Subject Rational Expectations Will Contaminate Randomized Controlled Medical Trials

We develop a rational expectations model of placebo effects. If subjects in seemingly-ideal single-stage RCTs form rational beliefs about breakthroughs based upon personal physiological responses, mental effects differ across medications received, treatment versus control. Consequently, the average cross-arm health difference becomes a biased estimator of the mean non-placebo physiological effect. Constructively, we show: bias can be altered through choice of control; high-efficacy controls mitigate upward bias; and unbalanced panels may be preferred since bias approaches zero as treatment probability approaches zero. Consistent with experimental evidence, our theory implies outcomes within-arm and cross-arm differences can be non-monotone in treatment probability