Multiple imputation regression discontinuity designs: Alternative to regression discontinuity designs to estimate the local average treatment effect at the cutoff

Abstract

The regression discontinuity design (RDD) is one of the most credible methods for causal inference that is often regarded as a missing data problem in the potential outcomes framework. However, the methods for missing data such as multiple imputation are rarely used as a method for causal inference. This article proposes multiple imputation regression discontinuity designs (MIRDDs), an alternative way of estimating the local average treatment effect at the cutoff point by multiply-imputing potential outcomes. To assess the performance of the proposed method, Monte Carlo simulations are conducted under 112 different settings, each repeated 5,000 times. The simulation results show that MIRDDs perform well in terms of bias, root mean squared error, coverage, and interval length compared to the standard RDD method. Also, additional simulations exhibit promising results compared to the state-of-the-art RDD methods. Finally, this article proposes to use MIRDDs as a graphical diagnostic tool for RDDs. We illustrate the proposed method with data on the incumbency advantage in U.S. House elections. To implement the proposed method, an easy-to-use software program is also provided.

Keywords:

• Causal inference
• Missing data
• Multiple imputation
• Potential outcome
• Regression discontinuity