Identifying own- and cross-price e ects using contingent valuation of college sport tickets

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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.

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 2 / 25

  • 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.

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 3 / 25

  • 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.

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 4 / 25

  • 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).

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 5 / 25

  • 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.

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 6 / 25

  • 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)

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 7 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 8 / 25

  • Data

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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 9 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 10 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 11 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 12 / 25

  • Results

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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 13 / 25

  • Results

    RUM estimation results

    Estimation of the unobserved correlation coefficients betweenequations:

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 14 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 15 / 25

  • Results Willingness to pay

    WTP, results

    Estimation of reservation prices (WTP): pji

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 16 / 25

  • 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

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 17 / 25

  • 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)

    Rosas (ORT & cinve) Own & Cross price effects August 19th 2016 18 / 25

  • 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

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

  • Results Own and Cross-price effects

    Cross-price elasticitiesExample of two sports: j , k