PaJoFo Ponderings

Calculating Incumbency Advantage

7 min read

Incumbency advantage is a hotly debated topic within congressional studies and has been given deep consideration by many scholars, both in the attempt to identify origin and to quantify and compare it over time. One foundational text of this study is Andrew Gelman and Gary King’s 1990 paper, Estimating Incumbency Advantage without Bias. While prior investigations of the data had found that incumbency advantage had grown over time, it was commonly believed that incumbency advantage had not existed until sometime after 1950. These investigations, Gelman and King argue, used methods that were biased, faulty, and statistically inefficient, and their paper established a simple method which when applied to empirical data accurately measures incumbency advantage and demonstrates that it existed prior to 1950 and has increased since then.1 Subsequent research would go on to refine and dispute the paper’s model and offer new and more rigorous explanations for the existence of incumbency advantage.2

Historical Context

Incumbency advantage is conceptually imprecise and has been defined in different ways in the scholarly literature. Gelman and King, in order to prevent bias and account for candidate quality and changes over time, define it as the follow: incumbency advantage in a single legislative district is the proportion of the vote won by the incumbent party in a district if the incumbent does not run subtracted from the share of votes won if the incumbent runs and aggregate incumbency advantage is the average of that calculation for all districts in a given election.3

Prior to their research, two key methods were used to quantify the advantage, sophomore surge and retirement slump. Sophomore surge measures the vote gain (or loss) seen when a member is reelected to a seat compared to their initial margin of victory. Gelman and King demonstrated that this method is biased to underestimate incumbency advantage, even when correcting for nationwide swing.4 Retirement slump is similar; it measures the difference in vote share between the incumbent’s vote share in their last election prior to their retirement and share won by the candidate of the new party; this method is also biased and overestimates incumbency advantage.5 The average of the two measures, known as the slurge, while hoped to be a better method because it compensates for the opposing biases of surge and slump is also demonstrated as biased and underestimate incumbency advantage.6 All of these methods suffer from limiting available elections to pull data from.7 This is a weakness observed in many of the other methods that Gelman and King survey; existing methods had limited data sets, selection biases, and used statistically inefficient steps to eliminate bias.8

Gelman and King’s Method

Gelman and King developed a new methodology to overcome the failings of the original models with a simpler and unbiased measure of incumbency advantage. They found that “a linear regression of votes on incumbency status, controlling for previous votes and partisan swing” was an effective and statistically efficient method of calculating incumbency advantage.9 The model allows for comparison of advantage between parties and admits a much larger data set than the aforementioned method, increasing statistical efficiency.

The model is not perfect. It assumes that the choice to run for reelection is separate from the final vote tally, so if incumbents choose not to run for reelection because they expect a loss, the “estimator would be inconsistent.”10 The authors assume that incumbents would only be of this opinion because of scandal, and that because scandal is rare, this is not a significant problem. Gelman and King also do not include all control variables that they could because the incumbency advantage is deemed to be the underlying cause of things like candidate quality of opponents.11 They address potential challenges to the assumptions of a regression model and for those that they don’t address, like “heteroscedasticity and (spatial) autocorrelation,” they claim are unlikely.12 The largest hole, an incomplete view of uncontested seats receives a separate section in the paper, and they conclude that the measure is likely a moderate underestimation due to the omission.13

Theoretical Findings

The model’s key theoretical findings are as follows. First, “incumbents do not base their decision of whether to seek reelection on their vote total in the previous election.”14 Second, that “there is little difference between personal incumbency advantage and our measure” and so “open seat candidates are not significantly weaker than incumbent candidates, after correcting for personal incumbency advantage.”15 And finally that the model worked to accurately determine incumbency advantage with a set of simulated data, and that sophomore surge and retirement slump were both biased.16

Empirical Findings

Once satisfied with the model, Gelman and King collected “electoral data from every election to the House of Representatives” from 1900 to the time of writing and used it to calculate incumbency advantage using the model.17 (They didn’t calculate incumbency advantage for years ending in two because they followed redistricting.) They found that the empirical results agreed with the theoretical analysis and sophomore surge was below true incumbency advantage and retirement slump consistently overestimated it. They analysis found that incumbency advantage had increased dramatically after 1950, but, in contradiction to prior authoritative assessments, did exist in the time before, just to a lesser degree.18

Impact on Broader Research

Gelman and King’s conclusions were rigorously demonstrated and accepted by many scholars in the field, but they did not explain why incumbency advantage exists or why it increased so sharply in the latter half of the twentieth century.19 Various other scholars went on the refine the Gelman and King model to provide deeper analysis of the topic. A modification of the model was used by Cox and Katz to find that the increase in the advantage was mostly based on an increase in the candidate quality differential.20 A later work by the same authors would conclude that the increase was due to the Supreme Court’s imposition of regular redistricting in Wesberry v Sanders was the root with a broader review of the literature, but this was disputed by several authors including Ansolahbehere and Snyder who found that incumbency advantage increased in a variety of positions, suggesting more systemic factors.21 Most contrary to accepted knowledge, Jefferey Stonecash’s book argues that modeling showing an increased incumbency advantage from the 1950s is incorrect and an artifact of data collection and inclusion criteria for races.22 Research on the subject on the subject of incumbency advantage is ongoing, but Gelman and King’s paper is a foundation for much continued research.

Bibliography

Andrew Gelman and Gary King. “Estimating Incumbency Advantage Without Bias.” American Journal of Political Science 34, no. 4 (November 1990): 1142—64.

Carson, Jamie, and Jason Roberts. “House and Senate Elections.” In The Oxford Handbook of the American Congress, 1. publ. in paperback, edited by Eric Schickler and Frances Lee. The Oxford Handbooks of American Politics. Oxford: Oxford Univ. Press, 2013.

Cox, Gary W., and Jonathan N. Katz. “Why Did the Incumbency Advantage in U.S. House Elections Grow?” American Journal of Political Science (Oxford) 40, no. 2 (May 1996): 478. 196890524; 02781967, p. 478. ProQuest Central; Social Science Premium Collection.

Footnotes

  1. Andrew Gelman and Gary King, “Estimating Incumbency Advantage Without Bias,” American Journal of Political Science 34, no. 4 (November 1990): 1142. ↩

  2. Jamie Carson and Jason Roberts, “House and Senate Elections,” in The Oxford Handbook of the American Congress, 1. publ. in paperback, ed. Eric Schickler and Frances Lee, The Oxford Handbooks of American Politics (Oxford: Oxford Univ. Press, 2013), 145—48. ↩

  3. Andrew Gelman and Gary King, “Estimating Incumbency Advantage Without Bias,” 1143. ↩

  4. Ibid., 1146—47. ↩

  5. Ibid., 1147. ↩

  6. Ibid., 1149. ↩

  7. Ibid., 1145. ↩

  8. Ibid., 1149—50. ↩

  9. Ibid., 1151. ↩

  10. Ibid., 1152. ↩

  11. Though they also state elsewhere that candidates in open seats are not significantly weaker than incumbents because of primaries. It is unclear why primaries would not have a similar effect for candidates running against incumbents. ↩

  12. Andrew Gelman and Gary King, “Estimating Incumbency Advantage Without Bias,” 1156. ↩

  13. Ibid., 1160. ↩

  14. Ibid., 1153. ↩

  15. Ibid., 1156. ↩

  16. Ibid. ↩

  17. Ibid., 1157. ↩

  18. Ibid., 1157—58. ↩

  19. Carson and Roberts, “House and Senate Elections,” 145. ↩

  20. Gary W. Cox and Jonathan N. Katz, “Why Did the Incumbency Advantage in U.S. House Elections Grow?,” American Journal of Political Science (Oxford) 40, no. 2 (May 1996): 478, 196890524; 02781967, p. 478, ProQuest Central; Social Science Premium Collection. ↩

  21. Carson and Roberts, “House and Senate Elections,” 146. ↩

  22. Ibid., 148. ↩

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