The Paradox of Policy-Relevant Natural Experiments

We examine robustness of evidence derived from ideal randomizations applied to atomistic subjects 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, clouding inference. Finally, treatment-control differences are contaminated absent quadratic adjustment costs. Constructively, we illustrate how inference can be corrected accounting for feedback and highlight factors mitigating contamination.