¹ At the time this paper was presented I was not aware of the note by Solow, Robert M., “Reply,” Review of Economics and Statistics, XL, no. 4, 11, 1958, 411 CrossRefGoogle Scholar, in which he states in elegant form the essence of the method presented here for obtaining, with the model I have used, the effects of technological change on productivity; I am grateful to Wm. C. Hood for calling it to my attention and for other suggestions. Nor until I read again Mr. Solow's article, “Technical Change and the Aggregate Production Function,” ibid., XXXIX, no. 3, Aug., 1957, 312, did I realize it was implied therein. Actually I had developed the method presented here several years ago and had outlined it in a memorandum discussed with various people at the University of Chicago in 1953 and with others at various times since then. Rather than undertake the task of rewriting the first part of the paper I leave it essentially as it was, despite its comparative pedestrianism, for two reasons. First, it may be useful to some people to have it in non-mathematical form. Second, its somewhat different emphasis raises a few points, to which I refer later, relevant to Mr. Solow's article, “Technical Change.”

It is evident from the discussion that I assume that factor prices are determined by the factors' marginal productivities.

I am grateful to Gideon Rosenbluth for many suggestions made in discussion of this paper.

² An analysis of six major sectors of the economy has also been done on the lines presented for the economy as a whole in Table I of this paper. These sectors are agriculture, manufacturing, mining, steam railways, telephones, and electric light and power. Actually I have ignored the effects of demand conditions rather than abstracted from them. The following treatment absorbs them in the production function.

³ References to all the relevant literature on the matter of measuring joint factor productivity would be very lengthy. The pioneer work being done by John Kendrick of the National Bureau of Economic Research, reported on in various annual reports and other publications of the Bureau, is the largest effort in this field. For agriculture the work of Schultz, T. W. in The Economic Organization of Agriculture (New York, Toronto, London, 1953)Google Scholar, is an early and valuable work. The articles most closely related to this paper are the two by Mr. Solow referred to in n. 1, and the following: Solow, Robert M., “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, LXX, 1956, 65 CrossRefGoogle Scholar; Hogan, Warren P., “Technical Progress and Production Functions,” Review of Economics and Statistics, XL, no. 4, 1958, 407.CrossRefGoogle Scholar The latter is a comment on Mr. Solow's “Technical Change,” and was the occasion for his “Reply.” I regret that, owing to its having come to me very late in the final revision of this paper, I have not made running references to Fabricant, Solomon, Basic Facts in Productivity Change (Princeton, 1959)Google Scholar, which contains some of Kendrick's series on productivity; I did use it however in revising the labour input series (see Table I, Sources, line 1).

⁴ Mr. Solow's method, in “Technical Change,” basically does this by subtracting relative changes in product caused by changes in inputs, wilh a given technology, from the total relative change in product actually observed.

⁵ Some final commodity prices have moved upward in relation to others fairly continuously; this is true of certain types of services. It is only recently, however, that these services have bulked tremendously large in the economy. Actually the output of a large part of the so-called service industries, such as trade and transportation, is paid for in commodity prices.

⁶ The difference over the period of 100 years covered in Table I is quite substantial. Differences do not appear on a large scale for shorter periods.

⁷ See Solow, “Reply,” 411, first two pars, of point 5.

⁸ The following discussion related to Figure 1 is well known and repeated merely for convenience. See, e.g., Boulding, Kenneth S., Economic Analysis (1st ed., New York, 1941), chap, XXIII, esp. 505 ff.Google Scholar

⁹ That is, “unambiguous” if capital and labour can be clearly defined and measured. Actually, of course, as has been frequently pointed out, the introduction of new technology may depend on changes in the quality of capital and labour. And capital does not include investment in human abilities and in knowledge.

¹⁰ Information to support this view for the whole period comes from U.S. Dept. of Commerce, National Income (1954); Kuznets, S. S., National Income and Its Composition, 1919-1938 (Princeton, 1941)Google Scholar; National Industrial Conference Board (Robert F. Martin), National Income in the United States, 1799-1938 (New York, 1939)Google Scholar; and Edward C. Budd, “United States Factor Shares, 1850-1910,” document of Conference on Research in Income and Wealth, 1957 (mimeo.).

¹¹ Though factor shares are not entirely constant, it seems to me that, for my purpose at least, it is best to treat the material as though the isoquants were basically such as to yield constant factor shares, and to regard aberrations of factor shares as short-run phenomena explained by other features of the economy, such as the extent of its utilization of resources. By this procedure I can easily get a production function that will fit at least approximately. It seems to me that Mr. Solow, in his “Technical Change,” really uses a Cobb-Douglas function for the calculation of changes over yearly intervals. The contours change, however, from one year to the next. These characteristics are implied by using a constant W ^k for each year but changing it from year to year. The problem of there not being an “unambiguous” measure of productivity change persists if contours are twisted as they shift.

¹² It is an important property of this type of measure of inputs that, if it is in index form, the choice of a base year makes no difference to the relative movements of the series.

¹³ For the economy as a whole, I feel there is a real argument for treating land as a separate input (it is less necessary and next to impossible for some of the sectors). By far the larger part of land values are urban site values and agricultural values, and site is very important even in the latter case. The increased utilization of land is in a very real sense the direct consequence of the application of increased capital and labour, and also of changes in technology. It is the last which made possible the use of much agricultural land.

¹⁴ The division of income between labour and property was obtained, sector by sector, from annual data for 1900–48, given in the income estimates of Martin, Kuznets, and the Dept. of Commerce (see n. 10); allowance was made for differences in concept among these estimates. Labour income includes income for the self-employed and family workers, imputed at the wage received by hired employees.The share of labour is the average for theperiod noted above.

The division of property income was made on the basis of the average ratio of the total value of the stock of capital, measured in current prices, to the total value of land in current prices, at decennial census dates, 1850-1940. The division of total property values between capital and land was obtained, sector by sector, from data obtained in decennial censuses from 1890 onward, from special reports of the Bureau of the Census and the Federal Trade Commission, and from Statistics of Income. It was estimated for the years before 1890 by projecting trends in ratios of capital to land in each sector. The use of ratios of the total value of the capital stock to the total values of land as an indication of these shares in property income is based on the assumption that the rate of return on the current dollar valuations of each is the same.

The movement of land values from 1940 to 1950 was obtained from Goldsmith, Raymond, A Study of Savings in the United States, III (Princeton, 1956), 15.Google Scholar The current value ratios of capital to land increased very moderately to 1930 but quite rapidly in the next two decades. A single ratio was used for the estimates of Table I, however.

¹⁵ For the source of the product series see Sources to Table I. Net income from international investment was removed from the product series to make it correspond to the capital stock series which excludes international investments. This procedure was used since movements in international property income do not correspond well with changes in international investments.

¹⁶ The estimates for the capital input series were obtained from direct estimates of capital stock. Some of the source data were in current prices; some on a depreciated original stock basis.

¹⁷ Dewhurst suggests that an unusually high percentage was unemployed in 1900. See Dewhurst, Frederic and Associates, America's Needs and Resources (New York, 1947), 695.Google Scholar

¹⁸ Historical construction cost indexes have frequently been obtained by weighting prices of material and labour by their shares in total costs. This method does not allow for improvements in productivity in on-site work.

¹⁹ The discussion of Table I that follows assumes that the production function that is used is realistic.

²⁰ Between the terminal years 1879 and 1929 the index of capital input that I used moved almost exactly like that derived from Simon Kuznets' data given in “Long Term Changes in the National Income of the United States of America since 1870“ in International Association for Research in Income and Wealth, Income and Wealth, Series II (Cambridge, 1952), 78, Table 11, col. 1.Google Scholar International capital items were removed from Kuznets' data to make the comparisons. In the years between, however, my index rose first more rapidly, then more slowly than Kuznets'. Had Kuznets' figures been used the index of capital productivity would have been: 1880, 100; 1890, 106; 1900, 91; 1910, 97; 1920, 90; 1929, 100.

²¹ This must be so of course from the nature of the procedures used in calculating each component.

²² See Solow, , “Reply,” 412 Google Scholar, second par.

²³ Kuznets, , “Long Term Changes,” 123 ff.Google Scholar

²⁴ The value of land in current prices has been used already in calculating the share of land in property income. The only additional information used is the interest rate. This test is useful only in checking the share of land in total income against that of labour. It does not provide a check against the “correctness’ of the index of land input. An index of the total value of land in current prices can be used as an index of average value per unit of land if land input is constant. But if, instead, a rising index of land input had been used, the capital values per unit of land, in current prices, would have been accordingly lower than those used herein.

²⁵ Money interest rates are probably affected more by short-term factors than many other prices. They were particularly influenced in 1940 by the depession and in 1950 by the easy money policies that were still being followed then.

²⁶ It should be kept in mind that the check on real prices of the services of capital goods is not entirely independent of the measure of the productivity, since the price index of capital goods has been used in obtaining the estimate of the capital stock.

²⁷ The extent to which technology may be causing a substitution of capital for land in the period after 1930 is hard to estimate. Land values were undoubtedly unduly depressed in 1940 and probably considerably depressed still in 1950. However, that there has been some substitution effect seems likely.

²⁸ In highly capital intensive industries a large saving can come only by substantially reducing capital inputs per unit of product. There is just not much labour to be “saved.”

²⁹ In some cases the use of aggregates from the beginning is more fruitful than attempts to build up from individual components. The developments following 1850 provide a relevant case. There were substantial increases, per unit of input, in the output of agricultural commodities and manufactures. However, the relocation and geographical specialization that took place necessitated substantially longer hauls. Not all the increase in output of agriculture and manufacturing, as conventionally measured, was a net gain.

³⁰ The derivation of these elasticities is well known. It should be noted that, with the Cobb-Douglas function, there need not be any point of capital saturation, as long as improved technology and increased labour input raise the marginal productivity at sufficiently rapid rates.