<p>This paper proposes a hybrid quantile regression framework for fixed effects panel data, with particular emphasis on its applicability to long panel settings. The procedure combines Bayesian inference for quantile-level components with a minimum distance principle for final aggregation. The proposed framework utilizes Pareto smoothed adaptive importance sampling and offers several notable advantages. First, compared with the frequency minimum distance estimation, it does not depend on the smoothing parameter selection and can obtain more accurate estimates. Second, it corrects inaccuracies in the asymptotic variance of the posterior distribution from Gibbs sampling, often based on the asymmetric Laplace likelihood. Third, compared with Gibbs sampling, the proposed method has significant computational advantages, including reduced computation time and lower memory usage, especially for the case with a large number of individuals. Diagnostics, prior sensitivity analysis, and computational efficiency of the method are discussed. Finally, we analyze the impact of the labor force participation rate and the all-transactions house price index on the unemployment rate across US states.</p>