Insights from Machine Learning for Evaluating Production Function Estimators on Manufacturing Survey Data

TL;DR

This paper evaluates different estimators for production functions using survey data, proposing a method to select estimators based on performance, and finds that structured models like Cobb-Douglas perform well in practice.

Contribution

It introduces a data-driven approach for selecting production function estimators and compares parametric and nonparametric methods on simulated and real survey data.

Findings

Proposed estimator achieves lowest weighted errors in simulations.

Cobb-Douglas explains at least 90% of variance in real data.

Application data improves estimator selection and benefits structured models.

Abstract

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.