A Measure of Technological Change and Returns to Scale

Abstract

JN order to account for the increase in output from I870 to I953, Professor Moses Abramovitz derives a measure which tells us how net national product per capita would have grown had the productivity of resources remained constant at base period levels while only the supplies of resources per head increased. 1 He infers that almost the entire increase in net product per capita is associated with the rise in productivity. 2 Since Professor Abramovitz utilizes base period weights proportionate to incomes going to labor and property, the measure of productivity increase assumes that the economy was operating under constant returns to scale in all periods when inputs were increasing and that all change is of the type.3 Our purpose in the present paper is to provide a measure by which changes in output can be decomposed into those changes attributed to advances in and technology and changes in output attributable to the exploitations of economies of scale. The method of measuring these magnitudes is based on an analysis of a production function. Although the method is applicable to any type of production function, the Cobb-Douglas form is used in the present paper. The analysis is based primarily on a series expansion of the production function and considers not only the capital and labor inputs as variables but the technologically determined parameters also as variables. That is, the parameters of the production function become functions of time in this conception. If all but the linear part of the expansion is suppressed and if the derivatives can be approximated by discrete changes, then it is possible to decompose changes in output over any discrete time period into output changes attributable to (a) the weighted change in inputs, (b) economies of scale (if they exist), (c) neutral change and (d) nonneutral change. The statistical procedure consists in fitting the production function to various time periods and isolating those in which there was no nonneutral change; we call these technological The resulting parameter estimates are stable with respect to one component of total output change. Then, for each of these epochs, we can measure (a), (b), and (c); the change in the parameter estimates between epochs permits the measurement of output change attributable to non-neutral change. In the present paper the method is confronted empirically with John Kendrick's data (see Appendix) for the United States nonfarm domestic sector, I890-I958. The results of the empirical confrontation may be anticipated here. In the analysis of the United States nonfarm domestic sector, the statistical method of tolerance intervals is employed to isolate the epochs. Three epochs are tentatively established: I890I9I8, I9I9-I937, I938-I958, that is, within each of these periods, the production function did not twist sufficiently so as to indicate a new non-neutral technology. The time shapes of economies of scale and the two types of change over the period I890-I958 are tentatively spelled out. It is found that economies of scale tended to exist in the first epoch while constant returns appeared to be evident in the last two; neutral change appears to be lowest in the first epoch and becomes increasingly more important in the second and third; non-neutral change traces a cycle over the overall time period, the *The authors would like to thank Professor John deCani for his comments. The computations in the paper were supported by The University of Pennsylvania Computer Center and The National Science Foundation. 1 Resource and Output Trends in the United States Since I870, Papers and Proceedings of the American Economic Association, XLVI (May I956), II. 2Ibid. 'Other measures of change that assume constant returns to scale have been developed by W. E. G. Salter (Productivity and Change (Cambridge, I960), 30-35, and fn. 1, 35). R. M. Solow, Technical Change and the Aggregate Production Function, this REVIEW, XXXIX (August 1957), 3I2-320.