Local Projection Inference in High Dimensions

TL;DR

This paper develops a method for estimating impulse responses in high-dimensional models using local projections combined with desparsified lasso, providing asymptotic normality and demonstrating good finite-sample performance.

Contribution

It introduces a novel approach that combines local projections with desparsified lasso for high-dimensional impulse response estimation, establishing asymptotic properties.

Findings

Estimator is asymptotically normal under general conditions.

Simulation shows strong finite-sample performance.

Applicable to macroeconomic policy analysis.

Abstract

In this paper, we estimate impulse responses by local projections in high-dimensional settings. We use the desparsified (de-biased) lasso to estimate the high-dimensional local projections, while leaving the impulse response parameter of interest unpenalized. We establish the uniform asymptotic normality of the proposed estimator under general conditions. Finally, we demonstrate small sample performance through a simulation study and consider two canonical applications in macroeconomic research on monetary policy and government spending.