Regression with a Slowly Varying Regressor in the Presence of a Unit Root
This paper considers the regression model with a slowly varying (SV) regressor in the presence of a unit root in serially correlated disturbances. This regressor is known to be asymptotically collinear with the constant term; see Phillips (2007). Under nonstationarity, we find that the estimated coefficients of the constant term and the SV regressor are asymptotically normal, but neither is consistent. Further, we derive the limiting distribution of the unit root test statistic. We may here observe that the finite sample approximation to the limiting one is not monotone and it is poor due to the influence of the collinear regressor. In order to construct a well-behaved test statistic, we recommend dropping the constant term intentionally from the regression and computing the statistics, which are still consistent under the true model having the constant term. The powers and sizes of these statistics are found to be well-behaved through simulation studies. Finally, these results are extended to general Phillips and Perron-type statistics.
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- Pierre Perron & Tomoyoshi Yabu, 2007.
"Estimating Deterministic Trend with an Integrated or Stationary Noise Component,"
Boston University - Department of Economics - Working Papers Series
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- Pierre Perron & Tomoyoshi Yabu, . "Estimating Deterministic Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2006-012, Boston University - Department of Economics, revised Feb 2006.
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- Bunzel, Helle & Vogelsang, Timothy J., 2005.
"Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis,"
Journal of Business & Economic Statistics,
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- Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
- Helle Bunzel & Timothy Vogelsang, 2003. "Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis," Econometrics 0304002, EconWPA.
- Phillips, Peter C.B. & Sun, Yixiao, 2003. "02.3.1. Regression with an Evaporating Logarithmic Trend Solution," Econometric Theory, Cambridge University Press, vol. 19(04), pages 692-701, August.
- Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
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