A Nonparametric Finite-Mixture Approach to Instrumented Difference-in-Differences, with an Application to Job Training

We develop a finite-mixture framework for nonparametric difference-in-differences analysis with unobserved heterogeneity correlating treatment and outcome. Our framework includes an instrumental variable for the treatment, and we prove non- parametric identification. We can thus relax the single index and stationarity as- sumptions of Athey and Imbens (2006) at the cost of adding slightly more structure on unobserved heterogeneity. We apply our framework to evaluate the effect of on-the-job training on wages, using novel French linked employee-employer data. Estimating a parametric version of our model with the help of an EM-algorithm, we find small ATEs and ATTs on hourly wages, around 4% in the year of training, falling to under 2% in the following year.