We consider essential heterogeneity in the impact of a large-scale Community-Driven Development (CDD) program in Senegal. Essential heterogeneity arises when unobservables determine the idiosyncratic gains from participation in a program, thereby generating correlation between treatment effects and selection. Standard instrumental variables estimates are shown to provide an extremely poor estimate of the impact of the program on child nutrition. Application of the local instrumental variables (LIV) estimator using semi-parametric techniques reveals extensive heterogeneity in the impact of the program, with children living in villages with unobservables that make them more likely to receive a completed project benefitting much more than children in villages whose unobservables induce a low likelihood of receiving a project. These techniques provide a sensible and easily applicable manner of assessing whether the decentralized allocation of projects that is inherent to CDD programs is resulting in those who benefit most from treatment actually receiving it.