ln r
jt
¼z
jt
β + γ ln a
jt
+ α ln q
jt
+ ν
jt
,
where r
jt
is advertising price, a
jt
is quantity of advertising, and ν
jt
is an unobservable.
Rysman’s instrument for usage, q
jt
, of directory j is the number of households who have
recently moved to market t. The instrument for advertising quantity includes cost shifters,
such as the local wage. The demographic shifters z
jt
include population coverage of the
directory. (Note that this variable is naturally excluded from Ryman’s nested logit model
of usage share.)
Fan (2013) follows Rysman in modeling advertiser demand (in column inches) as a
function of ad rate (in dollars), r
jt
, audience size (circulation), q
jt
, market number of
households, H
jt
, and an unobservable ν
jt
,
ln a
jt
¼λ
0
+ λ
1
ln H
jt
+ λ
2
ln q
jt
+ λ
3
ln r
jt
+ ν
jt
: (3.14)
Again, this equation has two endogenous variables and so requires at least two instru-
ments. The same Waldfogel-style instruments that Fan uses in the estimation of reader-
ship (circulation) can be used to estimate
(3.14). One interesting question is whether
those instruments are rich enough to independently shift both quantity and ad price.
Supply-side restrictions, discussed in the next section, may provide further restrictions
that aid in the estimation of advertising demand parameters.
In these examples, we see that the estimation of advertiser demand depends in part on
the richness of the available data. More complicated models tend to introduce further
endogenous variables, increasing the demand on instruments. Luckily, the same exoge-
nous instruments that shift choice sets in demand estimation can often serve as instru-
ments in the advertiser demand equation as well. To the degree that instruments are
not rich enough to estimate components of advertiser demand, supply-side restrictions
may help improve our estimates. We turn next to that supply side.
3.4. THE SUPPLY SIDE: CHOICE OF PRICES, AD QUANTITY,
AND OTHER CONTINUOUS CHARAC TERISTICS
Because of high fixed costs, relatively few media firms operate in an environment of per-
fect competition. In a traditional oligopoly framework, differentiated products firms are
often modeled as choosing prices conditional on product characteristics. In two-sided
media markets, firms may be setting prices to an audience and/or to advertisers. In some
cases (as noted in the previous section), we may treat the size of the audience as the
“quantity” being sold to advertisers, but in other cases we treat the quantity of advertising
(in, say, minutes or column-inches) as a decision separate from the size of the audience. In
these cases, increases in the quantity of advertising may drive down (or, possibly, up) the
size of the audience, setting up a classic marginal cost—marginal benefit analysis of ad
107Empirical Modeling for Economics of the Media
price or ad quantity. Going further, as in other industries, we often want to model endog-
enous choices related to non-price product quality and horizontal positioning.
In many cases, we can treat the variables (price, ad quantity, product quality) in the last
paragraph as continuous choices governed by a first-order condition. As is now tradi-
tional in empirical IO (going all the way back to the two-sided newspaper study of
Rosse (1970)), these first-order conditions can also be the basis of an instrumental vari-
ables or method of moments estimating equation.
As a concrete example,
Rosse (1970) considers monopoly newspaper markets. In
cross-sectional market t, there are two output measures, number of subscribers, q
t
, and
ad quantity, a
t
(say measured in column-inches per issue). These have associated prices
p
t
(subscription price) and r
t
(ad price). In Rosse, there is one endogenous quality mea-
sure, “news space,” y
t
. Fan (2013) adds additional possible quality measures, but for our
example we will stick to one. There are cost shifters, w
t
, like plant scale (which is treated as
exogenous). Demand shifters are in the form of a vector of demographics, z
t
, with some
elements of z
t
excluded from w
t
and vice versa. Rosse then specifies five equations, which
are the first-order conditions for the three endogenous variables, plus subscriber and
advertiser demand. We have already discussed the estimation of subscriber (audience)
demand and advertiser demand and this would be even easier in Rosse’s one-product
(monopoly) demand example. In particular, the same kind of demand-side instrumental
variable arguments holds.
Rosse’s innovation was to estimate the parameters of marginal cost(s) from first-order
conditions for optimal subscriber and advertising quantity. These first-order conditions
set marginal revenue equal to marginal cost, and so they rely on the demand side as well.
Updating Rosse slightly, we can begin with a simple single-product logit demand exam-
ple, as in
(3.6),
ln s
t
ðÞln 1 s
t
ðÞ¼z
t
β αp
t
+ γ
a
a
t
+ γ
y
y
t
+ ξ
t
: (3.15)
This is a simplified version of the
Fan (2013) demand system; she adds multiple differ-
entiated products, multiple quality levels, and possible random coefficients. As noted
in the demand section, Equation
(3.15) might be estimated by itself via IV methods,
but available instruments might be insufficient to identify coefficients on three endoge-
nous variables. The supply-side choices of prices and quality can aid in identification.
To fix ideas, we begin with a market that has only subscription revenue and no ad
revenue; this is a classic one-sided market. Following the more recent literature
(
Berry, 1994), we model marginal cost as mc q
t
, w
t
, θðÞ+ ω
t
, where ω
t
is an unobserved
cost shock and θ is a parameter to be estimated. The first-order condition for price is, as
usual, marginal revenue equals marginal cost.
q
t
+ p
t
@q
t
@p
t
¼mc q
t
, w
t
, θðÞ+ ω
t
: (3.16)
108 Handbook of Media Economics
This equation can be rewritten in a traditional form as price minus a markup equals
marginal cost:
p
t
q
t
@q
t
=@p
t
jj
¼mc q
t
, w
t
, θðÞ+ ω
t
: (3.17)
Because we assumed that marginal costs are linear in an unobservable, this equation is
linear in its “error term” and therefore can be easily estimated using traditional IV tech-
niques.
Rosse (1970), and many others, assume that the marginal cost is a linear function
of the endogenous variables and cost shifters. In the model without advertising, if mar-
ginal cost depends linearly on cost shifters, w
t
, and on output, Equation (3.17) becomes
p
t
q
t
@q
t
=@p
t
jj
¼θ
c
1
w
t
+ θ
c
2
q
t
+ ω
c
t
, (3.18)
where the θs are marginal cost parameters to be estimated.
Note that the markup in
(3.18) depends only on data and demand parameters; this
is a general feature of static monopoly and oligopoly pricing models.
Rosse (1970)
models linear monopoly demand, whereas in the case of logit demand (3.15) the
markup term is
q
t
@q
t
=@p
t
jj
¼
1
α
1
1 s
t
ðÞ
:
Price minus this markup, substituted into the left-hand side of
(3.18), can then be used as
the dependent variable in a linear IV regression to uncover the parameters of marginal
cost. Excluded demand shifters, together with Waldfogel- and BLP-style instruments,
can then identify the parameters on the endogenous variables.
Since demand parameters enter the markup term, there can be substantial efficiency
gains from estimating the demand and supply equations simultaneously, particularly if
there are sufficient instruments and/or exclusion restrictions so that the cost parameters
are over-identified when the markup function is known. In an extreme case, we could
estimate the slope of demand exclusively from the first-order condition, using the logit
form of the markup, as in
p
t
¼
1
α
1
1 s
t
ðÞ
+ mc q
t
, w
t
, θðÞ+ ω
t
: (3.19)
This approach relies on the logit functional form and would require some instrument
that causes variation in 1/(1 s
t
) separately from q
t
.
Even when using a demand model that is richer than the logit, pricing decisions may
provide as much or more information about demand substitution patterns as does direct
estimation of demand. For example, a firm whose product competes with a close sub-
stitute will choose a low markup (low price relative to marginal costs) as compared to
a product that does not face close substitutes.
109Empirical Modeling for Economics of the Media
Equation (3.18) illustrates a general principle of estimation via a first-order condition
for a continuous variable. One theme in this literature is to choose a functional form
that allows us to write (or rewrite) the first-order condition as an equation with a linear
error. This in turn allows estimation by traditional IV or “method of moments”
techniques.
In the two-sided media case, the modeling of cost shocks within the system of
first-order conditions becomes considerably more complicated and raises some issues
that are still at the forefront of the literature. We consider an example, inspired by both
Rosse (1970) and Fan (2013), where newspaper profit is given by revenue from both
subscribers and advertisers. The profit function is subscriber plus advertising revenue
minus cost,
p
t
q
t
+ r
t
a
t
Cq
t
, a
t
, y
t
, x
t
, ω
t
ðÞ
, (3.20)
where the endogenous variables shifting cost, ( q
t
, a
t
, y
t
), are output quantity, ad quantity,
and newspaper quality.
We model the firm as choosing prices p
t
and r
t
, with subscriber and advertising
demand equilibrating according to the assumed demand functions
q
t
¼D
q
p
t
, a
t
, y
t
, x
t
, ξ
t
, θ
d
, and (3.21)
a
t
¼D
a
r
t
, q
t
, z
t
, ν
t
, θ
a
ðÞ: (3.22)
Again, these demand functions could be estimated prior to a consideration of supply, or
they could be estimated simultaneously with supply.
Note that in the two-sided market, when demand is affected by advertising and vice
versa, subscriber and advertising quantities are determined simultaneously by the joint
demand system (
3.21 and 3.22). This raises a question of how to compute the effect
of a change in ad price on ad quantity. The direct effect is obvious, but there is an indirect
effect via the subscriber response to ad quantity, which in turn affects ad demand and so
forth.
Rysman (2004, pp. 495–496) notes this problem: “Estimating the first-order con-
dition in the price-setting game introduces serious difficulties because usage [consumer
demand] depends directly on [advertising] quantity … taking the derivative of the
demand curve with respect to price (in order to compute marginal revenue) would
require solving a fixed-point equation … complicating an already involved optimization
routine.”
In the yellow pages example,
Rysman (2004) avoids this problem by estimating a
quantity-setting model, where the yellow pages firms commit to a given “size” of the
directory and then receive a market-clearing price. As noted, Rysman’s data has a sub-
scription price of zero and so, following on from Equation
(3.22), we can simply consider
the inverse advertising demand function:
r
t
¼ D
a
ðÞ
1
a
t
, q
t
, z
t
, ν
t
, θ
a
ðÞ: (3.23)
110 Handbook of Media Economics
The marginal revenue from a change in advertising quantity is now well defined as
MR
a
¼
@ D
a
ðÞ
1
@a
t
+
@ D
a
ðÞ
1
@q
t
@D
q
@a
t
:
This nicely breaks out the direct and indirect effects of advertising quantity on revenue.
Jeziorski (2014) takes a similar approach in another industry (radio) without a subscrip-
tion price.
5
In some cases, we might be happy with a quantity-setting model. Indeed, Berry and
Waldfogel (1999)
consider an even simpler “Cournot” model of advertising supply. In
their model, listeners are “sold” directly to advertisers, so q
t
and a
t
are by definition equal.
Better programming choices (or new entry into a discrete radio format) increase listen-
ership and thereby cause a movement down a market-level advertising demand curve,
creating a new equilibrium ad price.
In the Jeziorski model with radio-ad minutes, the Cournot ad-quantity model might
capture an intuition that stations commit to a fixed number of ad minutes as part of an
implicit deal with consumers that a complementary share of the hour be devoted to pro-
gramming. However, in the yellow pages market, the Cournot assumption seems less
intuitive. The size of the yellow pages book can vary easily with the number of ads sold
and there seems very little reason to commit to a size. Rysman presents evidence, on the
other hand, that prices are posted and fixed to potential advertisers before the book is
printed. This is more suggestive of a price-setting model and in fact Rysman is clear that
he makes the Cournot assumption for practical reasons rather than as a necessarily
preferred model of the market.
As a solution to the problem of estimating the price-setting model in two-sided mar-
kets, we propose that the derivatives of subscription quantity and ad quantity with respect
to prices be computed via the implicit function theorem applied to
(3.21) and (3.22).
6
We
refer to these as the “total” derivatives dq
t
/dp
t
,dq
t
/dr
t
,da
t
/dp
t
, and da
t
/dr
t
. For example,
the term dq
t
/dp
t
accounts for the direct effect of the price change, @D
q
=@p
t
, as well as the
implicit indirect effect of that quantity change on a
t
and back to q
t
. Use of the implicit
function theorem is correct when the appropriate matrix of demand derivatives is invert-
ible. It has the great advantage of not requiring us to compute a solution to a system of
two-sided multi-product demand equations, thereby avoiding much of Rysman’s com-
putational objection.
Note that one can extend the implicit function technique to the oligopoly case. In an
oligopoly, the quantities of all the oligopoly competitors are equilibrating as one firm
changes its prices.
5
Fan (2013) avoids the issue by not placing advertising directly into the subscriber demand function,
although it is plausible that some consumers might value (or dislike) ads.
6
Fan (2013) has a related, but different, use of the implicit function theorem, which we discuss below.
111
Empirical Modeling for Economics of the Media
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