A forest with a regression discontinuity line.

Regression Discontinuity Designs: A User-Friendly Guide to Honest Forests

Reese Marlowe in Mind & Education August 2025 • 3 min read.

"Navigate the complexities of multivariate regression discontinuity designs with confidence, leveraging honest forest methodologies for robust results."

Regression Discontinuity (RD) designs are essential for researchers aiming to estimate treatment effects when assignment to a treatment is determined by whether an observed 'running variable' exceeds a specific threshold. While traditional methods often struggle with multiple scores or complex data, new approaches offer more robust and flexible solutions.

In a recent study, researchers Yiqi Liu and Yuan Qi delve into the challenges of estimating conditional treatment effects in RD designs with multiple scores. They explore and compare various estimation techniques, emphasizing the use of 'honest' random forests—a powerful tool for handling complex data structures.

Their work addresses critical issues in applying RD designs, particularly when dealing with multiple variables that influence treatment decisions. By evaluating different methods and providing clear guidance, Liu and Qi offer valuable insights for researchers and analysts across various fields.

Understanding Regression Discontinuity Designs

A forest with a regression discontinuity line.

At its core, a Regression Discontinuity (RD) design seeks to estimate the causal impact of a treatment or intervention by exploiting a clear threshold that determines who receives it. Imagine a scholarship program awarded to students who score above a certain level on an entrance exam. An RD design would compare outcomes for students just above and just below this cutoff to isolate the effect of the scholarship.

The key assumption is that, absent the treatment, individuals on either side of the threshold would have similar outcomes. This allows researchers to attribute any observed differences to the treatment itself. Traditional RD designs often use local linear regression—essentially fitting a straight line to the data on either side of the cutoff.

Clear Threshold: Treatment assignment is based on crossing a specific threshold.
Continuity Assumption: Potential outcomes are continuous around the threshold.
Local Estimation: Focus is on individuals close to the cutoff for comparison.

However, real-world scenarios often involve multiple factors determining treatment. For example, unemployment benefits might depend on age, prior employment history, and other criteria. This is where multivariate RD designs come into play, adding complexity but also offering a more realistic framework.

Honest Forests: A Path Forward

The work by Liu and Qi highlights the potential of honest regression forests and local linear forests as valuable tools in the RD framework. While challenges remain, these methods offer a promising avenue for handling the complexities of real-world data and provide researchers with a more robust and flexible approach to estimating treatment effects. By carefully considering the choice of estimator and employing appropriate techniques, researchers can unlock the power of RD designs to answer critical questions across diverse fields.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2303.11721,

Title: Using Forests In Multivariate Regression Discontinuity Designs

Subject: econ.em

Authors: Yiqi Liu, Yuan Qi

Published: 21-03-2023

Everything You Need To Know

What is a Regression Discontinuity (RD) design, and how does it work?

A Regression Discontinuity (RD) design is a research method used to estimate the causal impact of a treatment or intervention. It works by exploiting a clearly defined threshold in a 'running variable' that determines who receives the treatment. For example, if a scholarship is awarded to students who score above a certain cutoff on an exam, an RD design would compare the outcomes of students just above and just below that cutoff. The core idea is to compare the outcomes of individuals very close to the threshold, assuming that, in the absence of the treatment, their outcomes would have been similar. The design then attributes any observed differences to the treatment itself. The design relies on a 'Clear Threshold', a 'Continuity Assumption', and 'Local Estimation'.

What are the main challenges in applying Regression Discontinuity (RD) designs?

Traditional RD designs often face difficulties when dealing with multiple factors influencing treatment decisions. For instance, unemployment benefits might depend on age, prior employment history, and other criteria, adding complexity. The main challenges arise when multiple variables are involved, requiring multivariate RD designs. Moreover, when dealing with complex data, traditional methods like local linear regression may struggle to provide robust and reliable estimates. The need to handle multiple scores and complex data structures is a significant hurdle for researchers.

How do 'honest' random forests improve Regression Discontinuity (RD) designs?

The use of 'honest' random forests and local linear forests offers a promising avenue for handling the complexities of real-world data in Regression Discontinuity (RD) designs. These methods are particularly valuable when dealing with multiple factors that determine treatment assignment. Liu and Qi emphasize the use of 'honest' random forests as a powerful tool, because of its ability to handle complex data structures. By carefully choosing the estimator and employing appropriate techniques, researchers can improve the robustness and flexibility of their RD designs.

Can you explain the role of the 'running variable' and the threshold in an RD design?

The 'running variable' is a continuous variable that determines whether an individual receives a treatment. The treatment assignment hinges on this variable crossing a specific 'threshold'. In the example of a scholarship program, the entrance exam score serves as the 'running variable,' and the passing score acts as the threshold. Those whose 'running variable' value (exam score) is above the 'threshold' (passing score) receive the treatment (scholarship). The effectiveness of an RD design depends on the clear definition of this threshold and the assumption that individuals near it are similar in all respects except for the treatment.

What are the key takeaways from the work of Yiqi Liu and Yuan Qi on RD designs?

Yiqi Liu and Yuan Qi's research highlights the importance of using advanced methods such as 'honest' random forests in Regression Discontinuity (RD) designs. Their work emphasizes the challenges of estimating conditional treatment effects, especially when multiple variables influence treatment decisions. They show that 'honest' random forests and local linear forests are valuable tools. Their work guides researchers in selecting appropriate estimators and techniques to enhance the robustness and flexibility of RD designs. The primary takeaway is the need for more advanced methodologies to handle the complexities of real-world data, providing more reliable and accurate estimates of treatment effects.