Optimal Theoretic Advertising Stock Models: A Generalization Incorporating the Effects of Delayed Response from Promotional Expenditure

Econometric models of advertising effects incorporating the concept of advertising stock adopt the premise that prior as well as current advertising expenditure affect current sales. In general, stock may be viewed as an intangible demand-generating variable representing an accumulated effect of prior advertising expenditure. One of the weaker assumptions inherent to stock models to date is the specification of the distributed time lag governing the rate at which expenditure flow is manifested into advertising stock: advertising expenditure is assumed to generate maximum response immediately, then decay exponentially over time. This is not only theoretically unappealing, but also empirically dubious as well. Results from recent studies support the more general hypothesis that some time will elapse before the maximum response from advertising expenditure is realized. This paper offers three optimal theoretic models based on modal-delayed or "inverted V" distributed lag functions governing the time relationship between advertising expenditure and sales response. These theoretical models illustrate the implications of a delayed response to advertising expenditure. In particular it is shown that less general models (of the Nerlove-Arrow/Koyck type) overvalue the marginal physical product of advertising, thereby overspecifying the optimal level of advertising stock.