Difference-in-Differences with Interval Data

2025-12-09

AI Summary

Traditional difference-in-differences (DID) methods fail under interval-valued data—common in surveys and administrative records—because the parallel trends assumption becomes untestable or violated, yielding uninformative or counterintuitive causal estimates. To address this, we propose a “parallel shift” identification strategy that extends the DID framework to accommodate interval-valued outcome variables. Grounded in nonparametric identification and robust inference, our approach imposes no strong distributional assumptions on interval endpoints, thereby enhancing the validity and reliability of causal effect estimation under measurement imprecision. We demonstrate its practical utility through a reanalysis of the seminal minimum wage study, producing meaningful bounds on causal effects. This work provides a theoretically coherent and empirically tractable solution to the pervasive challenge of interval data in policy evaluation.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Difference-in-differences (DID) is one of the most popular tools used to evaluate causal effects of policy interventions. This paper extends the DID methodology to accommodate interval outcomes, which are often encountered in empirical studies using survey or administrative data. We point out that a naive application or extension of the conventional parallel trends assumption may yield uninformative or counterintuitive results, and present a suitable identification strategy, called parallel shifts, which exhibits desirable properties. Practical attractiveness of the proposed method is illustrated by revisiting an influential minimum wage study by Card and Krueger (1994).

Problem

• Extends DID to handle interval outcomes from surveys
• Addresses issues with naive parallel trends assumptions
• Proposes parallel shifts for better causal identification

Innovation

• Extends DID to interval outcomes
• Introduces parallel shifts assumption
• Revisits Card and Krueger study