Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies
提出一种工具变量方法，利用滞后水平的非线性变换作为工具，检验存在一般依赖性和异质性的面板单位根，允许截面依赖和协整，并重新定义假设，通过模拟和实际汇率数据验证，发现不支持购买力平价假说。
An IV approach, using as instruments non-linear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of co-integration across cross-sectional levels. Unbalanced panels and panels with differing individual short-run dynamics and cross-sectionally related dynamics are also permitted. We also more carefully formulate the unit root hypotheses in panels. In particular, using order statistics, we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV "t"-ratios, which are the bases of our tests, are asymptotically and normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual average statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, whereas other existing tests fail to perform properly. As an illustration, we apply our tests to the panels of real exchange rates, and find no evidence for the purchasing power parity hypothesis, which is in sharp contrast with the previous studies. Copyright Copyright © 2009 The Review of Economic Studies Limited.