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N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots

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  • Ted Juhl

    (University of Kansas)

  • Zhijie Xiao

    (University of Illinois)

Abstract

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.

Suggested Citation

  • Ted Juhl & Zhijie Xiao, 2000. "N-Consistent Semiparametric Regression: Partially Linear Models with Unit Roots," Econometric Society World Congress 2000 Contributed Papers 1532, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1532
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(04), pages 519-548, August.
    3. Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February.
    4. repec:cup:etheor:v:11:y:1995:i:5:p:912-51 is not listed on IDEAS
    5. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(05), pages 912-951, October.
    6. repec:cup:etheor:v:11:y:1995:i:2:p:331-46 is not listed on IDEAS
    7. 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.
    8. Boswijk, H. Peter & Lucas, Andre, 2002. "Semi-nonparametric cointegration testing," Journal of Econometrics, Elsevier, vol. 108(2), pages 253-280, June.
    9. 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.
    10. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1148-1171, October.
    11. 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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