μ
ijt
¼υ
ikt
σ
k
ðÞ+1σ
k
ðÞε
ijt
, (3.5)
with σ
k
2 0, 1ðÞ, a parameter that as σ
k
moves from zero to one places less weight on the
“logit” idiosyncratic taste component ε
ijt
and more weight on the systematic “taste for
nest k.” The distribution of the nest-taste term υ
ikt
changes with σ
k
.Atσ
k
¼0,
υ
ikt
¼0 and the model reduces to the pure logit. At σ
k
¼1, the model places no weight
on the product level ε
ijt
and the model predicts that within each nest only the good with
the highest mean utility will be purchased. An issue with the model is that the model is
not well defined outside when σ
k
falls outside of the range (0,1).
3.2.3 Identification of Demand Parameters
It is useful to start with an intuitive discussion of what kind of data variation will allow us to
learn about demand parameters. For a more formal treatment, see
Berry and Haile (2010,
2014)
. Mean utility levels are fairly easy: if two products have the same characteristics,
higher market shares translate into higher mean utility levels. Indeed, it is in general
possible to show in the discrete-choice context that given other demand parameters there
is a one-to-one map between the vector of market shares and the mean utility levels, δ
(see
Berry et al., 2013). For example, in the case of the pure logit with no random coef-
ficients model, the mean utility levels are just given by the classic log-odds ratio, ln(s
j
/s
0
),
where s
j
is the share of product j and s
0
is the share of the outside good. In the pure logit,
then, we can estimate the parameters of Equation
(3.2) via the linear relationship
ln s
j
ln s
0
ðÞ¼x
j
β + ξ
j
: (3.6)
If the observed and unobserved characteristics are uncorrelated, then this equation can
just be estimated via OLS. However, in many of the empirical examples below it is most
plausible to assume that some characteristics (such as price or observed quality) are cor-
related with ξ
j
. This suggests the use of instrumental variables methods. In the case of
price, natural instruments are exogenous cost shifters and, in the context of imperfect
competition, exogenous variables that shift markups. As we see in the examples below,
in media markets there is sometimes no price paid by the audience and the interesting
endogeneity issues involve other product characteristics, such as the nature of the media
content (radio format or newspaper political slant).
Moving to the random coefficients model of Equations
(3.3) and (3.4), identification
becomes more subtle. As noted, the random coefficients drive substitution patterns. Intu-
itively, we would learn about substitution patterns by exogenously changing the product
space—the number and characteristics of products offered to consumers—and then
observing the resulting change in demand. However, the model also contains
product-level unobservables. If we allowed these unobservables to change freely with
changes in the product space, we could always attribute all of the change in demand pat-
terns to the unobservables and none to fundamental substitution patterns. Thus,
98 Handbook of Media Economics
identifying substitution patterns requires some restriction on the way the unobservables
move as we make changes in the product space.
The necessary requirement is that the variables that change the product space are
exogenous in the sense that they are uncorrelated with the demand unobservables. This
is a familiar requirement for an instrument. Here, however, these instruments do not
“instrument for” a particular variable, but rather allow us to identify the parameters that
control substitution patterns. Intuitively, they have to change the product space in a man-
ner that reveals the relevant substitution patterns. The nature of these patterns varies with
the specification, which in turn is often driven by the data and questions at hand.
In the examples below, we illustrate the use of various types of instruments that are
useful both for handling endogeneity problems in mean utility and for identifying sub-
stitution patterns in a random coefficients style model. We discuss several broad candi-
dates for instruments briefly here and then elaborate and illustrate with various media
examples.
A first set of instruments involves cost shifters of own and rival firms. Own-cost
shifters are a natural instrument for own-price (and perhaps for other endogenous char-
acteristics) while rivals’ costs shift rivals’ prices and therefore help to trace out substitution
patterns in response to price. “Hausman instruments” are the prices of goods in other
markets, intended as proxies for common cost shocks (see
Hausman, 1996; Nevo,
2001
). If the prices are responding to common demand shocks as well, then the instru-
ments may not be valid.
A second set of instruments are direct measures of rival product characteristics, and the
number of different types of products. These instruments, sometimes called “BLP”
instruments following their treatment in
Nevo (2001), directly change the product space
and help to reveal substitution patterns. If the product characteristics are not exogenous,
but are (for example) chosen in response to demand shocks, then they will not be valid
instruments.
A third set of instruments are helpful when there is variation in the level of market
demographics and these demographics drive product choices. It is important that these
market demographic levels vary conditionally on whatever observed demographics, z
i
,
are in the utility specification
(3.4). This is especially useful when we can model the deci-
sions of individual consumers in markets whose overall demographic levels vary. It is also
useful in a “representative consumer” model where market shares are driven by the shares
of demographic groups but the product space is generated by the total population of
demographic groups. In the context of newspapers,
Gentzkow and Shapiro (2010) attri-
bute this idea to
George and Waldfogel (2003). Berry and Haile (2010) cite Waldfogel
(2003)
and refer to these instruments in general as “Waldfogel” instruments.
In addition to these three classes of instruments, identification can be aided by various
panel data/timing assumptions on the unobservable demand shocks. For example, we
might be willing to assume that demand follows an AR(1) process and that rival
99Empirical Modeling for Economics of the Media
characteristics are uncorrelated with the current-period innovation in the demand shock.
This amounts to a timing assumption that characteristics are chosen before the demand
innovation is observed.
3.2.4 Example of a Single-Parameter Nested Logit
To illustrate, it is useful to start with a very simple model using market-level data. Con-
sider the symmetric model of radio listening in
Berry and Waldfogel (1999). In their sim-
plest model, the only random coefficient is on a dummy variable equal to one for each
inside good (and zero for the outside good of no radio listening). Although the model is
too simple to capture many interesting features of radio listening, the nested logit func-
tional form nicely parameterizes the “taste for variety” in the aggregate data. In each
quarter-hour period, each listener in the metropolitan area has utility for radio station
j, given by the nested logit functional form
u
ijt
¼δ
t
+ υ
it
σðÞ+1σðÞε
ijt
,
which is a simple version of Equation
(3.5). In particular, Berry (1994) shows that this
model can be estimated via the equation
ln s
j
ln s
0
ðÞ¼x
j
β + σ ln
s
j
1 s
0
+ ξ
j
: (3.7)
Note that in this model the “within-group substitution parameter” σ is the coefficient on
the log of the “inside share” ln s
j
= 1 s
0
ðÞ
. In the case in which stations are assumed
symmetric, the within-group share reduces to (1/N), where N is the number of stations
in the market. If σ ¼1, then the log-odds ratio of shares is just proportional to 1/N as
there is no substitution from the outside good as N increases. In this case, the effect of
increasing N is pure “business stealing,” there is no growth in aggregate radio listening
as the number of choices grows. When σ is low, however, the aggregate audience grows
relatively rapidly as the number of choices increases.
If N were exogenous, we could estimate the substitution parameter via an OLS
regression. However, a moment’s reflection reveals that the number of stations in the
market is potentially related to unobserved determinants of the tendency to listen. For
example, in markets where consumers like radio, entry conditions for stations will be
favorable, giving rise to a relationship between entry and listening where the causality
runs from listening to entry, rather than the other way around. Hence, N is not an appro-
priate exogenous “instrument” to identify the substitution parameter.
The solution to this problem is a source of variation in the number of available stations
that does not enter the utility function of listeners. Again, instruments should (i) be
excluded from the individual-level utility function and yet (ii) shift the choice set.
Plausible characterization of the entry process provides guidance on instruments. As
Waldfogel has argued, media products make supply—entry and positioning—decisions
100 Handbook of Media Economics
based on characteristics of the entire market. Hence for local media products, variables
such as local population and aggregate local income are appealing instruments for the
number of local products. This approach assumes that even though individual-level
demographics may affect the consumption of media products, aggregate variables based
on these demographics have no direct effect on individuals’ consumption. This assumes
away various possible spillover and regional sorting (migration) effects.
In the case of radio,
Berry and Waldfogel (1999) estimate σ at the market level by
placing demographic shares in the utility function and then instrumenting (1/N) with
total market population. The estimates of σ are quite precise and indicate a moderately
high level of “business stealing.”
3.2.5 Further Examples of Audience Demand
Gentzkow and Shapiro (2010) consider demand for monopoly newspapers. The relevant
substitution here is all to the outside good of not subscribing to the newspaper. Gentzkow
and Shapiro focus on the question of “media slant,” that is, whether the language of the
news articles slants toward the political left or right. The paper develops very clever
language-based measures of slant for newspapers. The measure of reader slant is based
on political contributions at the level of the zip code, c, within metro newspaper markets.
In Gentzkow and Shapiro, a newspaper’s measured slant in market t is denoted y
t
.In
zip code c, ^r
ct
is an observed measure of readers’ political preference based on campaign
contributions. “True” reader slant is then modeled as r
ct
¼α + β^r
ct
, where the parameters
α and β translate the observed measure into the same location and scale as the measure of
newspaper slant. In the spirit of an “ideal point” Hotelling-style model, readers pay a util-
ity cost based on the distance between their preferred political location and the newspa-
per’s slant. As a function of true political preferences, utility is
u
ict
¼x
ct
β + γ r
ct
y
t
ðÞ
2
+ ξ
ct
+ ε
ijt
,
where ε
ijt
is the usual logit error, x
ct
is a vector of zip-code demographics (including a
market-specific dummy to control for overall newspaper quality), and ξ
ct
is the unob-
served zip-code level taste for the newspaper in market t. Expanding the square in the
ideal point model gives linear terms in y
t
r
ct
, r
ct
2
, and y
t
2
so that we can write the model as
u
ict
¼δ
ct
+ ε
ijt
,
where (after expanding the square and substituting in the observed preferences ^r
ct
)we
have the “mean utility” term
δ
ct
¼δ
t
+ x
ct
β + λ
0
y
t
^r
ct
+ λ
1
^r
ct
+ λ
2
^r
2
ct
+ ξ
ct
, (3.8)
where the λ parameters are functions of the “Hotelling distance” parameter γ, and the
parameters α and β relate the observed consumer slant measure to the true slant.
101Empirical Modeling for Economics of the Media
As in (3.6), Gentzkow and Shapiro can then invert the market logit share functions to
recover δ
ct
, which gives a linear estimating equation in the terms on the right-hand side of
Equation
(3.8). Gentzkow and Shapiro note that their measure of newspaper slant,
despite its advantages, likely contains some measure error. This suggests the use of an
instrumental variable to correct for measurement error. Such an instrumental variable
would also deal with the classic endogeneity concern that the unobservables can be cor-
related with the right-hand side product characteristics.
Gentzkow and Shapiro suggest a “Waldfogel” instrumental variable based on the
demographics of the overall market t; in particular they use the market share of Repub-
lican voters. The idea is that this variable shifts the newspaper’s choice of slant. The
implicit exclusion restriction is that, conditional on a given zip code’s preferences, the
overall market’s Republican share does not directly affect newspaper demand within
the zip code. This, for example, rules out spillovers across zip codes within markets.
The IV estimates in Gentzkow and Shapiro then reveal the “structural” effect of a
change in newspaper slant on zip-code-level readership, which in turn generates news-
paper profits. They then use a supply-side model to show that newspapers are roughly
choosing slant to maximize profits, as opposed to pursuing some other personal or polit-
ical agenda. We return to supply-side issues below.
Fan (2013) studies competition and mergers in the newspaper industry. As opposed to
the monopoly metro markets of Gentzkow and Shapiro, she considers overlapping
county-level markets for newspapers. She also emphasizes the endogeneity of both price
and (non-political) newspaper characteristics, which were implicitly included in the
market-newspaper term
δ
t
in Gentzkow and Shapiro. Depending on the county, c,
readers face different choice sets that include various suburban papers within larger met-
ropolitan regions. The utility function of reader i in county c for newspaper j is
u
ijc
¼x
j
β + y
jc
ψ + z
c
ϕ αp
j
+ ξ
jc
+ E
ijc
, (3.9)
where p
j
is the price of the newspaper and x
j
is a vector of endogenous characteristics
(news quality, local news ratio, and news content variety). The vector y
jc
contains
within-county newspaper characteristics assumed to be exogenous (e.g., whether the
headquarters city is in the county) and z
c
is a vector of county demographics. The term
ξ
jc
again captures unobserved tastes for the newspaper in a given county.
Once again, the vector of county-level market shares can be inverted to obtain the
mean utility terms
δ
jc
¼x
j
β + y
jc
ψ + z
c
ϕ αp
j
+ ξ
jc
:
There are now four endogenous variables, price, and the vector of endogenous charac-
teristics. It is likely that these are correlated with the unobserved taste ξ
jc.
For example, the
price is likely to be higher when the newspaper is unobservably more popular. This
makes the IV problem more difficult. Broadly speaking, Fan also makes use of modified
102 Handbook of Media Economics
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