Theory and Application of Local Weighted Shape Constrained Estimators for Analyzing Census of Manufacturing Data

Abstract

Efficiency and productivity analysis focuses on firm performance to obtain firm–level and industry–level economic structural insights. This study provides the theoretical and methodological basis for nonparametric production function estimation using local weighting and imposing shape constraints to avoid functional misspecification and to improve the interpretability of estimation results.

The first contribution is a model that combines a conventional local weighted estimator with monotonicity and global concavity constraints consistent with a production process with decreasing returns to scale. The second contribution is a model that imposes more complicated shape constraints allowing small firms to benefit from increasing returns to scale while still imposing decreasing returns to scale for large firms. This set of shape constraints is referred to as an S-shape production function and the relationship to the Regular Ultra Passum law is described. Further, an algorithm is proposed to estimate a production function satisfying the S-shape restriction, convex input sets and allowing for potentially non-homothetic input isoquants. The third contribution is a model that further extends the first two contributions to address the simultaneity issue using an instrumental variables approach. The proposed model imposes shape constraints in a Landweber–Fridman regularization. In addition to methodological contributions, simulation and application results are provided to demonstrate the improved finite sample performance and the interpretability of estimation results. Insights are gained for both Chilean and Japanese manufacturing by using the census of manufacturing data from these two countries.