Difference-in-Differences in the Presence of Unknown Interference

TL;DR

This paper examines how the Difference-in-Differences (DiD) method behaves when the assumption of no interference between units is violated, showing it identifies a contrast of effects but not individual causal effects without additional assumptions.

Contribution

It analyzes the identification issues of DiD estimands under unknown interference and proposes conditions under which causal effects can be separately identified.

Findings

DiD estimand identifies a contrast of causal effects, not individual effects.

Additional assumptions are needed for causal effect identification.

Revisits the Card and Krueger (1994) case study to illustrate results.

Abstract

The stable unit treatment value (SUTVA) is a crucial assumption in the Difference-in-Differences (DiD) research design. It rules out hidden versions of treatment and any sort of interference and spillover effects across units. Even if this is a strong assumption, it has not received much attention from DiD practitioners and, in many cases, it is not even explicitly stated as an assumption, especially the no-interference assumption. In this technical note, we investigate what the DiD estimand identifies in the presence of unknown interference. We show that the DiD estimand identifies a contrast of causal effects, but it is not informative on any of these causal effects separately, without invoking further assumptions. Then, we explore different sets of assumptions under which the DiD estimand becomes informative about specific causal effects. We illustrate these results by revisiting the seminal paper on minimum wages and employment by Card and Krueger (1994).