Thursday 10 April 2025
The quest for a more efficient and accurate way to estimate treatment effects in observational studies has been ongoing for decades. In recent years, researchers have made significant progress in developing novel methods that can better handle confounding variables and provide robust estimates of causal effects. One such approach is the partially linear regression discontinuity design (PLRD) framework, which combines elements of regression discontinuity designs and partially linear models to create a powerful tool for identifying treatment effects.
At its core, PLRD is designed to estimate the average treatment effect (ATE) by exploiting the discontinuity in treatment assignment at a specific threshold. The key innovation here is that PLRD uses a partially linear model to account for potential confounding variables, which can significantly improve the accuracy of the estimated ATE. This approach has been shown to be particularly effective in studies where there are concerns about omitted variable bias or when the relationship between the outcome and covariates is non-linear.
One of the primary challenges in implementing PLRD is selecting the optimal threshold at which to estimate the treatment effect. This requires careful consideration of the research question, data characteristics, and the potential for confounding variables. Fortunately, recent advances in statistical theory have provided new tools for choosing the optimal threshold, such as the use of cross-validation and regularization techniques.
In addition to its theoretical advantages, PLRD has been shown to perform well in a range of empirical applications. For example, researchers have used PLRD to study the impact of tax changes on economic outcomes, the effect of minimum wage laws on employment rates, and the relationship between education and labor market outcomes. In each of these cases, PLRD provided robust estimates of treatment effects that were consistent with theoretical expectations.
Despite its many advantages, PLRD is not without its limitations. One potential issue is that it requires a large enough sample size to accurately estimate the partially linear model. This can be challenging in cases where data is scarce or when there are concerns about data quality. Additionally, the choice of threshold can have significant implications for the estimated treatment effect, so careful consideration must be given to this step.
In recent years, researchers have made significant progress in developing new methods and tools for implementing PLRD. These advances have opened up new possibilities for applied research and have provided a powerful tool for estimating treatment effects in observational studies. As the field continues to evolve, it will be important to carefully consider the strengths and limitations of PLRD and to continue to develop new methods and tools that can improve our understanding of causal relationships.
Cite this article: “High-Dimensional Regression Discontinuity Inference with Applications to Economics and Finance”, The Science Archive, 2025.
Observational Studies, Treatment Effects, Partially Linear Regression Discontinuity Design, Plrd, Regression Discontinuity Designs, Partially Linear Models, Average Treatment Effect, Ate, Omitted Variable Bias, Confounding Variables, Causal Relationships
