Incumbency Advantage in State Legislatures: A Regression Discontinuity Analysis

Transcription

1 Claremont Colleges Claremont CMC Senior Theses CMC Student Scholarship 2017 Incumbency Advantage in State Legislatures: A Regression Discontinuity Analysis George John Vojta II Claremont McKenna College Recommended Citation Vojta, George John II, "Incumbency Advantage in State Legislatures: A Regression Discontinuity Analysis" (2017). CMC Senior Theses This Open Access Senior Thesis is brought to you by Scholarship@Claremont. It has been accepted for inclusion in this collection by an authorized administrator. For more information, please contact scholarship@cuc.claremont.edu.

2 Claremont McKenna College Incumbency Advantage in State Legislatures: A Regression Discontinuity Analysis submitted to Professor Cameron Shelton by George J. Vojta II for Senior Thesis Fall 2016 December 5 th, 2016

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4 Acknowledgements I am blessed to be surrounded by a large number of people who have been instrumental to my growth both as a student and as a person. These people fall into three groups: my family and friends, the institutions surrounding me, and my professors. Starting with my family, I would like to thank my mother, father, brother and sister (in no particular order other than seniority). You have helped me evolve from the self-proclaimed film major I was, to the self-proclaimed intellectual I am today. Also, thank you to my friends who have made my time at Claremont McKenna so enjoyable. To the institutions that helped shape the person I am today: Even though I moved on, I am eternally grateful to Northwestern University. It was there I discovered my passion for economics and fostered my scrappiness. To Terri Van Eaton and the FEI, I am thankful to you for giving me a research position, a place to work on this paper, and 100 Grand candy bars. Thank you Naina - for helping me make my thesis legible. And of course, I would like to thank Claremont McKenna College itself for taking me in as a transfer student at the start of my junior year. At the risk of sounding redundant, CMC has been a blessing to the student in me. Specifically, the Economics department here has been unbelievably generous. I have enjoyed every class, starting with Professor Marc Weidenmier s Intermediate Macroeconomics class and ending with Professor Yaron Raviv s Game Theory lectures. Finally, I owe a special thanks to three professors. To Professor Eric Helland: Although I never took one of your classes, my economics education has been fundamentally shaped by working with you. From working under you as an amateur research assistant (I would now describe my proficiency as novice ), to serving as your teaching assistant, and to seeking your guidance about literally anything and everything, I cannot express the gratitude I have for you. To Professor Arndt: Thank you for taking time out of each week to meet with me to ensure that this paper was as strong as it could be. While you were under no obligation to work on this project with me, you simultaneously demanded I stay on track and forced me to make sense, and if you ask around you might find that it can be difficult to get me to do either. Lastly, of course, to my reader Professor Cameron Shelton: Thank you. You have challenged me inside and outside of the classroom; first, in your Advanced Macroeconomics class and then in supervising me as I composed this thesis. There is no one on this planet more responsible for my caffeine intake. You manage to answer my onslaught of questions and s not only with a straight face, but also with enthusiasm. You have fostered my growth as an economist (if I can call myself that) more than anyone else. Thank you all, George

5 Abstract This paper measures the party incumbency advantage for the Democratic Party in state legislatures nationwide. To do so, this paper employs regression discontinuity design (RDD), following the structure laid out in Lee (2008). The results show a stronger incumbency advantage in state legislatures than the 8% figure found for U.S. House of Representative elections by Lee (2008), with a finding of a 14% advantage for lower houses nationwide and a 12% advantage for upper houses nationwide. Furthermore, this paper finds a strengthened incumbency advantage in states that hold their elections in offyears (34% in lower houses and 21% in upper houses). The paper concludes by suggesting that the boosted incumbency advantage for off-year states is a consequence of depressed voter turnout, testing this hypothesis using the Virginian lower house as a case study. Analysis suggests that the incumbency advantage drops substantially to 8% during years with a gubernatorial race and high voter turnout, and jumps substantially to 25% during years without a gubernatorial race and low voter turnout. However, large errors prevent these results from being statistically significant.

6 Table of Contents Introduction... 1 Methods... 6 Data Empirical Analysis Discussion References Appendix... 33

7 1 Section One Introduction Although the 2016 presidential election between President-elect Donald Trump and former Secretary Hillary Clinton monopolized the vast majority of the media s political coverage, this year there were over 500,000 elections for public offices. 1 With the ever-increasing influence of the public sector on all spheres of life, from social movements to the economy, it is only natural that we investigate what factors influence elections. One such factor is the incumbency advantage. There exists a plethora of literature examining the existence of both candidate and party incumbency advantages in United States politics; as Ansolabehere et al. (2007) notes, the existence and growth of the incumbency advantage has been well documented for general elections for all levels of the U.S. government. 2 Because this sentiment is echoed repeatedly in political science and economic literature alike, the interesting question is not whether the incumbency advantage exists, but instead why it exists and what factors affect it. In this paper, I build upon the ecosystem of political economic literature by measuring the size of the party incumbency advantage for the Democratic Party in state legislatures nationwide. To do so, I implement regression discontinuity design (hereafter RDD ), laid out in Lee (2008), to measure the incumbency advantage in state legislatures across the United States. This experiment is interesting because RDD has never been used to measure the incumbency advantage at the state level. While larger scale elections understandably command the vast majority of academic and media 1 Nir, David (2015) 2 Ansolabehere et al. (2007)

8 2 notoriety, local elections are unjustly ignored; these legislatures exert substantial economic pressures such as controlling state tax rates and implementing regulations that affect corporations. Additionally, in 2012 state government spending outpaced federal government spending as a percentage of the gross state product. 3 Because of these substantial economic pressures, state legislatures demand further investigation. There is precedent for the idea that economic conditions and political institutions can affect the magnitude of the incumbency advantage. In regards to American political institutions, Cox and Katz (2002) argues that the act of decennial gerrymandering protects incumbents from real political competition, which strengthens the incumbency advantage. Though the United States shows a virtually ubiquitous incumbency advantage, this is not the case in other countries. In fact, Uppal (2009) shows the importance of economic stability for the incumbency effect outside of the United States: the paper actually finds an incumbency disadvantage for Indian state legislatures, noting that states with lower availability of public goods, higher unemployment and larger levels of poverty show a relatively greater incumbency disadvantage. Societal and technological factors also appear to affect the incumbency advantage. Prior (2006) contends that the rise of television gives voters disproportionate amounts of information about their incumbents relative to their political challengers, which is seen as a compelling reason for the increasing incumbency advantage. In this first stage of the experiment, my findings are consistent with the consensus, as I record both a positive and highly statistically significant incumbency 3 Millsap, Adam (2015)

9 3 advantage for upper and lower houses nationwide. Additionally, my measures of 15% in upper houses and 12% in lower houses are both notably larger than the 8% figure found for the U.S. House of Representatives in Lee (2008). 4 This 8% figure from Lee (2008) is outside the 95 th percentile confidence interval of both the upper and lower houses, proving that these results are statistically larger. The fact that the incumbency advantage is larger for state legislatures is consistent with the notion set forth by Prior (2006) that when voters are given disproportionate information about two candidates, they will vote for the one they know more about. As evidenced by Rogers (2013), most citizens know very little about their state legislatures or their district s representative. However, Ansolabehere et al. (2007) points out that incumbency [is] one of the most important pieces of information in elections and voting. 5 The paper suggests that voters see incumbents as one of their own and that those currently in office are able to market their historical political successes. In contrast, political opponents to these seats rarely have any political experience at all. These ideas in conjunction form an argument that state legislatures elections inherently exhibit disproportionate information. Next, I analyze the incumbency advantage only in states that hold their elections in off-years (e.g. 2015, 2013, 201l) to assess the impact of insulating local elections from federal elections. Four states within the United States hold their local state elections during off-years that are necessarily separate from federal elections. These states are Louisiana, Mississippi, New Jersey and Virginia. While midterm election turnout is 4 Lee (2008) pg Ansolabehere et al. (2007) pg 5

10 4 already fairly low (only about 36.4% of eligible voters nationwide turned out to the polls in 2014), off-year election turnout tends to be even lower. For example, Virginia generally exhibits higher turnout rates than the national average on presidential years, 6 but had less than 30% of voters turn out for the 2015 state elections. This was down from already relatively low 41.6% turnout in the midterm election year 2014 (Table V). Turnout climbs when the gubernatorial race is on the ballot. Depressed turnout can have two possible effects on incumbency advantage. I hypothesize that off-year states demonstrate higher party incumbency advantage because the only people who turn out to vote in these districts are those in the dominant party s network, who are more excited and have more at stake in these smaller scale elections. These districts are already less competitive and more homogeneous than states as a whole as evidenced by Cox and Katz (2002), which argues that gerrymandering virtually eliminates real competition within individual districts. Here, I find that off-year states exhibit a higher incumbency advantage than the nationwide results: off-year lower houses demonstrate a boosted 34-point incumbency advantage (with 5.72% margin of error), placing the 14% national figure outside of the 95% confidence interval. Upper houses in off-year states show a 21-point advantage, up from 12% nationally. However, with 8.74% margin of error, the 12% number falls in the 95% confidence interval. The lower house result effectively refutes the alternative that those who vote in off-year elections are merely high information voters, because an increase in high information voters should undermine the incumbency advantage as they, theoretically, more highly scrutinize their candidates % turnout of eligible Virginian voters in 2012 versus the national average of 58%

11 5 To further support the point that low turnout boosts the incumbency advantage, I look at Virginia as a case study. First, I model Virginian voter turnout as a function of the presence of different elections, showing that off-year elections depress turnout by 7% while gubernatorial elections boost it by about 10%. To illustrate the impact of this deviation, I run RDD in Virginia during years with a governor on the ballot versus those where the governor is not on the ballot. While the average lower house incumbency advantage in Virginia is about 16%, during gubernatorial races (when turnout is higher) the incumbency advantage falls to only 8%. This 8% finding is insignificant and has a relatively high error term of 9.46%, signaling higher volatility in these years. When the governor seat is not on the ballot, the incumbency advantage jumps to over 25% with over 99% significance and 8.67% margin of error. However, because these two findings fall within the 95 th confidence interval of each other, they are not statistically different. Thus, the results cannot confirm the findings from the earlier off-year regressions nor reinforce the hypothesis that depressed turnout boosts incumbency advantage despite the separating deviations. The rest of the paper observes the following structure: Section Two discusses the implementation and efficacy of RDD, while Section Three examines the Inter-University Consortium for Political and Social Research data. Section Four discusses the empirical analysis and Section Five concludes with a discussion about the implications of the results.

12 6 Section Two Methods I follow Lee (2008) in measuring the party incumbency advantage for the Democratic Party via regression discontinuity design. The variable margin t (margin t-1 ) is calculated by taking the difference between the Democratic candidate s vote share and their highest performing opponent in this election (during the last election). This variable is positive when the Democratic candidate wins the election and negative when they lose. Similarly, a positive score for margin t-1 indicates a Democrat is the incumbent in the current election while a negative score indicates the Democrats are not the incumbent party. In the event that two Democratic candidates compete against each other in the same election, I simply drop the lowest performing Democrat. Margin(t) Regression function fit (Upper House) Margin(t-1) Sample average within bin Polynomial fit of order 4 Figure 2a Figure 2a illustrates the relationship between margin t and margin t-1. Taken from the aggregation of upper houses throughout the nation, this figure serves as a physical representation of the equation (1) we hope to analyze. Here, there is a noticeable discontinuity at the threshold margin t-1 = 0, or distinction between party incumbent and not.

13 7 margin t = β 0 + β 1margin t-1 + β 2d + ε where: d = 1 if margin t-1 > 0 d = 0 if margin t-1 < 0 (1) In equation (1), d indicates whether the Democratic candidate is the party incumbent. For the purpose of this experiment, we are most interested in analyzing the discontinuity (β 2) that occurs at the threshold margin t-1 = 0. This coefficient is only activated when margin t-1 > 0, symbolizing the boost a candidate gets when they are the party incumbent. Lee (2008) found an incumbency advantage (β 2) of ~ 8%. β 0 represents the fixed effects of a district, such as demographic and partisan make-up, political resources for the party, and other static indicators. β 1 represents the positive coefficient that measures the relative strength of the party by how they performed in the past election. This can be conceptualized by thinking about this as shorter term party popularity, where the better the Democrats did in election t-1, the more attractive they are to potential campaign investors, the more media attention they get, etc. Thus, I expect a positive relationship between the variables margin t and margin t-1. In a standard regression, one would expect the curve to be continuous and the limits to be equal. However, the reason that RDD is so provocative is because we expect a discontinuity at the threshold where: lim mmmmmmmmmmmm(tt 1) 0+ (β0 + β1margin(t 1) ) lim mmmmmmmmmmmm(tt 1) 0 (β0 + β1margin(t 1)) (2) Thus, the incumbency advantage can also be conceptualized by the equation (3).

14 8 β 2 = lim mmmmmmmmmmmm(tt 1) 0+ (β0 + β1margin(t 1) ) lim mmmmmmmmmmmm(tt 1) 0 (β0 + β1margin(t 1)) (3) Additionally, I calculate each candidate s probability of winning in election t, given their performance in election t-1 (hereafter ProbWin t ), by creating bins within margin t-1 and counting the fraction within the bin where Democrats were elected. With this new variable ProbWin t, I again run RDD to find the change in a candidate s probability of winning. Because the variables margin t and ProbWin t similarly represent the Democratic candidate s success in election t, I expect ProbWin t to display a similar relationship with margin t-1, shown mathematically by equation (4) and Figure 2b: ProbWin t = β 0 + β 1margin t-1 + β 2d + ε where: d = 1 if margin t-1 > 0 d = 0 if margin t-1 < 0 (4) Regression function fit (Upper House) Probability of Candidates in Election t Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 2b The key assumption required for RDD is random assignment, where observations cannot choose which side of the threshold they fall. Without this assumption, there is no way to analyze the impact of being an incumbent: candidates would just force themselves

15 9 to the winning side. Fortunately, the nature of elections allows us to satisfy this condition. As Lee (2008) explains: The crucial assumption here is that- even if agents can influence the vote there is nonetheless a non-trivial random chance component to the ultimate vote share It is plausible that there is at least some random chance element to the precise vote share. For example, the weather on election day can influence turnout among voters. 7 Density Kernel density estimate Density Kernel density estimate marginlast kernel = epanechnikov, bandwidth = marginlast kernel = epanechnikov, bandwidth = Figure 2c We can further test this assumption by performing a density test. If there exists a noticeable discontinuity in the density assignment at our target threshold (margin t-1 = 0), the validity of our experiment is at risk. This would suggest that candidates have a way of manipulating their score from being just below the threshold to just above the threshold. Table 1 shows the data passes the RD Manipulation Test to the 99th percentile (with a t statistic of ). Figure 2c illustrates the lack of a discontinuity at the threshold when implementing the density test. This makes sense intuitively as well; because only one candidate can win an election, if a candidate was able to force themselves on the winning 7 Lee (2008) pg 684

16 10 side of the threshold it would mandate that their opponent would fall barely below the threshold There is a noticeable jump at margin t-1 = 100 because state legislatures often run unopposed. Possible reasons a candidate would face no opposition include profound candidate popularity, strong dominance of the Democratic Party, etc. 9 Here there are a larger number on of observations on the right side of the threshold (35,547 versus 22,740). Because of this fact, the density function appears unbalanced but the number falling barely on each side of the threshold is actually very similar, (35,547(.015) = 533 and 22,740(.025) = 569).

17 11 Section Three Data This paper uses the state legislative election returns data set from the Inter- University Consortium for Political and Social Research (hereafter ICPSR ). With over 300,000 observations, this data set contains the general election results of all districts in the fifty states from the years 1967 to Each observation is composed of 59 variables that range from candidate vote share to the nicknames of a given candidate. However, this analysis only demands about fifteen of these variables, such as state and district identifiers, the vote shares of the various candidates and their opponents and party identifiers. As a result of the rise and dominance of the two-party system in United States politics since the 1950 s, virtually all general elections since then exemplify the Democrat-versus-Republican rivalry. Although instances do exist where Democrats run against fellow Democratic Party members or independents, this represents an extreme circumstance where the party is basically guaranteed victory. Otherwise the party would never support both candidates, as the party vote cannibalism would erode the party s chances to win the seat. Because of this symmetry, I only keep the Democratic Party s candidates for analysis. 10 Another issue with the data involves the impact of redistricting. As a result of decennial redistricting, we must drop observations in years ending with 2 (or in the case of states with odd year elections, 1). The districts during these years become 10 For these purposes, I identified seven different party markers in the data set as representative of the Democratic Party such as the Democratic-Farmer-Labor party in the United States.

18 12 fundamentally different when the lines are redrawn; as a result, the current electorate is not directly comparable to the prior electorate. Both Lee (2008) and Desposato et al. (2003) advocate for this procedure. In addition to dropping years due to redistricting, we must also drop multi-member districts with multiple offices awarded in a single election because the model does not account for these types of elections. This causes sufficient data loss so that that eight upper house and three lower house chambers cannot be estimated. 88 total chambers remain in our sample.

19 13 Section Four Empirical Analysis Section 4a Nationwide Upper and Lower Houses Margin(t) Regression function fit (Lower House) Margin(t-1) Sample average within bin Polynomial fit of order 1 Margin(t) Regression function fit (Upper House) Margin(t-1) Sample average within bin Polynomial fit of order 1 Figure 3a Figure 3b House β 2 (Equation 1) Std. Err. z P > z Lower House Figure 3a Conventional Bias-Corrected Robust Upper House Figure 3b Conventional Bias-Corrected Robust Table 2 (using first-order polynomials) Figures 3a and 3b illustrate the misspecified RD estimate of the incumbency advantage in lower and upper houses respectively. The figures represent the Democratic Party s margin of victory/defeat in election t (margin t ), by margin of victory/defeat in election t-1 (margin t-1 ): local averages and parametric fit. Table 2 records the discontinuity between the two local averages (β 2) as a measurement of the incumbency advantage. Democratic candidates falling on the right side of our threshold margin t-1 = 0 represent those with party incumbency because their party won in election t-1. For both the upper and lower houses, each point is the average of the independent variable for

20 14 winning in election t for intervals.270 wide to the left of the threshold and.174 wide on the right. As expected, we see both a positive relationship between margin t and margin t-1, in addition to a noticeable discontinuity at the threshold margin t-1 = 0. According to Table 2, using first-order polynomials, our party incumbency advantage (β 2) in the lower houses is about %, significant to the 99 th percentile (using robust standard errors), and is about % in the upper house (also 99% significant with robust standard errors). While both of these numbers are consistent with the hypothesis that the state legislature incumbency advantage is larger than the 8% figure found by Lee (2008), there is reason to believe that these estimations are over-exaggerated as a result of the restrictive firstorder polynomial. Figure 3a and 3b both appear to skew at the extremes, thus flattening out our regression while simultaneously raising the limit as margin t-1 approaches zero from the right side. Lee (2008) describes this phenomenon, stating: a linear regression specification [leads] to misleading inferences. 11 Because I only consider the disconnect at the threshold margin t-1 = 0, there are two ways to solve this problem. The first would be to drop the extreme results, focusing only on the margin t-1 between -50 and 50. The other option is to loosen the first-order polynomial from first-order to fourth, as this makes the fit much closer at all points. For the sake of this analysis, I will loosen the projections to a fourth-order polynomial. Lee (2008) advocates for this strategy, stating: To address this problem, polynomial approximations are used to generate simple estimates of the discontinuity gap. In particular, the dependent variable is regressed on a fourth-order polynomial in the Democratic vote share margin of victory, separately for each side of the threshold David Lee (2008) pg David Lee(2008) pg 688

21 15 As the experimenter, I must be careful with how far I loosen the polynomial restriction, as the fit can sometimes be overly loose. Later on in this experiment, I will only loosen to the second-order polynomial to avoid falling into this trap.

22 16 Margin(t) Regression function fit (Lower House) Margin(t-1) Sample average within bin Polynomial fit of order 4 Margin(t) Regression function fit (Upper House) Margin(t-1) Sample average within bin Polynomial fit of order 4 Figure 4a Figure 4b House β 2 (Equation 1) Std. Err. z P > z Lower House Figure 4a Conventional Bias-Corrected Robust Upper House Figure 4b Conventional Bias-Corrected Robust Table 3 (using forth-order polynomials) Figures 4a and 4b (along with Table 3) show the new estimations of the incumbency advantage. Again, the figures represent the Democratic Party s margin of victory/defeat in election t (margin t ), by margin of victory/defeat in election t-1 (margin t-1 ): local averages and parametric fit. Because our data does not change, each point is again the average of the independent variable for winning in election t for intervals.270 wide to the left of the threshold and.174 wide on the right. Utilizing fourth-order polynomials instead of first-order polynomials, I confirm my hypotheses that the incumbency advantage in state legislatures exists and is higher than what Lee (2008) finds for the incumbency advantage in the United States House of Representatives. According to Table 3, the party incumbency advantage (β 2) in the lower houses is actually

23 17 higher at %, while still significant to the 99 th percentile. However, the implementation of fourth-order polynomials dampens the effect in upper houses to % (significant to the 99 th percentile). Both of these numbers are still well over the 8% level found in Lee (2008).

24 18 Margin(t-1) Regression function fit (Lower House with flipped variables) Margin(t) Sample average within bin Polynomial fit of order 4 Margin(t-1) Regression function fit (Upper House with Flipped Variables) Margin(t) Sample average within bin Polynomial fit of order 4 Figure 5a Figure 5b Figures 5a and 5b show another econometric check, switching the variables margin t and margin t-1 when running the RDD. A key assumption made in this experiment is that there is a distinct advantage to being the incumbent (i.e. winning in election t-1). With this assumption comes the intuition that we should find a discontinuity at the threshold margin t-1 = 0. However, winning an election in time t should not affect how the Democratic Party performs in election t-1. While there should be a positive correlation between the two, as they both indicate the relative party strength, the threshold margin t = 0 does not make a candidate in t-1 a party incumbent. This is illustrated by Figures 5a and 5b which show virtually no discontinuity at the threshold margin t = 0.

25 19 Probability of Candidate Winning in Election t Regression function fit (Lower House) Probability of Candidates in Election t Regression function fit (Upper House) Margin(t-1) Sample average within bin Polynomial fit of order Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 6a Figure 6b House β 2 (Equation 1) Std. Err. z P > z Lower House Figure 6a Conventional Bias-Corrected Robust e e Upper House Figure 6b Conventional Bias-Corrected Robust e e Table 4 Figures 6a and 6b illustrate the RD estimate of the incumbency advantage for Democratic Party candidates in terms of the boost they get in the probability that they win in election t. This is conceptually different from the incumbency advantage found in Table 3, which is an estimation of the point boost in margin a party gets for winning in election t-1. Figures 6a and 6b plot the estimated probability of the Democratic Party winning in election t as a function of the Democratic Party s margin of victory/defeat in election t-1. Each point is the average of the independent variable for winning in election t for intervals.01 wide. Similar to Figures 4a and 4b, Democratic candidates on the left side of the threshold margin t-1 = 0 are not party incumbents in election t, while those on the right

26 20 side of the threshold are. It is important to note that I restrict the test to a second order polynomial as this is the best fit and does not over exaggerate the advantage. Again, there is a noticeable and large discontinuity at the threshold. Democratic candidates, whose party barely won in election t-1, exhibit a profoundly higher chance of winning in election t than those candidates whose party barely lost in election t-1. In the lower house, the increase in probability comes in at around 36% (99% significant), while the upper house records a 29% jump (99% significant). There is no other threshold where there appears to be a jump in our figures except at our incumbency threshold margin t-1 = 0.

27 21 Section 4b Off-Year States Margin(t) Regression function fit (Lower Houses Off Year) Margin(t-1) Sample average within bin Polynomial fit of order 2 Margin(t) Regression function fit (Upper Houses Off Year) Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 7a Figure 7b House β 2 (Equation 1) Std. Err. z P > z Lower House Figure 7a Conventional Bias-Corrected Robust Upper House Figure 7b Conventional Bias-Corrected Robust Table 5 Figures 7a and 7b illustrate the RD estimate of the incumbency advantage for the Democratic Party in the houses for states that hold their elections during off-years (Louisiana, Mississippi, New Jersey and Virginia). Similar to Figures 3a and 3b, these figures represent margin t by margin of victory/defeat in election t-1 using local averages and a parametric fit. For the houses, each point again is the average of the independent variable for winning in election t for intervals wide to the left of the threshold and wide on the right. Table 5 records our incumbency advantage as well as conventional and robust standard errors. In both chambers, we see an increase in incumbency advantage over our national findings: while the incumbency advantage

28 22 found in lower chambers was 14% nationwide, the incumbency advantage for states that hold their election in off-years is a staggering 33%. This figure dwarfs what we found in Section 4a, yet remains statistically significant to the 99 th percentile. Upper houses tell a similar story, jumping from 12% to over 20% (with over 98% significance). These findings confirm the hypothesis that holding elections in off-years adds an extra boost to the already substantial incumbency advantage that exists in state legislatures.

29 23 Regression function fit (Lower House Off Year) Regression function fit (Upper House Off Year) Probability of Winning in Election t Probability of Winning in Election t Margin(t-1) Sample average within bin Polynomial fit of order Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 8a Figure 8b House β 2 (Equation 1) Std. Err. z P > z Lower House Figure 8a Conventional Bias-Corrected Robust Upper House Figure 8b Conventional Bias-Corrected Robust Table 6 Figures 8a and 8b again illustrate the RD estimate of the incumbency advantage for the Democratic Party candidate in terms of the boost they get in the probability that they win, but this time only for states that hold their elections in off-years. Mirroring our process for state legislatures as a whole, Figures 8a and 8b plot the estimated probability of the Democratic Party winning in election t as a function of the Democratic Party s margin of victory/defeat in election t-1. Each point is the average of the independent variable for winning in election t for intervals.120 wide on the left of the threshold and.420 wide on the right. Here we show an increase in probability of winning of just over 36%, a figure marginally larger than the nation as a whole (while staying 99% significant) due to party incumbency, while upper houses exhibit nearly a 29% jump in

30 24 their probability of winning in election t. This is very similar to the aggregation of state legislatures nationwide.

31 25 Section 4c CASE STUDY: Gubernatorial Years and Virginia In looking at the table of voter turnout by year in the state of Virginia (Appendix Table 7), one notices that off-year elections generally display lower turnout than even years. To analyze the impact of off-year elections on Virginian voter turnout, I construct a new data set (Appendix Table 8) that creates dummy variables for off-year, gubernatorial races, presidential races, and decadal fixed effects dating back to Next, I regress the variable VoterTurnout on the newly constructed variables, Off, Governor, President, 10s, 00s, 90s and 80s in order to find the coefficients for equation (5): VoterTurnout = α o + α 1 Off + α 2 Governor + α 3 President + α 4 10s + α 5 00s + α 6 90s + α 7 80s (5) VoterTurnout Coef. Std. Err. t P > t Off Governor President s s s s α o Table 9 Table 9 shows the relationship between our dummy variables and voter turnout. Here, the baseline case is an even-year election with no president running with 1970s fixed effects. After controlling for decadal fixed effects, presidential elections and gubernatorial elections, I find that off-year elections depress voter turnout by 7%. However, just as expected, we find that the gubernatorial race helps boost voter turnout

32 26 by about 11%. This model explains a wide range of variability for Virginia voter turnout with an R 2 value = Because of the different effects between off-years and gubernatorial races, Virginia offers another natural experiment: how does the presence of a gubernatorial race affect the incumbency advantage? Based on the logic of the experiment thus far, we should expect a stronger incumbency advantage when there is no governor s race on the ballot, as higher turnout leads to lower incumbency advantage.

33 27 Regression function fit (Virginia Lower House All Years) Margin(t) Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 9a Margin(t) Regression function fit (Gubernatorial Race Years) Margin(t-1) Sample average within bin Polynomial fit of order 2 Margin(t) Regression function fit (Non Gubernatorial Race Years) Margin(t-1) Sample average within bin Polynomial fit of order 2 Figure 9b Figure 9c Virginia Lower House β 2 Std. Err. z P > z All Years Figure 9a Conventional Bias-Corrected Robust Years with Gubernatorial Race Figure 9b Conventional Bias-Corrected Robust Years without Gubernatorial Race Figure 9c Conventional Bias-Corrected Robust Table 10

34 28 Figures 9a, 9b and 9c (along with Table 10) show the estimations of the incumbency advantage for the Virginian lower house (representing the Democratic Party s margin of victory/defeat in election t (margin t ), by margin of victory/defeat in election t-1 (margin t-1 ): local averages and parametric fit). In the Virginian lower house as a whole, the incumbency advantage measures about 16 points (Fig. 9a) which is slightly higher than the national average. However, in years with a gubernatorial race where turnout goes up by about 11%, the incumbency advantage falls to only about 8 points. Contrastingly, when there is no gubernatorial race on the ballot, state legislatures see their incumbency advantage jump to over 25 points. Despite the paucity of data, the findings for the estimates of all years, and for years without a gubernatorial race are highly statistically significant. However, in years with a gubernatorial race, the significance falls below 65%.

35 29 Section Five Discussion With the deployment of regression discontinuity design, I analyzed the incumbency advantage of state legislatures nationwide. Using this strategy, I measured an incumbency advantage for state legislatures larger than that of the U.S. House of Representatives. While Lee (2008) found an 8% jump at the federal level, lower and upper houses nationally exhibit a 14 and 12-point boost respectively from the incumbency advantage. Our findings strongly indicate that the incumbency advantage is statistically larger in the state legislatures than the Lee (2008) findings, as the 8% figure falls outside of the 95% robust confidence interval for lower houses and the 95% conventional confidence interval for upper houses. Additionally, I found that the probability of winning for the incumbent party increases by 36% in lower houses and 29% in upper houses. Neither of these findings is as large as the Lee (2008) finding of a 45% jump in probability. This creates an interesting dichotomy. On one hand, party incumbency grants a larger boost in vote share margin for state-legislatures. On the other, the jump in the probability of winning due to party incumbency is actually larger for the U.S. House of Representatives. This suggests that state legislature elections are far more volatile than elections for the U.S. House of Representatives. Despite the fact that state legislature incumbency advantage is larger, there is a greater chance of deviating from that average and falling below margin t = 0. Intuitively, this can explained by factors such as the greater range of candidate/opponent ability and the support they get at the state legislature level: while Congressmen and their opponents are often adept political

36 30 veterans who get a vast majority of their party s political capital, a candidate for state legislature can range from true novice to up-and-coming political star. The results were highly statistically significant and passed the various tests needed to prove the efficacy of RDD. These findings are also consistent with the literature, which indicates that an incumbency advantage exists at every level of government and that lesser publicized political offices should display higher incumbency advantage due to disproportionate information about candidates. However, this is the first formal, causally identified test of that hypothesis. After measuring the incumbency advantage in state legislatures nationwide, I turned my attention to the off-year states, where I hypothesized that because these elections were held in years where turnout was at its lowest, these elections would reveal an even higher incumbency advantage than the nationwide measurement. Running RDD only on off-year states, the upper house jumped from a 12-point incumbency advantage for Democrats to a 20-point advantage. In the lower house, the incumbency advantage more than doubled to over 33 points. Again, my findings were highly significant, with only the incumbency advantage in the upper houses of off-year states marginally falling below 99 percent significance to 98 percent. I corroborate these findings by looking at how the presence of a gubernatorial race impacts the incumbency advantage in the Virginia Lower House. Virginia serves as a powerful case study because of the impact that both off-year elections and gubernatorial races have on voter turnout. Since people care substantially more about their governor

37 31 than state house representative, they turn out at a higher rate during a gubernatorial race. In those years, however, the incumbency advantage is lower than off-years with no major political election. This indicates that incumbent state legislatures are protected by having their elections in off-years. However, as a result of high error terms, the results are not statistically different. There are many possible extensions to this experiment. The combination of the data from the ICPSR paired with RDD allows one to find the incumbency advantage for any party for any state. Just as I was able to find the incumbency advantage for the lower house in Virginia, one can find the incumbency advantage for the state legislatures of most states (Tables 9 and 10 report my findings). However, it does not appear that simple explanations (such as legislature size) explain variation between states. I found virtually no correlation when regressing incumbency advantage on chamber size for each corresponding state and house.

38 32 References Academic Press Ansolabehere, Stephen. "Party and Incumbency Cues in Voting: Are They Substitutes?" Quarterly Journal of Political Science 1, no. 2 (2006): doi: / Ansolabehere, Stephen, John Mark Hansen, Shigeo Hirano, and James M. Snyder. "The Incumbency Advantage in U.S. Primary Elections." Electoral Studies 26, no. 3 (2007): doi: /j.electstud Carson, J. L., M. H. Crespin, C. J. Finocchiaro, and D. W. Rohde. "Redistricting and Party Polarization in the U.S. House of Representatives." American Politics Research 35, no. 6 (2007): doi: / x Carson, Jamie L., Erik J. Engstrom, and Jason M. Roberts. "Redistricting, Candidate Entry, and the Politics of Nineteenth-Century U.S. House Elections." American Journal of Political Science 50, no. 2 (2006): doi: /j x. Desposato, Scott W., and John R. Petrocik. "The Variable Incumbency Advantage: New Voters, Redistricting, and the Personal Vote." American Journal of Political Science 47, no. 1 (2003): 18. doi: / Erikson, Robert S., and Rocío Titiunik. "Using Regression Discontinuity to Uncover the Personal Incumbency Advantage." Quarterly Journal of Political Science 10, no. 1 (2015): doi: / Fowler, Anthony, and Andrew B. Hall. "Disentangling the Personal and Partisan Incumbency Advantages: Evidence from a Structural Regression Discontinuity Design." SSRN Electronic Journal, December doi: /ssrn Hainmueller, Jens, and Holger Lutz Kern. "Incumbency as a Source of Spillover Effects in Mixed Electoral Systems: Evidence from a Regression-discontinuity Design." Electoral Studies 27, no. 2 (2008): doi: /j.electstud Highton, B. "The Influence of Strategic Retirement on the Incumbency Advantage in US House Elections." Journal of Theoretical Politics 23, no. 4 (2011): doi: / Lee, David S. "Randomized Experiments from Non-random Selection in U.S. House Elections." Journal of Econometrics 142, no. 2 (2008): doi: /j.jeconom Levitt, Steven D. "Using Repeat Challengers to Estimate the Effect of Campaign Spending on Election Outcomes in the U.S. House." Journal of Political Economy 102, no. 4 (1994): doi: / Mckee, S. C. "Political Conditions and the Electoral Effects of Redistricting." American Politics Research 41, no. 4 (2012): doi: / x Mckelvey, Richard D., and Raymond Riezman. "Seniority in Legislatures." American Political Science Review 86, no. 04 (1992): doi: / Millsap, Adam. "State Government Spending Hits New Heights." Neighborhood Effects RSS. July 30, Accessed November 28,

39 33 Murphy, C., and A. Yoshinaka. "Are Mapmakers Able to Target and Protect Congressional Incumbents?: The Institutional Dynamics of Electoral Competition." American Politics Research 37, no. 6 (2009): doi: / x Prior, Markus. "The Incumbent in the Living Room: The Rise of Television and the Incumbency Advantage in U.S. House Elections." The Journal of Politics 68, no. 3 (2006): doi: /j x. Rekkas, Marie. "The Impact of Campaign Spending on Votes in Multiparty Elections." Review of Economics and Statistics 89, no. 3 (2007): doi: /rest Rogers, Steven M. "Accountability in a Federal System." PhD. Diss. Department of Politics, Princeton University, Uppal, Yogesh. "The Disadvantaged Incumbents: Estimating Incumbency Effects in Indian State Legislatures." Public Choice 138, no. 1-2 (2008): doi: /s Yoshinaka, A., and C. Murphy. "The Paradox of Redistricting: How Partisan Mapmakers Foster Competition but Disrupt Representation." Political Research Quarterly 64, no. 2 (2010): doi: / Yoshinaka, Antoine, and Chad Murphy. "Partisan Gerrymandering and Population Instability: Completing the Redistricting Puzzle." Political Geography 28, no. 8 (2009): doi: /j.polgeo Popular Press Hersh, Eitan. "How Democrats Suppress The Vote." FiveThirtyEight. November 03, Accessed December 01, Millsap, Adam. "State Government Spending Hits New Heights." Neighborhood Effects RSS. July 30, Accessed November 28, Montanaro, Domenico, Rachel Wellford, and Simone Pathe. "2014 Midterm Election Turnout Lowest in 70 Years." PBS. November 10, Accessed November 17, Nir, David. "Just How Many Elected Officials Are There in the United States? The Answer Is Mindblowing." Daily Kos. May 29, Accessed November 17, "Registration/Turnout Statistics." Virginia Department of Elections. December 1, Accessed December 01, Chicago/Turabian formatting by BibMe.org.

40 34 Appendix Figure 1 (Ansolbehere et, al (2001)). rddensity marginlast Computing data-driven bandwidth selectors. RD Manipulation Test using local polynomial density estimation. Cutoff c = Left of c Right of c Number of obs = > Model = unrestr > icted Number of obs BW method = > comb Eff. Number of obs Kernel = trian > gular Order loc. poly. (p) 2 2 VCE method = jack > knife Order BC (q) 3 3 Bandwidths (hl,hr) estimated estimated Bandwidth values Running variable: marginlast. Method T P> T Robust Bias-Corrected Table 1: Results from RD Density Test

41 35 Table 7: Virginia Voter Turnout by Year Year Voter Turnout Year (cont.) Voter Turnout (cont.)

42 Source: "Registration / Turnout Statistics." Virginia.gov

43 37 Table 8: Constructed Virginia Voter Turnout Data Set Year Voter Turnout President Even Governor Off 80s FE 90s FE 00s FE 10s FE *