A Decomposition Approach to Counterfactual Analysis in Game-Theoretic Models

Abstract

Decomposition methods are often used to produce counterfactual predictions of outcomes when a policy variable changes. The methods project the observed relationship between the policy variable and the endogenous variable to a counterfactual environment. However, when the endogenous variable is generated by an agent's strategy in a game-theoretic setting and the agent has an incentive to deviate from his strategy after the policy, such predictions are hard to justify. In this paper, we use a generic model of a Bayesian game with the solution concept of Bayes Correlated Equilibria of Bergemann and Morris (2016) and show that if the information structure is rich enough and the equilibrium selection rule satisfies a weak invariance property, decomposition-based predictions are identical to equilibrium-based predictions. This result opens up the possibility for applying a decomposition method for counterfactual analysis in various strategic settings without specifying and estimating details of the game. We illustrate our message by revisiting an empirical analysis in Ciliberto and Tamer (2009) on entry decisions of firms in the airline industry.