Bayesian Statistics and Marketing, 2nd Edition

7Simultaneity

Abstract

This chapter discusses the problem of Bayesian inference for models in which both the response variable and some of marketing mix variables are jointly determined. We can no longer focus only on the model of the distribution of the response variable conditional on the marketing mix variables. We must build a model which (at least implicitly) specifies the joint distribution of these variables conditional on a set of driving or “exogenous” variables. Section 7.1 provides a Bayesian treatment of the linear “instrumental” variables problem, a problem for which standard classical asymptotic methods have proved inadequate. Section 7.2 considers a system of supply and demand where the demand system is built up by aggregating consumer level choice models. Section 7.3 considers the situation in which simultaneity is present in a hierarchical model.

At the base of all the models considered so far is the distribution of a dependent variable (or vector) conditional on a set of independent factors. The classic marketing example is a sales response model in which quantity demanded is modeled conditional on marketing mix variables which typically include price and advertising measures. However, we should recognize that firms may set these marketing mix variables in a strategic fashion. For example, firms may consider strategic considerations or the response of other competitors in setting price. Firms may also set the levels of marketing mix variables by optimizing ...