The effect of data transformation on common cycle, cointegration, and unit root tests : Monte Carlo results and a simple test

In the conduct of empirical macroeconomic research, unit root, cointegration, common cycle, and related test statistics are often constructed using logged data, even though there is often no clear reason, at least from an empirical perspective, why logs should be used rather than levels. Unfortunately, it is also the case that standard data transformation tests, such as those based on Box-Cox transformation, cannot be shown to be consistent unless the assumption is made concerning whether the series being examined is I(0) or I(1), so that a sort of circular testing problem exists. In this paper, we discuss two quite different but related issues that arise in the context of data transformation. First, we address the circular testing problem that arises when choosing data transformation and order of integratedness. In particular, we propose a simple randomized procedure, coupled with simple conditioning, for choosing between levels and log-levels specifications in the presence of deterministic and/or stochastic trends. Second, we note that even if pre-testing is not undertaken to determine data transformation, it is important to be aware of the impact that incorrect data transformation has on tests frequently used in empirical works. For this reason, we carry out a series of Monte Carlo experiments illustrating the rather substantive effect that incorrect transformation can have on the finite sample performance of common feature and cointegration tests. These Monte Carlo findings underscore the importance of either using economic theory as a guide to data transformation and/or using econometric tests such as discussed in this paper as aids when choosing data transformation.