Beyond Sparsity: Local Projections Inference with High-dimensional Controls

Abstract: This paper presents a comprehensive local projections framework for estimating future responses based on current shocks, which is robust to high-dimensional controls and the underlying sparsity of the model.While methods like LASSO exist, they mostly rely on sparsity assumptions - most of the parameters are exactly zero, which has limitations in dense data generation processes. This paper proposes a novel approach that incorporates high-dimensional covariates in local projections without relying on sparsity constraints. Adopting the Orthogonal Greedy Algorithm with a high-dimensional AIC (OGA+HDAIC) model selection method, this approach offers advantages including robustness in both sparse and dense scenarios, improved interpretability by prioritizing cross-sectional explanatory power, and more reliable causal inference in local projections. In the simulation studies, I show that it is more robust to dense and more persistent scenarios than the conventional LP and the LASSO-based approach. 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.

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