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：本文针对面板数据提出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境下，允许增强分布灵活性、多变量异质性以及时间不变协变量的纳入。我们的方法基于贝叶斯框架，通过扩展广义非对称拉普拉斯分布，将偏度建模与分位数参数解耦。我们推导了一种高效的基于模拟的估计算法，在针对性模拟研究中展示了其性质与性能，并运用于边际似然计算以支持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中。实证结果揭示了租金与经济、人口及政策变量之间相互作用的有趣洞见，对关键建模特征进行了评估，并在几乎所有分位数及多个子样本中显著支持了额外的灵活性。因允许灵活建模而产生的实际差异可能非常显著，尤其是远离中位数的分位数。