Semiparametric Analysis to Estimate the Deal Effect Curve

The marketing literature suggests several phenomena that may contribute to the nature of the relationship between sales and price discounts. These phenomena can produce complex nonlinearities and interactions in the deal effect curve that are best captured with a flexible approach. Because a fully nonparametric regression model suffers from the curse of dimensionality, the authors propose a semiparametric regression model. Store-level sales over time are modeled as a nonparametric function of own- and cross-item price discounts and a parametric function of other predictors. The authors compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain superior performance. The results for three product categories indicate threshold and saturation effects for both own- and cross-item temporary price cuts. The authors also find that the nature of the own-item curve depends on other items' price discounts. Comparisons with restricted model specifications show that both the flexible main effects and flexible interaction effects contribute to the superior results for the semiparametric approach. The interaction effects are so complex that it is unlikely for any parametric model to be satisfactory. In a separate analysis, the authors illustrate how the shape of the deal effect curve depends on own-item promotion signals. There is a crossover interaction effect: For the item analyzed, feature advertising produces a higher sales effect up to a 20% discount, whereas display achieves higher sales for discounts in excess of 20%.