A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models

This note proposes a new decomposition of average treatment effects on nonnegative outcomes. It represents the total effect as a population-weighted sum of the effects for two groups: those induced to participate by the treatment and those participating regardless of it. The usual decomposition into extensive and intensive margins used in the literature is generally incompatible with such a causal interpretation. The difference between decompositions can be substantial and yield diametrically opposed results.