We model individual listening behavior by means of a random-coefficients multino-mial choice model as proposed by Berry et al. (1995) and Nevo (2000) (see also Wilbur (2008)). The main advantage of this model in comparison with the conventional multi-nomial logit model is that it allows for listener heterogeneity and flexible substitution patterns that depend on consumer characteristics.
In our model presented below we distinguish 10 different demographic groups (D=10), defined by five different age classes and gender.1 Each listener i with demo-graphics d (d=1, . . . , D) is assumed to listen to one of the Jtradio stations or engages in some non-radio activity, j=0, at a particular time t. The indirect utility function of listener i associated with listening to station j at time t is given by:
uijdt=αidtAjt+β0idtXjt+ξjdt+εijt, j=1, . . . , Jt, d=1, . . . , D, t=1, . . . , T (4.1)
where Ajt denotes the number of advertisements on radio station j at time t and Xjt is a K-dimensional vector of observable characteristics of radio station j at time t. In our empirical model the vector Xjt consists of the following 12 elements (K = 12):
a constant term, three quarterly dummies (to capture seasonal effects), three format dummies2, a dummy for national radio stations, a dummy for public radio stations, a dummy for radio stations that do not broadcast on the FM-band (no-FM stations), antenna power, and an interaction between not broadcasting on the FM-band and an-tenna power. ξjdtis unobserved station quality as perceived by demographic group d at time t, and εijtis an unobserved preference shock which follows a Type I Extreme Value distribution. In order to allow for station-fixed effects, we decompose ξjdtinto ξjdt =ξj+ξ˜jdtso that we can rewrite equation (4.1) as:
uijdt=αidtAjt+β0idtXjt+ξj+ξ˜jdt+εijt, j=1, . . . , J, d=1, . . . , D, t=1, . . . , T (4.2)
where αidtis a random parameter measuring the marginal utility from advertisements.
The K-dimensional vector βidtconsists of individual-specific random taste coefficients.
1The following five age groups are considered 10-19, 20-34, 35-49, 50-64, and 65 years of age or older (the reference group). The choice of this age classification is dictated by data availability.
2There are four formats which are pop, news, hits, and classical music (the reference group).
These random coefficients αidtand βidtvary with individual characteristics in the
where Zdtis a Z-dimensional vector of listeners’ demographics. In the empirical part of the paper we consider the following five individual characteristics (Z = 6): a gen-der dummy, malei, four age group dummies, and an interaction between the gender dummy and a binary variable which indicates that the listener is at least 35 years old.3 The((K+1) ×Z)-matrixΠ of coefficients measures the impact of demographic vari-ables on αidt and βidt. The vectorΣνit captures unobserved preference heterogeneity.
We assume that all elements of νitare standard normally distributed and mutually in-dependent. So,Σνit ∼N ID(0,Σ2)whereΣ is a diagonal matrix. Moreover, we assume that νitis independent of εijt.
The utility of engaging in non-radio activities (“the outside good” j= 0) is equal to:
ui0t=ξ0t+Π0Zdt+σ0νi0t+εi0t. (4.4) Since the parameters ξ0t,Π0tand σ0cannot be identified separately from the parame-ters of equations (4.1) and (4.3), we normalize the utility from the outside good to zero, i.e. we assume that ξ0t=0,Π0=0, σ0=0, and εi0t =0.
The model above implies that for individual i belonging to demographic group d utility associated with listening to station j at time t can be written as:
uijdt =δjdt(Xjt, Ajt, Zdt, ˜ξjdt; θ1) +µijt(Xjt, Ajt, νit; θ2) +εijt (4.5a)
where
θ1= (α, β0, ξ0j, vec(Π)0); θ2=vec(Σ) (4.5b) δjdt(Xjt, Ajt, Zdt, ξjt; θ1) =αAjt+β0Xjt+ [Ajt, X0jt]ΠZdt+ξj+ξ˜jdt (4.5c) µijt(Xjt, Ajt, νit; θ2) = [Ajt, X0jt]νit. (4.5d)
3Notice that the vector of demographic variables takes on the same value within each demographic group d (d=1, . . . , D). We therefore index this vector by d and not by i (i.e. Zdtinstead of Zit).
Individuals are assumed to listen to the radio station that maximizes their utility.
In the model above an individual is defined as a vector of station-specific shocks (νit, εi1t, . . . , εiJt)which implicitly defines the set of individual attributes that leads to choosing to listen to radio station j at time t:
Ajdt(X·t, A·t, δ·dt; θ2) =(νit, εi1t, . . . , εiJt)|uijt≥uikt, ∀k= {0, 1, . . . , Jt
(4.6)
where X·t = (X1t, . . . , XJtt), A·t = (A1t, . . . , AJtt)and δ·dt = (δ1dt, . . . , δJtdt).
We do not have a survey available which measures listening behavior at the indi-vidual level. Instead we observe in period t for each demographic group d conditional market shares Sj|dt(
Jt j=0∑
Sj|dt=1). The model above can be used to predict these market shares by integrating over the setAjdtof individual i belonging to demographic group d who choose radio station j at time t. These predicted market shares sj|dtare given by:
sj|dt(X·t, A·t, δ·dt; θ2) = Z
Ajdt
dPε∗(ε)dPν∗(ν) (4.7)
where P∗(·)denotes a joint population distribution function. In the equation above we exploit the assumption that the error terms νit and εit = (εi1t, . . . , εiJt)0 are mutually independent. By assuming that εijtis i.i.d. Type I Extreme Value distributed, equation (4.7) can be rewritten as:
Notice that if νit = 0 (no random preferences), the market share can be predicted by the well-known multinomial logit model. The integral presented in equation (4.8) does not have an analytic closed form so simulation is used to compute the market shares.
One possible way to estimate the parameters of the model is to minimize the distance between the actual market shares and the predicted market shares. This method how-ever will yield inconsistent estimates because Ajt is an endogenous right-hand side variable due to the two-sided nature of the radio industry. The Generalized Method of Moments (GMM) method proposed by Berry et al. (1995), which will be
summa-rized in Section 4.4, accounts for this endogeneity. At this place we like to stress that it is crucial to have demographic-specific market share data. We will show in Section 4.3 that there is considerable age and gender variation in listeners’ demand. We ini-tially tried to estimate the parameters without using demographic-specific data. We obtained very imprecise GMM estimates of especially theΠ-matrix which is defined in equation (4.3) (see also Wilbur (2008) for a similar result).
Once we have estimated the parameters of the model, the nationwide market share of station j, sj|t, can be predicted as follows:
sj|t=
∑
D d=1sj|dtPd|t
where Pd|tdenotes the population share of demographic group d in period t.