Estimation of a varying coefficient, fixed-effects Cobb-Douglas production function in levels

We propose a semiparametric varying coefficient estimator for a Cobb-Douglas production function for panel data with several practical features. First, we estimate the model without a log transformation to avoid induced non-negligible estimation bias. Second, we disentangle the impact of traditional inputs from that of environment variables, which impact output indirectly through altering the output elasticity of inputs and the state of technology via unknown functions. We introduce a linear index structure in the unknown functions to circumvent the curse of dimensionality, and allow the output elasticity of different inputs to depend on different environment variables. Third, our technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs and/or environment variables. Our estimator combines series and kernel methods for both the unknown parameters and functions. We demonstrate that the proposed estimator exhibits promising finite-sample performance. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

We propose a semiparametric varying coefficient estimator for a Cobb-Douglas production function for panel data with several practical features. The estimator accounts for the impact of traditional inputs and environment variables and allows for latent heterogeneity across individual units.