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Lasso Methods for Gaussian Instrumental Variables Models

35 Pages Posted: 12 Aug 2011  

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 - Booth School of Business - Econometrics and Statistics

Date Written: February 25, 2011

Abstract

In this note, we propose the use of sparse methods (e.g. LASSO, Post-LASSO, p LASSO, and Post-p LASSO) to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments in the canonical Gaussian case. The methods apply even when the number of instruments is much larger than the sample size. We derive asymptotic distributions for the resulting IV estimators and provide conditions under which these sparsity-based IV estimators are asymptotically oracle-efficient. In simulation experiments, a sparsity-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument-robust procedures. We illustrate the procedure in an empirical example using the Angrist and Krueger (1991) schooling data.

Suggested Citation

Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian, Lasso Methods for Gaussian Instrumental Variables Models (February 25, 2011). MIT Department of Economics Working Paper No. 11-14. Available at SSRN: https://ssrn.com/abstract=1908409 or http://dx.doi.org/10.2139/ssrn.1908409

Alexandre Belloni

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
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Cambridge, MA 02139
United States

Victor Chernozhukov (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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HOME PAGE: http://www.mit.edu/~vchern/

New Economic School

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Moscow, Skolkovo 143026
Russia

Christian Hansen

University of Chicago - Booth School of Business - Econometrics and Statistics ( email )

Chicago, IL 60637
United States
773-834-1702 (Phone)

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