Were Cobb and Douglas Prejudiced? A Critical Re-Analysis of Their 1928 Production Model Identification

Abstract

In 1928, Cobb and Douglas (C&D) presented a system analysis which established the first empirically identified production model, which forms the foundation for Solow's growth theory and research into productivity growth factors, such as "technological progress" and "human capital development". C&D claimed that their production model ("function") showed neutral economies of scale, i.e., constant returns to scale, with a labor production elasticity of 3/4 and a capital production elasticity of 1/4. A simple CLS analysis shows that C&D's data were incorrectly identified by an (n,q)=(3,1) linear model. C&D's claim that their neutral "constant returns of scale" was the inevitable scientific conclusion of their analysis was also incorrect, since that conclusion is strictly determined by their subjectively chosen projection direction. In fact, the data shows that with their model and identification technology constant, increasing and diminishing returns to scale are all three compatible with the uncertain data. Their (n,q)=(3,1) model was never identified with an acceptable level of scientific accuracy, with a maximum coefficient value variation of 212%. In contrast, a simple two-equation (n,q)=(3,2) system model can be accurately identified from C&D's data set, with an acceptable level of accuracy, with a maximum coefficient value variation of 7.4%.

Keywords: System identification, noisy data, production model, elasticities, projections, complete least squares, accuracy

JEL Classification: B23, B24, B49, C21, C31, C52, C53