Inference on treatment effects after selection amongst high-dimensional controls

Alexandre Belloni, Victor Chernozhukov and Christian Hansen
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Alexandre Belloni: Institute for Fiscal Studies

No CWP26/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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 where the number of controls may 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. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the 'post-double-selection' method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We also present a simple generalisation of our method to a fully heterogeneous model with a binary treatment variable. We illustrate the use of the developed methods with numerical simulations and an application that considers the effect of abortion crime rates.

Keywords: treatment effects; partially linear model; high-dimensional-sparse regression; inference under imperfect model selection; uniformly valid inference after model selection; average treament effects; average treatment effects for the treated (search for similar items in EconPapers)
Date: 2013-07-22
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (64)

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Related works:
Working Paper: Inference on treatment effects after selection amongst high-dimensional controls (2013)
Working Paper: Inference on Treatment Effects After Selection Amongst High-Dimensional Controls (2012)
Working Paper: Inference on treatment effects after selection amongst high-dimensional controls (2012)
Working Paper: Inference on treatment effects after selection amongst high-dimensional controls (2012)
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