Estimating a dose-response function with heterogeneous response to confounders when treatment is continuous and endogenous

To improve policy analysis by formulating a new approach to the estimation of treatment effects which vary in magnitude among treated units. The paper's approach to estimating an average treatment effect (ATE) and counterpart measures for the treated (ATET) and untreated (ATENT) allows for the estimation of a functional relationship between the magnitude of treatment and the treated units' response. In a study of public subsidies to private Italian firms' R&D efforts, we find significant variation in the degree to which public funding 'crowds out' private spending on innovative activities.