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Post-selection and post-regularization inference in linear models with many controls and instruments

Authors: Victor Chernozhukov , Christian Hansen and Martin Spindler
Date: 14 January 2015
Type: cemmap Working Paper, CWP02/15
DOI: 10.1920/wp.cem.2015.0215


In this note, we offer an approach to estimating structural parameters in the presence of many instruments and controls based on methods for estimating sparse high-dimensional models. We use these high-dimensional methods to select both which instruments and which control variables to use. The approach we take extends Belloni et al. (2012), which covers selection of instruments for IV models with a small number of controls, and extends Belloni, Chernozhukov and Hansen (2014), which covers selection of controls in models where the variable of interest is exogenous conditional on observables, to accommodate both a large number of controls and a large number of instruments. We illustrate the approach with a simulation and an empirical example. 

Technical supporting material is available in a supplementary appendix here.

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Now published:
Victor Chernozhukov, Christian Hansen and Martin Spindler May 2015, Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments, Journal article, American Economic Association

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