Estimation in Trending Time Series Models with Endogeneity

This paper studies the endogeneity problem in the linear regression model with deterministic trending time series.  The work complements the discussion in Phillips and Hansen (1990), which investigates the endogeneity problem in the cointegration regression. A nonparametric control function is employed to decompose the endogenous correlation between the error terms and thereby extends the linear regression model to a semiparametric partially linear model.  The conventional estimation methods for partially linear models remain valid though the usual identifiability  condition is not satisfied. Monte Carlo simulation presents the unbiasedness and consistency of the proposed estimator.  The model is then applied to estimate the long-run relationship between the aggregate personal income and consumption.