Capital Accumulation, Technological Change, and Economic Growth

Capital Accumulation, Technological Change, and Economic GrowthAuthor(s): M. C. UrquhartSource: The Canadian Journal of Economics and Political Science / Revue canadienned'Economique et de Science politique, Vol. 25, No. 4 (Nov., 1959), pp. 411-430Published by: Wiley on behalf of Canadian Economics AssociationStable URL: http://www.jstor.org/stable/138981 .

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CAPITAL ACCUMULATION, TECHNOLOGICAL CHANGE, AND ECONOMIC GROWTH*

M. C. URQUHART Queen's University

THIS paper is limited to a narrow portion of the field of economic growth. Its purpose is to discover how growth in the labour force, capital accumulation, and technological change have affected the movements of factor prices (particularly the return to capital) in a private enterprise economy. The question of what may happen to the return on capital, and indeed to all factor prices, is an old one. There is now material to provide some evidence of what has happened.

The first part of the paper deals briefly with the theory of the matter and provides a rough model.l The second part explores the dimensions which quantitative data for the United States for a period of 100 years put on the variables and parameters of the model. Finally there are some comments related to the possible bearing of the results on future changes in the economic variables dealt with. The analysis is entirely for the long period.

In what follows I take much that is commonly accepted for granted and use many obiter dicta, some of which are justified in footnotes.

THE THEORY AND MODEL

Very briefly, in an economy with a large measure of competition, the forces

affecting the course of factor prices in the general equilibrium are: (i) the supplies of the factors of production and changes therein; (ii) the technical conditions of production (technology) and changes therein; (iii) conditions of demand and the structural effects of their changes including the effects on demand both of changing per capita incomes and of changing relative prices;

*This paper was presented at the annual meeting of the Canadian Political Science Association in Saskatoon, June 4, 1959.

1At the time this paper was presented I was not aware of the note by Robert M. Solow, "Reply," Review of Economics and Statistics, XL, no. 4, Nov., 1958, 411, 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, "Techni- cal 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. 411

Vol. XXV, no. 4, Nov., 1959



Canadian Journal of Economics and Political Science

and (iv) viewed from a shorter period of time, dynamic effects, particularly the effects of complementarities among different sectors of a growing economy.

Since I shall deal only with the economy as a whole, I shall not deal with the effects of demand conditions.2 Nor shall I deal with dynamic effects. The exclusion of dynamic effects is, I feel, justified in this particular type of long- run analysis, since, with very large changes, static equilibria dominate the

dynamic effects of movements toward or about these static equilibria. The

limiting of the paper to the economy as a whole can be justified only by the

magnitude of the alternatives. An attempt will be made later to show that

interesting results can be obtained even on this level. This leaves us then to deal with the effects of, first, technological change,

and second, relative factor supplies on factor prices. It is at once clear that if we are to get very far we must be able to separate the effects of these two forces on factor prices. Consequently we must, if possible, obtain a measure of the effect of technological change on the productivity of the factors of

production taken jointly.3 We must also try to obtain a measure of the individual effect of changes in each factor supply.

A measure of joint factor productivity may be calculated by comparing the course of a single measure of output with a single measure of input.4 That there is any problem in obtaining single series for inputs and outputs respectively arises from variation in the composition of each group with the passing of time. The problem is one of aggregation.

The most satisfactory solution would be to obtain properties of production functions and to see how technological change alters these functions. We can do something of this kind on the input end and will devote a considerable amount of time to it. However, our knowledge of the output end is entirely inadequate for measuring aggregate output in this way.

Fortunately it is probably reasonably satisfactory to obtain a single measure of output by weighting the quantities of output of each product by some

2An 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.

3References 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 T. W. Schultz in The Economic Organization of Agriculture (New York, Toronto, London, 1953), 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: Robert M. Solow, "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, LXX, 1956, 65; Warren P. Hogan, "Technical Progress and Production Functions," Review of Economics and Statistics, XL, no. 4, 1958, 407. 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 Solomon Fabricant, Basic Facts in Productivity Change (Princeton, 1959), which contains some of Kendrick's series on productivity; I did use it however in revising the labour input series (see Table I, So,urces, line 1).

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

412



Capital Accumulation

measure of their importance, such as their price at some particular time. Except in a limited number of cases, changes in the relative prices of products have not ordinarily been great enough, nor have they always moved in a sufficiently systematic way in one direction or the other, to yield vastly different measures of aggregate output if the prices of one period are used rather than those of another.5 Consequently the ordinary procedure of weighting quantities of output by some set of prices to obtain total output (or its counterpart of deflating the total money value of final output by a price index) probably gives a reasonable index of output change. And this is what is used.

On the input side we proceed by using properties of production functions, for two reasons. First, relative factor prices have changed sufficiently, and in such systematic directions, that the choice of prices to be used makes a considerable difference to the movement of a joint input series obtained by using an arithmetical weighting of quantities of factors by their prices.6 A better alternative appears available. Second, we need some rationale of the productive process in order to see how changing factor quantities will affect their own prices.

We now proceed to try to get some notion of the nature of the input end of production functions. The exposition of what follows is very simple and short, if given in mathematical form.7 I shall try, however, to give it in non-mathematical form.

Assuming possibilities of substitution among factors of production, a given output may be obtained by varying the combinations of inputs.8 Such possible combinations of factors for a given output are represented diagrammatically by the familiar isoproduct curves or surfaces, henceforth called isoquants. Such curves are shown in Figure 1 for two factors of production, say labour, L, measured on the vertical axis, and capital, C, on the horizontal. As usual the points on the curve Qi represent various combinations of labour and capital that can produce one given amount of product. The curve Q2 represents combinations of labour and capital that produce another (larger) given amount of product. The actual combination of labour and capital used will be that which minimizes the money costs of production. In Figure 1, if the ratio of the price of capital to the price of labour were such as to give us a constant money-cost line of the slope of the HJ, we would produce on Q, at B.

Now consider isoquants Q, and Q2. In an economy with a given technology and with economies of scale absent we should expect that if all inputs were, say, doubled, output also would be doubled. In this case in Figure 1 if isoquant Q2 is twice as far from the origin as isoquant Qi (that is, if OD =

5Some 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.

6The 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.

7See Solow, "Reply," 411, first two pars. of point 5. 8The following discussion related to Figure 1 is well known and repeated merely for

convenience. See, e.g., Kenneth S. Boulding, Economic Analysis (1st ed., New York, 1941), chap. xxim, esp. 505 ff.

413




0 FIGURE 1

20A, OE = 20B, and OF - 20C), the product associated with Q2 would be twice that associated with Q1. Even when there are economies of scale, isoquant Q2 may still have the same position and shape but the product associated with Q2 may be more than twice the product associated with Q1. This would mean that the economies of scale are the same regardless of the

proportions in which factors are combined; they are the same when we move from A to D as when we move from B to E or C to F. In such a case as will

appear, we include increased productivity that comes from economies of scale with increased productivity caused by technological change.

One other characteristic of these curves should be noted. The slope of Q1 at A is the same as that of Q2 at D. The slope of QI at B is the same as that of Q2 at E, and so on. Hence with given ratios of factor prices, if we moved from Q1 to Q2 our most economical position would be obtained by exactly doubling the input of each factor. If the ratio of factor prices changes, output being given, the least-cost position moves along an isoquant to a new

point but this movement is merely a substitution of one input for another and not a change in total input. Consequently we will treat any pair of inputs on Q2 as double any pair of inputs on Q1.

If an improvement in technology reduces each pair of input requirements for a given output by the same proportion, that is, if the isoquants are shifted toward the origin in the same proportion at all points, an unambiguous measure of productivity change is possible.9 This means, in Figure 2, that with the change in technology, isoquant Qi has shifted from the line Q1 to the line labelled Q1'. Point A moves to point A', point B moves to B', point C to C';

9That 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.

414




0- NA/ 0 C

FIGURE 2

and the ratios AA': OA, BB': OB, and CC':OC are all equal, and the same is true for any other related pairs of points on Qi and Q1. At the same time another isoquant further out (not shown) will have shifted to assume the position of Qi; in other words the product associated with isoquant Q1 will have increased. In these circumstances the proportional saving in inputs for a given output is the same whatever their original make-up. The change in productivity is the same wherever we start. (In mathematical terms, if 7r

(product) is a function of L (labour) and C (capital), and a is a productivity factor, the production function is of the form r = af (L, C).)

Now if our original constant money-cost line was HJ, which was tangent to Qi at B, and if our relative factor prices had not changed when Q, moved to Q1', then, if output were not changed, our new (smaller) money-cost line would have been H'J', and that would mean that to produce a given output we had moved from B to B'. Both factors had been reduced in exactly the same proportion.

If, at the same time, the price of capital had in fact fallen in relation to the price of labour so that the new constant money-cost line tangent to Q1' was MN, the quantities of capital and labour used would have been those given by the point C'. The actual amounts of capital and labour have not been changed in proportion in moving from B to C'. The fact that we end up at C' rather than B' has been caused by the change in relative factor prices rather than technological change. In moving from B to C', inputs have been reduced in the proportion BB': OB or CC': OC, the two being equal. We shall discuss more fully later the reasonableness of the possibility that technological change may in fact usually move the isoquants toward the origin in the manner described heretofore.

Now in an actual empirical situation for an economy, the observations on input combinations are available from time series. We have only one observa-

415




tion for each time period. Consequently, since total factor inputs constantly change, we have only one observation on each isoquant.

The actually observed points are like those shown in Figure 3. For each succeeding observation the amount of capital has increased in relation to the amount of labour. And with a rise in the price of labour in relation to the price of capital, each point is on a flatter part of its isoquant. In addition to the changes in inputs, if technological change is neutral in its effects on factor requirements, the whole group of isoquants will have been shifting toward the origin from one decade to the next. However, if the isoquants are similar to those described above and are affected by technological change as we have

L 1950

\ 90

\V070

60 1880

0 C

FIGURE 3

suggested they might be, and if we know the shape of the isoquants so that we know how far apart they are, we can obtain a measure of the change in input to be compared with the change in output. It remains to obtain the shape of the isoquants.

The key to the possible shape of the isoquants lies in the relative constancy of factor shares in income over time, upon which comment has been made frequently and which is an observable fact.10 Let us take it for granted that it is appropriate to use aggregate isoquants for the whole economy. We have already noted that the actual point on an isoquant in the two factor case at which production will take place depends on the ratio of the price of capital to the price of labour. Minimizing cost will mean that the combination of factors used will be that for which the slope of the isoquant is

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

416



equal to the price ratio of the factors. Reverting to Figure 2, if we are pro- ducing on isoquant Qx', the factor combination used will be that of point B' if the ratio of the price of capital to the price of labour is such as to give a constant money-cost line of the slope of the line H''. It will be at point C' if the ratio of the price of capital to the price of labour gives a constant money- cost line of the slope of the line MN. Now if factor shares are constant, the relatively larger amount of capital at C' compensates for its relatively lower price to keep the ratio PCQo/PLQL constant, where PG and PL are the prices of capital and labour respectively and QO and QL their respective quantities.11

It is well known that the isoquants of the Cobb-Douglas function have exactly this property. The equation of the isoquant is Q = LkC1-k, where k is the share of income going to labour, 1-k the share of capital, and Q a parameter which is constant for any one isoquant. As we move from one isoquant to another away from the origin, the value of Q increases. And it increases exactly in proportion to the distance that the isoquant moves from the origin and hence in proportion to changes in the amounts of factor inputs. We compute our index of factor inputs12 from the equation Q = LkCl-k.

Empirically the value of k can be obtained very easily. It is simply the proportion of total factor income going to labour; and 1-k is the proportion going to capital. It is important to observe that the values of these exponents are not obtained by correlation techniques.

If there are three factors of production rather than two, the analysis is unchanged. Let T represent the third factor, land. The equation of an isoproduct surface, which we would now have, is

(1) Q = LCk2T,

where k1 plus k2 plus k3 = 1, each being positive and representing the share of the factor of which it is an exponent in total income.

Having obtained our series of joint inputs we compare them with our measures of output. From the comparison we obtain a measure of the effects of technological change on productivity. By using the series on individual factor inputs we also obtain measures of the movements of individual factor productivities.

This procedure permits us not only to measure the effects of technological change (including any economies of scale) on factor productivity, but also to obtain measures of marginal productivities under any given state of technology. For it is easy to compute how product output would be expected to increase,

llThough 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 Wk 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.

12It 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.

Capital Accumulation 417




technology being given, for an increase in any one factor, the others held constant.

All the foregoing having been done, we can compare the course of actual marginal productivities with real prices of factors of production as a check on the quality of the data with which we have been working.

THE QUANTITATIVE MATERIAL

We proceed now to actual data for the United States for the census dates from 1850 to 1950. The material is given in index series form.

The material on individual and joint factor productivities is given in Table 1. Briefly, capital (line 2) includes structures, machinery and equipment, and inventories measured in real terms and valued net of depreciation. The labour input (line 1) is based on man-hours of work, all types of labour being given equal weight. Land (line 3) is kept constant at 100; the increasing utilization of land may be regarded as the consequence of the application of larger amounts of labour and capital and improved technology to a fixed area of land.13 The shares of net income of the factors, used for exponents of factor inputs, to obtain the joint series (line 4) were 0.73 for land, 0.18 for capital, and 0.09 for land.14

The product series (line 5) is for real net national product (exclusive of net income on international investments). It is a measure of output of final products plus inventory change but excludes replacement of capital.15

13For 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.

14The 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 the period 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 Raymond Goldsmith, A Study of Savings in the United States, III (Princeton, 1956), 15. 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.

15For 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.

418



TABLE I INDEXES OF INPUT, OUTPUT, AND PRODUCTIVITY FOR THE WHOLE ECONOMY*

Base of all indexes: 1929 = 100

1850 1860 1870 1880 1890 1900 1910 1920 1929 1930 1940 1950t

Input 1. Labour 20 25.4 30.8 39.3 52 63 80.6 89.6 100 93.7 94.9 (108) 2. Capital 4.65 8.48 10.3 16 30 42.9 64.2 79.8 100 100 95.7 (116) 3. Land 100 100 100 100 100 100 100 100 100 100 100 (100) 4. Joint input 17.8 23.6 28.1 36.4 50 61.3 78.9 88.6 100 95.4 95.5 (108)

Output 5. Output 5.47 8.56 10.3 15.7 25.2 37.2 55.9 70.1 100 90 117.9 (182)

Productivity 6. General 30.7 36.3 36.7 43.1 50.4 60.7 70.8 79.1 100 94.3 123.4 (168) 7. Labour 27.4 33.7 33.4 39.9 48.5 59.1 69.4 78.2 100 96.1 124.2 (169) 8. Capital 117.6 100.9 100 98.1 84 86.7 87.1 87.8 100 90 123.2 (157) 9. Land 5.47 8.56 10.3 15.7 25.2 37.2 55.9 70.1 100 90 117.9 (182)

*The sources are given at the end of the article. tFigures are bracketed to indicate they were not prepared in as much detail as the figures for the other years.




The index of general productivity (line 6) is a measure of increased productivity caused by technological change (including economies of scale). It is obtained by dividing the index of output by the index of joint input. The indexes of individual factor productivities, lines 7, 8 and 9, are obtained by dividing the output index by the respective factor input indexes. Each factor

productivity is affected by general productivity and the relative quantities of each of the factors themselves.

Before noting some features of the results a word may be said about the

quality of the data. For the long sweep I think they are reasonably satisfactory. They seem reasonably consistent with the data for individual sectors for which the information on outputs is better. However one should not claim high accuracy. The underlying data are not all that might be wished and become

progressively less satisfactory the further back we go. In addition there were more specific problems. First, two years give particular difficulty-1870 and 1920, when prices were very high and unreliable for the deflation of output values and, to a lesser extent, of capital values.16 Moreover, those years followed wars which had disturbing effects on the economy. Second, prior to 1900, I did not have sufficiently satisfactory information on the number of unemployed to permit the adjustment of labour inputs for this factor. Fortunately most of these census years were reasonably good ones for employment.17 Third, the index of construction costs, used to deflate values of structures, has, I suspect, some secular upward bias owing to the nature of its construction: this would cause some downward bias of the value of capital in structures.'8 Fourth, the exigencies of particular years may have caused unusual fluctuations in output in the years covered; for instance 1920 was a bad year for agriculture and the depression of that year also lowered productivity in non-agricultural production. With these shortcomings in mind we may immediately observe a number of things from Table I.

1. Capital input increased much more than labour input. Between 1850 and 1929 the former increased more than twentyfold, the latter approximately fivefold. By our method of treatment land input did not change. Input as a whole rose nearly sixfold. After the depression of the 1930's capital input con- tinued to rise in relation to labour input.

2. Had the input of the factors of production all increased in the same proportion, it can be seen from the index of general productivity that their average physical productivity would have risen more than threefold from the beginning of the period to 1929, about fourfold to 1940, and more than fivefold by 1950.

With the type of function that we are using, each factor's marginal productivity, while not equal to its average productivity, moves in exactly the same proportion. (This proposition is easily demonstrated. With a function

16The 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.

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

18Historical 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 im- provements in productivity in on-site work.

420



P = L.73C.l8T.19, where P stands for product, the average productivity of say, labour, is

P L'.73

(2) -P L

C. 18

T.09 = L-.27 .C.18 T'09 L L

and the marginal productivity is

OP (3) 27C. 18 09 (3) = .73 L-'7C18 T09.

The two series move in the same proportion. If a productivity facter (l+r)t is added to the function it is the same for both average and marginal products.19) Hence marginal productivities would have changed in exactly the same proportion as average productivities. (Henceforth when I speak of changes in

productivity, unless otherwise noted, I shall mean both average and marginal.) 3. In actual fact, the average and marginal productivity of land rose by more

than eighteen times between 1850 and 1929 and by about thirty-three times by 1950. The increase in the productivity of land by 1929 was thus more than five times greater than would have been explained by the improvement in productivity caused by technological change; by 1950 it was about six times greater. This further large rise in the productivity of land is accounted for by the application of five times more labour and twenty times more capital to land by 1929 than in 1850; or five and a half times more labour and twenty-five times more capital by 1950.

4. The average and marginal productivity of labour rose by somewhat less than four times between 1850 and 1929 and by about six times by 1950. Both increases were somewhat more than the growth in productivity caused by technological change. This growth in labour productivity, somewhat larger than can be explained by technological change, was caused entirely by a relative increase in the quantity of capital which more than offset the effects of the relative decrease in the quantity of land.

5. The average and marginal physical productivity of capital actually fell by nearly 30 per cent from 1850 to 1890; it had recovered its 1850 level by 1940 and substantially exceeded it by 1950. Again conflicting forces were at work affecting the productivity of capital. First, the rise in general productivity (from technological change) by itself would raise the productivity of capital in like proportion. Second, the increase in the quantity of capital in relation to labour, and the even greater increase in relation to land lowered the productivity of capital. It was the compounding of these forces that led to the actual course of capital productivity throughout the period.20

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

20Between 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. 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.




TABLE II

INDEXES OF THE EFFECTS OF TECHNOLOGICAL CHANGE AND CHANGING FACTOR QUANTITIES ON INDIVIDUAL FACTOR PRODUCTIVITIES* Base of all indexes: 1850 = 100

1850 1860 1870 1880 1890 1900 1910 1920 1929 1930 1940 1950

A. Effect on productivity of land of:

1. Technological change 100 118 119 140 164 198 231 258 326 307 402 547 2. Increase of capital 100 111 115 125 140 149 160 167 174 174 172 178 3. Increase of labour 100 119 137 164 201 231 277 299 324 309 312 342 4. Combined effect 100 156 188 287 461 680 1,022 1,282 1,828 1,645 2,156 3,327

B. Effect on productivity of labour of:

5. Technological change 100 118 119 140 164 198 231 258 326 307 402 547 6. Increase of capital 100 111 115 125 140 149 160 167 174 174 172 178 7. Increase of labour 100 93.7 89 83.4 77.3 73.3 68.6 66.7 64.8 65.9 65.7 63.4 8. Combined effect 100 123 122 146 177 216 253 285 365 351 453 617

C. Effect on productivity of capital of:

9. Technological change 100 118 119 140 164 198 231 258 326 307 402 547 10. Increase of labour 100 119 137 164 201 231 277 299 324 309 312 342 11. Increase of capital 100 61.3 52.1 36.4 21.7 16.2 11.6 9.74 8.09 8.09 8.38 7.16 12. Combined effect 100 85.8 85 83.4 71.4 73.7 74.1 74.7 85 76.5 104.8 133.4

*The sources are given at the end of the article.



A sorting out of the effects of technological change and changes in factor

quantities is given in Table II. The effect on land productivity of technological change (Part A, line 1) is merely the general productivity index of Table I, line 6, changed to an 1850 base. The effect that the actual increase in capital would have had on land productivity had technology not changed and had land and labour inputs remained unchanged at their 1850 levels (line 2) is a computed item, obtained from the production function Q = L.73C 18T.09 by inserting the actual value for the quantity of capital into the function for each

year. Similarly the effect that the actual increase in labour would have had on land productivity had technology remained unchanged and had land and

capital inputs remained constant is shown in line 3. (Land itself actually remained constant in amount and there is no need to calculate how increases in it would have affected its own productivity.) The actual course of productivity of land (line 4) is a compounding of the effects of technological change, capital accumulation, and growth of the labour force (lines 1 to 3). Multiplication of the entries of the first three lines gives line 4.21

In Part B the one new feature is that an increase in the quantity of labour, other things held constant, lowers the productivity of labour.

Finally, in Part C, both technological change and increased quantities of labour again raise the average and marginal productivity of capital and increased quantities of capital lower its own marginal productivity.

Several conclusions are clear from Table II. First, the productivity of the various factors have all been increased greatly by the effects of technological change. It has been the most important single factor in raising the productivity of each factor between 1850 and 1950, though in the period between such was not always the case.

Second, the productivities of each factor have been affected in an important way by such changes as have taken place in the other factors. Increases in labour have been very important in increasing land and capital productivities, particularly from 1850 to 1910 and again from 1940 to 1950. Indeed, between 1850 and 1890 the increase in labour contributed more to the rise in land and capital productivities than did technological change. From 1890 onward technological change began to become the more important: had our indexes been based on 1890 this would have been apparent. Between 1910 and 1940 the increase in labour input was a relatively minor factor in raising capital and land productivities, though in the latter year there was much unemployment. The large increase in the 1940's reflects, in part, the disappearance of this unemployment.

The increase in capital (that is, the absolute increase) has also been important in raising the productivity of the other factors. Throughout the period, with the exception of 1930-40, its effect was to provide a continuous upward influence on the productivity of other factors. Capital increase by itself would have raised the productivity of labour by 75 per cent between 1850 and 1929.

Third, as would be expected, the increase in each factor depressed its own productivity. In the case of labour most of this effect was felt by 1900 and

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





practically all of it by 1920. Though relatively small it was not insignificant. Turning to capital we see that the very large increase in capital lowered its own marginal productivity tremendously and fairly steadily except in the 1930's.

We turn now to see how real factor prices (that is, the various costs of using a physical unit of an input for a given time), have behaved, and to see if there is a correspondence between them and the factor productivities of Table I. It is emphasized that the purpose of this procedure is solely to provide a check against the reliability of the data used heretofore by taking advantage of additional information that has some independence from that used previously; the data from which our outputs, inputs, and factor shares are calculated become increasingly less adequate the further we go back from 1929. Had our estimates of output and input series been exactly correct and had actual factor shares been perfectly constant, it would have been an arithmetical necessity for the real prices of the factors to have moved in proportion to their productivities and these tests would have been spurious.22

The best estimates that I could obtain, in a limited amount of time, are given in Table III. It is nearly self-explanatory.

The price series used to deflate money factor prices in order to obtain real factor prices is the implicit index obtained in deflating current dollar values of net national product to get constant dollar values. (See Sources, Line 2.)

Real wage rates (line 3) are obtained by deflating an index of (non-agricultural) hourly wage rates by the above price series. The real wage series rises less than the labour productivity series until 1930. But this should be expected, for the index of money wage rates, by its construction, reflects changes in wage rates of particular types of labour. It does not reflect shifts in average wage rates that are caused by a shift of labour from low wage to high wage industries. Kuznets has estimated that for the period from 1869-78 to 1919-28 as much as 40 per cent of the increase in labour productivity comes from inter-industry shifts of labour.23 After 1930, he finds, this effect disappears. Wage rates probably do not vary as much between industries as does productivity, nor do wage differentials necessarily correspond to differences in productivity. But the shifts among industries before 1929, particularly the shift from agriculture to other sectors, undoubtedly meant a movement from lower wage rate industries to higher ones.

The estimate for the real price of land services (line 8) is obtained by a circuitous route.24 An estimate of the capital value of land, in current prices, had been made in the preparation of the capital stock estimates and in split- ting the property share of income between land and labour. An index of this capital value of land (line 5) was multiplied by an index of money interest rates (line 6) to provide an estimate of the money price of land services

22See Solow, "Reply," 412, second par. 23Kuznets, "Long Term Changes," 123 ff. 24The 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.

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TABLE III INDEXES OF REAL FACTOR PRICES COMPARED WITH INDEXES OF REAL PRODUCTIVITY*

Base of all indexes: 1929 = 100

1850 1860 1870 1880 1890 1900 1910 1920 1929 1930 1940 1950

1. Hourly wage rates 2. General price level 3. Real hourly wage rates 4. Productivity

5. Value in current prices 6. Money interest rates 7. Money price of services 8. Real price of services 9. Productivity

A. LABOUR 15 17 29 26 30 31 40 100 100 97 122 261 45.9 49.6 74 57.5 52.4 49.6 59.5 124.5 100 96.2 83.9 150.1 33 34 39 45 57 63 67 80 100 101 145 174 27 34 33 40 49 59 69 78 100 96 124 169

B. LAND 3.42 6.88 9.86 12.3 19.4 25.3 48.1 112.1 100 100 72.8 132

(136.8)t 136.8 144.4 98.2 82.8 71 84.8 116.1 100 94.6 57.3 55.8 4.68 9.41 14.2 12.1 16.1 18 40.8 130.1 100 94.6 41.7 73.4

10 19 19 21 31 36 69 104 100 98 50 49 5 9 10 16 25 37 56 70 100 90 118 182

C. CAPITAL

10. Implicit price index of goods 36.1 39.8 62 48.3 45 45.7 53.4 122.8 100 97.2 95.2 199 11. Money price of services 49.4 54.4 89.5 47.4 37.3 32.4 45.3 142.6 100 92 54.5 111.2 12. Real price of services 108 110 121 82 71 65 76 115 100 96 65 74 13. Productivity 118 101 100 98 84 87 87 88 100 90 123 157

*The sources are given at the end of the article. tMoney interest rate for 1850 assumed the same as for 1860.




(line 7).25 This last was deflated by the index of product prices to give an estimate of the real price of land services (line 8). For comparative purpose the index of productivity of land from Table I is given in line 9.

For capital an implicit price index of the cost of capital goods in current

prices is multiplied by the index of the money rate of interest to give an index of the money price of capital services (line 11).26 This index, in turn, is deflated by the index of product prices to give an index of the real price of the services of capital (line 12). Our index of the productivity of capital from Table I is given in line 13.

The data for land show that the real price of land services (line 8) did not move up as rapidly as would be expected from the productivity indexes, though until 1930 the differences are not tremendous. There are two possible explana- tions for the divergence. The first is that the estimates of land values for earlier years are too high. The second is that changes in technology may have led to a substitution of capital for land; the actual ratios of the estimated current price capital values to those of land increased moderately until 1930 and then much more rapidly. The decline in land values after 1930 is un-

doubtedly in part a reflection of the attitudes that were general in the de-

pression. In any event the concept of land which includes primary product resources, site value for urban use, rights of way, and the like, is at best a mixed affair.

One would expect that the rate of return on capital in isolated years, such as we have, would reflect short-term conditions more than would real wage rates. The poorest correspondence between the real price of capital services and capital productivity comes in the years when it might be expected most: in 1870, 1920, and 1950, all following war; and in 1900 and 1940 following depressions. At those times, the real rate of return on capital, or, putting it another way, the real cost of capital, might be expected to be particularly affected by short-run influences. In 1950 the great rise in corporation income taxes would also affect the real price of capital services as calculated here.

The conclusions from these tests are rather paradoxical. For the period before 1929, which is most in need of testing, the tests do not suggest that the data being tested are wildly wrong. For the period since 1930, when the underlying estimates of the data for Table I are best, the correspondence of movements in the real prices of capital and land services with their productivities is very poor. The latter result may be partly explained by the fact that in 1940 and 1950, money interest rates are a poor indicator of true rates of returns on property. In addition, changes in technology may have worked strongly to substitute capital for land in this twenty-year period.27

25Money 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.

26It 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.

27The 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.

426




COMMENTS ON THE APPLICABILITY OF THE ANALYSIS

I feel that this type of analysis has a use in exploring the developments of the past. In fact it should be more applicable to the analysis of individual, more homogeneous sectors of the economy than to such a conglomerate as the whole economy. It has limitations, of course, and requires careful use.

It would be interesting to speculate also about the relevance of such an analysis to prediction; but this I do not feel disposed to do. However for those who wish to make their own speculations I would like to make a few points that may help.

The most important of these matters concerns the realism of expecting that technological change might shift isoquants toward the origin; the data appear to be largely consistent with the view that it has happened in the past. Much is made of the tendency to develop "labour-saving" inventions as the price of labour rises in relation to that of capital. But, reverting to our diagrams again (Figure 2), we note that as we move along an isoquant we gradually greatly reduce the quantity of labour that we can save and greatly increase the quantity of capital. A reduction of 10 per cent in both inputs will give us the same relative saving at whatever point we are on the isoquant. It may be just as easy to develop an improvement that saves labour and capital by the same proportion as it is to save one in greater proportion than another. It may be just as easy to develop an invention that shifts point B to B' as it is to develop one that shifts A to A' or C to C', and it is possible that these shifts may be made more easily than by developing alternative inventions which in effect twist the isoquants.28 The increased use of capital per unit of labour may possibly be explained in terms of movements along isoquants as relative factor prices change. Of course there may be entirely new inventions that ultimately have a great impact. The most spectacular historical example is that of the railway; and we can think of many others. But they take a long time first to make their mark and then to work themselves out. In the meantime the multitude of small changes that go on regularly from year to year continues.

This consideration leads us to ask if there is any meaning in dealing with the economy as a whole. Some large sectors such as agriculture, manufacturing, and mining have behaved very much like the whole economy. Others have not; for instance, between 1870 and 1920 inputs of capital and labour in the railways changed in almost exactly the same proportion, and the wage share of the income generated by railways rose substantially. There have also been substantial shifts in demand among sectors of the kind emphasized by Colin Clark. Despite these qualifications, in a growing economy, where there is much com- plementarity among sectors, all the sectors grow together, though some grow faster than others. Further, as capital falls in price in relation to labour, the price of goods using capital in large amounts falls, leading to the substitution of capital for labour as if the movement had been along an isoquant. For certain rough purposes a good deal can probably be learned at the aggregate level.29

Finally, although the input contours of the Cobb-Douglas production func- 28In 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." 29In 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 rele-

427




tion appear to fit the data of the past approximately, I do not know of any theoretical reason why they should. Nor do I know of any reason to expect that they should continue to fit as we move into new parts of the contours with increases in the capital-labour intensity, except that it has happened in the past. However, should the Cobb-Douglas function continue to fit, the

following properties are relevant to what might be expected in further growth. First, the elasticity of output remains constant, with respect to any input,

regardless of the quantity of that input. Second, and more important, the elasticity of the marginal productivity of

any factor with respect to its own input is also constant. In other words, ceteris

paribus, a given percentage increase in a factor always results in a given percentage decline in its marginal productivity whatever the starting input. With our function, this elasticity with respect to capital is -0.82; an increase of 10

per cent in capital always lowers its marginal productivity by 8.2 per cent. Third, the elasticity of the marginal productivity of any factor with respect

to another factor input is also constant. For example, a given percentage change in labour always raises the marginal product of capital by a given percentage whatever the starting level of labour input. With our function the latter elas-

ticity is 0.73.30 Fourth, it is possible that technological change may alter productivity in the

capital goods industries at a different rate than it alters it for the remainder of the economy. If it may be assumed that a given proportion of total current income will be saved in any event, the above matter may be of considerable importance in the short run but, unless the divergence in productivities continues to grow rapidly, it will be of little consequence in the long run. For example, suppose that, owing to there having been little improvement in the productivity of the capital goods industries for some time, the cost price of capital goods doubles, other prices remaining unchanged. The result will be that only half as much real capital will be added to the capital stock each year as would have been added had relative prices remained unchanged. Then the marginal productivity of capital will decline each year by only half the amount it would otherwise have declined. In the short run, since we start with a large capital stock, in terms of consumers' goods the real rate of return on a given amount of money put into new capital will be lowered substantially. In the long run, however, in an expanding economy, with the elasticities mentioned above, we will have half as much capital stock on hand as we otherwise would have, and its marginal physical productivity will be twice as high as it otherwise would be. But the real rate of return on a given money amount of new investment would be unaltered.

I mention these last points because, in a growing economy, we might expect changes in capital to be in some percentage rate rather than at an absolute rate.

vant 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.

3OThe 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.

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SOURCES OF DATA IN TABLE I

Line 1. Since this paper was first prepared, a better basis for estimating the labour input for the economy as a whole has become available in Solomon Fabricant, Basic Facts on Productivity Change. In it (pp. 42 ff.) are John Kendrick's estimates for man-hours of labour input in the private sector of the economy for 1889-1957. I have revised the labour input series for 1890-1950 to make use of Kendrick's estimates.

Kendrick's unweighted index was adjusted to make allowance for government employment on the basis of the ratio of general government employment to private employment in each year. For 1929 to 1950 this was done by using data in U.S. Dept. of Commerce, Survey of Current Business, National Income Supplement (1954), 202-3, and in U.S. Dept. of Com- merce, Business Statistics (1957 biennial ed.), 56 ff. The adjustments for government employment from 1929 back to 1890 were made on the basis of data given in Solomon Fabricant, The Trend in Government Activity in the United States since 1900 (Princeton, 1952), 168. The adjustment in the period from 1890 to 1929 was done on the basis of the "labor force in industries operated wholly by government as % of the total labor force." It would have made little difference if the adjustment had been made on "Employed government workers as % of all employed workers.'

This method of adjustment makes no allowance for relative changes in the hours of work of government and non-government employees. For hours of work in government service see Fabricant, Trend in Government Activity, 84-5, 257.

The series was carried back from 1890 to 1850 on the basis of the number of gainful workers, U.S. Dept. of Commerce, Historical Statistics (1949), Series D47, p. 64, adjusted for hours of work on the basis of data in the Aldrich report (see ibid., Series D107-10 and the source cited).

Line 2. Capital input is obtained from the sum of depreciated values, in 1929 prices, of structures, equipment, and inventories. Except for 1929 the index is for the capital stock at the beginning of the year; for 1929 the year-end stock, which is, of course, the same as that for 1930, was used.

Only the main outlines of the procedure for obtaining the capital stock can be given here. Figures for 1850-1940 were obtained, in the main by deflating capital stock estimates obtained from decennial census data, from other censuses for particular industries, from various reports such as Statistics of Railways, Statistics of Income, and the like. (The various estimates of wealth by the U.S. Bureau of the Census were used only incidentally, as they appeared to be inaccurate.) The estimates were made for structures, equipment, and inventories separately for sixteen sectors of the economy and then added. Residential housing was carried backward from 1900 to 1840 by estimating the number of household units and the costs of a housing unit; a rough check of the value in 1840, made possible from the costs of building houses given in the 1840 decennial census, seemed to show that this procedure was reasonably satisfactory.

In the source data the estimates of values of land, structures, and equipment were frequently given as one figure. From 1890 onward they were separated on the basis of data given in the censuses of 1890 and later, in industry reports, in Statistics of Income, and in other sources. (See S. S. Kuznets, National Product since 1869 (New York, 1946), for other sources.) The divisions before 1890 were made mainly on the basis of trend.

Adjustments for price change were made by price series obtained largely from N.B.E.R. publications, from Goldsmith's series used in his Study of Savings, from Historical Statistics, and the like. Estimates were made for both current and constant dollar values.

The figures for 1950 were obtained by linking Goldsmith's estimates of capital in all structures, in producers' durables, and in inventories, to the estimates used herein at 1940, given in Goldsmith, Study of Savings, III, 20-1.

I used the capital stock estimates rather than Kuznets' or Goldsmith's "perpetual inventory" estimates, since I wanted estimates for individual sectors as well as for the economy as a whole. An index of Kuznets' estimates, given in "Long Term Changes," 78, adjusted for international investments, for year-end values, follows: 1879, 15.8; 1889, 24.8; 1899, 39; 1909, 57.5; 1919, 77.9; 1929, 100. It can be seen that the correspondence of my series with Kuznets' is very good for 1879, though there are divergences in the period between 1879 and 1929.

Line 3. By our method land is kept constant at 100. Line 4. Obtained from lines 1 to 3 by inserting the values in these lines into the equation

Q = L-73 C.18 T.09. Line 5. The output index is from net national product in constant dollars exclusive of

payment on international property income account.

429




For 1900-50 it is from Goldsmith, Study of Savings, III, 427, 429, with international property income payments removed. The latter was done on the basis of data in Historical Statistics, 242, Series M17, M19, and in National Income Supplement (1954), 174-5. Goldsmith's estimates end in 1949. They were carried forward to 1950 on the basis of the increase from 1949 to 1950 of G.N.P. in constant dollars, given in the National Income Supplement (1954), 216-17.

The output index from 1900 backward to 1870 was obtained by deflating Martin's estimates of national income in current prices. (See his National Income in the United States, Table 1, p. 6.) For 1869, 1879, and 1889 the value used was an average of Martin's current price estimates deflated by the general price level (which he uses himself) and by Kuznets index for deflating national income, given in "Long Term Changes," 240. This procedure is based on the belief that Kuznets' price index is the most accurate and the fact that Martin used his own price indexes to inflate some of his series in real values to obtain his estimate of income in current values.

For 1859 and 1849 the estimates used are an average of King's estimate (from Kuznets, "Long Term Changes") deflated by Kuznets' price index, and Martin's estimate deflated by the general price level. Martin's estimates are for the years 1899-1900, 1889-90, etc. The deflated values of his estimates were linked to the Goldsmith output series at 1900.

The resultant series from the Martin data corresponds very well with a commodity output series given in Robert E. Gallman, "Commodity Output in the United States, 1839-1899" (mimeo.), presented at Conference on Research in Income and Wealth, 1957, and with estimates of current dollar income, given in Budd, "United States Factor Shares, 1850-1910,"' deflated by Kuznets' price index.

Lines 6 to 9. Line 5 divided by the appropriate input index from lines 1 to 4.

SOURCES OF DATA IN TABLE II

Lines 1, 5, and 9. From Table I, line 6, converted to an 1850 base. Lines 4, 8, and 12. From Table I, lines 9, 7, and 8 respectively, converted to an 1850 base. The remaining lines are calculated as described in the text.

SOURCES OF DATA IN TABLE III

Line 1. Hourly wage rates are the Bureau of Labor Statistics (B.L.S.) index of wages per hour in non-agricultural pursuits taken from G. F. Warren and F. A. Pearson, Prices (New York, London, 1932), 197, for the years 1850-1929; Warren and Pearson made an estimate for 1930. It was extended to 1940 by a B.L.S. index given in A. E. Burns et al., Modern Economics (New York, 1949), 488, and to 1950 by a rough index obtained by using average hourly earnings from U.S. Dept. of Commerce, Business Statistics (biennial ed., 1957), 74. See also U.S. Dept. of Labor, B.L.S. Bulletin no. 604, pp. 521, 574.

Line 2. The general price level for 1900 to 1949 was obtained by dividing Goldsmith's G.N.P. in current prices by G.N.P. in constant prices; see Goldsmith, Study of Savings, III, 427, 429. (Goldsmith, in effect, uses the same index for G.N.P. and N.N.P.) It was extended to 1950 on the implicit price index for deflating G.N.P. from the National Income Supple- ment (1954), 217. The index was linked at 1900 to Kuznets' index, given in his "Long Term Changes," 240.

Line 3. Line 1 - line 2. LUne 4. From Table I, line 7. Line 5. Obtained as described in Sources to Table I, Line 2. Where the estimates of land

values were in other than current prices they were adjusted by appropriate price indexes. Line 6. The index of money interest rates from 1860 to 1929 is from Macauley's

"Adjusted Index Numbers of Yields of American Bonds" in Historical Statistics, 280, averages of series N201 and N202. The estimates for 1929-50 (linked at 1929) were from N.I.C.B., Economic Almanac (1953-4), 119 (20-year bonds); see also Historical Statistics, 207, Series N199.

Line 7. Line 5 X line 6. Line 8. Line 7 - line 2. Line 9. From Table I, line 9. Line 10. Total value of capital in current prices divided by its total value in constant

prices. See Sources to Table I, Line 2. Line 11. Line 10 X line 6. Line 12. Line 11 + line 2. Line 13. From Table I, line 8.

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Capital Accumulation, Technological Change, and Economic Growth