'Size Does Matter': Demand and Pricing Implications of Market Potential Assumptions in the MNL Model

Abstract

Multinomial logit (MNL) is a ubiquitous model in marketing and economics used to explain and predict brand-level demand. While estimating the MNL on store-level brand sales data (as opposed to household-level brand choice data) within a product category, one requires, but does not observe, the market potential, i.e., the size of the available customer market. Researchers assume a specific fixed value for the market potential, sometimes justifying their assumption using institutional features of the market, before proceeding with the analysis. Different researchers have employed different assumptions about market potential. The innocuousness, or lack thereof, of the market potential assumption, in terms of model-based inferences, is unknown. In this research, using an extensive set of numerical simulations which span the full range of possible conditional market shares for brands, we study the empirical consequences of different assumptions about market potential on three sets of econometric estimates – (1) parameter estimates, (2) estimated brand-level own- and cross-price elasticities, as well as (3) derived optimal brand-level prices – yielded by the MNL model. We document the conditions under which serious estimation biases arise from making incorrect assumptions about market potential. Additionally, we delineate conditions under which the estimation biases are fairly modest. Overall, based on our simulations, we recommend that researchers estimate, rather than assume, the market potential when estimating MNL models in order to obtain unbiased estimates of demand and supply.