Composite dependent variables and the market share effect

Farris, Parry and Ailawadi (FPA) demonstrate that bias can arise in a regression involving a composite dependent variable where a subset of components of the dependent variable are used as explanatory factors. They correctly observe that the Jacobson and Aaker (JA) model has explanatory factors that are also components of the ROI dependent variable and, as such, is subject to ‘composite variable bias.’ FPA note that another way of viewing composite variable bias is that the coefficients in the model reflect not their impact on the dependent variable but rather their impact on the dependent variable less the elements of the components included as explanatory factors. As such, additional effects (analogous to indirect effects) may be present to the extent strategic factors influence the included components. FPA conclude that such bias explains the low estimate of the market share effect reported in JA. However, FPA’s attempt to replicate the present analysis and assess composite variable bias is flawed by a mistake in their analysis, i.e., their disaggregate models do not follow from the JA aggregate specification. The purpose of this note is to correctly assess the extent to which the JA estimate of the market share effect is affected by composite variable bias and to suggest approaches for modeling a composite dependent variable in the presence of unobservable factors. In particular, the authors (i) show that the disaggregate specifications of FPA do not follow from JA, (ii) look at specifications not subject to composite variable bias to investigate the magnitude of the composite variable bias in JA, and (iii) provide a disaggregate modeling framework that controls for unobservable effects.