Demand Estimation

Industrial Organization (UG)

Li Zhao, SJTU

Fall, 2016

The Choice Set

I Discrete choice models describe decision makers' choicesamong alternatives.

I The set of alternatives, called the choice set, needs toexhibit three characteristics.

I First, the alternatives must be mutually exclusive fromthe decision maker's perspective.

I Second, the choice set must be exhaustive, in that allpossible alternatives are included.

I Third, the number of alternatives must be �nite.

Random Utility Models

I A decision maker, labeled n, faces a choice among Jalternatives.

I The decision maker would obtain a certain level of utility(or pro�t) from each alternative.

I The utility that decision maker n obtains from alternativej is Unj .

I This utility is known to the decision maker but not, as wesee in the following, by the researcher.

I The decision maker chooses the alternative that providesthe greatest utility.

Choice to Probability

Unj = Vnj + εnj .

The probability that decision maker n chooses alternative i is

Pni = Pr(Uni > Unj , ∀j 6= i)

= Pr(Vni + εni > Vnj + εnj , ∀j 6= i)

= Pr(εnj − εni < −(Vnj − Vni), ∀j 6= i).

Choice to Probability

Unj = Vnj + εnj .

Pni = Pr(Uni > Unj , ∀j 6= i)

= Pr(Vni + εni > Vnj + εnj , ∀j 6= i).

Identi�cation of Choice Models

Unj = Vnj + εnj .

Pni = Pr(εnj − εni < −(Vnj − Vni), ∀j 6= i).

I Only di�erences in utility matter.I Take di�erence.

I The scale of utility is arbitrary.I Normalize one variance to 1.

Example - Logit

I A household's choice between a gas and an electricheating system.

I The utility the household obtains from each type ofsystem depends on

I the purchase price,I the annual operating cost, andI the household's view of the convenience and quality of

heating with each type of systemI U = β1 · PP + β2 · OC + ε.

Example - Logit (2)I A household's choice between a gas and an electric

heating system.

Ug = β1 · PPg + β2 · OCg + εg ;

Ue = β1 · PPe + β2 · OCe + εe .

I The di�erence of εgn = εg − εh follows a logisticdistribution with cumulative distribution

F (ε∗gn) =exp(ε∗gn)

1 + exp(ε∗gn).

Pr(Electric) = P(εgn = εg − εh < −(β1 · PPg + β2 · OCg ) + (β1 · PPe + β2 · OCe))

=exp(−(β1 · PPg + β2 · OCg ) + (β1 · PPe + β2 · OCe))

1+ exp(−(β1 · PPg + β2 · OCg ) + (β1 · PPe + β2 · OCe))

=exp((β1 · PPe + β2 · OCe)

exp((β1 · PPg + β2 · OCg ) + exp((β1 · PPe + β2 · OCe).

Random Coe�cients Model

Previous we assume

Ugi = β1 · PPgi + β2 · OCgi + εgi ;

Uei = β1 · PPei + β2 · OCei + εei .

Instead, we can assume Logit model but for agent i :

Ugi = β1i · PPgi + β2i · OCgi + εgi ;

Uei = β1i · PPei + β2i · OCei + εei .

And can assume βi is a function of individual i 'scharacteristics.

Motivation

I Products are bundles of characteristics, and consumershave preferences over these characteristics.

I Modeling products vs. modeling characteristics.

I Di�erent consumers have di�erent characteristics, so inthe aggregate all products are chosen.

I Aggregate demand depends on the entire distribution ofconsumers.

I Berry Levinsohn and Pakes (BLP 1995) is a method forestimating demand in di�erentiated product marketsusing aggregate data.

Why has BLP become popular?

I Demand estimation is critical element of marketinganalysis.

I BLP addresses three issuesI estimates di�erentiated product demand systems with

aggregate data;I uses discrete choice models with random coe�cients

(heterogeneity);I accounts for researcher unobservables that a�ect

consumer choice, and �rm's marketing mix choices,(endogeneity).

Canonical Aggregate Market Level Data

I Aggregate �Market� dataI Longitudinal: one market across time;I Cross-sections: multiple markets at one time;I Panel: multiple markets across time.

I Typical variables used in estimationI Aggregate quantity and market size;I Prices / product attributes;I Distribution of demographics (sometimes).

Basic Framework

I Consumer i's utility of consuming project j ∈ {1, 2, ...J}can be expressed as

uij = xjβi − αipj + ξj + εij .

I xj : are observable characteristics of project j .

I ξj :is unobservables characteristics of project j .

I pj : price of product j .

I αi , βi : consumer-speci�c taste parameters.

I εij : unobserved taste preference.

I We assume the existence of an outside good j = 0 whichgives utility 0.

Estimation

uij = xjβi − αipj + ξj + εij .

(βi , αi) ∼ Normal .

I Market shares and share inversion.I Suppose we know parameters and (xj , pj), we can use the

model to predict market share sj ;I Conversely, if we observe (xj , pj , sj) this reveals

information of underlying utlity functions and hence theinformation about parameters.

I BLP use GMM.

I There are more technical issues involved, for example, theendogeneity of prices, which we skip for now.

Outline

Discrete Choice Models

BLP

ApplicationsNevo (2001) - RTE cereal marketPetrin (2002) - MinivanBerry and Jia (2010) - Airline

Nevo (2001) Background

I Nevo, A., 2001. Measuring market power in theready-to-eat cereal industry. Econometrica, 69(2),pp.307-342.

I Ready-to-Eat Cereal Industry in U.S.I Highly concentrated;I High price-cost margins;I Large advertising-to-sales ratios;I Aggressive introduction of new products.

Three Sources of Price-Cost Margins (PCM)

I This paper empirically separate price-cost margins intothree sources:

I A �rm is ability to di�erentiate its brands from those ofits competition.

I If two brands are perceived as imperfect substitutes, a�rm producing both would charge a higher price thantwo separate manufacturers.

I Main players in the industry could engage in pricecollusion.]

I Even with PCM higher than 45%, the author concludesthat pricing in the RTE cereal industry is approximatelynon-collusive.

Model - Firm (1)

I F �rms, each of which produces some subset, Ff of thej1, ..., J di�erent brands of RTE cereal.

I Pro�ts of �rm f are

Πf =∑j∈Ff

(pj −mcj)Msj(p)− Cf

I M is the size of the market;I sj(p) is the market share of brand j , which is a function

of the prices of all brands;I Cf is the �xed cost of production.

Model - Firm (2)

I Pro�ts of �rm f are

Πf =∑j∈Ff

(pj −mcj)Msj(p)− Cf .

I Bertrand-Nash equilibrium in prices:

sj(p) +∑r∈Ff

(pr −mcr )∂sr (p)

∂pj= 0.

I In matrix �rm: s(p)− O · (p −mc) = 0, or equivalently

p −mc = O−1 · s(p)

Demand

I T markets, It consumers.

I Indirect utility of consumer i from product j at market t is

uijt = xjβi − αipjt + ξj + ∆ξjt + εijt .

I X : advertising, calories, sugar, mushy, �ber, all-family,kids, adults.

I (α, β) ∼ N[(a, b),Σ) where (a, b) are functions ofdemographic variables.

I Like BLP, we could drive market share from indirect utility

sjt(x , p·t , δ·t ; θ).

I Therefore we know p −mc .

Comparing PCM

sj(p) +∑r∈Ff

(pr −mcr )∂sr (p)

∂pj= 0.

p −mc = FUNCCON(s(p)).

I From the estimated demand functions, we can calculatethe right hand side s(p) for each of the three conducts

I Single product �rms;I Current ownership of all bands;I Price Collusion.

I Observed PCM based on accounting estimates. About31% ∼ 46%.

I Observed PCM falls into the con�dence interval of PCMpredicted by �rst two models.

I It falls out of the con�dence interval of PCM predicted bycollusion model.

Outline

Discrete Choice Models

BLP

ApplicationsNevo (2001) - RTE cereal marketPetrin (2002) - MinivanBerry and Jia (2010) - Airline

Petrin (2002) - Introduction

I Petrin, A., 2002. Quantifying the Bene�ts of NewProducts: The Case of the Minivan. Journal of PoliticalEconomy, 110(4).

I The minivan innovation.I In the early 1970s Ford proposed the �Mini/Max,� an

alternative to the family station wagons and full-size vansof the day.

I Introduced in 1984 by Chrysler Corporation, the DodgeCaravan (its minivan) was an immediate success.

I General Motors (GM) and Ford quickly responded,introducing their own versions of minivans in 1985 (GMAstro/Safari) and 1986 (Ford Aerostar).

Model and Data

uij(θ) = δj(θ) + µij(θ) + εij .

I Aggregate quantity and market size;

I Prices / product attributesI Type: small wagons, minivans, sport-utilities, full-size

vans.

I Feature: horsepower, weight, size, frond wheel drive, airconditional standard, economic indicator.

I Distribution of demographics (sometimes).I Income, family size, mid-age.

Counterfactural

I Each �rm has a pro�t function

Πf = M∑j∈Ff

(pj −mcj)sj(p)− Cf .

p −mc = FUNC (s(p)).

I From the data, we can recover mc .

I We can solve for new equilibrium price vectors underdi�erent counterfactual (removing Minivan from choiceset).

I We can then calculate pro�ts, markup, etc undercounterfactual.

Outline

Discrete Choice Models

BLP

ApplicationsNevo (2001) - RTE cereal marketPetrin (2002) - MinivanBerry and Jia (2010) - Airline

Berry and Jia (2010) - Introduction

I Berry, S. and Jia, P., 2010. Tracing the woes: Anempirical analysis of the airline industry. AmericanEconomic Journal: Microeconomics.

I The airline industry went through tremendous turmoil inthe early 2000s with four major bankruptcies and twomergers.

I By 2004 the industry's output had recovered from thesharp post-9/11 downturn and has been trending upwardsince

I If more passengers traveled and planes were fuller, whatcaused the �nancial stress on most airlines?

Background

I Perhaps the bursting of the dot-com bubble andimprovements in electronic communications havedecreased the willingness-to-pay of business travelers.

I Another potential change in demand stems from thetightened security regulations after 9/11.

I The various search engines have dramatically reducedconsumers' search costs, and allowed them to easily �ndthe most desirable �ights.

I The expansion of the low cost carriers (LCC).

I The advent of regional jets with di�erent plane sizes,allows carriers to better match aircraft with market size,and hence enables carriers to o�er direct �ights tomarkets that formerly relied on connecting services.

I The cost of jet fuel.

The Model

uijt = xjtβr − αrpjt + ξjt + νit(λ) + λεijt .

I Consumer of type r : business or tourists.

I Demand is a�ected by fares; the number of connections,destinations, and average daily departures; distance anddistance squared; a tour dummy; the number of slotcontrolled airports; and carrier dummies.

I Cost if a�ected by: distance, connection, hub and slots.

Counterfactual Analysis

To examine how legacy carriers' pro�ts were a�ected bychanges in demand, changes in marginal cost, and LCC'sexpansion, the authors calculate counterfactual pro�ts andrevenue for

I 2006 attributes and marginal cost but 1999 demandparameters;

I 2006 product attributes and demand , but 1999 marginalcost parameters;

I 2006 product attributes, demand and marginal costparameters, but excluding LCCs from the markets;

I 2006 product attributes, but 1999 demand and marginalcost parameters, and excluding LCCs.

Main Conclusions

80% of the decrease in legacy carriers' variable pro�ts can beexplained by

I A more elastic demand,

I A higher aversion toward connecting �ights,

I Increasing cost disadvantages of connecting �ights,

I Expansion of low-cost carriers.

Summary of Demand Estimation

I The study of demand is perhaps the most commonexample of structural modeling in Industrial Organization.

I We model demand as a discrete choice problem.I We model Bertrand-Nash competition.

I What questions can demand estimation answer?I Demand, pricing, merger simulation, welfare,

counterfactual, etc.

I What we didn't discuss.I How to link parameters to observed market shares

I Simulation and contract mapping.

I How to deal with endogeneity in prices.I Instrumental variables.