This condition is the same as in the two-good multi-product pricing case: the product of
the “own-good” demand slopes cannot equal the product of the cross-good pricing
effects (p
t
on a
t
and r
t
on q
t
). If this knife-edged condition does not hold, then the
first-order conditions can be solved for the unobservables as a function of data and
parameters.
These unobservables are then interacted with instruments to form moment condi-
tions in the same manner as in the BLP supply side. If the instrument vector is I
t
, then
these moment conditions are
E ωθðÞjI
t
ðÞ¼0,
where ω(θ) is the vector of cost errors.
3.5. THE SUPPLY SIDE: POSITIONING AND ENTRY
The prior section discussed supply-side models of continuous choice. However, many
supply decisions are discrete, most importantly the decision to enter a market or market
segment at all. Many media economics questions, like the degree of product variety or the
degree of competition, are often best answered via models of entry into markets and
sub-markets.
The previously discussed models of user (listener, viewer, reader) demand for pro-
gramming, in conjunction with advertiser demand for ads, generate important ingredi-
ents that are very useful for entry modeling. Entry modeling, in turn, has two natural
applications. First, data and a demand model give predictions for revenue associated with
different entry configurations; from these it is possible to infer operating costs (or at least
bounds on them). Second, and perhaps more important, given estimates of costs as well as
an equilibrium notion, it is also possible to calculate policy counterfactuals. For example,
what is the welfare consequence of a merger or the entry consequence of a tax on oper-
ating costs?
Media markets vary substantially in the size of fixed costs in relation to market size;
and this relationship in turn determines what task an entry model needs to accomplish.
Newspaper markets, for example, tend to have roughly one product per market, so an
entry model needs to determine both whether a firm will operate and its positioning in
product space. In markets such as television and radio broadcasting, markets support mul-
tiple products (
Berry and Waldfogel, 1999). Entry models need therefore to determine
the number of products operating and, in some applications, a more complicated equi-
librium determination of the number of products of each type.
When fixed costs are low enough to allow multiple products, then the important
supply-side decisions include both whether to enter and, if so, with what characteristics.
It is instructive to begin with the case in which entrants are symmetric (so that the only
decision is whether to enter). We then turn to the case with differentiation.
114 Handbook of Media Economics
Following on from Bresnahan and Reiss (1988, 1991), much of the empirical entry
literature proceeds without demand models, instead relying only on data on the number
of firms/products operating in a market. Suppose that firms offering either identical or
symmetrically differentiated products may enter a market. Drawing on the broadcast
media context, assume that costs are purely fixed, where fixed costs in market t are
denoted F
t
. In the simplest models, we assume that fixed costs are the same for every firm
in a given market or market segment.
The most basic idea for estimation is just revealed preference. In a complete informa-
tion pure-strategy Nash equilibrium, if we see a firm operating in a given context it must
be profitable given the environment and the actions of other firms. If a potential product
is not offered, then we infer that adding that product to the market would not be
profitable.
In particular, if we see one firm operating in a market, we can infer that the profit
accruing to the single firm is non-negative but that the per-firm profits accruing to
two firms would be negative. Similarly, when we see N
t
firms operating, we can infer
that per-firm profits for the N
t
firms are positive but would not be if N
t
+ 1 firms entered.
To be more formal, following Bresnahan and Reiss, assume that there are a large
number of ex ante identical entrants and that per-firm post-entry revenue is r(N
t
, x
t
, θ),
with x
t
a vector of revenue shifters and θ a vector of parameters to be estimated. Profits
are π N
t
, x
t
, F
t
, θðÞ¼rN
t
, x
t
, θðÞF
t
. The condition for N
t
firms to enter into a complete
information pure-strategy Nash equilibrium is then
rN
t
, x
t
, θðÞF
t
> 0 > rN
t
+1,x
t
,θðÞF
t
or
rN
t
, x
t
, θðÞ> F
t
> rN
t
+1,x
t
,θðÞ:
(3.29)
If we make a parametric functional form assumption on F
t
and assume it is independent of
x
t
, then Bresnahan and Reiss note that this takes the form of a classic “ordered probit” or,
more generally, an ordered choice model. The probability of the N
t
firm equilibrium is
just the probability that F
t
falls within the bounds rN
t
+1,x
t
,θðÞ,rN
t
, x
t
, θðÞ½. This prob-
ability then forms the basis for a straightforward method of moments estimator.
Berry and Tamer (2007) note that the competitive effect of N
t
on per-firm revenue
(or variable profit more generally) is highly dependent on the assumed functional forms
for per-firm revenue and the distribution of F
t
. Sometimes the necessary functional form
restrictions are credible, and sometimes not. We might obtain more credible estimates of
the fixed-cost distribution if we use information on prices and quantities to estimate the
per-firm revenue function. In the context of media markets, this is done in
Berry and
Waldfogel (1999)
. They estimate the parameters of r(N
t
, x
t
, θ) using models of listener
and advertising demand, as discussed above. Their economic question is the magnitude
of excessive entry, which depends on the incremental cost of an additional product, F
t
.
They follow Bresnahan and Reiss in estimating the parameters of this distribution
via MLE.
115Empirical Modeling for Economics of the Media
To illustrate, given a simple logit model and a symmetry assumption the share of
population consuming the “inside share” is Ne
δ
=1+Ne
δ
.IfM is market size and
p is the revenue per consumer, per-firm revenue when N products operate is
rN
ðÞ
¼ e
δ
=1+Ne
δ
pM and per-firm revenue with one more than the observed number
of firms is rN+1ðÞ¼e
δ
=1+ N +1ðÞe
δ
pM. Given the structure of the bounds in
(3.29),
the ability to calculate counterfactual revenue at N+1 firms is particularly important.
Given estimated fixed costs for each market, we can solve the model for the free entry
equilibrium. By construction, this yields the observed entry pattern. What is more useful,
however, is that we can also use the estimates, along with the structure of the model, to
solve for meaningful counterfactuals such as the welfare maximizing equilibrium or the
equilibrium outcome that would result if a profit maximizing monopolist operated all of
the firms in the market.
3.5.1 Entry Models with Differentiation
We next consider a model of entry into a differentiated product space. Imagine that there
is a discrete set of product-type “bins” and that firms can freely enter into any of these
product bins. In radio, these product types might be observed programming formats. Dif-
ferentiation complicates entry modeling because equilibrium now involves not just a sca-
lar number of products, but a vector consisting of the number of products of each type.
Now, there is not necessarily a unique Nash equilibrium to an entry game (see
Mazzeo,
2002; Tamer, 2003
). The straightforward Bresnahan and Reiss MLE approach relies on a
unique map from the unobservable fixed costs to the observed entry outcome, but this
map is not unique in the presence of multiple equilibria. We discuss here some modeling
approaches for entry and equilibrium in the presence of differentiation, beginning with a
model with two types of consumers and two types of products.
When entering products are differentiated into discrete types that are imperfect sub-
stitutes for one another—as in the case of radio broadcasting—then while finding an
equilibrium production configuration is more complicated than in the symmetric case,
inference about fixed costs is relatively straightforward. This is the case explored in
Berry
et al. (2015)
. We observe some configuration of horizontally differentiated products,
which we can summarize as a vector whose elements are the number of products of each
type. Again, we assume that there are a very large number of ex ante identical potential
entrants, who consider entry into any one of the possible horizontal entry positions (for-
mats). Fixed costs are the same for every possible entrant in a given format. The observed
configuration is by assumption profitable for each operating station, while additional
entry in a particular format would render operators in that format unprofitable. Hence,
observed revenue per station provides an upper bound on fixed costs for stations of that
type, while demand-model-derived counterfactual estimates of revenue per station (with
one more entrant in the format) serve as lower bounds on format fixed costs.
116 Handbook of Media Economics
For example, with two entry positions, the fixed costs in format 1 must satisfy a con-
dition similar to
(3.29),
rN
1t
, N
2t
, x
1t
, θðÞ> F
1t
> rN
1t
+1,N
2t
,x
1t
,θðÞ, (3.30)
where (N
1t
,x
1t
,F
1t
) are respectively the number, revenue shifters, and fixed costs in
format 1, and N
2t
is the number entering in format 2.
8
Once again, it is key that the
counter-factual revenue at N
1t
+ 1 can be estimated from the data on format listening
and advertising demand. A simple insight in
Berry et al. (2015) (BEW) is that these
bounds can be used directly in counterfactual analysis, with no need for further estimation
of the distribution of fixed costs. By using merely the necessary condition expressed by
(3.30), Berry et al. (2015) avoid the entire issue of estimation under multiple equilibria. In
many cases, the bounds are quite tight and allow BEW to make relatively clear statements
about the degree of excess entry.
Berry et al. (2014) pursue a different approach to entry with differentiation. One
prominent feature of media markets is the sharp difference in preferences in groups
between, say, blacks and whites (or Hispanics and non-Hispanics). This provides some
motivation for classifying products into two types, targeting one of two groups of
consumers.
If one has estimated a demand model with two types of consumers—say blacks
(B) and whites (W)—and two types of products, then it will give rise to two per-station
revenue functions: r
W
(N
W
,N
B
) and r
B
(N
W
,N
B
). That is, per-product revenue for each
product type depends on the number of own-type products and the number of
other-type products. In the extreme example that members of one group do not consume
the other type of product, the functions simplify to r
i
(N
i
), i ¼B,W.
Free entry means that products enter as long as the per-product revenue (assumed
symmetric within type) exceeds fixed costs. Hence
r
W
N
W
, N
B
ðÞ> F
W
> r
W
N
W
+1,N
B
ðÞ, and
r
B
N
W
, N
B
ðÞ> F
B
> r
B
N
W
,N
B
+1ðÞ:
In addition, the fact that we observe (N
W
,N
B
) as an equilibrium implies that no firm cur-
rently in one format would prefer to switch to the other format. These conditions pro-
vide bounds on fixed costs, as in
(3.30).
Berry et al. (2014) develop a model along these lines for radio, which they use to infer
the welfare weight that the fictitious planner underlying free entry attaches to black and
8
The condition is easily extended to more than two formats. Recall that in cases with variable costs, the per-
firm revenue function would be replaced by a per-firm variable profit function. We might learn about
variable costs from a subscriber price first-order condition, as in the prior section, or there might be addi-
tional variable cost parameters to estimate from the entry first-order conditions. This later case requires
more complex econometric “bounds” techniques.
117
Empirical Modeling for Economics of the Media
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