Essays on High-Dimensional Econometrics without Sparsity and Bounds on Standard Errors

Abstract

This dissertation develops econometric methods to address key challenges in inference and estimation, particularly in high-dimensional settings. The first two chapters introduce inference without restrictive sparsity assumptions, employing the Orthogonal Greedy Algorithm with High-Dimensional AIC (OGA+HDAIC) for model selection. The third chapter focuses on standard error estimation when empirical moments are derived from multiple data sources. Chapter 1 presents a Local Projections (LP) framework for estimating dynamic responses to shocks with high-dimensional controls. Traditional methods like LASSO rely on sparsity conditions, limiting their effectiveness in dense settings. I propose an OGA+HDAIC-based approach that enhances robustness, interpretability, and efficiency. Simulations and empirical applications illustrate its advantages. Chapter 2, coauthored with Harold D. Chiang and Yuya Sasaki, develops a novel inference method for high-dimensional regression and instrumental variable models in a cross-sectional setting. Unlike existing methods, it remains valid without sparsity constraints. Simulations highlight its advantages over LASSO- and random forest-based methods. Chapter 3, coauthored with Yuya Sasaki, examines inference challenges when combining empirical moments from dependent data sources, such as surveys and administrative records. This chapter constructs both lower and upper bounds on standard errors using best-possible distributional bounds, accounting for finite-sample randomness and broadening their applicability in empirical research. Together, these chapters contribute to econometric inference by developing techniques robust to high dimensionality and improving standard error estimation in modern data environments.