Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments

TL;DR

This paper introduces a method for estimating causal parameters in linear models with many controls and instruments by leveraging high-dimensional sparse estimation techniques, extending previous methods to handle large variable sets.

Contribution

It extends existing methods to simultaneously select relevant controls and instruments in high-dimensional linear models, enabling more accurate causal inference.

Findings

Method successfully selects relevant variables in simulations.

Empirical example demonstrates practical applicability.

Improves inference accuracy with many controls and instruments.

Abstract

In this note, we offer an approach to estimating causal/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 BCCH2012, which covers selection of instruments for IV models with a small number of controls, and extends BCH2014, 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 online appendix.