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,
Econometrica 56, 931–954). It is proved 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 that 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.We thank Bruce Hansen, Roger
Koenker, Helmut Lütkepohl, Peter Phillips, three referees, and
participants of the 8th World Congress of the Econometric Society and the
10th Midwest Econometrics Group Meeting for helpful comments on an earlier
version of this paper. This investigation was supported by the University
of Kansas General Research Fund allocation 2301789-003.