Lasso Methods for Gaussian Instrumental Variables Models
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Victor11-14.pdf
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Author(s)
Belloni, Alexandre
Chernozhukov, Victor
Hansen, Christian
Date Issued
February 25, 2011
Publisher
Cambridge, MA: Department of Economics, Massachusetts Institute of Technology
Series/Report no.
Working paper (Massachusetts Institute of Technology, Department of Economics);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.
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