Estimating Incumbency Advantage and Its Variation, as an Example of a Before–After Study

Incumbency advantage is one of the most widely studied features in American legislative elections. In this article we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century. Our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. More generally, our multilevel model represents a new method for estimating effects in before–after studies.

[1]  Gary King,et al.  Estimating the Probability of Events that Have Never Occured: When is Your Vote Decisive? , 1998 .

[2]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[3]  Gary W. Cox,et al.  The Increasing Advantage of Incumbency in the U. S. States , 1993 .

[4]  Christopher H. Achen.  The Statistical Analysis of Quasi-Experiments , 2023 .

[5]  Stephen Ansolabehere,et al.  Using Term Limits to Estimate Incumbency Advantages When Officeholders Retire Strategically , 2004 .

[6]  Robert S. Erikson.  The Advantage of Incumbency in Congressional Elections , 1971, Polity.

[7]  Gary King,et al.  Enhancing Democracy Through Legislative Redistricting , 1994, American Political Science Review.

[8]  David S. Lee.  Randomized experiments from non-random selection in U.S. House elections , 2005 .

[9]  B. Carlin,et al.  Spatial Analyses of Periodontal Data Using Conditionally Autoregressive Priors Having Two Classes of Neighbor Relations , 2007 .

[10]  T. Louis.  Estimating a population of parameter values using Bayes and empirical Bayes methods , 1984 .

[11]  G. Casella,et al.  The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models , 1996 .

[12]  Lyn Ragsdale.  The Fiction of Congressional Elections as Presidential Events , 1980 .

[13]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[14]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[15]  Xiao-Li Meng,et al.  Posterior Predictive Assessment of Model Fitnessvia Realized , 1995 .

[16]  Stephen Ansolabehere,et al.  The Incumbency Advantage in U.S. Elections: An Analysis of State and Federal Offices, 1942–2000 , 2002 .

[17]  Gary W. Cox,et al.  Why Did The Incumbency Advantage In U.S. House Elections Grow , 1996 .

[18]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[19]  A. Tsiatis,et al.  Efficiency Study of Estimators for a Treatment Effect in a Pretest–Posttest Trial , 2001 .

[20]  James L. Payne,et al.  The Personal Electoral Advantage of House Incumbents, 1936-1976 , 1980 .

[21]  J. R. Alford,et al.  Increased Incumbency Advantage in the House , 1981, The Journal of Politics.

[22]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[23]  J. Hodges,et al.  Posterior bimodality in the balanced one‐way random‐effects model , 2003 .

[24]  Danny Kopec,et al.  Additional References , 2003 .

[25]  J. Hodges.  Some algebra and geometry for hierarchical models, applied to diagnostics , 1998 .

[26]  R. Fildes.  Journal of the American Statistical Association : William S. Cleveland, Marylyn E. McGill and Robert McGill, The shape parameter for a two variable graph 83 (1988) 289-300 , 1989 .

[27]  Gary W. Cox,et al.  ELBRIDGE GERRY ’ S SALAMANDER The Electoral Consequences of the Reapportionment Revolution , 2002 .

[28]  Andrew Gelman,et al.  Treatment Effects in Before‐After Data , 2005 .

[29]  S. Ansolabehere,et al.  Old Voters, New Voters, and the Personal Vote , 2000 .

[30]  Andrew Gelman,et al.  Applied Bayesian Modeling And Causal Inference From Incomplete-Data Perspectives , 2005 .

[31]  Shigeo Hirano,et al.  The incumbency advantage in U.S. primary elections , 2007 .

[32]  G. Jacobson,et al.  The Marginals Never Vanished: Incumbency and Competition in Elections to the U.S. House OfRepresentatives, 1952-1982 , 1987 .

[33]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[34]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[35]  Stephen Ansolabehere,et al.  The Decline of Competition in U.S. Primary Elections, 1908-2004 1 , 2005 .

[36]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[37]  A. Gelman,et al.  Estimating Incumbency Advantage Without Bias , 1990 .

[38]  J. Hodges,et al.  Identification of the variance components in the general two-variance linear model , 2008 .

[39]  Steven D. Levitt,et al.  Decomposing the Sources of Incumbency Advantage in the U. S. House , 1997 .

[40]  Gary King,et al.  Systematic Consequences of Incumbency Advantage in the U.S. House Elections , 1991 .

[41]  G. Jacobson,et al.  Strategy and choice in congressional elections , 1981 .

[42]  Michael Krashinsky,et al.  The Effects of Incumbency in U. S. Congressional Elections, 1950-1988 , 1993 .

[43]  Xiao-Li Meng,et al.  The Art of Data Augmentation , 2001 .