Parametric (polynomial) models are popular in research employing regression discontinuity designs and are required when data are discrete. However, researchers often choose a parametric model based on data inspection or pretesting. These approaches lead to standard errors and confidence intervals that are too small because they do not incorporate model uncertainty. I propose using Frequentist model averaging to incorporate model uncertainty into parametric models. My Monte Carlo experiments show that Frequentist model averaging leads to mean square error and coverage probability improvements over pretesting. An application to [Lee, D. S. 2008. “Randomized Experiments From Non-Random Selection in US House Elections.” Journal of Econometrics 142 (2): 675–697.] shows how this approach works in practice, and how conventionally selected models may not be ideal.
Breiman, L. 1992. “The Little Bootstrap and Other Methods for Dimensionality Selection in Regression: X-Fixed Prediction Error.” Journal of the American Statistical Association 87 (419): 738–754.10.1080/01621459.1992.10475276)| false
Cohen, A. 1965. “Estimates of Linear Combinations of the Parameters in The Mean Vector of a Multivariate Distribution.” The Annals of Mathematical Statistics 36 (1): 78–87.10.1214/aoms/1177700272)| false
Cook, T. D. 2008. “’Waiting for Life to Arrive’: A History of The Regression-Discontinuity Design in Psychology, Statistics and Economics.” Journal of Econometrics 142 (2): 636–654.10.1016/j.jeconom.2007.05.002)| false
Liang, H., G. Zou, A. T. K. Wan, and X. Zhang. 2011. “Optimal Weight Choice for Frequentist Model Average Estimators.” Journal of the American Statistical Association 106 (495): 1053–1066.10.1198/jasa.2011.tm09478)| false
Oreopoulos, P. 2006. “Estimating Average and Local Average Treatment Effects of Education When Compulsory Schooling Laws Really Matter.” The American Economic Review 96: 152–175.10.1257/000282806776157641)| false
Raftery, A. E., D. Madigan, and J. A. Hoeting. 1997. “Bayesian Model Averaging for Linear Regression Models.” Journal of the American Statistical Association 92 (437): 179–191.10.1080/01621459.1997.10473615)| false
Sun, Y. 2005. “Adaptive Estimation of the Regression Discontinuity Model.” Unpublished Manuscript, University of California, San Diego. http://econweb.ucsd.edu/~yisun/ard.pdf (accessed February 17, 2015).
Wallace, T. D. 1977. “Pretest Estimation in Regression: A Survey.” American Journal of Agricultural Economics 59 (3): 431–443.
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