Industry Dynamics : From Elemental to Aggregate Models ∗

Elemental models of the form pioneered by Ericson and Pakes (1995) capture the dynamics of a finite number of heterogeneous firms as they compete in an industry. Available algorithms can determine Markov perfect equilibrium behavior, though computational requirements become onerous when there are more than a few incumbent firms. Aggregate models of the form pioneered by Hopenhayn (1992), on the other hand, assume that firms are infinitesimal and infinite in number. The industry state in stationary equilibrium is constant due to averaging effects among firms, and this dramatically simplifies analysis and computation of equilibrium behavior. This paper unifies these two separate threads of economic research by providing conditions under which stationary equilibria of aggregate models approximate Markov perfect equilibria of elemental models arbitrarily well in asymptotically large markets. Our conditions require that the distribution of firm states in stationary equilibrium obeys a certain “light tail” condition. Stationary equilibria in aggregate models are closely related to oblivious equilibria in elemental models, as introduced in Weintraub, Benkard, and Van Roy (2007). We also study this connection and show that the set of oblivious equilibria approaches the set of stationary equilibria in asymptotically large markets. JEL classification numbers: E22, L11, L13 ∗We have had very helpful conversations with José Blanchet, Juan Escobar, and Assaf Zeevi. Correspondence: gweintraub@columbia.edu; lanierb@stanford.edu; bvr@stanford.edu.