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Beyond Cobb-Douglas: Estimation of a CES Production Function with Factor Augmenting Technology

February 2011

Written by: Devesh Raval

Working Paper Number:

CES-11-05

Abstract

Both the recent literature on production function identification and a considerable body of other empirical work on firm expansion assume a Cobb-Douglas production function. Under this assumption, all technical differences are Hicks neutral. I provide evidence from US manufacturing plants against Cobb-Douglas and present an alternative production function that better fits the data. A Cobb Douglas production function has two empirical implications that I show do not hold in the data: a constant cost share of capital and strong comovement in labor productivity and capital productivity (revenue per unit of capital). Within four digit industries, differences in cost shares of capital are persistent over time. Both the capital share and labor productivity increase with revenue, but capital productivity does not. A CES production function with labor augmenting differences and an elasticity of substitution between labor and capital less than one can account for these facts. To identify the labor capital elasticity, I use variation in wages across local labor markets. Since the capital cost to labor cost ratio falls with local area wages, I strongly reject Cobb-Douglas: capital and labor are complements. Now productivity differences are no longer neutral, which has implications on how productivity affects firms' decisions to expand or contract. Non neutral technical improvements will result in higher stocks of capital but not necessarily more hiring of labor. Specifying the correct form of the production function is more generally important for empirical work, as I demonstrate by applying my methodology to address questions of misallocation of capital.

Document Tags and Keywords

Keywords Keywords are automatically generated using KeyBERT, a powerful and innovative keyword extraction tool that utilizes BERT embeddings to ensure high-quality and contextually relevant keywords.

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:
production, macroeconomic, manufacturing, labor productivity, labor, produce, productivity estimates, capital, capital productivity, productivity firms, productivity shocks

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:
Metropolitan Statistical Area, Annual Survey of Manufactures, Internal Revenue Service, Standard Industrial Classification, Bureau of Labor Statistics, Center for Economic Studies, Ordinary Least Squares, Total Factor Productivity, Cobb-Douglas, Administrative Records, Longitudinal Business Database, Chicago Census Research Data Center, Generalized Method of Moments, North American Industry Classification System, 2010 Census

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