Insights from machine learning for evaluating production function estimators on manufacturing survey data

National statistical organizations often 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 assumption 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. Using 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. Finally for the five largest manufacturing industries, we find that a 30% sample, on average, achieves 60% of the R-squared value that would have been achieved with a full census; however, the variance across industries and samples is large.