Shrinkage quantile regression for panel data with multiple structural breaks

We consider a shrinkage quantile regression model for high-dimensional panel data with multiple structural breaks. The structural breaks are assumed to be common across all individuals, but may vary across different quantile levels while sharing an identical location shift effect. We impose an L-1 penalty on the individual effects and an L-1-type fusion penalty to estimate both the slope coefficients and the structural breaks by combining information at multiple quantile levels. The proposed method can detect "partial" changes of the regression coefficients and consistently estimate both the number and dates of the breaks with probability tending to 1. We establish the asymptotic properties of the proposed regression coefficient estimators as well as their post-selection counterparts, where the dimensionality of the covariates is allowed to diverge. Simulation results demonstrate that the proposed method works well in finite-sample cases. Using the proposed method, we obtain many interesting results by analyzing a dataset concerning environmental Kuznets curves.