Technical Progress in U.S. Manufacturing Sectors, 1948-1973: An Application of Lie Groups

The purpose of this paper is to apply the theory of Lie transformation groups as developed by the first author, and derive a testable model of production and technical change. The econometric model is then applied to data derived by F. Gollop and D. Jorgenson for U.S. manufacturing industries for the years 1948-1973. This is the first empirical work in economics to incorporate the theory of Lie transformation groups, so the results are new, but they are also interesting. Using Zellner's seemingly unrelated regression equations method of generalized least squares produces an estimate of a model for the 21-industry system which has a high degree of explanatory power: The system's weighted-R2 is 0.9675 and all coefficients are statistically significant at the 5% level (on the basis of t-tests). While the "form" of technical change in a given industry of the model is probably new, it is easily characterized within the Lie group structure and the system estimate is statistically significant.