Flexible estimation of price response functions using retail scanner data

Kalyanam and Shively [1998. Estimating irregular pricing effects: a stochastic spline regression approach. Journal of Marketing Research 35 (1), 16–29] and van Heerde et al. [2001. Semiparametric analysis to estimate the deal effect curve. Journal of Marketing Research 38 (2), 197–215] have demonstrated the usefulness of nonparametric regression to estimate pricing effects flexibly. The empirical results of these two studies, however, also revealed that nonparametric regression may suffer from too much flexibility leading to nonmonotonic shapes for price effects. In this paper, we show how the problem of nonmonotonicity can be dealt with without losing the power of flexible estimation techniques. We propose a semiparametric approach based on Bayesian P-splines with monotonicity constraints imposed on own- and cross-price effects. In an empirical application, we illustrate that flexible estimation of own- and cross-price effects can improve the predictive validity of a sales response model substantially, even when price response curves were constrained to show a monotonic shape, as suggested by economic theory. We also discuss the consequences from an unconstrained estimation of price effects.