  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.
