Demand Estimation When There are Unobservable Substitutions Amongst Choice Alternatives

Abstract

Accurate estimates of the future demand and the substitution probabilities between products are important inputs for retail assortment optimization. However, these quantities are difficult to estimate as the estimation involves understanding and modeling of consumer’s choice behavior when a complete choice set is available as well as when the choice set is incomplete (i.e., their response to out-of-stock situations). In this paper, we propose a prospect theory based reference dependent preference structure for consumer choice and use the information available in store scanner sales and inventory data to estimate both the true demand for the products as well as the substitution probabilities between products. We use a combination of theoretical arguments, simulations, and empirical analysis to establish that the proposed reference dependent logit (RDL) model yields robust and efficient estimates. We also compare the performance of RDL against the multinomial logit, two models that use exogenous substitution probabilities, and experts’ opinions regarding what the true substitution probabilities could be.