Lie Group Methods and the Theory of Estimating Total Productivity

Abstract

The methods of Lie group theory (see Sato [1980]and [1981]) can be applied in several illuminating ways to the theory of productivity estimation. One such application is to the question of whether or not technical progress may be estimated independently of returns to scale. The main theoretical result is that only in certain cases is technical progress necessarily indistinguishable from a scale effect. In part A of section I we review the development of this result. In part B of section I, we review the Sato/Kendrick [1963]method of estimating technical progress, and we generalize the Sato [1970]method to the case of n ≥ 2 factors of production. In part C, we show that the Kendrick/Sato method cannot be used to separately estimate technical progress and a scale effect. We also show how the Sato [1970] method can be extended to allow separate estimation of technical progress and a scale effect.