Deflator selection and generalized linear modelling in market-based regression analyses

The scale factor refers to an unknown size variable which affects some or all observed variables in a multiplicative fashion. The scale effect studied by several researchers in market-based regression analyses is defined here as the intriguing combination of coefficient bias and heteroscedasticity caused by the scale. Deflation is the most popular technique used in previous market-based studies to mitigate the scale effect. Selection of a suitable deflator, however, remains as a difficult and challenging task due to the lack of a general statistical framework for this type of research. In this article, we establish a general statistical framework for deflator and model selection. We argue and show that the existence and severity of the scale effect can be identified and measured using the Average Absolute Values of Studentized Residuals and the Relative Total Prediction Error for stratified firm groups. The proposed framework consists of five major components. Results from our simulation studies and sensitivity analyses show that if the true scale variable is used as a deflator to produce one of the deflated candidate models, this model can be correctly identified using the proposed strategy, even if the working model is mildly misspecified. In addition, our studies show that the generalized linear modelling method can be very useful for mitigating the scale effect when the unknown true scale variable is related to the whole set of independent variables through the so-called mean function.