerattributes (or other summaries)

2. A large micro sample that matches consumers’ attributes to theirpurchases.

In case [1], we can add a few “micro moments” to aggregate model. Incase [2] we can estimate the model at the


Micro Data on Demand Example: Petrin

Petrin on the Minivan

Petrin (2002) is an example that, like the original BLP, makes use of someaggregated data on the consumers who buy a car. In Petrin’s case, thislets him better estimate the demand for a new characteristic.

Idea of the minivan: build a “car” with many seats that isn’t a “truck” byexpanding the vertical height of a passenger car. This innovation wasimmediately popular with families. What is the social value of theinnovation in the product space?

Since this is a “new characteristic,” we can only analyze ex post(pre-introduction, there can be no data on demand for the characteristic.)



Petrin’s exercise:

Petrin (2002): estimate a demand and cost side from the observed data,and then recompute equilibrium prices and quantities from a choice setthat does not include the minivan. Of course the problem is that the othercars produced might not have been the same had the Minivan not beenintroduced . . . but you have to start somewhere.

Petrin uses pretty much the same specification as BLP, but brings in alsomicro first-choice moments obtained from the CEX, by simply addingmoment restrictions corresponding to purchase probabilities and carcharacteristics interacted with individual attributes.



Welfare Gain

There are two sources of welfare gain. One is the added consumer surplusof the non-marginal Minivan producers. The other is the fall in prices formost other family cars. Petrin results indicate that the addedcompensating variation for those who purchased a Minivan; it is about1/7th the cost of the vehicle. Or roughly a 3% gain in income for about1% of US Households (roughly one in ten households buy a car every year,and one in ten of those cars are Minivans).



Petrin discuss the role of the logit errors in possibly over-stated the returnto new product introduction, particularly for the second, third minivan andso forth.

The consumer data reduce the importance of the ε’s and reduce thewelfare gain, but it is still a big number.

It is these kind of numbers that get the profession excited about newgoods, R&D, and growth; but remember this was a highly successfulinnovation. Maybe one or two innovations like this have occured in the carindustry over the last twenty years, and they do alot of R&D.


Example: “MicroBLP”

Microblp.

Example: Berry, Levinsohn, and Pakes (2004). Even given themethodological improvements in Berry, Levinsohn, and Pakes (1999), itwas still not clear that we could estimate substitution parameters fromdemand alone. Therefore, we looked for information on

I consumer data

I any direct data on substitution?



MicroBLP Data

The micro data we add here is the The CAMIP data. General MotorsCorporation’s data used for marketing and product quality programs. Datainclude

I vehicle characteristics, prices, and sales (similar to product level dataalready in use except of higher quality)

I household characteristics by vehicle purchased (age, income, familysize, . . . broken down by vehicle purchased)

I second choice vehicles ( generated as the reply to the question: “Ifyou did not purchase this vehicle, what vehicle would you purchase?”)

Note however that unlike previous studies, this has only one cross section.



“Micro BLP” utility

Utility includes both random coefficients and interactions of consumerattributes with x ’s.

Uij = δj + Σkrxjkzirβork + Σklxjkνilβ

ukl + εij , (34)

whereδj = Σkxjkλk + ξj . (35)



As noted, interactions of consumer characteristics and productcharacteristics are needed for reasonable cross price elasticities. Now havetwo such interaction terms.

I Observed consumer characteristics (the zi ) and product characteristics(Term is Σkrxjkzirβ

ork .)

I Unobserved consumer characteristics (the νi ) and productcharacteristics(Term is Σklxjkνilβ

ukl .)



Added information in first choice micro data: matches individualscharacteristics to:

I probabilities of purchasing a car.

I match between car characteristics and consumer attributes

I sometimes also second choice vehicles.

(1) and (2) should provide alot of information on the value of the outsidealternative, and on the importance of interactions of observed consumerand observed product characteristics. (3) is a little like having a panel, asit changes the choice set; and in a particularly relevant way. This lets uspick up the effects of unobserved individual attributes. (1) and (2) shouldbe able to determine the impact of observed attributes on second choices;if second choices are even closer to first choices than predicted by (1) and(2), then it is because there are unobserved attributes.



Sources of Information.

I random sample of consumers

I choice-based sample; samples purchasers and finds out theircharacteristics.

Often, data from marketing firms is choice-based, requires correction for“choice-based” sample.



Own and Cross Characteristic Elasticities and Micro Data

Here are some general points to keep in mind.

I The benefit of having the “first choice” micro data is that it matchesobserved individual attributes to the products those individualschoose. Consequently, the contribution of that data will bedetermined by the importance of the observed attribute data indetermining individual demands (by the βork , and the variance of thezi ). Formally if βork ' 0 the aggregate purchase proportions (i.e.aggregated data on sales and characteristics) are sufficient statisticsfor the micro first choice data (i.e. we revert to BLP’s problem).



The unobserved individual attributes (the νi ) differentiates this modelfrom the standard microdata based logit model, and focuses attention ontwo issues.

1. A substantive issue:. what is the “quality” of the observed individualattribute data (are most of the attributes that cause differentpreference intensities for different product characteristics observed?)

2. A computational issue: if the νi are important the individual choiceprobabilities have to be simulated, and this complicates theestimation algorithm. Leads to desire to “Test” the null βulk = 0.



There is little intuition leading us to expect that the first choice data willhelp us identify the impact of unobserved individual characteristics onpreferences when the choice set doesn’t change across observations (as isthe case with a single cross-section of data; recall that then if βork = 0,then the product level data are sufficient statistics for the problem).However the unobserved characterisitcs do affect the relationship betweenfirst and second choices (regardless of the importance of observedattributes).



Unobserved Product Characteristics and Micro Data

The micro data enables us to estimate a separate constant term for eachchoice, our

δj = Σkxjkλk + ξj

and the vectorβ ≡ (βo , βu)

I.e. β can be estimated without assuming anything about the distributionof the ξj .



However, sinceδj = Σkxjkλk + ξj (36)

we need λ to compute elasticities w.r.t. the product attributes (includingprice). Different assumptions on the joint distribution of the observablecharacteristics and the {ξj} would allow us to estimate the λk , but theassumptions that would identify the model when we add the micro dataare no different then the assumptions that would identify it when onlymacro data are available.



Once again, It follows that the basics of the simultanaeity problem are thesame whether we have micro, or only macro, data. On the other hand wecan get estimates of β without λ, so we can do things like analyze theimpact of new goods without solving the simultanaeity problem.



Estimation Issues

Assumptions on Unobserved Product Attributes.

I Estimate (β, δ) pointwise.

I Make assumption on the distribution of ξ (eg. E [ξ|x ] = 0, as inBLP), and estimate (β, λ) instead of (β, δ).

Tradeoff: We gain efficiency if the assumption is right but looseconsistency if it is wrong. Choose to estimate (β, δ) (and then perhapsinvestigate assumption) because there is so much data.



Computational Choices; Dimension of Search.

I Search over (β, δ). [δ alone has over 200 parameters.]

I Two step estimator. Use the contraction mapping in BLP andproduct level data to solve for δ as a function of (β, sN ,Pns), i.e. forthe δN,ns(β) that solves

s(β, δ,Pns) = sN

then search over β to match the model’s predictions to the CAMIPdata.

Choose to use δN,ns(β).



Summary:Nested Method of Moments Algorithm.

I First step. As in BLP we first find, for any given β, the value of δwhich makes the aggregate shares derived from the model just fit theproduct level demands

I Second step. Substitute δN,ns(β) for δ, into the model, and computethe model’s predictions for the micro data moments as a functiononly of β. Select β that minimizes a distance between the momentspredicted by the model and the moments in the data.

I Calculation of Moments. The CAMIP sample is “choice based” – itcontains nj random draws on the characteristics of households whopurchased car j . So we match the data on consumer atttributesconditional on a purchase of car j to the model’s predictions. (UseBayes’ Law).



Estimating the λ

Recall thatδj = Σkxjkλk + pjλp + ξj .

We expect pj to be correlated with ξj , so even if the δj were known, wewould need to use instruments in order to obtain consistent estimates ofthe parameters of this equation. Unlike BLP, who had twentycross-sections with which to estimate this equation, we only have the datafor 1993. This suggests a precision problem similar to BLP’s; but this timeonly for a subset of the parameters of interest (the λ). We are particularlyinterested in λp, since it plus the other parameters already estimateddetermines all own and cross price elasticities.



To add information we can add an assumption on marginal cost and apricing equation as in BLP or we can find prior information on λp. Weused three estimates. One of zero (implicit in usual stuff), one from ourown two equation model as in BLP, and one from GM’s estimate of anaggregate elasticity of one. Levels vary markedly with the estimate of λpbut cross sectional pattern do not (see tables 14 and 15). Note that asmight have been expected from looking at the second choice dataelasticities are particularly low for light trucks. This means markups arehigher here, and we might expect the addition of new vechicles in these“niches”.



Prediction Exercise:

Introducing a Mercedes SUV.∗

Model Price Old Share New Share New - Old ShareNEWCAR 33.659 0.0000 0.0762 0.0762

Biggest Declines in Sales.FORDEXPL 24.2740 0.2518 0.2373 -0.0144JPGRNDCH 25.8490 0.1475 0.1376 -0.010CHS10BLZ 22.6510 0.1106 0.1071 -0.0036TO4RUNNR 25.5480 0.0380 0.0347 -0.0033NISSPATH 24.943 0.0397 0.0375 -0.0022Luxury cars∗∗ top 4 .1610 .1565 -.0045All Vehicles n.r. 9.711 9.711 .000

∗ See the text for the characteristics of the new car.∗∗ Cars priced above $30, 000.



Discontinue Oldsmobile Division.

Old Share New Share New-Old ShareAll Oldsmobiles .237 0 -.237All GM 3.126 3.016 -.110All Cars 9.711 9.695 -.016

Non-Olds Share Changes.CHELUM 0.1354 0.1548 0.0194BUILES 0.1216 0.1336 0.0120PONGAM 0.1322 0.1441 0.0119HONACC 0.2955 0.3039 0.0084

Olds Share ChangesOLDCIE 0.0676 0.00 -0.0676OLDSUP 0.0594 0.00 -0.0594OLDn88 0.0498 0.00 -0.0498OLDACH 0.0333 0.00 -0.0333OLDn98 0.0187 0.00 -0.0187OLDSBRAV 0.0083 0.00 -0.0083



“MicroBLP” uses only one market and so relies on second choice data to“vary the choice set” and identify substitution patterns. Still no interestingvariation in price.

Cross-market micro data is more useful.

Example just accepted to Science: work by Levinsohn and Mobarak on thechoice of latrines (or not) in Bangladesh. Price variation andprice-variation is exogenous and person-specific from experimental design.But: want to know the role of peer effects: endogenous market share is inthe micro utility function. Variation in experimental intensity (acrossvillages) is a potential instrument for the endogenous village market share.



Goeree (2008): firms choose both advertising and price.

Advertising alters the consumer’s “consideration set” while price influencesdemand conditional on the consumer being aware of the good.

Could have a logit probability of being aware of the good times a BLPstyle demand conditional on consideration.



One more “micro” example: Capps, Dranove, and Satterthwaite (2003)(see also Ho (2009).)

Competition between hospitals in different markets. Great consumer data:diagnosis of illness, location, etc. These interact with hospitalcharacteristics in different markets: location of hospital with location ofpatient, severity of illness with “university hospital”, etc. The hospital mayin “in network” or not (much more expensive.)



Supply side is harder: bargaining between hospitals and insurancecompanies.

The demand estimates intuitively set the value of the hospital to thenetwork (how unhappy are consumers if the hospital is left out of thenetwork) and this should set the “threat point” of the hospital innegotiations.

See also new work by Gautam Gowrisankaran and Town (2015).


Nonparametric Identification

Identification

10-15 years after the original BLP paper, there were still questions aboutidentification. Is the model “really identified” on market-level data? Givenconsumer-level data? What is the role of the BLP instruments? Of costshifters? Other possible instruments?


Nonparametric Identification

Nonparametric Identification: Why?

Identification: assuming away problems of sample size, what could welearn in principle if we saw the population distribution of observed data?

1. How should we think about parametric estimates?

Are functional form/distributional assumptions approximations forestimation or essential maintained hypotheses?

2. What can, in principle, be learned from typical observables?

I what restrictions on the model are important?I what types of variation in the data are important?

3. Step toward new nonparametric/semiparametric estimators?


Nonparametric Identification Market Level Demand

Berry and Haile (2014) on Identification using MarketLevel Data

Berry and Haile (2014)Formal identification is interesting even if we are going to use parametricmodels in the end.

Focus on what instruments are needed / useful



Issues in Identification

Goal: counter-factual policy analysis in an extended “supply and demand”differentiated products framework.

Two classic issues in the Identification of Demand

1. Endogeneity of prices

2. Role of Functional Form Assumptions

In the end, we will need exogenous variation in the data that reveals [1]the effect of prices and [2] the nature of substitution patterns.



Endogeneity

Endogeneity of price (and possibly of product characteristics), comes fromthe presence of market-level unobserved demand factors. In now commonempirical IO practice, we model an unobserved product/market leveldemand unobservable that is possibly correlated with price and that alsoexplains why model doesn’t fit perfectly.



Functional Form

Functional Form Assumptions can often impose answers about cross-priceelasticities and markets. CES and pure market-level Logit restrictions areclassic – these can “estimate” elasticities from almost no data, but theanswer comes almost exclusively from functional form.

We want to allow for more flexible functional forms. In principle, proveresults for “non-parametric” case, although in practice probably use“flexible” functional forms.



Index, Inversion and Instruments: Logit Example

Begin with the simplest example: logit demand of consumer i for productj in market t

uijt = xjtβ − αpjt + ξjt + εijt

Note that we have an logit index in this model:

δjt = xjtβ − αpjt + ξjt

The logit market shares (purchase probabilities) are non-linear in the in theproduct index, δ:

sjt =eδjt

1 +∑

k eδkt



The index, shares and pricesThis is trivially solved – inverted – for the index that includes theunobservable, here using the share of the “outside good” 0:

δ = ln(sjt)− ln(s0t).

Here, the index is a function of the share vector. We will greatly generalizethis. Remembering the definition of the index,

ln(sjt)− ln(s0t) = xjtβ − αpjt + ξjt .

This looks like a 2SLS regression, need instruments for price (recall thatxjt instruments “for itself.”) To look even more like what we do later,

re-write again as:

xjt + ξjt =1

β(ln(sjt)− ln(s0t)) +

α

βpjt

LHS is a tightly parameterized function of shares and price.Steven T. Berry Yale University, Cowles Foundation and NBEREmpirical Models of Differentiated Products June 18-19, 2015 178 / 341


Non-logit substitution

The logit model has ridiculous substitution patterns that depend only onmarket shares, not x . If put log-price in the index, looks like CES withmany goods, also ridiculous for actual empirical work.



Nested Logit

Logit “within” and “across” groups of products (“nests”) but at leastricher than the pure logit.

At the market level, has an extra parameter on the log “within groupshare.”

ln(sjt)− ln(s0t) = xjtβ − αpjt + (1− λ) ln(sj/g ,t) + ξj .

Useful, but still restrictive. What we the extra IVs for with-group share?Numbers / quality of other goods? To look even more like what we dolater, re-write again as:

xjt + ξjt =1

β

(ln(sjt)− ln(s0t)− (1− λ) ln(sj/g ,t)

)+α

βpjt

LHS is a more complicated function of shares and price.



Random Coefficients Logit

McFadden, Hausman and Wise (1978) and Berry, Levinsohn and Pakes(BLP, 1995) add random coefficients to the logit, e.g.

uijt =∑k

xjktβik − αpjt + ξjt + εijt

βik = βk + σkνik

With νik standard normal.But what identifies the new parameters ρ?Instruments that shift substitution patterns? BLP instruments? Are thesesufficient? Necessary?



The “BLP Inversion”

It is now nonlinear in the parameters.

Not the usual way to write it, but if one x does not have a randomcoefficient can write the “BLP inverse” as

x(1)jt + ξjt =

1

β1δj

(st , pt , x

(2), θ)

)

where “mean utility” δ has to be computed numerically and depends on asmall number of parameters.

Again, our method generalizes this to an arbitrary unknown function ofshares and prices, which is like a generalized discrete choice model with anindex restriction on one of the x ’s and on the demand unobservable ξ.Need instruments for shares and prices. The way the shares enter thefunction govern the “substitution” patterns, as in the nested logit.



Classic Instruments

I Cost shifters or proxies for cost shifters.

I “Hausman” instruments: prices of goods in other markets (assumingcommon cost, but not demand, shocks.)

I “BLP” instruments: exogenous characteristics of other goods(variation in rival’s x ’s changes substitution patterns.)

I “Waldfogel” instruments: conditioning on the demand anddemographics of an individual consumer, use as instruments thedistribution of attributes of other consumers (which shift availableproducts.) Or, like Ying Fan, use consumer attributes (or market size)in cost-related markets.



In the existing empirical literature, no formal argument about when, forexample, the “BLP instruments” are sufficient, alone, to identify demand?With the functional form assumption, “easy” to get “enough”instruments, but is this all functional form?


Nonparametric Identification Model

Demand Notation

I consumer i , market t, products j ∈ JtI “market”⇐⇒ choice set

I “product”=“good”=“choice”

I xjt , exogenous observables (product dummies ok)

I pjt ∈ R, endogenous observables (price)

I ξjt ∈ R, market/choice-specific unobservable

I 0 ∈ Jt , “outside good”, Jt = |Jt | − 1

I choice set (market) ⇐⇒{Jt , {xjt , pjt , ξjt}j∈Jt

}


Nonparametric Identification Random Utility

Preferences: Random Utility

The random utilities, conditional on prices and on observed andunobserved characteristics, are i.i.d. across consumers and markets, withejoint distribution

Fv (vi1t, . . . , viJt |xt , pt , ξt) .where we condition on the “choice set.”Unless we want cardinal utility or to consider Pareto improvements (wherewe need to map utility into the “addresses” of consumers) we don’t needto consider the “utility function” and the “distribution of utilityparameters (tastes).”

This more general treatment of utility makes the identification resultsfollow much more easily (as opposed to starting with semi-parametricfunctional forms.)


Nonparametric Identification Random Utility

Restrictions

I All market-specific unobserved heterogeneity is in ξjt . General untilwe assume it is a scalar.

I Next: add an index assumption.


Nonparametric Identification Index

Restrictions on Preferences

Two real restrictions:

I Assume a scalar unobservable ξjt .I Quality Index:

I Partition xjt =(x

(1)jt , x

(2)jt

), x

(1)jt ∈ R and let

δjt ≡ x(1)jt β + ξjt

= x(1)jt + ξjt

Henceforth condition on x (2) and drop the superscripts. The model is thencompletely general in x (2).



In the index δ, x (1) and ξ are perfect substitutes, a strong assumption. Insome cases, can relax to

δjt = g (xjt) + ξjt ,

g(·) an unknown strictly monotonic function.

Intuition is that we are going to use the index to capture the effect of anexclusion restriction that xjt and ξjt only enter the utility of good j .



Market Demand

Integrating over utility in the usual way gives us the market sharefunctions:

sjt = σj(δt , pt), j = 0, . . . J

sjt is observed data

Note that if we identify the unobservable, we see demand directly. This isall we want in many cases. To recover the distribution of cardinal utility,can further assume a utility function that is linear in price (otherwise, notnecessary.)



Another Example: Continuous Demand

Don’t need discrete choice. With continuous demand, can define shares as

sjt =qj(δt , pt)

q0 +∑

k qk(δt , pt)

with fixed q0 > 0

With continuous demand, the index δjt might shift the marginal rate ofsubstitution between good j and “money spent outside the market.” SeeBeckert and Blundell (2008).

We will need the goods to be weak substitutes in terms of the share sjt ,but it turns out this is consistent with a degree of complementarity in qjt .



Monotonicity

Our assumptions will imply that sj(δt , pt) is strictly increasing in δj .


Nonparametric Identification Inversion

The Problem of Multidimensional Demand

Even outside of discrete choice, in a differentiated products demandsystem, an unobserved increase in the desirability of one product will effectthe demand for all products.

We deal with this by “inverting” the demand system, solving for theunobserved shock to each product and then identify demand vianonparametric “instrumental variables” style restrictions on theunobservables.



Inversion

Berry, Gandhi, and Haile (2013) extend prior proofs to show that thenon-parametric inverse

δjt = σ−1j (st , pt)

is unique.

This result extends / complements older demand / math-econ literatureon the uniqueness of demand inverses (can also apply to inverse in p.)



Conditions for Unique Inverse

I Weak substitutes across all goods (in shares). δjt up (pjt down)implies skt , k 6= j , down.

I Some strong substitution: in particular Connected Strict Substitutes.There must be a path of strict substitution from each good to an“outside good.”

The outside good can be “natural” (purchase no automobile) or elseartificially defined to make the condition work. WIth discrete choice weaksubstitutes is not a restriction. With continuous goods, can have a high(but restricted) degree of complements and still have substitution in theshares as defined above.



Substitution Patterns for Inversion

We can represent the pattern of substitution with the directed graph of amatrix Σ (δ) whose elements are

Σj+1,k+1 =

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

The directed graph of Σ (δ) has nodes (vertices) representing each goodand a directed edge from node k to node ` whenever good k substitutes togood ` at δ.



Connected Substitutes

Assume:For all δ ∈ X ∗, the directed graph of Σ (δ) has, from every node k 6= 0, adirected path to node 0.

The condition requires that for any distinct products j and j ′, there be a“path of substitution”, possibly indirect, from j to j ′

An implication (given substitution and monotonicity) is that if all the δ’sin set K strictly increase, there is some good k /∈ K (maybe good 0)whose share declines.

“All the goods are in the same market.”



Figure1:Directedgraphsof�(x)forx2~ X�(xequalsminusprice)insomestandard

modelsofdi¤erentiatedproducts.Panela:multinomiallogit,multinomialprobit,mixed

logit,etc.;Panelb:modelsofpureverticaldi¤erentiation,(e.g.,MussaandRosen(1978),

Bresnahan(1981b),etc.);Panelc:Salop(1979)withrandom

utilityfortheoutsidegood;

Paneld:RochetandStole(2002);Panele:independentgoodswitheitheranoutsidegood

oranarti�cialgood0.

11


Nonparametric Identification Market Level Instruments

Identification via Instruments

Once we know that the inversion is unique, in the market data case we canwrite:

xjt + ξjt = σ−1j (st , pt)

Estimating the inverse is as good as estimating the market share (demand)function. And now its linear in the errors, so can use existing and extendednonparametric IV literature.

To estimate, put restrictions of the form: unobservables are [a] meanindependent or [b] fully independent



Identification via Instrumentscont

Our equationxjt + ξjt = σ−1

jt (st , pt).

“almost” has the form of a classic non-parametric IV regression with alinear error, as in Newey & Powell (2003)

yi = Γ (xi ) + εi

Although the endogenous and exogenous variables enter differently, we caneasily repeat Newey-Powell argument using our equation. Instrumentshave to be “rich enough” in a precise way. But: what are the instruments?



Instruments in the Market Case

In our modelxjt + ξjt = σ−1

j (st , pt).

There are 2J endogenous variables on the RHS: the prices and the shares.As in the nested logit, the shares are capturing the “substitution patterns.”

The J xjt ’s (“BLP” instruments) are available and necessary; assume theseare mean independent of ξjt . But still need J more instruments – costshifters or Hausman instruments?

One possibility: variation in the “BLP instruments” reveals the role ofshares (substitution) while product-specific cost-side instruments revealthe role of price.

In this fully non-parametric context, need a lot of instruments! Maybequite reasonable if dimension of choice set is small (voting?)



How to Reduce the Number of Needed IVs?

1. More functional form restrictions.

2. More Data Consumer-level data (matching choices to consumerattributes, holding the unobserved product characteristics fixed) canidentify substitution patterns without instruments, using somerestrictions on utility.


Nonparametric Identification Functional Form Restrictions

Functional Form RestrictionsCan use the fully parametric models from the beginning, with afinitie-dimensional parameter:

xjt + ξjt = σ−1j (st , pt , θ).

Or impose semi-parametric restrictions. Putting p into the index gives

xjtβ − pjt + ξjt = σ−1j (st),

which can be re-written as a problem of identifying the price-inverse ofdemand

pjt = σ−1j (st) + xjtβ + ξjt .

With no interactive “brand j dummies” can impose symmetry andexchangeability

pjt = σ−1(sj , s−j) + xjtβ + ξjt

giving the one equation across all products (can use within-marketvariation.)



Example: Analog of Nested Logit

Inverse is exchangeable within nest.

Example: Local Competition

The assumption that competition is “local” can reduce the number ofproduct shares and prices that enter the inverse. Extreme case is a“generalized vertical model” with products ordered by price to give

xjt + ξjt = σ−1(sj−1,t , sj ,t , sj+1,t , pj−1,t , pj ,t , pj+1,t).

regardless of the total number of products.



Different Kinds of Functional Form Restrictions

1. Parametric on the utility function + distribution of “tastes”(McFadden, BLP – traditional.)

2. Semi-parametric on the index or the properties of σ−1

(exchangeability)

3. directly parameter on the inverse function itself. Have to obeymonotonicity and invertiability assumptions



Example of (2) + (3): generalized non-nested groups

xjtβ − αpjt + ξjt =

ln(sjt)− θ0ln(s0) + θ1 ln(s1) + θ2 ln(s2) + θ3 ln(s3)

where s1 is the sum of shares of the products in group 1, etc. If the θ’s areall positive, the monotonicity assumptions are satisifed. Don’t know inadvance what random utility model generates this, but with supportconditions could solve for the random utilities afterwards.


Nonparametric Identification Identification: Micro Data

Micro Data

See Berry and Haile (2010) (revision in process).

Key data:

I yit indicator for the choice of consumer i in market t.I zijt , involves an individual-product interaction, e.g.

I distance to hospital, school, retailerI family size × car sizeI household exposure to product advertisingI consumer / plan specific predicted Rx drug plan cost



Utility Restrictions with Micro Data

We now assume an index in the consumer / product attribute:

λijt = g(z1ijt) + ξjt

for g(·) unknown and increasing. Similar to before, condition on z(2)

(perfectly general) and drop the superscripts on z .

Gives product choice probabilities of

sj = σj(λijt , xt , pt)

Again, don’t have to specify the functional form of utility and thedistribution of consumer tastes. Again, quasi-linearity will allow us touncover the distribution of utility.



Observed Consumer Purchase Probabilities

In each market t we observe the purchase probabilities associated withdifferent values of z . Let the vector z t(s) be the z that generates apurchase prob. vector s in market t. Our inversion result makes sure thisis unique.

Common Choice Probability We assume that the support of z issufficiently large (relative to the support of ξ) that (at least conditional ona price p) in every market there is a consumer type z who purchases thegood with probability s0.



Inversion in the Micro Case

For a given purchase probability, s, that is observed in a market we canonce again invert to find the index that explains it:

λtj (s0) = σ−1

j (s0, xt , pt)

Substituting in for the index:

g(z tj (s0)

)+ ξjt = σ−1

j (s0, xt , pt)

Have to choose an s0 such that the support of z is big enough to find z rt

in every market.

Turns out, we can learn the function g(·) from local variation in s withinmarkets (the unobservable drops out!) and then use (e.g.) Newey-Powellacross markets to uncover the rest.



Given some assumptions, the derivative of zjt(s0) exists via the implicit

function theorem and is given by

∂zjt(s0)

∂sj=∂σ−1

j (s0, pt)/∂sj

∂gj(zjt(s))/∂zj. (37)

Further, we can observe this derivative by varying s about s0.

These derivatives are “observables” that we use to identify the functiong(·).



g(z tj (s0)

)+ ξjt = σ−1

j (s0, pt)

Given differentiability,

∂g(zj(s0))

∂z

∂zj(s0)

∂sj=∂σ−1

j (s0, pt)

∂xj

Note that ξ drops out.



For some market t (say t = 1), with price p we can WLOG choosezt=1(s0) as a value at which we normalize ∂gj(zj)/∂zj = 1. For each j , wecan then identify the derivative

∂σ−1j

(s0, pt=1

)∂qj

=∂gj(zj)

∂zj

∂zj ,t=1(s0)

∂qj=∂zj ,t=1(s0)

∂qj. (38)

This gives us the derivatives of σ−1 at a given (s0, p).



Now define the support of zt(s0) conditional on a price vector p = pt as

Z(pt). It follows from (38) that for each value of z ∈ Z(pt=1) we can nowidentify

∂gj(z)

∂zj=∂σ−1

j (q, pt=1)/∂qj

∂zj(q)/∂qj(39)

This gives us the derivatives of g over some region.



What we need next is a series of cumulatively overlapping sets

Z(p1), Z(p2), Z(p3), . . .

whose union is ∪p∈PZ(p).



Knowing g(·), we now have a non-parametric IV estimating equation

g(z tj (s0)

)+ ξjt = σ−1

j (s0, xt , pt)

running across markets. It’s important that s0 is fixed across markets, sowe don’t need instruments for the substitution patterns, we learn thesefrom the micro data!.



Instruments for p include

I Cost shifters, including Hausman IVs.

I “Waldfogel” Instruments (features of the distribution of z .) Worksbecause we have ruled out spill-overs or sorting, so that conditioningon a given consumer’s zijt is all that matters for consumer-leveldemand. But aggregate demographics (income, etc.) matter for price(and later, for entry, location and variety).



Even Stronger Micro Results

Stronger conditions give even stronger results on micro data, see againBerry and Haile (2010).

Assume (roughly)

I Utility is linear in zijtI and zijt has full support.

Then we can uncover the marginal distribution of utility for one good,which is shifted by only one scalar endogenous variable, pjt . One costshifter, or else one “BLP instrument” alone, are is enough!



Micro Data: Summary

In summary, then, micro data can greatly restrict the number of requiredinstruments by using variation in consumer attributes to “trace out”substitution patterns, leaving us “only” to instrument for the effect ofprices.

If price enters in a simple way, or else under the strongest of conditions onmicro utility and the support of attributes, we can identify the model withas few as one instrument.


Nonparametric Identification Identification of Supply (MC)

Supply Side

Can estimate classic oligopoly supply side either

1. by imposing a static equilibrium assumptions, backing out marginalcosts and then estimating a marginal cost function, or

2. with stronger instruments, uncovering the marginal cost unobservablebefore imposing the oligopoly supply side and then

3. can test a variety of equilibrium assumptions

For a full treatment of supply side identification, see Berry and Haile(2014).



Oligopoly MC

The f.o.c.’s of “all” multiproduct static oligopoly models can be invertedto solve for marginal costs

mcjt = ψj (st ,Mt ,Dt (st , pt) , pt) .

where the ψj function varies by model. Everything on the RHS is knownonce demand is identified and the oligopoly assumption is imposed.Putting a classic error structure on mc , we can identify it from

mcjt = c j (Qjt ,wjt , ) + ωjt

using “classic” nonparametric IV methods. There is only one endogenousvariable (quantity), but an abundance of instruments so the oligopolyassumption is testable.



Alternative Approach to MC

I Don’t specify the oligopoly model, but assume that an unknown ψj

solves for MC

I Put an index assumption on MC : κjt ≡ w(1)jt γj + ωjt .

I Can identify the cost index without knowing the oligopoly model.This puts stronger requirements on the IVs (have to be truly excludedfrom demand) but permits a particularly strong (pointwise) test ofany oligopoly assumption.



Figure 1

P

tE0tmc

ψ= 0DD1tmc ψt it

DD

q

ψ= 1t it

MR

Qtq

(a)

P

tE0tmc

′tE

′0tmc

0

′=1 1

t tmc mc ψ 0it

ψ′0it

q

ψit

Qtq

ψ1it

ψ′1it

(b)

This figure shows the “Bresnahan” intuition, but there are many possiblechanges (in the true model) that should keep qty and the cost index fixedwhile changing the appropriate oligopoly analog of marginal revenue. In afalse null, these changes will incorrectly predict changes in quantity.



Simultaneous Identification of S & D

The series of papers, building on earlier work by Matzkin, also discusseshow to constructively prove identification by change of variable methodsthat use the entire system of demand and supply (oligopoly first-orderconditions) together.

This approaches strengths the IV assumption to independence betweenerrors and instruments.

The results show a trade-off between [i] support conditions on theexogenous data and [ii] quality shape restrictions on the density of theunobservables.


Nonparametric Identification Advice and Conclusion

Practical Advice

I Intuition for identification is largely correct: need exogenous changesin “choice set” (characteristics of rival’s etc.) to identify substitutionpatterns and cost/markup shifters to deal with price endogeneity.

I The most general nonparametric approach would be possible only ifthe number of choices is very small and the number of markets islarge. Otherwise, functional form assumptions will play their usualroles: [i] to smooth the data and [ii] to reduce dimensionality.

I Functional form assumptions might be made as usual on the utilityfunction, or else on the inverse market share function directly.

I Alternatively, micro consumer data can identify substitution patternswithout instruments, leaving only the problem of instrumenting forprice.



Conclusion

Our interpretation: mostly positive overall message

I with limited structure, identification holds under standard IVconditions

I key requirement: adequate instruments. Nature and number ofrequired of instruments depends on assumptions and on availability ofmicro data.



Before: some doubts in profession about identification, even forsemi-parametric BLP model

After : even less restrictive models are NP identified, under sameconditions required for elementary models (e.g., IV regression). Moreclarity as to what sources of variation (what instruments) are requiredunder different conditions.


Endogenous Product Characteristics

Product Variety

In differentiated products markets, competition in the space of horizontaland vertical quality may be as important as competition in price.Understanding competition in quality and in product characteristics isimportant to

I the welfare analysis of markets,

I anti-trust policy,

I marketing,

I etc.

For example, in anti-trust analysis the U.S. Dept. of Justice focuses onchanges in price and not much on changes in product characteristics andquality. In many markets, this is quite odd.



Characteristics and Welfare

There are not typically good “welfare theorems” about endogenous varietyand location in an oligopoly model. We can have too much or too littleenter, firms can locate too close to each other or else too far. Firms may“waste” resources in entry or in building better products, to the degreethat they are trying to shift market share rather generate new consumerwelfare.




Models often involve either

1. Entry into a discrete space of product characteristics: “Entry models”(later), or

2. Conditional on Entry, continuous product choice via a first-ordercondition.


Endogenous Product Characteristics Continuous Characteristics

Continuous Characteristics

With continuous characteristics, we can think of modeling the choice ofobserved characteristics via a Nash equilibrium first-order condition foreach observed characteristic. Need sufficient instruments to do this!

Rosse (1970) modeled monopoly newspapers as choosing number of pages(size) in addition to ad quantity and subscription price. All his functionalforms were linear, making estimation into a classic linear simultaneousequations problem.


Endogenous Product Characteristics Example: Fan (2013) Newspapers Mergers

Example: Fan (2013) Newspapers Mergers

Fan (2013) newspaper competition and mergers.

Newspapers are a straightforward multi-sided market. Charge price to bothsubscribers and advertisers. Newspapers also choose “quality” as well asamount and type of content (local vs. national news.)

In a merger, changes to characteristics may be as important as changes inprice.



Fan, contFan (2013) considers overlapping county-level markets for newspapers.She also emphasizes the endogeneity of both price and (non-political)newspaper characteristics. Depending on the county, c , readers facedifferent choice sets that include various suburban papers within largermetropolitan regions. The utility function of reader i in county c fornewspaper j is

uijc = xjβ + yjcφ+ zcφ− αpj + ξjc + εijc

where pj is the price of the newspaper and xj is a vector of endogenouscharacteristics (news quality, local news ratio and news content variety).The vector yjc contains within county newspaper characteristics assumedto be exogenous (e.g. whether the headquarters city is in the county) andzc is a vector of county demographics. The term xijc again capturesunobserved tastes for the newspaper in a given county. Once again, thevector of county-level market shares can be inverted to obtain the meanutility terms



Fan, cont

There are now four endogenous variables, price and the vector ofendogenous characteristics. It is likely that these are correlated with theunobserved taste. For example, the price is likely to be higher when thenewspaper is unobservably more popular. This makes the IV problem moredifficult. Broadly speaking, Fan also makes use of modified Walfogel styleinstruments, interacted with exogenous rival characteristics (BLPinstruments). In her case, she uses consumer demographics in the othercounties served by a rival newspaper. For example, the headquarterscounty is taken as exogenous, so that the demographic levels in thatcounty are available as instruments.



Fan, cont

In Fan (2013), the Waldfogel style instruments include other countieseducation level, median income, median age and urbanization. Fan (2013)considers extending the model of to include random coefficients on someof the characteristics. As noted, random coefficients allow for richersubstitution patterns than simple logit models. For example, if someconsumers have a larger than average taste for local news, they will likelysubstitute from one locally focused paper to another one, whereas the purelogit generates substitution patterns that vary only withdemographic-specific market shares. It not clear whether Fan has adequateinstruments for this purpose, and so she models only one randomcoefficient (on local news).



Fan, advertising

Fan also models advertising demand, with similar instruments, giving us anadvertising quantity equation that depends on the newspaper subscriptionquantity and on the price of advertising, rj .



Fan-like Profits and Costs

Simplifying, profits for a single-country paper are then

ptq(pt , xt , zt , yt , ξt) + rta(rt , qt , ηt)− C (qt , xt , yt , ωt)

withC = C (qt , at , yt , xt , θ) + ωqqt + ωaat + ωyyt

It is very helpful that the errors ω are linear shocks to incremental costs.



Endogenous quality via a first-order condition

We can easily write focs for the prices, similar to the ones we havediscussed before. If quality is chosen simultaneously to price, the foc forquality is[pt −

(∂C

∂qt+ ωq

)]∂Dq

∂yt+

[rt −

(∂C

∂at+ ωa

)]∂Dq

∂yt

∂Da

∂qt−(∂C

∂yt+ ωy

)This is linear in the ω’s, as are the focs for q and r . If these three focs areinvertible to solve for the three cost-shocks ω’s, then we can implement asupply-side GMM procedure, with the unobservable cost shocks meanindependent of instruments. (Fan actually has quality chosen before price).


Variety via Discrete Entry

Discrete Entry into Differentiated Locations

We can apply techniques from the IO entry literature to generateendogenous variety via entry into a discrete product space. In an oligopolyequilibrium, we may still need exogenous variation that shifts my rival’slocation, which affects my entry decision.


Variety via Discrete Entry

Some Models

I Bresnahan and Reiss (1991b) looked at symmetric entry, ex-postdifferentiation.

I Berry (1992) and Ciliberto and Tamer (2009) consider models wherethe differentiation is ex ante, prior to entry.

I Reiss and Spiller (1989) and Berry and Waldfogel (1999) estimatedvariable profits outside the entry model,

I Mazzeo (2002) considered discrete product segments (“quality”) andex-post differentiation (ordered models), needs strong assumptions onorder to get unique equil.

I Seim (2006) uses private info

I Jia (2008) adds network effects in geographic entry

I Manski (many papers) – use incomplete models, maybe get bounds.

I Ishii (2004), Pakes-Porter-Ho-Ishii (2006) – similar ordered modelsplus bounds estimation.


Variety via Discrete Entry Simple Entry Models

Intro to Bresnahan and Reiss

Bresnahan and Reiss (1991b), Bresnahan and Reiss (1988), Bresnahan andReiss (1991a)Look at retail and professional firms in small isolated markets.Profits in market i are

π(Ni ) = Miv(Ni , xi , θ)− Fi

with Mi being market size, Ni , the number of firms, xi are firmcharacteristics and Fi are fixed costs.

Nash Equilibrium implies that

π(Ni ) > 0 > π(Ni + 1).

orMiv(Ni , xi , θ) > FCi > MiV (Ni + 1, xi , θ).


Variety via Discrete Entry Simple Entry Models

Estimation by Ordered Probit

Given a distributional assumption on FC , the Nash Equilibrium condition

Miv(Ni , xi , θ) > FCi > Miv(Ni + 1, xi , θ).

generates an ordered probit. If FC ∼ Φ(·) then the likelihood of N firms is

Φ(Miv(Ni , xi , θ))− Φ(Miv(Ni + 1, xi , θ)).

and one can estimate θ by MLE.


Variety via Discrete Entry Identification of B & R

Review: The Monopoly Entry problem

Here we review the results of Matzkin (1992) and others, using thepotential monopoly entry example. Profits of an entering firm are:

π(xi ,Fi ) = v(xi )− Fi ,

where v is the deterministic variable profit and F the random fixed cost.In a cross-section of markets, entry occurs when v(xi ) > Fi . We observethe entry probabilities p(xi ).An immediate problem is that any monotonic transformation of both vand F results in the same entry probabilities.How bad a problem is this?



Non-Robustness to Monotonic Transformations

How bad is the problem? For many issues, not bad at all. Assume F isi.i.d. Then p(xi ) = Φ(v(xi )) is one such monotonic transformation of v ,and it reveals

I ∂p/∂x

I The sign of the effect of an x on v

I The relative effects:∂v/∂x1

∂v/∂x2

This is the kind of problem in, e.g. Berry ’92. (What is the sign andrelative magnitude of “airport presence” in entry and profits?)



Qualitative Shape Restrictions

But what if we want to know the full shape of V ? Matzkin ’92 suggestsqualitative shape restrictions, preferably derived from theory, together withan i.i.d. assumption on F .E.g. assume constant marginal costs, then for many models variable profitis proportional to population, v(x) = zi v(xi ) where z is population.Sketch of Matzkin’s proof: for some x ′ normalize units so that v(x ′) = 1.Then p(z , x ′) = Φ(z), which reveals the distribution of F , Φ, and fromthis get the other values of v . Done!(Matzkin considers broader class of v ’s that are h.d.1 in some subset of x .)



Weaker Assumptions?

Following Manski and others, conditional quantile (median) restrictions onthe distribution of F can also reveal v(x) up to units, although not the fulldistribution of F .But in the Monopoly case, not sure why we even care about the full shapeof v .One issue: “nature of competition”.



Bresnahan and Reiss, Ordered Entry

The B & R model is a simple extension of the Monopoly model withidentical potential entrants. Variable profits decline in the number offirms, y : vy (x).With an i.i.d. F , we have

Pr(y = 0|x) = 1− Φ(v1(x))

Pr(y = 1|x) = Φ(v1(x))− Φ(v2(x))

Pr(y = 2|x) = Φ(v2(x))− Φ(v3(x))

· · ·

B & R estimate by fully parametric MLE and ask: how fast does v declinein y?



The Economic Question in B & R

What is the value of v2(x)v1(x) ?

Think of benchmark models:

1. Fixed Prices: v2(x)v1(x) = 1/2.

2. Cournot Competition: v2(x)v1(x) ∈ (0, 1/2)?

3. Homogeneous Goods Bertrand: v2(x)v1(x) = 0?

Can think of similar ratios for other y .But these ratios are not robust to monotonic transformations, andso the economic parameter of interest is not non-parametricallyidentified in B & R without Matzkin-style shape restrictions.In fact, there is a monotonic transformation that sets the ratio to anythingbetween 0 and 1.



B & R use the Shape Restriction in Population

We can write the B&R model as series of threshold-crossing models:

Pr(y ≥ 1|x) = Φ(v1(x))

. . .Pr(y ≥ n|x) = Φ(vn(x))

and so restricting variable profits to be proportional to population willidentify vy (and indeed over-identify Φ, so that we could allow Φy (F ) aswith perhaps upward-sloping supply of the fixed asset.)



Identification Lessons from the B & R Model

Without qualitative shape restrictions, the object of interest (the “natureof competition”) cannot be identified, but with one natural (thoughrestrictive) shape assumption, the nature of competition is fully identified.Here, the binary threshold crossing literature is enough, but it will notenough be in more complicated models.



Additional Data

Add p and q to the data set, estimate variable profit from this. All that isleft to the entry model is fixed cost.



Using price and qty data in entry model

Example: Berry and Waldfogel (1999) on radio entry. We will consider a(2014) version of this model, focusing on entry into horizontal and verticalentry locations.



Discrete Types of Firms

Mazzeo (2002) Mazzeo considers the model without heterogeneity in fixedcosts, but with different types of firms:Profits for any firm choosing quality level t = (1, . . . ,T ) in market m areassumed to be

πtm = xmβt + g(N1, . . . ,NT , θt) + εtm.

where N = N1, . . . ,NT is the vector of the number of firms of each type.The parameters (specific to each type) are βt on the market level variablesand θt , which parameterizes the effect of own-type and other-typecompetition.

Now existence and equilibrium are even worse, but ad-hoc assumptions onthe order of entry help.Application is to motels at highway intersections (1-star, 2-star, etc.)



Seim

Seim (2006) introduces asymmetric information into an econometricmodels of potential entrants’ location decisions.Specifically, Seim models aset of N potential entrants deciding in which one, if any, of L locationsthey will locate. In Seim’s application, the potential entrants are videorental stores and the locations are Census tracts within a town.

If potential entrant i enters location l , it earns

πil(nl , xl) = xlβ + θll

N∑j 6=i

Djl +∑h 6=l

θlh∑k 6=i

Dkh + νil (40)

Each store treats the other stores’ Djh as random variables whencomputing the expected number of rival stores in each location h.



By symmetry, expected prob of rival entry as ph = E (Dkh) and the N ofexpected rivals is (N − 1)ph.Note convenient linearity of π in Dkh

EDπil(n, xi ) = xlβ + θll(N − 1)pl + (41)

+∑j 6=l

θlj(N − 1)pj + νil

= πl + νil .



To calculate the Nash equilibrium entry probabilities p1, ..., pL we mustsolve the nonlinear system of equations

p0 =1

1 +∑L

l=1 exp(πl)(42)

p1 (43)

=exp(π1)

1 +∑L

l=1 exp(πl)(44)

(45)...

...... (46)

pL =exp(πL)

1 +∑L

l=1 exp(πl)(47)

(48)



Seim argues that for fixed N, an solution to this equilibrium system existsand is typically unique, although as the relative variance of the ν’sdeclines, the problem approaches the discrete problem and it seems thatthe non-uniqueness problem faced in perfect informationsimultaneous-move could reoccur. The single location model discussionabove illustrates how and why this could happen.


Variety via Discrete Entry Entry Models with More Data

Using price and qty data in entry model

Example: Berry and Waldfogel (1999) and Berry, Eizenberg and Waldfogel(2015). Here, we do not try to learn about variable profits, but rather useprice and quantity data to learn variable profits and then all that is left arethe values of fixed cost.

Berry, Eizenberg and Waldfogel (2015) consider entry into a twodimensional product location space of horizontal and verticaldifferentiation.


Variety via Discrete Entry Example: Berry, Eizenberg and Waldfogel 2014

Berry, Eizenberg and Waldfogel

In Berry, Eizenberg and Waldfogel (2014) , we present a very simple modelof entry into a discrete product space that allows for point estimates ofthe parameters of variable profits and bounds on fixed costs.

Applying this model to the Radio Industry, we consider optimal productvariety in terms of the number of stations in different radio formats(“rock”, “country”, etc.)

Extensions include: vertical quality, joint ownership, merger analysis.



Background on Radio

I There is a long theoretical literature on the inefficiency of free entryinto oligopolistic markets. New firms “steal business” from existingfirms: a negative externality. Lower prices for existing consumers andthe intro of new varieties create an offsetting positive externality.

I Excessive entry into radio industry has often been suggested.



Berry and Waldfogel, 1999

They use new data and simple methods to estimate the extent of andwelfare loss from excess entry in radio broadcasting.

Results from BW ’99

I First, look only at market participants: broadcasters advertisers.Welfare loss from free entry, as opposed to the socially optimum N, is40% of industry revenue. A big number?

I There is still the positive externality to listeners. If listeners value anhour of listening at about 15 cents an hour, then welfare loss tomarket participants would be just offset by external benefit tolisteners.

But they had to assume symmetric stations, no differentiation by format,etc.



Variety and Multiple Equilibria

I Can easily introduce variety into the post-entry variable profits model(e.g. BLP, nested logit, etc.), although “product characteristics” cannow be endogenous.

I BUT: often lose unique equilibrium

I Example: for 2 varieties (N1,N2), both (2,1) and (1,2) might beequilibria.

I This is why Berry & Waldfogel assumed symmetry: otherwise can’testimate via MLE.



Estimation with Multiple Equilibria

I Here, we use a simple extension of the “semi-parametric” Bresnahanand Reiss bounds, avoid estimating the distribution of F altogether.

I Much simpler than current, general econometric method, but veryspecific to the model

I Harder part is extending to unobserved vertical quality


Variety via Discrete Entry BEW 2014 Entry and Variety

Outline of Model

1. Stations produce listeners, who make a free choice as to listening.Listeners care about format and within format stations are more“similar”. Formally, use nested logit. Most general model includesdiscrete unobserved quality levels.

2. Stations sell listeners to advertisers. Advertisers’ demand is downwardsloping in the share of the population who listen. Simple constantelasticity functional form.

3. There is free entry into a discrete product space (formats) and astatic Nash equilibrium. No unique equilibrium: entry problem is nolonger a Bresnahn-Reiss style ordered probit.

(1) and (2) give variable profit function, (3) adds fixed costs.



Observed Data and Variable Profits

No Variable Cost (but add endogenous fixed cost of “quality” later).

In market t, format k , We observe:

I ad price pt ,

I format share skt ,

I stations numbers Nkt ,

I market demographics xt ,

I population Mt .

At observed vector Nkt , observed variable profits are

Vkt = pt(st)Mtskt

At market outcome, variable profit Vkt is just observed revenue, Rkt .



Counter-Factual Variable Profits

To create bounds on fixed cost, also need variable profits at Nkt + 1.

To get this counter-factual, need to

1. Estimate model of listening demand skt(xt ,Nkt ,N−k,t , θd , ξkt),

2. Estimate model of Advertising Price pt(xt , st , ωt , θ).



How to Model the Product Space

I “Ex-Ante” vs. “Ex-Post” differentiation: with ex-ante, have tospecify number and characteristics of potential competitors. Forairlines (Berry ’91) and Chain Stores (Jia, ’06) this might mightsense, but other times is quite arbitrary.

I Continuous v.s Discrete product space. Easier to specify“counterfactual profits” (profits of the “next entrant”) with discretespace.

Herewe use ex-ante identical entrants into a discrete space of product“segments”, both horizontal and vertical.



Listening Model: Horizontal case

I Discrete-choice model: listen to one of the “inside” stations, orchoose outside option (not listening to commercial radio)

I Nested-logit, 11 nests (ten format categories + “not listening”)

I Listener i ’s utility from listening to station j , which belongs to formatcategory g , in market t, is given by:

uijgt = xgtβ + ξgt︸︷︷︸δgt

+νigt(σ) + (1− σ)εijgt

I x includes: market average income, share college educated, shareBlack & Hispanic, regional dummies, format dummies, interactions(“country× South”); ξgt taste shock



uijgt = xgtβ + ξgt︸︷︷︸δgt

+νigt(σ) + (1− σ)εijgt

I Comments:

1. Implies within-format symmetric mean-utility & market share2. Complication: account for in-metro vs. out-metro (“home dummy”)3. 0 ≤ σ < 1 a business-stealing parameter (highest as σ → 1)

I νigt has the unique distribution derived by Cardel (1997) which dependson the parameter σ

I νigt → 0 as σ → 0



Estimation of Horizontal Differentiation Model

I For a station in format g , market t (follow Berry 1994):

ln(sjt)− ln(s0t) = xgtβ + σln(sj/g ,t) + ξgt

1. One observation for each format-market pair; Within-format symmetryimposed: sjt = Sgt/Ngt , sj/g ,t = 1/Ngt

2. The above adjusted to allow for home vs. nonhome stations (so reallytwo observations for each format-market pair)

3. Estimation using 2SLS accounting for the endogeneity of sj/g ,t withinstruments (i) market population (ii) number of out-metro stations(taken to be exogenous) (iii) number of out-metro stations in sameformat

4. Selection challenge for “Urban,” “Spanish,” “Religious”



Table 1: Description of the Dataset

Variable Units Mean Std. Deviation Minimum MaximumShare in-metro % 0.111 0.026 0.030 0.151Share Out-metro % 0.015 0.023 0.000 0.104N1 (in-metro) integer 19.644 7.565 4.000 45.000N2 (out-metro) integer 7.209 8.320 0.000 37.000Population millions 1.016 1.687 0.075 14.481Ad Price $ 570.480 237.653 258.222 2691.177Income 10,000$ 4.584 0.860 2.482 8.010College % 21.200 5.370 10.200 37.100

Computed using the 163 markets with full data, see text.

1



Format Classification

Table 2: Classification of Formats into Ten Categories

Format Group Formats Included

”Mainstream” Adult Cont. Hot AC Modern AC Soft AC Adult Altern.Classic Hits 80s Hits

CHR CHR

Country Country Classic Cntry. Trad. Country

Rock Rock Active Rock Modern Rock Classic Rock

Oldies Oldies

Religious Religious Cont. Christ. Black Gospel Gospel S. Gospel

Urban Urban Urban AC Urban Oldies Rhythmic Old.

Spanish Spanish Span.-Oldies Span.-Adult Alt Span.-C. Christ Span.-CHRSpan.-Cl. Hits Span.-EZ Span.-Hits Span.-NT Span.-Relig.Span.-Talk Tejano Tropical Reg’l Mex. Span.-Stand.Ranchero Romantica

News/Talk News/Talk News Talk Hot Talk Bus. NewsSports Farm

Other Variety Bluegrass Blues cp-new AmericanaPre-teen Ethnic Silent A22 A26A30 N/A Jazz Smooth Jazz DanceClassical Adult Stand. Easy List.

1



Table 4: The listening equation - base case (horizontaldifferentiation)

Table 4: The listening equation - base case (horizontaldifferentiation)

Region Dummies northeast 0.122*** Interactions hispXspan 0.352***(0.042) (0.036)

midwest 0.0974** blackXurban 0.506***(0.041) (0.050)

south -0.0506 southXreligious 0.809***(0.041) (0.095)

Demographics black -0.0681*** southXcountry 0.316***(0.014) (0.072)

hisp -0.0233** Corr. Parm. σ 0.519***(0.0097) (0.063)

income -0.00258 In-metro dummy 0.639***(0.017) (0.082)

college -0.0630** Constant -5.325***(0.027) (0.15)

Format Dummies includedObservations 1919R-squared 0.72

1


Variety via Discrete Entry BEW Listening Model with unobserved quality

Allowing for Both Horizontal & Vertical Differentiation

I Two important new challenges:

1. How to define / measure quality?

I Allow quality to be an unobserved station characteristic

2. Deal with endogeneity of quality (more likely to enter as “high qualityCountry” if market’s unobserved taste for Country is high?)

I Incorporate market-format fixed effects

I Caveats: allowing quality differentiation in Mainstream andNews/Talk only (explain below); out-metro automatically defined aslow quality



Intuition for Identifying Unobserved Quality

High-quality stations have high demand—a high “mean utility” δ. Butacross markets, δ can be because of an unobserved taste for ratio formats.Stations get high preference for free, but have to pay for quality, so wantto distinguish these.

Therefore, look at within market demand difference within format. Simply,within market-format, more popular stations are higher quality. Onlyproblem is this requires multiple levels of quality per market-format.



Utility with Station Quality

The utility for listener i from listening to station j in format g , in market tis assumed to have the usual nested logit structure we defined before,

ui ,j ,t = δjt + νigt(σ) + (1− σ)εijt ,

with “mean utility” for station j now given by

δjt = γq · qjt + γh · hjt + ψgt .

In the mean utility, qjt is the quality level of a station, hjt is a “home”dummy variable for in-metro stations and (γq, γh) are parameters to beestimated. For simplicity quality takes on two values: 0 (“low”) and 1(“high”).



Discrete Quality Levels

Quality qjt hjt utility term

out-metro 0 0 0in-metro low 0 1 γh

in-metro high 1 1 γh + γq



Format-Market Fixed Effect

The term ψgt is a format-market fixed effect, capturing the mean taste forformat g in market t. This depends in turn on both observed andunobserved components,

ψgt = dgtλ+ ξgt ,

where dgt is a vector of observed variables, λ is parameter to be estimatedand ξgt is still the unobserved listener taste for format g in market t.



Identifying and Estimating Station Specific Quality

The number of listeners in each market is large and quality levels shouldbe reflected in listening shares. We thus try to identify and estimate adiscrete quality parameter for every station in every market.

Note that the relevant asymptotics for the estimation of quality involvesthe number of sampled listeners per market, not the number of stations ormarkets. Within a market, stations shares have a multinomial distribution.Since quality levels are discrete, conditional on identification, estimationwill be super-efficient.



Identification of Station Level Quality

I As usual, for identification arguments, we assume an infinite sampleof listeners.

I If there are two levels of within format/market share, then the higherlevel is higher quality.

I If there are not, then the problem is harder. We can also use thecomparison to any out-metro stations shares. If the in-metro sharesare “much higher,” then they are high quality. This is shown formallybelow.

I If, for example, there is only one in-metro station (or all in-metroshares are the same) and no out-metro, then we haveset-identification: either the stations are all high quality or all lowquality.



Identification and ψ

Consider a market where all the in-metro stations have the same marketshare within some format. For any guess at the quality level of stations inthe market, there is a value of ψgt that explains the observed commonlevel of shares.



Using Within Market Shares

Because the market-format taste does not effect the within format shares,we can avoid this potential problem of non-identification if we focus on thewithin format shares. This is similar to the idea of “differencing out” afixed effect to deal with endogeneity. To proceed, let

κ1 ≡ γq/(1− σ),

κ2 ≡ γh/(1− σ),

and let the vector κ ≡ (κ1, κ2).



Within Market Nested Logit

The nested logit then implies that conditional on choosing format g theexpected probability of choosing station j in market t (the “within formatshare”) is given by

pj/gt(κ, q) =exp(κ1 · qjt + κ2 · hjt)∑`∈g exp(κ1 · q`t + κ2 · h`t)

,

where q is notation for the long vector of quality levels for all markets’stations. The expression in depends only on the quality levels in the givenmarket-format.



Identification Steps for Quality

1. identify κ using data on markets where differences in shares identifyquality levels.

2. use κ, together with out-metro shares, to identify quality levels inadditional markets.



Remaining Partial Identification

This leaves us with one remaining case of partial identification:market/formats with no out-metro station and identical shares forin-metro stations. In these market/formats, we know that either [i] allstations are high quality or [ii] all stations are low quality.

Our base case approach is to estimate demand from the market/formatswith out-metro stations and then to look for bounds on counterfactuals forthe set identified cases.



Back to IV for σ

Note that having identified qualities, we move back to the usual case ofBerry (1994) with a nested logit where all characteristics are observed(although recall that the unobservable taste variable ξgt is at the level ofthe format, not station.)

Thus, the remainder of the demand identification problem is standard andwe will continue to need an instrument variables approach to identify theformat-market level taste parameters (γq, γh, σ) (as opposed to thecomposite station-quality parameters (κ1, κ2) that are identified from thewithin format choice problem.)



Instruments Again

As in the pure horizontal model, we assume that the unobservedformat-level taste shifter is mean-independent of a set of instruments,

E [ξgt |Zgt ] = 0.

In the empirical application, we let Zgt contain the market’s population,the number of the market’s out-metro stations, and the number ofout-metro stations in the same format, as well as the d covariates.



Table 5: Demand Parameters with Vertical Quality

Parameter Estimate SE

σ – business stealing 0.589 0.017γq – high quality 0.604γh – lower quality 0.466blackXurban/10 5.555 0.001hispXspan/10 3.962 0.002region dummies includedformat dummies includeddemographics included

1

Quality could not be determined in 10.4% of News-Talk market-formatsand 27% of Mainstream formats. Our base case uses only market-formatswhere quality can be determined with probability 1 (because there is anout-metro station.)


Variety via Discrete Entry BEW Ad Price

Demand from Advertisers

We treat stations as “producing” listeners and then selling them toadvertisers. For now, a very simple inverse ad-demand function.The demand from advertisers for listeners in market t is modeled by adownward-sloping, constant-elasticity specification:

ln(pt) = xtα− ηln(st) + ωt

Popl. and out-metro stations are instruments for endogenous share. Mightbe able to have this vary by format / demographic, but data is pretty badfor this.



Notes on Advertiser Demand

It would be nice to let ad demand vary with demographics of listeners, butwe have limited price variation in our data. Some recent work usesindustry “estimated” prices for individual stations. Sometimes theseappear to just be informed guesses. There is an obvious trade-off here inusing less reliable data to estimate a more realistic model.

So far we have not used the less reliable data and so we keep the addemand model (unrealistically) simple.



Table 6: Advertiser Demand

OLS IVnortheast -0.0746 -0.0739

(0.064) (0.063)midwest 0.0835 0.0799

(0.061) (0.059)south 0.0148 0.0132

(0.060) (0.059)income 0.0567* 0.0606**

(0.030) (0.029)college 0.167*** 0.164***

(0.043) (0.042)black -0.0231 -0.0242

(0.021) (0.020)hisp -0.0120 -0.0124

(0.014) (0.013)−η -0.541*** -0.510***

(0.062) (0.072)Constant 4.492*** 4.554***

(0.17) (0.18)Observations 163 163R-squared 0.52 0.52

1


Variety via Discrete Entry BEW Entry and Fixed Costs

Equilibrium in Product Segments

Once we have listening demand and the (inverse) advertising demandequation, we have estimated variable profits.

Segment Fixed Costs

To recover fixed-costs (constant across products within segments) need tohave a model of equilibrium market structure.



Static Complete Info Nash

A good assumption for work that relies on the cross-sectional naturedistribution of market structure. With no explicit dynamics, we would likefirms to choose the best-response to rival’s actions – otherwise why don’tthey move? Justification for cross-sectional study is [i] population anddemographics are strong instruments and [ii] firms are in “long-run”equilibrium.

In a dynamic model, some private info makes more sense – firms might besurprised to find themselves in a bad location and then move away.



Bounding the Distribution of Fixed Costs

Complete Info Static Nash Equilibrium

I No variable costs. F has to be less than observed revenue.

I Also, F has to be greater than counterfactual revenue at (Nkt + 1).

I Construct counterfactual revenue from listening demand and ad-priceequation (including values of unobservables.)

I Can’t do this for markets with Nt = 0; selection discussed below.



Bounds on F

We know thatRkt > Fkt

This provides an upper bound for F , making only the assumption that Rand F are constant within segment.

Lower Bound on F : in equilibrium,

Vk(Nkt + 1, yt , xt , θ0) < Fkt .

We get bounds in each market without making any assumption on thedistribution of fixed costs.


Variety via Discrete Entry BEW Results

Table 9: Welfare analysis in the base case (horizontal only)

Observed OptimalWelfare ($ millions) 11,977 13,779Mean In-Metro Listening Share (%) 11.10% 8.15%Mean Ad Price ($) 570.48 662.54

1

BUT! This is for market participants only.



Table 10: Optimal Structure with QualityTable 10: Optimal and observed market structures, horizontal and

vertical differentiation

A. Formats with a single quality level:

Mean # Mean # Mean optimalobserved optimal reduction

CHR 1.06 0.85 20.2%Country 2.10 1.02 51.3%Rock 2.33 1.04 55.3%Oldies 1.02 0.86 16.2%Religious 1.66 0.77 53.5%Urban 1.50 0.71 52.6%Spanish 1.34 0.50 63.0%Other 2.12 1.01 52.3%

B. Formats with quality differentiation:

Format: Mainstream News/Talk

Low q High q Low q High q

Mean # observed 1.18-1.95 1.40-2.17 1.83-2.02 1.06-1.25Mean # optimal 0.37-0.66 0.56-0.86 0.79-0.89 0.40-0.51Mean optimal reduction 44.1%-81% 38.6%-74.2% 51.3%-61.2% 51.7%-67.6%

1



Overprovision of Quality

Out of 90 markets with observed high-quality Mainstream stations, in 72cases welfare can be unambiguously improved by converting one of thosestations to low quality operation. An even higher rate, 94.9%, applies tothe News/Talk format. On the other hand, there are no cases where amarket has observed low-quality stations—in either format—andconverting one of them to high quality would unambiguously improvewelfare.

Our analysis of local changes to quality offerings, therefore, reveals apattern of over-provision of quality at the margin.



BEW Conclusion

Methodologically, we develop a model of entry into an unobservablediscrete quality space, and combine this with a straight-forwardset-identified model of entry and fixed costs.

Substantively,

I Introducing richer tastes for variety reduces, but hardly eliminates, theproblem of excess entry due to profit shifting.

I Similarly, heterogeneous quality does not much effect the overallexcess entry result, and there is some evidence of the (local)over-provision of quality.

I In this particular context, the excess entry may or may not be offsetby unpriced gains to listeners.


Further Applications Media Bias and Reputation

Media Markets / Preference Externalities

Media markets have several interesting features:

I Often two-sided markets (revenue from consumers and advertisers).“Platforms”

I High fixed costs relative to marginal costs

I Public Policy issues: political/social diversity of viewpoints,distribution monopolies (cable, fiber to home).



Media Bias and Reputation

Self-confirming bias – can media competition reduce this? (to somedegree)



“Preference Externalities”

Where do product choice sets come from?Waldfogel story:

I Politics are thought to result in the tyranny of the majority.

I Classic competitive markets offer the “freedom to choose.”

As Friedman (1962) famously put it, [e]ach man can vote, as itwere, for the color of tie he wants and get it; he does not have tosee what color the majority wants and then, if he is in theminority, submit.



But when fixed costs are large relative to the market, only a subset ofproducts will be offered.

Which products are offered will depend on your neighbors preferences.Implications for urban economics, trade, health care, media markets, etc.



Media Slant

Gentzkow and Shapiro (2010)

Newspaper bias in news stories: does it come from owner preferences orreader preferences?

Policy question: does owner concentration effect politics?



GS – Slant

I Develop a text-based measure of political “slant”

I Use this is a simple Hotelling-like differentiated products (monopoly)model.

I Calculate the optimal (profit max) political location of the firm – isthere any evidence that owners systematically deviate from this?



GS Slant: text analysis

2005 Congressional Record:

Most Popular 2 word D phrases: private accounts, trade agreement,American People

Most Popular 2 word R phrases: stem cell, natural gas, death tax.

Weight them by the biggest difference in use.



GS Reader Problem

In zip code z , readers have their own political slant, rz , measured bypolitical contributions from the zip code (pretty noisy and weighted to therich.)

Ideal ideological point:idealz = α + βrz

Hotelling utility:

uizn = uzn − γ(yn − idealz)2 + εijn



GS Demand

uzn = Xzφ0 + Wznφ

1 + ξmn + νzn

Expand the square, substitute in terms, use logit, get

ln

(Szn

1− Szn

)= δmn + λd0ynrz + λd1 rz + lambdad2 r

2z + Xzφ

0 + Wznφ1 + νzn



Measurement error in yn (but not rz) handled by instruments – Rn is theoverall share of republicans and rzRn is excluded. This is a Waldfogel likeinstrument – politics of others in the metro determines yn. Fixed effectabsorbs the market-level taste ξmn.


Some Further Examples Hospital Mergers

Hospital Mergers in the US

Traditional analysis of hospital mergers was not based on any strongeconomic model. Hospitals are strongly differentiated in location, but alsoin speciality. “Community” hospitals are good for a broken arm, big-cityuniversity hospitals are much better for major illness (cancer, etc.)

How to analyze a merger? US Federal Trade Commission has adopted anexplicit demand-based differentiated products framework. Recent researchhas focused on how to develop a “supply side” based on the fact that, inthe US, hospital and private health insurers bargain contracts (how muchthe insurer will pay the hospital for non-elderly care.)


Hospital Choice

Capps, Dranove, and Satterthwaite (2003) and Ho (2009)) modelcompetition between hospitals in different markets. Great consumer data:diagnosis of illness, location, etc. These interact with hospitalcharacteristics in different markets: location of hospital with location ofpatient, severity of illness with “university hospital”, etc. The hospital mayin “in network” or not (much more expensive.)

These authors estimate a logit model with rich consumer (diagnonsis andlocation) data that interacts with rich hospital data. Substitution betweenhospitals varies a lot by diagnosis, not just hospital characteristics.


Hospital Choice

Supply side is harder: bargaining between hospitals and insurancecompanies. See Ho (2009) and more recent work byGautam Gowrisankaran and Town (2015).

As intuition for supply, the demand estimates intuitively set the value ofthe hospital to the network (how unhappy are consumers if the hospital isleft out of the insurer network) and this should set the “threat point” ofthe hospital in negotiations.


Hospital Choice

Merger analysis could be based on

I Change in Concentration

I Some Demand Based Measure (WTP for adding a hospital to anetwork, from a logit, Capps, Dranove, and Satterthwaite (2003)?)

I Full Merger Simulation?

Christopher Garmon (US Federal Trade Commission), “The Accuracy ofHospital Merger Screening Methods,” shows that logit-based WTP isreasonably well-correlated with post-merger price changes. Change inconcentration only picks out the most extreme worst merger.

Full merger simulation based on the logit and a very simple supply modeldoes not do well. Better models or data?


Hospital Choice

Example: Gowrisankaran Nevo and Town

Gautam Gowrisankaran and Town (2015)At hospital j , patient i with diagnosis d covered by insurance m gets utility

uijd = xijdβ − cidwdpmd + εijd .

where c is a co-insurance term, wd is a diagnostic weight and p is specificto the insurer/hospital. The choice set of hospitals varies by insurer (agood instrument or not?)

The price / insurance interaction is interesting, but this is a standardmicro-logit, otherwise.


Hospital Choice

GNT Price Bargaining


Hospital Choice



Hospital Choice

GNT Backing out MC

A key point then, is that GNT can still solve for mc as a function of all thedemand and bargaining parameters. They think of the sum of thetraditional and bargaining terms in the foc as a “bargaining adjusted”demand effect.

After estimating the model, they find that a proposed hospital merger inVirginia, which was turned down by the FTC, would have substantiallyraised prices.


Conclusion

Conclusion

There is now a great variety of methods for analyzing productdifferentiation, including static demand and oligopoly pricing. Furtherextensions allow us to analyze endogenous variety and quality, either viafirst-order conditions for continuous variables or entry models of discretedifferentiation.We leave fully dynamic models to another day.


Conclusion

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