Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator |
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Authors: | Matei Demetrescu Christoph Hanck |
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Institution: | 1. Hausdorff Center for Mathematics and Institute for Macroeconomics and Econometrics , University of Bonn , Bonn , D-53113 , Germany;2. Department of Economics , Econometrics and Finance , Rijksuniversiteit Groningen, Groningen , 9747AE , Netherlands |
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Abstract: | The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministic trends. The standard normality of the Cauchy test is exploited to obtain a standard normal panel unit root test under cross-sectional dependence and time-varying volatility with an orthogonalization procedure. The article’s analysis of the joint N, T asymptotics of the test suggests that (1) N should be smaller than T and (2) its local power is competitive with other popular tests. To render the test applicable when N is comparable with, or larger than, T, shrinkage estimators of the involved covariance matrix are used. The finite-sample performance of the discussed procedures is found to be satisfactory. |
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Keywords: | Asymptotic normality Cross-dependent panel Integrated process Joint asymptotics Nonstationary volatility Time-varying variance |
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