Mergers between Multi-Product Firms with Endogenous Variety: Theory and an Application to the Ready-To-Eat Cereal Industry

Abstract

When multi-product firms endogenously choose their product variety, mergers can have welfare effects that go well beyond their immediate impact through prices. The structural models needed to quantify these effects, however, quickly become computationally intractable as the number of products grows. In this paper, I propose a dynamic structural model of multi-product firms and endogenous product variety that bypasses this dimensionality problem. I show that, under a nested logit demand assumption, firms introduce/remove products in a pre-determined order. As a result, the number of products each firm supplies is a sufficient statistic for the identity of the products themselves and, therefore, for all market outcomes and firms’ continuation strategies. I use this result to argue that the strategies and states that need to be considered to solve the model are a small fraction of the whole strategy set and state space, making it possible to estimate the model using standard techniques in structural econometrics. I apply the model to the Ready-To-Eat Cereal Industry and use it to simulate a hypothetical merger between two large players. Results show that ignoring endogenous product variety leads to a 30% overestimation of the post-merger number of products and a 19% underestimation of consumer welfare loss.