Randomized control trials are sometimes used to estimate the aggregate benefit from some policy or program. To address the potential bias from selective take-up, the randomization is used as an instrumental variable for treatment status. Does this (popular) method of impact evaluation help reduce the bias when take-up depends on unobserved gains from take up? Such "essential heterogeneity" is known to invalidate the instrumental variable estimator of mean causal impact, though one still obtains another parameter of interest, namely mean impact amongst those treated. However, if essential heterogeneity is the only problem then the naïve (ordinary least squares) estimator also delivers this parameter
there is no gain from using randomization as an instrumental variable. On allowing the heterogeneity to also alter counterfactual outcomes, the instrumental variable estimator may well be more biased for mean impact than the naïve estimator. Examples are given for various stylized programs, including a training program that attenuates the gains from higher latent ability, an insurance program that compensates for losses from unobserved risky behavior and a microcredit scheme that attenuates the gains from access to other sources of credit. Practitioners need to think carefully about the likely behavioral responses to social experiments in each context.