Explaining stationary variables with non-stationary regressors

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Abstract
When variables included in an OLS regression are stationary, conventional statistical measures such as t-statistics and R 2's – in addition to a priori information from economic theory – are the standard indicators used to assess the performance of the hypothesized model. However, if the variables under consideration are non-stationary, such conventional measures no longer have the usual interpretation. With recent developments in time-series analysis, namely cointegration, researchers are able to deal with models containing non-stationary variables effectively. A standard cointegration model, however, requires all variables included in the regression to be of the same order of integration. In this paper we consider a regression in which the dependent variable is integrated of order zero, I(0), while the explanatory variables are integrated of order one, I(1). Conventional statistical measures are inapplicable because the regressors are not stationary. On the other hand, cointegration statistics are inapplicable because the variables are not of the same order of integration. This letter proposes a methodology on how to evaluate the performance of such a model.