Simple Markov-perfect industry dynamics

Posted by D. Daniel Sokol

Jaap H. Abbring (CentER, Department of Econometrics & OR, Tilburg University), Jeffrey R. Campbell (Federal Reserve Bank of Chicago), and Nan Yang (VU University Amsterdam and Tinbergen Institute) analyze Simple Markov-perfect industry dynamics.

ABSTRACT: This paper develops a tractable model for the computational and empirical analysis of infinite-horizon oligopoly dynamics. It features aggregate demand uncertainty, sunk entry costs, stochastic idiosyncratic technological progress, and irreversible exit. We develop an algorithm for computing a symmetric Markov-perfect equilibrium quickly by finding the fixed points to a finite sequence of low-dimensional contraction mappings. If at most two heterogenous firms serve the industry, the result is the unique "natural" equilibrium in which a high profitability firm never exits leaving behind a low profitability competitor. With more than two firms, the algorithm always finds a natural equilibrium. We present a simple rule for checking ex post whether the calculated equilibrium is unique, and we illustrate the model's application by assessing how price collusion impacts consumer and total surplus in a market for a new product t! hat requires costly development. The results confirm Fershtman and Pakes' (2000) finding that collusive pricing can increase consumer surplus by stimulating product development. A distinguishing feature of our analysis is that we are able to assess the results' robustness across hundreds of parameter values in only a few minutes on an off-the-shelf laptop computer.