Identification-robust inference for the LATE with high-dimensional covariates

TL;DR

This paper develops a robust inference method for the local average treatment effect (LATE) in high-dimensional settings, using an orthogonalized test and double machine learning to improve size control and applicability.

Contribution

It introduces an orthogonalized Anderson-Rubin test and an easy algorithm for high-dimensional LATE inference, effective under weak identification and high dimensionality.

Findings

Better size control in simulations under weak identification and high dimensionality.

Outperforms conventional methods in simulation studies.

Wider confidence intervals in real data applications.

Abstract

This paper presents an inference method for the local average treatment effect (LATE) in the presence of high-dimensional covariates, regardless of the strength of identification. We propose an orthogonalized Anderson-Rubin test statistic that maintains uniformly valid asymptotic size. We provide an easy-to-implement algorithm for inferring the high-dimensional LATE by inverting our test statistic and employing the double/debiased machine learning method. Simulation results show that our test achieves better size control under both weak identification and high dimensionality, outperforming conventional alternatives. Applying the proposed method to railroad and population data to study the effect of railroad access on urban population growth, we observe wider confidence intervals than those obtained using conventional methods.