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Identifying own- and cross-price effects using

contingent valuation of college sport tickets

XXXI Jornadas de Economia del BCU, Montevideo

Francisco RosasUniversidad ORT Uruguay & cinve

Santiago AcerenzaUniversidad ORT Uruguay

Peter F. OrazemIowa State University

August 19th 2016

Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 1 / 25

Background

Broad Motivation

Willingness to pay for different goods is an important area ofstudy in economics and also an important input for theproductive sector.

Understanding willingness to pay if a consumer already boughtanother good is important to make optimal bundling policies.

Revealing unobserved complementarities between goods is alsoimportant to understand consumer behavior.

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Background

Specific Motivation

National Collegiate Athletic Association (NCAA) is very popularin the US, but only yields surpluses for a couple of the sports.

This implies a considerable burden to University administrators.

Spending on sports of Division I-A Universities amounted to$7785 million, and generated revenues for $8220 million.

Very heterogeneous reality by sport, or by mens and womenssports, or by University within Division.

An important factor for increasing revenues is attendance tocollege sport games.

For that, understanding the demand for sport tickets, willingnessto pay for sports, and the relationship between sports is animportant input to generate maximizing revenue policies.

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Background

Objectives

For that, we estimate an eight-variate probit model that allowsus to identify not only important own demand parameters butalso some unobserved correlations shared by all the sports.

This eight-variate framework will allow us estimate unconditionaland conditional willingness to pay for sports.

We aim also to generate information that if accounted for,promoters can generate cross-marketing strategies to increaseattendance and revenues.

Finally, we aim to produce a framework that can be generallyapplicable to other settings.

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Background

Related literature

Contingent valuation methods to elicit preferences

Willingness to pay for basketball and baseball venues (Johnsonand Whitehead, 2000).For attracting a professional hockey team (Johnson, Groothuis,and Whitehead, 2001).For retaining professional football and basketball teams(Johnson, Mondello, and Whitehead, 2007).For supporting amateur sports and recreation programs(Johnson et al. 2007).

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Background

Related literature

Previous applications of multi-variate Probits

Ashford and Swoden(1970) applied the model to a biologicalsystem.Contoyannis and Jones (2004) use it for studying healthproduction function and the parameters of lifestyle equations.Chib and Greenberg (1998) applied it to commuting choice andbuying a car choice;.Young et al. (2009) uses it in the modeling of the types ofclaim in a portfolio of insurance policies.Amemiya (1978) developed a variant of the multivariate probitwhere one of the variables is partially observed.

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Data

Sample

Generated a rich data through an artificial environmentdeveloped in the undergraduate population at Iowa StateUniversity.

In 2007, random sample of 2000 students, invited by Email to aweb-based survey.

Response rate 23.5% (470 individuals)

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Data

Sample

Each individual was given the opportunity to purchase or refusea ticket to attend a college game.1) women basketball, 2) men basketball, 3) football, 4)volleyball, 5) wrestling, 6) gymnastics, 7) hockey, 8) womensoccer

Prices were randomly generated from a uniform distributionswith mean in the market price.

Asked demographic information and questions related toparticipation and interest in sports

We require sufficient variation in prices to identify individualsbehavior.Because each respondent received a randomly drawn price,there is no correlation with the control variables

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Data

Descriptive StatisticsSuccess of the price randomization; a plot of the probability of apositive purchase response by random price offered: Law of demand

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Data

Descriptive StatisticsDifferences in demand between people who purchased football ticketsand those who did not. Possible complementarities between the twosports; will be formally tested later

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Model

Random Utility Model (RUM)

Suppose latent utility B ji of ticket purchase for sportj = 1, 2, ..., J for individual i . It sets an J = 8 equations system

B ji = j0 +

j1P

ji + Zi

j ji

Where P ji is the exogenously offered price to i for sport j , Zi is avector of individual characteristics and ji the unobserved factor.

As each ticket purchase decision is viewed as independent(time), unobserved factors are correlated

1i2i...Ji

N0,

1 1j... . . . ...1j 1

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Model SUR estimation results

Random Utility Model (RUM)

The likelihood function of the model, arising from computing allthe combinations of purchase-not purchase, is:

ni=1

log(J [q1i (

10+

11P

1i +Zi

1), ..., qJi (J0 +

J1P

Ji +Zi

J),QQQ ])

where J is the J-variate Standard Normal Distribution fcn

qji = 2 Bji 1

Qjk = qj qk , for j 6= k , and Qjk = 1 for j = k is J J matrix of correlation coefficients between equations

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Results

RUM estimation resultsSimulated maximum likelihood estimation of seemingly unrelatedmodel. Dependent variable: Binary choice of purchasing ticket ofsport j : B ji

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Results

RUM estimation results

Estimation of the unobserved correlation coefficients betweenequations:

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Results Willingness to pay

WTP or Reservation prices

Parameter estimates of the SUR model are used to computeReservation prices

Defined as the price at which individual is indifferent betweenpurchasing or not sport j ticket

Pr [B ji = 1] = [j0 +

j1p

ji + Zi

1] = 0.50

for all j and for all i

where is the uni-variate Standard Normal Distribution fcn

We compute a reservation price for each individual, and for eachsport: pji

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Results Willingness to pay

WTP, results

Estimation of reservation prices (WTP): pji

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Results Conditional willingness to pay

Conditional reservation prices

Dropping subscript i , we compute a reservation price for sport jthat equalizes to 0.5 the expected value of purchasing a ticket ofsport j (B j = 1), CONDITIONAL on purchasing a ticket ofsport k (Bk = 1), and given the observed decision for (k)

0.5 =Pr [B j = 1,Bk = 1,Bk = bk ]

Pr [Bk = 1,Bk = bk ]

0.5 =J [(

j0 +

j1p

jk + Zj), (k0 +

k1P

k + Zk), . . . ,QQQ ]

J1[(k0 + k1P

k + Zk), . . . ,QQQ ]

pjk implicitly solves this non-linear equality, using Bisection method

Compute a CONDITIONAL reservation price for each individual, and foreach pair of sports: pjki

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Results Conditional willingness to pay

Conditional reservation prices, resultsPercentage increment of Conditional reservation prices relative to

Unconditional reservation price:pjki p

ji

pji

Conditional reservation prices are higher than their unconditionalcounterparts for each combination of sportsPeople who already have a ticket to one sport (j) have higherwillingness to pay for the other sport (k)Complementarity between all sports, this is in line with results ofunobserved correlations (jk)

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Results Own and Cross-price effects

Own-price elasticities

We compute both own- and cross-price elasticites (and marginaleffects), directly from the likelihood estimation

The probability of purchasing a ticket for sport j represents theestimated demand of individual i for sport j .

The own-price elasticities of individual i for sport j is:

jji =1

n

ni=1

Pr [B ji = 1]

P ji

P jiPr [B ji = 1]

This is straightforward to compute

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Results Own and Cross-price effects

Cross-price elasticitiesExample of two sports: j , k