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 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 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 of the dispersion in measured productivity.