N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots
We develop unit root tests using additional stationary covariates as suggested in Hansen (1995). However, we allow for the covariates to enter the model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988). We retain a linear structure for the autoregressive component and show that the parameter is estimated at rate N even though part of the model is estimated nonparametrically. The limiting distribution of the unit root test statistic is a mixture of the standard normal and the Dickey-Fuller distribution. A Monte Carlo experiment is used to evaluate the performance of the tests under various linear and nonlinear specifications for the covariates. We find that the tests are powerful when there is a nonlinear effect and experience a minimal power loss when the covariates have a linear effect or no effect at all.
|Date of creation:||01 Aug 2000|
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- Peter C.B. Phillips, 1993.
"Robust Nonstationary Regression,"
Cowles Foundation Discussion Papers
1064, Cowles Foundation for Research in Economics, Yale University.
- Hansen, Bruce E., 1995.
"Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power,"
Cambridge University Press, vol. 11(05), pages 1148-1171, October.
- Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
- Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(04), pages 519-548, August.
- Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
- Boswijk, H. Peter & Lucas, Andre, 2002.
"Semi-nonparametric cointegration testing,"
Journal of Econometrics,
Elsevier, vol. 108(2), pages 253-280, June.
- M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
- Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February.
- repec:cup:etheor:v:11:y:1995:i:5:p:912-51 is not listed on IDEAS
- Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
- repec:cup:etheor:v:11:y:1995:i:2:p:331-46 is not listed on IDEAS
- Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(01), pages 1-23, February.
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