Weighted symmetric tests for a unit root: response functions, power, test dependence and test conflict
The most frequently applied test statistics for a unit root are the Dickey-Fuller $ \hat \tau $ tests, which are built into many econometric packages along with MacKinnon's empirical response functions. This article provides empirical response functions for some easy to compute alternative test statistics that are generally much more powerful than the Dickey-Fuller $ \hat \tau $ tests; specifically, these are the Dickey-Fuller $ \hat \rho $ tests and the weighted symmetric versions of the $ \hat \tau $ and $ \hat \rho $ tests. The empirical response functions presented here take into account adjustments for lag length in the maintained regression, and also extend the design of the simulation experiments compared to previous work. A second aspect of this study concerns the widespread practice in applied econometrics of using more than one test for the same feature without an assessment of the implications for the cumulative significance level and probability of test conflict. Tests for a unit root being are a leading example of this practice. Using the extended set of unit root tests considered here, the extent of test dependence is simulated and overall type one error calculated. Two empirical applications illustrate the key principles.
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Document Type: Research Article
Publication date: 2003-05-01