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 non-zero probability exists for the occurrence of a crisis event, which damages the brand’s baseline sales when the crisis occurs. Because managers don’t know when the crisis will occur, its random time of occurrence induces a stochastic control problem, which we solve analytically. More importantly, we gain an insight that the envisioning of possible crises alters managers’ rate of time preference: anticipation enhances impatience. Building on this insight, we then derive optimal feedback advertising strategies to discover the effects of crisis likelihood and damage rate. We prove that the optimal pre-crisis advertising decreases as the crisis likelihood (or the damage rate) increases. In addition, we develop continuous-time estimation method to estimate sales dynamics and feedback strategies simultaneously using discrete-time data. Applying it to market data from the Ford Explorer’s rollover recall, we furnish evidence to support the proposed model. Further extending the empirical literature, 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 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