Choosing Between Levels and Logs in the Presences of Deterministic and Stochastic Trends
In macroeconometrics, unit root tests are typically performed using logs. While this is sensible from a theoretical macroeconomic perspective, there is no clear reason, particularly from an empirical perspective, why logs should be used rather than levels. Further, standard unit root tests assume linearity under both the null and the alternative hypthesis. Violation of this linearity assumption can result in severe size and power distortion, both in finite and large samples. Finally, casual inspection of gnp per capita, for example, plotted against its fitted linear deterministic trend (see Figure 1) gives no clear indication that a loglinear specification should be preferred to a linear specification. thus, it is reasonable to address the problem of data transformation before running a unit root test. In this paper we propose a simple completely consistent procedure for choosing between levels and log-levels specifications in the presence of deterministic and/or stochastic trends.