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Difference-in-Differences in the Presence of Unknown Interference

Fabrizia Mealli, Javier Viviens

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).

Difference-in-Differences in the Presence of Unknown Interference

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).
Paper Structure (11 sections, 7 theorems, 26 equations, 2 tables)

This paper contains 11 sections, 7 theorems, 26 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Difference-in-Differences under interference
  3. Notation and set-up
  4. Canonical DiD under the no-interference assumption
  5. DiD under partial interference
  6. DiD under unknown interference
  7. Alternative identification strategies under unknown interference
  8. Assumptions on the unobserved trends of $Y(0,\boldsymbol{0},\boldsymbol{0})$.
  9. Assumption on the causal effects $\tau^{1}$ and $\tau^{0}$
  10. Application: revisiting card_minimum_1994
  11. Concluding remarks

Key Result

Proposition 1

Under Assumptions as:no_anti, as:no_hid, as:sutva and as:pt_sutva, the ATT (Estimand est:att) is identified by the DiD estimand.

Theorems & Definitions (7)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6
  • Proposition 7