Iv‐based Cointegration Testing in Dependent Panels With Time‐varying Variance

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract 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 timevarying 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 (2002, J 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. Terms of use: Documents in

Multiple Testing for No Cointegration under Nonstationary Volatility

“…In spite of standard null asymptotics, the test has power in the same neighbourhoods as the Johansen () trace test, and is typically more powerful for alternatives close to the null. In this respect, it thus improves upon earlier nonlinear IV‐based cointegration tests we propose (Demetrescu, Hanck and Tarcolea, ) in the single‐unit case. Unfortunately, the present approach based on the non‐integrable sign‐IV, unlike that of Demetrescu et al .…”

“…Moreover, a test for no cointegration can be built on the joint test for α i = 0 . Unlike the case of integrable instruments (Demetrescu et al ., ), the individual t ‐statistics are not asymptotically independent. But (cf.…”

“…Here, Ω i can be consistently estimated by , the sample covariance matrix of the residuals , leading to an estimator (see the proof of Proposition , in particular, equation (4) in Appendix S1). The results hold irrespective of H i , and no heteroskedasticity‐consistent standard errors are required, unlike for integrable IVs (Demetrescu et al ., ).…”

“…Unfortunately, the present approach based on the non‐integrable sign‐IV, unlike that of Demetrescu et al . (), does not yield independent single‐unit statistics in the panel, leading us to favour the more heuristic panel approach of combining P ‐values.…”

Panel Cointegration Testing in the Presence of Linear Time Trends

“…In particular, the more recent paper by Miller [5], building on nonlinear instrumental variable likelihood-based rank tests, allows for cross-correlation between the units. Similarly, recent single-equation tests by Chang and Nguyen [6] or Demetrescu et al [7] also rely on nonlinear instrumental variable estimation, while the vast majority of such panel tests builds on ordinary or fully modified or dynamic least squares (LS). Here, we study exactly this class of LS-based single-equation panel tests for the null of either cointegration or no cointegration.…”