Knowledge that Transforms

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.

Ryutaro Komiya, Technological Progress and the Production Function in the United States Steam Power Industry, The Review of Economics and Statistics, Vol. 44, No. 2 (May, 1962), pp. 156-166

E M PI RI CALLYBASED generalizations about labor mobility patterns usually are generalizations about that minority of the labor force which consists of hourly-rated manual workers. These generalizations are further limited in most instances to the patterns described by such workers within local labor markets. Such are the confines, for the most part, of the mobility literature a literature inspired by distrust of and dissatisfaction with the conventional model.1 Subject to the constraining influence exerted by the emphasis on market imperfections of the empirical studies, however, our generalizations about mobility for the majority of the labor force and for movement by manual workers among labor markets, rest essentially on our expectations that the predictive implications of the classical model would not be disappointed were they tested. This paper subjects one aspect of those expectations to a test centered around net civilian migration by state in relation to earnings levels by state. In lieu of wage differences as the allocator of labor supplies, the labor market studies, especially the New Haven study, have advanced the job vacancy thesis workers respond to job openings. Wage differences are regarded as of little importance in the allocation process in the sense that the adjustment of labor supplies to the changing needs of industry is more or less independent of wage differences. Because the focus of the present study is on long distance mobility, interstate movement, the following expression of the job vacancy thesis is particularly relevant:

SINCE I929 there has been a substantial change in the location of manufacturing in the United States. The direction of redistribution has fairly consistently been from north to south and from east to west. In I929 the South and West together accounted for less than one out of every four United States manufacturing employees and for only one-fifth of value added by manufacture. By I958 1 their share of United States manufacturing had increased to one-third as measured by either variable. This change has had a significant impact on the political, social, and economic life of the nation. The consequences for businessmen, labor leaders, and government officials have been strong, direct, and sometimes painful. Inevitably, the question that arises is why? Why did this change occur? What were the historical developments and economic forces that determined its extent and direction? The purpose of this paper is to delineate the outlines of an answer to this question. In particular, we shall examine and reject the hypothesis that regional shifts in demand or markets were the major determinant of locational change. Area differentials in the rate of growth of manufacturing are the result of area differentials in the rate of growth of individual industries and of area differences in industrial structure. The latter refers to the extent to which an area's industries are those which, at the national level, are experiencing rapid or slow growth. If an area has predominantly fast-growing industries, we say it has a structure. If it has predominantly slow-growing industries, we refer to its structure as unfavorable. 2 The first point to be made is that the redistribution of manufacturing since I929 has been primarily the result of area differentials in the growth of individual industries rather than the result of differences in industrial structure. This need not always be true. The shift of industry to the Southeast in England in the inter-war decades was attributed more to differences in industrial structure than to area differentials in the growth of specific industries.3 In the United States, I929-I954, the comparative growth of manufacturing employment by state, unadjusted, was highly correlated with comparative growth, adjusted for industrial structure. (Spearman's coefficient of rank correlation equals +.8 ii.) Comparative growth, unadjusted, showed no correlation with the extent to which a state had a comparatively favorable or unfavorable industrial structure. (Coefficient of rank correlation equals + .003.) 4 Table i presents the comparative gain or loss of manufacturing in each Census division between I929 and I954, and shows it divided into two parts. The first represents the sum of the comparative gains or losses of individual industries. The second, or remainder, is a rough measure of the influence of industrial structure.5

HE current chaos in metropolitan fiT nance stems from two different sets of problems. The first, which we label traditional, are exemplified by such expressions as: ever-increasing demands for service, inadequate tax base, archaic tax structure, lack of planning, and other familiar expressions. Without doubting that these problems are acute and in need of attention, we wish to consider an overlooked second set of problems. The second set of problems arises when the budget functions of governments are placed within the context of the newly developed theory of public finance.' Here, governments are seen as performing certain overall budget functions provision of goods and services, income redistribution, and economic stabilization. However, except for the provision of one class of goods and services, namely, social goods, little attention has been focused on the budget problems involved in applying the newer theory to lower levels of government and the attendant problems of fiscal federalism which arise. We will argue that much of the chaos in metropolitan finance arises from a misunderstanding of the budget functions to be performed. The heart of the problem, it will be shown, lies in the vertical relations between governmental units. Under fiscal federalism the failure to solve problems of vertical relations, in turn, gives rise to certain horizontal conflicts between governmental units. While our discussion applies to lower-level governments in general, we focus attention on metropolitan areas where the problems are more vividly illustrated. The analysis will be structured in terms of the various budget functions which governments perform. The provision of social goods will be considered briefly. Next, we look into certain interferences with consumer sovereignty (merit goods) which governments undertake. Finally, issues involved when governments redistribute income will be considered.2 For each function we postulate a set of vertical rules ordering the relations between governments. This ordering will enable us to highlight the issues involved.

Robert Triffin, Herbert Grubel, The Adjustment Mechanism to Differential Rates of Monetary Expansion among the Countries of the European Economic Community, The Review of Economics and Statistics, Vol. 44, No. 4 (Nov., 1962), pp. 486-491

Albert Rees, Herbert Kaufman, Samuel J. Eldersveld, Frank Freidel, The Effect of Economic Conditions on Congressional Elections 1946-1958, The Review of Economics and Statistics, Vol. 44, No. 4 (Nov., 1962), pp. 458-465