IV-Based Cointegration Testing in Dependent Panels with Time-Varying Variance

While the limiting null distributions of cointegration tests are invariant to a certain amount of conditional heteroskedasticity as long as global homoskedasticity conditions are fulfilled, they are certainly affected when the innovations exhibit time-varying volatility. Worse yet, distortions from single units accumulate in panels, where one must anyway pay special attention to dependence among cross-sectional units, be it time-dependent or not. To obtain a panel cointegration test robust to both global heteroskedasticity and cross-unit dependence, we start by adapting the nonlinear instruments method proposed for the Dickey-Fuller test by Chang (J of Econometrics 110, 261--292) to an error-correction testing framework. We show that IV-based testing of the null of no error-correction in individual equations results in asymptotic standard normality of the test statistic as long as the t-type statistics are computed with White heteroskedasticity-consistent standard errors. Remarkably, the result holds even in the presence of endogenous regressors, irrespective of the number of integrated covariates, and for any variance profile. Furthermore, a test for the null of no cointegration---in effect, a joint test against no error correction in any equation of each unit---retains the nice properties of the univariate tests. In panels with fixed cross-sectional dimension, both types of test statistics from individual units are shown to be asymptotically independent even in the presence of correlation or cointegration across units, leading to a panel test statistic robust to cross-unit dependence and unconditional heteroskedasticity. The tests perform well in panels of usual dimensions with innovations exhibiting variance breaks and a factor structure.