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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.