High-dimensional conditional factor model

This paper studies estimation and variable selection in conditional factor models with high-dimensional instruments, where the coefficient matrix exhibits a low-rank and row-sparse structure. We propose a multi-stage estimation procedure that combines nuclear norm regularization and adaptive group LASSO regression to consistently estimate latent factors and row-sparse loading coefficients, while selecting relevant instrumental characteristics. We establish theoretical results for estimation consistency, selection consistency, and post-LASSO inference for estimators of factors and loading coefficients at multiple stages. Furthermore, we implement a singular value thresholding procedure to determine the number of factors. Simulation results demonstrate the effectiveness of our estimators in consistently estimating factor loadings, selecting the appropriate number of factors, and conducting inference. Finally, we apply the proposed method to an empirical study on asset return prediction, showcasing its practical utility in real-world applications.