Modeling temporal treatment effects with zero inflated semi-parametric regression models: the case of local development policies in France

A semi-parametric approach is considered to estimate the variation along time of the effects of two public policies that were devoted to boost rural development in France. This statistical approach combines the flexibility and modularity of additive models with the ability of panel data to deal with selection bias and to allow for the estimation of dynamic treatment effects. Since we face a kind of zero inflated phenomenon that cannot be dealt with a continuous distribution, we introduce a mixture model with a mass at zero and a continuous density. We find evidence of interesting patterns of temporal treatment effects with relevant nonlinear policy effects. The adopted semi-parametric modeling also offers the possibility of making a counterfactual analysis at an individual level. The methodology is illustrated on a few municipalities for which the evolution of the potential outcomes is estimated and compared under the different possible treatments.