When Demand Projections are Too Optimistic: A Structural Model of Product Line and Pricing Decisions

Abstract

A methodology is proposed to estimate structural models of product line competition. This methodology enables researchers to estimate demand systems accounting for the endogeneity of the mix of products available in each market, an issue which is typically ignored in the empirical literature. In particular, it is observed that not accounting for this form of endogeneity leads to overoptimistic estimates of total demand due to a sample selection bias. More importantly, biased estimates of demand can generate inaccurate inferences about consumer welfare or imply misleading managerial recommendations.

The proposed model jointly considers the interplay between consumer preferences, pricing and assortment decisions. Consumer demand is characterized by a utility maximization process with unobserved heterogeneity in consumer preferences. Price decisions are assumed to be the outcome of a Bertrand-Nash game among firms offering differentiated products. Product line decisions are modeled using a Bayesian-Nash equilibrium concept where firms form beliefs about the profits of their competitors and anticipate the prices and demand they would observe for any given set of products that could be introduced in the market. The estimation approach is implemented relying on parallelization decomposing some of the most computationally intensive steps into a series of independent and much smaller problems.

The methodology is illustrated using both simulated and real data, where the latter refers to purchases in the liquid laundry detergent product category. The results show that ignoring this form of endogeneity leads a researcher to overestimate the demand, prices and profits for products that have not yet been introduced in the market, while for existing products market shares and profits are substantially underestimated when performing policy simulations involving the addition of products to current assortments.

Keywords: Structural models, product line decisions, assortment, pricing, competition, demand estimation, sample selection, industrial organization

JEL Classification: C10, C13, C15, D21, D22, D43, L10, L11, L13, M31