Robust Dynamic Estimation

Managing marketing resources over time requires dynamic model estimation, which necessitates specifying some parametric or nonparametric probability distribution. When the data generating process differs from the assumed distribution, the resulting model is misspecified. To hedge against such a misspecifkation risk, the extant theory recommends using the sandwich estimator. This approach, however, only corrects the variance of estimated parameters, but not their values. Consequently, the sandwich estimator does not affect any managerial outcomes such as marketing budgeting and allocation decisions. To overcome this drawback, we present the minimax framework that does not necessitate distributional assumptions to estimate dynamic models. Applying minimax control theory, we derive an optimal robust filter, illustrate its application to a unique advertising data set from the Canadian Blood Services, and contribute several novel findings. We discover the compensatory effect: Advertising effectiveness increases and the carryover effect decreases as robustness increases. We also find that the robust filter uniformly outperforms the Kaiman filter on the out-of-sample predictions. Furthermore, we uncover the existence of a profit-volatility trade-off, similar to the returns-risk trade-off in finance, whereby the volatility of profit stream decreases at the expense of reduced total profit as robustness increases. Finally, we prove that, unlike for-profit companies, managers of nonprofit organizations should optimally allocate budgets opposite the advertising-to-sales ratio heuristic; that is, advertise more (less) when sales are low (high).