Productivity and the product scope of multi-product firms: A test of Feenstra-Ma

Feenstra and Ma (2008) develop a monopolistic competition model where firms choose their optimal product scope by balancing the profits from a new variety against the costs of 'cannibalizing' sales of existing varieties. While more productive firms always have a higher market share, there is no monotonic relationship between firms' productivity level and their choices of product scope. In the model having a higher market share means that firms are hurt more by the 'cannibalization effect'. Therefore, the incentive to add more products weakens as productivity rises. This leads to Lemma 3 in Feenstra and Ma (2008): There is an inverted U-shaped relationship between firms' productivities and the range of varieties they choose to produce. This empirical note takes this Lemma to the data for firms from German manufacturing industries. Empirical evidence is in line with the results from the theoretical model.