2010/12/06 by Alexandre Belloni, Victor Chernozhukov, Belloni, Alexandre +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Methodology (stat.ME) #Monetary Policy and Economic Impact #Spatial and Panel Data Analysis #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1012.1297
openalex publication_date 2010/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we propose to use sparse methods (e.g. LASSO, Post-LASSO, sqrt-LASSO, and Post-sqrt-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.