1. law, govt and politics
2. politics
3. elections

Competition and dynamics in the tone of political advertising
campaigns: theory and evidence
Paul B. Ellickson, Simon Business School, University of Rochester
Mitchell J. Lovett, Simon Business School, University of Rochester
Ron Shachar, Interdisciplinary Center, Arison School of Business
April 2, 2015
Abstract
Why do political advertising campaigns tend to start positive and turn negative? Do the candidates
differentiate in the tone of their ads or not? When a candidate switches tone, what is the probability
that her rival will do the same? This study presents theory and evidence that answer these questions and
provide a deeper understanding of the competition and dynamics in tone in political advertising.
We start by presenting an analytical model that has some novel implications. For example, whereas
a candidate is likely to intensify the negativity of her ads when her rival becomes more negative, such
dependency is less likely when her rival becomes more positive.
We test this theory using daily panel data at the candidate level in the congressional elections of
2000, 2002 and 2004. As suggested by the model, we find that the tone of the ads tends to become more
negative as time passes, but not in the last leg of the campaign when it instead becomes more positive.
Furthermore, as implied by the model, candidates tend to adopt the same tone (rather than differentiate)
and when one of them switches tone, the other is likely to do the same but only if the shift is in the
negative direction.
1
Introduction
This paper tackles an issue that has received significant attention from practitioners and the news media,
but relatively little from academic scholars—the dynamics of negative advertising in political campaigns. By
“negative advertising”, we refer to cases in which an ad discusses the competitor explicitly or implicitly. Not
only has negative advertising been increasing over the past several years, it also has become the predominant
1
message tone. Advertising is estimated to have been as much as 90% negative in the 2012 U.S. presidential
race and between 70-75% negative in the 2010 Congressional races.1 Whereas the media and academic
scholars have focused on whether these ads promote democracy and contribute to civil discourse, we instead
tackle the candidates’ decisions to adopt a negative tone and examine (a) how these decisions change over
the course of the campaign, (b) whether the candidates tend to differentiate in the tone of their ads or not,
and (c) whether they are inclined to change their tone together. To this end, we develop a theoretical model
of candidate behavior and analyze empirically a rich dataset of advertising dynamics in political campaigns.
Political advertising decisions, and especially those concerning the content of the ads, receive considerable
attention from both scholars and the media. By studying these decisions, we shed light on the growing
literature on advertising content decisions (Anderson and Renault 2006, Mayzlin and Shin 2011, Kuksov,
Shachar and Wang 2013). The current study focuses on the degree of negativity in the content decision and,
unlike much of this literature, (1) examines these decisions in a dynamic setting, and (2) allows the news
media to play a role in determining the effectiveness of ads and their content.
While political ads, including negative ones, have been previously studied by academic scholars, it is
usually in the context of voter behavior. Very few studies, particularly empirical ones, focus on candidates’
decisions to go-negative and the factors that affect these decisions. The exceptions are on factors such as
front-runner status (Harrington and Hess 1996, Skaperdas and Grofman 1995, and Thielman and Wilhite
1998), the quality of the candidates (Polborn and Yi 2006 and Hao and Li 2013), and prior knowledge of the
candidates and the budget allocated for advertising (Lovett and Shachar 2012).2 Unlike these studies, we
examine not only the decision to go-negative, but also its dynamics during the campaign. Furthermore, we
study these decisions both theoretically and empirically.3
Two earlier empirical findings provide our point of departure. The first relates to the pattern of negativity
during the campaign. Goldstein and Freedman (2002) show that, as election day draws nearer, candidates
tend to become more negative (see also Moody 2012). The second deals with the competitive nature of the
race. Lovett and Shachar (2011) and Che et al. (2007) find evidence suggesting that candidate negativity is
at least weakly associated with the corresponding negativity of their opponent.
Motivated by these two empirical findings, we introduce a simple analytical model whose aim is to shed
light on the choice of advertising content in a dynamic setting. The model has three periods and includes
1 See http://www.washingtonpost.com/wp-srv/special/politics/track-presidential-campaign-ads-2012/ downloaded on July
10, 2014 for the Presidential data and http://mediaproject.wesleyan.edu/2010/11/01/an-uptick-in-negativity/ downloaded on
the same date for congressional.
2 Several papers examining commercial settings provide models in a similar setting to negative advertising but have different
objective functions and price decisions as central elements. For example, Chen et al. (2009) study “combative” advertising,
which shifts customer preferences away from the competitor’s product, and show the effect of such advertising on equilibrium
prices and profits in a commercial setting.
3 One previous study that includes dynamics in the empirical investigation is Che et al. (2007) who found that candidates
choose the ad tone conditioned on how many negative and positive ads the opponent aired the day before.
2
two candidates who compete to win an election, which is held at the end of the last period. The voter’s
utility depends on the good and bad traits of each candidate. She learns about these traits from ads as well
as from the news media. The only decision of the news media, in each period, is whether or not to cover
the election campaign. The choice to actively cover the campaign depends on its degree of negativity. The
candidates are always “digging for dirt” on their rivals and if they find some, they need to decide whether
to use it in their ads - i.e. the decision to go negative depends on the availability of information about their
rival. Furthermore, in solving the model we show that candidates do not always use negative information
immediately and that forward-looking considerations can be related to the decision to delay its use.
The solution of the theoretical model is consistent with the two aforementioned empirical regularities,
but provides additional novel predictions. First, we find that while negativity is expected to increase during
the campaign (as documented previously), in some cases it is actually expected to decrease close to Election
Day. Second, we find asymmetry in the interaction between the candidates – while a candidate is likely to
intensify the negativity of her ads when her rival becomes more negative, such interaction is less likely when
her rival becomes more positive. In other words, candidates tend to move together when changing the tone
of the campaign in the negative direction, but tend to act independently when becoming more positive. This
theoretical finding might explain why previous empirical work found only weak evidence for the dependency
of the candidate’s negativity on that of her rival. On top of these predictions (which shed a new light on the
empirical regularities) the model offers additional testable implications, such as that the candidates are more
likely to use the same tone, rather than a different one, at each point in time.
We examine the model’s predictions using data on the elections for the U.S. House of Representative in
2000, 2002 and 2004. For each of these election years we have panel data at the candidate level in all races
in which two major party competitors air at least some ads. The total number of candidates is 498. The
unit of time is a day and the panel includes the 70 days leading up to Election Day. For each candidate and
day, we know which candidate aired each ad and whether each ad was positive or negative. Our data set also
includes a count of the news media reports on the races.
The empirical analysis supports each of the model’s implications. First, we find that while negativity is
indeed increasing during the campaign, it is actually decreasing close to Election Day. Specifically, we find
that negativity peaks 10 days before the end of the race and then drops, in the last leg of the campaign, by
about 20 percent. Second, the candidates adopt the same tone in their ads, rather than a different one (i.e.
both are positive or both are negative), 73% of the time. Furthermore, it turns out that positivity spans
(i.e. periods in which both candidates use a positive tone) are more frequent and longer than negativity
spans and that periods in which the candidates are using different tones are common but brief, indicating
their transitory nature. Third, there is indeed asymmetry in the interaction between the candidates – i.e.
3
candidates tend to move together when changing the tone of the campaign in the negative direction, but
not when it becomes more positive. Specifically, we find that if the rival adopts a negative tone after both
candidates used a positive one, the probability that the focal candidate switches to negative is at least 80
percent higher compared with the case that the rival did not change tone. On the other hand, a switch in
tone by the rival after both used a negative one is not correlated with a change in tone by the focal candidate.
Furthermore, the data on media coverage provide a preliminary indication that it might contribute to this
asymmetry.
Together these new findings form the following picture of dynamic negativity in political campaigns. The
tone of the ads tends to become more negative as time passes, but not in the last leg of the campaign when
it becomes more positive. Candidates tend to adopt the same tone and then shift tone together, unless the
shift is in the positive direction, and the news media seems to be partially responsible for this asymmetry.
Furthermore, these novel findings were identified by the theoretical model and thus can be explained by it.
In the rest of this paper we describe the model and its solution (section 2), the data and the empirical
results (section 3). The final section concludes.
2
Model
Two candidates, denoted by j and j 0 , compete to win the vote of a representative individual. To capture the
temporal dynamics of an election, we assume that the election campaign lasts three periods, denoted by t,
ending with Election Day.
In subsection 2.1 we describe the setting of the model – i.e. the action space and decision rules of the
candidates, the news media and the voter and then, in subsection 2.2, we turn to the solution of the model.
While the setting is quite general, the role of the news media (as described below) makes it more relevant for
congressional elections than presidential. Throughout the exposition, we will refer to the voter as a male, to
the focal candidate, j, as a female, and to her rival, j 0 , as a male.
2.1
2.1.1
Setting
Candidates
We assume that the candidates traits are the basis for voters decisions. As in Lovett and Shachar (2011),
each candidate has good traits denoted by a (e.g., effective manager) and bad traits denoted by b (e.g.,
performs badly under pressure). At the start of period 1, each candidate knows her own good traits but none
of her rival’s bad traits. To learn of her rival’s bad traits, a candidate must engage in opposition research,
4
which we refer to colloquially as “digging for dirt.” We assume that both candidates are engaged in this
opposition research in every period (see, for example, Huffman and Rejebian 2012). The outcome of this
effort is random with the following three possibilities: s/he finds (1) nothing, (2) a minor bad trait or (3) a
major bad trait. The probabilities of each of these outcomes are 1 − q L − q H , q L , and q H respectively, and
let q L > 0, q H > 0, and q L + q H < 1.
We model political advertising via a message sent to the voter by each candidate in every period. Formally,
let mj,t denote the message of candidate j in period t. Each message can contain one trait, be it a good trait regarding the focal candidate or a bad one for her rival. Formally, mj,t ∈ {good trait of j, minor bad trait of j 0 ,
major bad trait of j 0 }. To reflect candidate familiarity with herself, we assume that she knows at least three
of her own good traits. It is therefore feasible to run only positive ads, should she choose to do so.
The decision over which message to send is a central focus of the model and is discussed below as part of
the model’s solution. In other words, the “go-negative” versus “go-positive” decisions are equilibrium results
of the model.
2.1.2
News Media
Most congressional campaigns do not attract close attention from the news media. However, following
previous studies, we assume that when dirt surfaces, the campaign becomes more attractive from the news
perspective and the media is more likely to cover it (Haynes and Rhine 1998; Arnold 2006; Geer 2012).
We confirm this basic relationship in our data (described later), finding that media coverage increases when
at least one candidate airs a negative ad following a period in which both candidates air only positive ads
(see appendix A). To reflect this bias toward negativity by the news media, we assume that a campaign is
covered by the media only if at least one message of the candidates contains a major bad trait of her opponent.
Furthermore, when the news media finds interest in a congressional campaign (i.e., in the candidates and
their traits), it is likely to last for a short time beyond when the information first surfaces. To capture this
behavior of the press, we let ct be an indicator variable that is equal to one if the media is covering the
campaign and zero otherwise and assume that ct = 1 iff mj,τ = {major bad trait of j 0 } for any j and for
τ ∈ {t − 1, t}. To further reflect the news media bias toward negativity, we assume that it covers (and
echoes) only the messages with bad trait information and does not pay attention to any messages containing
good traits.
2.1.3
The voter
The representative voter believes that each good trait will improve the performance of the candidate, if
elected, whereas each bad trait will decrease it. Thus, in practice, his decision rule is quite simple: weighing
5
the good and bad traits of each candidate and voting for the one whose “balance sheet” dominates, taking
into account the relative importance of minor versus major bad traits. Accordingly, the individual votes for
j iff
X
X
H
L
G
δt vj,t
+ vj,t
+ vj,t
>
δt vjH0 ,t + vjL0 ,t + vjG0 ,t
t
(1)
t
where
H
vj,t
= v H if mj,t ={major bad trait of j 0 } , and zero otherwise
L
= v L if mj,t ={minor bad trait of j 0 }, and zero otherwise
vj,t
G
vj,t
= v G if mj,t ={good trait of j}, and zero otherwise
δt = δct + (1 − ct )
Equation (1) reflects our assumption that the perception of candidates traits is influenced by the media
coverage.4 Consistent with Haynes and Rhine (1998) and Geer (2012), we assume that δ > 1 to capture
the degree to which media coverage enhances the perception of these traits. Accordingly, the individual’s
perceptions of the impact of a good trait, a minor bad trait and a major bad trait on the voter’s utility are
v G , v L and v H , respectively, without media coverage and v G , δv L and δv H with such coverage. Note that
media coverage only enhances the bad traits since, as mentioned above, it only reports these and not the
good ones.
Finally, we assume that v H >v G >v L and that δv H >δv L >v G . The first inequality is straightforward,
simply reflecting the “major” and “minor” aspects of the bad traits. The second inequality allows the media
coverage to have a meaningful impact, since, if the media coverage was not allowed to change the ordering
of these perceptions, it would not have a material role in the model.
So far we have described the action space of the candidates, the media and the voters, and the decision
rules of the last two. In the next subsection, we solve the model and derive the decision of the candidates as
well. These will allow us to understand both the time trend of negativity during the campaign as well as the
response functions of the candidates.
2.2
Equilibrium: candidates’ negativity over the campaign
We now turn to the patterns of negativity in equilibrium: the proportion of time that the candidates use the
same (versus different) tone, the length of each type of equilibrium, and finally the interaction between the
candidates.
For each of these analyses we need to calculate the probability that the message of, say, candidate j is
4 Of course, another way to write equation (1) would be by subtracting from each candidate her bad traits rather than adding
them to her rival. The two approaches are identical in our setting.
6
negative at time t for t = 1, 2, 3. To simplify the exposition, let nj,t be an indicator variable equal to 1 if the
message of candidate j is about j 0 s bad trait (i.e., mj,t = {minor bad trait of j 0 } or {major bad trait of j 0 } )
and 0 otherwise.
We note that it is easy to show that in all but one case, the decisions of a forward-looking candidate are
the same as those of a myopic candidate. Further, for this one specific sequence of events, forward-looking
candidates would only differ for a subset of the parameter space. To assist the reader in following the model’s
solution we start by presenting it for a myopic candidate and then describe the solution for a forward-looking
one.
2.2.1
To increase or decrease, and when? (The pattern of negativity)
The simplest probability of negativity, corresponding to the first period, is:
prob(nj,1 = 1) = q H + q L q H
(2)
The intuition behind this is as follows: First, it is easy to show that if the candidate finds a major bad trait
in period 1 she has no incentive to delay using it. This event is captured by the first element in equation (2).
Second, if she discovers a minor bad trait, she uses it only if the media covers the campaign (otherwise using
one of her good traits is more effective).5 Note that the media covers the campaign in the first period only
if her rival found a major bad trait (and uses it, which as already mentioned is always optimal). This event
is captured by the second element in (2), q L q H . Third, of course, if she finds no bad trait she has to air an
ad about one of her good traits.
The probability of negativity for the second period is:
prob(nj,2 = 1) = q H + q L q H + q L (1 − q H ) q H 2 − q H + 1 − q L − q H q H (1 − q H )q L
(3)
where the first two elements are exactly the same as in the corresponding probability for the first period and
for the same reasons. The next two elements represent two dynamic forces in this model, linking actions
across time. The intuition behind these two elements is as follows: unlike period 1, in period 2 a candidate
airs an ad with a minor bad trait even if her rival did not reveal a major bad trait at the same time. This
happens either (a) if any of the candidates revealed a major bad trait in the previous period which led the
media to cover the campaign in periods 1 and 2, and she draws a minor bad trait in period 2, or (b) if she
has an unused minor bad trait from period 1 and her rival aired a major bad trait in this period (leading
the media to start covering the campaign). The first event, which we term the “continued coverage effect”
5 Recall
that v G >v L and that δv L >v G .
7
is captured by the third element in equation (3), and the second event, which we term the “stock effect” is
represented by the fourth element in this equation.6 These two dynamic aspects lead to an increase in the
tendency to “go negative” in the second period compared with the first.7 In other words, consistent with the
first empirical regularity, the model implies an increase in negativity between the first and the second period.
The probability that j is negative in the third period is:
prob(nj,3 = 1) = q H + q L q H + q L (1 − q H ) q H 2 − q H
2
+ 1 − q H − q L q H 1 − q H q L 2 − q L − 2q H
(4)
The only difference between the probabilities of negativity in periods 2 and 3 is in the last element, the
“stock effect”, which is now multiplied by 1 − q H 2 − q L − 2q H . Since 1 − q H 2 − q L − 2q H can be
either above or below 1, negativity might increase or decrease in the last period.8 The following statement
summarizes this result.
Implication 1: For any value of q L and q H , negativity is more likely in the second period than in the first
(i.e. prob(nj,2 = 1) > prob(nj,1 = 1) j ∈ {1, 2}). In contrast, the relationship between negativity
in the third and the second periods depends on the specific parameter values. For some, negativity
is more likely in the third than in the second (i.e. prob(nj,3 = 1) > prob(nj,2 = 1) j ∈ {1, 2}) and
for others it is less likely (i.e. prob(nj,3 = 1) < prob(nj,2 = 1) j ∈ {1, 2}).
The logic behind this result is the following. In the transition from period 1 to 2 the stock can only increase
(since it is zero in the first period) leading to a higher potential for negativity. However, in the transition
between periods 2 and 3, the stock can either increase (due to the increase in the length of time in which the
candidate can build a stock) or decrease (due to the increase in the opportunities to use the stock) leading
to an ambiguous effect on negativity.
Panel (a) in Figure 1 highlights the parameter space that leads to an increase versus a decrease in negativity
from the second to the third period. The figure illustrates that a downtrend in negativity (red/dark area) is
indeed consistent with a meaningful subset of the parameter space.
6 Specifically,
the “continued coverage effect” is represented by q L (1 − q H ) q H 2 − q H . The first two elements capture the
case in which in this period candidate j found a minor bad trait while her rival found nothing and the element q H 2 − q H
is the probability
that the media started covering the campaign in the previous period. The “stock effect” is represented by
1 − q L − q H q H (1 − q H )q L . The first two elements stand for the case that, in the second period, candidate j did not find
anything about her rival, but the rival did. Specifically, he revealed a major bad trait that then led to media coverage. In such
a case, candidate j cannot send any negative ads unless she uncovered a bad trait in period 1, but was not able to use it. The
probability of this event is (1 − q H )q L .
7 Formally, we find that:
h
i prob(nj,2 = 1) − prob(nj,1 = 1) = q L (1 − q H ) q H 2 − q H + 1 − q L − q H q H (1 − q H )q L > 0
8 For
example, this element is equal to
9
20
when q H = 0.5 and q L = 0.1 and it is equal to
8
117
100
when q H = 0.1 and q L = 0.5.
Figure 1: Change in Negativity from 2nd to 3rd Period (for Myopic and Forward-looking with Waiting):
Yellow (light) area is where negativity increases, and red (dark) area is where it decreases from the second
to the third period.
Furthermore, the left panel (for myopic candidates) identifies the role of q H and q L in determining whether
we get a downtrend or an uptrend in the third period. It shows that an uptrend is more consistent with
high q L rather than high q H (e.g. q L values as high as 1 can support the uptrend in negativity, whereas only
values less than .3 for q H can support it). This is due to the fact that q L (the chance of finding a minor
bad trait) is building a stock while q H (the chance of finding a major bad trait and thus getting the media
interested in the campaign) is draining it.
As mentioned above, when candidates are forward-looking the solution needs to be adjusted. It is easy
to show that a forward-looking candidate might delay the use of major dirt found on her rival in the second
period in one specific sequence of events and for a subset of the parameter space (see Appendix C). This
happens when a candidate who found no dirt on her rival in the first period and a major bad trait in the
second faces an opponent who found a minor bad trait in both periods.9 In such a case, if candidate j uses
the major bad trait immediately, the media would cover the campaign in periods 2 and 3 and her rival would
use both minor bad traits. If she waits, her rival would use only one minor bad trait. At the same time, there
are still reasons for her to act immediately (e.g. the prospect that she will reveal another major bad trait in
the next period and would be able to use it as well). Accordingly, her decision to delay or not depends on
the prospects of finding yet more dirt in period 3 (i.e. on q L and q H ) and on the value of each outcome (i.e.
G L H
v , v , v ). The subset of the parameter space for which delay is appealing is identified in Appendix C
and denoted by R.
9 Note
that we assume that the fruits of this effort are common knowledge.
9
For this subset of the parameter space, panel (b) of figure 1 presents the areas for which there is an increase
versus a decrease in negativity from the second to the third period. Since the forward-looking incentive to
delay implies that negativity might move from the second to the third period, the downtrend in negativity
(red/dark area) is less common. That said, even for this subset of the parameter space we still find that
negativity might decrease toward the end of the campaign.
For illustrative purposes, consider the pair of parameters q L = 0.4 and q H = 0.25. For this pair, there is
an downtrend in negativity in period 3 outside of R and an uptrend inside R. In other words, for this pair,
the trend depends on v G , v L , v H . Note that the pair q L = 0.4 and q H = 0.25 is reasonable and will be
used in the next subsections for illustrative purposes. It is reasonable because it means that the probability
of finding a minor bad trait is more likely than the prospect of revealing nothing (0.4 > 0.35) and it is much
more likely than the probability of digging up a major bad trait (0.4 > 0.25).
The downtrend in negativity close to Election day is a novel and testable implication. Furthermore, it is
inconsistent with one of the empirical regularities that motivated this study – i.e. that negativity increases
throughout the campaign. In the empirical work below we will revisit this empirical regularity and examine
more carefully the tone of the campaign close to Election day in order to test the model’s implication.
To be clear, the specifics of our results – the increase in negativity in the second period and a possible
decrease in the last – are closely related to the specifics of the model and especially to (a) the use of a
three period model and (b) allowing only one period of continued coverage. However, the model provides
value above and beyond the specifics of the results – especially by highlighting some interesting aspects of
the patterns of negativity that have not been discussed before, such as the “stock effect,” the “continued
coverage effect,” and the forward-looking incentive to delay.
From an intuitive standpoint, by identifying the dynamic effects, the model suggests that at some point
in a campaign, one of the candidates is likely to uncover severely damaging information on her competitor
and use it in her ads. This is going to attract the attention of the news media covering this race. The
media coverage and its focus on negativity will encourage both candidates to use any stocked information
they have on their competitor’s bad traits, as their value is now enhanced. Thus, the race will enter a phase
of intense negativity. This phase will end when either the media loses interest in the story or the stock of
new information runs dry. Of course, in practice it is possible for a race to experience more than one span
of negativity. Furthermore, at the aggregate level, given the randomness of the process of uncovering dirt,
as the campaign proceeds we should expect to find more and more races getting into a negativity span and
that on average negativity is expected to rise and then possibly fall.
10
Figure 2: Probability of both players having the same tone
2.2.2
To adopt the same (or different) tone, and for how long?
We are now ready to look more closely at the actions of the candidates and see whether they tend to adopt
the same tone (in this subsection) and whether they tend to move together (in the next subsection). In
Appendix C.3 we prove the following result.
Implication 2: Candidates are more likely to use the same tone than take different tones (i.e. prob(nj,t =
nj 0 ,t ) > prob(nj,t 6= nj 0 ,t ) for every t).
This result is also illustrated in Figure 2 which details the probabilities under the full range of parameters.
In the figure, the area in which the probability of using different tones is the highest is for q H around 0.5 and
for q L close to zero. The rationale behind this is that for these values the chances are highest that one of the
candidates reveals a major bad trait about her rival and the rival cannot respond (unless he also happened
to reveal a major bad trait). The probability that the two candidate are using the same tone is higher the
lighter the area in the figure. However, while the light areas with high q H are characterized by a negative
tone by both candidates, those with low q H are characterized by a positive tone. For the parameters we use
for illustrative purposes (i.e. q L = 0.4 and q H = 0.25) the probability that the two candidates are using the
same tone is quite high, namely 0.79.
During the campaign the equilibrium tone is likely to switch, as illustrated in subsection 2.2.1. For
example, a positive span in the beginning of the campaign might be followed by a negative one. This raises
a question with respect to the length of each one of the possible spans. For example, which span is likely
to last longer: positive or negative? Figure 3 addresses this question for forward-looking candidates (the
myopic case is quite similar). The figure illustrates that the answer depends on the values of both q L and q H .
11
Figure 3: Average length of span of each action pair for forward-looking candidates (myopic is qualitatively
similar).
Consider first low values of q L (which also means low stock levels): for low values of q H we can expect long
spans of positivity; for medium values of q H we expect long spans in which one of the candidates is using a
negative tone while the rival’s messages are positive; and finally, for high values of q H , the longest spans are
for negative messages by both candidates. Now consider higher values of q L : the implications for the same
tone spans are quite similar to the above, but the “different tone spans” are much shorter. The rationale is
simple: for high levels of q L the prospect that one candidate goes negative while the rival cannot match is
low. For the parameters we use for illustrative purposes the length of the positive span is longer than the
negative one (1.27 versus 1.03) and both are longer than the “different tone” case (0.54).
We return to the issues discussed in this subsection shortly, using data to examine empirically whether
same tone is indeed more common. Furthermore, we also estimate the length of each type of span.
2.2.3
To move together or not? (The interaction between the candidates)
As in any competitive setting, we are interested in the interaction between the players. In this specific setting
it is interesting to examine whether a candidate is more likely to change tone when the rival adopts a new
tone. In other words, do the candidates tend to change their tone together or not? Furthermore, we find it
especially interesting to analyze the candidates’ tendency to move together following a period in which both
used the same tone – positive or negative.
12
Figure 4: Reaction to competitor tone switches in period 3: Panel (a) is the increase in the probability of
going negative in response to the rival’s switching to a negative tone as compared to when the rival stays
positive, (b) is the same but for a switch to positive tone, and (c) is the difference between (a) and (b). The
figure contains probability increases, not percentage increases.
Letting pt (a | b, c, d) = P rob (nj,t = a|nj 0 ,t = b, nj,t−1 = c, nj 0 ,t−1 = d), the following statement summarizes the result (which is shown in appendix C.2).
Implication 3:
(a)
Following a period in which both candidates used a positive tone, a candidate is more likely to
adopt a negative tone when her rival switches his tone to negative than when he does not (i.e.,
pt (1|1, 0, 0) > pt (1|0, 0, 0) for every t).
(b)
However, following a period in which both candidates were negative, their choices of switching to
a positive tone are independent in period 2 (i.e., p2 (0|0, 1, 1) = p2 (0|1, 1, 1)), and
(c)
for period 3:
p3 (1|1,0,0)
p3 (1|0,0,0)
>
p3 (0|0,1,1)
p3 (0|1,1,1)
> 1.
In other words, the effect of switching tone following both players having a common tone depends on whether
the common tone is positive or negative. In particular, switching toward negative seems to be more “contagious.” We refer to this phenomena as an “asymmetric interaction.” The technical details behind these
findings appear in appendix C.2. However, figure 4 provides a numerical illustration of this asymmetry for
the transition from period 2 to 3. Note that the forward-looking considerations are taken into account both
in the appendix and in the figures.
In figure 4 panel (a), the axes represent q L and q H and the contours indicate the increase in the probability
13
of shifting toward negative in period 3 when the opponent adopts a negative tone. As should be apparent,
the likelihood of moving together in the negative direction is always positive and quite high for much of
the parameter space. In contrast, figure 4 panel (b) demonstrates that the likelihood of moving together
in the positive direction is high for a only small subset of the parameter space. Finally, figure 4 panel (c),
which represents the difference between the first two figures, reveals visually the asymmetry in the interaction
between the candidates: at every point in the feasible parameter space, the likelihood of moving together
in the negative direction is larger than such a move in the positive direction and for much of the parameter
space it is considerably larger.
The intuition behind the “asymmetric interaction” relies on the role of the media coverage. In our model,
switching to a negative tone when both players were previously positive implies that the media is starting
to cover the campaign. This coverage increases the attractiveness of using an available minor bad trait and
thus the likelihood of both players switching to negative. Note that if candidate j found a major bad trait
and goes negative, the only event in which her rival does not do the same is if he has no negative traits in
his stock and found none this period as well.
Switching to positive is quite different. In fact, if both players were negative in period 2, there is only one
case in which the move by one player depends on the move by the other in period 3. The specifics of the case
are: (i) in period 1, at least one of the candidates found a major bad trait, (ii) in period 2, both candidates
found a minor bad trait, and (iii) in period 3, candidate j found a minor bad trait. In such a case, candidate
j’s action depends on whether her rival j 0 found a major bad trait or not. Specifically, if her rival was not
able to find a major bad trait, he will have to switch to a positive tone and she will have to do the same.
To get a sense of the magnitude of this effect, consider the parameters we have been using for illustrative purposes (q H = 0.25 and q L = 0.4).
For these values, we get that the probabilities of j
turning negative conditional on the action of j 0 are P rob (nj,3 = 1|nj 0 ,3 = 1, nj,2 = nj 0 ,2 = 0) = 0.929 and
P rob (nj,3 = 1|nj 0 ,3 = 0, nj,2 = nj 0 ,2 = 0) = 0.049. In contrast, the probabilities for turning positive are
P rob (nj,3 = 0|nj 0 ,3 = 0, nj,2 = nj 0 ,2 = 1) = 0.49 and P rob (nj,3 = 0|nj 0 ,3 = 1, nj,2 = nj 0 ,2 = 1) = 0.24. Thus,
while the lift in negativity is over 0.88, the lift in positivity is less than 0.25. Figure 4 panel (c) illustrates
that this magnitude is widespread for moderate levels of q L and for moderate and higher levels of q H .
This “asymmetric interaction” is a sharp and novel result that enables us to go to the data with a clear
and discriminating test. Specifically, it is interesting to examine in the data whether the tendency to move
together (following a period in which both candidates used the same tone) indeed depends on whether the
switch is toward negative or positive. Furthermore, the asymmetry may explain why previous studies – which
did not distinguish between periods of increases and decreases in negativity – found only a relatively weak
correlation between the actions of the candidates.
14
Before moving into the description of the data, the estimation and the results, let’s summarize the main
takeaways from the model. First, negativity should increase during the campaign but it may decrease
towards its final days. Second, candidates tend to adopt the same tone rather than use different ones. Third,
candidates are likely to move together in the tone of their ads and such tendency is especially high when
the move is in the negative direction. In the empirical analysis, we test these implications directly and also
examine some additional implications identified in this theoretical section, such as the length of “tone spans”
and the role of the news media.
3
Data and Analysis
3.1
Data description
Our data focus on the U.S. congressional elections held in 2000, 2002, and 2004 and include time series
information on both advertising tone and media coverage within each race.
The advertising tone data are based on a technology developed by the Campaign Media Analysis Group
(CMAG)that records every ad on broadcast TV and some cable channels in a storyboard format. These
data provide advertising for all candidates who ran in the races contained in the top 75 Nielsen designated
media areas (DMAs) in 2000 and the top 100 DMAs in 2002 and 2004. Since the traditional kick-off of the
advertising campaign is Labor Day, the timeframe of our analysis is the 70 days leading up to Election Day
when most advertising spending occurs. To obtain a sample relevant to our theoretical framework, we only
include races with two major parties and some advertising on at least one day in the 70 day period. This
results in 249 races and 498 major party candidates.
The CMAG data contain thousands of unique advertisements. This information is coded by the Wisconsin
Advertising Project (WAP) along various dimensions. Central to this study, the data contain information on
who the ad supports, when it was aired, and what tone it took. The original tone categories are “promote,”
“attack,” and “contrast.” We follow the prior literature (Lovett and Shachar 2011) and code each ad as either
negative (contrast or attack, to reflect at least some discussion of the opponent) or positive (promote). While
on 53% of days candidates choose not to air ads, 85% of these are before the candidate airs their first ad of
the campaign. After airing the first ad it is quite rare to find days without ads (only 15%).10 At the same
time, on 25% of days the candidate airs both some positive and some negative ads. Accordingly, we treat
candidates as having three possible strategic positions when airing at least one ad: positive (all positive ads),
negative (all negative ads), or mixed (some positive and some negative ads). We note that the composition
10 For the analysis in subsection 3.4 we need to code the tone for any day after the first ad was aired. For days without ads we
assumed that the tone remained as in the last advertising day. We have tested robustness against alternative approaches (e.g.
dropping cases with no advertising) and find qualitatively similar results.
15
Unconditional on Switching
From Negative
From Mixed
From Positive
From No Ads
To Negative
0.89
0.07
0.00
0.01
To Mixed
0.07
0.88
0.04
0.00
To Positive
0.00
0.03
0.90
0.03
To No Ads
0.04
0.02
0.05
0.95
Conditional on Switching
From Negative
From Mixed
From Positive
From No Ads
To Negative
0
0.62
0.04
0.28
To Mixed
0.61
0
0.46
0.06
To Positive
0.04
0.24
0
0.67
To No Ads
0.35
0.15
0.50
0
Table 1: Observed Tone Switching Probabilities
of ads within days that are mixed is tilted towards negative (60 versus 40 in terms of percentage) and that
of all days on which a candidate airs an ad, 41 percent are only positive ads, 30 percent only negative, and
29 percent mixed.
The media coverage data are based on information from a well-known source – newslibrary.com. Using
the web search tool on newslibrary.com, we obtain the total number of articles in local newspapers pertaining
to each candidate on a given day. To bolster the precision of our measure (i.e., to ensure all relevant articles
are included) we used various alternative spellings for each candidate in the search tool. We describe the
specific construction of the media variable later (when it is used).
While the model considered a three period campaign, the data cover 70 days. Since we do not wish
to structurally estimate the model but rather to test its implications (e.g., the candidates are likely to use
the same tone), the mismatch in the units of time does not pose a problem. This mismatch requires only
one adjustment: in the analysis of the interaction between the candidates we do not require them to “move
together” on the same day but rather within a time frame of a few days (as explained in subsection 3.4).
3.2
To increase or decrease, and when? (The pattern of negativity)
In this subsection we examine the first implication of the theoretical model – that negativity should increase
over the course of the race, but might decrease towards the end. To get a preliminary “feel” for the issue we
start with some descriptive statistics, before moving to the direct evidence.
Table 1 provides an initial view into the nature of switching across races. The upper part of the table
presents the transition matrix where the rows represent the tone on day d − 1 and the columns the tone on
day d. While a tone tends to persist for a while, changes in tone are not rare. For example, if a candidate ran
a positive campaign in d − 1, there is an almost ten percent chance that she will switch tone on the following
day. Given that the unit of time in the table is a day, this implies that switching is quite common.
The lower part of the table presents the same matrix but only for days in which the candidate switched
16
10
20
30
40
50
60
70
0.0 0.5 1.0
−1.0
Neg (−1), Mixed (0), and Pos (1)
0.0 0.5 1.0
−1.0
Neg (−1), Mixed (0), and Pos (1)
0
0
10
20
10
20
30
40
50
60
70
40
50
60
70
50
60
70
Day (70=election)
0.0 0.5 1.0
−1.0
Neg (−1), Mixed (0), and Pos (1)
0.0 0.5 1.0
0
30
Day (70=election)
−1.0
Neg (−1), Mixed (0), and Pos (1)
Day (70=election)
0
10
20
30
40
Day (70=election)
Figure 5: Example Advertising Strategies Over Time
(thus, the diagonal includes only zeros). The main insights from this view of the data are that: after a period
with no ads (which occurs mostly in the first days of the campaign) candidates tend to adopt a positive
tone; after a period with a positive tone they tend to either switch back to “no ads” or to “mixed”; from
“mixed” they tend to switch to negative. In other words, a likely pattern is no ads, positive, mixed and then
negative.11
This “likely pattern” is quite consistent with the empirical regularity we started with. This pattern comes
across also in the four races included for illustration in Figure 5. For each day in each race, the figure presents
the tone category selected by each of the two candidates (one candidate in black/dark and the opponent in
red/light). Indeed, the tendency to shift toward negative is apparent even with this crude measure. A key
goal of the analysis below is to examine this in a systematic way and to see whether this trend might change
close to Election Day – a possibility raised by our model. To do that we aggregate across all races.
The result of this aggregation appears in the first panel of Figure 6 which reports, for every day, the
percent of candidates who aired only positive ads (dashed line), alongside those who aired only negative
(black line), and those who used mixed (red/gray line). The trend is clear and is consistent with the basic
prediction of the model – there is a decreasing pattern for positive advertising and increasing pattern for
11 Other observations from the table are: direct shifts between positive and negative are relatively rare, with mixed being a
more common transition; and shifting to mixed from negative is more common than the reverse.
17
negative and mixed for most of the campaign. This finding is also consistent with Goldstein and Freedman
(2002). A novel implication of the model above relates to the the pattern in the final days before the elections.
It turns out that, as suggested by the model, in the last ten days of the campaigns, we observe a decline
in negativity. Specifically, the difference between the negativity at the peak, 10 days before the end of the
race, and negativity on the last day is significant (mean=0.078, p-value=.02). In contrast, the proportion of
candidates who adopt “only positive ads” and “mixed” strategies each increase slightly during this period.
To examine the robustness of this novel finding, we check whether it is due to a selection bias. Specifically,
it is possible that the decline in negativity close to Election Day is due not to a shift in the behavior of the
candidates, as suggested by our theory, but rather by candidates with low budgets entering races late.
Specifically, say that candidates with low budgets can only afford to advertise close to Election Day and
further that (for one reason or another) they tend to adopt positive messages (for example, we have already
shown that campaigns tend to start positive). If so, the evidence presented above, at the aggregate level,
would not be due to variation in candidates’ actions across time, but rather to variation across candidates
entry patterns.
To explore this possible confound, we split our sample into two parts. In the first segment, we include
only races that began more than a month (30 days) before the election and in the second we include the
rest. The second panel of Figure 6 presents the pattern for the longer races (i.e. those that started more
than a month before the election). The pattern is quite similar to the one reported above with an increase
in the proportion of negative advertising during the campaign up until the last two weeks and then a sharp
decrease until Election Day. In other words, if anything, the phenomenon is even stronger when one focuses
on the longer races. As before, the difference between the peak at 16 days before the end of the race and the
last day is statistically significant (mean=0.121, p-value=.004). It turns out that the same pattern exists for
the shorter races as well. As one might expect though, the turning point for the shorter races occurs even
closer to Election Day – negativity drops sharply in the last six days of the campaign (last panel of Figure
6). However, in this case, the decline is not statistically significant from the peak at 6 days before to the end
of the race (mean=.062, p-value=0.22) possibly due to the smaller sample size.
Another way to see these trends is by fitting a polynomial on the campaign-level negativity data. The
results of such an analysis (using a cubic polynomial) for all three cases (i.e., all races, those that started late,
and those that started early) are presented in Figure 7, which depicts the predicted values for the negativity
trend throughout the campaign. With this approximation, the decreasing negativity in the latter part of the
race is clear in all three cases (details of the fitted polynomials are discussed in appendix B). This evidence
further supports the phenomenon of decreasing negativity late in the race.
Overall, this evidence sheds a new light on the pattern of negativity. While previous studies suggested
18
Figure 6: Aggregate Advertising Strategies Conditional on Advertising
that negativity peaks close to Election day, our findings demonstrate that it peaks approximately two weeks
earlier. Our theoretical model (which motivated this examination) offers one interpretation of this result –
during the campaign the candidates have enough opportunities to use the information on the bad traits of
their opponent, and close to Election day they run out of stock. Recall that in the model the candidates are
forward looking and their incentive to delay the use of the bad traits is accounted for.
3.3
To adopt the same (or different) tone, and for how long?
The model suggests (Implication 2) that the candidates are more likely to use the same tone than to differ
in tone. Using the categorization of negative-mixed-positive (i.e., post first ad) we find that in 51% of the
observations the candidates use the same tone (e.g., the two candidates are purely negative in their messages).
This percentage increases to 73% when we lump together the “mixed” and “negative” categories. Using such
a categorization makes sense for three reasons: (1) the model only allows two categories, (2) as mentioned
above, the composition of ads within days that are mixed is tilted towards negative, and (3) while “mixed”
include some positive ads, such days are likely to be perceived as part of a “negative span.”
The histograms in Figure 8 provide additional details on the degree of synchronization in the actions
of the candidates. These histograms not only split the “same tone” category between days in which the
competing candidates are negative, mixed, or positive, but they also present the length of each span. The
first insight from these histograms is that there are more observations in which the two candidates adopt a
19
Figure 7: Aggregate Proportion Negative Against Fitted Proportion Negative
20
Figure 8: Histogram of span lengths for action pairs
positive tone than occasions in which both adopt a negative tone (132 versus 120).
Furthermore, it turns out that “positive spans” are not only more common, but also longer – on average
a positive period lasts 10.1 days versus 6.1 days for pure negative spans.12 This finding portrays a world in
which both candidates air positive messages as the default state, but one that is interrupted by quick bursts
of negativity. This perspective might also suggest that states in which one candidate uses a positive tone
while her rival adopts a negative one are transitory by their nature. The data in Figure 8 on the frequency
and length of such states seem to support this perspective. These states are very common (there are more
such spans than when candidates are on the same tone), but at the same time brief. The average length in
days for asymmetric tone spans is 4.3, 4.5, and 3.8 for negative-mixed, negative-positive, and mixed-positive,
respectively.
3.4
To move together or not? (The interaction between the candidates)
An important and unique prediction of the model (Implication 3) is the asymmetry in the interaction between
the candidates. Specifically, we show theoretically that following a period in which both candidates used a
positive tone, a candidate’s decision to switch to a negative tone depends on the choice of her rival: she is
more likely to go negative if her rival switched tone than if he did not. However, switching tone following a
12 Of
course, lumping negative and mixed together leads to longer span length (10.6).
21
period in which both were negative is either independent on her rival’s behavior or weakly dependent.
In the logistic regression analysis below, we analyze this implication of the model. Our sample for this
analysis only includes observations that come immediately after periods in which the two candidates adopted
the same tone (be it positive or negative). The theory implies that when there is a switch in tone by the rival
candidate, the focal candidate is likely to do the same and switch her tone as well. We now translate this
implication from the theoretical model to an empirical analogue in our daily data. Consider the following
illustrative case. In day d, the two candidates air positive messages. On the following day, d + 1, the focal
candidate stays positive, but the rival candidate switches tone. Our model predicts that the focal candidate
is likely to switch tone as well on day d + 2.
Our regressors capture the actions of the candidates on d+1 and the dependent variable captures the choice
of the focal candidate on day d+2. Specifically, the regressors are focal stay and focal stay*rival switch where
focal stay is an indicator variable for the event that the focal candidate does not change tone on d + 1 while
focal stay*rival switch is an indicator variable for the event that the rival switches tone on that day, d + 1.
The dependent variable is focal switch, an indicator variable for the event that the focal candidate switches
tone on day d + 2. The test of our theory rests on the coefficient of the interaction variable focal stay*rival
switch. We expect it to be positive – i.e. if following a day in which the two candidates adopted a positive
tone one of them switched, the other will do the same. Furthermore, our theory also suggests that in the
mirror case – i.e., the one in which the two candidates adopted a negative tone initially – the coefficient will
be either close to zero or zero.
The full regression reported in Table 2 appears more involved than the one described, but the basic logic
is the same. Here is a brief description of all additional elements in this table. First, we pool together the
cases in which in day d the two candidates adopted a positive tone with the cases in which both aired only
negative ads. As a result, the variable rival switch can be either rival switch negative or rival switch positive.
Second, we control for day of week effects, time trends, time since last switch, and (since, as shown above,
the tone of the campaign tends to become more negative), we allow the time trends to depend on the tone
adopted by both candidates on day d. We expect candidates’ switching probabilities to be higher (as time
passes) when their tone on day d is positive rather than negative and the empirical model will allow for
this.13 Third, since it is not clear a priori how many days it takes for a candidate to react to a switch by her
rival, we estimate the model several ways, each time using a different lag between the day in which the rival
switched and the one in which the focal candidate might change tone (or not). The number of days between
the two is denoted by k, where k ∈ {1, 2, 3, 4}. The sample sizes for each of these models are around 5000.14
13 The
rationale behind the inclusion of the “time since last switch” variable relates to the wear-out effect of advertising.
The specific numbers are 5216, 5094, 4990, and 4876 for k = 1, . . . , 4 respectively. The size of the samples decreases
with k because the number of observed advertising periods declines with further lags (i.e., as one gets earlier in the election
14 (a)
22
The estimates, reported in Table 2, are consistent with the model’s implications and shed new light on
the nature of negative advertising competition. First, when a candidate is switching tone and becomes more
positive, the focal candidate does not do the same on any of the following days. Specifically, the coefficients
of focal stay*rival switch positive vary widely, ranging from -0.35 (for a lag of four days) to 0.71 (for a lag
of two days) and none of them are significantly different from zero.15 Second, consistent with our theory,
whereas candidates do not move together with their rival when he changes his tone to positive, they do move
together when the rival becomes more negative. This result holds almost irrespective of the length of the
lag.16 Furthermore, the coefficient of focal stay*rival switch negative is quite stable – ranging from 0.66 to
0.82.
To illustrate the magnitude of these effects we consider the probability of a specific, yet representative
case. The case is the third day of the week, after 7 days with the same tone and 40 days since the beginning
of the race.17 In this case, when the opponent stays positive,the probability that the focal candidate turns
negative on the following day, i.e. k = 1, is 0.05. On the other hand, this probability jumps by 86 percent to
0.093 if the opponent would have switched his tone to negative. Note that the increase by over 80 percent
is not unique to the representative case selected. Furthermore, the projected increase is even more dramatic
for k 6= 1 – e.g., for k = 3 the increase in the probability is of 115 percent. Thus, the tendency to move
together in tone is not only statistically significant, but also very meaningful. A key aspect of these estimates
is that both implications are supported by the data and thus, as predicted by the model, there is a significant
asymmetry in the tendency of the candidates to move together in the positive versus the negative direction.
These estimates demonstrate, for the first time, that there is a clear interaction between the candidates in
the dynamics in the tone of political campaigns. While in subsection 3.3 we have shown that, in each point
in time, the candidates are more likely to use the same tone rather than different, here we show that they
also tend to move together. This evidence sheds new light on the use of tone in political campaigns. The
theory presented in section 2 offers an interpretation of these new findings. Furthermore, by showing that
the interaction is different between positive and negative switches, we also provide an explanation for why
earlier studies (who lumped together the two types of switches) did not find solid support for the interaction
campaign). Note, that the number of observations takes into account also the missing observations for the media coverage
variable (used in the next subsection). This is done for ease of comparison between the results of this subsection and the next
one. The results of this subsection are not sensitive to this choice.
(b) Two final technical notes on the setting of the estimation. First, in the analysis we focus on cases in which the rival (who
switched tone on d) did not switch back on d + k for any k ≤ 4. Second, any switch in tone (e.g. switching from positive to
mixed or positive to negative) is counted as a switch in the analysis.
15 For k = 2, the point estimate for a reaction to a positive switch is largest and nearly significant at the 0.05 level, but still
smaller than that of negative in the same period.
16 It does not hold for an immediate reply – i.e. within one day. Note though, that even in the one day case the coefficient
has the expected sign and the value of the t-statistics is quite high – 1.93. Later we discuss a potential reason for the lower
significance in that day.
17 While, of course, the exact numbers differ for different days into the race, day of the week, and time since last tone switch,
the basic pattern is similar. Most cases have a difference whose relative magnitude is similar to this.
23
Base Change Rate
Lag 1
−1.33
(.517)
(.508)
(.533)
(.540)
SelfSame
−1.83
−1.65
−1.17
−.912
(.212)
(.198)
(.204)
(.213)
.664
.726
.819
.785
(.344)
(.363)
(.364)
(.385)
SelfSame OppMoreNeg
SelfSame OppMorePos
Time Trend Neg/100
(Time Trend Neg/100)2
(Time Trend Neg/100)
3
Time Trend Pos/100
(Time Trend Pos/100)2
Lag 2
−1.46
Lag 3
−2.20
Lag 4
−2.26
.358
.713
−.121
−.348
(.385)
(.390)
(.604)
(.730)
−2.33
−1.38
2.88
3.59
(5.36)
(5.24)
(5.42)
(5.43)
−.805
17.4
15.1
2.00
(17.6)
(17.0)
(17.2)
(17.3)
−21.3
−20.6
−8.89
−6.39
(16.4)
(16.9)
(16.4)
(16.4)
−1.47
3.52
6.21
5.67
(5.48)
(5.36)
(5.66)
(5.81)
−7.14
18.9
−4.92
−9.20
(19.0)
(18.3)
(19.3)
(19.9)
−26.0
−.307
.080
−2.20
(18.6)
(17.8)
(18.9)
(19.4)
−.636
−.864
−1.68
−2.80
(1.75)
(1.81)
(1.91)
(2.05)
.089
1.49
3.17
5.10
(3.91)
(3.85)
(3.91)
(4.09)
−.178
.205
−.047
−.173
(.219)
(.212)
(.209)
(.215)
.194
.201
.174
.062
(.203)
(.197)
(.202)
(.199)
−.216
−.495
−.538
−.660
(.226)
(.235)
(.234)
(.235)
DayOfWeek 4
−1.40
−1.02
−1.08
−.872
(.329)
(.266)
(.270)
(.244)
DayOfWeek 5
−.345
−.340
−.254
−.485
(.229)
(.215)
(.211)
(.220)
DayOfWeek 6
−.260
−.134
−.141
−.201
(.221)
(.203)
(.207)
(.209)
ln(Likelihood)
1018.1
1095.4
1094.9
1075.4
(Time Trend Pos/100)3
Time Since Switch/100
(Time Since Switch/100)2
DayOfWeek 1
DayOfWeek 2
DayOfWeek 3
Table 2: Candidate Reactions
24
Figure 9: Media coverage time patterns: Average daily (black solid line) and weekly (red dotted line) media
coverage. Day 70 is election day.
between the actions of the candidates - the optimal reaction depends on the prior tone.
The coefficients of the control variables are also consistent with expectations. For example, as time passes
the candidates are more likely to switch out of a positive tone state than out of a negative one. Interestingly,
(a) the time trends for both positive and negative suggest increasing probabilities of switching until about the
middle of the race (for instance, for the regression that allows one day to respond (k = 1), that takes place
around week 39 and 42, respectively, for positive and negative), when the probability begins to decrease,
and (b) we find that the tendency to switch tone among these races is lowest on Sunday. We also note
that the control variables are estimated with similar values across the four lags (except for the day of the
week variables, which change meaning because of the different lags). Furthermore, the results above are not
sensitive to the inclusion (or exclusion) of these control variables.
3.4.1
Media and the tendency to move together
While none of the model’s implications mention the news media, the data we collected on the media might
be able to shed some preliminary light on the conditions under which the candidates move together or not.
25
Recall that, in the theoretical model, the tendency to move together in the negative direction is due to
the media’s bias toward negativity. Specifically, this bias implies that, when one of the candidates reveals a
major bad trait, the media starts covering the campaign and this leads both candidates to use any negative
information they have on their rival sooner rather than later. Therefore we expect that the tendency to move
together in the negative direction would depend on whether the media coverage is indeed high. Accordingly,
we created a binary variable that indicates the top quartile of media coverage (Media High).18 Note also
that given the media’s assumed lack of interest in positive ads and its tendency not to cite such ads, we do
not expect the media to play a role when the rival switches toward positive.
Before presenting the results of this analysis we provide a brief set of descriptive statistics for this variable.
Figure 9 presents the time patterns for daily (black solid line) and weekly (red dotted line) coverage. Three
regularities are evident: (1) the media coverage increases over time, (2) there is some daily seasonality, and
(3) on the top of the daily seasonality, there is large daily variation, even in the average across races. These
patterns suggest that the measure is relatively noisy.
The noisiness of the media coverage variable (which must be partially due to measurement error) calls
for caution in interpreting any results using this variable. Nonetheless, it is worth noting that the pattern of
increase in the media coverage over time is consistent with the idea that media coverage plays a role in the
increase in negativity over time for most of the election campaign.
Table 3 presents the results of the previous analysis (i.e., move together or not) with an interaction with
the media variable. It turns out that the media coverage contributes to the estimation when k = 1 but not
when k > 1 . Let’s start with the case in which the rival became more negative. For k = 1 the candidate
tends to become more negative as well so long as the media coverage is high but not if the coverage is low.
Specifically, the coefficient of focal stay*rival switch negative is 1.49 (1.44 + 0.05) with high media coverage
compared with only 0.05 with lower levels of media coverage and the difference between the two is statistically
significant (1.44 with p-value=0.018).19 This finding is consistent with the model. Furthermore, the results
are also consistent with the model for the case in which the rival became more positive providing further
evidence of the asymmetric movement described above. In such a case the coefficient of focal stay*rival
switch negative is not different from zero for any level of media coverage.
As discussed earlier, our measure of media coverage is quite noisy. Thus, the results here should be
18 Since the focus of our study and analysis is on time-variation within a campaign, we scale the media coverage measure (for
each race) by the total number of articles about the two candidates over the full 70 days before the election. This approach (a)
focuses on daily variation in news coverage, and (b) eliminates race specific effects in media coverage.
19 Recall that the estimate of the “reaction coefficient” was 0.66 when we did not distinguish among the different levels of
media coverage (Table 2). Moreover, this coefficient was not significant in Table 2 and now it is. Note that this pattern can
help to explain why we did not obtain a significant effect for a lag of one day in the analysis of section 3.4. Specifically, we were
mixing cases where the candidate wished to respond because media was high with cases where they did not wish to respond
because media was low.
26
Base Change Rate
Lag 1
−1.32
(.517)
(.507)
(.534)
(.539)
SelfSame
−1.83
−1.65
−1.17
−.907
(.212)
(.198)
(.204)
(.213)
.052
1.02
.910
.780
(.522)
(.390)
(.412)
(.441)
SelfSame OppMoreNeg
SelfSame OppMorePos
SelfSame OppMoreNeg MediaHigh
SelfSame OppMorePos MediaHigh
Time Trend Neg/100
(Time Trend Neg/100)2
Lag 2
−1.44
Lag 3
−2.19
Lag 4
−2.26
.176
.683
−.260
−7.20
(.477)
(.487)
(.733)
(26.6)
1.44
−1.40
−.361
3.47
(.685)
(1.09)
(.842)
(5.42)
.582
.078
.492
7.95
(.773)
(.774)
(1.26)
(26.6)
−2.16
−1.61
2.79
3.47
(5.38)
(5.23)
(5.42)
(5.42)
−.349
16.6
15.7
2.33
(17.6)
(17.0)
(17.2)
(17.2)
(Time Trend Neg/100)3
−20.5
−21.1
−9.19
−6.85
(16.9)
(16.3)
(16.4)
(16.4)
Time Trend Pos/100
−1.29
3.48
6.22
5.71
(5.48)
(5.35)
(5.65)
(5.80)
−7.27
(Time Trend Pos/100)2
18.2
−4.98
−9.27
(19.0)
(18.3)
(19.3)
(19.9)
(Time Trend Pos/100)3
−25.3
−.184
.140
−2.21
(18.5)
(17.8)
(18.8)
(19.4)
Time Since Switch/100
−.725
−.910
−1.67
−2.88
(1.75)
(1.81)
(1.91)
(2.05)
.217
1.64
3.14
5.23
(3.93)
(3.86)
(3.91)
(4.09)
−.190
−.215
−.048
−.168
(.220)
(.212)
(.210)
(.215)
.177
.192
.175
.067
(.203)
(.197)
(.202)
(.199)
−.227
−.506
−.539
−.654
(.226)
(.235)
(.234)
(.235)
DayOfWeek 4
−1.43
−1.02
−1.08
−.874
(.329)
(.266)
(.271)
(.244)
DayOfWeek 5
−.343
−.356
−.253
−.479
(.229)
(.215)
(.211)
(.220)
DayOfWeek 6
−.279
−.139
−.140
−.205
(.222)
(.203)
(.207)
(.209)
ln(Likelihood)
1015.4
1094.3
1094.8
1073.3
(Time Since Switch/100)2
DayOfWeek 1
DayOfWeek 2
DayOfWeek 3
Table 3: The Role of the News Media
interpreted with caution. At the same time, note that the noisiness of this measure might be responsible for
the lack of significance for k > 1.20 Nonetheless, the basic finding of a media amplification is encouraging.
4
Conclusion
This study presents theory and evidence on the dynamics of negative advertising in political campaigns.
Using data from campaigns for the U.S. House of Representatives in 2000, 2002 and 2004 we find that the
tone of the ads tends to become more negative as time passes, but not in the last leg of the campaign, when
it becomes more positive. Candidates tend to adopt the same tone and move together, unless the move is
20 Furthermore, note also that in the model the media react only when the increase in negativity by one of the candidate is
based on a major bad trait. Our data do not differentiate between different types of increases in negativity, which might be also
responsible for the lack of significance for k > 1.
27
in the positive direction, and it seems that the news media is partially responsible for this. Positivity spans
(i.e., periods in which both candidates use a positive tone) are more frequent and longer than negativity
spans and periods in which the candidates are using different tones are common but brief, indicating their
transitory nature.
These new findings on the dynamics and competition in tone of political advertising campaigns were
motivated by a theoretical model and thus can be explained by it. The relationship between the model and
the empirical work has two sides. On the one hand, the model should be considered as only one possible
interpretation of these new empirical findings. These interesting findings call for additional interpretations
and theories that can be suggested and tested by future studies. On the other hand, the model provides some
insights over and beyond its role in motivating and interpreting the empirical work. For example, it identifies
two different reasons to stock-up bad information on a rival. First, when discovering a minor bad trait about
the opponent the candidate stocks up unless the media is covering the campaign. This stocking up effect is
for a simple reason – the direct impact of negative ads on voters depends on media coverage. Second, when
revealing a major bad trait, the forward-looking candidate might stock-up and use it only in the last period
in order to limit her rival’s ability to use all his stock against her. In previous campaigns (e.g., the swiftboat
attack on John Kerry), we have observed such late breaking attacks. Another nice feature of the model is
that it can explain all the empirical findings with only two parameters, q L and q H .
That said, it is worth noting that the theoretical model was not constructed for structural estimation.
It splits the time between Labor Day and Election Day into three major periods, while the data is daily
with 70 time periods. As a result we cannot identify the pair q L , q H that best fits the data. Furthermore,
almost all of the model’s implications hold for any pair of qs. Still, it is encouraging to find that the only
implication that is sensitive to the values of the parameters (i.e., the downtrend in negativity in the last leg
of the campaign) is consistent with the pair used for illustration (q L = 0.4 and q H = 0.25). Recall that this
pair is reasonable because it means that the probability of finding a minor bad trait is more likely than the
prospect of revealing nothing (0.4 > 0.35) and it is much more likely than the probability of digging up a
major bad trait (0.4 > 0.25). Notice that this pair is also consistent with the length of spans as discussed in
subsection 3.3. Future research might enrich the theoretical model to take it directly to data.
The role of media coverage in the model, and to some degree also the preliminary empirical results with
the media coverage variable, identifies a new angle for studies in marketing. While the interaction between the
quantities of advertising and news media (or paid media and earned media) has recently received attention,
this study redirects the focus toward content issues. These issues are not specific to the political setting. For
example, one of the most memorable ads of all time (“1984” by Apple) owes its success to the reaction of the
news media. The content of the ad (which was aired only twice) grabbed the attention of the news media
28
and the rest is history. Future research might wish to enrich our understanding of integrated marketing
communications by adding a “content dimension.” Such effort can benefit from the growing availability of
content analysis in the digital era.
By demonstrating that there are some interesting interactions in the dynamics of a political campaign,
this study might also spark research on related questions such as whether a candidate should start strong or
finish strong and how should she allocate her resources across the “battlefield.” The allocation decision is
similar to the one studied here not only due to its dynamic nature, but also because interaction between the
candidates is likely to play an important role.
29
A
Effect of Tone Changes on Media Coverage
Our model assumes that when dirt surfaces, the campaign becomes more attractive from the news perspective
and the media is more likely to cover it. Here we examine whether media coverage is indeed higher after one of
the candidates shifts toward negative advertising. Such evidence would provide support for the fundamental
underpinnings of our model. Recall that Geer (2012) demonstrates a similar pattern with presidential election
data.
In the analysis we use the data described in Section 3 and the setting discussed in subsection 3.4. Briefly,
the dependent variable is media coverage in period t and we focus on cases in which two periods earlier
the candidates were both positive or both negative. Our independent variables relate to the actions of the
candidates in period t − 1: AnyN egative is an indicator variable for the event that either candidate shifts
negative, and AnyP ositive indicates a shift toward positive. As in subsection 3.4 we also condition on a time
trend, day of week dummies and include an intercept. For this analysis, we have 5,216 cases. The results are
presented in Table 4.
The estimates support the assumptions of the model. First, we find that an opponent’s shift toward
negative advertising leads to a significant increase in media coverage (0.24 with t-stat=2.84). Second, we find
that a shift toward positive does not have any such effect. We also note unsurprisingly that the time trends
(jointly) and day of week effects (jointly, but also mostly individually) also obtain statistical significance.
Although these results are quite encouraging, one should treat them with caution for two reasons. First,
as noted in Section 3, the media coverage data is rather noisy. Second, our model assumes that the media
only responds to negative ads that reveal “major” bad traits. Given that the current empirical test does not
differentiate between high and low bad traits, it does not match one-to-one with the theoretical model. That
said, it seems likely that if we were able to single out the ads with high bad traits, the empirical support
would have been even stronger.
B
Details of Polynomial Time Fitted to Negativity Patterns
We describe here our analyses of the time pattern in negativity. For this analysis, we used a linear regression
of negativity on a polynomial of time before Election Day (where 1 is the day of the election and 70 is 70
days before the election). We applied polynomials of increasing order until no improvement in model fit was
obtained. We applied the analysis to three sets of data (1) the full data, (2) the data containing races that
started less than 30 days before Election Day and (3) those that started more than 30 days before Election
Day.
30
Intercept
1.10
(.127)
MoreNegative
.239
(.084)
MorePositive
.033
(.091)
Time Trend
.553
(1.31)
2
Time Trend
−1.77
(4.14)
Time Trend3
4.61
(3.87)
DayOfWeek 1
.091
(.070)
DayOfWeek 2
−.175
DayOfWeek 3
−.269
(.068)
(.068)
DayOfWeek 4
.411
(.069)
DayOfWeek 5
−.351
DayOfWeek 6
−.083
(.069)
(.068)
R2
.062
Table 4: Media Coverage
Races
All
¿30 Days Before Election
≤30 Days Before Election
Model
Quadratic
Cubic
Quartic
Quadratic
Cubic
Quartic
Quadratic
Cubic
Quartic
SSE
3403.7
3401.8
3401.8
2700.4
2692.4
2692.0
683.34
681.97
681.86
SSE Difference
F-statistic
p-value
1.86
0.05
9.02
0.23
0.00
0.63
7.97
0.37
39.09
1.82
0.00
0.18
1.37
0.11
6.59
0.51
0.01
0.48
Table 5: F-tests for best fitting polynomial order for negativity as function of time
Table 5 presents the results of the anova for each of the datasets on the quadratic, cubic, and quartic
polynomials. Based on the F-tests, in all three cases the cubic is clearly the polynomial order that best fits
the data. We also present the coefficients and standard errors for the best fitting model in Table 6. In each
case the best fitting cubic has an S shape (positive first order, negative second order, and positive third order
terms). Notice that the top concave portion is capturing the drop in negativity close to the end of the race as
described in section 2. The fitted curve along with the average M ediaCoverage for each period is presented
in Figure 7 in the main body of the paper.
31
Variable
Intercept
Time/100
(Time/100)2
(Time/100)3
All Periods
0.32 (0.01)
0.44 (0.17)
-2.29 (0.62)
1.88 (0.62)
¿30
0.26
1.34
-5.07
4.26
Days
(0.02)
(0.20)
(0.69)
(0.68)
≤ 30
0.34
1.82
-22.43
46.27
Days
(0.03)
(0.98)
(7.9)
(18.0)
Table 6: Coefficients and standard errors for best fitting (cubic) time trend model of negativity
C
Technical Details of Theoretical Model Results
C.1
The pattern of negativity with the strategic delaying incentive
As mentioned in the text: “...a forward-looking candidate might delay the use of dirt found on her rival in
one specific sequence of events and for a subset of the parameter space.” Furthermore, the text also describes
the specific sequence of events. Briefly, delaying is appealing when in period 2 one candidate with no stock
draws H while her rival draws L in periods 1 and 2.
Here we (a) describe the the subset of the parameter space for which the candidates decides to delay, and
(b) the impact of the strategic incentive on the pattern of negativity. In the next subsection we describe the
effect of the strategic incentive on the interaction between the candidates.
The subset of the parameter space. The following two equations presents the incentive to play a
high bad trait now (Bnow ) and the incentive to wait (Bwait ).
Bnow = δ ∗ vH + δ ∗ qH ∗ vH + δ ∗ qL ∗ vL + qN ∗ vG –(δ ∗ vL + qH ∗ δ ∗ vH + δ ∗ vL (qN + qL )) =
δ(vH –vL ) + qN ∗ (vG − δ ∗ vL )
Bwait = vG + δ ∗ vH –(vG + qH ∗ δ ∗ vH + (1 − qH ) ∗ δ ∗ vL ) = δ(qN + qL ) ∗ (vH − vL )
Comparing these two incentives, we get that the candidate decides to wait if δ(vH –vL )+qN ∗(vG −δ∗vL ) <
δ(qN + qL ) ∗ (vH − vL ), which can be simplified to δ ∗ vH ∗ qH + qN ∗ vG < δ ∗ vL (qH + qN ).21 Let R be the
set of q L and q H for which this condition holds. This condition defines the subset of the parameter space –
i.e. R – where the incentive to delay is stronger than the incentive to use the H. This incentive implies that
the probabilities of going negative in the 2nd and 3rd periods will differ inside versus outside the subspace.
The impact on the pattern of negativity. As a result of the strategic delaying, both the second and
third period probabilities of going negative differ from the myopic case. Directionally, the second period is
going to be less negative (because there is a case in which the H will be delayed and so the tone of both players
is positive). The probability of this occurrence is 1 − q L − q H q H q L q L . When adjusting the probability of
going negative in the second period (as it appears in the text for the myopic case) we need to subtract it (i.e.
1 − q L − q H q H q L q L ). This leads to the period two negativity of
21 Note
that this condition can hold for arbitrary values of qN and qH .
32
prob(nj,2 = 1) = q H +q L q H +q L (1−q H ) q H 2 − q H + 1 − q L − q H q H (1−q H )q L − 1 − q L − q H q H q L q L
The third period, however, will be more negative under the strategic incentive than without it. The
reason for the increase in negativity is, of course, the candidate who delayed. She will surely use the stocked
H in period 3 even if she draws no bad traits in this period. Thus, she might become more negative. Notice
that her rival will be negative in the third period in any case. In the case of no-delay, he would be negative
since he has at least two Ls (from periods 1 and 2). In the case of delay, he clearly has enough negativity in
his stock and might even get H in the last period. Thus, period 3 might be more negative and the added
3
probability is 1 − q L − q H q H q L q L . As a result, the updated probability of negativity in period 3 is
prob(nj,3 = 1) = q H + q L q H + q L (1 − q H ) q H 2 − q H
2
2
+ 1 − q H − q L q H 1 − q H q L 2 − q L − 2q H + 1 − q L − q H q H q L q L
(5)
These probabilities are used to create figure 1 panel (b). In this figure it is clear that the parameter values
for which negativity increases is larger under strategic waiting than without it.
C.2
The interaction between the candidates with strategic delaying
Here we present the calculations behind Figure 4 which describes the reaction of candidate j to a switch in
tone by her rival. These calculations take into account, among others, the forward-looking incentive to delay.
We start by considering the case of switching toward positive. For the transition from period 1 to 2 we get:
P rob (nj,2 = 0|nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 1) = 1 − q H − q L
P rob (nj,2 = 0|nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 1) = 1 − q H − q L
Of course, in this case it is obvious that switching by the rival (i.e., candidate j 0 ) has no impact on the actions
of the focal candidate (i.e., j).
Next we consider the case in which the rival switches to a negative tone in period 2. To simplify notation
and make the equations less cumbersome, we use the short-hand qH = H, qL = L, (1 − qH − qL ) = N ,
and M = H(2 − H). Furthermore, we first present the calculations for myopic candidates and then add the
33
forward-looking incentive. Notice that in order to show that:
P rob(nj,2 = 1|nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0) > P rob(nj,2 = 1|nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0)
all we need to show is that22 :
P rob(nj,2 = 1, nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0)P rob(nj,2 = 0, nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0) >
P rob(nj,2 = 1, nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0)2
which means that we need to show that:
2
2
N (2L + H) + N L(2 + 2L) + L2 (2 − H) H (N + L)4 > N 2 H(N + L)
This is equivalent to showing that:
2
N (2L + H) + N L(2 + L) + L2 (2 − H) (N + L)4
2
H [N 2 (N + L)]
>1
or that:
N 2 (2L + H) (N + L)4
2
H [N 2 (N + L)]
+X >1
where
X≡
N L(2 + L) + L2 (2 − H) (N + L)4
2
H [N 2 (N + L)]
>0
This can be rewritten as:
(2L + H)(N + L)2
+X >1
HN 2
and since (N + L)2 > N 2 and (2L + H) > H the above is true and we have shown that a candidate is
more likely to switch her tone to negative if the rival did the same. All in all, the above indicates that for the
transition from the 1st to the 2nd period, the probability of going negative when the opponent goes positive
is smaller than the probability of going negative when the opponent goes negative.
This tendency to act the same as the rival for a negative switch is also true for the subset of the parameter
space R under forward-looking candidate behavior. Following the logic above, we need to show that:
22 Recall
that
P rob(nj,2 = 1|nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0) =
P rob(nj,2 = 1|nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0) =
P rob(nj,2 = 1, nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0)
P rob(nj,2 = 1, nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0) + P rob(nj,2 = 0, nj 0 ,2 = 1, nj,1 = nj 0 ,1 = 0)
P rob(nj,2 = 1, nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0)
P rob(nj,2 = 1, nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0) + P rob(nj,2 = 0, nj 0 ,2 = 0, nj,1 = nj 0 ,1 = 0)
34
2
2
N (2L + H) + N L(2 + L) + L2 (2 − H) H (N + L)4 + L2 HN > N 2 H(N + L)
This is equivalent to showing that:
2
N (2L + H) + N L(2 + L) + L2 (2 − H) (N + L)4 + L2 HN
2
H [N 2 (N + L)]
>1
or that:
2
N (2L + H) (N + L)4
H
[N 2 (N
2
+ L)]
+ X0 > 1
where
0
X ≡
N L(2 + L) + L2 (2 − H) (N + L)4 + L2 HN + N 2 (2L + H) L2 HN
2
H [N 2 (N + L)]
>0
This can be rewritten as:
(2L + H)(N + L)2
+ X0 > 1
HN 2
and since (N + L)2 > N 2 and (2L + H) > H the above is true and we have shown that the tendency
to act the same as the rival for a negative switch is also true for the subset of the parameter space R under
forward-looking candidate behavior.
Next we present the transitions from period 2 to 3. These transitions are the focus of the analysis in the
main body of the paper, including Figure 4.
We start by presenting the conditional probabilities of switching tone to negative for the set of parameters
for which delaying is not an attractive option, i.e., not inR.
2
2
P rob(n3,2 = 1|n3,1 = 1, n2,1 = n2,2 = 0) =
+2HL+2HN +N 2 )H(2L+H)+N 2 (2N L+L2 )H2K+L2 (4N 2 +4N L+L2 )H(N +K)
N (H
N 2 (H 2 +2HL+2HN +N 2 )HK+N 2 (2N L+L2 )H(N +2K)+L2 (4N 2 +4N L+L2 )H(N +K)
P rob(n3,2 = 1|n3,1 = 0, n2,1 = n2,2 = 0) =
N 2 (H 2 +2HL+2HN +N 2 )N H+N 2 (2N L+L2 )HN
N 2 (H 2 +2HL+2HN +N 2 )(N +L(N +L))+N 2 (2N L+L2 )(2(L+N )2 +HN )+L2 (4N 2 +4N L+L2 )(L+N )2
For the subset of the parameter space for which delaying is possible (i.e., in R), the probabilities become
2
2
P rob(n3,2 = 1|n3,1 = 1, n2,1 = n2,2 = 0) =
+2HL+2HN +N 2 )H(2L+H)+N 2 (2N L+L2 )H(2K)+L2 (4N 2 +4N L+L2 )H(N +K)+N HL2
N (H
N 2 (H 2 +2HL+2HN +N 2 )HK+N 2 (2N L+L2 )H(N +2K)+L2 (4N 2 +4N L+L2 )H(N +K)+N HL2
35
P rob(n3,2 = 1|n3,1 = 0, n2,1 = n2,2 = 0) =
N 2 (H 2 +2HL+2HN +N 2 )N H+N 2 (2N L+L2 )HN
N 2 (H 2 +2HL+2HN +N 2 )(N +L(N +L))+N 2 (2N L+L2 )(2(L+N )2 +HN )+L2 (4N 2 +4N L+L2 )(L+N )2
While the probabilities above describe the case of switching to a negative tone the ones below are for the
events in which the candidate switch in the positive direction. We start by considering the set of parameters
not in R for which delaying is not attractive. We get:
P rob(n3,2 = 1|n3,1 = 1, n2,1 = n2,2 = 0) =
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))(H+L)N +N LH(3L+H)N +L2 H 2 N (N +K)
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))(H+L)+N LH(3L+H)(K+H)+L2 H(2L+H)+L2 H 2 (N +K)K
2
P rob(n3,2 = 1|n3,1 = 0, n2,1 = n2,2 = 0) =
H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))N 2 +L2 H(N +K)(N +L)2
(N
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))N +N LH(3L+H)N +L2 H(N +K)((N +L)2 +HN )
When we consider the subset R for which delay might be possible, we get:
P rob(n3,2 = 1|n3,1 = 1, n2,1 = n2,2 = 0) =
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))(H+L)N +N LH(2L+H)N +L2 H 2 N (N +K)
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))(H+L)+N LH(2L+H)(K+H)+L2 H(2L+H)+L2 H 2 (N +K)K
2
P rob(n3,2 = 1|n3,1 = 0, n2,1 = n2,2 = 0) =
H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))N 2 +L2 H(N +K)(N +L)2
(N
(N 2 H(4L+H)+(H 2 +2HL+2HN )(H 2 +2HL))N +HN )+N LH(2L+H)N +L2 H(N +K)((N +L)2 +HN )
These probabilities are used to generate figure 4that is presented in subsection 3.4. This figure illustrates
the “asymmetric reaction function” numerically for the transition from period 2 to 3.
C.3
Proof that same tone is more likely
We prove for periods 1 and 2 that the candidates are more likely to use the same tone. In period 1, the
probability of different tone is 2HN . Since the maximum value of 2H(1 − H) is 0.5, and N < (1 − H) (recall
L > 0) we know for sure that 2HN < 0.5.
In periods 2 the probability of different tone is (ignoring forward looking for now):
Pr(E0 ∩ E1 )2HN +Pr(E0 ∩ E2 )HN +Pr(E0 ∩ E3 )0+Pr(E0C )2N (1 − N )
where the events are defined as follows: E1 = {none of the candidates has a stock} , E2 = {one of the candidates has a stoc
E3 = {both candidates have a stock}, and E0 = {media was off in previous period}.
We have already shown that 2HN is smaller than 0.5, and of course HN and 0 are also smaller than 0.5.
Thus, while 2N (1 − N ) can be equal to 0.5 (when N = 0.5) the resulting weighted average of 2HN , HN , 0,
36
and 2N (1 − N ) must be smaller than 0.5.
In period 3 the probability is
Pr(E0 ∩ E1 )2HN +Pr(E0 ∩ E2 )HN +Pr(E0 ∩ E3 )0+Pr(E0C ∩E1 )2N (1 − N ) + Pr(E0C ∩E2 )N +Pr(E0C ∩E3 )0
We analyzed this quantity numerically and included it in the analysis presented in section 3.3.
Finally, forward looking does not change much. In period 2 it is replacing a cases in which both were
negative with one in which both are positive, and thus changes nothing and in period 3 it is replacing
something with a case of negative-negative and thus weakly increase the probability of same tone.
37
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