Ideological Signaling and Incumbency
Advantage
Zachary Peskowitz∗
I develop a novel explanation for the incumbency advantage based on the ability of incumbents to signal ideologically distinct positions from their parties. Using
voter-level data from the CCES and controlling for unobserved district heterogeneity,
I find that voters in House elections primarily use information about the ideology
of candidates’ parties to infer the location of challengers while they instead rely
on information about the individual candidates’ ideologies to place incumbents. In
higher-profile Senate elections, the difference between challengers and incumbents is
trivial. Decomposing the incumbency advantage into valence and signaling components, I estimate that 14 percent of incumbency advantage in House elections is from
the signaling mechanism while it explains only 5 percent of the advantage in Senate
contests. I also find that a 50 percent increase in party polarization would increase
incumbency advantage by 3 percentage points.
Key words: congressional elections, candidate experience, incumbency advantage
∗
Assistant
Professor,
Department
of
Political
Science,
Emory
University,
[email protected]. I thank seminar audiences at UIUC, Ohio State, Yale,
the Harris School and Cyrus Aghamolla, Steve Callander, Kyle Dropp, Nick Eubank, Morris
Fiorina, Alex Frankel, Justin Grimmer, Wesley Hartmann, Alex Hirsch, Keith Krehbiel, Neil
Malhotra, Greg Martin, Eleanor Powell, Chris Stanton, Ken Shotts, and Jonathan Wand for
many helpful comments. I thank Gary Jacobson for generously providing his data on candidate
experience in House elections. An earlier version of this paper circulated under the title “Candidate
Positioning, Partisan Brands, and Election Outcomes.”
1
More than forty years of empirical research on Congressional elections has documented the existence of an incumbency advantage,1 decomposed its sources into
various components of the political environment,2 and identified its variation over
time.3 The standard conception of incumbency advantage is that the effect is purely
valence.4 In this view, incumbency is a characteristic of a candidate, such as seniority,5 or a resource, like the franking privilege,6 that affects all voters’ evaluation of
the candidate in an identical fashion that is independent of ideology. I argue that
this standard conception obscures a key component of incumbency advantage: the
ability of incumbents to develop an ideological record distinct from their parties. I
show that voters have different information at their disposal about the ideological locations of candidates that varies with the candidates’ experience. This informational
mechanism generates an incumbency advantage that systematically varies with the
underlying ideological characteristics of candidates, parties, and the district electorate.
The idea that incumbents can use roll-call votes in the legislature to signal ideological positions that are in line with the district and distinct from the party is
not new, but its empirical relevance and effects on incumbency advantage has yet
to be systematically examined. As Arnold (1990) notes, incumbents and challengers
have very different opportunities to build an ideological record. “House members
1
Erikson (1971)
Cox and Katz (1996), Levitt and Wolfram (1997)
3
Alford and Hibbing (1981), Gelman and King (1990), Abramowitz, Alexander and Gunning
(2006)
4
Stokes (1963) provides the canonical treatment of valence in elections.
5
McKelvey and Riezman (1992)
6
Mayhew (1974), Cover and Brumberg (1982)
2
2
face between 400 and 600 roll-call votes each year, and even after discounting for
procedural and other minor motions, they quickly establish a long list of recorded
positions. Challengers may or may not have previous records to defend, depending
on what previous offices they may have held.” Building on this insight, I develop and
estimate a model to reveal the electoral importance of this difference between the
informational environment of incumbents and challengers.7
I develop an empirical model of how voters estimate the ideological location of
House candidates. In the model, voters weight the candidates’ individual and party
ideological positions to generate an expected candidate location and the values of the
weights are allowed to vary across levels of candidate experience.8 I use self-reported
vote intentions and candidate, party and self ideological locations to estimate the
parameters of the model via maximum likelihood estimation procedure. I then use
this framework to calculate the incumbency advantage and decompose its magnitude
into valence and signaling components using the estimated parameter values. Using
survey responses from the Cooperative Congressional Election Study and controlling
for district unobserved heterogeneity, I identify four main results. First, I find that
7
Similar assumptions play an important role in theoretical models of elections such as Duggan
(2000) and Bernhardt, Câmara and Squintani (2011). In these models, voters only know the
population-wide distribution of challengers’ ideology, but have more precise information about the
ideology of incumbents.
8
In the empirical analysis, I operationalize experience as whether a candidate is an incumbent,
has previously held state-level elected office, or has not perviously held state-level elected office using
Gary Jacobson’s data on House elections. In the Senate, I operationalize experience as whether the
candidate is an incumbent or challenger. It is important to note that the candidate characteristics
I refer to with the shorthand of “experience” are bundled with other candidate attributes, such as
public awareness, access to financial resources, and the like. I employ the shorthand “experience”
over a term such as “quality” because experience in office is the concept I am measuring. As Green
and Krasno (1988) and others have argued, “quality” is a broader set of candidate features, which
includes characteristics like celebrity and occupational status, than experience in elected office.
3
voter perceptions of incumbents’ ideological locations in House elections are largely
based on the individual positions that incumbents take while perceptions of challengers’ locations are heavily dependent on the party’s ideological location. Voters
place an even larger party weight on the ideological positions of inexperienced challengers relative to experienced challengers. In Senate elections, there is no statistical
or substantive difference between the party weights voters place on incumbents and
challengers. Second, I decompose the estimated incumbency advantage into its signaling and valence components and find that the signaling mechanism explains 10-20
percent of the incumbency advantage in House elections. In contrast, I find that,
consistent with the informational mechanism, the signaling effect is smaller in Senate elections where candidates are typically better-known and receive more intense
media coverage relative to House elections. Third, I find that the incumbency advantage exhibits important cross-district heterogeneity. There is a suggestive evidence
of a quadratic relationship with the magnitude of incumbency advantage and district
ideology with more moderate districts exhibiting higher levels of incumbency advantage. Fourth, I investigate how inter-party polarization affects the magnitude of the
incumbency advantage. The empirical framework allows me to make out-of-sample
predictions about the evolution of incumbency advantage for alternative variable
values. I find through a series of microsimulations that the average incumbency advantage would increase by roughly 3 percentage points with a 50 percent increase
in voter perceptions of party polarization. The preferred specifications include electoral district fixed effects9 so the results only exploit within-district variation in the
9
The analysis includes both House and Senate elections. In the case of House elections I include
congressional district fixed effects and in the case of Senate elections I include state fixed effects.
4
incumbency status of candidates and lend credibility to the causal interpretation of
the findings.
This paper contributes to three literatures. First, this paper is part of the vast
literature on the estimation and decomposition of the incumbency advantage. Researchers have distinguished between direct office holder benefits, quality differentials
between incumbents and challengers, and the scare-off effect. I do not decompose the
incumbency advantage between direct-office holder benefits, quality differentials, and
the scare-off effect because this has been done in previous research such as Levitt and
Wolfram (1997) and Hirano and Snyder (2009).10 Instead, I label the combination
of these effects valence because they are valued equally by all voters and do not attempt to quantify their relative importance. I supplement the previous literature by
illuminating an alternative source of the incumbency advantage based on the ability
of incumbents to differentiate themselves ideologically from their parties that has not
received prior empirical attention.
Second, I contribute to the literature on how voter processing of ideological information operates and affects vote choice in elections.11 In an important study, Rahn
(1993) provides laboratory experimental evidence that fictional candidates’ partisan
labels dominate issue positions in voters’ evaluation of candidates for office. In the
experimental design, the fictional candidates’ incumbency status is not manipulated
across treatment and control so there is no attempt to discern if this information
In the text, I slightly abuse language and refer interchangeably to these as district fixed effects.
10
Using election returns from state legislative multimember districts, Hirano and Snyder (2009)
find that the scare-off effect is quantitatively small. Using a regression discontinuity design in U.S.
House elections, Hall and Snyder (2015) also find that the scare-off effect is small.
11
Conover and Feldman (1989), Rahn (1993), Burden (2004), Butler and Powell (2014)
5
processing varies across levels of candidate experience. As discussed above, there
are compelling theoretical reasons to believe that partisan labels are more informative about the ideology of relatively less known challengers compared to incumbents.
In this paper, I document an important interaction between how voters interpret
partisan and individual ideological information with the level of experience that candidates possess.12 While partisan affiliation conveys some ideological information
to voters, the magnitude of this informational effect is much more important for
House challengers (both experienced and inexperienced) than for House incumbents
and I uncover no meaningful differences across challengers and incumbents in Senate contests. These empirical findings suggest a role for candidate experience in how
partisan labels affect ideological inferences that has not received systematic attention
in the experimental literature.
Finally, my findings contribute to the literature on the design of electoral institutions to produce electoral accountability in an environment with entrenched incumbents.13 Many observers of American politics find the existence of an incumbency
advantage normatively troubling. To the extent that incumbency advantage is due
to an uneven electoral playing field between incumbents and challengers, as opposed
to unmeasured differences in candidate quality,14 its existence potentially weakens
the accountability mechanism between citizens and legislators. Entrenched incum12
Relatedly, Carson et al. (2010) study the effect of partisan loyalty on electoral performance.
They find that voters punish candidates for high levels of partisan loyalty and that this effect is
more important than ideological distance. Unlike Carson et al. (2010), I examine the effects of both
candidates’ ideological positions, candidate experience, and partisan affiliation affect vote choice.
Incorporating their perspective on the divergent effects of partisan loyalty and ideological distance
is a promising avenue for future research.
13
Ashworth (2006)
14
Stone et al. (2010)
6
bents who are electorally insulated from competition are less responsive to citizens’
preferences15 and have weaker incentives to provide constituency service.16 Holbrook
and van Dunk (1993) discuss some of the large literature on the consequences of electoral competitiveness and its absence on citizens’ political participation and policy
outcomes.
The bulk of evidence suggests that incumbency advantage’s effects on electoral
competition has a meaningful effect on the performance of American democracy. Understanding the causes of the incumbency advantage and their relative magnitudes is
essential for evaluating alternative electoral rules that aim to reduce its effects in the
electoral arena. Gowrisankaran, Mitchell and Moro (2008) discuss a number of institutional rules, such as matching funds for challengers, mandates for equal air time,
and term limits, that could reduce the welfare losses that emerge from pro-incumbent
electoral bias. Gersbach (2010) argues that a higher vote hurdle for incumbent candidates in order to induce additional provision of effort and improve voter welfare on
the part of elected officials. Attempts to design political institutions need to account
for how incumbency advantage varies across districts. The optimal reelection hurdle in a Gersbach (2010)-style model would vary with underlying district ideological
characteristics.
The analysis raises several open questions about how the mechanisms documented
here might travel to other political settings. While the empirical estimates are specific
to the U.S. political context, marked by presidentialism and a well-defined two-party
system, and the period of 2006 to 2012, the mechanisms highlighted here of vot15
16
Griffin (2006)
Dropp and Peskowitz (2012)
7
ers placing weights on candidate and party positions to form ideological expectations
may occur in other political systems as well. In parliamentary systems, voters may be
less concerned with the individual policy positions of legislative candidates because
of the inability to cast separate votes for the executive and legislature. In political
systems where parties do not have well-defined ideology, voters may instead place a
higher weight on candidate ideology. Investigating variation in individual and party
weights across political contexts systematically is a promising avenue for future research. In this paper, I focus on the relatively narrow factor of candidate experience
and its effect on voter information about candidate and party ideology. There are
other features that may affect the relative weights that voters place on party and individual candidate ideological information and these potential mechanisms warrant
attention in future research. In particular, contested primaries, marked by higher
levels of media coverage and campaign advertising, may provide more information
about candidates that persists to the general election. Similarly, high levels of congruence between media markets and congressional districts17 may lead to citizens
who have higher levels of information about congressional candidates’ ideologies.
The remainder of the paper is organized as follow. In the next section, I describe
the empirical framework that guides the estimation. In the third section, I describe
the CCES and candidate experience data that I employ to estimate the model. In the
fourth section, I present the main results. I examine the model fit relative to other
alternative models. In the fifth section, I examine how the estimated incumbency
advantage varies across districts and provide evidence that incumbency advantage
17
Snyder and Strömberg (2010)
8
is higher in ideologically moderate districts. I then investigate how out-of-sample
changes in inter-party polarization would affect the magnitude of the incumbency
advantage. I also motivate and discuss a series of robustness checks, which are
included in the Online Appendix. The final section concludes.
Empirical Framework
Two candidates, one with a Democratic and one with a Republican affiliation, are
competing for election in each district, d = 1, ..., D at time periods t = 1, ..., T . Each
candidate campaigns by announcing an ideological location18 in a unidimensional policy space. Voters are uncertain about the exact ideological location of candidates in
the policy space.
Each candidate’s ideal policy is unknown to the voter. The voter, indexed by n,
estimates a Democratic candidate’s ideological location, x̂Dem
ndt , as a linear function of
Dem
the voter’s perception of the party’s position, xDem
ndt , and candidate’s position, x̃ndt .
The voter places a weight of λ on the party’s location and 1 − λ on the candidate’s
position. I allow the relative weight placed on the party location to vary across levels
of candidate experience. In the empirical analysis, I allow each of these parameters to
take on three distinct values, λI , λEC , λIEC where the subscripts refer to incumbents,
experienced challengers, and inexperienced challengers.19 Hence, in House elections
λ is a 3 by 1 vector of coefficients where each element corresponds to a distinct level
18
Throughout the article, I use the term
Jacobson’s data on whether challengers are experienced or inexperienced is only available for
House elections. For Senate elections, I only use two categories of candidates: incumbents and
challengers.
19
9
Dem
of candidate experience and xDem
ndt and x̃ndt are each 3 by 1 vectors of candidate
and party positions that take on the value 0 when a candidate does not possess the
relevant experience level at t.
0 Dem
0 Dem
x̂Dem
ndt = λ xndt + (1 − λ )x̃ndt
The function for Republican candidates is defined analogously. To estimate the
weights that voters place on candidates’ ideological locations, I more completely
specify the voter’s utility function. Voters have symmetric preferences with a unique
ideal point in the policy space, x∗ndt . Voters’ utility is determined by both the ideological distance between their ideal points and the location of the candidate and
non-policy characteristics of the candidate and the election year. Consistent with
the empirical findings of Berinsky and Lewis (2007), I specify a linear absolute loss
function for the policy component of the voter’s utility function.
∗
Dem
∗
0
Dem
U (x̂Dem
+ αd + vt + β 0 zndt + ζndt
ndt , xndt ) = −γ|x̂ndt − xndt | + δ Expdt
The ExpDem
are candidate valence levels that are operationalized using the vector of
dt
candidate experience data20 and δ is a vector of coefficients on candidate experience.
The γ parameter allows the importance of policy relative to non-policy factors to vary,
with the limiting case being γ = 0 and policy having no effect on voter decisions. The
αd are district fixed effects which accommodate unobservable cross-district variation
20
There are certainly other dimensions of candidate valence that the simple measure of candidate
experience is not capturing. I use valence as a shorthand to refer to the direct effect of experience
on respondents’ vote probability, as opposed to the party weight effect.
10
in the propensity to support the Democratic candidate, the vt are year fixed effects
which account for national partisan swings,21 zndt is a column vector of K observable
individual-level demographic characteristics which affect the probability of voting for
the Democratic candidate, and β is a K by 1 vector of coefficients.22 The ζndt is a
voter-specific idiosyncratic and unobservable preference shock that is orthogonal to
the covariates. In the base specification, I do not allow respondent self-identified
partisanship to affect the voter’s utility for the two candidates, but instead posit
ideology as the primitive that affects the probability of vote choice. In a robustness
check, I allow the respondent’s utility for each candidate to vary with the respondent’s
self-identified partisanship.
The voter selects the Democratic candidate if the utility from the Democrat
exceeds the utility from the Republican:
∗
Dem
∗
0
Dem
U (x̂Dem
+ αd + vt + β 0 zndt + ζndt
ndt , xndt ) = −γ|x̂ndt − xndt | + δ Expdt
Rep
Rep
∗
0
∗
> −γ|x̂Rep
ndt − xndt | + δ Expdt = U (x̂ndt , xndt )
(1)
In the base specification, I assume that the ζndt are identically and independently
distributed normally with mean 0 and variance 1 to generate a probit model for
the voter’s choice probability. After rearranging the inequality in Equation 1 and
using the symmetry of the normal probability density, the probability that the voter
21
McGhee (2008)
The voter’s utility function for the Republican candidate is similarly defined. However, I omit
the district and year fixed effects and individual-level demographics from the Republican utility
function because these variables do not vary across the Democratic and Republican candidate and
cannot be separately identified in the estimation.
22
11
chooses the Democratic candidate is then given by:
P rndt (Vote Dem)
Rep
0
∗
0
Dem
∗
− ExpRep
= Φ(−γ|x̂Dem
ndt − xndt | + γ|x̂ndt − xndt | + δ (Expdt
dt ) + αd + vt + β zndt )
The likelihood function over voters, electoral districts, and election cycles is then:
L(Vote Demndt ; α, β, δ, γ, λ, v) =
YYY
t
d
P rndt (Vote Dem)Vote Demndt (1 − P rndt (Vote Dem))1−Vote Demndt
n
I estimate the parameters by maximizing the likelihood function and compute the
standard errors with the block bootstrap23 where the blocks are defined as districts
in House elections and states in Senate elections. To implement the block bootstrap,
I draw a sample of districts or states with replacement, where the number of drawn
districts or states in the bootstrap replication sample is equal to the total number of
districts of states in the true sample. I then estimate the parameters of the model
on the resulting bootstrap sample. I repeat this procedure 250 time for 250 block
bootstrap replications and then calculate the standard deviation of the coefficient
estimates across the 250 replications. The resulting standard deviation is my estimate
of the standard errors.24 The purpose of the block bootstrap is to allow for arbitrary
correlation in the error terms within districts or states and is analogous to clustering
23
Efron and Tibshirani (1993)
I perform the identical procedure to calculate other quantities of interest that are functions of
the coefficient estimates, such as the proportion of the estimated incumbency advantage that is due
to the signaling mechanism.
24
12
the standard errors at the district or state level in a closed-form calculation of the
standard errors. I separately estimate the parameters for House and Senate elections.
The framework advanced here is motivated by the belief that voter information
about candidate ideology systematically varies with the level of candidate experience and that there may be important differences in these patterns across House
and Senate elections. In the Online Appendix, I directly investigate this possibility
with a series of district fixed effects regressions on how survey respondents’ information about candidate ideology varies with candidate experience. In House contests,
respondents are more willing to estimate candidate ideology when the candidate is
an incumbent relative to experienced challengers and inexperienced challengers. In
Senate contests, the pattern is more ambiguous. I also find that the variability of
the candidate ideology estimates within a candidate-district-year is smaller for incumbents and experienced challengers relative to inexperienced challengers in House
contests. These results illustrate that in House contests there is systematic and
monotonic variation in voter information about candidate ideology with respect to
the level of candidate experience and less of a systematic pattern in Senate elections.
The framework allows me to decompose the incumbency advantage into valence
and signaling components. The total incumbency advantage represents the difference in average vote share between an incumbent standing for reelection and the
counterfactual where the incumbent is replaced with a challenger (either experienced
or inexperienced). I now define the incumbency advantage and its valence and signaling components for the case of a Democratic incumbent being replaced with an
inexperienced challenger. Other incumbency advantages, such as that of a Republi-
13
can incumbent being replaced with a Republican experienced challenger, are defined
DemIEC
= 1)|1DemI
= 1) denote the counterfacanalogously. Let P r(Vote DemC
ndt (1ndt
ndt
tual vote probability of a Democratic incumbent who is replaced with a Democratic
DemIEC
= 1)
= 1)|1DemI
inexperienced challenger. Similarly, let P r(Vote DemCV
ndt (1ndt
ndt
denote the counterfactual vote probability of a Democratic incumbent who is replaced with a Democratic inexperienced challenger, but holding the signaling parameters constant at their incumbent values and changing the valence parameters to
DemIEC
those of an inexperienced challenger. P r(Vote DemCS
= 1)|1DemI
= 1) is
ndt (1ndt
ndt
the signaling counterfactual where the valence parameters are held constant and the
signaling parameters are changed to their inexperienced challenger level. The total
district respondent-weighted incumbency advantage for district d is25 :
Total Inc Advd =
=
Nd
1 X
DemIEC
P r(Vote Demndt |1DemI
= 1) − P r(Vote DemC
= 1)|1DemI
= 1)
ndt
ndt (1ndt
ndt
Nd n=1
Nd
1 X
0 Dem
∗
0 Rep
0 Rep
∗
0
Dem
0
DemI
Φ(−|λ0 xDem
− ExpRep
= 1)
ndt + (1 − λ )x̃ndt − xndt | + |λ xndt + (1 − λ )x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
Nd n=1
0 Rep
∗
0
DemIEC
0
DemI
−Φ(−|λ0 xDemIEC
+ (1 − λ0 )x̃DemIEC
− x∗ndt | + |λ0 xRep
− ExpRep
= 1)
ndt
ndt
ndt + (1 − λ )x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
The approach allows me to decompose the portion of the incumbency advantage due
to valence and signaling. The valence component is defined by holding the party
weight variables constant and varying the valence variables:
25
To emphasize the role of the party weight parameters in determining the magnitude of the
incumbency advantage, I substitute in the expressions for x̂Dem
and x̂R
net into the incumbency
ndt
advantage equations. Also, I economize on notation by defining Nd as the number of respondents in
a district during cycles where the Democratic candidate is an incumbent. Nd is defined analogously
for different conditioning events, such as the Republican candidate serving as an incumbent.
14
Valence Inc Advd =
=
Nd
1 X
DemIEC
P r(Vote Demndt |1DemI
= 1) − P r(Vote DemCV
= 1)|1DemI
= 1)
ndt
ndt (1ndt
ndt
Nd n=1
Nd
1 X
0 Dem
∗
0 Rep
0 Rep
∗
0
Dem
0
DemI
Φ(−|λ0 xDem
− ExpRep
= 1)
ndt + (1 − λ )x̃ndt − xndt | + |λ xndt + (1 − λ )x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
Nd n=1
Rep
Rep
I
Dem
∗
∗
0
DemIEC
0
DemI
−Φ(−|λI xDem
− ExpRep
= 1)
ndt + (1 − λ )x̃ndt − xndt | + |λxndt + (1 − λ)x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
Similarly, the signaling component of the incumbency advantage is defined by varying the party weight parameters to reflect the counterfactual where the Democratic
incumbent is replaced with an inexperienced challenger and holding the valence parameters constant:
Signaling Inc Advd =
=
Nd
1 X
DemIEC
P r(Vote Demndt |1DemI
= 1) − P r(Vote DemCS
= 1)|1DemI
= 1)
ndt
ndt (1ndt
ndt
Nd n=1
Nd
1 X
0 Dem
∗
0 Rep
0 Rep
∗
0
Dem
0
DemI
Φ(−|λ0 xDem
− ExpRep
= 1)
ndt + (1 − λ )x̃ndt − xndt | + |λ xndt + (1 − λ )x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
Nd n=1
0 Rep
∗
0
Dem
0
DemI
−Φ(−|λ0 xDemIEC
+ (1 − λ0 )x̃DIEC
− x∗ndt | + |λ0 xRep
− ExpRep
= 1)
ndt
ndt
ndt + (1 − λ )x̃ndt − xndt | + δ̂ (Expdt
dt ) + α̂d + v̂t + β̂ zndt |1ndt
Note that the valence and signaling components do not necessarily sum to equal the
total incumbency advantage due the the nonlinearity of the normal cumulative distribution function.26 To construct a legislature-wide estimate of the incumbency
advantage and its components I weight each district or state equally.27 As the framework makes clear, there are a variety of theoretically distinct incumbency advantages
26
In the empirical application, I find that the sum of these quantities is typically very close to 1.
The number of survey respondents in each district and state are not equal so weighting each
respondent equally would overweight districts and states with a relatively high number of CCES
respondents. The CCES also includes case weights for each individual respondent. As a robustness
check, I estimate the parameters by maximizing the weighted likelihood function. In the Online
Appendix, I report these weighted results and show that the findings are quite similar for the
unweighted and weighted estimates.
27
15
that the empirical literature has generally not distinguished from one another. My
primary interest is in the incumbency advantage defined by the counterfactual where
an incumbent candidate is replaced with a challenger so that both candidates lack
the advantages of incumbency. This is the appropriate counterfactual for analyzing
an institutional reform such as a one-term limit. An alternative incumbency advantage is defined by the counterfactual where challengers are given the advantages
of incumbency. This is the appropriate counterfactual for analyzing an institutional
reform such as matching the level of campaign expenditures of challengers with those
of incumbents.
Data
My primary source of data on vote choice, voter information, and individual demographics is the Cooperative Congressional Election Study. The CCES surveys
approximately 30,000 individuals each electoral cycle asking them a wide variety of
political questions, including their vote intentions in the 2006, 2008, 2010, and 2012
congressional elections.
28
In the 2012 House elections, some respondents are drawn
into new districts with potentially different incumbent candidates than in 2010 due
to decennial redistricting. Even though a candidate is an incumbent they may not
be as well known to these “new voters”29 and the party informational weights might
be higher as a result for this subset of voters. As a robustness check, I restrict the
28
Ansolabehere (2010a; 2011; 2010b), Ansolabehere and Schaffner (2012) In 2006 and 2008, the
CCES solicited ideological positions on a 0 to 100 scale while in 2010 and 2012 ideological positions
are placed on a seven-point scale. To make the ideological locations comparable across election
cycles, I linearly transform all positions to lie on a -0.5 to 0.5 scale.
29
(Ansolabehere, Snyder and Stewart 2000)
16
estimation to the sample of House districts from 2006-2010 and find very similar
results.
I merge these survey data with Gary Jacobson’s data on candidate experience
in House elections.30 Jacobson’s data include information on whether a challenger
has previously held state elective office and I employ this measure of candidate experience in my empirical analysis. I allow the information parameters to vary across
inexperienced and experienced challengers in all of the models. I separately estimate
models for House and Senate elections. While Jacobson’s data on candidate experience covers all House elections in the sample, I do not have data on whether Senate
candidates have previously held state-level elective office. For Senate elections, I
classify all non-incumbent candidates as challengers.31 Instead of pooling House and
Senate elections, I estimate the model separately on each set of data and allow the
parameters to vary arbitrarily across elections for each of the chambers.
I restrict the main estimation sample in two ways. First, I remove all elections
that are unopposed or only have one major party candidate.32 Second, I remove
all respondents who do not report an estimate for the ideological location of the
major party candidates and parties. For specifications that include respondent demographics as covariates, I drop observations where one or more of the covariates
is missing. Tables 1 and 2 report summary statistics for the sample for House and
Senate elections.
30
These data are used in Jacobson (1989) and many other papers on House elections.
The CCES records whether Senate candidates are incumbents or challengers and I use this
information as my data source.
32
I do include open seat elections where there are two major party challengers in the estimation
and these contests are important for identifying the effects of the other parameters in the model.
31
17
Table 1: House Summary Statistics
Variable
Mean
Vote Democrat
0.475
Voter Ideology
0.083
Republican Party Ideology
0.27
Democratic Party Ideology
-0.268
Republican Candidate Ideology 0.288
Democratic Candidate Ideology -0.127
Republican Incumbent
0.449
Democratic Incumbent
0.43
Republican Exp. Challenger
0.195
Democratic Exp. Challenger
0.178
Republican Inexp. Challenger
0.356
Democratic Inexp. Challenger
0.393
N
Std. Dev.
0.499
0.308
0.216
0.238
0.21
0.308
0.497
0.495
0.396
0.382
0.479
0.488
64409
Min.
0
-0.5
-0.5
-0.5
-0.5
-0.5
0
0
0
0
0
0
Max.
1
0.5
0.5
0.5
0.5
0.5
1
1
1
1
1
1
Variable
Mean
High School
0.378
Two-Year College
0.097
Four-Year College
0.241
Postgraduate
0.136
Female
0.432
African-American
0.076
Latino
0.067
Asian
0.008
Weekly Religious Attendance
0.293
Real House Income (Thousands) 76.294
N
Std. Dev. Min. Max.
0.485
0
1
0.296
0
1
0.428
0
1
0.343
0
1
0.495
0
1
0.265
0
1
0.249
0
1
0.089
0
1
0.455
0
1
45.539
5
184.26
56621
The paper heavily leverages the self-reported ideological locations of voters and
their estimates of candidate locations. While I cannot directly validate the ability
of voters to place themselves and candidates in an ideological space, I can examine
whether these self and candidate placements are correlated with other commonlyused measures of ideology to assess the external validity of these measures. In the
18
Table 2: Senate Summary Statistics
Variable
Mean
Vote Democrat
0.491
Voter Ideology
0.075
Republican Party Ideology
0.277
Democratic Party Ideology
-0.273
Republican Candidate Ideology
0.18
Democratic Candidate Ideology -0.211
Republican Incumbent
0.253
Democratic Incumbent
0.468
Republican Challenger
0.747
Democratic Challenger
0.532
N
Variable
Std. Dev.
0.5
0.31
0.215
0.235
0.292
0.267
0.435
0.499
0.435
0.499
67166
Mean
High School
0.385
Two-Year College
0.098
Four-Year College
0.247
Postgraduate
0.138
Female
0.443
African-American
0.089
Latino
0.075
Asian
0.009
Weekly Religious Attendance
0.287
Real Household Income (Thousands) 76.114
N
Min.
0
-0.5
-0.5
-0.5
-0.5
-0.5
0
0
0
0
Max.
1
0.5
0.5
0.5
0.5
0.5
1
1
1
1
Std. Dev. Min. Max.
0.487
0
1
0.297
0
1
0.431
0
1
0.345
0
1
0.497
0
1
0.285
0
1
0.263
0
1
0.093
0
1
0.452
0
1
45.818
5
184.26
58875
Online Appendix, I report scatter plots of the mean CCES self-reported ideology
and Tausanovitch and Warshaw’s (2013) multilevel regression with post-stratification
measure of district ideology derived from public opinion surveys. To investigate
whether CCES respondents are able to locate candidates in the ideological space, I
use Bonica’s (2014) Campaign Finance scores as the measure of candidate ideology
and examine its relationship with the average CCES ideological placement for each
19
candidate.33 The correlation between mean district CCES self-reported ideology and
the MRP measure is 0.8444 in the House and 0.7644 in the Senate and the correlation
between mean district placements of candidates and Bonica’s CF scores is 0.8446 in
the House and 0.8249 in the Senate. These aggregate results suggest that CCES
respondents’ placements are meaningful measures of ideology that are systematically
related to other measures of ideology used in the literature.34 However, it is important to note that I do not use these aggregate measures in the estimation and
instead only use individual level ideological estimates in the discrete choice model.
If there are systematic differences across respondents in how the respondent defines
the ideological scale, using aggregate data might be misleading.
The CCES solicits a large number of respondent-specific demographic and political characteristic from respondents. I include a large number of these responses as
additional control covariates in the analysis. I include indicators for female, AfricanAmerican, Latino, Asian, attend religious services weekly, and the highest level of
respondent educational attainment among the four categories: high school degree,
two-year college degree, four-year college degree, and post-graduate degree. I also
include respondent reported household income. The CCES asks respondents to report their income as a categorical variable defined by income ranges. The income
categories are not standard across the waves of the CCES. I take the midpoint of the
33
I use Bonica’s (2014) measure of candidate ideology over Poole and Rosenthal’s (1997) DWNOMINATE scores because Bonica’s approach allows for the estimation of both incumbent and
challenger ideological locations while the roll-call based DW-NOMINATE only provides estimates
of incumbent ideology. Bonica (2014) reports a 0.92 correlation between his CF scores and commonspace DW-Nominate scores.
34
Future work could further improve the measurement of ideological locations by employing the
methods of Hare et al. (2015) to correct for respondent-level differences in perceptions of ideological
space.
20
nominal income categories. For top-coded values above $150,000, I fix nominal income at $175,000. I then adjust the nominal income levels using the Consumer Price
Index and express all dollar amounts in real 2012 terms. In the Online Appendix, I
report the CCES question numbers for all variables that I use in the estimation.
Results
Table 3 reports the coefficient estimates and incumbency advantage quantities for
House elections. The top portion of the table reports the estimated coefficients from
the maximum likelihood vote choice model. The first column reports results from
the base specification with only year fixed effects. The second column adds state
fixed effects to the specification. The third column includes House district fixed
effects and are the most credibly identified regression results. The specification with
district fixed effects relies only on within-district variation in the incumbency status
of candidates to identify the parameter estimates. As an additional robustness check,
in the fourth column I include the complete set of individual demographic covariates
described above.35
35
In the interest of space, I omit these coefficients from the tables. The additional coefficient
estimates and standard errors are available from the author.
21
Table 3: House Elections
Party Weight (Incumbent)
Party Weight (Exp. Chall)
Party Weight (Inexp. Chall)
Incumbent
Experienced Challenger
Inexperienced Challenger
Dem Inc Adv (Exp Chall)
Rep Inc Adv (Exp Chall)
Dem Inc Adv (Inexp Chall)
Rep Inc Adv (Inexp Chall)
Dem Signaling (EC proportion)
Rep Signaling (EC proportion)
Dem Signaling (IEC proportion)
Rep Signaling (IEC proportion)
Observations
Log-likelihood
Year FE
State FE
District FE
Respondent Covariates
(1)
0.310
(0.013)
0.443
(0.020)
0.732
(0.017)
1.166
(0.011)
0.967
(0.017)
0.866
(0.014)
0.029
(0.003)
0.028
(0.003)
0.050
(0.002)
0.050
(0.003)
0.137
(0.030)
0.067
(0.017)
0.078
(0.015)
0.038
(0.008)
64,409
-15036
Yes
No
No
No
(2)
0.315
(0.017)
0.447
(0.025)
0.751
(0.015)
1.176
(0.011)
0.965
(0.017)
0.859
(0.014)
0.030
(0.003)
0.030
(0.003)
0.053
(0.002)
0.052
(0.003)
0.139
(0.036)
0.067
(0.021)
0.079
(0.020)
0.038
(0.011)
64,409
-14867
Yes
Yes
No
No
(3)
0.317
(0.016)
0.446
(0.019)
0.751
(0.015)
1.100
(0.013)
0.963
(0.017)
0.916
(0.017)
0.020
(0.003)
0.019
(0.003)
0.036
(0.003)
0.034
(0.003)
0.189
(0.048)
0.095
(0.029)
0.105
(0.023)
0.054
(0.013)
64,409
-14407
Yes
No
Yes
No
(4)
0.303
(0.010)
0.433
(0.015)
0.740
(0.013)
1.100
(0.006)
0.977
(0.011)
0.922
(0.009)
0.018
(0.002)
0.017
(0.002)
0.034
(0.001)
0.032
(0.001)
0.190
(0.032)
0.089
(0.018)
0.099
(0.014)
0.047
(0.007)
56,621
-12629
Yes
No
Yes
Yes
Parameter estimates and incumbency advantage estimates for House elections. Block bootstrap standard errors in parentheses are
clustered at the district level.
22
A few striking patterns are revealed in the table. First, the party weights that
voters use to estimate the ideological location of inexperienced challengers are dramatically higher than those for incumbents and experienced challengers. Across the
four specifications, the party weights range from 0.732 to 0.751 for inexperienced
challengers, 0.433 to 0.447 for experienced challengers, and 0.303 to 0.317 for incumbents. These results are very stable across the alternative model specifications
and are precisely estimated. I reject the null that any of the informational weights
are equal.36 Second, incumbents have the highest conditional probability of winning a citizen’s vote, followed by experienced challengers, and then inexperienced
challengers. This monotonic ordering of conditional vote probability with candidate
experience is consistent with a wide array of previous research.37 Again, the point
estimates are quite stable across the specifications. The presence of district fixed
effects and respondent-level covariates does not exert a large influence on these coefficient point estimates, but the model fit improves appreciably with these variables,
as evidenced by the decrease in the log-likelihood.
The bottom portion of Table 3 displays the House average estimated incumbency
advantage and its decomposition broken out separately for Republican and Democratic candidates relative to both experienced and inexperienced challengers. The
electoral advantage that an incumbent secures relative to an inexperienced challenger
ranges from approximately 3.2 to 5.3 percentage points and relative to an experienced
challenger from approximately 1.7 to 3 percentage points across the specifications.
36
Also, note that the party weight parameter estimates are strictly in the (0, 1) interval. The
estimation is completely unconstrained so this result provides evidence in support of the ideological
signaling model.
37
Jacobson (1989)
23
These magnitudes are somewhat smaller than the 5-10 percentage points or so typically estimated in the literature using post-World War II House elections.38 However,
in recent work Jacobson (2015) finds that the incumbency advantage has declined
significantly since 2000, reaching a low of 3-3.7 percentage points in the 2014 cycle.
Despite using individual survey data, as opposed to aggregate election returns, and
employing a very different estimation approach, my estimates of the incumbency
advantage from 2006-2012 are quite consistent with Jacobson’s findings. While the
party weight and experience effects are extremely stable even when district fixed
effects are added to the specification, the incumbency advantage results are more
variable across the specifications. In the analysis below that makes use of estimated
incumbency advantage, I rely on the preferred specification that includes district
fixed effects and respondent-level covariates.
The final four rows of the tables display the proportion of incumbency advantage that is attributable to the ideological signaling mechanism. In the preferred
specification that include district fixed effects and individual covariates, the proportion of the incumbency advantage relative to experienced challengers explained by
the signaling mechanism is 0.19 for Democratic candidates and 0.089 for Republican
candidates. The proportion of the incumbency advantage relative to inexperienced
challengers explained by the signaling mechanism is smaller at 0.099 for Democratic
candidates and 0.047 for Republican candidates. While the Democratic and Republican estimated incumbency advantages are very close to one another within each
specification, the cross-party differences are starker for the signaling decomposition.
38
Gelman and King (1990), Lee (2008)
24
Democratic incumbents derive approximately twice as much of their incumbency advantage from the signaling mechanism than Republican candidates. One potential
explanation for this finding is the difference in how the average voter evaluates the
ideology of their Democratic House candidate compared to the Democratic party as
a whole. As revealed in Table 1, the average CCES respondent in the sample places
the Democratic Party at -0.268 while the Democratic candidate is located at the
more moderate -0.127. In contrast, the average voter locates Republican candidates
at 0.288 and the Republican Party at 0.27. As a result, the increased ability for
a candidate to separate oneself from the party that is derived from incumbency is
relatively more valuable for Democratic House candidates and this is reflected in the
incumbency advantage decomposition.
Table 4 reports the coefficient estimates and incumbency advantage quantities
for the Senate. The table is organized identically to the House table, except, as
discussed above, I do not have data on whether a Senate challenger is experienced
or inexperienced and I only include state fixed effects in the estimation. The first
column reports the base specification with only year fixed effects. The second column
reports the specification with state fixed effects and the third column results include
individual respondent demographics in the estimation.
There are several important differences between the House and Senate results.
First, the party weights for Senate incumbents are substantially larger than the party
weights in the House. Second, the difference in party weights between incumbents
and challengers is trivially small and statistically insignificant. Both of these results
are consistent with a more nationalized electoral environment in Senate electoral
25
Table 4: Senate Elections
(1)
Party Weight (Incumbent)
0.717
(0.078)
Party Weight (Chall)
0.770
(0.043)
Incumbent
1.112
(0.021)
Challenger
0.887
(0.021)
Dem Inc Adv
0.030
(0.007)
Rep Inc Adv
0.035
(0.010)
Dem Signaling (proportion) 0.062
(0.111)
Rep Signaling (proportion)
0.097
(0.178)
Observations
67,166
Log-likelihood
-15105
Year FE
Yes
State FE
No
Respondent Covariates
No
(2)
0.704
(0.069)
0.759
(0.041)
1.108
(0.021)
0.891
(0.020)
0.028
(0.006)
0.032
(0.007)
0.078
(0.119)
0.074
(0.106)
67,166
-14351
Yes
Yes
No
(3)
0.694
(0.083)
0.735
(0.042)
1.110
(0.020)
0.890
(0.020)
0.028
(0.006)
0.032
(0.006)
0.057
(0.140)
0.051
(0.110)
58,875
-12456
Yes
Yes
Yes
Parameter estimates and incumbency advantage estimates for Senate elections. Block bootstrap standard errors in parentheses are
clustered at the state level.
contests. Most importantly, the proportion of the incumbency advantage attributable
to the signaling mechanism is only about 0.05, substantially lower than in House
contests. Additionally, the proportions of incumbency advantage attributable to the
signaling mechanism for Republican and Democratic candidates is much closer to
one another than in the case of the House elections. Recall that in House elections,
voters believe that the Democratic party is significantly to the left of the average
26
Democratic candidate, but do not have similar beliefs about Republican candidates.
In Senate contests there is no such asymmetry between Democratic and Republican
candidates.
Model Fit
Before quantifying cross-district variation in incumbency advantage, I evaluate the
model fit of the ideological signaling model relative to two plausible alternative specifications. First, I consider the possibility that voters do not use information about
candidates’ ideologies in their voting decision. This corresponds to setting γ = 0
in Equation 1. Under this scenario, voters only evaluate candidates based on their
valence and the additional covariates that predispose the voter toward either the
Democratic or Republican candidate. I fix γ = 0 and estimate the remaining parameters by maximizing the constrained likelihood function. I refer to this specification as
the no policy model. The no policy model is an important benchmark to investigate.
Some scholars argue that ideological positions play a small role in congressional elections compared to other factors39 Second, I consider the possibility that the voter’s
reported value of the candidate’s location on the CCES is actually the weighted estimate, x̂ndt , as opposed to the voter’s perception of the candidate’s position, x̃ndt . To
operationalize this model I use the voters’ reported location of the Democratic and
Rep
Republican candidates for x̂Dem
ndt and x̂ndt in Equation 1. I refer to this specification
as the alternative information model.40
39
Wright and Berkman (1986) provides an overview of this scholarly debate and argues that
electorates in Senate contests are responsive to candidate policy positions.
40
I test the alternative information model both because it is an interesting behavioral hypothesis
and because it is reasonable to disagree about how voters are interpreting the CCES questions. In
27
I use the fitted probabilities of the full model and the no policy and alternative
information models to classify each CCES respondent as a predicted vote for the
Democratic or Republican candidate and then plot the receiver operating characteristics curve for each model.41 Receiver operating curves that are more bowed out
relative to the 45 degree line have higher explanatory power than models with less
area under the curve.
As shown in the ROC graphs in Figure 1, the ideological signaling model has the
best classification success of the three models in both House and Senate elections.
While even the no policy model performs notably better than a model with no predictive power, adding the policy preferences of voters and candidates to the utility
function significantly improves classification accuracy. The alternative information
model, where voters use their self-reported candidate locations as the posterior estimates, performs better than the no policy model, but is notably worse than the
ideological signaling model. Comparing the House and Senate, we see only minor
differences between the two chambers with the alternative information model per2006 and 2008, the CCES describes a 0-100 ideological scale and then asks the respondent “[w]here
would you place [name of candidate]?”. In 2010 and 2012, the CCES asks respondents “How would
you rate each of the following individuals and groups?”, provides a prompt with the name of the
candidate, and then presents the respondents with the seven-point ideology scale ranging from “Very
Liberal” to “Very Conservative.” I use the model fit to adjudicate between the two interpretations
of what information the voters are providing on the survey.
41
A receiver operating characteristics curve plots the false positive rate (the proportion of observations where the respondent reports a Democratic vote intention that are incorrectly classified to
vote for the Republican) against the true positive rate (the proportion of observations where the
respondent reports a Democratic vote intention that are correctly classified to vote for the Democrat) using alternative cutoff values for the prediction. For example, the classifier could choose to
use the cutoff of 0.5: a respondent who has a predicted probability of voting for the Democratic
candidate greater than 0.5 is classified as a Democratic vote, otherwise the respondent is classified
as voting for the Republican. To construct the plots, I calculate the false and true positive rates
using alternative cutoffs between 0 and 1 inclusive in increments of 0.05.
28
Reciever Operating Characteristics Curve
1
Reciever Operating Characteristics Curve
1
0.9
0.9
0.8
0.8
0.7
True Positive Rate
True Positive Rate
0.7
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
Full Model
Alternative Information Model
No Policy Model
No Predictive Power Model
0.1
0
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
False Positive Rate
0.7
0.8
0.9
Full Model
Alternative Information Model
No Policy Model
No Predictive Power Model
0.1
0
1
(a) House Elections
0
0.1
0.2
0.3
0.4
0.5
0.6
False Positive Rate
0.7
0.8
0.9
1
(b) Senate Elections
Figure 1: Receiver operating characteristics curve for classification accuracy of survey
respondents’ reported vote intention in House and Senate elections. The graphs
are based on the fitted probabilities of three competing models: the full ideological
signaling model, the no policy model where the γ parameter in the voter’s utility
function is set equal to 0, and the alternative information model where the voter’s
posterior estimate of the candidate’s location is set at the reported value instead of
the weighted value. All three curves are based on models estimated with the full
set of district fixed effects and respondent demographic characteristics. The curves
plot the false positive rate against the true positive rate for alternative classification
cutoff values. The dashed line at 45 degrees is the no discrimination line that would
prevail for a model that had no classification accuracy.
forming slightly better in House elections.
The Cross-Section of Incumbency Advantage
Most empirical research on incumbency advantage is concerned with estimating an
average incumbency effect. The theoretical framework shows that incumbency advantage can differ dramatically depending on the distribution of preferences within
29
a district. Figure 2 plots the density of incumbency advantage in the House relative
to experienced and inexperienced challengers and in the Senate. The density plots
reveal significant cross-district variation in the magnitude of incumbency advantage.
For the incumbency advantage relative to inexperienced challengers in the House,
there are a handful of districts where the incumbency advantages is very close to
zero or even negative, the mode is around 0.04, and there are a small number of
districts with values above 0.06. The plot is quite similar relative to experienced
challengers, but the mode is shifted to the left and there is less dispersion. The
incumbency advantage density in the Senate is similar, but displays an event tighter
density without the extreme values present in the House districts.
While the presence of cross-district variation in incumbency advantage has received little attention in the past, the relationship of the incumbency advantage to
political characteristics of districts is more interesting to observers of American electoral politics. Specifically, I investigate how the ideological predispositions of districts
affects the magnitude of incumbency advantage. In moderate districts where large
portions of the electorate have ideal policies that are located in the interior of the
parties’ positions, an incumbent is able to stake out a location closer to the moderate electorate. In contrast, a challenger with the exact same individual location is
perceived as having an ideological location closer to their relatively extreme party.
The signaling value of incumbency is generally less important in extreme districts.42
42
In extreme districts where the incumbent is a member of the opposite party (e.g. an extreme
liberal district with a Republican incumbent), the ability to distinguish of the incumbent to distinguish herself from the party is electorally valuable. However, there are empirically very few extreme
districts where a member of the ideologically opposite party serves as an incumbent legislator so
this hypothetical scenario does not have an important effect on the cross-district variation in the
magnitude of incumbency advantage.
30
Density of District Average Incumbency Advantage (House Elections)
Density of District Average Incumbency Advantage (House Elections)
70
30
Democratic Inc Adv (Inc to Exp)
Republican Inc Adv (Inc to Exp)
Democratic Inc Adv (Inc to Inexp)
Republican Inc Adv (Inc to Inexp)
60
25
50
20
40
15
30
10
20
5
10
0
−0.1
−0.05
0
0.05
0.1
0.15
0.2
0.25
0
−0.1
0.3
−0.05
0
(a) House Elections
0.05
0.1
0.15
0.2
0.25
0.3
0.35
(b) House Elections
Density of State Average Incumbency Advantage (Senate Elections)
40
Democratic Inc Adv
Republican Inc Adv
35
30
25
20
15
10
5
0
−0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(c) Senate Elections
Figure 2: Density function of district average incumbency advantage for Democratic
and Republican incumbents in House and Senate elections.
This intuition suggests that incumbency advantage will be higher in moderate districts and lower in more extreme districts. The exact value of incumbency advantage
will vary subtly with the location of the candidates, parties, voters, and individual
characteristics of the voters. To examine how incumbency advantage varies empir31
ically as a function of district ideology, I regress the district estimated incumbency
advantage on two measures of district ideology.43 The first measure is the mean CCES
respondent ideology self-placement for each district and state. The second measure
of district and state preferences is the multilevel regression with post-stratification
derived from public opinion surveys developed by Tausanovitch and Warshaw (2013).
Figure 3 displays plots of the incumbency advantage relative to both experienced and inexperienced challengers against the CCES mean district ideology and
Tausanovitch and Warshaw (2013) MRP ideology estimate in the House. Figure 4
reports the plots for the Senate. The estimated incumbency advantage displays a
suggestive quadratic relationship where incumbency advantage is maximized in the
most moderate districts. While the relationship between estimated incumbency advantage and district ideology is less precisely estimated in Senate contests due to the
small sample size, there is still a statistically significant quadratic relationship for
the CCES measure of state ideology.
The results are consistent with Ashworth and Bueno de Mesquita’s (2008) theoretical predictions and Hirano and Snyder’s (2009) empirical finding that incumbency
advantage is higher in more competitive electoral districts. Hirano and Snyder (2009)
attribute some of the overall increase in incumbency advantage to higher direct officeholder benefits in competitive districts. The mechanism here is instead based on
cross-district differences in the electoral value of the ability to distinguish a candidate’s ideological location from the party’s.
43
The results are specific to the ideological configuration of parties, candidates, and voters in the
2006-2012 sample period and would vary in a different political context.
32
Estimated District Incumbency Advantage
−.02
0
.02
.04
.06
Estimated District Incumbency Advantage
0
.1
.2
−.1
−.25
−.15
−.05
.05
.15
Mean District CCES Respondent Ideology
Estimated District Incumbency Advantage
.25
−.25
Fitted values
−.15
−.05
.05
.15
Mean District CCES Respondent Ideology
Estimated District Incumbency Advantage
.25
Fitted values
−.1
Estimated District Incumbency Advantage
−.02
0
.02
.04
.06
Estimated District Incumbency Advantage
0
.1
.2
(a) House Elections: Incumbency Advantage (b) House Elections: Incumbency Advantage
Relative to Inexperienced Challengers
Relative to Experienced Challengers
−1
−.5
District MRP Ideology
Estimated District Incumbency Advantage
0
.5
−1
Fitted values
−.5
District MRP Ideology
0
Estimated District Incumbency Advantage
.5
Fitted values
(c) House Elections: Incumbency Advantage Rel- (d) House Elections: Incumbency Advantage
ative to Inexperienced Challengers
Relative to Experienced Challengers
Figure 3: Scatter plots and quadratic fits
Party Polarization’s Effect on Incumbency Advantage
One advantage of specifying a complete individual-level model is that it allows me
to investigate the effect of out-of-sample changes on incumbency advantage. While
there are many potential applications, I briefly focus on the effect of inter-party
polarization on incumbency advantage. The framework suggests that increases in
33
NM
MA
AK
WV
UT
SD
MT
TX
RI
NH DE WY
HI VAAZ
FL
NY
OH
PA TN
KS
MINJ
KY
WIMO
ID
AL
CA
IA
WA
OK
IL
NV
LA
NCGA
MN
MS
OR
MD
SC
AR
CO
NE
Estimated State Incumbency Advantage
.02
.03
.04
.05
Estimated State Incumbency Advantage
.02
.03
.04
.05
NE
ND
ME
ME
AK
NM
DE
VA
FL
MI PA
HI
NJ
CA
OR
SD
WY
UT
AZ
OH
WI
KS
MO
IA
SC
NV
GA
NC
WA
IL
MD
MT
NH
NY
MA
WV
TX
RI
MN
TN
KY
AL
ID
OK
LA
MS
AR
CO
VT
.01
.01
VT
ND
−.25
−.15
−.05
.05
.15
Mean State CCES Respondent Ideology
Estimated State Incumbency Advantage
.25
−.4
Fitted values
−.2
0
State MRP Ideology
Estimated State Incumbency Advantage
(a) Senate Elections
.2
.4
Fitted values
(b) Senate Elections
Figure 4: Scatter plots and quadratic fits
polarization create increased obstacles for challengers, particularly those attempting
to win seats in moderate districts. When challengers compete in ideologically moderate or opposed districts they are burdened by the relatively extreme ideological
labels of the parties they are affiliated with. While a challenger may attempt to
convey that they are ideologically proximate to the district median, this is difficult
to do because of the high party ideological weight that voter place on challengers.
Increasing polarization typically exacerbates this problem for challengers because
now the challenger’s party is now even more distant from the district median. In
contrast, increases in polarization can be beneficial to incumbent candidates because
the party weights that voters place on incumbents are smaller. The ideological information conveyed through incumbency more valuable to candidates in the increased
polarization scenario. While most of the normative literature on polarization focuses
on its consequences for gridlock and policymaking within the legislature44 , the per44
McCarty, Poole and Rosenthal (2006)
34
spective advanced here illustrates that polarization can also have the effect of further
entrenching incumbents.
The theoretical framework and parameter estimates allow me to quantify how
hypothetical changes in polarization would affect the incumbency advantage. To accomplish this, I simply scale individual CCES respondents’ estimate of each party’s
ideological location by a polarization multiplier. I then use the estimated coefficients from the full model reported in column 4 of Tables 3 and 4 to compute the
legislature-wide incumbency advantage for the given polarization multiplier. I repeat this procedure for all polarization multipliers between 0.5 and 2 inclusive in
increments of 0.1.
Figure 5 reports the simulated incumbency advantage for alternative party polarization scenarios in the House and Senate. As the figure makes clear, the incumbency
advantage is increasing in party polarization in both House and Senate elections.
However, the slope of this effect is significantly steeper in the House than in the
Senate. This finding is consistent with the result that informational effects are larger
in the House than in the Senate. Moreover, party polarization has a much greater
effect on the incumbency advantage defined by moving incumbents to inexperienced
challengers relative to the incumbency advantage defined by moving incumbents to
experienced challengers. This is also consistent with the informational advantage that
experienced challengers have relative to inexperienced challengers in House elections.
The results also allow the direct examination of out-of-sample counterfactuals. The
figures illustrate that reducing citizens’ perception of party polarization by 50 percent
would essentially eliminate the incumbency advantage in the House and Senate. In-
35
0.14
0.12
Simulated Incumbency Advantage as Function of Party Polarization (House Elections)
0.14
0.12
0.1
Estimated Incumbency Advantage
Estimated Incumbency Advantage
0.1
0.08
0.06
0.04
0.02
0.08
0.06
0.04
0.02
0
0
-0.02
-0.02
-0.04
0.5
Simulated Incumbency Advantage as Function of Party Polarization (Senate Elections)
Democrats (Incumbents to Challengers)
Republicans (Incumbents to Challengers)
Democrats (Incumbents to Experienced Challengers)
Republicans (Incumbents to Experienced Challengers)
Democrats (Incumbents to Inexperienced Challengers)
Republicans (Incumbents to Inxperienced Challengers)
1
1.5
-0.04
0.5
2
Polarization Multiplier
1
1.5
2
Polarization Multiplier
(a) House Elections
(b) Senate Elections
Figure 5: Simulated incumbency advantage as a function of party polarization. Party
polarization is increased or decreased by multiplying each respondent’s estimate of
the ideological location of the parties by a polarization multiplier. The dashed vertical
line represents a polarization multiplier of 1, which is equivalent to the observed
incumbency advantage in the sample. The models are estimated with the parameters
from the full model, which include both district- or state-fixed effects and individual
respondent demographic covariates.
creasing party polarization by 50 percent would increase the incumbency advantage
from approximately 2 percent to 5 percent in the House and from approximately 2.8
to 5.6 percent for Democrats and 3.2 to 6.7 for Republicans in the Senate.45 These
are large percentage point increases that illustrate how further increases in polariza45
At first glance, this result may seem to be in conflict with Jacobson’s (2015) finding that the
incumbency advantage has decreased in recent election cycles. However, in addition to the increase
in perceived partisan polarization, other features of the electoral system have also changed over
time so it is difficult to attribute the trends in the magnitude of the incumbency advantage that
Jacobson identifies as due to changes in polarization. A feature of the approach employed here is
that I am able to isolate one mechanism and examine its effect on the magnitude of the incumbency
advantage. A drawback of the approach is that partisan polarization may directly affect other
input variables, such as candidate and citizen locations, so holding these variables constant may
not capture the total effect of partisan polarization on the incumbency advantage.
36
tion may not only affect internal legislative policymaking, but may also spillover to
the electoral arena.
Robustness
In the Online Appendix, I implement a number of robustness checks. Across the
robustness checks there are relatively minor changes to the point estimates and
standard errors of the coefficient and incumbency advantage estimates. First, I
re-estimate the model on the restricted sample of House elections before 2012 to
address concerns that the results are contaminated by redistricting between the 2010
and 2012 electoral cycles. Second, I account for the differences in how the CCES
solicits ideological information between the 2006 and 2008 waves and the 2010 and
2012 waves of the study. As mentioned above, I use ideological responses on a 0-100
point scale from the 2006 and 2008 CCES and a seven-point scale from the 2010 and
2012 versions of the CCES. While I standardize all ideology values to take on values
between -0.5 and 0.5, there is still a potential that the finer grid available for ideology
estimates in 2006 and 2008 is affecting the results. To alleviate this concern, I round
all of the 2006 and 2008 ideology responses to their corresponding values on a sevenpoint interval between -0.5 and 0.5 and re-estimate the models with the transformed
ideology scores. Third, I impute missing values of candidate estimates by taking the
average report from voters in the same election district. Many of the respondents
in the CCES refrain from reporting an estimate of the Congressional candidate’s
ideological location. In the base specification, these respondents are removed from
the estimation sample. If the removed respondents have systematically different pa37
rameters than the included respondents then the parameter estimates will be biased.
To investigate the possible extent of this bias, I include omitted respondents by imputing the missing candidate locations using the average district estimate. Fourth,
I weight the results by the case weights used in the CCES. The CCES oversamples
certain subpopulations, such as likely voters. To accommodate the possibility that
the unweighted results generate biased parameter estimates, I weight the likelihood
function and estimate the parameters with this weighted likelihood function. Fifth,
I include the respondents’ self-reported partisanship as additional covariates in the
vote-choice equation. I use respondents’ three-point partisan identification and include self-reported Democrats and Republicans as two additional indicator variables
in the regression equation to allow the probability of voting for the Democratic congressional candidate to vary across self-reported Democrats and Republicans.46 A
concern with this approach is that some of the variation in self-reported partisanship
may be due to respondents’ ideology and, as a result, the estimated effect of partisanship will include some of the effect of ideology. Absent a credible research design to
disentangle the effects of individual ideology and partisanship on vote choice, these
results should be interpreted with caution. Unsurprisingly, the coefficient estimate
on Democratic partisanship is positive and the coefficient estimate on Republican
partisanship is negative. More interestingly, the ordering of the party weights is preserved and the magnitudes are statistically distinguishable from one another in the
case of House elections. With the inclusion of these partisan identity covariates, the
overall pattern of results is very similar to the base specification.
46
The omitted category includes all respondents who identify as Independents, respond don’t
know, or decline to answer the question.
38
Conclusion
I have developed and estimated a model of voter learning about candidate ideology
that generates an incumbency advantage. The empirical analysis shows that voters
in House elections believe incumbents are located closer to the individual ideological positions that the candidates take while challengers are closer to the positions
of their parties. However, the difference between incumbents and challengers are
substantively and statistically insignificant in Senate elections. The parameter estimates generate an incumbency advantage due to the ability of incumbents to signal
ideological positions distinct from their parties. I decompose the incumbency advantage into its valence and ideological signaling components and find that the signaling
component is larger in House elections than Senate elections. Using the estimated
parameters from the individual-level voter model I find that the magnitude of the incumbency advantage systematically varies with the ideological characteristics of the
districts and is highest in moderate districts. I also find that increases in the level of
partisan polarization would increase the magnitude of the incumbency advantage.
The results have important implications for the measurement of incumbency
advantage, voter processing of partisan ideological information, and the design of
electoral institutions in the presence of electorally entrenched incumbents. The
individual-level estimates of the magnitude of the incumbency advantage are similar to estimates previous research has found from aggregate election returns. Unlike
most prior empirical research, which has focused on estimating a legislature-wide
incumbency advantage, the individual-level estimates naturally allow me to examine
how incumbency advantage varies across districts. I find suggestive evidence that the
39
incumbency advantage is higher in moderate districts where the ideological signaling
mechanism is most valuable to candidates. While previous research has emphasized
the importance of partisan information in citizens’ evaluations of candidates’ ideology, I find that there is an interaction between party ideological information and
candidate experience in House elections. Incumbents are less beholden to the ideological information contained in their party than experienced and inexperienced
challengers. Voters place the highest party weight on inexperienced challengers. Finally, the analysis illustrates that attempts to level the playing field between incumbents and challengers through the design of electoral institutions depend critically
on cross-district differences in the magnitude of the incumbency advantage.
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