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

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