THIS paper was undertaken for two purposes: (1) to uncover additional quantitative information about the structure of price behavior and (2) to see the extent to which such information could be enlarged as a result of studying price data arrayed by stage-ofprocess. Wholesale price indexes of the Bureau of Labor Statistics (BLS) have long been arranged this way, among others, and components of the Consumer Price Index can be developed that relate to these wholesale indexes. The study of price indexes by stage-of-process can be viewed as an approximation to the type of study that could be conducted in an inputoutput framework, if time-series data were available for I-0 industries. The research consisted of testing theories of price behavior whose determinants could be measured for sectors relevant to the explanation of price behavior by stage-of-process (these are shown in figure 1). This led to the selection of a set of price equations for consumer and producers' goods and their intermediate inputs. Additional equations were estimated for service prices and wages so that a nearly complete price sub-model could be developed. This model was then used to explore the structure of price determination. The stage-of-process approach differs from other studies of price behavior, most of which have sought to explain the deflator for private GNP and its components or the wholesale price index (WPI) for the manufacturing sector and its major subdivisions durable and nondurable goods. Such studies have not used the most relevant price series. The series that should be used are those reflecting the prices at which firms in a sector sell their output to customers outside of the sector. These prices are reflected more closely at high levels of aggregation by using stage-of-processing indexes rather than any other components of the WPI. In a recent review of empirical research on price behavior, Nordhaus (1972) concludes that most specifications and interpretations of price models have proceeded without the benefit of formal theory. While the testing of hypotheses is the focus of the present research, the effort encounters the common difficulties in so doing the lack of precise specification of any but the most simplistic models, poor or missing data, and estimation problems. To preview a conclusion, price behavior is difficult to explain and no one theory can be shown to be superior to all others. At least for the present, it appears that forecasting and policy formulation based on the structure of price determination must combine theory with professional judgments about which reasonable persons may disagree. Given these circumstances, the results of exploring price data by stage-of-process yields some interesting and potentially useful results.

Murray Brown, Joel Popkin, "Reply" to R. G. Gregory, "A Measure of Technological Change and Returns to Scale: A Comment", The Review of Economics and Statistics, Vol. 47, No. 4 (Nov., 1965), pp. 454-457

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.