Beyond Random Assignment: Credible Inference of Causal Effects in Dynamic Economies

Abstract

Random assignment is insufficient for measured treatment responses to recover causal effects (comparative statics) in dynamic economies. We characterize analytically bias probabilities and magnitudes. If the policy variable is binary there is attenuation bias. With more than two policy states, treatment responses can undershoot, overshoot, or have incorrect signs. Under permanent random assignment, treatment responses overshoot (have incorrect signs) for realized changes opposite in sign to (small relative to) expected changes. We derive necessary and sufficient conditions, beyond random assignment, for correct inference of causal effects: martingale policy variable. Infinitesimal transition rates are only sufficient absent fixed costs. Stochastic monotonicity is sufficient for correct sign inference. If these conditions are not met, we show how treatment responses can nevertheless be corrected and mapped to causal effects or extrapolated to forecast responses to future policy changes within or across policy generating processes.

Keywords: Natural experiments; Policy evaluations; Dynamic environments; Random treatment; Causal effects