Testing for Unit Roots and Cointegration Using Covariates

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9412339 Hansen The most common model used in applied econometrics to study the properties of time series is the "unit root model." A multivariate generalization of univariate unit roots which allows for common unit root components is the model of cointegration. In most applications, testing for unit roots or cointegration are viewed as useful preliminary steps in the building of an empirical models. But in many cases, cointegration emerges as an implication of an economic model and cointegration tests can be used to directly test the model. Examples include studies of the life-cycle model, the present value model of stock prices, real business cycle models, models of the term structure of interest rates, a model of intertemporal consumption, and the long-run money demand function. But unit root and cointegration tests can not be used for many economic applications because they are not powerful enough to discriminate among competing hypotheses given the typical number of observations available in economic data. This project develops a method for increasing the power of unit root and cointegration tests dramatically by using information that is ignored by more conventional methods, generalizes this method to all cases, uses the technique of local-to-unity asymptotics to investigate the adequacy of the asymptotic approximations in finite samples, and reexamines the Nelson- Plosser data set to see if the improved tests can shed light on the stochastic properties of the series.