Inference on Treatment Effects After Selection Amongst High-Dimensional Controls

Understand

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls.

• Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances.
• Our analysis allows the number of controls to be much larger than the sample size.
• To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown.