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

A semi-parametric approach is proposed to estimate the variation along time of the effects of two distinct public policies that were devoted to boost rural development in France over the same period of time. At a micro data level, it is often observed that the dependent variable, such as local employment, does not vary along time, so that we face a kind of zero inflated phenomenon that cannot be dealt with a continuous response model. We introduce a mixture model which combines a mass at zero and a continuous response. The suggested zero inflated semi-parametric statistical approach relies on 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. In this multiple treatment analysis, 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 and compared with parametric linear approaches on a few municipalities for which the mean evolution of the potential outcomes is estimated under the different possible treatments.