Scale Factor, R 2 , and the Choice of Levels versus Returns Models
分析规模因子对回归R²的影响，发现其无法解释水平模型与回报模型R²的差异，支持模型选择应基于研究问题而非规模问题。
This paper analyzes a potential scale effect on the regression R 2 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 R 2 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.