Concerning the Logical Consistency of Multivariate Market Share Models

Naert and Bultez have examined the logical consistency of market share models 3. They raise serious questions about the logical consistency of my previous study, a market share model of the sales of several competing brands 1, 2. I believe their criticism is misplaced. There are two basic questions: (1) whether a linear stochastic process could have generated the sum-constrained data, and (2) whether a linear model can predict sum-constrained estimates of the dependent variable. After resolving these two questions, the uses of logically consistent models and the implications for my original study will be considered.