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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)

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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.

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Publisher Info
Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1532.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1532

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  1. Lucas, Andr?, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February. [Downloadable!]
  2. repec:cup:etheor:v:11:y:1995:i:5:p:912-51 is not listed on IDEAS
  3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  4. Peter C.B. Phillips, 1993. "Robust Nonstationary Regression," Cowles Foundation Discussion Papers 1064, Cowles Foundation, Yale University. [Downloadable!]
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  5. repec:cup:etheor:v:11:y:1995:i:2:p:331-46 is not listed on IDEAS
  6. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
  7. Boswijk, H. Peter & Lucas, Andr‚, 1997. "Semi-nonparametric cointegration testing," Serie Research Memoranda 0041, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
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  8. 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. [Downloadable!]
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