Estimating Irregular Pricing Effects: A Stochastic Spline Regression Approach

Abstract

Markets respond to prices in complex ways. Multiple factors such as price points, odd pricing, and just-noticeable differences often cause steps and spikes in response. The result is market response functions that are frequently nonmonotonic. However, existing regression-based approaches employ functions that are inherently monotonic, which thereby limits representation of important irregularities. In this article, the authors use a stochastic spline regression approach in the framework of a hierarchical Bayes model that permits the estimation of irregular pricing effects and apply the approach to data sets from several product categories. A simulation study indicates that the stochastic spline approach is flexible enough to accommodate irregular response functions. The empirical results show that there are irregularities in own-price response for most of the brands examined and that there are important profit implications of these irregular response functions in pricing decisions. The authors find that the irregularities in the response functions include sales increases associated with odd prices in the range of 12% to 76%, flatness at the extremes of the range of observed prices, and kinks in the response function that are consistent with segmentation effects.