We propose a complete framework for model-free difference-in-differences analysis with covariates, where model-free means data-driven, in particular nonparametric estimation and testing, variable and scale choice. We start with searching for the preferred data setup by simultaneously choosing...

Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value...

This paper introduces average treatment effects conditional on the outcomes variable in an endogenous setup where outcome Y, treatment X and instrument Z are continuous. These objects allow to refine well studied treatment effects like ATE and ATT in the case of continuous treatment (see Florens...