A control function approach for testing the usefulness of trending variables in forecast models and linear regression

Many predictors employed in forecasting macroeconomic and finance variables display a great deal of persistence. Tests for determining the usefulness of these predictors are typically oversized, overstating their importance. Similarly, hypothesis tests on cointegrating vectors will typically be oversized if there is not an exact unit root. This paper uses a control variable approach where adding stationary covariates with certain properties to the model can result in asymptotic normal inference for prediction regressions and cointegration vector estimates in the presence of possibly non-unit root trending covariates. The properties required for this result are derived and discussed.