Spatial Unit Roots

当通货膨胀率或失业率等数据序列在一段时间内高度相关时，很难确定因果关系的方向。 不考虑这种随着时间推移的高度相关性会导致错误的结论。因此，当经济学家从随时间高度相关的数据中得出结论时，他们开发了纠正这种相关性的方法。 没有方法来纠正在不同地点测量的经济变量之间的强相关性，例如美国不同通勤区的收入，房价或犯罪率。 该研究开发了新的方法来校正跨空间的经济变量之间的强相关性，以帮助研究人员做出正确的推断。 该研究开发了一个正式的框架来研究这种影响，推导出检测强空间相关性的测试，并提出了从强相关的空间数据中恢复有效结论的方法。由于强相关的空间数据是相当普遍的，这项研究可能对如何在社会科学和其他领域得出正确的经验结论具有重要意义。 本研究的结果将有助于改善美国城市地区的住房和犯罪政策等考虑空间因素的政策制定。本研究使用四个项目来调查“单位根”型强空间依赖的后果。 所提出的方法呼应了时间序列文献中相应的概念和结果：该项目提出了一般空间“单位根”型I（1）过程的模型;然后建立了一个泛函中心极限定理，证明了这种I（1）过程的大样本高斯过程近似。然后将I（1）模型推广到空间“局部到单位”模型，该模型表现出长程、平稳依赖性，并表征了空间I（1）变量回归推断的大样本行为，并确定伪回归对于空间I（1）数据和时间序列I（1）数据一样是一个问题。最后，研究开发渐近有效的空间单位根和平稳性测试，推断局部到单位参数，并建议策略，以获得有效的推断与持久性（I（1）或局部到单位）的空间过程的回归。 除了对计量经济学文献的贡献外，本研究的结果将改善政策制定，特别是城市政策，其中空间依赖性往往非常强。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

When data series, such as inflation or unemployment rates are highly correlated over time, it is difficult to establish the direction of causation. Not accounting for such high correlation over time leads to wrong conclusions. Economists have therefore developed methods to correct for such correlation when drawing conclusions from data that are highly correlated over time. There are no methods to correct for strong correlation among economic variables that are measured at different locations, such as income, housing prices, or crime rates, across different US commuting zones. This research develops new methods to correct for strong correlation among economic variables across space to help researchers make correct inference. The research develops a formal framework to study such effects, derives tests to detect strong spatial correlation, and suggest methods to restore valid conclusions from strongly correlated spatial data. Since strongly correlated spatial data is quite common, this research could have important implications for how to draw correct empirical conclusions in the social sciences and beyond. The results of this research will improve policy making that involves consideration of space, such as housing and crime policies in US urban areas.This research uses four projects to investigate the consequences of "unit root"-type strong spatial dependence. The suggested methods echo corresponding concepts and results in the time series literature: The project suggests a model for general spatial "unit-root"-type I(1) processes; it then establishes a Functional Central Limit Theorem justifying a large sample Gaussian process approximation for such I(1) processes. The I(1) model is then generalized to a spatial "local-to-unity" model that exhibits long-range, stationary dependence as well as characterize the large sample behavior of regression inference with spatial I(1) variables and establish that spurious regression is as much a problem with spatial I(1) data as it is with time series I(1) data. Finally, the research develops asymptotically valid spatial unit root and stationarity tests, inference for the local-to-unity parameter, and suggest strategies for obtaining valid inference in regressions with persistent (I(1) or local-to-unity) spatial processes. Besides contributions to the econometrics literature, the results of this research will improve policy making, especially urban policies, where spatial dependence tends to be very strong. The results will also help establish the US as a global leader in spatial econometrics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.