Regression discontinuity aggregation, with an application to the union effects on inequality

TL;DR

This paper extends the regression discontinuity design to aggregate treatment settings, enabling causal inference in complex scenarios like state-level analyses, and demonstrates its application to union effects on inequality in the US.

Contribution

It introduces two novel estimation procedures for RD designs with aggregated treatments, broadening the scope of causal inference in such contexts.

Findings

Higher unionization rates reduce wage inequality within state-industry cells.

The proposed methods identify local average causal effects under standard RD assumptions.

Application to US data shows credible variation from close unionization elections.

Abstract

We extend the regression discontinuity (RD) design to settings where each unit's treatment status is an average or aggregate across multiple discontinuity events. Such situations arise in many studies where the outcome is measured at a higher level of spatial or temporal aggregation (e.g., by state with district-level discontinuities) or when spillovers from discontinuity events are of interest. We propose two novel estimation procedures - one at the level at which the outcome is measured and the other in the sample of discontinuities - and show that both identify a local average causal effect under continuity assumptions similar to those of standard RD designs. We apply these ideas to study the effect of unionization on inequality in the United States. Using credible variation from close unionization elections at the establishment level, we show that a higher rate of newly unionized workers in a state-by-industry cell reduces wage inequality within the cell.