Semiparametric analysis to estimate the deal effect curve

The marketing literature suggests several phenomena that may contribute to the shape of the relationship between sales and price discounts. These phenomena can produce severe nonlinearities and interactions in the curves, and we argue that those are best captured with a flexible approach. Since a fully nonparametric regression model suffers from the curse of dimensionality, we propose a semiparametric regression model. Store-level sales over time is modeled as a nonparametric function of own-and cross-item price discounts, and a parametric function of other predictors (all indicator variables). We compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain better performance on average. The results for three product categories indicate a.o. threshold- and saturation effects for both own- and cross-item temporary price cuts. We also show how the own-item curve depends on other items’ price discounts (flexible interaction effects). In a separate analysis, we show how the shape of the deal effect curve depends on own-item promotion signals. Our results indicate that prevailing methods for the estimation of deal effects on sales are inadequate.