Income mobility measures provide convenient and concise ways to reveal the dynamic nature of regional income distributions. Statistical inference about these measures is important especially when it comes to a comparison of two regional income systems. Although the analytical sampling distributions of relevant estimators and test statistics have been asymptotically derived, their properties in small sample settings and in the presence of contemporaneous spatial dependence within a regional income system are underexplored. We approach these issues via a series of Monte Carlo experiments that require the proposal of a novel data generating process capable of generating spatially dependent time series given a transition probability matrix and a specified level of spatial dependence. Results suggest that when sample size is small, the mobility estimator is biased while spatial dependence inflates its asymptotic variance, raising the Type I error rate for a one-sample test. For the two-sample test of the difference in mobility between two regional economic systems, the size tends to become increasingly upward biased with stronger spatial dependence in either income system, which indicates that conclusions about differences in mobility between two different regional systems need to be drawn with caution as the presence of spatial dependence can lead to false positives. In light of this, we suggest adjustments for the critical values of relevant test statistics.

中文翻译：

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存在空间依赖性的收入流动性测度推论

收入流动性措施提供了方便而简洁的方式来揭示区域收入分配的动态性质。有关这些措施的统计推论非常重要，特别是在比较两个区域收入体系时。尽管已渐近导出了相关估计量和检验统计量的分析抽样分布，但在区域收入系统内小样本环境中以及同时存在空间依赖性的情况下，它们的性质仍未得到充分研究。我们通过一系列蒙特卡洛实验来解决这些问题，这些实验需要提出一种新颖的数据生成过程的建议，该过程能够在给定转换概率矩阵和指定水平的空间依赖的情况下生成空间相关的时间序列。结果表明，当样本量较小时，迁移率估计量有偏差，而空间依赖性增加了其渐近方差，从而提高了一次样本测试的I型错误率。对于两个区域经济体系之间的流动性差异的两样本检验，在任何一个收入体系中，规模趋于越来越偏向于更高的空间依赖性，这表明需要得出关于两个不同区域系统之间的流动性差异的结论。谨慎绘制，因为空间依赖性的存在可能导致误报。有鉴于此，我们建议对相关测试统计数据的临界值进行调整。在任何一个收入体系中，其规模趋于越来越偏向于空间依赖性更强，这表明需要谨慎得出关于两个不同区域体系之间流动性差异的结论，因为空间依赖性的存在会导致误报。有鉴于此，我们建议对相关测试统计数据的临界值进行调整。在任何一个收入体系中，其规模趋于越来越偏向于空间依赖性更强，这表明需要谨慎得出关于两个不同区域体系之间流动性差异的结论，因为空间依赖性的存在会导致误报。有鉴于此，我们建议对相关测试统计数据的临界值进行调整。