Optimal Advertising When Envisioning a Product-Harm Crisis

How should forward-looking managers plan advertising if they envision a product-harm crisis in the future? To address this question, we propose a dynamic model of brand advertising in which, at each instant, a nonzero probability exists for the occurrence of a crisis event that damages the brand's baseline sales and may enhance or erode marketing effectiveness when the crisis occurs. Because managers do not know when the crisis will occur, its random time of occurrence induces a stochastic control problem, which we solve analytically in closed form. More importantly, the envisioning of a possible crisis alters managers' rate of time preference: anticipation enhances impatience. That is, forward-looking managers discount the present--even when the crisis has not occurred--more than they would in the absence of crisis. Building on this insight, we then derive the optimal feedback advertising strategies and assess the effects of crisis likelihood and damage rate. We discover the crossover interaction: the optimal precrisis advertising decreases, but the postcrisis advertising increases as the crisis likelihood (or damage rate) increases. In addition, we develop a new continuous-time estimation method to simultaneously estimate sales dynamics and feedback strategies using discrete-time data. Applying the method to market data from the Ford Explorer's rollover recall, we furnish evidence to support the proposed model. We detect compensatory effects in parametric shift: ad effectiveness increases, but carryover effect decreases (or vice versa). We also characterize the crisis occurrence distribution that shows that Ford Explorer should anticipate a crisis in 2.1 years and within 6.3 years at the 95% confidence level. Finally, we find a remarkable correspondence between the observed and optimal advertising decisions.