1 Introduction
Does winning an election cause a party to be more likely to win the next election? The intuition seems obvious incumbents win re-election at high rates. But disentangling the causal effect of incumbency from the confounding fact that good candidates who attract votes in one election tend to attract them in the next is a serious identification challenge.
Lee [2008] provides a landmark solution using regression discontinuity design (RDD). The key insight is simple and elegant: in elections decided by a margin close to zero, the winner is as good as randomly assigned. A Democrat who wins with 50.1% of the vote and one who loses with 49.9% are, by assumption, otherwise identical in all relevant respects. The discontinuity at the 50% threshold identifies the causal effect of winning.
This case study explains the design, the data, the findings, and why the paper became a landmark both in political science and in the methodological literature on RDD.
2 The Causal Question
The question is: what is the effect of winning a U.S. House election on the probability of winning the subsequent election in the same district?
Let $W_{it}=1$ if the Democratic Party wins district i in election t. The running variable is the Democratic vote share margin: $M_{it}=$ (Democratic vote share) -0.5. The treatment is $D_{it}=1[M_{it}\ge0]$ (Democrats win when they get more than 50%).
The RDD estimand is the local average treatment effect at the threshold:
where $Y_{i,t+1}$ is the Democratic vote share in the subsequent election.
3 Data
Lee [2008] uses data on all U.S. House general elections from 1946 to 1998 a total of roughly 13,000 district-election observations. The running variable is the Democratic candidate's share of the two-party vote. Districts with uncontested races are excluded.
The richness of historical U.S. election data is one reason this setting is ideal for RDD: there are many observations near the threshold, enabling precise local polynomial estimation without relying on extrapolation from distant observations.
4 The Identification Argument
The RDD identifies the incumbency advantage under the continuity assumption: the con- ditional expectation of potential outcomes is continuous in the vote margin at the 50% threshold. Near the threshold, whether a party wins or loses is essentially determined by factors that are as good as random late-deciding voters, turnout shocks on election day, minor polling errors.
Lee [2008] formalises this with a model in which each candidate exerts some campaigning effort, but a random election-day shock determines the margin. Parties close to 50% have essentially random outcomes, so the discontinuity at the threshold is valid.
The continuity assumption is directly testable in several ways:
- Covariate balance: Pre-determined characteristics of districts (e.g., 1940 census de- mographics) should show no discontinuity at the threshold. Lee finds no such discon- tinuities.
- McCrary density test: There should be no manipulation of the running variable no systematic bunching of observations just above 50%. Lee finds a smooth density at the threshold [McCrary, 2008].
- Placebo cutoffs: Testing for discontinuities at fake thresholds (e.g., 45%, 55%) should show no effects. They do not.
5 Estimation
Lee [2008] estimates local linear regressions separately on each side of the threshold. The baseline specification is:
$Y_{i,t+1}=\alpha+\tau D_{it}+\beta_{1}M_{it}+\beta_{2}M_{it}D_{it}+\epsilon_{it}$ (2)
where the slope $\beta_{1}$ captures the relationship between vote margin and subsequent vote share among losers, and $\beta_{2}$ allows this slope to differ for winners. The RD estimate captures the discontinuous jump at the threshold.
Various bandwidth choices and polynomial orders are used for robustness. The modern CCT optimal bandwidth [Calonico et al., 2014] and bias-corrected inference are now standard for this type of analysis, though Lee [2008] predates these refinements.
6 Key Findings
The main result is striking: winning an election by a bare margin causes the Democratic Party's vote share in the subsequent election to jump by approximately 8 percentage points.
The effect is similar when the outcome is the probability of winning the subsequent election close winners are roughly 40-45 percentage points more likely to win the next election than close losers.
Figure 1: Stylised representation of the Lee (2008) RD discontinuity. The Democratic vote share in the next election jumps discontinuously at the 50% threshold.
7 Why Is the Incumbency Advantage So Large?
Lee [2008] attributes the estimated 8-percentage-point gain to the structural advantages of holding office:
- Access to resources (franking privilege, staff, casework)
- Name recognition and media coverage
- Ability to shape policy in ways that please constituents
- Deterrence of strong challengers (candidate emergence effects)
Crucially, the RDD design separates these incumbency advantages from the confounding that plagues OLS: the fact that districts with strong candidates in period t tend to have strong candidates in period $t+1$ regardless of who won.
8 Influence on the Methodology Literature
Beyond its substantive contribution, Lee [2008] became a methodological landmark for two reasons.
First, it provided a crisp formulation of the RDD as a "local randomised experiment." Near the threshold, treatment is as good as randomly assigned, so standard randomisation- inference logic applies. This interpretation later formalised by Cattaneo et al. [2015]-made RDD more intuitive to researchers trained in experimental methods.
Second, it demonstrated the power of falsification tests (covariate balance, density test, placebo cutoffs) as a standard toolkit for validating RDD. These tests are now universally expected in applied RDD papers.
9 Limitations and Extensions
- LATE interpretation: The RD identifies the incumbency effect for parties that win close elections not for all elections. If the effect is different in safe seats, external validity is limited.
- Compound treatment: "Winning" bundles together incumbency, fundraising ad- vantages, and candidate deterrence. The RDD cannot disentangle which mechanism drives the effect.
- Dynamic effects: The paper estimates the effect on the next election. Long-run effects (two or three cycles out) have been examined in follow-up work, finding that the incumbency advantage persists but decays over time.
10 Conclusion
Lee [2008] is a model of clean causal identification. By exploiting the near-random variation in election outcomes near the 50% threshold, it recovers a large and robust estimate of the incumbency advantage approximately 8 percentage points in subsequent vote share. The paper's influence extends beyond political science: it established the template for validating RDD with falsification tests and articulated the "local randomisation" interpretation that remains central to how applied researchers think about regression discontinuity.
References
- Lee, D.S. (2008). Randomized experiments from non-random selection in U.S. house elec- tions. Journal of Econometrics, 142(2):675-697.
- Calonico, S., Cattaneo, M.D., and Titiunik, R. (2014). Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica, 82(6):2295-2326.
- McCrary, J. (2008). Manipulation of the running variable in the regression discontinuity design: A density test. Journal of Econometrics, 142(2):698-714.
- Cattaneo, M.D., Frandsen, B.R., and Titiunik, R. (2015). Randomization inference in the regression discontinuity design: An application to party advantages in the U.S. Senate. Journal of Causal Inference, 3(1):1-24.
- Imbens, G.W. and Lemieux, T. (2008). Regression discontinuity designs: A guide to practice. Journal of Econometrics, 142(2):615-635.