Standard measures of productivity display enormous dispersion across farms in Africa. Crop yields and input intensities appear to vary greatly, seemingly in conflict with a model of efficient allocation across farms. In this paper, we present a theoretical framework for distinguishing between measurement error, unobserved heterogeneity, and potential misallocation. Using rich panel data from farms in Tanzania and Uganda, we estimate our model using a highly flexible specification in which we allow for several kinds of measurement error and heterogeneity. We find that measurement error and heterogeneity together account for a large fraction perhaps two-thirds to three-quarters -- of the dispersion in measured productivity. We suggest that the potential for efficiency gains through reallocation may be relatively modest. Acknowledgement : We are grateful for comments from Chris Barrett, Stefano Caria, Stefan Dercon, Andrew Foster, Talip Kilic, Karen Macours, and seminar participants at Yale, Oxford CSAE, UCLA, Northwestern, Heidelberg, Exeter, CEMFI Madrid, Manchester, Tufts, Hebrew University, and Universitat Autonoma de Barcelona.