The Price of Silence.
Media Competition, Capture,
and Electoral Accountability
Federico Trombetta∗
Department of Economics
The University of Warwick
First version: May 2015
This version: February 27, 2016
Abstract
Is competition in the mass media market a good deterrent against media capture, i.e. against attempts, from the political side, to influence the contents of
media reports? In this paper we show (both theoretically and empirically) that
this is not always the case. Building on the mainstream models of media capture,
we allow for voters’ heterogeneity in their interest for political news and we model
the media market as a two-sided one, proving that the effect of competition on the
possibility of capture can be non-monotonic. In particular, when competition increases above a certain threshold, then it may make cheaper, for a bad politician, to
capture enough media outlets and to stay in power. Intuitively, even if competition
increases the number of information providers that the bad politician has to silence
in order to win the elections, it also reduces their profits. And, when profits are
low, media outlets may be more willing to sacrifice their independence in exchange
for bribes. When this second effect prevails, the total equilibrium cost of capture
decreases in the number of outlets.
On top of this, we show that the “deterrence effect” of competition increases with
∗
F.Trombetta@warwick.ac.uk. ESRC support is gratefully acknowledged. Previous versions of this
paper circulated under the title “Media Competition, Capture, and Electoral Accountability”. I thank
my supervisor, Ben Lockwood, for his invaluable help and advice. I also thank Carlo Beretta, Martijn
Huysmans, Guido Merzoni, Kirill Pogorelskiy, Andrea Prat, Francesco Squintani, Giulio Trigilia, Michela
Boccola, Andy Ferrara, Robert Gay OP, Martina Miotto, Tilko Swalve and the participants to the 2016
Warwick Economics PhD Conference and the MRes Dissertation Colloquium (University of Warwick).
They all provided very useful comments and suggestions. Of course, all the mistakes are mine.
1
the fraction of voters interested in politics. Finally, we study the consequences of
these results in terms of welfare and political accountability, and we test empirically
our main findings in a cross-country comparison.
Keywords: Political Agency, Mass Media, Competition, Media Capture.
JEL: D72, D73, D78, L82.
1
Introduction
1.1
Motivation and contribution
Free media have been seen as powerful guarantors of political accountability, both
theoretically (e.g. Besley 2006) and empirically (e.g. Ferraz and Finan 2008). However,
they may be powerful enough to determine the electoral outcome and promoting a bad
candidate, even when voters are fully rational and “bayesian” (Prat 2014, Anderson and
McLaren 2012). As a consequence, the incumbent politician may be interested in controlling what media outlets report, in order to give to the voters a sufficiently positive
image of himself and to stay in power. This paper looks at the effect of competition in
influencing the incentives towards media capture, proving innovative results. The current
view of the literature1 is stressing the positive effect of competition in avoiding capture:
raising the number of outlets is commonly seen as a way to reduce the influence that
the incumbent politician may have on what media report. However, the introduction of
less strict assumptions on voters’ heterogeneity and on the media market structure shows
that the reality may be more complex.
In particular, this paper shows (both theoretically and empirically) the existence of a nonmonotonic relationship between media competition and media capture, obtained when
voters are allowed to be heterogeneous in their interest for politically related news and
the media market is modelled as a two-sided one, where outlets are interested in selling
contents to the readers2 and advertisement space to the advertiser. These modifications,
in an otherwise standard model of political agency and media, lead to the aforementioned
non-monotonicity: increasing the number of media outlets makes capture more expensive
1
The seminal paper is Besley and Prat (2006), but the same idea is in Gentzkow and Shapiro (2008),
Prat and Strömberg (2013), Torrens (2014), Gehlbach and Sonin (2014).
2
We refer to readers as consumers of media contents for simplicity. However, the paper is agnostic
with respect to the type of media firm (newspapers, televisions, websites etc).
2
as long as the number of outlets is below a certain threshold. When the threshold is
passed, raising competition makes capture cheaper.
Our theoretical model builds on Besley and Prat (2006) adverse selection political agency
game. Voters act as principal while the incumbent (of good or bad type) is the agent.
Media outlets may receive a common, verifiable signal about the type of the incumbent,
and may be bribed by the bad politician in order not to reveal that. Hence, outlets face
a trade off between publishing the signal and enjoying the audience-related rents and
accepting the politician’s bribe instead. Differently from Besley and Prat (2006), in this
paper not all the voters are interested in politically related news, hence not all of them
will become aware of the incumbent’s type if only a small fraction of the outlets is publishing the signal. Moreover, audience-related rents are determined as optimal strategies
in a two-sided market where outlets are selling contents to the readers and advertisement
space to a monopolist advertiser, interested in placing his adverts where the readers are.
In this setting, raising the number of outlets increases the number of players that the
incumbent politician may want to silence (as in Besley and Prat 2006), but it also reduces
the outside option for captured outlets, that would have to compete with more subjects
and hence can enjoy lower audience-related rents. As a consequence, they may be more
willing to sacrifice their independence in exchange for money. The prevailing of the first
or of the second effect generates the non-monotonicity.
Together with this, we are able to characterize the threshold where the effect of competition on the equilibrium cost of capture changes sign (i.e. where competition starts
making capture cheaper). We show that it is increasing in the fraction of voters interested
in political news and that, as a consequence, media competition is more likely to be a
good deterrent against capture when this fraction is high. On the empirical side, we can
show that, in a cross-country comparison, the correlation between the number of daily
newspaper titles and the level of media freedom can be properly described by a reverse-U
shaped relationship, consistently with the findings of the model. Finally, we show that
the effect of media competition on the ex-ante voters’ welfare is non-monotonic as well,
since welfare is strictly decreasing in the ex-ante probability of media capture.
3
1.2
Discussion and real life examples
The main result of our model is perhaps surprising and somewhat counterintuitive.
But does it also make sense in the real world? Of course, it is very hard to measure
media capture empirically, since “influence” is something hard to observe (and that can
be generated in many different ways, more or less formal: from bribing to buying advertisement space). However, looking at something related but not coincident with media
capture (i.e. media bias), Hamilton (2004) points out that the increase in the number of
U.S. TV channels reduced the share of unbiased outlets. Specifically, “in the late 1960s,
U.S. television households received an average of only seven channels. In that broadcast
environment, each major network had the incentive to offer unbiased news coverage to
attract audiences in the tens of millions. By 2000, households received an average of
sixty-three channels. In that universe, a cable programmer would be happy to capture
the attention of a million viewers. A conservative cable channel program might not attract ten million viewers, but it might draw two million viewers. This logic of niche
programming gave rise to the Fox News Channel ”3 . Consistent with the idea that more
competition may not be necessarily good, Hamilton (2004) notes that “the impact of the
number of competitors on the quantity and quality of reporting is actually a question left
open by economic theory”4 . It is unlikely that the answer about media capture is not
affected by any trade-off.
Moreover, it is possible to find anecdotal confirmation for the two steps leading to our
result: firstly, competition has a negative effect on outlets’ profitability. Secondly, financially weak outlets may be more willing to accept political influence.
For the first step, Cagé (2014) has precise estimations about the effects of an exogenous
increase in media competition on profitability, noticing that “entry reduces the circulation of incumbent newspapers by nearly 25 %”, and this implies a 20 to 36% reduction
in revenues, 14 to 29% reduction in size and a 9 to 13% reduction in the share of hard
news.
Moving to the second step, many different sources point out that the media is more
easily influenced when revenues are low. The last edition of the Media Sustainability
Index (IREX 2015), for example, stresses that “[o]verall the issue seems to be that media
3
4
Hamilton (2004), pag. 3, italics added.
Hamilton (2004), pag. 21.
4
have been weakened by a poor economy and been preyed upon by political money, or
political pressure has weakened the economic environment in which media operate, thus
making it easier for political money to distort the market and put independent media at
a strong disadvantage”5 . Writing about Bulgaria, the same report notices that “most
traditional media operate at a financial loss, which leads to compromises with editorial
independence. With few exceptions, the big advertisers enjoy complete media support.
As public institutions remain the biggest advertisers, any government regardless of its
political affiliation receives media support”6 . Similarly, the website worldaudit.org points
out the risk of political influence on financially weak media in Albania: “many independent media outlets are hampered by a lack of revenue. Publishers and media owners tend
to dictate editorial policy based on political and economic affiliations, which, together
with the employment insecurity journalists face, nurtures a culture of self-censorship”. An
explicit (even if anecdotal) relationship between competition and media capture can be
seen in the FYR of Macedonia, as highlighted by fairpress.eu (Iloska 2014). The country
is characterized by a “large number of broadcast and print outlets in comparison with its
population size”. Despite this, the “Macedonian media are subject to severe interference
and political pressure. [...] In the last few years the Government was regularly criticized
for its liberal use of promotional advertising, leading to increased financial dependence
of media and increasing the number of outlets that favour its position”. Moreover, the
Turkish newspaper “Today’s Zaman” (Zibak 2015) was recently claiming that “the diversity and abundance of media outlets in Turkey do not necessarily guarantee the presence
of a free, independent and pluralistic media”7 . This highlights two things: on the one
hand, the existence of free media even in a country with potential important problems of
media capture; on the other hand, the fact that a very competitive market is not enough
to avoid these problems.
Finally, the last piece of anecdotal evidence comes from Drago et al. (2014) and van der
Wurff and van Cuilenburg (2001). First of all, Drago et al. (2014) find that the entry of
newspapers increases the re-election probability of the incumbent: this is at odds with
Besley and Prat (2006), but it is consistent with our approach. Moreover, they find
that “competition matters”, meaning that the effect of entry does not disappear as more
5
IREX (2015), pag. ix, italics added.
IREX (2015), pag. xi, italics added.
7
Today’s Zaman, Turkish daily news, 20-04-2015.
6
5
newspapers are on the market, and in our model we will try to go more in depth than the
standard monopoly vs duopoly approach. Van der Wurff and van Cuilenburg (2001) find
empirical evidence of a different effect of the degree of competition in the Dutch television
market on program diversity. While moderate competition increases diversity, extreme
competition reduces the investment in content development. Despite not being related
with media capture, this paper provides empirical evidence of possible non-monotonic
effects of competition, similar to our main result.
The remainder of this paper is as follows. Section 2 reviews the relevant literature, section 3 describes the setting of the model while we derive the equilibrium in section 4. We
comment on the main results and assumptions in section 5 and derive the comparative
statics in section 6. Section 7 is dedicated to the political consequences of media capture and some welfare analysis while section 8 presents possible ways to test the model
empirically. We conclude in section 9.
2
Related literature
This paper aims to contribute to different branches of the economic literature, from
the political economy of mass media to the economic regulation of the media market,
with particular attention on media capture and on the effects that media competition
has on political outcomes via media capture. Of course, the literature on these topics is
growing exponentially and, as a consequence, in this section we will briefly mention the
most important contributions, highlighting similarities and differences with our paper.
2.1
Mass media and political economy
Not surprisingly, given its importance, the relationship between media and politics has
been widely studied in the political economy literature, and detailed and comprehensive
reviews are provided by Prat and Strömberg (2013) and Strömberg (2015). In this review,
we look briefly at the effects of competition on different “types” of media bias, highlighting
the main differences with our approach.
6
2.1.1
Demand and supply driven bias
In terms of demand driven bias (i.e. bias caused by the demand side of the media
market), the most notable examples here are Strömberg (2004), Mullainathan and Shleifer
(2005), Gentzkow and Shapiro (2006), Bernhardt et al. (2008) and Chan and Stone
(2013). As pointed out by Gentzkow and Shapiro (2008), competition appears to have
mixed effects when we are referring to demand-driven bias. Generally speaking, this
class of models explains bias starting from the heterogeneous views of the readers, that
media are incentivized to pander in their profit-maximization decision. This channel is
potentially very interesting, but for what concerns the basic model considered in this
paper, we decided to “switch off” the ideology/demand-side channel in order to focus
on the direct effects of competition on media bias without other potential confounding
factors.
The second possible source of bias internal to the media market comes, of course, from the
supply-side. As extensively discussed by Baron (2006) and Hamilton (2004), journalists,
as well as media owners, usually have their own political ideas, and may also have the
incentive to use the media in order to defend their interests. Up to a certain extent,
they may be willing to sacrifice profits if they have important “private” objectives. This
literature includes Baron (2006), Anderson and McLaren (2012), Duggan and Martinelli
(2011) and Prat (2014).
The approach of these models is closer to ours, since media capture happens on the
supply side of the media market. However, there are two important differences. First
of all, these are generally not fully fledged political agency models. Journalists and
media owners may have political interests, but of course they are not responsible to the
voters, and the political environment is typically over-simplified. Secondly, these models
generally assume that media owners have specific political interests, without actually
explaining why this may be the case. Of course, one of the possible explanations for such
editorial decisions is pressure coming from the political environment, and this is precisely
the object of the literature on media capture.
2.1.2
Media capture
The seminal paper about media capture is Besley and Prat (2006), which will also
provide the basic framework from which we depart in the model studied in this paper.
7
Given the necessity to capture the whole industry, in equilibrium the politician will either
silence every outlet or none of them, and has to pay to each of them monopoly profits.
As a consequence, the cost of media capture (and hence politicians’ turnover and voters’
welfare) monotonically increases in the number of outlets.
Petrova (2008) and Corneo (2006) look at media capture too, even if in this case the
capturing entities are interest groups or particular factions of society. Vaidya and Gupta
(2009) study the effect of media competition on corruption via media capture, finding
a mixed result: when there are positive externalities among the outlets (i.e. when both
outlets revealing the signal is more than twice as strong as a single outlet revealing it)
then a duopoly may be cheaper to be captured than a monopoly, while the opposite
is always true in case of negative externalities. It has to be noted, however, that this
result is obtained in a setting pretty different from the standard media capture models
reviewed so far8 . Moreover, their approach is different to that of our model: firstly, we
keep the standard assumption of hard signals and the full political agency setting, with
strategic politicians, media and readers/voters. Secondly, we look at competition trying
to model it better than the very reduced form used so far, and going beyond the simple
duopoly/monopoly comparison.
Finally, Gehlbach and Sonin (2014) look at the link between media bias and a continuous
outcome to which the government is interested: political “mobilization”. In terms of
competition, the results are analogous to Besley and Prat (2006): since the outlet with a
smaller bias would be able to attract the whole audience, then the government interested
in controlling the media has to buy the whole industry, whose cost is increasing in the
number of outlets.
Our modelling strategy shares with Gehlbach and Sonin (2014) the importance given to
a precise structure for the advertisement market, related to readership and so on. We
will go further in that way by modelling it in a precise two-sided setting. However, our
political setting is quite different (and closer to Besley and Prat 2006) since we do not
assume a particular “bad” nature of the government and citizens are interested in being
governed by a “good” type.
Of course, empirical evidence for media capture is hard to find, since it is neither appar8
First of all, the model is not concerned with political agency, since there are no voters and the
government is not accountable. Secondly, signals are “soft”, i.e. they can be wrong with positive
probability. Third, their focus is on corruption (with the government that always prefers it) rather than
on political accountability.
8
ent nor precisely defined. Probably the most direct insight comes from McMillan and
Zoido’s (2004) study on Fujimori’s media control mechanism in Perù, showing the huge
costs he had to pay to silence media channels (with respect to members of the congress
or judges). Di Tella and Franceschelli (2011) find that there is a negative correlation
between advertisement bought by the government and the space dedicated to scandals
in Argentinian newspapers, while Hamilton (2004) relates the emergence of independent
newspapers (rather than politically affiliated) with the increasingly important advertisement market, and a similar result is also in Petrova (2011). Finally, Petrova (2008) finds
empirical evidence supporting her theoretical prediction about media freedom being decreasing in income inequality in democracies.
Generally speaking, the result that the number of media outlets decreases the possibility
of capture is quite common in the theoretical literature. And, as long as it is necessary
to silence the whole industry, this result holds. Moreover, as we will show below, it holds
also for some set of parameters (and number of firms) when partial capture is a possible
equilibrium outcome. Nevertheless, the result is much less general once we allow for the
possibility of some freedom in the media industry (even in case of capture) and we provide
a better model of the media market. In these cases, keeping the assumptions about hard
signals and in a political agency setting, it is possible to show that an increase in the
number of media outlets may, for some parameters, reduce the cost of media capture.
2.2
Media competition and the advertisement market
A first point that separates our approach from the standard models of media capture
is the attempt of looking more closely at the media market. In particular, our model is
related to those stressing the importance of the “two-sidedness” of the market of media
(Argentesi and Ivaldi 2005). Ellman and Germano (2009), for example, use a two-sided
market model in order to see the effect of the advertisement industry on media bias,
while similarly Godes et al. (2009) and Dukes (2006) use a two-sided model to study how
media competition affects pricing strategies and content quality choices respectively. In
our model, we basically “incorporate” their approach (media outlets selling copies to the
readers, i.e. competing on prices, and advertising space to the advertisers, i.e. competing
on quantities) in our standard media capture political agency framework.
Finally, the importance of the advertisement market on the media industry has been
9
highlighted by two “symmetrical” contributions. On the one hand, Germano and Meier
(2013) show, in a model of commercial media bias (i.e. where media outlets are silenced
by the advertisers), that as the number of outlets increases, the bias is reduced, since the
advertisement revenues are shared by a higher number of media and hence conquering
the audience (via lower bias) becomes relatively more important. On the other hand,
Blasco et al. (2015) highlights that competition in the advertisement market is not
sufficient to eliminate the commercial media bias. The relevance of this literature for our
model is twofold: first of all, it highlights the importance of the two-side condition in
the media market, which cannot be disregarded. Secondly, it stresses the relevance of
the advertisement industry and of advertisers’ decisions. In our model of course we will
switch off the commercial media bias, since we focus on the political environment. But,
interestingly, buying advertisement space is one of the ways through which politicians
may try to influence the media.
2.3
Economic regulation of media and theoretical framework
This paper aims to contribute to the literature on media market regulation as well.
Since there is no general agreement about what a “healthy” broadcasting sector is (Seabright
and von Hagen 2007), we point out that the role of competition, when related with media
capture, may be more complex than the standard answer given by the political economy
literature. Polo (2005) studies whether market incentives are powerful enough to guarantee internal and external pluralism in the media market, finding that the differentiation
triggered by the market does not necessarily extend to political views, and that internal
pluralism is limited by the personal interests of media owner. Torrens (2014) looks, from
a normative perspective, to the optimal media market structure, taking into account the
possibility of media capture. The basic welfare trade-off is given by the fact that, in
his model, more media outlets imply a lower probability of capture but also higher fixed
costs to be supported without an increase in the amount of information available. It is
interesting to note, however, that Torrens’ (2014) main effect of the number of outlets
on the possibility of capture is analogous to Besley and Prat (2006) precisely because he
shares the same assumption about the fact that a single media outlet publishing the news
10
is enough to inform the whole electorate9 .
Finally, it is worth mentioning the theoretical framework of this model: the idea of a
principal agent supervisor model with hard signals comes from Tirole (1986), while the
two-sided market literature (and the idea that media are a platform in this type of market)
can be referred to Rochet and Tirole (2003).
3
The model
It is a principal-agent-supervisor pure adverse selection model, where the voters act
as principal, the incumbent politician (he) is the agent and media outlets (she) act as
supervisors, potentially captured by the agent. We keep the same timing and most of the
assumptions of Besley and Prat (2006), adding two modifications. Firstly, voters have
different costs in information processing of political news, hence not all of them become
informed once one media outlet publishes the news about the politician. Secondly, the
media market is modelled as a two sided market where outlets sell advertisement space
to a monopolist advertiser willing to pay more for an higher readership, and contents to
the voters/consumers.
3.1
The game
In period 1 an incumbent of type θ ∈ {b, g} is in power, with P r (θ = g) = γ. The
“good” incumbent chooses the policy that maximizes voters’ welfare, while the “bad”
one is only a rent seeker. While in power, he earns a rent equal to R. As in the baseline
of Besley and Prat (2006), we keep the problem as a purely adverse selection one, so
when a good incumbent is in power voters’ payoff is 1 while when a bad incumbent is
in power this payoff is 0. If the incumbent is good, media outlets receive no signals (i.e.
s = ∅), while if he is bad they receive with probability q ∈ (0, 1) a verifiable signal s = b
revealing his type10 . Every media outlet has then the possibility to choose her reporting
strategy, defined as s˜i ∈ {b, ∅}. If s = ∅, then the only option available is s˜i = ∅, since
9
Outside the formal economic modelling, Hollifield (2006) highlights the possibility of a reverse-U
shaped relationship between competition and journalistic performance, listing many different channels
that may bring to it. Differently from that paper, we focus on media capture only, we derive the nonmonotonic relation as a result of a formal, game theoretical model and we look directly at the effects of
political and commercial forces.
10
Following Besley and Prat (2006), it is assumed that voters cannot observe the signal directly.
11
there are no signals and news cannot be fabricated. However, if s = b, by revealing the
news (i.e. setting s˜i = b) media outlet i enters in the media market. Following most
of the literature on media competition (Rochet and Tirole 2003, Ellman and Germano
2009, Dukes 2006, Godes et al. 2009), we model this market as a two-sided one. Outlets
sell advertisement space to a monopolist advertiser, who is willing to pay a higher price
if its advertise goes on outlets with a higher readership. Moreover, outlets make money
also by selling their contents to the consumers. If the outlet decides for s˜i = ∅, then she
stays out of the media market11 . Following Besley and Prat (2006), we assume:
1. Only verifiable news can be reported;
2. Signals can only be bad;
3. All media have the same information.
Differently from them, however, we allow for some heterogeneity in voters’ political information processing cost, meaning that some of them will be interested in political news
and some of them will not. This microfounds the fact that the politician needs to capture
only a fraction λ ∈ [0, 1] of media outlets in order to stay in power. Formally, we assume
the existence of two types of consumers/voters12 . α of them are “interested” voters, that
are exactly like every voter of Besley and Prat (2006). In particular, they are interested in
political news and willing to buy contents related with this type of news from any outlet
willing to publish them (up to an exogenous individual reservation price p̄ ∼ U [0, 1]).
Moreover, in terms of bayesian updating, note that it is enough that one outlet publishes
the news in order to let them all become informed about the signal13 . As quite standard
in these models, we assume that every reader/voter buys at most one piece of news.
The other 1 − α voters are “rationally ignorant”, meaning that they have no interests
in spending money or effort to buy politically-related contents. A way to formalize this
11
This is only a normalization. Everything is the same if we assume that every outlet is part of
the “ordinary” media market, where they make some non-negative profits, and then some of them, by
choosing s˜i = b, enters in the “politically related” media market where they can make extra profits, on
top of the “ordinary” ones.
12
In total, consumers/voters are a large number normalized to 1.
13
In equilibrium they will all buy the content, but even if some of them decides not to do so because
the price is above his p̄, still he is making a decision knowing that the news has been published, and he can
still use this information to update his beliefs. This assumption on the exogenous reservation price is not
affecting the equilibrium characterization. It is necessary only to solve the case of a monopolist publisher,
that is facing a trade off between contents price and readership. In our equilibrium the contents price
will be 0 even in case of a monopolist publisher, hence all the “interested voters” will buy the content.
12
assumption is in terms of information processing costs. As pointed out by Hamilton
(2004), the existence of “rationally ignorant” voters is consistent with a downsian framework. Voters should be willing to acquire information if the cost of doing so is lower than
the expected benefit of electing the right politician times the probability of being pivotal.
In this model we abstract from pivotality considerations, since this would quickly lead
to the well known “turnout paradox”. What we assume, together with sincere voting
and that everyone votes, is that α voters can process information at no costs, while the
remaining fraction can do so only at a cost k > 1, hence greater than the benefit given by
the election of the right politician. So, even without any pivotality consideration, it is not
worth for them to spend time and effort in reading news, not even when they are free of
charge. However, if someone else explains them all the story, then this has no information
processing cost for them14 . Note that this assumption does not imply irrationality of any
sort among these voters. Moreover, the presence of many “rationally ignorant” voters is
one of the ways Hamilton (2004) uses to justify the underprovision of relevant political
news, hence they are known to play a crucial role in shaping the media market incentives.
We assume that voters know their type and that α ∈ (0, 1) is common knowledge. How
ever, a fraction p m
of these “rationally ignorant” voters become exogenously informed
n
∂p( m )
while talking with their neighbours. We assume ∂ mn > 0, p (0) = 0 and p (1) = 1: the
(n)
idea is that the higher is the fraction of media outlets publishing the news, the bigger
is the fraction of “rationally ignorant” voters that just “jump into the news” becoming
informed, since the topic is “hot”15 .
The number of media outlets, n, is exogenously given and it will be the main aspect
of our comparative statics analysis. In general, media outlets derive revenues from two
sources: audience-related revenues and money from the politician. The former are the
profits derived from selling contents to the readers and advertisement space to a monopolist advertiser, in a way described in details in section 4.2. Regarding the latter, the
incumbent can offer ti ≥ 0 to each media outlet, conditional on her not reporting his true
14
The idea is that there is a difference between putting effort to read and understand a newspaper
article, looking for the important parts, checking its consistency and so on, versus being informed by a
friend, who has already processed the information.
15
In practice, there is individual uncertainty but not aggregate uncertainty. The single “rationally
ignorant” voter does not know if he is uninformed because there is nothing to see or because he is not
included in the fraction that becomes informed. However, there is no uncertainty on the dimension of
this fraction. Note that this idea of fraction of voters becoming informed is somewhat similar to the
approach of Besley and Burgess (2002).
13
type16 . The politician offers a vector of individual transfers {ti }i=1,...,n . Outlets observe
it17 and each of them simultaneously decides whether to accept the individual offer or
not. We assume the existence of a transaction cost τ ∈ [1, ∞) capturing institutional
constraints to corruption. Hence, a transfer ti gives to the outlet an amount
ti
.
τ
Defining
P
I the set of media that accepts the offer, the incumbent gets a payoff of R − i∈I ti if
P
he is elected and of − i∈I ti if he is voted out of office. At the end of period 1, voters
decide whether to confirm the incumbent or to choose a challenger that is good with
probability γ. In period 2 payoffs for both periods are paid: voters will have a payoff of
1 if the politician in power is a good type and a payoff of 0 if the politician in power is a
bad type, while the incumbent politician receives his office rents R.
3.2
Summary of the timing
1. θ is realized. If θ = g then s = ∅ with probability 1. If θ = b then R is realized
(drawn from a distribution FR ) and it is known by the incumbent (and by the
outlets if they receive the signal s = b. However, they cannot communicate R to
the voters18 ). The distribution is common knowledge of the voters. Moreover, s = b
with probability q and s = ∅ with probability (1 − q). The incumbent observes the
media signal and decides {ti }i=1,...,n .
2. Each media i observes s and {ti }i=1,...,n and decides whether to accept or reject ti .
If she rejects, she reports the true signal (if s = b) competing with the other outlets
that reported the news, if she accepts she reports s˜i = ∅ and her payoff is
ti
.
τ
Note
that every outlet decides on the individual offer only.
3. If s˜i = b for some i, the two-sided market of media determines the optimal choices
in terms of price of the content and price and quantity of advertisement space sold.
“Interested” voters buy the content and learn the incumbent’s type, while a fraction
of “rationally ignorant” voters become informed as well. If s˜i = ∅ for ∀i then
p m
n
16
Following Besley and Prat (2006), we assume that every outlet is able to commit not to report the
true type of the incumbent once she receives the payment.
17
On this respect, the present model is close to the 2001 working paper version of Besley and Prat
(2006). We are working on a version of the model where outlets observe only the individual offer. In
that case, the equilibrium existence proof requires a refinement of out of equilibrium beliefs, but nothing
changes in terms of equilibrium outcomes.
18
This assumption makes the game between the incumbent and the outlets much more tractable, but
it does not affect the results.
14
none buys media contents.
4. Consumers/voters vote. If the incumbent is voted out, the new incumbent is randomly drown with P r (θ = g) = γ. Period 1 ends.
5. In period 2 payoffs for both periods are paid and the game ends.
4
Equilibrium derivation
As in Besley and Prat (2006), we focus on symmetric pure strategy perfect Bayesian
equilibria with sincere voting. We solve the model backward, starting from the voters’ choices and then back to the two-sided media market and the politician’s decisions,
showing the existence of an equilibrium with a non-monotonic effect of n on capture.
4.1
Voters’ choice
Irrespective of their type, voters’ information set is binary (i.e. they read the news
or not, and hence they are informed about the politician’s bad type or not). Of course,
there is an equilibrium in which informed voters decide to vote out the incumbent, while
uninformed voters (i.e. voters observing s˜i = ∅) keep him in power. To see this, let
us start with “interested” voters, that behave exactly as the voters in Besley and Prat
(2006), i.e. they will all become immediately informed if at least one outlet publishes.
Note that
P r (θ = g|s˜i = b) = 0 < γ
Moreover, suppose the voters belief that the bad politician is able to silence all the media
0
with probability19 σ ∈ [0, 1]. Then, again by Bayes’ rule,
P r (s˜i = ∅|θ = g) P r (θ = g)
P r (s˜i = ∅|θ = g) P r (θ = g) + P r (s˜i = ∅|θ = b) P r (θ = b)
γ
=
γ + [(1 − q) + qσ 0 ] (1 − γ)
P r (θ = g|s˜i = ∅) =
19
Voters do not know the realization of R, but they know that it is a random variable drawn from
0
a generic cumulative distribution function FR . Note that σ is the probability of total media capture
conditional on having a bad incumbent and on the media having received the signal about his type.
15
From this, we derive that
P r (θ = g|s˜i = ∅) ≥ γ
is true when
1−σ
0
q≥0
and hence it is never sequentially rational to vote out the incumbent20 when s˜i = ∅.
Consider now the fraction of “rationally ignorant” voters. We assume that the single
voter, despite knowing his type, does not know if she is observing s˜i = ∅ because she
belongs to the fraction that would stay uninformed anyway or because there is no signal to
be transmitted. Of course, she is still rational and hence she assigns a probability σ to the
event of (partial or total) media capture21 and a probability p m
to her belonging to the
n
fraction of rationally ignorant voters that would become informed in case of publication
of the signal and capture. In other words,
P r (s˜i = ∅|capture, θ = b, s = b) = 1 − p
m
n
So, every “rationally ignorant” voter observing s˜i = ∅ would update her belief in the
following way:
P r (θ = g|s˜i = ∅) =
γ
γ + (1 − q) + qσ 1 − p
m
n
(1 − γ)
This happens because, when the incumbent is a bad type, the voter observes s˜i = ∅ when
there is no signal to be transmitted (this happens with probability (1 − q)) and when
there is signal to be transmitted, but there is capture and she belongs to the fraction of
voters that stays uninformed (and this event has probability qσ 1 − p m
). Given this,
n
20
As a tie-breaking rule, we are assuming that the indifferent voter will confirm the incumbent.
0
Note that σ and σ are not the same thing. The latter is the probability that the whole industry
is silenced. This is relevant for the “interested” voters, since they all become informed if a single outlet
0
publishes the news, hence when only partial capture is necessary, then σ = 0. On the other hand, σ is
the probability that some outlets are captured (both conditional on having a bad incumbent and s = b).
Moreover, note that σ is the probability of capture conditional on having a bad incumbent and on the
media having received the signal about his type. Note that the voters are able to work out the fraction
of media outlets a bad incumbent needs to capture in order to stay in power and the fact that a bad
incumbent will either capture just enough outlets or none of them.
21
16
we have that
P r (θ = g|s˜i = ∅) ≥ γ
is true when
m 1≥σ 1−p
n
So it is always optimal for the “rationally ignorant” voter observing s˜i = ∅ to confirm the incumbent. Trivially, they will vote out the incumbent after s˜i = b since
P r (θ = g|s˜i = b) = 0.
Are these equilibrium strategies unique? As in Besley and Prat (2006), in equilibrium
it is optimal for voters reached by the signal to vote out the incumbent and for uninformed voters to keep him. It is trivial to see this for informed voters, given that signals
cannot be fabricated and hence they know that the incumbent is bad with probability 1.
Suppose now that there exists an equilibrium where uninformed voters will vote out the
incumbent as well. Then, it is pointless for the bad politician to silence the media, and
hence the voters’ posterior when observing s˜i = ∅ are strictly higher than the prior22 . As
a consequence, it is not sequentially rational to vote out the incumbent23 .
4.2
Two-sided media market subgame
Suppose that m ∈ [1, n] outlets are publishing the news, and hence competing for
advertisement revenues and readers. Define as M the set of outlets that decided to
publish the news. The timing of the subgame is as follows, and reminds Ellman and
Germano (2009)24 :
1. Every media outlet i ∈ M sets the price of its content, pi ≥ 0, getting as a conseP
quence a readership ri ≤ α such that m
i=1 ri = α. We assume that “interested”
voters/consumers are buying the content (one copy each) as long as it publishes
the political news and as long as pi ≤ p̄, where p̄ is a positive individual reservation
price. We assume that p̄ ∼ U [0, 1]. Since these consumers/voters are interested
22
If the bad incumbent never silences the media, then the posterior probability of a good incumbent
P r(s˜i =∅|θ=g)P r(θ=g)
γ
after s˜i = ∅ is P r (θ = g|s˜i = ∅) = P r(s˜i =∅|θ=g)P
r(θ=g)+P r(s˜i =∅|θ=b)P r(θ=b) = γ+(1−q)(1−γ) . Note that
then P r (θ = g|s˜i = ∅) > γ is true for q > 0, and hence satisfied.
23
Moreover, note that for every possible value of σ, given the tie-breaking rule we are assuming, it is
better to confirm the incumbent when s˜i = ∅.
24
The idea behind this timing is that readership choices and editorial choices tend to be stable, while
you can sign advertising contracts based on them. However, this timing choice is not crucial for the
results of this paper.
17
only in the political news, and this news will be the same in every outlet, they treat
the m outlets as homogenous products, and hence they will all buy their copy from
the outlet setting the lowest price.
2. Given the readership, outlets and the monopoly advertiser determine the quantity
of space to be sold as advertisement space.
As a consequence, every media outlet i ∈ M derives profit from readership and from
advertisement space. Formally,
Πi = Πr,i + Πa,i
(1)
where Πr,i and Πa,i are the profits that outlet i makes from readership and from advertisement space respectively.
We solve the subgame backward. Hence, when the decision on the quantity and price
of advertisement is made, the readership of every outlet has already been determined.
We assume that the (monopolist) advertiser’s problem is
m
m
X
X
√
max
ri yi −
qi yi
y1 ,...,ym
i=1
i=1
where yi is the quantity of space bought on outlet i, ri is the readership of that outlet
(determined in stage 1) and qi is the market price of a unit of space on outlet i.
The justification for this objective function lies in the literature on advertisement and the
media market. As pointed out by Hamilton (2004), “once people are watching a program
or reading a news entry, advertisers care about the chance to divert their attention to a
commercial product”. So, following this idea and similarly to the microfoundation of advertiser’s demand in Ellman and Germano (2009), we assume that each reader/consumer’s
demand of the advertised good is increasing and concave in the quantity of advertisement
on the outlet he buys (for analytical convenience, we assume the power of 12 . However, it
has to be noted that only the concavity assumption is crucial for our results). In other
words, the quantity of advertisement space boost the demand for the advertised good at
a decreasing rate. As in Ellman and Germano (2009), the advertiser is interested in the
total demand of the good, so she multiplies the individual demand determined by the
quantity of advertisement on outlet i times the readership of that outlet, summing across
all outlets publishing the signal. This leads immediately to our objective function. Note
18
that, like in Dukes (2006), the objective function is additively separable in the media
outlets; moreover, it is linear in the readership as in Ellman and Germano (2009) and it
exhibits decreasing marginal returns in the quantity of advertisement space like in Godes
et al. (2009).
As it can be easily seen, the problem is concave and, from the first order conditions, we
can derive the inverse demand function for every outlet, given by
ri
qi = √
2 yi
∀i ∈ M
Moving now to the outlets, each of them will choose yi to maximize its profits, knowing
how the market would react to her decision. As a consequence, the problem for every
outlet i is the following:
max (qi (yi ) − c) yi
yi
ri
s.t. qi (yi ) = √
2 yi
(2)
c is the cost of producing advertisement space (in terms of foregone “useful” space on
a newspaper or a website etc.) that is strictly positive but arbitrarily small. For reasons
that will be justified soon, we assume c ≤ α8 .
Solving (2), we derive that
yi∗ =
ri2
16c2
and as a consequence
qi∗ = 2c
So, the profits from advertisement for the media outlet are given by
Π∗a,i =
ri2
16c
that is strictly increasing in ri . Note that the advertiser is also making positive profits
on every outlet, since
Π∗ADV,i = ri
ri
r2
r2
− 2c i 2 = i
4c
16c
8c
where Π∗ADV,i is the equilibrium profit level for the advertiser on outlet i.
Going backward to stage 1, it is easy to note that, as long as m ≥ 2, the standard
19
features of a Bertrand competition apply in this setting. Every outlet will try to undercut the others in order to conquer more readership, noticing that ri = 0 if pi > pj for at
least one j ∈ M . Given the zero marginal cost assumption, the only equilibrium is the
one where pi = pj = 0 for ∀i, j ∈ M . As a consequence, ri = rj =
α
m
∀i, j ∈ M 25 and
Π∗r,i = 0 ∀i ∈ M . Given this and equation (1), the profits that every outlet who decides
to publish the news makes on the market are given by
Πi =
α2
16cm2
∀i, j ∈ M
(3)
and as a consequence this will be the minimal amount of bribes from the politician acceptable by each outlet in equilibrium.
Of course, Bertrand competition does not apply when m = 1. The monopolist media
outlet will face a trade-off between a positive price for the copies (hence, lower readership and lower revenues from advertisement) and the maximization of the readership.
Recalling that the reservation price is assumed to be p̄ ∼ U [0, 1], then we can derive the
different demand levels faced by the monopolist (assumed to be outlet i without loss of
generality) for different prices. In particular, profits from readership are given by
Πr,i = pi D (pi ) α
where the demand, as a function of pi , is:



0


D (pi ) =
1



 1−p
if pi ≥ 1
if pi = 0
i
if pi ∈ (0, 1)
and of course the total profits are given by
Πi = Πr,i + Πa,i = pi D (pi ) α +
1
(D (pi ) α)2
16c
We can immediately rule out every solution where pi ≥ 1. Hence, the monopolist outlet
problem is:
25
Since voters are indifferent between the publishing media, we assume for tractability that they split
equally between them.
20
max pi (1 − pi ) α +
pi ∈[0,1)
1
[(1 − pi ) α]2
16c
(4)
We claim the following lemma:
Lemma 1 If c <
α
8
then the unique solution of the monopolist outlet problem is pi = 0.
Proof. Note that, after few manipulations, the objective function of (4) can be written
as
h (pi ) := α
α
h α
α i
− 1 p2i −
− 1 pi +
16c
8c
16c
(5)
so the function is quadratic in pi . Moreover, note that h (pi ) = 0 ∀pi ≥ 1 and that
h (0) =
α
16c
> 0. A necessary condition for an interior solution is, of course, the concavity
of (5), hence
i.e. if c <
α
,
8
α
16c
− 1 < 0 or c >
α
.
16
However, this is not sufficient. In fact, if
α
8c
− 1 > 0,
then h (pi ) would reach its maximum for a pi < 0, that of course is ruled
out by the constraints. Hence, if
α
16
< c < α8 , then the only admissible solution is pi = 0,
since the function would be strictly decreasing for pi ∈ [0, 1). Moreover, note that if
c<
α
,
16
then h (pi ) is a convex function in pi ≥ 0. There are two possibilities, in this case.
Either the minimum of the function is in pi ≥ 1 or it belongs to the interval (0, 1). In the
first case, h (pi ) would be strictly decreasing in (0, 1), and as a consequence the solution
of the maximization problem is pi = 0. The same is true also for the second case, since
the function would be strictly convex in [0, 1] and as a consequence the maximum can be
only on a corner. Since h (0) > 0 = h (1), then the unique solution is pi = 0, and this
completes the proof.
As proved in Lemma 1, as long as c is small enough even the monopolist outlet behaves
in the same way as in the “Bertrand competition” environment, and as a consequence
Π∗r,i = 0 and Π∗i = Π∗a,i =
α2
.
16c
We consider formally the case of c >
α
8
in Appendix
1, but it has to be noted that the assumption is not determining our result in any way.
Assuming c small enough allows us to write the cost function of the capture in a “unified”
way irrespective of n, m and λ (otherwise, it would be a step function, as we show in the
Appendix). However our main result, i.e. the non-monotonic effect of n on capture, is
not affected by this assumption: we can derive it because, when there are outlets that
the politician does not need to capture, then the outside option of captured media is
lowered by this (potential) competition, making them cheaper. And this effect does not
21
depend on the characterization of monopoly profits in case of a single firm publishing,
but it involves directly the existence of some competition on the “publishing” market
and, hence, the Bertrand features would apply. Finally, note that many types of media
outlets offer their contents for free (websites, most of the tv channels, radio channels,
free newspapers), deriving 100% of their profits from advertisement. And, as pointed out
by Ellman and Germano (2009), revenues from advertisement account for 50-80% of the
total revenues of “standard” newspapers. Hence, our assumption is not far from reality.
4.3
Optimal number of silenced media
In order to determine the optimal number of outlets he would like to silence, the politician takes into account the fact that all the α “interested” voters will become informed
once a single outlet publishes the news, while the fraction of the other 1 − α “rationally
ignorant” voters that become informed is increasing the fraction of media reporting the
m
news. For the sake of tractability, we assume that p m
= n , but our results are qualn
itatively unchanged if we use other increasing functions of
m
n
instead. Hence, if every
outlet publishes the news, then all the voters become aware of the type of the politician,
while of course if m = 0 then none of them is. In order to stay in power, given that
in equilibrium it is optimal for the informed voters to vote out the incumbent, the bad
politician needs at least 50% of the voters to be uninformed26 . Of course, since getting a
higher percentage of uninformed voters is irrelevant in terms of re-election, but is costly
in terms of bribes, the politician will choose m such that
α + (1 − α) p
Note that, if α ∈
m
n
=
1
2
1
,
1
, i.e. if there is a majority of “interested” voters, then we go
2
back to Besley and Prat (2006) model, where the bad politician has to silence the whole
industry. Hence, the interesting case is when α ∈ 0, 12 . On this respect, Hamilton
(2004) points out that “interested” readers/voters are usually a minority, if compared
with “rationally ignorant”. Hence, the case we are considering is likely to reflect reality.
26
As an indifference breaking rule, we give a small “incumbency advantage” to the politician in power
assuming that, in case of a 50-50 result, he would be re-elected.
22
Given the functional form of p
m
n
assumed above, the politician chooses
m=
1 − 2α
n
2 (1 − α)
As a consequence, if we define as λ the fraction of outlets that the politician has to silence
in order to be re-elected, we can see that, in case of capture, it is optimal for him to have
1−λ=
1 − 2α
2 (1 − α)
and hence
λ∗ =
1
2 (1 − α)
(6)
Given that λ∗ is not a function of n, from now on we define λn the number of outlets
that the politician silences in equilibrium. Note that there are many equilibria, given
the possible combinations of outlets silenced by the politician, but given our symmetry
assumption they will be unique, up to a permutation of the outlets silenced.
4.4
Politician’s problem and “capture condition”
Given the results above, in equilibrium the bad politician will either capture a number
of media big enough to guarantee his re-election (λn) or none of them, when it is too
costly to do so. We claim that there exists an equilibrium where the politician offers
ti
τ
=
α2
16c((1−λ)n+1)2
to λn outlets and 0 to the others, if R is high enough. Otherwise, he
offers 0 to everyone.
The formal derivation of this equilibrium is in Appendix 3. Note, however, that there are
no unilateral profitable deviations. Outlets not receiving any bribe cannot do anything
different than publish the signal. On the other hand, the politician has to pay to every
bribed outlet her outside option, i.e. the profits each of them would make if, when λn
outlets are captured, she would decide to deviate from accepting the offer, publishing
the news and hence competing with the other (1 − λ) n free outlets. In this case, then,
m = (1 − λ) n + 1 and hence the profits, following (3), would be
α2
.
16c((1−λ)n+1)2
The
politician has to pay this amount of money to all the λn outlets he needs to capture and,
h
i
α2
given the transaction cost τ , then the total amount to be paid is λnτ 16c((1−λ)n+1)2 .
Moreover, the politician cannot hope to stay in power bribing a lower number of outlets
23
(as we saw above) or with a lower offer, since it would be rejected. It is optimal for the
bad politician to bribe the outlets if this amount is lower than the office rent he could
realize by staying in power in period 2 (defined as R), and hence the capturing condition
is
α2
λnτ
≤R
16c ((1 − λ) n + 1)2
(7)
As it is quite immediate to see, the effect of n on this condition is non trivial. On one
hand, raising n while keeping the rest of the parameters constant implies, as in Besley
and Prat (2006), that the politician has to silence more outlets. But, on the other hand,
raising n also increases the competition in the slice of market that remains free (if this
exists, of course) lowering, as a consequence, the outside option for every firm and hence
making capture more attractive (and cheaper, for the politician). Given this, we can
state the first result of this paper.
Proposition 1 If λτ α2 > 64c (1 − λ) R, i.e. if media capture is not too cheap, then there
exists a pure strategy symmetric perfect bayesian Nash equilibrium where we have media
capture for n ≤ n and for n ≥ n̄, i.e. the effect of the number of media on the possibility
of capture is non-monotonic.
Proof. In order to have media capture the following condition has to be realized:
h
i
α2
λnτ 16c((1−λ)n+1)
≤ R.
2
The existence of the equilibrium has been shown in the text above27 . We need only to
prove the fact that n has an effect on the possibility of capture, i.e. to rule out that there
is media capture irrespective of n. Rearranging (7), we get
−16cR (1 − λ)2 n2 + λτ α2 − 32c (1 − λ) R n − 16cR ≤ 0
For simplicity, we treat n as continuum variable. The case of discrete values of n is
considered in Appendix 2. Note that the LHS defines a concave function of n. Hence,
we define −16cR (1 − λ)2 n2 + (λτ α2 − 32c (1 − λ) R) n − 16cR := f (n). Moreover, when
n = 0, f (n) = −16cR. In order to save notation and to keep our proofs simpler, we now
define:
κ := 16cR (1 − λ)2
27
It is part of our research agenda to work on the unicity proof, of course up to a permutation of the
silenced outlets, at least in terms of equilibrium outcomes.
24
β := λτ α2 − 32c (1 − λ) R
δ := 16cR
Noticing that κ and δ are all always positive by construction, we can rewrite our function
as
f (n) = −κn2 + βn − δ
Since we have capture when f (n) ≤ 0, the condition for having a non monotonic effect
of n on capture is that the vertex should lie in the first quadrant. Its coordinates are
xV =
yV =
β
2κ
β 2 − 4κδ
4κ
We prove that, if λτ α2 > 64c (1 − λ) R, then the vertex lies in the first quadrant. We
require, first of all,
xV =
β
>0
2κ
That is true when λτ α2 > 32c (1 − λ) R. Moreover, we need
yV =
β 2 − 4κδ
>0
4κ
This condition implies β 2 − 4κδ > 0, i.e.
λτ α2 − 32c (1 − λ) R
2
> 1024c2 R2 (1 − λ)2
Solving, we obtain λτ α2 −32c (1 − λ) R > 32c (1 − λ) R, that leads to λτ α2 > 64c (1 − λ) R.
Of course the other solution is λτ α2 − 32c (1 − λ) R < −32c (1 − λ) R, but we can rule
it out since λτ α2 is always positive. Since we need both conditions to be realized, this
will happen when λτ α2 > 64c (1 − λ) R. n and n̄ are then simply defined as the points
where f (n) = 0.
Note that this implies that media will be captured when their number is either too low
(as in Besley and Prat 2006) or too big (i.e. our modelling innovation) since competition
would, at some point, make them so cheap that it will be convenient, for the incumbent,
to silence them. In order to give a better intuition of the results, we simulated the model
25
setting α = 0.4, R = 1.4, τ = 5 and c = 0.04 obtaining Figure 1.
Model simulation with α = 0.4, R = 1.4, τ = 5, c = 0.04
Cost, rents
1.5
1.4
1.3
1.2
1.1
1.0
5
10
15
20
Number of media outlets
Figure 1: equilibrium cost of capture (blue line) and office rents (orange line) for different values of n when α = 0.4,
R = 1.4 τ = 5 and c = 0.04.
The blue line represents the total cost that the bad politician has to pay in order to
capture enough media outlets to stay in power in period 2, while the orange line is the
second period office rent R. Given his incentive structure, it is optimal for the politician
to capture some outlets when the latter line is above the former, hence when n is low
enough and big enough. Moreover, the graph shows the effect of n on the equilibrium
cost of capture: it increases the cost for low enough n, making capture more difficult,
but after the maximum an increase in n is actually making capture cheaper. This is due
to the fact that, at that point, n makes the outside option sufficiently small to overcome
the increased number of outlets to be silenced.
5
Additional results and comments on the assumptions
The main difference, in terms of results, between our model and Besley and Prat
(2006), is the non-monotonic effect of n on the possibility of media capture and, hence,
on voters’ welfare. Their model captures only the “first half” of the story we are able to
26
tell in this work, i.e. the fact that an increase in n makes media capture (weakly) more
difficult. This is true also in our case: raising n from below to above n moves the industry
from captured to free media. However, there is also another effect of an increase in n,
i.e. the fact that the market is more competitive, hence outlets can make smaller profits
and they are cheaper when captured. When this second effect prevails on the first one,
more media competition can (weakly) increase the range of parameters for which capture
is possible. If n increases from something included in the interval (n, n̄) to something
above n̄ then the bad incumbent becomes able to capture enough firms to stay in power.
In order to see more clearly the “ceteris paribus” effects of n, we can look at how it
changes the total cost of capture, keeping every other parameter constant. Formally, let
us define the cost of capture as
α2
K := λnτ
16c ((1 − λ) n + 1)2
(8)
Hence, differentiating (8) with respect to n, we obtain
λτ α2 ((1 − λ) n + 1)2 − 2 ((1 − λ) n + 1) (1 − λ) n
∂K
=
∂n
16c
((1 − λ) n + 1)4
Given our assumptions on the parameters,
∂K
≥ 0 iff
∂n
(1 − λ) n + 1 − 2 (1 − λ) n ≥ 0
And, as a consequence,
∂K
1
≥ 0 iff n ≤
∂n
1−λ
We can formalize this result in a proposition:
Proposition 2 Competition in the mass media market increases the equilibrium cost of
capture as long as the number of outlets is below
2(1−α)
.
1−2α
Above this threshold, competition
decreases the equilibrium cost of capture.
Proof. Provided in the text, just noticing that the maximum of the equilibrium cost
function is reached when n =
1
1−λ
Defining the maximum n∗ :=
and that in equilibrium λ∗ =
1
,
1−λ
1
.
2(1−α)
we can see that n increases the cost of capture
(hence making capture more difficult) as long as the competition is not too strong, i.e.
27
as long as n < n∗ , while the opposite is true when n > n∗ . Interestingly, n∗ leads to a
corollary to Proposition 2, i.e. the “complementarity” between α and the positive effect
of competition on the cost of capture. We formalize this result in the next corollary.
Corollary 2 n∗ is increasing in the fraction of “interested” readers/voters, and it tends
to ∞ as this fraction approaches the 50%.
Proof. Recalling from (6) that λ∗ =
1
,
2(1−α)
we replace this in the definition of n∗
obtaining, after few algebric manipulations,
n∗ =
2 (1 − α)
1 − 2α
Taking the derivative,
dn∗
2
=
dα
(1 − 2α)2
that is always positive, as claimed. Moreover,
lim1 n∗ = +∞
α→ 2
and this completes the proof.
As anticipated, this result underlines the “complementary effect” of “interested” voters
and competition. In particular, the higher is the fraction of “interested” voters, the
greater is the set of values of n for which more competition increases the cost of capture,
hence - as we will prove below - where competition has a positive effect on voters’ welfare.
This implies that competition is more likely to be a good solution against media capture
in countries with high levels of political interest, while it is more likely to have negative
effects where the interest is low.
Finally, note that the condition λτ α2 > 64c (1 − λ) R states that media capture must not
be too easy. In fact, when it is violated, then we have capture for every value of n. To
see its implications more clearly, we can rewrite it as
1−λ
τ α2
> 64c
R
λ
28
or, exploiting the fact that λ is a function of α in equilibrium, as
τ
2 (1 − α)
> 64c
R
α2
The first formulation highlights that the transaction costs cannot be too low, that the
office rents cannot be too high and that the ratio between free and captured outlets, in
equilibrium, cannot be too big. Otherwise, capture would be too easy or too profitable.
The second formulation highlights the role of α: the bigger it is, the smaller is the RHS,
since a very small α would imply the necessity of silence only a limited number of outlets.
In terms of assumptions, our model shares most of the structure of Besley and Prat
(2006), with few exceptions we will discuss here. First of all, we relax the assumption
about the fact that one outlet publishing the news is enough to inform the whole electorate. On this respect, it has to be noted that, when λ = 1, then we simply go back
to Besley and Prat’s result, that is embedded in our model. We study the theoretical
possibility that λ can be less than 1, but we do not exclude the case λ = 1.
Gentzkow and Shapiro (2008) use the argument of re-broadcasting as a justification for
the extreme assumption in Besley and Prat (2006). Of course, if there is perfect rebroadcasting, their assumption is justified. However, note that “silenced” media may not
be willing to re-broadcast anything, since they have been compensated in order not to
do so. Moreover, in reality there are many ways of re-broadcasting a news item. What
matters in our model is the message transmitted to the readers about the type of the
incumbent, and - even if it is not (yet) captured in our model - the same news can be
re-broadcasted in many ways. Even a “hard” signal, e.g. a phone conversation about a
politician talking about bribes, can be presented as “the politician is taking bribes” but
also as “yes, he made that call, but it is taken out of the context. And however everyone takes bribes”. The second way, of course, is the same as re-broadcasting the news
without giving any information about the politician’s type. Moreover, it has to be noted
that even in places traditionally associated with problems related with media capture
(e.g. Italy), the capture never reached the whole media industry (not even the whole
television industry when Mr Berlusconi was at the same time Prime Minister and owner
of the main 3 private television stations). McMillan and Zoido (2004), for example, point
out that Montesinos was not bribing the whole media industry, choosing the outlets with
29
a highest viewership/readership, and this is consistent with our model. Hence, for the
sake of realism, the possibility that λ < 1 should at least be considered.
The second modelling modification is about the two-sided structure of the media market,
outlets pricing and commercial decisions and so on. On this respect, there is a substantial
amount of literature pointing out the importance of this particular market structure, and
in our case the results are qualitatively different when we include a more realistic media
market. Hence, we think that our modification is justified.
6
Comparative statics
We have already shown the main result of this paper, i.e. the non-monotonic effect
of n on the possibility of media capture. The rest of the comparative statics, however, is
consistent with Besley and Prat (2006), implying also that our main result is driven by
the two modifications we impose to the model, while keeping the rest as close as possible
to the original paper. We summarize (and prove) the main comparative statics results in
Proposition 3.
Proposition 3 Ceteris paribus, and assuming λτ α2 > 64c (1 − λ) R, media freedom is
increasing in the transaction costs (τ ) and in the fraction of interested readers/voters
(α), while it is decreasing in the office rent (R).
Proof. first of all, we define the interval of media freedom as F := n̄ − n, i.e. as the
interval of n where the market cannot be captured by the politician. Moreover, we note
that
n̄ =
β+
p
β 2 − 4κδ
2κ
β−
p
β 2 − 4κδ
2κ
and
n=
where β, κ and δ are defined as in the proof of Proposition 1. As a consequence,
p
β 2 − 4κδ
F =
κ
Now we can differentiate F with respect to the relevant parameters and derive the main
30
comparative statics results. First of all,
− 1
∂β
∂F
11 2
=
β − 4κδ 2 2β
>0
∂τ
κ2
∂τ
because all the terms are positive, noticing that
write F as
q
∂β
∂τ
= λα2 ≥ 0. Secondly, we can explicitly
(λτ α2 − 32c (1 − λ) R)2 − 1024c2 R2 (1 − λ)2
F =
16cR (1 − λ)2
that simplifies to
F =
p
λ2 τ 2 α4 − 64cR (1 − λ) λτ α2
16cR (1 − λ)2
Hence,
h
∂F
=
∂R
1
2
i
(λ τ α − 64cR (1 − λ) λτ α ) (−64c (1 − λ) λτ α ) 16cR (1 − λ)2
+
2
16cR (1 − λ)2
2 2
1
2 −2
4
−
16c (1 − λ)2
2
p
λ2 τ 2 α4 − 64cR (1 − λ) λτ α2
2
16cR (1 − λ)2
Note that both terms at the numerator are negative, while the denominator is positive.
As a consequence,
∂F
<0
∂R
Finally, we replace λ with its explicit solution as a function of α. After few algebraic
manipulation, we find that
F =
(α − α2 )
p
α2 τ 2 − 64cRτ (1 − 2α)
8cR (1 − 2α)
Hence,
∂F
=
∂α
8cR (1 − 2α)
+
h
i
p
8cR (1 − 2α) (1 − 2α) α2 τ 2 − 64cRτ (1 − 2α)
+
[8cR (1 − 2α)]2
h
1
2
− 12
2 2
(α τ − 64cRτ (1 − 2α))
+
i
(2τ α + 128cRτ ) (α − α )
2
[8cR (1 − 2α)]2
p
16cR (α − α2 ) α2 τ 2 − 64cRτ (1 − 2α)
[8cR (1 − 2α)]2
31
2
+
Note that everything is positive as long as α−α2 > 0, that is always true for α ∈ (0, 1).
As a consequence,
∂F
>0
∂α
and this completes the proof.
Together with the consistency with Besley and Prat (2006), it has to be noted that
Proposition 3 makes intuitive sense. High office rents imply stronger incentives for the
politician to bribe the media, since he has more to gain from staying in office. On the other
hand, countries with a stronger tradition of media independence, or with a better legal
system (both captured by the transaction costs), are associated with a greater interval
of free media. Finally, the result on the fraction of interested voters is consistent with
Hamilton (2004), that finds in the existence of too many “rationally ignorant” voters one
of the reasons for the underprovision of politically relevant news from the media system.
7
Effects on welfare and political accountability
Following Besley and Prat (2006), we look now at the (ex ante) welfare of the voters,
and at how it is affected by the presence of media capture. As already mentioned, office
rents R are assumed to be drawn from a generic distribution FR , with support <+ . As
a consequence, the ex ante probability of media capture, conditional on having a bad
incumbent in power and on s = b, is defined as
α2
σ := P r R ≥ λnτ
16c ((1 − λ) n + 1)2
= 1 − FR λnτ
α2
16c ((1 − λ) n + 1)2
With this definition, the probability that a bad incumbent is voted out is (1 − σ)q and, as
a consequence, the expected turnover is (1 − γ)(1 − σ)q. Hence, it is decreasing in σ. In
the standard Besley and Prat (2006) model, since n was monotonically decreasing σ, then
n was supposed to increase the expected turnover. Interestingly, Drago et al. (2014) finds
that this is not the case, at least for the entry of local newspapers in Italian municipalities.
In our model, under some conditions n increases σ, lowering as a consequence the expected
turnover. And this is consistent with Drago et al. (2014).
32
Finally, the ex ante voters’ welfare is defined as
W := γ(2) + (1 − γ) [q (1 − σ) γ]
(9)
because the good incumbent would be re-elected for sure, leading to a payoff of 1 in each
period. On the other hand, the bad incumbent is voted out with probability q(1 − σ),
and in that case the new politician is good with probability γ. If confirmed, the bad
incumbent would bring a payoff of 0 in both periods.
As expected, (9) shows that voters’ welfare is decreasing in the probability of media
capture. As a consequence, the effect of n on W is, again, non-monotonic. When n < n∗
we have the same result as Besley and Prat (2006): competition makes capture more
costly and hence less likely, ceteris paribus, and as a consequence it has a positive effect
on voters’ welfare. On the other hand, differently from Besley and Prat (2006), we
find that - when n > n∗ - competition has a negative effect on voters’ welfare, making
capture cheaper. This result suggests that some carefulness is needed when thinking
about competition as a tool for avoiding media capture. Under some conditions, the
effect can be counterproductive.
8
Empirical Test
8.1
Empirics and potential concerns
The empirical verification of these results is quite a complex task, that requires dealing
with multiple issues. The strategy we outline here is only a first possible attempt, and an
important part of our research agenda concerns solving the problems we are highlighting
here.
First of all, media capture is rarely observed or recorded. Even if we model the politicianmedia outlet transactions in terms of bribes, there are many other ways through which a
bad incumbent can influence what media report. Not all of them are illegal, like buying
advertisement space or deciding editors, directors etc. Secondly, it is hard to find quasiexperiments able to identify exogenous shocks of media competition.
The literature has explored two alternative ways: cross-country comparisons (e.g Petrova
2008) and discrete variation in the number of local media (e.g. Drago et al. 2014 and
33
Cagé 2014). As a first attempt, given the current data availability, we will try to pursue
the first one, even if probably the second one is stronger in terms of identification. The
problem with the latter is the lack of measures of media freedom at municipal or provincial level. Moreover, it is not obviously true that the readership area of a newspaper
coincides with the local institutional borders.
Given these issues, our empirical strategy is similar to Petrova (2008), where the predictions of the model are tested running an OLS regression in a cross-country environment
using a panel of countries and media freedom scores as proxy for the possibility of media
capture. It has to be clear that - given the data availability and the empirical strategy
- we are just measuring correlations, without any claim of causality. That would require
an instrument or a quasi-experimental setting.
8.2
Data description
We built a panel with 4 years28 of observations (2001-2004) and 184 countries. As a
proxy for media freedom we use the score of the political environment from the “Freedom
of the Press” index produced every year by the American NGO Freedom House. The score
goes from 1 to 4029 and evaluates the level of media freedom from political influence in
every country, leaving aside both economic and legal constraints to what media report30 .
In order to capture media competition, expressed in the model as the number of media
outlets, we use data from the Global Media Survey 2005-2006 realized by the Unesco
Institute for Statistics, that contains the number of daily newspaper titles per million of
inhabitants for the period 2000-200431 . Moreover, we have a dummy indicating whether
a country was a democracy in the period of interest32 and some controls: GDP per capita
in PPP, average years of schooling for male and female older than 25 and a dummy equal
to 1 if parliamentary elections happened in that year. The summary statistics for the
28
This time limitation is essentially due to data availability: we could find a reliable and consistent
account of the number of daily newspaper titles for this period only.
29
The original score measures the level of influence, hence 0 is a country with media completely free
from political influence and 40 is a country with the highest possible level of influence. However, since
we need to measure media freedom, we use as outcome variable 41-original score.
30
These are captured by the other two environments.
31
At the moment, we cannot say whether some of these newspapers belong to the same editorial
group, or we do not know the market share. It is our objective to address these concerns.
32
According to the Freedom of the World report, Freedom House. When the democratic status
changes, we put 1 if a country was a democracy for at least 3 years.
34
main variables is summarized in Table 1.
Variable
Media freedom
# outlets
GDP per capita
Schooling
Elections
Democracy
Obs.
730
562
691
552
529
728
Mean
23.633
3.37
10589.49
7.232
0.282
0.615
St. Dev.
10.27
4.339
12619.16
2.999
0.450
0.487
Min
1
0
238.955
0.979
0
0
Max
40
26.01
71336.38
13.096
1
1
Table 1: Summary statistics for the main variables. Media freedom is given by 41 minus the original Freedom of the
Press score for the Environment B; # outlets is the number of daily newspaper titles per million of inhabitants, GDP
per capita is expressed in PPP, Schooling is the average number of years spent at school for male and female older than
25, Elections is a dummy indicating whether paliamentary elections happened in a particular year.
8.3
Model and results
The model we estimate is the following33 :
mfit = µt + β1 nit +
β2 n2it
+
J
X
γj xjit + it
(10)
j=1
where mfit is the score of media freedom in country i at time t, µt is time fixed effect,
nit is our measure of competition (i.e. number of daily newspaper titles per million of
inhabitants), xit is a J-dimensional vector of controls and it is the error term, assumed
to be orthogonal to nit .
We have two objectives to be achieved by the estimation of (10): first of all, a necessary
condition for the existence of a non-monotonic relationship between n and mf requires
that βˆ1 > 0 and βˆ2 < 0. Secondly, we compare the quadratic model with the linear one,
implied by most of the theoretical approaches used so far, in terms of goodness of fit.
Our results are summarized by Table 2. Column 1 is the linear model, impled by Besley
and Prat (2006). Column 2 is the quadratic model implied by our theoretical results,
column 3 is the quadratic model with GDP per capita as a control and column 4 adds
time FE34 .
First of all, note that we run our regressions using democracies only: the idea is that
media capture is an issue in countries where elections are competitive, media are relevant
33
I thank Ben Lockwood and Martina Miotto for helpful comments on this issue
Adding country FE is probably asking too much to the dataset, given the limited number of observations. The signs of the coefficients are still correct, but country FEs absorb all the significant
variation.
34
35
Dep. variable: media freedom
(1)
(2)
(3)
linear
quadratic
+ controls
0.704∗∗∗
1.546∗∗∗
1.889∗∗∗
(0.168)
(0.343)
(0.609)
# outlets
(# outlets)2
-0.051∗∗∗
(0.015)
(4)
+ time FE
1.955∗∗∗
(0.612)
-0.105∗∗
(0.041)
-0.110∗∗∗
(0.042)
0.0003∗∗∗
(0.0001)
0.0003∗∗∗
(0.0001)
Schooling
-0.273
(0.381)
-0.308
(0.380)
Elections
0.050
(0.369)
N
278
0.489
0.004
(0.368)
Y
278
0.501
GDP per capita
Time FE
N
R2
∗
p < 0.10,
N
337
0.180
∗∗
p < 0.05,
∗∗∗
N
337
0.226
p < 0.01
Table 2: Regression results for democracies only. The dependent variable is always the media freedom score.
Column 1 is the linear model, column 2 is the quadratic one, column 3 adds our controls and column 4 adds time
fixed effects. Country level clustered standard errors are in parentheses.
and the incumbent cannot explicitly censor them35 . Looking at table 2, it has to be
noticed that the quadratic model fits the data better than the linear one, both in terms
of AIC and rMSE. In particular, the AIC for the linear model is 2240.177 while it is
2222.549 for the quadratic model. The rMSE is 6.698 for the linear and 6.515 for the
quadratic model.
Secondly, β̂1 and β̂2 are consistent with our hypothesis of non-monotonicity: the sign
is correct and they are both significantly different from zero, individually and jointly.
Moreover, both the sign and the significance are robust to the introduction of our control
and of time FE, and even the magnitude is not changing too much.
Clearly, these signs could be consistent also with an increasing and concave relationship.
In order to address this concern, we compute the maximum of the parabola described
by column 4 regression coefficients, noticing that it lies well within the bounds of n36 .
Hence, for n high enough, an increase in competition is associated with a reduction in
the media freedom score, and the level of competition where this happens is in between
the lower and the upper bound of n in our sample.
35
36
However, results are similar when we use the whole sample.
In particular, using the specification of column 4, the maximum is in n = 8.87.
36
The non-monotonicity derived from the model is also confirmed if we look at Figure 2,
Unexplained variation in media freedom
-10
0
10
-20
showing the partial correlation between media freedom and the number of media outlet.
0
5
10
Number of outlets
democracies
linear fit
15
20
quadratic fit
Figure 2: Partial correlation graph between media freedom and the number of outlets. Blue points are the
residuals of the regression of media freedom on GDP per capita, Schooling, Elections dummy and time FE.
We also draw the linear and the quadratic fit.
Blue dots represent the residuals from the regression of our media freedom score on
GDP per capita, schooling, elections and time fixed effect, hence they are the variation
of media freedom unexplained by these. The idea is that this unexplained variation is (at
leats partially) capturing the effect of media competition on media freedom, and as the
quadratic fit line is showing, this effect is non-monotonic in the number of outlets, with
the shape we expect from the theoretical model.
Finally, it has to be acknowledged that it is impossible to give any causal interpretation
to these estimates, since we cannot rule out neither reverse causality nor the endogeneity
of the main explanatory variable: it is hard to control for variables like hidden common
interests between publishers and politician. However, this is a first attempt to test our
prediction. Our future agenda entails dealing with such problems.
37
9
Conclusions
This paper contributes to the political economy literature on media capture showing
that competition in the mass media market is not necessarily a good deterrent against
political attempts to influence the media industry. Building on the Besley and Prat
(2006) seminal model and relaxing two assumptions, we are able to show the existence
of an equilibrium where excessive competition may make capture cheaper. Moreover, we
show that this effect is somehow mirrored in the data, where the correlation between the
number of media outlets and the media freedom score can be represented by a reverse
U-shaped parabola.
Our results are promising. They highlight that - even with pretty simple modifications
of the standard model - the effect of competition on media capture and political accountability may be less straightforward than what has been thought: counterintuitively,
under some conditions, “too much” competition makes capture cheaper. Moreover, there
is some complementarity between the effectiveness of competition as a capture deterrent
and the fraction of voters interested in political news, consistently with the idea that an
excessive percentage of rationally ignorant voters may generate underprovision of useful
political information (Hamilton 2004). Therefore, there is space for further research that
would help in building up the “applicable, microfounded theory of optimal media regulation” defined as a research goal by Prat and Strömberg (2013).
Of course, this model can be enriched, trying to overcome some simplifying assumptions
and limitations, and checking whether the main results hold. In particular, we will add
moral hazard to the present pure adverse selection framework, moving closer to the standard models of political agency. Media entry can be endogenized, looking at the effect of
fixed costs and entry barriers. The probability of finding information about the incumbent’s type can be endogenized as well, for example as a result of ex ante investments
by the media outlets. We can also introduce competition between advertising firms and
try to find a better way to microfound the voters/readers decision about buying contents. More generally, it would be interesting to study also the “other direction” of the
channel highlighted here, i.e. the power of media in determining political agenda. All
these modifications, together with possible improvements in the empirical strategy, are
valuable goals for further research.
38
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Appendix 1: Relaxing the assumption on c
As we proved in Lemma 1, if m = 1 and c <
α
,
8
then even the monopolist outlet
chooses a price pi = 0 for his contents. We consider now the case of m = 1 and c > α8 .
Under these conditions, the problem of the monopolist outlet has an interior solution.
So, we solve
max pi (1 − pi ) α +
pi ∈[0,1)
1
[(1 − pi ) α]2
16c
Since the objective function is strictly concave in the relevant interval, the FOCs are
sufficient for a global maximum. Differentiating with respect to pi and setting the result
equal to 0 we obtain
2
(1 − pi ) α (−α) + α (1 − 2pi ) = 0
16c
After few manipulations, and reminding that c > α8 , we solve for p∗i finding
p∗i =
8c − α
16c − α
In this case,
D (p∗i ) = 1 − p∗i =
41
8c
16c − α
and as a consequence
Π∗i
8c − α
8c
1
=
α+
16c − α 16c − α
16c
8c
16c − α
2
that, after few simple manipulations, simplifies to
Π∗i =
4cα
16c − α
Given this, the cost of capture for the politician, K, has now to be expressed as a
step function:

 nτ 4cα
16c−α
h
K=
α2
 λnτ
if (1 − λ) n = 0
i
16c((1−λ)n+1)2
if (1 − λ) n > 0
The logic is the following: if the politician has to capture the whole industry, then
- as in the standard Besley and Prat (2006) model - every deviating outlet would be a
monopolist, and as a consequence the politician has to pay him the foregone profits as a
monopolist. Otherwise, the same logic of the main body of this paper applies. As we have
already pointed out, however, if the politician has to capture the whole industry then the
“monotonic” result of Besley and Prat (2006) always applies, irrespective of whether the
optimal price chosen by the monopolist outlet would be 0 or
8c−α
.
16c−α
Our result, instead,
is true when there is some degree of competition in the outside option faced by a bribed
media, hence when (1 − λ) n > 0.
Appendix 2: Discrete changes in n
In the main body of this paper we have considered n as a continuous variable. This
is a good approximation when the number of media outlets is very large, but it is less
precise when this number is small. However, treating n as a discrete variable does not
change the main result of the paper, i.e. the non-monotonic effect of competition on the
possibility of media capture. The difference is that, due to rounding issues, the equivalent
of Proposition 1 has to be stated in a different (and somewhat weaker) way. In order to
have an idea about the behaviour of the cost function when n is discrete, we parametrized
the model producing Figure 3.
42
Figure 3: cost of capture for different values of n when λ = 0.9, α = 0.44, τ = 1 and c = 0.03.
The number of media outlet is on the x-axis, while the cost necessary to silence enough
of them in order to have a bad incumbent re-elected is on the y-axis. In terms of other
parameters, λ = 0.9, α = 0.44, τ = 1 and c = 0.03. As it appears quite clearly in the
graph, the rounding issue plays a role. In particular, the cost of capture is increasing in n
as long as the number of outlets is such that the politician has to silence the whole market,
then it jumps down when n goes from 9 to 10 because of the competition effect given by
the possibility of having one free media (this lowers the outside option of every captured
media and hence the cost). The behaviour is similar for the remaining parts of the graph,
with jumps when n goes from 19 to 20, from 29 to 30 and so on. Note, however, that the
slope of the cost function is progressively decreasing as n grows, because n enters at the
denominator with a power of two. Ultimately, the cost would converge to 0 as n goes to
infinite. From these considerations, we can claim the following proposition, that is the
equivalent of Proposition 1 with discrete n and highlights the non-monotonic result.
Proposition 4 If there is at least one configuration of the market with free media characterized by a number of outlets n∗ > 1, then the effect of n on the cost of capture is non
monotonic.
Proof. We complete this proof dividing the argument in two lemmas.
Lemma 3 If there is at least one configuration of the market with free media character0
ized by a number of outlets n∗ > 1, then moving to n∗ from some n < n∗ increases the
cost of capture.
43
Proof. In terms of integer, the cost of capture can be written as
α2
K = dλne τ
16c (b(1 − λ) nc + 1)2
Suppose now that the market of media is free for n = n∗ , hence
α2
dλn e τ
>R
16c (b(1 − λ) n∗ c + 1)2
∗
0
0
0
Consider now n = n∗ − 1. Note that in this case either λn = dλn∗ e − 1 or λn =
dλn∗ e. Moreover, note that, assuming α ∈ 0, 12 , then λ ∈ 12 , 1 . As a consequence, it is
always possible to pick at least one n∗ such that dλ (n∗ − 1)e = dλn∗ e−1. When this is the
0
0
case, since λn = dλn∗ e−1, the of course (1 − λ) n = b(1 − λ) n∗ c. Hence, to sum up,
0
0
0
there exists n∗ and n = n∗ − 1 such that λn < dλn∗ e and (1 − λ) n = b(1 − λ) n∗ c.
0
As a consequence, when n raises from n to n∗ the cost of capture increases as well,
making capture (weakly) more difficult.
Lemma 4 If there is at least one configuration of the market with free media charac00
terized by a number of outlets n∗ > 1,then there exists some n > n∗ where we observe
media capture.
Proof. As n becomes large, dλne τ
h
α2
16c(b(1−λ)nc+1)2
i
converges to λnτ
h
α2
16c((1−λ)n+1)2
i
.
Moreover, note that
α2
lim λnτ
=0
n→∞
16c ((1 − λ) n + 1)2
00
Hence,
of R such that R > 0, there will be an n such that
taking any value
00 α2
< R, so where the market is captured. And this completes
λn τ
2
16c(b(1−λ)n00 c+1)
the proof.
The combination of these two Lemmas shows that the effect of n on the possibility of
capture is non monotonic, since a change in n can increase or decrease K.
Note that, for different set of parameters, we can always find conditions where ∃ n∗ > 1
such that there is no capture when n = n∗ . Moreover, there is capture for some n < n∗
and for some n > n∗ . First of all, suppose λ ∈ 21 ; 23 . Then, we have capture for n = 1,
free media for n = 2 and capture again for n = 3 as long as the following condition is
44
true: 8c αR2 < τ ≤ 16c αR2 . The logic is that we need to verify simultaneously the following
set of inequalities:
τ
2τ
α2
≤ R (capture when n = 1)
16c
α2
> R (free media when n = 2)
16c
α2
≤ R (capture when n = 3)
16c (1 + 1)2
Suppose now λ ∈ 32 ; 34 . Then, if 8c αR2 < τ ≤ 16c αR2 we have capture for n = 1, free
2τ
media for n = 2 and n = 3 and capture again for n = 4. It continues with this logic untill
λ ∈ 76 ; 78 , where we have capture for n = 1, free media for n ∈ [2, 7] and capture for
n = 8 when 8c αR2 < τ ≤
64 R
c .
7 α2
For higher level of λ it is enough to raise the number of
captured media before the free media interval, or to find conditions for the capture of a
big enough n, where the presence of a sufficient number of free outlets reduces the cost.
9
and 16
c R < τ ≤ 64
c R , we have capture for n = 1 and
For example, when λ ∈ 89 ; 10
3 α2
9 α2
n = 2, then free media for n ∈ [3, 9] and capture again for n = 10. And so on. Moreover,
as it is clear from the figure, we can see that as n increases the cost of capture function
moves closer to zero. This is due to the fact that, for any value of λ (different from 1, of
course), at some point it is always the case that some outlet can be allowed to be free.
This lowers the outside option and, via the mechanism induced by competition on the
advertisement market, and interestingly (1 − λ)n is squared at the denominator, hence
at some point (irrespective of how small 1 − λ is) the effect of an increase in n will be
stronger at the denominator than at the numerator.
Appendix 3: Equilibrium in the politician-outlets game
In order to characterize formally the equilibrium in the game between the politician
and the outlets, we follow closely the proof used by the 2001 working paper version of
Besley and Prat (2006).
First of all, it is without loss of generality to order the observed vectors of transfers
{ti }i=1,...,n such that t1 ≤ t2 ≤ ... ≤ tn . Defining Ii = 1 if outlet i accepts the offer and
Ii = 0 if she rejects it, we characterize the best response recursively.
45
Given I1 , I2 , ..., Ii−1 , Ii = 1 if and only if
ti ≥
τ α2
2
P
16c i − j<i Ij
(11)
Since the LHS is nondecreasing in i and the RHS is nonincreasing in i, there must be a
k ∈ [0, n] such that Ii = 1 for every i ≥ k + 1 and Ii = 0 otherwise.
Note that this implies tk <
τ α2
.
16c(k+1)2
τ α2
P
2
16c(k− j<k Ij )
=
τ α2
16c(k)2
and tk+1 ≥
τ α2
P
2
16c(k+1− j<k Ij )
=
As a consequence, an outlet i ≤ k does not want to deviate accepting the
offer because
ti ≤ tk <
τ α2
τ α2
≤
2
P
16c (k)2
16c i − j<i Ij
And a similar type of reasoning shows that i ≥ k + 1 does not want to deviate rejecting
the offer, since
ti ≥ tk+1 ≥
τ α2
τ α2
=
2
P
16c (k + 1)2
16c i − j<i Ij
Hence, equation (11) describes actual best responses. Finally, note that in equilibrium
k = (1 − λ) n, because the incumbent does not need to capture (1 − λ) n outlets, and
hence the first (1 − λ) n offers can be equal to zero. Then, the lowest positive transfer
must satisfy
tk+1
τ α2
≥
16c ((1 − λ) n + 1)2
Appendix 4: Data sources
List of variables and their source:
• Media freedom score: 41 minus the Environment B score from the Freedom of the
Press (Freedom House);
• Number of Newspaper Titles per million of inhabitants: from UNESCO Institute
for Statistics, Global Media Survey 2005-2006.
Available at: http://data.uis.unesco.org/Index.aspx?queryid=234;
• GDP per capita: GDP per capita in PPP in current international dollars, from UNESCO Institute for Statistics, demograpic and socio economic indicators. Available
46
at: http://data.uis.unesco.org/Index.aspx?queryid=234;
• Democracy: country considered an electoral democracy in the years of interest, according to Freedom of the World report, Freedom House. If 2 or more no, then 0.
Otherwise 1. https://freedomhouse.org/report-types/freedom-world.VfGdxxFVhBc;
• Turnout: parliamentary elections in period 2001-2004. Only one observation for
most of the countries. If more than one, we use the average. Source: Institute for
Democracy and Electoral Assistance.
Available at: http://www.idea.int/vt/viewdata.cfm;
• Schooling: from Quality of Government dataset, average between 2000 and 2005
average schooling year, 25+, male and female, from the Barro and Lee dataset.
• Election: dummy =1 if it was an election year (for parliamentary, lower/unique
chamber elections. No presidential only, no referendums only). I use the ESPV
September 2010 dataset
(https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/17901). Moreover, we coded some missing observations using online sources. In particular, we
used mainly electionguide.org, provided by the International Foundation for Electoral Systems (IFES), an international nonprofit dedicated to strengthening electoral democracy. We used Wikipedia when data from electionguide.org were not
available.
References for data sources
Barro, R. J. and Lee, J. W. (2013) A new data set of educational attainment in the world,
1950-2010, Journal of development economics, 104, 184-198.
Freedom House, Freedom of the Press database, https://freedomhouse.org/report-types/freedompress.
Freedom House, Freedom in the World database, https://freedomhouse.org/report-types/freedomworld.
Institute for Democracy and Electoral Assistance, http://www.idea.int/vt/viewdata.cfm.
International Foundation for Electoral System, electionguide.org.
Johnson, J. W. and Wallack, J. S. (2010) ELECTORAL SYSTEMS AND THE PERSONAL
VOTE. Update of database from Particularism Around the World,
http://dss.ucsd.edu/ jwjohnso/espv.html.
47
Teorell, J., Dahlberg, S., Holmberg, S., Rothstein, B., Hartmann, F. and Svensson, R. (2015)
The Quality of Government Standard Dataset, version Jan15, University of Gothenburg:
The Quality of Government Institute, http://www.qog.pol.gu.se.
UNESCO Institute for Statistics, http://data.uis.unesco.org/.
48