Shrinkage estimation of censored quantile regression for panel data models with grouped latent heterogeneity

This study proposes a grouped fixed-effects censored quantile regression (GFE-CQR) for panel data where the individual effects exhibit heterogeneity across groups and the group structure is unknown. We propose a shrinkage estimation method that allows covariates to be correlated with unobserved individual heterogeneity. Using an informative subset-based grouping algorithm to account for the censored data, we demonstrate that the proposed method achieves asymptotically correct grouping. We use penalized technology to shrink individual coefficients to group-specific coefficients where both the number of groups and group memberships can be unknown a priori. The proposed GFE-CQR estimator is consistent and asymptotically normal. A Monte Carlo simulation shows that the GFE-CQR estimator has superior finite-sample performance. An empirical analysis of household portfolio choices reveals that wealth and market returns negatively influence the share of safe assets, while education exhibits a U-shaped relationship across quantiles. Moreover, individuals allocate a larger share of their portfolios to safe assets as they age. The coefficient estimates for most variables vary significantly across quantile levels, indicating substantial heterogeneity in their effects.