Abstract

http://ssrn.com/abstract=2051129
 
 

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Inference on Treatment Effects after Selection Amongst High-Dimensional Controls


Alexandre Belloni


Massachusetts Institute of Technology (MIT) - Operations Research Center

Victor Chernozhukov


Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Christian Hansen


University of Chicago Graduate School of Business

May 3, 2012

MIT Department of Economics Working Paper No. 12-13

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 illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates.

Number of Pages in PDF File: 67

Keywords: treatment effects, partially linear model, high-dimensional-sparse regression, inference under imperfect model selection, uniformly valid inference after model selection

JEL Classification: C10, C51

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Date posted: May 5, 2012  

Suggested Citation

Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian, Inference on Treatment Effects after Selection Amongst High-Dimensional Controls (May 3, 2012). MIT Department of Economics Working Paper No. 12-13. Available at SSRN: http://ssrn.com/abstract=2051129 or http://dx.doi.org/10.2139/ssrn.2051129

Contact Information

Alexandre Belloni
Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )
77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States
Victor Chernozhukov (Contact Author)
Massachusetts Institute of Technology (MIT) - Department of Economics ( email )
50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)
HOME PAGE: http://www.mit.edu/~vchern/
New Economic School
47 Nakhimovsky Prospekt
Moscow, 117418
Russia
Christian Hansen
University of Chicago Graduate School of Business ( email )
Chicago, IL 60637
United States
773-834-1702 (Phone)
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References:  56
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