Retrospective causal inference via matrix completion, with an evaluation of the effect of European integration on cross-border employment

TL;DR

This paper introduces a matrix completion method for retrospective causal inference in panel data, specifically addressing later-treated and always-treated units, and applies it to study European integration's impact on cross-border employment.

Contribution

The paper develops a novel matrix completion approach with propensity-score and elapsed-time weighting for causal inference in complex panel data settings.

Findings

Border opening nearly doubled cross-border employment in Eastern Europe.

Method effectively imputes counterfactual outcomes in the absence of never-treated units.

Application demonstrates the impact of European integration milestones on labor mobility.

Abstract

We propose a method of retrospective counterfactual imputation in panel data settings with later-treated and always-treated units, but no never-treated units. We use the observed outcomes to impute the counterfactual outcomes of the later-treated using a matrix completion estimator. We propose a novel propensity-score and elapsed-time weighting of the estimator's objective function to correct for differences in the observed covariate and unobserved fixed effects distributions, and elapsed time since treatment between groups. Our methodology is motivated by studying the effect of two milestones of European integration -- the Free Movement of persons and the Schengen Agreement -- on the share of cross-border workers in sending border regions. We apply the proposed method to the European Labour Force Survey (ELFS) data and provide evidence that opening the border almost doubled the probability of working beyond the border in Eastern European regions.