Rational Expectations and the Paradox of Policy-Relevant Natural Experiments

In recent years, policy experiments using large microeconomic datasets have gained ground in macroeconomics. Imposing rational expectations, we examine robustness of evidence derived from ideal natural experiments applied to atomistic agents in dynamic settings. Paradoxically, once experimental evidence is viewed as sufficiently clean to use, it then becomes contaminated by ex post endogeneity: Measured responses depend upon priors and the objective function into which evidence is fed. Moreover, agents' policy beliefs become endogenously correlated with their causal parameters, severely clouding inference, e.g. sign reversals and non-invertibility may obtain. Treatment-control differences are contaminated for non-quadratic adjustment costs. Constructively, we illustrate how inference can be corrected accounting for feedback and highlight factors mitigating contamination