SGER: Nonlinear IV Approach to Inference in Nonstationary Panels

该项目探讨了一种非线性IV方法，在一般的非平稳面板与单位根的推断。 该方法依赖于标准的IV方法与工具构建的非线性变换的综合过程。尽管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。我们的单位根的面板测试是简单地基于个人的非线性IV的t-比率，这是什么，但通常的t-比率的基础上的IV估计作为工具，滞后水平的可积变换。这种基于非线性IV的测试具有许多期望的性质，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具有高斯极限分布，更重要的是，它们在不同的横截面单元上是渐近独立的。渐近高斯性和独立性确实在非常温和的条件下成立，允许横截面依赖性和异质性。 相反，以前所做的几乎所有相关工作都假设跨部门的独立性或跨单个单元的特定形式的依赖性。不用说，假设横截面的独立性是非常不现实的许多经济小组的利益。任何关于横截面依赖性形式的假设也可能严重限制检验的适用性。我们的渐近性只要求时间维度很大，所以测试对于具有大和小横截面尺寸的面板都有效。 拟议的单位根检验不仅考虑了更新的横截面依赖性，而且还考虑了水平上横截面单位之间协整的存在。不平衡的面板和面板与异质个人shortrun动态和横截面相关的动态也是允许的。所提出的测试也使得有可能更仔细地制定单位根和协整假设面板，并使用顺序统计量来测试和反对存在的单位根和协整，只有一小部分的个别单位。目前可用的测试都不能用于测试这样的一般面板中的单位根。一些初步的模拟表明，我们的非线性IV为基础的测试表现非常好，在有限的样本，即使是面板相对较小的时间和横截面尺寸。

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.