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 settingswithout 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.
When a government announces a new policy in a strategic setting, such as changes to taxes or tariffs, it creates additional signals through media reports or studies on the policy which may be used by economic agents. This may result in a new predicted outcome that is not captured by the analysis based on Bayes Nash equilibria . In this paper, we adopt Bayes Correlated Equilibrium of Bergemann and Morris (2016) and develop a method of counterfactual analysis that can be used for such situations. We show that, under an invariance condition for the equilibrium selection rule , the equilibrium-based prediction in this setting is interval-identified by the decomposition-based prediction which can be estimated without specifying the details of the game such as payoffs or distribution of unobserved heterogeneity. This approach greatly simplifies the counterfactual analysis in strategic settings, including those with multiple equilibria, as it eliminates the need to recover the set of equilibria in the post-policy game. We illustrate our message by revisiting an empirical analysis in Ciliberto and Tamer (2009) on entry decisions of firms in the airline industry.
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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
When a government announces a new policy in a strategic setting, such as changes to taxes or tariffs, it creates additional signals through media reports or studies on the policy which may be used by economic agents. This may result in a new predicted outcome that is not captured by the analysis based on Bayes Nash equilibria
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use a generic model of a Bayesian game with the solution concept of Bayes Correlated Equilibria
adopt Bayes Correlated Equilibrium
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show that if the information structure is rich enough and the
develop a method of counterfactual analysis that can be used for such situations. We show that, under an invariance condition for the
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satisfies a weak invariance property, decomposition-based predictions are identical to
, the
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predictions. This result opens up the possibility for applying a decomposition method for
prediction in this setting is interval-identified by the decomposition-based prediction which can be estimated without specifying the details of the game such as payoffs or distribution of unobserved heterogeneity. This approach greatly simplifies the
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various strategic settingswithout specifying and estimating details of the
strategic settings, including those with multiple equilibria, as it eliminates the need to recover the set of equilibria in the post-policy