Scale Factor, R2, and the Choice of Levels versus Returns Models

This paper analyzes a potential scale effect on the regression R2 to determine if a scale factor can reconcile the arguments concerning the choice between the price levels model and the returns model. Analytically, it is shown that the scale effect depends on the unknown scale-free economic relation and is generally unpredictable. This makes it difficult to choose one model over the other on the basis of controlling for a scale problem. Empirically, it is shown that a scale factor cannot explain the observed discrepancy between the R2 patterns from the levels and the returns models. The results support the view that the two models likely represent two different economic relations and that the model choice depends on the researcher's belief and the research question at hand rather than any scale factor concerns.