Difference-in-Differences with Interval Data

TL;DR

This paper extends the difference-in-differences methodology to handle interval data, addressing challenges with traditional assumptions and proposing a new identification strategy called parallel shifts, demonstrated through a minimum wage case study.

Contribution

It introduces a novel extension of DID for interval outcomes and proposes the parallel shifts identification strategy, improving causal inference in survey and administrative data.

Findings

The parallel shifts approach provides more reliable causal estimates with interval data.

Application to the Card and Krueger (1994) study illustrates practical advantages.

Naive extensions of DID with interval data can lead to misleading results.

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).