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Lasso Methods for Gaussian Instrumental Variables Models


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

February 25, 2011

MIT Department of Economics Working Paper No. 11-14

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.

Number of Pages in PDF File: 35

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Date posted: August 12, 2011  

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: http://ssrn.com/abstract=1908409 or http://dx.doi.org/10.2139/ssrn.1908409

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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