Unified Inference for Panel Autoregressive Models With Unobserved Grouped Heterogeneity*

This paper considers unified estimation and inference in panel autoregressive (PAR) models. The PAR coefficients are assumed to contain a latent group structure that allows the degree of persistence for each time series to be heterogeneous and unknown. We propose a novel penalized weighted least squares approach to simultaneously identify the unknown group membership and consistently estimate the PAR coefficients, regardless of whether the underlying PAR process is stationary, unit-root, near-integrated, or even explosive. Theoretically, we establish the classification consistency, oracle properties, and unified asymptotic normal distributions for the proposed Lasso-type estimators. Empirically, we apply our data-driven method to uncover the existence of firm-level hidden bubbles in the U.S. stock market that have not been accounted for in previous studies.