In the marketing literature there does not seem to be a widely accepted answer to the question of whether, when purchasing brands in a given product category, consumers react differently to a reduction in price and an increase in the deal discount. Previous studies that have attempted to address this issue have assumed that prices and deals have a linear effect on a brand's indirect utility. In this article, we estimate the utility of price and discount nonparametrically. Instead of imposing a linear structure on this function, we require only that it be decreasing in price and increasing in deal amount. This specification allows for a general pattern of interaction effects between prices and deals to influence the systematic component of utility. Consistent with the recent literature on estimating brand choice models, we account for heterogeneity in brand preferences across consumers. We use both a semiparametric approach, in which the distribution of the stochastic components of brand utilities is specified parametrically, and a fully nonparametric approach, in which this distribution is left unspecified. We carry out our empirical analyses on household scanner panel datasets for four different product categories. Our empirical results reveal deviations from linearity in deal effects. In particular, deal effects appear to be concave for some products.
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