Inference in high-dimensional regression models without the exact or $L^p$ sparsity

TL;DR

This paper introduces a novel inference method for high-dimensional regression models that does not rely on exact or $L^p$ sparsity, using a combination of advanced algorithms and machine learning techniques.

Contribution

The paper presents a new inference approach that achieves root-$N$ asymptotic normality without requiring traditional sparsity assumptions, applicable to high-dimensional regression and IV models.

Findings

Demonstrates superior finite-sample performance over LASSO and random forest methods.

Validates the method through simulation studies under less sparse conditions.

Applies the approach to production analysis with Chilean firms.

Abstract

This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information criterion, and double/debiased machine learning. The method of inference for any low-dimensional subvector of high-dimensional parameters is based on a root-$N$ asymptotic normality, which is shown to hold without requiring the exact sparsity condition or the $L^p$ sparsity condition. Simulation studies demonstrate superior finite-sample performance of this proposed method over those based on the LASSO or the random forest, especially under less sparse models. We illustrate an application to production analysis with a panel of Chilean firms.