Local Projections Inference with High-dimensional Controls without Sparsity

Abstract: This paper presents a comprehensive local projections (LP) framework for estimating future responses to current shocks, robust to high-dimensional controls without relying on sparsity assumptions. The approach is applicable to various settings, including impulse response analysis and difference-in-differences (DiD) estimation. While methods like LASSO exist, they often rely on sparsity assumptions—most parameters are exactly zero, limiting their effectiveness in dense data generation processes. I propose a novel technique incorporating high-dimensional covariates in local projections using the Orthogonal Greedy Algorithm with a high-dimensional AIC (OGA+HDAIC) model selection method. This approach offers robustness in both sparse and dense sce- narios, improved interpretability, and more reliable causal inference in local projections. Simulation studies show superior performance in dense and persistent scenarios com- pared to conventional LP and LASSO-based approaches. In the empirical application, applying the proposed method to Acemoglu, Naidu, Restrepo, and Robinson (2019), I show efficiency gains and robustness to a large set of controls. Additionally, I examine the effect of subjective beliefs on economic aggregates, demonstrating robustness to various model specifications.

Keywords: local projection, high-dimensional covariates, double/debiased machine learning