Simple Markov-Perfect Industry Dynamics

This paper develops a tractable model for the computational and empirical analysis of infinite-horizon oligopoly dynamics. It features aggregate uncertainty, sunk entry costs, stochastic idiosyncratic technological progress, and irreversible exit. We develop a fast algorithm for computing a symmetric Markov-perfect equilibrium that finds the fixed points of a finite sequence of low-dimensional contraction mappings. If at most two heterogenous firms serve the industry, the result is the unique symmetric "natural'' equilibrium in which a firm with high flow profit never exits leaving behind a low flow profit competitor. We use this to demonstrate numerically that the welfare gains from directly correcting potential duopolists' suboptimal exercise of entry and exit options can dwarf those from indirectly doing so by changing the market's static competitive conduct. The hundreds of equilibrium calculations this requires take only a few minutes on an off-the-shelf laptop computer. When the market can support more than two firms, our algorithm always finds a natural equilibrium. We present a simple rule for checking ex post whether the calculated equilibrium is unique, and we also show that the algorithm is fast enough for empirical work by simulating the estimation of the model's parameters with indirect inference