Synthetic Factor Shares, The Elasticity of Substitution, and the Residual in Soviet Growth

Abstract

In studies of factor productivity in the Soviet economy, as in many other economic investigations, it has been necessary to make some assumption about the degree to which capital and labor are substitutable for each other. In many, if not most, the investigators have implicitly, and often explicitly, assumed either unitary elasticity of factor substitution, i.e., the renowned Cobb-Douglas function, or infinite elasticity of substitution, the arithmetic function [2-5] [7] [10] [12] [13]. Recent analyses of the American and other economies [1] [6] [8] [9] suggest, however, that a numerical value less than one, perhaps on the order of 0.5, may be more nearly consistent with the statistical evidence. Since the elasticity of substitution may be regarded as an index of diminishing returns, and since inputs of capital and labor have been growing at highly disparate, perhaps unprecedentedly disparate, rates in the USSR, it is of particular interest to ask if the traditional assumptions are indeed suitable. Would a closer approximation to the truth be given by the estimates for other countries? In the current state of our knowledge on the Soviet Union can we shed any light on the appropriate value for the elasticity of substitution? If it could very well have been less than unity, as in fact our calculations suggest, what are the implications for quantitative estimates of the sources of Soviet growth? Recently published data on capital and labor inputs and on synthetic factor shares in income [2] [10] have made it possible to suggest some tentative answers to these questions, which is the purpose of this paper. We shall proceed as follows. In section II we analyze data on growth of labor and capital and on synthetic factor shares to obtain a range of implied values for the elasticity of substitution. In section III we use these values to obtain further implications, those pertaining to the part of growth in output explained by combined input of capital and labor and the part left to be explained by other factors. II Factor Inputs, Synthetic Factor Shares, and the Elasticity of Substitution