Equilibrium Counterfactuals: Joint Estimation and Control with Structural Models
The objective of applied structural microeconometrics is to identify policy-invariant parameters so alternative policies can be assessed. However, the common practice of treating policy changes as zero probability "counterfactuals" violates rational expectations: Agents understand policy changes are positive probability events which the structural estimation is intended to inform. We analytically characterize the implications for moment-based parameter inference. As shown, if a policy change is optimal, inference is biased. Further, the standard identifying assumption, constant partial derivative sign, is neither necessary nor sufficient with policy control. We offer an alternative identifying assumption: constant total deferential sign with inference-policy feedback. It is shown that under this assumption, rational expectations can be imposed computationally (algorithmically) to generate unbiased inference and optimal policy. The quantitative importance of these effects in applied settings is illustrated by calibrating the Leland (1994) model to the Tax Cuts and Jobs Act of 2017.