Surreal illustration merging RDD and DiD bridges.

DiD You Know? How 'Difference-in-Discontinuities' is Changing Economic Analysis

Elliot Brynn in Business & Economy June 2025 • 4 min read.

"Explore the groundbreaking econometric technique combining RDD and DiD for sharper insights in economic policy and beyond."

In the realm of economic analysis, researchers constantly seek more refined tools to dissect the intricate relationships between policies and outcomes. Enter the difference-in-discontinuities (DiDC) design, an innovative econometric method that's capturing attention for its ability to bridge the gap between traditional regression discontinuity (RDD) and difference-in-differences (DiD) designs. Think of it as the Swiss Army knife for economists, combining the best features of two established techniques to tackle complex scenarios.

Traditional RDD excels at evaluating sharp discontinuities, like policy changes implemented based on a specific threshold (e.g., income eligibility for a program). DiD, on the other hand, compares changes in outcomes over time between a treatment group and a control group. However, each has its limitations. RDD can be vulnerable to confounding factors at the discontinuity, while DiD relies on the often-shaky assumption of parallel trends between the groups.

The DiDC design steps in as a powerful hybrid, leveraging both the discontinuity-based and the time-based sources of variation. By examining the difference in the discontinuity effect before and after a policy change, DiDC aims to eliminate the impact of confounding factors that might otherwise bias the results. It's a sophisticated approach that offers potentially more accurate and reliable estimates of treatment effects. But how does it work, and why is it gaining traction?

DiDC: A Deeper Dive into the Mechanics

Surreal illustration merging RDD and DiD bridges.

At its core, DiDC seeks to isolate the causal effect of a treatment (like a new policy) by comparing changes around a specific threshold over time. Imagine a scenario where a city implements a new business tax break for companies with fewer than 50 employees. A simple RDD would compare the economic performance of companies just above and just below the 50-employee cutoff after the tax break is implemented. However, this might not account for other factors that differentiate these companies.

Here's where DiDC shines. It would compare the difference in economic performance between these near-cutoff companies before and after the tax break. By looking at how the discontinuity changes over time, DiDC controls for time-invariant confounders – those pre-existing differences between the groups that don't change with the policy. This approach rests on some key assumptions:

Continuity: Potential outcomes are continuous around the threshold, meaning there are no sudden jumps in the outcome variable for reasons other than the treatment.
Discontinuity in Treatment Probability: There's a clear jump in the probability of receiving the treatment at the threshold.
Time-Invariance of Confounding Effects: Any confounding effects at the threshold remain constant over time. This is a crucial assumption, suggesting that any pre-existing differences between the treatment and control groups don't change as a result of the policy.
Independence of Treatment Effect and Confounding Policy:The treatment effect should not be affected by the confounding policy.

These assumptions are critical for DiDC to deliver valid results. While the continuity and discontinuity assumptions are standard in RDD, the time-invariance and independence assumptions are unique to DiDC and require careful consideration.

The Future of DiDC: Opportunities and Challenges

The difference-in-discontinuities design offers a powerful new tool for economists and policy analysts. By combining the strengths of RDD and DiD, it provides a more robust approach to estimating treatment effects in complex settings. However, like any econometric method, DiDC relies on key assumptions that must be carefully considered. As research on DiDC continues to evolve, we can expect to see even more innovative applications of this technique in the years to come, further refining our understanding of the intricate relationships that shape our world.

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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.2405.18531,

Title: Difference-In-Discontinuities: Estimation, Inference And Validity Tests

Subject: econ.em stat.ap

Authors: Pedro Picchetti, Cristine C. X. Pinto, Stephanie T. Shinoki

Published: 28-05-2024

Everything You Need To Know

What is the core purpose of the Difference-in-Discontinuities (DiDC) design in economic analysis?

The core purpose of the Difference-in-Discontinuities (DiDC) design is to provide a more robust method for evaluating treatment effects, particularly in complex scenarios. It aims to refine the understanding of how policies and other interventions impact outcomes by combining the strengths of Regression Discontinuity (RDD) and Difference-in-Differences (DiD) designs. This hybrid approach helps economists isolate the causal effect of a treatment, like a new policy, by comparing changes around a specific threshold over time, thus mitigating the influence of confounding factors.

How does Difference-in-Discontinuities (DiDC) improve upon Regression Discontinuity (RDD) and Difference-in-Differences (DiD) individually?

Difference-in-Discontinuities (DiDC) enhances upon the limitations of both Regression Discontinuity (RDD) and Difference-in-Differences (DiD). RDD can be susceptible to confounding factors near the discontinuity threshold, while DiD relies on the assumption of parallel trends between treatment and control groups, which may not always hold true. DiDC overcomes these limitations by examining the difference in the discontinuity effect *before* and *after* a policy change, effectively controlling for time-invariant confounders that might otherwise bias the results. This allows for more accurate and reliable estimates of treatment effects by leveraging both discontinuity-based and time-based sources of variation.

What are the key assumptions that must hold true for the Difference-in-Discontinuities (DiDC) design to yield valid results?

For the Difference-in-Discontinuities (DiDC) design to deliver valid results, several key assumptions must be met. These include continuity of potential outcomes around the threshold, a clear discontinuity in treatment probability at the threshold, time-invariance of confounding effects (meaning any pre-existing differences between groups remain constant over time), and independence of the treatment effect and any confounding policies. Adherence to these assumptions is crucial for ensuring that the analysis accurately isolates the causal impact of the treatment being studied.

Can you provide a practical example of how the Difference-in-Discontinuities (DiDC) design might be used in the real world to evaluate a policy?

Consider a city implementing a business tax break for companies with fewer than 50 employees. Using Difference-in-Discontinuities (DiDC), the analysis would involve comparing the economic performance of companies just above and just below the 50-employee cutoff *before* and *after* the tax break. By examining the difference in performance around this threshold over time, DiDC can isolate the impact of the tax break by controlling for any pre-existing differences between the companies that might affect their performance, which could be missed by simply comparing the companies' performance only *after* the tax break.

What are the main challenges and future opportunities associated with the Difference-in-Discontinuities (DiDC) design?

The main challenges associated with the Difference-in-Discontinuities (DiDC) design involve ensuring the validity of its key assumptions, particularly the time-invariance of confounding effects and the independence of the treatment effect and any confounding policy. Future opportunities lie in exploring more innovative applications of DiDC across various fields, leading to a deeper understanding of complex relationships and policy impacts. As the technique evolves, further research will likely refine its methodologies and expand its applicability, making it an even more valuable tool for economists and policy analysts.