Toward a Fuller Understanding of the Incumbency Advantage in State Legislative Elections: A Quasi- Experimental Approach

Transcription

1 Wesleyan University The Honors College Toward a Fuller Understanding of the Incumbency Advantage in State Legislative Elections: A Quasi- Experimental Approach by 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

2 Contents 1 Introduction 3 2 Theory 11 3 Measuring the Incumbent Advantage Introduction Quasi-Experimentation at the Margin Between Winning and Losing Electoral Rematches Repeat Competitors Facing New Opponents Additional Independent Variables Conclusions The Growth of the Incumbency Advantage Decomposing the Incumbency Advantage Dealignment Electoral Politics over time Measuring Partisan Swings Discussion Conclusions Conclusion 55 1

3 Acknowledgments 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. 2

4 Chapter 1 Introduction 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; 3

5 CHAPTER 1. INTRODUCTION 4 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 ahighersalaryandcanserveinthatcapacityfull-time,providingmoretimeto 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

6 CHAPTER 1. INTRODUCTION 5 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, 1977). 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 {θ winner } = 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 {θ winner } =4/5. For this uniform distribution of θ, E{θ winner } =1 1 n+2. where nisthenumberofcandidatestheelection stwoparticipantshavewoncombined. lim (1 1 )=1, suggesting that if incumbents always ran for re-election, then n n+2 incumbent candidate quality would converge to 1. As a consequence, if voters prefer higher quality candidates, incumbent re-election rates would converge to 100%. 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 1 This result as well as the other results in this paragraph are readily demonstrated by numerical simulation.

7 CHAPTER 1. INTRODUCTION 6 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

8 CHAPTER 1. INTRODUCTION 7 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

9 CHAPTER 1. INTRODUCTION 8 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 aregressiontopredicteithertheprobabilityofelectionattimet=2orthemargin 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 0fromtheright. Similarly,forlosersofthepreviouselection,theinterceptis 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 asimilarquasi-experimentalregressiondiscontinuitydesignforstatelegislative data in Uppal s paper, which analyzes data from 45 states with single-

10 CHAPTER 1. INTRODUCTION 9 member districts in the years , 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 (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 rise. 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

11 CHAPTER 1. INTRODUCTION 10 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.

12 Chapter 2 Theory 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. 11

13 CHAPTER 2. THEORY 12 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,σθ) 2 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 + ε θ where ε θ is an error term drawn from the distribution N(0,σε). 2 Each candidate s policy position is dictated by his party, with the two parties, LandR,havingpolicypositionsµ L and µ R, 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, µ L = µ R, with µ L <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,σx) 2 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 u L >u R,i.e.if:

14 CHAPTER 2. THEORY 13 But note that because µ L = µ R, µ 2 L = µ 2 R,sothesquaredtermscancel, meaning that the median voter will choose the L candidate when: s L s R > 2x (µ R µ L ). 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 Lhaswontheelectionatt=1. Fortheelectionatt=2,giventhatµ L and µ R are held constant because they are characteristics of the party structure and the incumbent s underlying ability, θ L,remainsthesame,theincumbentisusuallythe 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 s L s R is infinitesimally small, the voter chooses based on an ideological preference. It could be that the incumbent advantage holds here as well because (µ L γ) 2 < (µ R γ) 2,indicatingthatonepartyissimplyideologically closer to the median voter than the other, this should be an unstable choice of

15 CHAPTER 2. THEORY 14 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 (µ L γ) 2 =(µ R γ) 2,thentheincumbent 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, s L s R > 2x (µ R µ L ). Because µ R µ L 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 re-election. 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

16 CHAPTER 2. THEORY 15 an incumbent gets re-elected. Define s L s R = s m.intheopenelectionatt=1, E {s m } =0.Butbecauseofselectionbias,thisisnottrueinsubsequentelections. If the L candidate wins when s L s R 2x (µ R µ L ) > 0,thentheLcandidate is favored to win when E {s L s R 2x (µ R µ L )} > 0. If we assume that the long-term partisan preference of the electorate, γ =0, this condition simplifies toe {s m } > 0. Because s m is the difference between two normally distributed random variables, the probability of an L victory is given by Φ( sm σ ε ) where Φ is the cumulative density function of the normal distribution with mean 0 and variance σ θ.becauseoftheselectioneffect, E {s m } > 0, which implies that E Φ( sm σ ε ) > 1 2. 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( sm σ ε ). 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 σ ε : σ ε Φ( sm σε ) σ ε )= Φ ( sm σ 2 ε 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 well. The framework laid out here is useful in providing testable hypotheses on which

17 CHAPTER 2. THEORY 16 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.

18 Chapter 3 Measuring the Incumbent Advantage 3.1 Introduction 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 17

19 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 18 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

20 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 19 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{s m } = 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

21 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 20 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 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 throughout. 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 again. 3.2 Quasi-Experimentation at the Margin Between Winning and Losing 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

22 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 21 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.

23 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 22 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 r 2 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 acandidateischosentotakeofficeatrandom, 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 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

24 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 23 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 Pofelectionatt=2are generally of the form P = 1 1+e (a+bm) 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 1 1+e a. where a and b are estimated by the least-square logistic regression algorithm. 3.3 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

25 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 24 on the ballot and being an incumbent for both the candidate, a, and his opponent -a: P (election at t 2 for candidate a (margin of victory at t 1 =0)=c 1 i a + c 2 b a + c 3 i a + c 4 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, thenuppal soriginalmodelcan 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

26 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 25 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.

27 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 26 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, 1983). 3.4 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 aquasi-experimentalsetting. Uponanalysis,therewere166suchcasesinthedata 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

28 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 27 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.

29 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 28 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

30 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 29 existed as a subset of his data, so this methodological misstep was ultimately not impactful. 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 t 2 for candidate a (margin of victory at t 1 =0)= c 1 i a + c 2 b a + c 3 i a + c 4 b a = c 1 1+c 2 1+c 3 0+c = c 1 0+c 2 1+c 3 0+c = c 1 1+c 2 1+c 3 0+c = c 1 0+c 2 1+c 3 1+c Solving this system of equations gives, c 1 =.125, c 2 =.115, c 3 =.085 and

31 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 30 c 4 =.135. Because c 2 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 adeeperflawinthemodel.what smoreimportantthantheexactcoefficient. If instead one makes the simplifying assumption that c 3 = c 1 and c 4 = c 2 then the t=1 losers facing new opponents case can be ignored and the coefficients can be recomputed with the following as follows:.74 = c 1 1+c 2 1 c 3 0 c = c 1 1+c 2 1 c 2 0 c This alternative specification gives c 1 =.105, c 2 =.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. 3.5 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

32 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 31 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 = 1 1+e (a+bm+cx) 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. Variable Coeff. -Repeat Challengers Coeff. -New Challengers Legislative Session * * District Size ** *** Spending * * : 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

33 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 32 unimportant. 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. 3.6 Conclusions 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 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-

34 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 33 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 ahigh-qualitychallenger. Whilesection5ofthis

35 CHAPTER 3. MEASURING THE INCUMBENT ADVANTAGE 34 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.

36 Chapter 4 The Growth of the Incumbency Advantage 4.1 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 35

37 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 36 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 c 1 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 c 2 over the same period. To test this, the 4 coefficients were measured for each year even year in the data set. Years ending in 2areexcludedsothattheeffects 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 that Cox and Morgenstern analyzed. As figure 4.1 indicates, the increase in the ballot

38 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 37 Figure 4.1: Estimates for coefficients c 1 and c 2 are plotted along with a best fit line through their points. For c 1,theslopeoftheline.-007peryearandthet-valueis-.98, indicating that the slope of the line is closer to 0 than the plotted value with probability.65. For c 2,theslopeoftheline.011peryearandthet-valueis1.87, indicating that the slope of the line is statistically significant at the 90% confidence level. 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 c 1 +c 2 ) over time. Note that c 1 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

39 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 38 Figure 4.2: The total incumbency advantage, defined as c 1 + c 2,forthefullspanofyears. 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

40 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 39 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.

41 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 40 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. 4.2 Dealignment 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,

42 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 41 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.

43 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 42 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 Indeed, it is true that the difference in measured incumbency advantage between the two parties has not been so great as it was in But this should not be seen as proof that dealignment has taken place because we also see substantial partisan swings in 1984, 1994 and 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. 4.3 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

44 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 43 Figure 4.5: Each party s incumbency advantage, defined as c 1 + c 2,overtheyears 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

45 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 44 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, 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

46 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 45 Difference in incumbency advantage, defined as c 1 + c 2,betweenthetwoparties, 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-

47 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 46 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 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 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. 4.4 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) = 1 1+e (y+.094m), 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

48 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 47 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 When reading this graph, each point should be thought of as a swing added on to the previous election. Consider the years 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

49 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 48 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.

50 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 49 Figure 4.9: Increase in vote share from an initial open election to a subsequent election by party. 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.

51 CHAPTER 4. THE GROWTH OF THE INCUMBENCY ADVANTAGE 50 Figure 4.10: 4.5 Discussion 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