Toward a Fuller Understanding of the Incumbency


Toward a Fuller Understanding of the Incumbency
Wesleyan University
The Honors College
Toward a Fuller Understanding of the Incumbency
Advantage in State Legislative Elections: A QuasiExperimental Approach
Bradley T. Spahn
Class of 2011
A thesis submitted to the
faculty of Wesleyan University
in partial fulfillment of the requirements for the
Degree of Bachelor of Arts
with Departmental Honors from the College of Social Studies
Middletown, Connecticut
April, 2011
1 Introduction
2 Theory
3 Measuring the Incumbent Advantage
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Quasi-Experimentation at the Margin Between Winning and Losing 20
Electoral Rematches . . . . . . . . . . . . . . . . . . . . . . . . .
Repeat Competitors Facing New Opponents . . . . . . . . . . . .
Additional Independent Variables . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 The Growth of the Incumbency Advantage
Decomposing the Incumbency Advantage . . . . . . . . . . . . . .
Dealignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electoral Politics over time . . . . . . . . . . . . . . . . . . . . . .
Measuring Partisan Swings . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Conclusion
This thesis could not have been possible without the tolerance and encouragement of my advisor Elvin Lim. For taking on a student who was only halfprepeared at best and guiding me with a gentle hand, I owe you a debt of Gratitude. This thesis would also not have been possible without the freedom to
explore and learn R offered to me by Andrew Drechsler at Strategic Telemetry. In
that same vein, many thanks are also owed to Katharine Lauderdale for helping
this new R user cope with countless trivial problems. But most importantly, this
thesis would never have occurred without the twenty-two years of preparation by
my parents Tom and Linda Spahn. Though my mother did not survive to see me
write it, this thesis could never have been completed without her. It is dedicated
to her memory.
Chapter 1
The Incumbency Advantage in American Politics has been perhaps the single
most studied topic in the American sub-field. Its existence and persistence has
not only driven a broad and diverse literature, but has also created important
consequences for the reality of American politics. Any spirited discussion of the
problems that malign the United States Congress must, by obligation, if not tradition, include a discussion of the incredibly high rate of re-election of Congressional
incumbents. While the most important component of this effect is probably the
drawing of partisan districts rather than any particular electoral phenomenon, the
fact that incumbents are electorally privileged for any reason is cause for interest
and close study.
Drawing on work that dates back to Robert Erikson’s 1971 article first identifying the incumbent advantage in U.S. Congressional elections and Mayhew’s 1974
book Congress: The Electoral Connection that addressed the institutional framework through which incumbent advantage is perpetuated, a detailed literature
has developed quantifying the incumbency advantage and analyzing both empirically and theoretically the various factors that contribute to the congressional
incumbent advantage’s growth since the 1960’s (Erikson, 1971; Ferejohn, 1977;
Mayhew, 2004). Though the literature has focused on Congress, studies of incumbent advantage in state legislatures have provided a kind of natural experiment
by which to measure and compare the effects of the various explanatory variables
of incumbent advantage. Two important developments have emerged from this
literature: candidate quality has stood out as the most important contributor
to the increase in incumbency advantage since 1960 and legislative spending has
been shown to correlate with increased incumbent vote share (Cox and Katz, 1996
and King, 1991). This legislative spending is said to contribute not only to officeholders’ ability to provide constituents with government services, but it also
provides candidates with political staffers who help prepare them for the next
election. Finally, higher legislative spending usually means that legislators receive
a higher salary and can serve in that capacity full-time, providing more time to
garner media coverage for their work in the legislature and prepare for the next
election (Carey, Niemi and Powell, 2000).
While the United States Congress has rightly been the subject of most of
the incumbency literature, the wealth of data now available on state legislative
elections has made it ripe for analysis. Unlike the United States Congress, which
defines partisanship and receives ample coverage in the media, state legislators
operate in relative obscurity. But perhaps more importantly, their are a lot of
them. For political science then, the states offer a testing ground by which more
rigorous statistical procedures might be applied to test theories about the politics
of incumbency in general as well as to learn about how the phenomenon is manifest
in these state elections themselves (Uppal, 2009).
There are essentially three different ways to conceive of the incumbency advantage: incumbent victory, the retirement slump, and the sophomore surge. The
incumbent victory phenomenon is a recognition that, in general, incumbents tend
to get re-elected. This is a totally unsurprising trend because even if candidates
running in open-seat elections are of random quality, the fact that the incumbent
actually won indicates that they were at least better than someone, and likely
better than average. Measurements of incumbent re-election rate and incumbent
margin of victory are plagued by selection bias. All things being equal, voters
tend to prefer candidates that they perceive to be of higher quality. Thus, chosen
candidates can be expected to be of higher quality than their opponents (Ferejohn,
To illustrate the phenomenon, assume that a candidate’s quality, θ, is drawn
from a uniform distribution between 0 and 1 and that their quality cannot be
directly measured but is instead only revealed at the point that their quality is
compared with another candidate’s at election. For two challengers in a primary,
the expected value of the winner’s θ is 2/3.1 θ for the winner is higher because
the electorate selects candidates of higher quality. By the same process, if this
candidate goes on to face a candidate that has never won an election before, then
E {θwinner } = 3/4. However, if in a general election a primary election victor
faces another primary election victor, then the winner of that election will have
E {θwinner } = 4/5. For this uniform distribution of θ, E{θwinner } = 1 − n+2
. where
n is the number of candidates the election’s two participants have won combined.
= 1, suggesting that if incumbents always ran for re-election, then
incumbent candidate quality would converge to 1. As a consequence, if voters
prefer higher quality candidates, incumbent re-election rates would converge to
The incumbency literature has rightly converged on candidate quality, broadly
defined, as the primary driver of incumbent victory, though this result is singularly
unsurprising. As this simple model demonstrates, candidates that win elections
should be of higher quality than candidates that have been through fewer selection
This result as well as the other results in this paragraph are readily demonstrated by numerical simulation.
processes. This selection effect is so overwhelming that it overwhelms the more
interesting effects associated with being a member of the incumbent party, having
previously appeared on the ballot and having served in the office for which the
candidate stands for election.
The second incumbency phenomenon is the retirement slump, which refers to
the decline in electoral prospects for an office-holder’s party after the office-holder
retires. If one were to hypothesize that the electorate decides to vote solely along
partisan lines, then this slump would argue against the hypothesis and suggest
that qualities specific to a candidate, rather than the party, are relevant to interpreting electoral outcomes (Lee, 2008). The difference between the incumbent’s
last election vote total and the vote total for the member of his party who seeks
to replace him represents any electoral partisan swings as well as the difference
between the incumbent’s candidate quality and his replacement’s as well as the
incumbency advantage, which accrued to the incumbent but not to his replacement.
The trouble with the retirement slump measurement is that these two qualities, quality and incumbency, aren’t readily separable, thus making it impossible
to control for them. While the phenomenon is interesting in itself, it isn’t a
measurement of the incumbency advantage per se, but rather the measure of an
incumbent party effect. Further, when one considers that incumbents often retire strategically, often because they expect that a particularly tough election lies
ahead, the picture gets muddied further. For these reasons, the retirement slump
measurement is a particularly bad way to assess the magnitude of the incumbency
advantage, even if it is worthy of study on its own.
The final way to assess the incumbency advantage is to study the sophomore
surge phenomenon . This phenomenon refers to the the increased vote share and
likelihood of victory enjoyed by first-time incumbents when compared to their
previous election when they ran as a challenger. The difference between their
likelihood of victory and vote share in the initial election(which I’ll call t=1) and
their running for re-election to their sophomore term(t=2) is influenced by partisan swings in the electorate, increased name recognition from having previously
appeared on the ballot, and the benefits of incumbency(Butler, 2009). While this
method would appear to be fraught with the same sort of inseparability issues
as the other two methods, some clever statistical tricks can be employed to isolate these effects. To control for the incumbency effect, one can identify open
elections(those that have no incumbent running) and compare the vote total and
probability of re-election for the same candidate in this initial open election and
the candidate’s first re-election campaign.
Chapter 2 will begin by presenting Ashworth and De Mesquita’s model of
the incumbency Advantage (Ashworth and de Mesquita, 2008). In the model,
candidates are endowed with an ideology and a quality which they signal to a
median voter. Ashworth and DeMesquita build an empirically testable model
of the sophomore surge phenomenon that this chapter will selectively rebuild and
then address later in Chapters 3 and 4 using a regression discontinuity design. This
model is particularly fruitful in providing empirically testable predictions because
it deals in depth with the comparative statics of the incumbency advantage under
partisan swings and variation in office visibility.
The trouble with studying all cases of sophomore surge following an open
election is that incumbents that won an their initial election will be, on average, of
higher quality than the opponent they beat. From the quality-distribution model
presented earlier, one can also conclude that incumbents can also be expected to be
of higher quality than their re-election challenger as well, making their re-election
both unsurprising and at least in part a function of their higher than average
quality, rather than as a product of the incumbent advantage alone. Further, it
might be the case that the relationship between a candidate’s margin of victory in
an initial election and the candidate’s subsequent margin of victory is not unitary,
implying that the difference between the two is partially a function of the original
margin of victory.
To control for these factors, one can implement a regression discontinuity design to estimate the effect of having previously run and served in office for candidates that barely won their election (Hahn, 2001). The procedure involves fitting
a regression to predict either the probability of election at time t=2 or the margin
of victory in that election as a function of the margin of victory in the previous
of election at t=1. The intercept of this regression line with the line through the
margin of victory at t=0 represents the probability of election or the margin of
victory for candidates that won (or lost) with 0 votes. Thus, for winners at t=1,
the intercept is the limit of the predicted quantity as margin of victory goes to
0 from the right. Similarly, for losers of the previous election, the intercept is
the limit of the quantity being predicted as the margin of victory goes to 0 from
the left. If the incumbency advantage is truly an effect that accrues to incumbents, then we should expect to see a difference between the intercepts of the bare
losers and the bare winners(Uppal, 2008). If, on the other hand, that which its
referred to as the incumbency advantage is in fact exclusively a function of having
appeared previously on the ballot, then one should expect to see no statistically
significant difference between the intercepts for bare winners and bare losers, but
that both intercepts will be above the null hypothesis predicted intercept of no
ballot appearance or incumbent effects.
The regression discontinuity design was first applied to the incumbency literature by Lee in analyzing the retirement slump effect (Lee, 2080). Uppal used
a similar quasi-experimental regression discontinuity design for State Legislative
data in 2009. Uppal’s paper, which analyzes data from 45 states with single-
member districts in the years 1968-1989, quantifies the advantage that bare winners enjoy over bare losers in general elections. He estimates that bare winners
tend to win 70% of the time while bare losers win at t=2 roughly 40% of the
time. Uppal’s paper, however, ignores many important variables that are important predictors of electoral performance. After applying Uppal’s methodology to
elections that take place from 1968-2003 (a longer time period than Uppal uses),
Chapter 3 separates bare winners and bare losers into two categories: those that
run against new competitors at time t=2 and those that face electoral re-matches.
These natural experiments allow for the disaggregation and measurement of the
effects of having served in office and having previously appeared on the ballot.
This chapter will also briefly assess the particular state-specific qualities that lead
to better outcomes for incumbents. Contrary to earlier studies, conducted when
less data was available or where less sophisticated methods were used, this analysis
indicates that legislative district size is the most consistent institutional predictor
of incumbent re-election rates.
Using this same regression discontinuity design method to measure the incumbency advantage, Chapter 4 will turn to assessing theories about the incumbency
advantage’s change over time and its variation by party. While the results here
confirm earlier studies’ findings that the state-level incumbency advantage has
increased over time, I find that the nature of the advantage is such that present
theories about dealignment and legislative spending are inadequate to explain its
This thesis hopes to not only empirically assess many of the extant theories
about the incumbency advantage, but also to draw parallels between dynamics
in the incumbency advantage and the American political scene more generally.
In the past, the incumbency advantage has been treated as phenomenological
and chiefly a by-product of political institutions. Fascinating though it is when
viewed in these terms, the political component has largely been removed from
the incumbency advantage story. By breaking out the incumbency advantage by
year and by political party, a rich picture of the American political scene emerges.
When the political fortunes of the most vulnerable political actors in the system
are analyzed systematically, they reveal not only a new understanding of the
phenomenon they embody, but also a new story about the rise of the Republican
party in the period under study.
In Chapter 4 I invoke the term “Clear and Hold” to describe the steady ascendance of Republicans in the state legislatures. While the rise of Republicans
in the period is widely acknowledged, this thesis identifies a new and interesting
aspect of this ascendance. By turning successive waves median voters toward the
Republican party, a picture of a growing Republican dominance emerges. This
is a story that parallels the national story of Republican ascendance, but in a
more drawn-out way. If there is one singularly striking quality of the incumbency
advantage in state legislatures, it is that it is ultimately reflective of the national
political scene. This quality has been largely ignored in previous treatments of
the phenomenon, but the chapters that follow paint a more complete picture of
the phenomenon than has ever been offered before.
Chapter 2
The various factors that contribute to the incumbency advantage are both
complicated and not readily separable. For a formal model to be useful, it must
capture only what is essential about whatever phenomenon is being modeled while
also not assuming what it attempts to demonstrate. In public choice settings,
where strategic interactions between electoral competitors vie to win the votes
of utility-maximizing voters, theoretical models have the potential to become extremely complicated as layers of nuance are built into the model. Instead, simple
models from which general conclusions can be drawn should be preferred.
Ashworth and de Mesquita have developed such a model of electoral competition that illustrates how the incumbency advantage can arise out of simple assumptions about candidate signaling and voter behavior (Ashworth and De Mesquita,
2008). This section will proceed by explaining the model’s baseline assumptions
and then using these to describe the baseline behavior of their model. Ashworth
and de Mesquita then proceed to relax their assumptions in order to demonstrate
the behavior of the model under more realistic circumstances. Throughout the
whole process, their focus is on deriving monotonic relationships between their
variables, relationships that can be tested empirically later on.
Their model seeks to simulate the behavior of two-party electoral competition
for office in a single member district. In the model, all parameters are random
variables chosen from Normal distributions where distributions of mean � , and
standard deviation σ 2 are labeled N(�,σ 2 ). In the model, there is an initial,
open-seat election at time t=1 and then a subsequent election t=2 where the
incumbent from the election at t=1 faces a new challenger from the opposing
party. Subscripts refer to the candidate’s party, either left or right, denoted by L
or R, and the time, either 1 or 2.
Each candidate has an innate ability, θ , drawn from the distribution N(0,σθ2 )
that does not change from one election to the next. However, the electorate
doesn’t measure a candidate’s ability directly, but rather receives one signal, s,
about each candidate’s ability for each election cycle. The signal is of the form
s = θ + εθ where εθ is an error term drawn from the distribution N(0,σε2 ).
Each candidate’s policy position is dictated by his party, with the two parties,
L and R, having policy positions µL and µR , respectively, where each is a point in
the one-dimensional policy-space. The parties’ policy positions could eventually
be treated as choice variables, but for now, µL = −µR , with µL < 0.
Voters assign each candidate a utility u = s − (x∗ − µ)2 where x* is the
voter’s ideal point. Because two party elections are decided by the median voter,
which I will refer to simply as “the voter,” x* will refer to the voter’s ideal point,
drawn from N(γ,σx2 ) where γ is the electorate’s median partisan leaning. γ can be
thought of as the persistent preferences of the electorate’s median voter, while x*
is the voter’s ideological ideal point for a particular election. Voters will choose
the L candidate if uL >uR , i.e. if:
But note that because µL = −µR , µ2L = µ2R , so the squared terms cancel,
meaning that the median voter will choose the L candidate when: sL − sR >
2x∗ (µR − µL ).
To model the first election, choose values for all of the variables and run them
through the objective function above. The winner of this election will be referred
to as the incumbent. Because this author has liberal leanings, I’ll assume that
L has won the election at t=1. For the election at t=2, given that µL and µR
are held constant because they are characteristics of the party structure and the
incumbent‘s underlying ability, θL , remains the same, the incumbent is usually the
victor for the same reasons he won the election at t=1: his policies were preferred
by the electorate, he was of higher quality or both. Put simply, the electorate
selects better candidates at t=1 and they continue to be better candidates at t=2.
In the special case where the loser also decides to run at t=2, the only source of
uncertainty with regard to repeat incumbent victory comes from the fact that the
quality and ideology signals are subject to uncertainty and the voter’s ideal point
might shift. However, with repeated trials, one should find that incumbents are
victorious more often that not, a prediction universally confirmed in the literature
(Butler, 2009).
Consider candidates that win at t=1 because they are of higher quality than
their opponent. In the model all candidate qualities are drawn from the same
distribution, but the quality of incumbents at t=2 tend to be higher because of
the selection effect modeled in chapter 1. Though the authors choose a different
distribution for candidate quality, the phenomenon holds for both. However, at
the limit where sL − sR is infinitesimally small, the voter chooses based on an
ideological preference. It could be that the incumbent advantage holds here as
well because (µL −γ)2 < (µR −γ)2 , indicating that one party is simply ideologically
closer to the median voter than the other, this should be an unstable choice of
ideology as the disfavored party is incentivized to move closer to the median voter’s
ideal point. However, if the parties are ideologically equidistant from the median
voter’s partisan preference, i.e. if (µL − γ)2 = (µR − γ)2 , then the incumbent
should have no advantage at t=2. More generally, in elections at t=1 where
there is no difference in quality and the parties are ideologically equidistant from
the persistent partisan preferences of the electorate, Ashworth and de Mesquita
do not predict that the incumbent has any increased probability of winning the
subsequent election. Testing this prediction will be the primary focus of the
beginning of chapter 3.
One further consequence of this model relates to candidates elected in ideologically unfavorable environments. Consider a candidate L running in an election
where x∗ > 0. For L to win, the candidate must meet the selection criteria specified earlier, sL − sR > 2x∗ (µR − µL ). Because µR − µL is defined to be positive,
the candidate must signal that he is of higher quality than his opponent. For
candidates that win in such an environment, the expectation value of their quality is higher than it would be in an ideologically neutral environment because
they overcame an ideological obstacle to win the election. If γ < x∗ , then L can
expect to win as an incumbent because he can expect the electorate to moderate
while his quality remains much higher than the average challenger. Conversely,
candates from the ideologically favored party should expect to be disadvantaged
in the subsequent election as their is no expectation that they are of higher quality than their opponent and their ideological position is likely to be less favored
at t=2. Thus, in elections where one party does particularly well, candidates of
that party are expected o have diminished electoral prospects when they run for
If we define incumbent advantage as the increased likelihood that an incumbent
gets re- elected, then we can construct a simple function for the probability that
an incumbent gets re-elected. Define sL − sR = sm . In the open election at t=1,
E {sm } = 0. But because of selection bias, this is not true in subsequent elections.
If the L candidate wins when sL − sR − 2x∗ (µR − µL ) > 0 , then the L candidate
is favored to win when E {sL − sR − 2x∗ (µR − µL )} > 0. If we assume that the
long-term partisan preference of the electorate, γ = 0, this condition simplifies
toE {sm } > 0. Because sm is the difference between two normally distributed
random variables, the probability of an L victory is given by Φ( sσmε ) where Φ is the
cumulative density function of the normal distribution with mean 0 and variance
σθ . Because of the selection effect, E {sm } > 0, which implies that E Φ( sσmε ) > 12 .
One interesting extension of their model is to consider how changes in the variance of the σ terms influence the incumbent advantage. Ashworth and de Mesquita
argue that higher profile elections will lead to better media coverage and, in general, more effort informing voters about the candidates’ positions (Ashworth and
de Mesquita, 2008). Thus, for higher profile elections, the uncertainty embedded
in the quality and ideological signals should be lower.
For the balanced electorate, the probability of L winning is given by Φ( sσmε ).
To derive the effects on the incumbency advantage of increased uncertainty in the
quality signal, as would be expected in lower-profile elections, differentiate with
respect to σε :
Φ( sσmε )
−Φ� ( sσm )
This comparative static is negative because cumulative density functions have
positive first derivatives by definition (Ashworth and de Mesquita, 2005). Thus,
as the visibility of an office increases, the incumbent advantage should increase as
The framework laid out here is useful in providing testable hypotheses on which
empirical models of the incumbent advantage can be evaluated. In subsequent
chapters, Ashworth and de Mesquita’s explanation for the incumbency advantage
as well as their predictions about partisan swings and higher visibility offices
will be evaluated empirically. The models developed here is just the beginning
upon which a richer and more empirically-minded framework of the incumbency
advantage will be built. Chapter 3 will test Ashworth and de Mesquita’s prediction
of no incumbency advantage for candidates of average quality. Later in that
chapter, by linking population to office visibility, my extension of their prediction
about the change in the incumbent advantage with changes in signal quality will
be evaluated. Finally, in Chapter 4, their hypothesis that candidates swept into
office with a favorable partisan swing will endure lower rates of re-election will be
tested against the data. Ashworth and de Mesquita lay down a rich and highly
testable framework that Chapters 3 and 4 will thoroughly evaluate.
Chapter 3
Measuring the Incumbent
Isolating and measuring the Incumbency Advantage has long been a challenge for Political Scientists. After the phenomenon of increasing incumbent vote
margins was first identified by Erikson, various statistical techniques have been
developed to measure the incumbency advantage as both an increased probability of re-election and as an increased vote share for incumbents (Erikson,1971).
Though the literature has focused on the incumbency advantage in U.S. House
elections, newly compiled data of state legislative election results has opened up
new avenues for exploration that allow for more advanced analyses than has been
possible previously. In particular, this new data, which includes some 259,000
individual candidate vote totals, allows for robust statistical techniques to be applied to measuring the incumbency advantage as well as to test theories about its
development over time and its change over time(Carsey et al, 2004). This more
segmented view reveals a rich degree of variation in the incumbency advantage
that generally reflects larger national trends while also exhibiting novel behavior.
Because their is simply so much more data to be analyzed at the state level than
for the Congress, theories that could not be rigorously tested can now be explored
empirically for the first time.
With this in mind, this chapter should be thought of as an effort at proving
causally that the benefits of incumbency are in fact consequences of incumbency
and not some other phenomenon. Further, unlike much of the literature which has
focused on the increased vote-share enjoyed by incumbents, this chapter, like the
rest of the thesis, will focus on the probability of re-election (Jacobsen, 1987). In
general, incumbents are elected at such high rates that discerning variation in their
re-election rates is nearly impossible, making the vote-denominated incumbency
measure a natural substitute. This is unfortunate, however, because the amount
by which incumbents win is much less politically salient than whether they are reelected or not. Whether an incumbent wins by one vote or one hundred thousand,
so long as she is re-elected, the political consequences are largely the same. To the
effect that the margin of victory does matter, it is only relevant insofar as it relates
to the probability of re-election. With the possible exception of the candidate’s
ego, there are no material differences that stem from the margin of victory in
some initial election if the candidate’s long-term prospects of re-election are the
same. As such, this chapter will follow Uppal in focusing on the probability of
re-election rather than increased margin of victory (Uppal, 2009).
Like all of the analysis in the next two chapters, this focus on probability of
re-election is only possible because of the wealth of data available for state legislatures. As such, it should not be thought of a repudiation of the vote-denominated
incumbency literature so much as a recognition of the greater possibilities available at this level of analysis (Jacobsen, 1987). That these data have not been
exploited to their fullest potential is both surprising and fortuitous. But in any
case a rich political landscape is revealed herein.
The central question of the incumbency literature is why the incumbency advantage exists. The previous two chapters dealt at length with the effect of electoral selection at some initial election. Barring a voter preference against incumbents, one should expect, in general, for incumbents to be re-elected. Controlling
for this selection effect is the central challenge of the incumbency literature. The
holy grail of the incumbency literature is a measurement equivalent to a randomized experiment where candidates are randomly assigned to serve in office, after
which their electoral performance can be measured. Unfortunately, the cost of
conducting such an experiment is unacceptably high, requiring quasi-experimental
methods to be employed. One such method, first applied to the sophomore surge
effect by Uppal, is a regression discontinuity design (Uppal, 2009). This chapter will employ such a research design to measure the effect of having previously
appeared on the ballot or having served in office on a candidate’s chances of
re-election and vote total in the subsequent election. The method works by identifying cases where voters, in the aggregate, were close to indifferent between the
two candidates, and using these cases to calculate a logistic regression model that
estimates the magnitude of the effect when the margin of victory is 0 votes. At
the margin between winning and losing, purely random events like changes in the
weather can decide elections, providing a natural random assignment mechanism
for election outcomes.
The theory presented in the last chapter suggest that at the margin, E{sm } =
0. Thus, the probability that the winning candidate is re-elected, assuming γ = 0,
is Φ(0) = .5. If there is an incumbency advantage even at the margin , then
candidates that win an initial open election by 0 votes should go on to win their
subsequent election more than half the time. Further, to check that this effect
does indeed arise from incumbency and is not simply a consequence of having run
in a previous election, one can parse the chances of election for candidates that
ran and marginally lost in the previous election. If there is indeed an incumbency
advantage, then one should expect these marginal losers to win less often than
marginal winners in a subsequent election.
The analysis that follows was performed on a data set from 1967-2003 of every
state legislative general election result in single member districts (Carsey, 2004).
Though primary and multimember district data were available, they were set aside
here so that the same regression discontinuity research design could be applied
To set up the analysis, legislative elections with no incumbent running and
where the victor beats their opponent by less than 20% are identified. The victor’s
performance in subsequent elections was then recorded as was the performance
of the second-place finisher in the open election, if that candidate chose to run
Quasi-Experimentation at the Margin Between Winning and
As a first test to see whether Ashworth and de Mesquita’s prediction that
bare winners should win only half the time, I followed Uppal’s methodology and
grouped all of the winners based on their margin of victory, and then calculated
the portion of candidates with that margin of victory that go on to win re-election
at t=2 (Uppal, 2009). For instance, if 12 of 20 candidates that win the original
election by between 5% and 5.5% of the vote win re-election, then that range of
vote margins is assigned a probability of winning of 60%.
In figure 3.1, the probability of winning re-election for a given margin of victory
is plotted, with the blue lines representing the best-fit for the points to each side
Figure 3.1:
This graph shows the empirical probability of a candidate winning their first reelection campaign given their margin of victory in the first election. The grey areas
indicate the 95% confidence intervals around the regression lines, i.e. the “true”
regression will fall within the grey area with probability .95, given the empirical
distribution of the data.
of the vertical line where the margin of victory equals 0. Each dot represents
the probability of winning for a margin within .16% of the center of the point.
This margin was chosen because it maximized the r2 value of the regression line,
though the value of the intercept, which is the value of interest, was not sensitive
to the aggregation parameter chosen. For winners in the previous election, the
intercept of the line is .77, indicating that candidates that win an initial open
election will win re-election in the same district 77% of the time. This value
varied no more than 1% depending on the size of the margins of victory that were
combined together to measure a probability, indicating that the result is robust
with respect to this aggregation parameter. For the intercept, t = 24.7, indicating
that the incumbency advantage exists in this model with near statistical certainty.
This result is damning for the two-quality model of electoral selection. Even if
a candidate is chosen to take office at random, she will be re-elected 27% more
often than the model predicts. This suggests that in addition to choosing between
candidates based on their ideology and exogenously assigned quality, voters value
the qualities unique to incumbents, but not typically held by challengers.
Similarly, losers of the initial election win the seat the second time they run
for it just 43% of the time if they run against the sitting incumbent. This measurement is similarly robust with respect to changes in the vote aggregation and
changes in the lower limit of included margins of victory(i.e. those who initially
lost by more than 10%). The t-value for the intercept is -2.32 indicating that
the null hypothesis, that the intercept is actually .5, can be rejected with 95%
confidence . As such, these regressions show with a very high level of statistical
certainty that the incumbency advantage exists in state legislative elections for
the period.
From here forward, this chapter departs from Uppal’s framework in two important ways: by using logistic regressions and by disaggregating electoral rematches
from new pairings. Uppal chose to aggregate voters in the manner used above
(but aggregating margins of victory in .5% intervals) and then fit a fourth-degree
polynomial to the result (Uppal, 2009). Because the regression is predicting a
binary variable: a win or a loss, a logistic regression model is typically thought of
as more appropriate. Such a methodology has the advantage of not being sensitive
to the aggregation parameter chosen, thus removing some of the model-selection
bias. While the graphs in sections 3.3 and 3.4 will continue to use a strictly-linear
version of Uppal’s aggregation technique because it’s easier to understand visually, the models being estimated will instead be logistic regression models. While
regression models predicting a probability P of election at t=2 are generally of
the form P =
the “intercept” reported will not be a in the equation,
but instead P(m=0) where x is the margin of victory in the election at t=1. In
other words, the intercept is equal to
. where a and b are estimated by the
least-square logistic regression algorithm.
Electoral Rematches
While Uppal’s application of the regression discontinuity design to state legislative election data was a major step forward, he neglected to recognize that the
elections at t=2 were of two different forms. Most of the elections at t=2 featured incumbents running against new challengers, but there were also instances
in which the challengers from the previous election ran again while the incumbent
did not. Finally, there are those cases in which both of the original contestants
decided to run at t=2, leading to an electoral rematch. In such cases where both
candidates have run before, the effect of having previously appeared on the ballot
is controlled for, and the effect of actually serving in office can be measured. To
incorporate this extension, consider a model that separates a previous appearance
on the ballot and being an incumbent for both the candidate, a, and his opponent
P (election at t2 for candidate a | (margin of victory at t1 = 0)=c1 ia + c2 ba +
c3 i−a + c4 b−a + .5
In this equation, i is a dummy variable indicating incumbency, and b is a
dummy variable indicating whether the candidate had appeared on the ballot
before. If b is measured to be small relative to i, then Uppal’s original model can
stand as roughly complete. However, as will be demonstrated by the electoral
rematch data, the results dramatically indicate that these three types of elections
should be considered separately, indicating a dramatic flaw in Uppal’s model.
At the margin, winners of an initial open election can be expected to beat
their previous opponents with probability 60.5%, this result is statistically significant at well above the 99.9% confidence level. Because the losers and winners
are running against one another, the results are symmetric about P=.5. As such,
repeat challengers can be expected to lose 39.5% of the time and this result is
again significant at well-beyond the 99.9% confidence level, as expected. By this
measurement, for two candidates that essentially tie in the election at t=1, actually serving in office increases the odds of re-election by 26% over the expected
probability of victory for the loser in such an election.
This is a remarkable natural experiment, as it shows that when nearly everything is controlled for, voters still prefer incumbents. Borrowing from Ashworth
and de Mesquita’s theoretical framework, one should expect that at the margin,
the two candidates are of equal quality (Ashworth and de Mesquita, 2008). Further, because Democrats and Republicans are nearly equally represented on both
sides of the margin, there is no persistent ideological preference for one party or
another. There are precisely two qualities that differ between the election at t=1:
time has passed, and one candidate has served in office. These two factors in
Figure 3.2:
The probability of winning for a given vote margin. There are 527 candidates
represented on each side of the graph, elections were grouped into the nearest
percentage point and then plotted. The grey area represents the 99% confidence
interval around the plotted points.
combination make, on average, 13% of the electorate shift their support to the
incumbent candidate. As such, the incumbent effect must be significant, but it
also must not be based solely on scare-off effects either. While this set of test cases
does not imply that Jacobsen and Kernell’s scare-off effect, whereby incumbents
enjoy high rates of re-election at least in part because high-quality challengers are
dissuaded from running campaigns with a low-chance of success, does not exist, it
does imply that this recruitment effect is insufficient to explain the totality of the
incumbency advantage and that new explanations must (Jacobsen and Kernell,
Repeat Competitors Facing New Opponents
The other two sets of cases in the data are incumbents facing new challengers
and losers running again but against a new opponent. Unsurprisingly, the former
category is by far the most common type of election, as failed challengers are
normally deterred from running again. The latter category is the most remarkable
however, as it allows a direct measurement of one type of incumbency advantagehaving previously appeared on the ballot, without having to correct for the effect
of actually serving in office. This natural experiment has not been analyzed in the
literature, so this is the first attempt at disentangling these two distinct effects in
a quasi-experimental setting. Upon analysis, there were 166 such cases in the data
set. As can be observed from looking at figure 3.3, there is a clear discontinuity at
the margin between the two groups, confirming that for these cases as well there
is an advantage to actually serving in office beyond having appeared on the ballot.
Figure 3.3 is particularly interesting as it shows a natural experiment made
available in the state election data. The left side of the graph shows losers that
chose to re-run but without facing a rematch from their previous opponent. The
Figure 3.3:
The left side of the graph is plotted based on 166 losers of an initial election who
choose to run in the subsequent election, while their opponents do not. The right
side consists of 4262 incumbents who choose to run for re-election and face new
challengers. Because the left side of the graph has so few points, the grey area
indicates the 90% confidence interval around the regression line rather than the
95% confidence interval used elsewhere. Finally, while the graph indicates that
the intercept for the losers is .68, this quantity is sensitive to the aggregation
parameter. However, a logistic regression model offers a more robust estimate for
this intercept.
specific source of the previous appearance advantage is up for debate, as it could
come from increased candidate quality gained from the experience of having run
before, voter familiarity with the candidate’s name or the strategic allocation of
resources from other political actors seeing the seat as vulnerable for the incumbent party. But at the margin, these candidates are indistinguishable from the
candidates on the other side of the margin except that the candidates on the right
served in office and the candidate on the left did not.
These elections offer the most opportunity for inference about the incumbency
advantage because they allow for the separation and estimation of the previous
appearance advantage and the incumbency advantage in a quasi-experimental
setting. In a two-party election, the odds of any particular candidate winning
election at the margin is .5, which is also the estimate for the intercept for the
null hypothesis. Thus the total incumbent advantage can be thought of as being
the sum of the previous appearance effect and the effect from legislative service.
At the margin, the probability of winning election against a new challenger after
losing in the previous election is .615, this quantity is statistically distinct from
the null hypothesis prediction of .5 at the 90% confidence level. Note that this
estimate is different than the one that appears in the graph. If instead of a
logistic regression, a pure linear probability model were used, where the binary
dependent variable of winning at t=2 is predicted by margin of victory at t=1,
the intercept estimated is .605 and is greater than .5 at the 90% confidence level.
This thesis doesn’t employ linear probability models because they violate the
homoskedasticity assumption of the least-squares regression algorithm, but they
are a useful check nonetheless. The difference between the estimate of .68 from
Uppal’s method and the decidedly lower estimates from the latter two methods
is a strong indication that Uppal’s choice of regression models is not appropriate
for these data. Of course, Uppal didn’t recognize that this natural experiment
existed as a subset of his data, so this methodological misstep was ultimately not
Returning to the measurement of the previous appearance effect, its magnitude
relative to the legislative service effect offers much to consider. Because the literature has focused on incumbent advantage rather than the previous appearance
effect, the literature examining the sources of the incumbent effect has focused on
qualities that would best be described as being a consequence of actual service
in office. However, given that roughly half of the benefit of being an incumbent
comes from merely having run before, and presumably, doing well, explanations
must account for this component of the total effect. Explanations that focus solely
on attributes of legislative service that would not accrue to bare losers are only
answering half of the question.
For incumbents facing new challengers when they run for re-election, the intercept is .74 and is statistically significant at the 99.9% confidence level. This
intercept should be thought of as the sum of the legislative service effect and the
ballot appearance effect. Because the natural experiment of bare losers that run
again against new challengers measures the ballot appearance effect directly, the
legislative service effect is just the difference between the two intercepts.
Returning to the model stated in section 3.3, we can now solve for the coefficients of the four dummy variables.
P(election at t2 for candidate a | (margin of victory at t1 =0)= c1 ia + c2 ba +
c3 i−a + c4 b−a + .5
.74 = c1 1 + c2 1 + c3 0 + c4 0 + .5
.615 = c1 0 + c2 1 + c3 0 + c4 0 + .5
.605 = c1 1 + c2 1 + c3 0 + c4 1 + .5
.395 = c1 0 + c2 1 + c3 1 + c4 1 + .5
Solving this system of equations gives, c1 = .125, c2 = .115, c3 = −.085 and
c4 = −.135. Because c2 in particular is subject to some uncertainty because
of the relatively few elections that went into calculating the intercept of losers
facing a new opponent, these coefficients are subject to some uncertainty, though
they are correctly signed to at least the 90% confidence level. Readers may note
that the coefficients as measured don’t strictly make sense because they yield
slightly different predictions for competing candidates in the same election, i.e.
an incumbent running against a new challenger is predicted to win 74% of the
time while a new challenger running against an incumbent is expected to win 28%
of the time, this mismatch should be attributed to measurement error rather than
a deeper flaw in the model. What’s more important than the exact coefficient.
If instead one makes the simplifying assumption that c3 = −c1 and c4 = −c2
then the t=1 losers facing new opponents case can be ignored and the coefficients
can be recomputed with the following as follows:
.74 = c1 1 + c2 1 − c3 0 − c4 0 + .5
.605 = c1 1 + c2 1 − c2 0 − c2 1 + .5
This alternative specification gives c1 = .105, c2 = .135, a slightly higher
estimate of the ballot effect and a lower estimate of the legislative service effect.
Either specification is adequate, though the rest of this thesis will use the first
model because it incorporates all three types of sophomore surge types of elections
rather than just two.
Additional Independent Variables
Finally, in the tradition of Cox and Morgenstern and Carey, Niemi and Powell,
this chapter will explore what sorts of independent variables other than margin
of victory at t=1 are useful in predicting the likelihood of winning re-election for
incumbents (Cox and Morgenstern, 1993; Carey et al, 2000). While I’ve grown
skeptical of this line of inquiry in part because of a lack of clear testable theories
pertaining to the various variables being tested, the results are included here as
much to show the arbitrariness of past work on the subject as to actually add to
the general understanding of the subject. For each of the 45 states included in the
model, the average population of the district (measured in thousands of people) at
the most recent census was included as well as the length of the legislative session
over a two-year period. When these variables was included in the regression
model P =
one at a time, where x is the variable being tested and c
is its coefficient, both turned out to have small but statistically significant effects
on the incumbency advantage for incumbents facing both new challengers and
repeat challengers. Finally, following Cox and Morgenstern, legislative spending
per representative was added to the regression for elections that took place in the
90’s, the decade where such data was most readily available. Because of the small
number of total cases, the regression was not performed for losers at t=1 facing
new opponents.
Coeff. -Repeat Challengers Coeff. -New Challengers
Legislative Session
District Size
* : p<.1; ** : p<.5; *** : p<.01
While all of the variables presented above are statistically significant, the total
magnitude of their effect is small compared to the size of the incumbency advantage in general or even the error bars around the estimate of the intercept. Thus,
while these factors are interesting as a way of gaining some insight into what
variables are predictive versus which variables are not (legislator salary, total legislative spending, and legislative spending per constituent all had effects that were
not statistically significant). Ultimately their contribution is largely minor and
The one important conclusion to draw from this table is that district size positively correlates with an increased probability of incumbents getting re-elected.
In Chapter 2, Ashworth and de Mesquita’s intuition about the effects of increased
electoral visibility on the incumbency advantage was derived in detail, and the
comparative static indicatedthat increased visibility should lead to an increased
incumbency advantage, as was observed.
While it would be a major breakthrough to construct a model that would
predict the incumbency advantage as a function solely of institutional factors, I am
pessimistic in this regard. Ultimately the variation in the incumbency advantage
is much greater than the effect of any of these institutional factors. Further, as
will be shown repeatedly in Chapter 4, the political dynamics of the particular
year in which an election is taking place have a much larger effect than any of
these institutional variables. Nothing has been published in this area since 2000,
which might be because of a lack of interest, but it’s more likely because of a
lack of importance. While the paucity of analysis in the literature of the political
variation in the incumbency advantage discussed in Chapter 4 is a major oversight,
the lack of attention paid to institutional factors seems entirely appropriate given
their small contribution to the overall effect.
This chapter has developed a statistical model of the incumbency advantage using a more robust statistical technique than has been applied in the past. Though
Uppal’s work estimating the incumbency advantage using a regression discontinuity design for the years 1968-1989 was a major step forward, he failed to recognize
that the exact typology of the election had a very large effect on the ultimate mag-
nitude of the incumbency advantage. By taking this next step and splitting the
regression discontinuity design into the three different types of elections, independent measurements of the effect of legislative service and a previous appearance on
the ballot were produced. Surprisingly, the magnitude of benefit of having previously appeared on the ballot is almost as large as the benefit of having previously
appeared on the ballot.
Because these quantities were measured for elections in which there should, on
average, be no quality difference between the two candidates, Ashworth and de
Mesquita’s model of the incumbency advantage failed to hold at the limit where
the quality difference between the two candidates approached zero. On the one
hand this is indicative of a shortcoming in their model. On the other, it indicates
the difficulty in explaining the empirical reality of the incumbency advantage.
There are, to my knowledge, five types of explanations for the existence of
the incumbency advantage: incumbents are of higher quality than their challengers, incumbents are better partisan matches for their constituencies, incumbents scare off potential challengers, incumbents use their offices to indirectly buy
votes from their constituents and incumbents have better name recognition than
non-incumbents in the electorate(Abramowitz, 1975; Ferejohn, 1977; Cox and
Morgenstern, 1993; Jacobsen, 1983; King, 1991). The first and second explanations are controlled for in this model because at some initial election voters were
essentially indifferent between the two candidates, but they then came to prefer
the winner over the loser after the winner served in office. At the point that this
effect occurs both for repeat challengers and for new challengers indicates that
quality and ideology do not adequately explain the incumbent advantage. That
bare winners beat the bare loser in the previous election almost two-thirds of the
time indicates that the incumbent advantage persists even when the incumbent
has not been able to scare off a high-quality challenger. While section 5 of this
chapter confirms that legislative spending is an important piece of the puzzle, it
doesn’t explain why it is the case that repeated electoral contestants who never
hold office tend to do better than new contestants. Finally, while it might be the
case that incumbents and repeat electoral contestants simply have better name
recognition than their opponents, it strikes me as unlikely that in very low visibility offices that this effect would play any role at all. My subjective impression,
open to rigorous testing, is that most voters don’t know who their state legislators are, given that fewer than half could identify their representative in Congress
(Abramowitz, 1975).
Perhaps the most interesting aspect of the incumbent advantage is that it’s so
hard to explain. While many political scientists have tried to float explanations,
they don’t hold up to close scrutiny for the state legislative case. It goes without
saying that shooting down theories is easier than constructing them, but these
theories need to be scrutinized and rejected. It might be that some combination
of many factors, all of which cannot simultaneously be controlled for offers the best
explanation, but at present, no theory of the incumbent advantage is sufficient to
explain its empirical reality.
Chapter 4
The Growth of the Incumbency
Decomposing the Incumbency Advantage
Chapter 3’s main contribution was to recognize and quantify the different
components of the incumbent advantage and its manifestation in state legislative
elections. This chapter will proceed by measuring the incumbent advantage’s
components across time and by party to address the extant theories about the
incumbency advantage’s increase over the last 30 years of the previous century.
One of the important results in the state legislature literature is Cox and
Morgenstern’s finding that the vote-denominated incumbency advantage in state
legislative elections increased from 1968 to 1986 in the 13 states for which data was
then available (Cox and Morgenstern, 1993). Their explanation for this occurrence
was that state legislatures’ operating budget, measured on a per member basis,
increased over the same period. Though chapter 3 found that legislative spending
was indeed predictive of the incumbency advantage, it is categorically unable
to explain the existence (and, as we shall see, the rise) of the previous ballot
appearance effect.
Specifically, they found that when they included legislative spending per legislator along with the year as independent variables in their regression model of
the vote-denominated incumbency advantage, that legislative spending was significantly more predictive than the temporal component. Their explanation was
that as state legislators had more resources made available to them, these legislators would apply these resources to legislative casework and spend more time
campaigning because they receive higher pay. The implication, of course, is that
these are advantages that would only accrue to incumbents and not to losers that
previously appeared on the ballot and run for re-election.
Using the model outlined in chapter 3, the temporal legislative spending hypothesis can be tested. If Cox and Morgenstern’s explanation is correct, then one
should expect to see an increase in c1 over time. Further, if legislative spending
is the sole explanation for the hypothesis, then one should also expect to see no
statistically significantly increase in c2 over the same period. To test this, the 4
coefficients were measured for each year even year in the data set. Years ending in
2 are excluded so that the effects of redistricting are controlled for in the analysis.
Because fewer than 5 bare losers went on to run against new challengers in the
years 1988 and 1998, these two years are excluded from this analysis so as not to
bias the data with wildly uncertain estimates.
Figure 4.1 casts doubt on the legislative spending hypothesis because the advantage to serving in office actually declines or remains constant with time. Instead, the advantage of having previously appeared on the ballot increases over
time, indicating that institutional factors embedded in the political system but
not specific to having served in office drive the increase over these thirty years.
Notice as well that that same effect is observable in just the years 1968-1986 that
Cox and Morgenstern analyzed. As figure 4.1 indicates, the increase in the ballot
Figure 4.1:
Estimates for coefficients c1 and c2 are plotted along with a best fit line through
their points. For c1 , the slope of the line .-007 per year and the t-value is -.98,
indicating that the slope of the line is closer to 0 than the plotted value with
probability .65. For c2 , the slope of the line .011 per year and the t-value is 1.87,
indicating that the slope of the line is statistically significant at the 90% confidence
effect overwhelms the incumbent-specific effect, with an overall increase of .4% per
year in the advantage that accrues to incumbents running against new challengers.
Of course, this analysis doesn’t strictly contradict the temporal legislative
spending hypothesis; rather, it indicates some other correlated variable that also
impacts both incumbent and non-incumbent repeat office seekers would provide a
better explanation for the increase in the incumbency advantage (defined as c1 +c2 )
over time. Note that c1 even decreases in the time-period they study, indicating
that their office-holder advantage is essentially an artifact of their aggregating
the two terms, rather than looking to the natural experiment offered by losing
candidates that re-run for the same seat against a new challenger for more detail.
One possibility, about which data is not yet available, is that resource allocations have become more decisive in winning elections. Because resources are
deployed strategically by donors, presumably with the intention of winning support on issues before the legislature later on, they are more inclined to donate to
Figure 4.2:
The total incumbency advantage, defined as c1 + c2 , for the full span of years.
The slope of the line is .004 with a t-value of 2.1, indicating that the line has a
positive slope with 95% confidence.
campaigns they regard as having a higher chance of success. Given that the incumbent advantage exists, this suggests that a positive feedback mechanism might
exist whereby high rates of incumbent re-election in the past lead to even higher
rates in the future. If campaign spending has indeed become more important in
winning elections, than this feedback mechanism would increase the incumbency
advantage over time and explain the trend observed in the data.
As an interesting alternative measure of the officeholder advantage, consider
the electoral prospects of first-time bare incumbents facing off again against their
previous challenger, as shown in figure 4.3. Since both they and their opponent
have appeared previously on the ballot, the previous-appearance effect is controlled for, leaving only legislative service as the characteristic difference between
the two candidates. As can be readily observed, there is no upward or downward
trend across the graph, indicating that the advantage offered to incumbents over
their previous challengers hasn’t increased over time. As these elections are entirely independent from the elections detailed in figures 4.1 and 4.2, we now have
further verification of the general stagnancy of legislative service effects over the
Figure 4.3:
The portion of incumbents that win re-election facing repeat challengers shows
no upward or downward trend over time. While I cannot explain the very-low
incumbent re-election rate in 1990, though it would likely be an interesting subject
of future study.
period studied. Happily, the measurement of this effect is free from any bias from
incorrect model specification, suggesting that any explanation for the increase in
the incumbency advantage over time must be an account of the increased electoral
prospects of candidates making a repeat appearance on the ballot rather than of
actually serving in office.
In their article on the growing incumbency advantage in U.S. House elections,
Cox and Katz summarize two other explanations for the growing incumbency
advantage in state legislative elections (Cox and Katz, 1996). One, referred to
as the dealignment theory, posits that over time, voters became less attached to
parties and more attached to the personal characteristics of their legislators. In
particular, Mayhew suggests that that over time voters became dissatisfied with
parties as a cue for who to vote for and choose instead to look to candidatespecific qualities like incumbency (or, presumably, having previously appeared on
the ballot) to decide who to vote for (Mayhew, 2002).
If Mayhew is correct, then over time we should expect to see less of a difference
in the electoral prospects between the two parties as partisan swings become
less important and other qualities become more predictive of re-election in any
particular year. To test this hypothesis, I’ve broken up the sample by party
and measured the probability of re-election for first-time incumbents facing new
challengers and first-time incumbents facing their previous opponent again. I then
plotted the absolute value of the difference between the two parties’ performance
for each set of candidates. If Mayhew’s hypothesis is correct, one should see a
marked decline over the thirty years for which data is available. This is because,
if, as Mayhew predicts, a candidate’s political party were less important to voters,
Figure 4.4:
than partisan swings would become smaller in magnitude over time as voters cared
less about the partisan affiliation of their state legislator.
Because figure 4.4 shows no discernable trend in party effects over time for
either type of electoral contest at t=2, Mayhew’s dealignment story is very much
called into question. Further, even if the party data corroborated the dealignment
thesis, it still doesn’t explain why the rise in the incumbency advantage was
caused by an increase in the advantage from having previously appeared on the
ballot, rather than actual service in office. Though it’s conceivable that a voter
might actively value having seen a candidate’s name before more over time, this
would seem to indicate that voters were becoming less politically informed, rather
than more interested in a particular candidate’s history of political participation.
Indeed, the most surprising thing about the partisan breakdown of the incumbency
advantage over time is how profoundly exposed state legislators were to national
partisan swings that they could not possibly have taken a part in causing.
When evaluating the dealignment hypothesis, it’s hard to imagine dealignment not happening to at least some degree after the high watermark of partisan
differentiation of 1974. Indeed, it is true that the difference in measured incumbency advantage between the two parties has not been so great as it was in 1974.
But this should not be seen as proof that dealignment has taken place because
we also see substantial partisan swings in 1984, 1994 and 1996. It’s telling that,
from figure 4.5, the parties flipped having more success getting their incumbents
re-elected many more times in the latter part of the period than at the beginning.
While this indicates that voters were less loyal to a political party than they were
in the past. That is, they were no longer as aligned with a party, it does not mean
that personal qualities played a large role. Based on this, it isn’t so much that
moderate voters that swing elections were dealigned so much as they were more
frequently realigned in the latter half of the period. Put simply, voters haven’t
become detached from parties, they’ve grown more fickle towards them.
But if legislative spending cannot explain the rise in the incumbency advantage
over time as the candidates it benefits are not uniquely more successful and the
dealignment hypothesis doesn’t fit with the continued relevance of parties, what
is left to explain the rise? The answer must lie in the general political environment in which these candidates run. Namely, as repeat candidates become more
successful relative to new challengers over time while the electoral prospects of
repeat candidates facing one another are steady, the explanation for the increase
must rely specifically in the difference between repeat candidates and new ones.
Electoral Politics over time
The most striking example of a partisan swing is the 1974 election. Fueled
by disgust over Watergate, voters across the country punished Republicans in
Figure 4.5:
Each party’s incumbency advantage, defined as c1 + c2 , over the years 1970-2000
Congress, dramatically increases the Democrats’ advantage in both houses of
Congress and, as we see here, state legislatures. Perhaps the most notable victim
was future President George H.W. Bush, who lost what would have otherwise
been a safe seat in the Senate that year. While it’s a stretch to assign blame
for Watergate to Republican Congressmen, it’s possible to construct a narrative
whereby they share some complicity with Nixon for the atmosphere in Washington. These data, however, represent only freshman state legislators who barely
won their seat against a challenger of the opposing party. These are perhaps the
most un-empowered officeholders imaginable, superior only to municipal officials
in their influence over the actions of the President or the national party. Yet these
freshmen Republicans were routed at the polls that year, winning their seats only
35% of the time, less than half as often as the long-term trend.
Unsurprisingly, the Republicans that barely won their initial election in 1974
fared very well when they were up for re-election, winning 20% more of the time
Figure 4.6:
Incumbent re-election rate for incumbents facing new challengers by party. The
horizontal axis is the year of the initial election when they first took office, 19681998.
than their Democratic counterparts first elected in that same year, as demonstrated in figure 4.9. The pattern of a large swing election being followed by a
reversal of each party’s electoral fortunes relative to the other party is common
and occurs in all three major swing years from the data (1974, 1984 and 1994).
However, the “snap-back” is not enough to undo the effects of the initial election,
suggesting that though large partisan swings usually produce a partisan swing in
the opposite direction, this counter-swing is smaller than the initial swing and fails
to erase the initial gains. This pattern is most clear in figure 4.8. This pattern has
important consequences for our understanding of realignment and partisan gains,
as we see that Republicans are ascendant in the period being studied, a trend
that tracks well with larger national trends. Interestingly, just as Presidents tend
to lose seats in Congress during mid-term elections, in every mid-term election
year other than 1998 the President’s party has done a worse job re-electing their
incumbents than the opposition. Of course, 1998 was an exception to this trend
in Congress as well, suggesting once again surprising parallels between national
Difference in incumbency advantage, defined as c1 + c2 , between the two parties,
computed as Democratic advantage minus Republican Advantage
Figure 4.7:
politics and these vulnerable incumbents.
This is an opportunity to test Ashworth and de Mesquita’s hypothesis that
incumbents swept into office on partisan tides should be less successful than winners of the opposite party that were able to buck the tide and take office anyway.
Empirically, the corollary to their hypothesis is that the party that has better
partisan prospects one year should have a lower incumbent advantage in the next
election cycle. From Figure 4.6, we should expect the black line to cross the 0
partisan advantage mark between most elections. However, of the 9 time periods
measured that don’t stretch over decennial redistricting, a partisan switch only
occurs 4 times. While there’s no specific model available to test whether this is a
statistically significant repudiation of the hypothesis, it certainly indicates that a
great deal of skepticism is warranted.
What explains the low number of partisan switches observed over the time pe-
riod? When one party’s freshman incumbents outperform the others even though
both barely won the previous election, it’s an indication that the position of the
median voter is moving. The difference in party performance, as shown in figure
4.7, shows that Republicans were broadly ascendant in the period from 1970-2000
and that one of the party’s large swing elections, 1984 wasn’t a one-off event, but
was instead a final lurch in a series of advances for Republicans starting in 1976.
Essentially, partisan swings are not time-independent events, but rather come one
after the other, indicating that after the electorate swings toward one party, the
expectation shouldn’t be for a complete swing back toward the other, but rather
a continued swing in that direction.
Measuring Partisan Swings
To estimate just how powerful these swing elections are in moving public perception toward the ascendant party, I used the data from bare winners seeking
re-election to estimate how far the median voter swung in each such election. To
compute this quantity, I used the logistic regression equation estimated from Incumbents seeking new challengers to estimate the incumbent’s equivalent margin
of victory for a normal election. In 1994 freshman Republicans who barely won
their initial election win re-election 95% of the time. The logistic regression equation fitted for the entire set of incumbents facing new challengers for each year
is P (m, y) =
where P(m) is the probability of winning re-election
as a function of m, the margin of victory in the initial open election, and y, the
intercept for that particular year for incumbents from both parties. .094 is the
coefficient measured across the entire data set. It wasn’t re-measured for each
year so that the ratio of probability of victory to margin of victory that produces
the measurement would simulate an average election, rather than simulating the
result for a particular swing election. Normally, for a first-time incumbent to have
a probability of winning re-election of 95%, he would have had to win the initial
open election by roughly 27%. This means that in districts where the partisan
split was initially even, for the purposes of estimating the incumbency advantage,
there was a 27% partisan swing.
The results of this computation for each year where there is a measurable swing
is plotted in figure 4.11. When reading this graph, each point should be thought
of as a swing added on to the previous election. Consider the years 1974-1980.
Though Republicans were decimated with a 27.5% swing toward the Democrats
in that election, they were able to recover this deficit and actually increase it, such
that by 1980, the total partisan swing for the period is 5.4% toward the Republicans. By steady electoral gains in getting Republican incumbents re-elected at
higher rates than Democrats, conservatives were able to undo the political damage
from the Watergate affair and leave the decade with a net gain for Republicans
by this measure. Because the area under the curve for the period is greater above
the line than below it, one can conclude that this was a period of Republican
Ascendancy in the states, just as it was at the federal level.
Of course, by switching to the vote-denominated incumbency advantage, one
can compute a more direct estimate of each year’s partisan swing for marginal
incumbents. Across all years, the average margin of victory for an incumbent
that wins his initial election by an infinitesimal number of votes and goes on to
face a new challenger is approximately 17.5%. Figure 4.9 shows the estimated
margin of victory for an incumbent that barely wins an initial election by party
for each year. This margin of victory was estimated by running a linear regression
to predict margin of victory at t=2 as a function of margin of victory at t=1 for
all incumbents facing new challengers that win their initial election by less than
20% of the vote. The graph reports the y-intercept of the linear regression for
Figure 4.8:
An estimate of the partisan swing based on the success rate the dominant party
had in getting their marginal incumbents re-elected is plotted above. Because
there was such a small difference in incumbent re-election rates in 1988 and 1990,
these two points were excluded from the graph.
Figure 4.9:
Increase in vote share from an initial open election to a subsequent election by
each party at each year.
The persistent success of Republicans in moving the median voter rightward
since 1974 is both surprising and impressive. Every time the plot in figure 4.8 or
4.10 is above zero, Republicans are gaining ground relative to Democrats. While
Democrats have certainly responded by moving to the center and trying to co-opt
traditionally Republican pro-trade and pro-market positions, the reality is that
all of these estimates amount to a dramatic period of conservative realignment
over the latter thirty years of the twentieth century. But rather than starting
with Reagan’s election in 1980, the realignment starts with a tepid Republican
recovery from the Watergate election of 1974 but that continues to advance the
party through 1996, when Democratic prospects finally turn around.
Figure 4.10:
If one imagines a continuum of electoral district laid out in order of the ideological preference of the district’s median voter, then electoral gains are achieved by
turning marginal seats into safe seats and previously safe seats for the other party
into marginal seats. Through this process of turning median voters’ preferences
toward the Republican party, Republican’s gains in winning marginal seats were
locked-in at much higher rates than Democrats. Though both parties succeeded
in getting their marginal incumbents re-elected at rates higher than 50%, with
the sole exception of Republicans in 1974, Republicans simply did a better job of
advancing the party.
Realignment is usually conceived of as consisting of a decisive single election
where voters speak with one voice and call for change, but that’s simply not what
these data suggest. Rather, because of the persistent effects of the incumbency
advantage, incumbents are hard to unseat, but unseating them isn’t impossible.
If the average incumbent receives an extra 17% of the vote because he has
previously served in office, then a partisan swing of 17% in the opposite direction
is required to unseat an incumbent who won office with an infinitesimal margin of
victory. But based on the estimates above, a 17% swing is hardly unheard of. On
the contrary, there is a partisan swing of at least that size in 5 of the 13 elections
in the sample. Given that these partisan swings are larger than the incumbency
advantage itself, dealignment cannot stand as an explanation of the increase in
the incumbency advantage over time. If dealignment requires that party become
less important than candidate-specific qualities over time, then partisan swings
should not overwhelm the incumbency advantage so often in the period. But
further, the fact that Republicans persistently gain in the middle of the period is
further evidence that party is important for this period. Unless it was the case
that Republicans were in some way personally superior to Democrats over the
By the same token, realignment is a wanting theory as well. While a particular
election might be characterized as a realignment after the fact, there’s no particular quality of a realignment election in isolation sufficient to characterize it as such.
While it’s not inherently problematic to engage in historical re-telling about the
importance and meaning of an election, the empirical reality of how realignments
play out seems to not fit with the idea of a realignment happening in or being
facilitated by a single election. On the contrary, electoral realignment is not so
much an occurrence as a process. 1980 is often referred to as a realignment, but
by the measure of probability of re-election for marginal incumbents, that year
was less important than both 1978 and 1984 and of roughly equal magnitude but
opposite direction to Democratic gains in 1986. Indeed, while 1994 is also pointed
to as a realignment, it comes at the end, rather than at the beginning of a period
of Republican gains and is of lesser magnitude to the Democratic gains of 1974.
Why is it the case that the election of 1974 that preceded a series of gains for the
opposite party was not a realignment and 1994 was? By looking at either election
in isolation, the reason is by no means clear.
To understand the phenomenon of political gains better, one should think not
of the realigning election but rather the realigning period. The period under study
was a period of realignment towards Republicans because they were able to make
gains year after year, making median voters into Republican voters and bringing
previously Democratic seats back into play. It’s certainly true that 1980 and 1994
were more rhetorically exceptional than 1978, 1984, 1986 or 1996 and thus left a
more lasting impression on the American political consciousness. That Reagan
is still held up as a kind of standard-bearer for Conservatism and The Contract
for America continues to be discussed and emulated is a sign that not all election
years are of equal historical importance. But from the Schumpeterian viewpoint
that democracy only exists at the ballot box, these elections were not particularly
remarkable. They made electoral gains of a size and magnitude comparable to
many others.
Of the several two-part wartime clichés to gain prominence in the American
consciousness: “Shock & Awe,” “Divide & Conquer,” etc. one stands out as particularly apt: “Clear & Hold.” For a party to make durable electoral gains that allow
it to enact a policy realignment, they must clear electoral space by turning new
districts that were formerly held by the opposition party and turn them into safe
seats for their own. As the Southern Strategy turned safe Democratic seats into
safe Republican seats, Republicans were left to incrementally put new seats into
play by clearing out incumbent Democrats, whether through their own retirement
or defeat at the ballot box, and holding these newly held seats for their party.
This pattern is reflected in the incumbent advantage data analyzed and re-
ported here. The overall Partisan Swing to Republicans during the nearly two
decade span from 1976 to 1994 happened incrementally. Through most of this
period, Republican candidates that won their initial election by only a marginal
number of votes-were re-elected at a much higher rate than Democrats. That two
equivalently successful candidates went on to such different results in the next
election, and that Republicans had the upper hand in this subsequent election
more often than not indicates that the period was one of realignment but that no
year’s election results in particular distinguish it as the realignment year.
After picking apart the two pervasive theories explaining the rise of the incumbency advantage, now is the time to address where a convincing explanation might
be found. One common explanation for the incumbency advantage’s existence is
that incumbents tend to scare-off high quality challengers. At the point that the
incumbent won the previous election by a small margin, one would expect that
challengers would judge the incumbent as vulnerable and of low-quality, thus making a run more likely. However, if candidate quality is not simply a characteristic
of the individual but is instead an increasing function of electoral experience, then
average-quality competitors in an open-seat election become high-quality incumbents when they run for re-election. Potential Challengers who judge themselves
to be of high quality would then recognize that the seat is less vulnerable than
it was previously, and would choose to pursue other opportunities. To test this
theory, one can look to electoral re-matches, as detailed in figure 4.3, because
the effect of the experience of having previously run for the seat is controlled for.
That incumbents that run again against their previous opponent shows no sign
of an increasing over time suggests that candidate quality gained from running
previously is the most likely candidate for an explanation of the phenomenon. As
new data emerges from states that implement campaign finance reform programs,
future researchers should be able to assess whether having run previously gives
candidates an advantage in fund raising, and whether such programs mitigate this
Unfortunately, this analysis has been more critical than constructive. At the
beginning of this chapter, at least two viable theories existed to explain the rise of
the incumbency advantage over the last thirty years. However, in light of the data
presented here, they simply fail to explain the rise of the incumbency advantage
in the states during the time period for which data is available. It is my hope that
new data, particular about campaign spending, will emerge that can shed more
light on these issues. However, any further theorizing is merely conjecture. The
continued relevance of parties combined with the increasing benefits of a previous
appearance on the ballot and a declining benefits of service in office leave little
available in the literature to explain the dynamics of the incumbency advantage in
the states. Finding a convincing causal explanation will always be difficult so long
the paucity of district and election specific data persists. However, this chapter has
hopefully pointed future researchers in the right direction. Because it is electoral
experience rather than legislative experience that has actually driven the increase,
Political Scientists will have to look to politics, rather than to government, to find
an answer.
Chapter 5
The Incumbency Advantage is a deeply confusing, surprising and perhaps intractable phenomenon in American politics. Put in combative terms, this thesis
could be thought of as an attempt to push measurements of the incumbency of
advantage to its limits, to a place where most theories would suggest that it should
no longer exist. And yet it persists. Contrary to the thinking on the subject that
paints the phenomenon as a singular trend in a larger narrative of American politics, it is in fact profoundly embedded in these politics. By taking up an analysis
of the incumbency advantage by party over time, I find that much of the larger
partisan narrative over the last thirty years of the twentieth century is reflected
in the partisan dynamics of the incumbency advantage itself.
There’s a sense in which the politics of freshman state legislators that barely
won a first term is profoundly dull. They hold none of the great power that
accrues to federal office-holders or even the more senior members of their own
legislative assemblies. If politics is power, then the cases studied here are the
antithesis of power. They are powerless, maximally vulnerable. In the absence
of an incumbency effect, half of these legislators would be swept out of office the
next time they were up for election. Yet they persist. This thesis has not once
addressed the case of a specific legislator. If asked, I could not put a name to
even one of them. But together they reveal a surprisingly rich portrait of politics
contested at the margins of political survival.
Too much of the incumbency literature focuses on long-serving house members
who continue to win re-election year after year. Because their constituents select
them time and again over their challengers, they can be expected to be of higher
quality than their opponents. As such, one should expect that they would be
reelected. This approach to the incumbency advantage is profoundly dull and
not particularly relevant to the contestation of power that is rightly the subject
of Political Science. It might be the case that the surprising thing about the
incumbency advantage is not so much that power is contested, but rather the
absence of such contesting. But I’ve argued that in most of the cases other papers
have studies, this contestation should not be expected in any mode of analysis.
This thesis, on the other hand, sought out a sharp contrast. Through a quasiexperimental methodology it identified those elections that offer the most contestation and the richest detail and pushed these cases as far as they would go. In
the process, several new phenomena have been identified and many long-standing
theories have been subject to tests that they could not explain, and thus could
not withstand.
The substantive middle section of this thesis began by laying out in clear but
minimalist detail Ashworth and de Mesquita’s model of the incumbency advantage. It is likely the most sophisticated and inclusive model of the incumbency
advantage in the literature, from which three testable hypotheses were derived
(Ashworth and de Mesquita, 2008). First, they predict that when an incumbent
barely has an advantage over his opponent in some initial election, then that lack
of an advantage will persist at re-election and no incumbency advantage will be observed. Put another way, when the median voter is nearly indifferent between two
candidates at t=1, the voter will, on balance, persist in that indifference between
the two candidates at t=2. By measuring a very large incumbency advantage
in the set of electoral rematches, this particular hypothesis from Ashworth and
de Mesquita was proven false. Second, they predict that higher visibility offices
will lead to higher incumbency advantages because voters will get better signals
about the incumbent’s quality. Using days spent in legislative session and district
size, I found that this effect is indeed found in the state legislative elections data.
Finally, they predict that partisan swings in one direction will be counteracted
by lower incumbency advantages for the winners in that swing in the subsequent
election. Because this prediction failed in 5 of the 9 test years it could be applied
to, this hypothesis was also strongly discredited through empirical testing.
Next came the heart of the thesis, measuring the magnitude of the incumbency advantage using an improved variation on Uppal’s regression discontinuity
design and applying it to the full period of elections 1968-2003. Here again this
thesis took up one of the major papers in the field and applied thorough empirical
reasoning to test and extend its conclusions. A closer look at the structure of the
data showed that Uppal had aggregated four distinct categories of repeat candidates: incumbents facing new challengers, incumbents facing repeat challengers,
bare losers facing a new opponent and bare losers facing a rematch against their
previous opponent, and aggregated them into merely winners and losers. Not
only did Uppal miss an extremely important predictive variable in his analysis by
aggregating candidates in the way he chose, but he also missed an opportunity to
measure a new effect that had never appeared before in the literature. By controlling for and measuring the effect of having previously appeared on the ballot, this
thesis was able to present for the first time a disaggregation of the incumbency
advantage. As it turns out, nearly half of the value of being an incumbent didn’t
come from being an incumbent at all. Rather, it came from having previously
appeared on the ballot. The magnitude of this effect was measured two different
ways, both of which indicate pointed to similar results, making the finding very
But the fact that this effect existed isn’t the end of the story. Rather, the
change in the two components of the incumbency advantage over time was used
to evaluate the leading theses regarding the rise of the incumbency advantage
in the states. Cox and Morgenstern argued that the increase could be ascribed
to increased legislative spending on a per legislator basis. However, when the
components of the incumbency advantage were broken out, it turned out that
part of the incumbency advantage that legislative spending would actually affect
actually declined over the period.
Finally, the incumbency advantage’s variation by party over the final thirty
years of the Twentieth Century was found to be reflective of larger trends in the
nation’s political culture. These data suggest that the Reagan revolution was not
Reagan’s revolution at all, but rather began four years prior as the most vulnerable
incumbents to come out of the Watergate era were the first in a sustained wave
of Republican gains amongst the cadre of vulnerable freshman legislators. No one
could argue that these freshmen legislators were more important than Reagan in
affecting the turn toward conservatism of the 1980’s, but they do tell a story about
a wave that was building before Reagan came on to the scene to build it.
Contrary to their individual political circumstances, these vulnerable freshman
legislators tell a story of Republican ascendance that has not been told before.
That the country moved to the right in this period is hard to question, but the
story that the seeds of this revolution were sown by some of the weakest actors in
American politics has been underplayed.
This thesis has been short in new explanations for the existence and persistence
of the incumbency advantage. If anything, this thesis’ most significant contribu-
tion has been to question and refute all of the leading theories on the subject. In
this author’s judgment, there’s no theory or set of theories today that adequately
explain all of the phenomena identified herein.
It may be that the way forward lies in a new theory, but I question whether
such a theory could be constructed on the empirical groundwork that this thesis
lays out. Instead, the next step is to learn more about individual voter’s motivations when it comes to choosing between otherwise indistinguishable candidates.
Continuing to mine data from the U.S. house for clues about the incumbency
advantage will not lead to new insights; there’s simply not much left. The future
of the this phenomenon is to be found in new data being made available. I suspect that a pleasing explanation lay ahead, but it certainly does not lay in any
explanation proffered thus far. This thesis buries for good many of the theories
of the past, but it opens up a new more textured field upon which future theories
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