This article develops a random effects quantile regression model for panel data that allows for increased distributional flexibility, multivariate heterogeneity, and time-invariant covariates in situations where mean regression may be unsuitable. Our approach is Bayesian and builds upon the generalized asymmetric Laplace distribution to decouple the modeling of skewness from the quantile parameter. We derive an efficient simulation-based estimation algorithm, demonstrate its properties and performance in targeted simulation studies, and employ it in the computation of marginal likelihoods to enable formal Bayesian model comparisons. The methodology is applied in a study of U.S. residential rental rates following the Global Financial Crisis. Our empirical results provide interesting insights on the interaction between rents and economic, demographic and policy variables, weigh in on key modeling features, and overwhelmingly support the additional flexibility at nearly all quantiles and across several sub-samples. The practical differences that arise as a result of allowing for flexible modeling can be nontrivial, especially for quantiles away from the median.

翻译：本文针对面板数据开发了一种随机效应分位数回归模型，该模型在均值回归可能不适用的情况下，能够增强分布灵活性、处理多元异质性并纳入时间不变协变量。我们的方法基于贝叶斯框架，并借助广义非对称拉普拉斯分布，将偏度建模与分位数参数解耦。我们推导出一种高效的基于模拟的估计算法，通过针对性模拟研究验证其性质与性能，并将其用于计算边际似然以实现正式的贝叶斯模型比较。该方法被应用于全球金融危机后美国住宅租金率的研究。实证结果揭示了租金与经济学、人口学及政策变量之间有趣的相互作用，评估了关键建模特征，并显著支持了几乎所有分位数及多个子样本中额外灵活性的必要性。允许灵活建模所带来的实际差异可能不可忽视，尤其是在远离中位数的分位数处。