We study the optimal levels of advertising and promotion budgets in dynamic markets with brand equity as a mediating variable. To this end, we develop and estimate a state-space model based on the Kalman filter that captures the dynamics of brand equity as influenced by its drivers, such as the brand's advertising and sales promotion expenditures. By integrating the Kalman filter with the random coefficients logit demand model, our estimation allows us to capture the dynamics of brand equity as well as to model consumer heterogeneity using store-level data. Using these demand model estimates, we determine the Markov perfect equilibrium advertising and promotion strategies. Our empirical analysis is based on store-level scanner data in the orange juice category, which comprises two major brands--Tropicana and Minute Maid. As expected, we find that sales promotions have a significant positive effect on consumers' utility and induce consumers to switch to the promoted brand. However, there is also a negative effect of promotions on brand equity that carries over from period to period. Overall, we find that while sales promotions have a net positive impact both in the short term and in the long term, the implied total profit elasticity including the long-term effect is smaller than the short-term profit elasticity. Correspondingly, we expect myopic decision makers to allocate higher than optimal expenditures to sales promotions. Our results from the supply-side analysis reveal that the actual promotion levels for both brands are indeed higher than the optimal budgets for the forward-looking (long-term orientation) as well as the two-year planning horizon scenarios. Hence, it may be profitable for both brands to reduce their promotion levels. Further, we find that although the forward-looking promotional spending levels are higher for the smaller brand, Minute Maid, it is market leader Tropicana that spends more on sales promotions. Turning to optimal advertising budgets, we find that the equilibrium forward-looking advertising levels are higher for Tropicana, the brand that has higher brand equity and a higher responsiveness to advertising. Further, as expected, the optimal forward-looking advertising levels are higher than the myopic levels and the two-year planning horizon levels for both brands. However, the forward-looking advertising levels are lower than the actual advertising expenditures for both brands. This implies that even when we consider the long-term effects of advertising, the brands are overspending on advertising.
