Organizations like census bureaus rely on non-exhaustive surveys to estimate industry population-level production functions. In this paper we propose selecting an estimator based on a weighting of its in-sample and predictive performance on actual application datasets. We compare Cobb-Douglas functional assumptions to existing nonparametric shape constrained estimators and a newly proposed estimated presented in this paper. For actual data, specifically the 2010 Chilean Annual National Industrial Survey, a Cobb-Douglas specification describes at least 90% as much variance as the best alternative estimators in practically all cases considered.