Unlock Causal Insights: How Regression Discontinuity Design Works

Causal inference seeks to determine whether a variable such as a policy or treatment causes changes in another variable like health outcomes or economic growth. Among many causal methods, Regression Discontinuity Design (RDD) is a particularly clever tool, and this article introduces its basic principles and applications.

Introduction to Regression Discontinuity

Regression Discontinuity uses a pre‑specified “cutoff” or “threshold” to compare outcome variables on either side of that point, thereby inferring causality.

The idea behind RDD is very ingenious. In the “gold standard” of causal inference, randomised controlled trials are reliable because randomisation makes the two groups roughly comparable, after which an intervention is applied to one group to observe its effect.

However, interventions are rarely easy to randomise. Imagine studying whether attending university affects future income and trying to randomly assign high‑school seniors to either attend university or not—people would not consent to such randomisation. Thus, many social studies cannot conduct randomised experiments.

RDD does not create a real intervention; instead it seeks a naturally occurring setting that resembles a randomised trial. This setting is usually a rule or policy that assigns individuals to treatment based on a quantitative standard (the cutoff).

The cutoff provides a natural dividing line, allowing comparison of individuals just above and just below it.

Key Idea

RDD assumes that individuals on either side of the cutoff are very similar in all other respects. For example, students whose exam scores are just above or just below a passing line are likely indistinguishable on many characteristics. Therefore, any observed difference in outcomes near the cutoff can be attributed to the intervention rather than other factors.

Consider a scholarship program that awards funds only to students whose exam scores exceed a certain threshold. The threshold is the “cutoff.” Students who miss the cutoff by one point and those who just pass are otherwise similar, so differences in their later outcomes (e.g., college enrollment or earnings) can be used to estimate the causal effect of receiving the scholarship.

Core Assumptions

To ensure RDD validity, two main assumptions must hold.

First, aside from the treatment variable (e.g., scholarship receipt), all other factors influencing the outcome should vary smoothly around the cutoff. This is known as the continuity assumption .

Second, individuals cannot precisely manipulate their position relative to the cutoff (e.g., students cannot perfectly control their exam score). Hence, near the cutoff, receiving the treatment is effectively randomised.

Implementation Steps

1. Identify a clear intervention threshold or cutoff.

2. Collect data on individuals on both sides of the cutoff, including outcome variables (such as academic performance or income) and relevant covariates.

3. Use regression analysis or other statistical techniques to compare outcomes across the cutoff and estimate the causal effect of the intervention.

In education, researchers use RDD to assess scholarship impacts on academic performance; in economics, it evaluates tax policy effects; in public policy, it measures outcomes such as the impact of minimum wage laws on employment.

RDD is a clever design for estimating causal effects in observational data. It applies to contexts with a clear cutoff or threshold, helping researchers draw more precise and reliable causal conclusions, provided the treatment assignment near the cutoff mimics randomisation. — Author: Wang Haihua

Regression discontinuity, causality evident.