  Organizations like U.S. Census Bureau rely on non-exhaustive surveys to
estimate industry-level production functions in years in which a full Census is
not conducted. When analyzing data from non-census years, we propose selecting
an estimator based on a weighting of its in-sample and predictive performance.
We compare Cobb-Douglas functional assumptions to existing nonparametric shape
constrained estimators and a newly proposed estimator. For simulated data, we
find that our proposed estimator has the lowest weighted errors. 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 providing two
insights: the benefits of using application data for selecting an estimator,
and the benefits of structure in noisy data.
