Counterfactual Equivalence in Macroeconomics

Counterfactuals in structural models are the leading paradigm for analyzing policy rule changes because they are immune to Lucas Critique. However, they are less credible whenever they lack robustness to variations in primitives across models, which is typically hard to check. Relatedly, researchers building models have to make difficult choices regarding which mechanisms are relevant for analyzing particular policy rules. I propose a novel method to tackle these and other problems in macroeconomics. It rests on the insight that many models which are well approximated by a linear representation are both observationally equivalent under a benchmark policy and yield an identical counterfactual equilibrium under an alternative policy. Characterizing a set of models that satisfy this principle of Counterfactual Equivalence simply requires describing whether their equilibrium equations satisfy a number of linear restrictions. I illustrate various applications of this principle, including: (1) quantifying how fiscal unions contribute to regional stabilization by constructing a counterfactual US economy without fiscal integration, (2) analyzing which micro-foundations are relevant when studying unemployment benefits policy in search models of the labor market, and (3) showing how to falsify a set of counterfactually equivalent models using observed policy experiments.