We propose several novel consistent specification tests for quantile regression models which generalize former tests by important characteristics. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow for parameterizing the conditional quantile functions by appropriate basis functions, rather than parametrically.We are hence able to test for functional forms beyond linearity, while retaining the linear effects as special cases. In both cases, the induced class of conditional distribution functions is tested with a Cram\'{e}r-von Mises type test statistic for which we derive the theoretical limit distribution and propose a practical bootstrap method. To increase the power of the first test, we further suggest a modified test statistic using the B-spline approach from the second test. A detailed Monte Carlo experiment shows that the test results in a reasonable sized testing procedure with large power. Our first application to conditional income disparities between East and West Germany over the period 2001-2010 indicates that there are not only still significant differences between East and West but also across the quantiles of the conditional income distributions, when conditioning on age and year. The second application to data from the Australian national electricity market reveals the importance of using interaction effects for modelling the highly skewed and heavy-tailed distributions of energy prices conditional one day, time of day and demand.
翻译:我们建议了几个新的一致的量化回归模型规格测试,这些测试将以前的测试概括为重要特性。 首先,我们允许共变效应以四分位数为依存和非线性。 其次,我们允许通过适当的基础功能而不是参数参数来参数化有条件的量化函数。 因此,我们能够测试超出线性功能的功能形式,同时保留线性效应作为特殊情况。 在这两种情况下,有条件分配功能的诱导类别都用Cram\'{e}r-von Mises 类型测试统计数据来测试,我们据此得出理论限制分布,并提出实用的靴子方法。为了提高第一次测试的功率,我们进一步建议使用第二个测试的B-spline方法来参数来参数化有条件的量化的量化函数。一个详细的蒙特卡洛实验表明,测试的结果是具有相当规模的测试程序,而这种测试则将线性效应保留在线性效应中,同时作为特殊情况,我们在2001-2010年期间对东德和西德之间有条件收入分配功能的诱因类别进行测试时,不仅存在着巨大的差异,而且在有条件收入分配的孔体格之间,在调整年代和年份之间也存在着一种实际的陷阱式方法。 为了提高第一个测试能力,我们进一步建议,我们用第二个应用了用B- S- s- falalal imalal imal imal imal imme imal immeal imme lapal des a lapal lapal lad ladal des a a y lad d dal ladal lades lades lades lades lades lades lades a lades lades lake lake lake lades lades lake lades lades lades a lades a dal laine a ladal ladal ladal la la la la la ladal ladal ladal ladal ladal ladal ladal ladal ladal la ladal ladal ladal ladal ladal ladal ladal lad laine laut laine lades