This paper studies the asymptotic properties of a nonstationary partially linear regression model. In particular, we allow for covariates to enter the unit root (or near unit root) model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988). It is proven that the autoregressive parameter can be estimated at rate N even though part of the model is estimated nonparametrically. Unit root tests based on the semiparametric estimate of the autoregressive parameter have a limiting distribution which is a mixture of a standard normal and the Dickey-Fuller distribution. A Monte Carlo experiment is conducted to evaluate the performance of the tests for various linear and nonlinear specifications.
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Find related papers by JEL classification: C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
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