SGER: Nonlinear IV Approach to Inference in Nonstationary Panels

该项目探索了一种在具有单位根的一般非平稳面板中进行推断的非线性IV方法。该方法依赖于标准的IV方法，仪器由集成过程的非线性变换构成。虽然该方法实现起来非常简单，但它为测试面板中的单元根提供了极其有效的工具。我们对面板中单位根的检验简单地基于单个的非线性IVt-比率，这些t-比率只不过是基于IV估计量的通常的t-比率，而使用滞后水平的可积变换作为工具。这种基于非线性IV的测试具有许多理想的特性，并且可以用于非常一般的模型。检验统计量在每个横截面水平上都有高斯极限分布，更重要的是，它们在不同的横截面单元上是渐近独立的。渐近的高斯性和独立性在允许横截面依赖性和异质性的非常温和的条件下确实成立。相比之下，以前所做的几乎所有相关工作都假定不是横截面独立，就是跨单个单位的特定形式的依赖。不用说，对于许多感兴趣的经济小组来说，跨领域独立性的假设是非常不切实际的。对横截面相关性形式的任何推定也可能严重限制测试的适用性。我们的渐近性只要求时间维度很大，所以这种检验方法对大、小截面尺寸的板都是有效的。所提出的单位根检验不仅允许新息的横截面相依性，而且还允许横截面单位在水平上存在协整。不平衡面板和具有不同个体短程动态和横截面相关动态的面板也是允许的。拟议的检验还使人们有可能更仔细地制定面板中的单位根和协整假设，并使用顺序统计量来检验单位根和协整的存在与否，只在个别单位的一小部分中进行检验。目前可用的任何一种测试都不能用来测试这种通用面板中的单位根。一些初步模拟表明，我们的基于非线性IV的测试在有限样本中表现得非常好，即使对于时间和横截面尺寸相对较小的电池板也是如此。

The project explores a nonlinear IV approach to inference in general nonstationary panels with unit roots. The approach relies on the standard IV methods with instruments constructed from nonlinear transformations of integrated processes. Though the methodology is very simple to implement, it provides extremely effective tools for testing unit roots in panels. Our tests for unit roots in panels are simply based on individual nonlinear IV t-ratios, which are nothing but the usual t-ratios based on the IV estimators using as instruments the integrable transformations of lagged levels. Such nonlinear IV based tests have many desirable properties and can be used for very general models. The test statistics have Gaussian limit distributions at each cross- sectional level, and more importantly, they are asymptotically independent across different cross-sectional units. The asymptotic Gaussianity and independence indeed hold under very mild conditions that allow for cross-sectional dependency and heterogeneity. In contrast, virtually all of the related work done previously assumes either cross- sectional independence or specific forms of dependency across individual units. Needless to say, the assumption of cross-sectional independence is highly unrealistic for many economic panels of interest. Any presumption on the form of cross-sectional dependency may also severely restrict the applicability of the tests. Our asymptotics only require the time dimension to be large, so the tests are valid for panels with both large and small cross-sectional dimensions. The proposed tests for unit roots allow not only for the cross-sectional dependencies of nnovations, but also for the presence of cointegration across cross-sectional units in levels. Unbalanced panels and panels with heterogeneous individual shortrun dynamics and cross-sectionally related dynamics are also permitted. The proposed tests also make it possible to more carefully formulate the unit root and cointegration hypotheses in panels, and use order statistics to test for and against the presence of unit roots and cointegrationin only a fraction of individual units. None of the currently available tests can be used to test for unit roots in such general panels. Some preliminary simulations indicate that our nonlinear IV based tests perform very well in finite samples even for panels with relatively small time and cross-sectional dimensions.