Taking a New Contour: A Novel Approach to Inference in Nonstationary Panels

众所周知，许多常用的单位根检验的分布理论是不标准的。本项目为这些发行版和相关发行版开发了一种新颖的方法。对于给定的样本量，通常可以得到统计量的抽样分布。因此，为了统计推断的目的而使用统计量的常规抽样分布意味着对统计量的实现值沿分布轮廓的可能性进行评估，由固定的样本量给出。本课题采用不同的轮廓来获得统计量的抽样分布，即固定平方和给出的轮廓。对于平稳时间序列的观测值，对于大样本，平方和是样本数量的常数倍，因此等平方和的轮廓具有常规的统计性质，用于平稳数据的统计分析。但非平稳数据的统计性质是不同的。提出的研究为非平稳面板的统计推断开发了这个新的框架。具体来说，众所周知，非平稳面板的横截面依赖关系是非常难以处理的。非平稳模型通常具有非标准且依赖于干扰参数的分布。面板中的测试组合了为每个单独单元计算的统计信息，因此，如果跨单个单元进行汇总，则单个测试统计信息的非标准分布和讨厌的参数依赖性问题会变得更加严重。使用标准的统计推断方法进行统计推断即使不是不可能，也是很困难的。但是，如果使用在所有横截面单元上具有相同平方和的样本来计算单个检验统计量，则模型产生没有麻烦参数的标准正态渐近，并且这些面板上的统计推断现在容易得多。更广泛的影响：本项目将为非平稳面板的统计分析建立一个新的框架，这将为计量经济学理论家开发新的方法来有效地处理非平稳面板开辟新的机会。本文还将提供一套新的可靠的工具来进行非平稳面板的推理。鉴于非平稳面板在国际金融、宏观经济学、产业组织和劳动经济学等领域的使用已经并将在未来更加广泛，本研究的成果将对经济学的理论和实证研究产生深远的影响。为了促进新方法的实施，研究者将准备一个程序包并分发给应用研究人员。

It is well known that the distributional theories for many of the commonly used unit root tests are nonstandard. This project develops an original approach to these and related distributions. The sampling distribution of a statistic is usually obtained for a given sample size. Using the conventional sampling distribution of the statistic for the purpose of statistical inference thus implies evaluation of the likelihood of a realized value of the statistic along the contour of the distribution, given by the fixed sample size. This project takes a different contour in obtaining the sampling distribution of a statistic, i.e., the contour that is given by the fixed sum of squares. For the observations from stationary time series, the sum of squares becomes a constant multiple of the sample size for large samples, so the contour of the equi-squared-sum has conventional statistical properties for statistical analysis of stationary data. But the statistical properties are different for nonstationary data. The proposed research develops this new framework for statistical inference in nonstationary panels. Specifically, it is well known that the cross-sectional dependencies in nonstationary panels are extremely difficult to handle. The nonstationary models in general have distributions that are nonstandard and dependent upon nuisance parameters. The tests in panels combine the statistics computed for each individual unit, so the problem of nonstandard distributions and nuisance parameter dependencies of the individual test statistics becomes aggravated if aggregated across individual units. Statistical inference is difficult if not impossible using standard statistical methods of inference. But if the individual test statistics are computed using the samples which have the same sum of squares across all cross-sectional units, then the models yield standard normal asymptotics free of nuisance parameters and statistical inference on these panels is now much easier.Broader Impacts: This project will build up a new framework for the statistical analysis of the nonstationary panels, which will open up new opportunities for the econometric theorists to develop new methodologies to effectively deal with nonstationary panels. A set of new reliable tools to do inference in nonstationary panels will also be provided. Given that the use of nonstationary panels has become, and will be even more so in the future, widespread in such fields as international finance, macroeconomics, industrial organization and labor economics, the outputs from this research could have a far-reaching impact on both theoretical and empirical research in economics. To facilitate implementation of the new methods, the investigator will prepare a program package and distribute it to applied researchers.