May 1972 Part II

By DALE W. JORGENSON and ZVI GRILICHES

Issues in Growth Accounting A Reply to Edward F. Denison

Page 1. Introduction.. ___ 65 2. Measurement of Output 67 2.1. Introduction. 67 1. Introduction 2.2. Consumption, investment, labor, and . 68 2.3. and quantity of output. 68 3. Measurement of Capital Input 69 IN our paper, "The Explanation of cially valuable since his objectives are 3.1. Introduction. ___ 69 Change" [60], we examine similar to ours and his approach is 3.2. Perpetual inventory method- 69 the measurement of total factor pro- carefully articulated with national in- 3.3. Price of investment ._ 70 ductivity from tlie perspective pro- come and expenditure accounts. 3.4. Price of capital services 72 3.4.1. Introduction...... 72 vided by tiie economic theory of Although Denison's objectives and 3.4.2. Household sector. 72 . From the accounting point our objectives are similar, any attempt 3.4.3. Noncorporate sec- of view the major innovation in our to integrate his approach to produc- tor______72 approach is in the integration of tivity measurement into national ac- 3.4.4. Corporate sector__ 73 productivity measurement with na- 3.5. Price and quantity of capital counts for and wealth gives services 74 tional accounts for income, saving, rise to serious difficulties. The first 4. Relative Utilization of Capital______.. 74 and wealth. Our main substantive important difficulty arises from a basic 4.1. Introduction.... _ 74 conclusion is that growth in real confusion between depreciation and re- 4.2. Measurement of relative uti- factor input rather than growth in placement that underlies all of Deni- lization- ____ 75 total factor productivity is the pre- 4.3. Actual and potential capital son's work. Denison measures net services.-. 76 dominant source of growth in real national product as gross product less 5. Measurement of Labor Input 77 product. replacement; the correct definition is 5.1. Introduction.-., :__ 77 Both our approach to productivity gross product less depreciation. The 5.2. Hours of work. 77 measurement and our substantive con- error in measurement of total product 5.3. Price and quantity of labor clusions require much further analysis services 78 carries over to Denison's measure of 6. Measurement of Total Factor Produc- and testing. Edward F. Denison has total factor input, since the vdue of tivity _ .__'_ 79 made an important contribution to total product is equal to the of 6.1. Introduction 79 this further analysis and testing in total factor input as an accounting 6.!2. Alternative measures of pro- his paper, "Some Major Issues in ductivity change______80 identity. 6.3. Sources of U.S. economic Productivity Analysis: An Examination A second important difficulty in growth, 1950-62______80 of Estimates by Jorgenson and Gril- Denison's approach arises from an in- 7. Major Issues in Growth Account ing___ 80 iches" [25]. In this paper Denison consistency between his treatment of 7.1. Introduction 80 examines our approach from the van- depreciation in the measurement of 7.2. Scope of product 80 tage point of methods developed in 7.3. Index numbers 83 total product and his treatment of re- 7.4. Capital and labor weights... 84 his study, Why Growth Rates Differ placement in the measurement of cap- 7.5. Weights for components of [28]. Denison's contribution is espe- ital input. This inconsistency results in capital and land--- 84 a contradiction between the income 7.6. Measurement of capital and NOTE.—Professors Jorgenson and Griliches land______87 are both members of the Department of accounts that underlie productivity 7.7. Utilization adjustment 88 Economics, Harvard University. A version measurement and the wealth accounts 7.8. Labor input 89 of this paper was presented at the 12th that underlie the measurement of cap- 7.9. Conclusions and sugges- Conference of the International Association ital input. Although Denison's measure tions for further research, 89 for Research in Income and Wealth in Footnotes __ 90 Ronneby, Sweden, August 30-September 4, of total factor productivity is con- References 92 1971. sistent with national income and ex- 65

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penditure accounts, it is impossible to as part of factor input. An important measure employed by Denison. Even integrate his measure into national objective of our approach to pro- though the details of the measurement saving and wealth accounts. ductivity measurement is the integra- procedure are quite different for the Further difficulties arise in Denison's tion of capital input into national two estimates, the empirical results are allocation of property income among accounts for income, saving, and wealth. very similar. Both measures of labor assets. First, Denison employs nominal Our estimates of product and factor input differ substantially from measures rates of return rather than real rates input, consumption and investment, based on unweighted man-hours, such of return in measuring income from the and labor and capital services are as those of Abramovitz [1], Kendrick supply of capital services. As a con- presented in Section 2 below. [61, 62] and Solow [70]. In Section 5 sequence his allocation of property In Section 3 we present estimates of we compare our measure of labor input income among assets is inconsistent capital input implementing our ap- with alternatives incorporating addi- with the integration of property in- proach in much greater detail than in tional detail. come into accounts for saving and our original study. The new estimates In Section 6 we present revised es- wealth. Second, Denison's classification permit us to distinguish among com- timates of total factor productivity. of assets ignores important differences ponents of property income correspond- Revised estimates of capital input in direct taxation of property income ing to sectors of the economy that require data on property income by by legal form of organization. His differ in legal form of organization. legal form of organization, an analysis allocation of property income fails to These estimates provide for a much of the tax structure for property in- reflect the impact of the tax structure more staisfactory integration of direct come, and the incorporation of measures on rates of return of different types of taxation of property income into factor of relative utilization of capital stock. assets. input accounts. Estimates of capital stock already The purpose of this paper is to com- We have attempted to validate incorporated into productivity studies pare our approach to productivity our original measures by checking provide an important part of the measurement with Denison's. For this our data against a more comprehensive empirical basis for revised estimates of purpose we present a new set of esti- body of supplementary evidence—es- capital input. Ultimately, satisfactory mates of total factor productivity for pecially evidence on investment goods estimates will require the integration the period 1950-1962 covered in Deni- in Section 3 and data on changes of productivity measurement with ac- son's study, Why Growth Rates Differ in the relative utilization of capital counts for income, saving, and wealth. [28]. These estimates, prepared by in Section 4. In constructing a new Productivity measures of this type are Christensen and Jorgenson,1 implement set of estimates Christensen and Jorgen- available for the United States for the our approach in much greater detail son have been able to incorporate new period 1929-67,4 but much further than the estimates given in our earlier data. In the most difficult area of work remains to be done in refining study. The new estimates and the empirical research, the measurement and extending these estimates. methods employed in obtaining them of relative utilization, they incorporate Section 7 summarizes the results of are presented in Sections 2-6 below. In cyclical as well as secular changes these revisions, compares them with Section 7 we compare these results with in relative utilization into their measure our original estimates, reviews Denison's and our own earlier ones and of capital input.2 In reviewing their Denison's objections to them, and ex- assess the quantitative importance of work in Section 4 and in response to plores some of the remaining unresolved the differences. Denison's comments we have reached issues. Our original conclusions are The first step in productivity the conclusion that the scope of our changed somewhat, primarily as the measurement is to define measures of original adjustments for changes in result of the reduction in the magnitude product and factor input in current relative utilization should be reduced. and scope of the relative utilization prices. Product is divided between con- In the measurement of real factor adjustment. The resulting estimates of sumption and investment; factor input input, rates of growth of labor and growth in total factor productivity are is divided between labor and capital capital input are averaged to obtain the closer to Denison's estimates than our input. Investment and capital input are rate of growth of total factor input, original ones, but still significantly linked through for using relative factor shares as weights. lower. Our revised estimates meet, we saving and wealth. Investment in The measurement of aggregate labor believe, all of Denison's valid objections reproducible tangible capital assets is input as developed by Denison, Gri- to our original procedures. We have part of the national product and also liches, and others,3 amounts to applying preserved, however, the major con- part of saving. Investment less deprecia- the same principle of aggregation to the clusion of our original paper: Growth tion plus capital gains is equal to the individual components of labor input. in total input is a major rather than change in the value of the corresponding Rates of growth of the components are a minor source in the growth of national capital asset from period to period. averaged to obtain the rate of growth output. The estimated residual change Capital assets underlie capital serv- of total labor input, using relative in total factor productivity is smaller ices. The treatment of capital assets shares in the value of labor input as than asserted by other investigators as part of wealth must be consistent weights. Our measure of labor input but not so small as was implied by our with the treatment of capital services does not differ conceptually from the original estimates. This requires a 66 SURVEY OF CURRENT BUSINESS May 1972

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revision of the implication of our to labor of comparable quality may value of the flow of services is imputed original paper that all of output growth also differ by age, race, sex, or occupa- from data on rental values of compar- could be accounted for by a corrected tion and these differences should be able structures. Capital services from version of total input within the con- reflected in the measurement of labor consumers' durables and producers' input. Finally, a more detailed in- durables used by nonprofit institutions ventions of national income measure- vestigation of possible contributions to are not treated symmetrically with ment. This does not seem to be the growth associated with in services from owner-occupied housing case. the process of research and educational and institutional structures. Purchases Further progress in explaining pro- activities would be worthwhile. It is of consumers7 durables are included in ductivity change will require allowing still our belief that the correct research personal consumption expenditures and the rates of return to differ among strategy in this area is to refine and purchases of producers' durables by different types of investment and extend the accounts so as to minimize nonprofit institutions are included in among industries and not only among the contribution of the unexplained private investment, but the flow of legal forms of organization. Returns residual. capital services from this equipment is not included in the value of private product. We treat the services of owner- 2. Measurement of Output utilized consumers' durables symmetri- cally with the services of owner- occupied housing and the services of 2.1 Introduction ment is not included in investment producers' durables utilized by non- We define the value of output and goods output, as defined below, so that institutions symmetrically with factor input from the point of view of factor input accounts for domestic and those of structures occupied by these the producer. For each sector of the foreign sectors are not comparable. institutions. Purchases of new con- economy we measure revenue as pro- In the U.S. national income and sumers' durables and purchases of ceeds to the sector and outlay as ex- product accounts the services of owner- producers' durables by nonprofit insti- penditures of the sector. The value of occupied housing and structures utilized tutions are transferred from personal output is net of taxes on output while by nonprofit institutions are included in consumption expenditures to private the value of input is gross of taxes on the product of the private sector. The investment, leaving the value of total input. The resulting concept of gross value added is intermediate between Table 1,—Production Account, Gross Private Domestic Product and Factor Outlay, United gross product at prices, which States, 1958 (Current Prices)0 is the concept of output employed in [Billions of dollars] our earlier study, and gross product at factor cost. Line Product Total For any concept of gross product the 1 Private gross national produ ct (table 1.7) $405.2 fundamental accounting identity for 2 — Income originating in government enterprises (table 1.13) . 4.8 productivity measurement is that the 3 — Rest of the world gross national product (table 1.7) 2.0 4 -J- Services of consumers' durables (our imputation) . . _ _ 39.6 value of output is equal to the value of 5 -j- Services of durables held by institutions (our imputation) .3 input. Denoting the price of aggregate 6 — Federal indirect business tax and nontax accruals (table 3.1) . . 11.5 output by £, the quantity by T, and the 7 + Capital stock tax (table 3.1, footnote 2) price and quantity of aggregate input 8 — State and local indirect business tax and nontax accruals (table 3.3) . _ __ 27.0 input p and X, we may represent this 9 -j- Motor vehicle licenses (table 3.3) .8 10 + Property taxes (table 3.3) ... . 13.8 identity in the form: 11 -f Other taxes (table 3.3) 2.9 12 -|- Subsidies less current surplus of Federal government enterprises (table 3.1) 2.7 13 — Current surplus of state and local government enterprises (table 3.3) . _. 1.8 14 = Gross private domestic product 418.2 In measuring total factor productivity we confine our attention to the private Factor outlay domestic economy. In the U.S. national 1 Capital consumption allowances (table 1.9) 38.9 income and product accounts the value 2 -f- Business transfer payments (table 1.9) 1.6 3 -|- Statistical discrepancy (table 1.9) . 1.6 of government services is equal to the 4 -J- Services of consumers' durables (our imputation) _ . 39.6 5 5 + Services of durables held by institutions (our imputation) .3 value of labor services by definition. 6 + Certain indirect business taxes (product account above. 9 -f- 10 + 11) 17.4 The services of capital input in the 7 -f- Income originating in business (table 1.13) 312.2 government sector are ignored, so that 8 — Income originating in government enterprises (table 1.13) 4.8 product accounts for private and gov- 9 -f- Income originating in households and institutions (table 1.13) 11.4 ernment sectors are not comparable. 10 = Gross private domestic factor outlay . - 418.2 For the rest of the world sector invest- ' All table references are to The National Income and Product Accounts of the United Statet, 1989-1986[6$]. May 1972 SURVEY OF CURRENT BUSINESS 67

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product unaffected. We impute the Table 3.—Gross Private Domestic Product, 1950-62 (Constant Prices of 1958) value of services of consumers7 durables 7 Gross private Gross private Consumption Consumption Investment Investment and producers durables owned by insti- domestic pro- domestic pro- goods pro- goods pro- goods pro- goods pro- Relative share Year duct, quan- duct, price duct, quan- duct, price duct, quan- duct, price of investment tutions from rental values implied by tity index index tity index index tity index index goods product (billions of (1958=1.000) (billions of (1958=1.000) (billions of (1958=]. 000) (percent) the imputed flow for owner- 1958 dollars) 1958 dollars) 1958 dollars) occupied housing and institutional 1950_... 328.8 0.818 214. 766 0.828 113. 904 0.801 0.339 structures. We add the resulting service 1951._._ 351.3 0. 874 228. 302 0.880 122. 926 0.864 0.346 flow to the product of the private 1952 .._._ 360. 3 0.896 237. 211 0.905 122. 982 0.880 0.335 1953.... 378.8 0.898 247. 510 0.909 131. 163 0.879 0.339 sector, increasing the value of the total 1954. _.. 375. 7 0.913 250. 210 0. 927 125. 154 0.886 0.323 product. The values of gross private 1955--.- 406.6 0. 921 262. 751 0.936 143. 861 0. 894 0.343 1956____ 416.2 0.952 272. 847 0.956 143.261 0.945 0.341 domestic product and factor outlay for 1957.... 422.6 0.982 280. 978 0.978 141.571 0. 989 0.337 the year 1958 are presented in table 1. 1958.... 418.2 1.000 287. 791 1.000 130. 419 1.000 0.312 1959____ 445. 5 1.017 300. 561 1.020 144. 976 1.013 0.324 1960. _._ 457. 1 1.033 309. 834 1.044 147. 261 1.010 0. 315 2.2 Consumption, investment, 1961.... 466.1 1.045 320. 175 1.060 145. 733 1.012 0.303 labor, and capital 1962_._. 495.1 1.057 334.799 1.075 160. 428 1.019 0.312 In measuring total factor produc- tivity we find it useful to divide total product between consumption and in- equivalent employees in the same and factor outlay in current prices for vestment goods and total factor outlay sector. Our estimates of nonfarm pro- 1950-62 are given in table 2. Total between capital and labor services. In prietors and employees are those of the product is divided between gross priv- the U.S. national income and product Office of . Our ate domestic investment and gross accounts total output is divided among estimates of unpaid family workers are private domestic consumption. Total durables and structures output (which those of Kendrick, allocated among factor outlay is divided between labor we denote investment goods output) sectors in proportion to the number of compensation and property compensa- and nondurables and services output proprietors in each sector.7 Our esti- tion. (which we denote consumption goods mates of persons engaged in the farm output). Our definition of services out- sector are from Kendrick. 2.3. Price and quantity of output put includes the services of consumers7 All outlay on factors of production durables and institutional durables not allocated to labor is allocated to We turn next to the measurement of along with the services output included capital. Outlay on capital services in- real product. Product is allocated be- in the U.S. accounts. cludes property income of the self- tween consumption and investment The value of private domestic factor employed; profits, rentals, and ; goods. Consumption goods include non- outlay includes labor compensation of capital consumption allowances; busi- durable and invest- employees in private enterprises and in ness transfer payments; the statistical ment goods include durable goods and private households and nonprofit in- discrepancy; indirect business taxes structures. We construct quantity index stitutions, plus the labor compensation that are part of the outlay on produc- numbers of output for these two types of self-employed persons.6 In measuring tive factors, such as motor vehicle of output from data for the corres- labor compensation of the self-employed licenses, property taxes, and other ponding components of gross national we assume for each sector that average taxes; and the imputed value of the product in constant prices. The product labor compensation of proprietors and services of consumers' durables and of the rest of the world and govern- unpaid family workers is equal to the producers' durables utilized by institu- ment sectors is composed entirely of average labor compensation of full-time tions. 8 Gross private domestic product services. The price index for the prod- uct of each of these sectors is assumed Table 2.—Gross Private Domestic Product and Factor Outlay, 1950-62 (Current Prices) to be the same as for services as a [Billions of dollars] whole. Quantity index numbers for the Year Gross private Investment Consumption Labor Property services of consumers' durables and domestic product goods product goods product compensation compensation institutional durables are constructed

1950 269.0 91.2 177.8 156.3 112.7 as part of our imputation of the value 1951 307.2 106. 2 200. 9 177.4 129.8 1952 323 0 108.2 214.7 188.9 134.0 of these services. The value of output 1953 _ _ __ 340.1 115.3 225.0 202. 7 137.4 from the point of view of the producing 1954 343.0 110.9 232.0 200.8 142.1 1955 374.5 128.6 246.0 216. 5 158.1 sector excludes certain indirect business 1956 396.3 135.3 260. 9 234.0 162. 3 taxes less subsidies. The price of out- 1957 . _ _ . 415.0 140.0 274. 9 246.0 169.0 1958 418.2 130.4 287. 8 245. 1 173.1 put is implicit in the value of output 1959 453.2 146.8 306.4 265. 5 187. 6 and the quantity index of output de- 1960 472.3 148.8 323.5 278. 7 193.6 1961 487.0 147.4 339.5 284.7 202.3 scribed above. Price and quantity in- 1962 _ 523.3 163.5 359.8 302.6 220.7 dexes for gross private domestic product are presented in table 3. 68 SURVEY OF CURRENT BUSINESS May 1972

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the personal income tax and indirectly through property taxes. We measure the corporate rate of return before personal income taxes but after cor- :>. Measurement of Capital Input poration income taxes.

3.2. Perpetual inventory method

3.1. Introduction Corporations utilize services from The starting point for a revised index residential and nonresidential struc- of real capital input is the estimation of Our original estimates of capital in- 7 put distinguished among five categories tures, producers durable equipment, capital stock by the perpetual inventory of capital input—land, residential and nonfarm inventories, and land. We method. In discrete time the perpetual nonresidential structures, equipment, employ the capital service prices for inventory method may be represented and inventories. Our approach has now in the form: Table 4.—Relative Proportions ot Capital been extended by Christensen and Stock by Sector, 1958 Jorgenson [19, 20] to 16 classes of assets, separating inventories into farm and Sector where K is the end-of-period capital nonfarm categories and adding con- it Asset class Corporate Noncor- House- \ stock, Iit the quantity of investment sumers' durables to the other asset business porate holds business and. insti- occurring in the period, and '/** the categories. Each asset category has been tutions rate of replacement, all for the ith allocated among corporate, noncorpo- Consumers' investment good. For each type of rate, household, and institutional sec- durables 0 0 1 00 9 investment good we follow these steps tors. This classification of assets Nonresidential in estimating capital stock by the permits a much more satisfactory treat- structures. _ _ .72 .18 .10 Producers' perpetual inventory method: (1) a ment of the taxation of income from durables _ .68 .31 .01 benchmark is obtained, (2) the invest- capital services. The original classifica- Residential ment series in current prices from the tion of assets was not sufficiently de- structures .08 .07 .85 U.S. national accounts is deflated to tailed to permit a fully satisfactory Nonfarm inventories. - ' _ . . .82 .18 0 obtain a real investment series, (3) treatment of the tax structure. The rela- Farm inventories 0 1.00 0 a rate of replacement is chosen, and tive proportions of capital stock by Land. _ . .19 .50 .31 (4) the stock series is computed using asset class for each sector for 1958 are the perpetual inventory method des- given in table 4. cribed above. Benchmarks for 1958, We have divided assets among sec- corporate capital input developed by rates of replacement, and price indexes tors of the private domestic economy Hall and Jorgenson [52, 53] for de- for each capital good are given in table that differ in the tax treatment of preciable assets, modified to include 5. Price indexes for each asset class property income. Households and insti- 10 7 indirect business taxes, including for 1950-62 are given in table 6. tutions utilize the services of consumers property taxes. Corporate property Our method for separating price and and institutional durables, owner- income is taxed directly through the quantity components of a flow of cap- occupied dwellings, institutional struc- corporation income tax and through ital services is based on the corres- tures, and land. No direct taxes are levied on this property income, but part Table 5.—Benchmarks, Rates of Replacement, and Price Indexes Employed in Estimating of the income is taxed indirectly through Capital property taxes. To incorporate property taxes into the capital service price, we 1958 bench- Replacement Asset class mark (billions rate Deflator (sources given below) add the rate of property taxation to the of 1958 dollars) rate of return, the rate of replacement, 0 and the rate of capital loss. Non- Consumers' durables _ 115 2 0 200 Implicit deflator, national product accounts. b corporate business utilizes services from Nonresidential structures 136 1 056 Constant cost 2 deflator. residential and nonresidential struc- Producers' durables 123 4 138 Implicit deflator, national product accounts." 5 tures, producers7 durable equipment, Residential structures 226.2 .039 Constant cost 2 deflator. Nonfarm inventories- 80 3 Investment: Implicit deflator, national product nonfarm and farm inventories, and land 0 accounts. Assets: BLS wholesale priced index, held by that sector. This property in- goods other than farm products and food. come is taxed directly through the per- Farm inventories 24 6 Investment: Implicit deflator, national product accounts." Assets d : BLS wholesale price index, sonal income tax and indirectly through farm products. property taxes. We measure the non- Land 322 2 Goldsmith.* corporate rate of return before personal » NIP [66], table 8.1. <* BLS [15]. & Captial Stock Study [49]. • Goldsmith [35], tables A-5 and A-6. income taxes. ° NIP [66], tables 1.1 and 1.2. May 1972 SURVEY OF CURRENT BUSINESS 69

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pondence between asset prices and To infer the capital service price from aggregating capital services by Johansen service prices implied by the equality the sequence of asset prices, we first and Sorsveen [56]. Arrow [4] has pro- between the value of an asset and the write the asset price as the discounted vided formulas for the service price for the value of its services. This corres- value of future services, an arbitrary sequence of replacements. pondence is the counterpart in price In Arrow's formula the rate of replace- estimation to the relationship between 1 -£n ment n{, which we have assumed con- investment and changes in capital it, stant for each class of assets, is replaced stock used in estimation of national by a weighted average of rates of wealth by the perpetual inventory where TS is the rate of return in period s, g_t is the price of the ith investment replacement over the lifetime of the method. Data on asset prices, rates of t asset. replacement, and investment are re- good at time t and pft is service price of quired for perpetual inventory esti- the ith investment good. Solving for the 3.3, Price of investment goods 11 service price, we obtain mates of capital stock. Our method The price indexes used by Christensen for separation of property compensation and Jorgenson in constructing the capi- between the price of capital services tal stock series differ from our original and its quantity requires the same data Given the sequence of asset prices ones in using the national income im- as the perpetual inventory method for {<$}, the rate of replacement M*> and plicit deflator for producers' durable measurement of capital stock, together the rate of return rt, we obtain the equipment and the WPI as the deflator with data on property income and the perpetual inventory estimate of the of the stock of inventories. There is tax structure. Data on p^dperty com- service price of the ith investment good enough evidence that the various official pensation by legal form of organization, PS. capital deflator series are biased upward such as those presented in the U.S. The correspondence between asset during this period for us to be unwilling national income and product accounts, prices and service prices implied by the to concede that our original attempt to are essential for incorporating the perpetual inventory method is precisely substitute something else (the CPI du- effects of the tax structure. This the same correspondence that underlies rables index) for the official equipment straightforward extension of the per- the measurement of net capital stock. investment deflator was an error. While petual inventory method makes it As Denison points out, ". . . net this is not the place to go into great possible to allocate property income stock measures . . . the discounted detail, there is ample evidence that among different classes of assets. value of future capital services." 12 components of the WPI, which in turn To make the correspondence between The measurement of net capital stock are a major source of deflators for the asset prices and service prices explicit is well established in social accounting producers' durables investment, are (or we must specify the relationship be- practice; our formula for the perpetual at least have been) rather poor measures tween the quantity of an asset acquired inventory estimate of the capital service of price change. The WPI is based at one date and the quantity of the price is an immediate implication of almost entirely on company and service flow of the asset at future dates. accounting methods for net capital papers and association reports. More- In our perpetual inventory estimates of stock. This formula may be generalized over, for a variety of reasons, it has had the stock of assets, we have assumed to alternative assumptions about the much less resources devoted to it rela- that the service flow from the ith in- time pattern of the service flow asso- tive to the CPI. All this has combined vestment good declines geometrically ciated with an asset. The formula to produce what we believe to be a over time, developed by Haavelmo [50] for a con- significant upward drift in components stant service flow over the lifetime of the of this index during the post-World asset has been suggested as a means of War II period.13 Table 6.—Price Indexes by Class of Asset, 1950-62 [1958=1.000]

Consumers' Structures, non- Producers' Investment, Assets, nonfarm Investment, Assets, farm Year durables residential and durables nonfarm inventories farm inventories Land residential inventories inventories

I960 0.878 0.763 0.752 0.800 0.833 1.000 1.027 0.706 1951 .942 .836 .809 .919 .920 1.200 1. 195 .760 1952 _ . .954 .881 .822 .840 .899 1.429 1.127 .785 1063 .943 .895 .835 .786 .906 1.500 1. 022 .786 1954 _.... .929 .897 .840 .808 .909 1.200 1.008 .811 1955 _ .919 .902 .859 .917 .929 1.250 .945 .850 1956 .. .949 .959 .918 .944 .970 .667 .932 .897 1957 .984 1.001 .975 1.143 .997 1.000 .958 .951 1958 . _ . 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1959 1.014 1.006 1.020 1.000 1.018 (a) .938 1.069 1960 1.009 1.005 1.022 1.031 1.018 1.000 .935 1. 143 1961 1.006 1.008 1.021 .944 1.013 1.500 .924 1.222 1962 1 008 1 024 1 023 1 019 1 013 1 000 .943 1.306

* Investment in constant prices is zero. 70 SUEVEY OF CUEEENT BUSINESS May 1972

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Our example of consumer durables of most of the producers' durables but drift in the WPI which was due to ihe was not intended to claim that the rather that such a comparison allowed particular way in which its data were particular items were representative one to detect the magnitude of the collected. The difference between the movement of prices for these identical items in the two index sources was Table 7.—Evidence on Drift in Components of WPI interpreted not as property of the particular items, but as an estimate of Approximate Item Reference Period drift in percent the bias introduced by the basic per year a procedure used in collecting the whole- Identical consumer durables b (10 items) CPI 1947-49-1958 1.9 sale price data. The latter, we assumed, Circuit breakers Dean-DePodwin c 1954-59 4.0 was generalizable to most of the other Dean-DePodwin 1954-59 .7 WPI items. Power transformers d Power transformers Census _. 1954-63 1.2 Actually, there is quite a bit more Steam generators Dean-DePodwin 1954-59 1.9 Steam generators Census * 1954-63 6.4 evidence on this point than was alluded Electric equipment Dean-DePodwin 1954-59 . .. 1.2 to in our original paper and some of it Electric equipment Census d 1954-63 1.9 Electric equipment Barzel/. _ _ 1949-59 4.4 is presented in table 7. The first line Railroad equipment Association of American Rail- 1961-67 .8 recapitulates the CPI-WPI identical roads.* durables comparison. The other com- h Tractors Fettig 1950-62 . .6 parisons can be divided into three Tubes, automobile Flueck* 1955-59 1.4 groups: (1) transaction price data Batteries, vehicle Flueck < . 1949-60 6.3 Storage batteries Census d 1954-63 2.9 (circuit breakers and power trans- Plumbing and heating Census d 1954-63 1.2 formers from the Dean-DePodwin study Oil burners Census d 1954-63 2 8 Warm air furnaces _ Census d . 1954-63 1.1 and tubes and batteries prices from Metal doors _ Census d .. . . . Flueck's staff report); (2) more detailed d 1954-63 .7 Bolts and nuts Census __ . _ 1954-63 2.3 attention to quality change and/or d Internal combustion engines . Census 1954-63 1 8 more analysis of the changing specifi- d Elevators and escalators Census 1954-63 1 i cations of the priced items, sometimes d Pumps and compressors Census 1954-63 2 0 via regression techniques (Dean-De- d Integrating instruments _ Census . 1954-63 3 1 Podwin and Census on steam d Electric welding Census 1954-63 —1 1 generators, Barzel on electric equip- d Electric lamps _ Census 1954-63 1 i ment, the Association of American d Trucks Census 1954-63 3 Railroads on railroad equipment prices, a Last column is the average change, over the specified « Census unit values, adjusted for capacity and horsepower and Fettig on tractor prices); and (3) period, in the particular WPI component relative to the differences, 1963 Census of Manufactures [8], Vol. IV, Indexes estimated price change ever the same period in the alter- of Production, Appendix A. wider coverage and transaction pricing native source. f Barzel [5]. Indexes in table 3 holding size constant are * The following items were compared for this period: essentially flat throughout this period. A similar story is (Census unit values data). automobiles, tires, radios, refrigerators, sewing machines, also told by the indexes in table 6, where size is taken into ranges, washing machines, vacuum cleaners, toasters, and account. The last, Census based, set of furniture. s Joint Equipment Committee Report [58] shows no o Dean and DePodwin [23] and an unpublished appendix significant increase in the "cost" of locomotives and freight data (summarized in table 8) is partic- to the original General Electric version. and passenger cars during this period. d 1963 Census of Manufactures [8], Vol. IV, Indexes of * Fettig 129], table 6, p. 609. ularly interesting since one might have Production, Appendix A. < J. Flueck [32]. expected that unit values would them- selves be upward biased due to the Table 8.—A Comparison oi OBE Producers5 Durables Investment Deflators With Census secular shift to more elaborate, higher Unit Value Indexes, 1962 (1954=100) "quality" models. In fact, they and all the other additional comparisons point Percent direct a Census a Drift in Category coverage by data (cross OBE * percent strongly to the existence of an upward from Census weights) per year bias in the comparable WPI com- Furniture and fixtures 42 110 9 119 1 0 8 ponents, at least in the recent past. Our Fabricated metal products 4. 34 117 3 121 7 implied estimate of this upward drift Engines and turbines 54 93 3 134 7 4 2 Construction machinery ... 20 126 2 132 0 g of 1.4 percent per year between 1950 Metalworking machinery... 42 122 9 137 2 1 2 and 1962 is quite consistent with the Special industry machinery 20 119 3 138 7 1 7 e new evidence presented in this table. General industry machinery 15 116 9 131 4 1 3 Service industry machinery 27 82 3 100 9 2 3 While it is not used in the productivity Electric machinery 27 98 7 112 0 1 4 computations we borrow from Christen- d 4 Trucks and buses . 91 118 0 122 5 sen and Jorgenson we are willing to Ships and boats 27 100 1 116 6 1 7 Railroad equipment 46 132 1 128 3 — 3 stand by this part of our original estimates.14 °1963 Census of Manufactures [8], Vol. IV, Indexes ofProduc- less than 15 percent coverage from Census sources. For a tion, Appendix A. comparison of tractor price indexes see table 7. Our substitution of the new OBE b NIP [66], Table 8.8. For tractors, agricultural machinery, « OBE definition includes also materials handling ma- mining and oil field machinery, office equipment, passenger chinery. "constant cost 2" construction deflator cars, aircraft, and instruments Census unit values are based on d Four separate Census categories aggregated using 1963 shipments as weights. for the comparable implicit GNP de- May 1972 SUEVEY OF CURRENT BUSINESS 71

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flator component is not ideal and could employed. Market rates are used effective tax rate is the ratio of taxes be improved on. The "constant cost 2" as a basis for imputing the implicit as a component of total space-rental deflator is an average, implicitly, of wage rates paid to the self-employed.18 value to the asset value of owner- the Bureau of Public Roads highway The main obstacle to application of this occupied dwellings, including both structures, the Bureau of Reclamation method to capital services on a com- structures and land. The value of serv- pumping and power plant indexes, prehensive basis is the lack of sufficient ices of institutional structures is the and the A.T. & T. and Turner con- data on market rental values. space-rental value of institutional struction cost indexes. The latter two To impute capital service prices we buildings. To estimate the rate of are basically input price rather than must estimate rates of return for return we divide the space-rental values output price indexes with some feeble corporate business, noncorporate busi- of owner-occupied dwellings and insti- adjustment for productivity changes.15 ness, and households and institutions.19 tutional buildings, less associated pur- The Bureau of Reclamation indexes are As an accounting identity for each chases of goods and services for dwell- hard to interpret and seem to be based, sector the value of all capital services ings, less current replacement values, to a large extent, on list prices of raw is equal to total property income. We accrued capital losses, and taxes as a materials. A recent study by Gordon measure the value of capital services for component of total space-rental value [40] indicates that the constant cost each sector before either corporate or for dwellings by the current asset value 2 index may also be biased upward to personal income taxes, but we measure of owner-occupied dwellings and insti- an unknown degree.16 It is likely, there- the rate of return after corporate in- tutional structures, including land. fore, that if a more accurate construction come taxes and before personal income Our measurement of the output of price index were used it would imply a taxes. In each sector asset prices and the producing sector differs from that higher rate of growth in the structures stocks, rates of replacement, and pa- of the U.S. national income and product component of capital input than was rameters describing the tax structure accounts in the treatment of consumers' estimated in our original paper and is are given as data. The rate of return and institutional durables. We assign also used in this one. In short, more for each sector is chosen at each point personal consumption expenditures on remains to be done in this area but we of time so as to maintain the identity durables to gross investment rather believe that our original procedures between property income and the value that to current consumption. We then were on the right track. The estimates of all capital services in the sector. add the service flow from consumers' we borrow from Christensen and Each capital service flow may be and institutional durables to the value Jorgenson are conservative in their expressed as the sum of four terms, of output and the value of capital input. choice of investment deflators. depending on the rate of return, the The value of each service flow is the rate of replacement, the rate of capital product of the service price given 3.4. Price of capital services losses accrued, and the rate of property above and the corresponding service 3.4-1- Introduction.—The second step taxation. Since property taxes are de- quantity. The values of these service in the construction of a revised index ducted from corporate income in deter- flows enter the product and factor of real capital input is to divide the mining corporate profits for tax outlay accounts given in table 1. We value of capital services between price purposes, the component of each capital assume that the rate of return on dur- and quantity with price corresponding service flow corresponding to property ables is the same as that on structures to the rental rate and quantity as the taxes is simply added to the other for the household sector. The effective amount of capital services utilized. components. Similarly, the property tax rate on consumers' durables is the This division is precisely analogous to tax component of each capital service ratio of the following State and local the separation of the value of labor flow for the noncorporate and house- personal taxes—motor vehicle licenses, services between a wage rate and the hold sector is simply added to the rest. property taxes, and other taxes—plus quantity of labor services. For property Accordingly, our first step in estimat- Federal automobile use taxes to the with an active rental market the separa- ing rates of return for the three sectors current asset value of consumers' dur- tion may be carried out by means of is to deduct all property taxes from the ables. The effective property tax rates market data on rental rates and cor- value of property compensation. on household property and the rate of responding data on the employment of 3.4-2. Household sector.—Our meas- return for the household sector are capital. This method may be extended surement of the flow of capital services presented in table 9. from rental property to property uti- for the household sector is independent 3.4.3. Noncorporate sector.—In meas- lized by its owners if market rental of the measurement of flows of capital uring the rate of return for the non- values reflect the implicit rentals paid services for the corporate and non- corporate business sector we first esti- by owners for the use of their property. corporate sectors. The value of services mate the effective tax rate on noncorpo- An imputation of this type is employed of owner-occupied farm and nonfarm rate property. We deduct property in the U.S. national income and product dwellings is the space-rental value of taxes on owner-occupied residential accounts in the measurement of serv- dwellings less associated purchases of real estate from State and local business ices of owner-occupied housing.17 A goods and services. We assume that the property taxes to obtain State and local precisely analogous imputation occurs proportion of purchases is the same for property taxes for corporate and non- in measuring labor services of the self- farm as for nonfarm dwellings. The corporate sectors.20 We allocate business 72 SURVEY OF CURRENT BUSINESS May 1972

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Table 9.—Effective Tax Rates and Rates of Return, Household and Noncorporate Sectors, Our estimate of the effective rate of 1950-62 (Annual Rates) the investment tax credit is based on Effective tax rate Effective tax rate Effective tax rate Rate of return, Rate of return, estimates of investment tax credit for Year on owner- on owner-utilized on noncorporate household sector noncorporate occupied residen- consumers' property sector corporations by the Office of Business tial real estate durables Economics. The effective rate is defined 1950 0.009 0.008 0.018 0.063 0.178 as the amount of the investment tax 1951 .009 .007 .017 .103 .214 1952_ .009 .007 .018 .062 .121 credit divided by gross private domestic 1953 _ .009 .007 .019 .030 .089 investment in producers' durables by 1954 .010 .007 .019 .032 .108 1955 .011 .007 .020 . 040 .114 corporations. We assume that the 1956 .012 .007 .019 .083 .127 effective rate of the investment tax 1957.. .012 .007 .020 .069 .127 1958 .013 .007 .020 .035 .116 credit is the same for corporations and 1959 .013 .007 .020 047 103 for noncorporate business. Although 1960 .014 .008 .021 043 096 1961 .015 .008 . 022 .047 .099 the nominal rate of the investment tax 1962 . _ . .015 .009 022 058 111 credit is 7 percent, certain limitations on its applicability reduce the effective rate considerably below this level.23 The present values of depreciation deductions on new investment depend motor vehicle licenses between corporate by the value of noncorporate assets- on depreciation formulas allowable for and noncorporate sectors in proportion The effective tax rate on noncorporate tax purposes, the lifetimes of assets to the value of producers' durables in property and the rate of return in the used in calculating depreciation, and each sector; similarly, we allocate other noncorporate sector are given in table 9. the rate of return.24 A reasonable State and local business taxes and 8.4.4- Corporate sector.—In measuring approximation to depreciation practice Federal capital stock taxes in propor- the rate of return for corporate business is provided by the assumption that the tion to the value of all assets in each we begin by estimating the effective tax straight-line depreciation formula was sector. The effective tax rate on non- rate on corporate property. We add the only one permitted for assets corporate property is the ratio of the State and local business property taxes, acquired up to 1953 and that an accel- sum of property taxes, motor vehicle business motor vehicle licenses, other erated depreciation formula, sum of licenses, and other business taxes allo- business taxes, and Federal capital the years' digits, was employed for cated to the noncorporate sector to the stock taxes for the corporate sector to assets acquired during the period 1954- value of all assets held by the sector, obtain total property taxes. The effec- 62.25 Given depreciation formulas and including producers' durables, residen- tive tax rate on corporate property is lifetimes for tax purposes, calculation tial and nonresidential structures, in- the ratio of these taxes to the value of of present values of depreciation deduc- ventories, and land. all assets held by the corporate sector, tions requires an estimate of the rate The value of capital services for the including producers' durables, resi- of return for discounting these deduc- noncorporate sector is the sum of in- dential and nonresidential structures, tions. We assume that this rate of come originating in business, other than inventories, and land. We measure return was constant at 10 percent.26 income originating in corporate busi- corporate property income less property Substituting the present values of de- ness, income originating in government taxes as income originating in corporate preciation deductions into expressions enterprises, and interest and net rent of business, less compensation of employ- for capital service prices we reduce the owner-occupied dwellings and institu- ees, plus corporate capital consumption unknown variables to two, the effective tional structures, less labor compensa- allowances, plus business transfer pay- corporate tax rate and the rate of tion in the noncorporate sector, includ- ments.22 The value of corporate capital return in the corporate sector. Corre- ing imputed labor compensation of input, which is equal to corporate sponding to these two unknowns, we proprietors and unpaid family workers, property income, depends on the effec- have two equations. The first relates plus noncorporate capital consumption tive corporate income tax rate, the rate corporate property income and the sum allowances, less capital consumption of return in the corporate sector, the of values of the individual capital serv- allowances of owner-occupied dwellings investment tax credit, and the present ices. The second relates corporate in- and institutional structures, and plus values of depreciation deductions for come taxes and the effective tax rate indirect business taxes allocated to the nonresidential structures, producers' on corporate income, applied to the noncorporate sector, as outlined above. durables, and residential structures. corporate income tax base, less the We also allocate the statistical dis- Corporate income taxes less the investment tax credit. We measure crepancy to noncorporate property investment tax credit are equal to the corporate income taxes as Federal and income.21 To obtain our estimate of the effective tax rate applied to corporate State corporate profits tax liability. noncorporate rate of return we deduct property income, less property taxes Since the two equations are independ- property taxes and the current value and less deductions for capital con- ent, we may solve for values of the of replacement, add accrued capital sumption, expressed as proportions of effective corporate tax rate and the gains on noncorporate assets, and divide current capital service flows after taxes. corporate rate of return in each time May 19Y2 SUKVEY OF CURRENT BUSINESS 73

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Table 10.—Tax Structure and Rate ol Return, Corporate Sector, 1950-62 (Proportions and Annual Rates)

Present value of Present value of Present value of Effective tax Effective rate Statutory rate Effective tax Statutory tax depreciation depreciation depreciation Rate of return, Year rate on cor- of investment of investment rate on cor- rate on cor- deductions, deductions, deductions, corporate sector porate property tax credit tax credit porate income porate income nonresidential producers' residential structures durables structur/es

1950 0.015 0 0 0.481 0.420 0.273 0.397 0.262 0 10 1951 .014 0 0 ,521 .508 .273 .397 262 15 1952 .014 0 0 .462 .520 .273 .397 .262 .07 1953 .015 0 0 .477 .520 .273 .397 .262 06 1954 .015 0 0 .476 .520 .413 .543 .400 06 1955 .016 0 0 .479 .520 .425 .560 .412 09 1956 - -. .016 0 0 .477 .520 .438 .579 .426 .12 1957 . . .016 0 0 .468 .520 .453 .596 .439 .10 1958 .016 0 0 .465 .520 .469 .614 .456 .05 1959 .016 0 0 .494 .520 .486 .632 .473 .07 I960 .016 0 0 .487 .520 .486 .632 .473 .06 1961 .017 0 0 .479 .520 .486 . 632 .473 .06 1962 .017 .037 .070 .480 .520 .486 .632 .473 .08

period. Variables describing the corpo- numbers. We note that the overall as by businesses. Price and quantity rate tax structure and the corporate service price and quantity indexes in- indexes of potential capital services for rate of return for 1950-62 are presented clude capital services from assets held corporate, noncorporate, and household in table 10. by households and institutions as well sectors for 1950-62 are given in table 11.

3.5. Price and quantity of capital services 4. Relative Utilization of Capital In separating the value of capital in- put into price and quantity components our basic accounting identity is that 4.1. Introduction better approximated by the "unem- for each sector the value of all capital ployment" of one kind of capital services or property compensation is It has been common to assume that (power-driven equipment), implicitly equal to the sum of the values of the one may be able to approximate the assuming a proportionality relationship individual capital services. In construct- of capital by the un- between this type of capital and other ing Divisia index numbers of capital employment of labor. Solow [71] as- capital, than by the assumption of service price and quantity we combine sumed that there is a proportionality proportionality between the employ- service prices and quantities by class of relationship between these concepts ment of all labor and of all capital. asset for all sectors. Finally, we com- (and his capital measure included land It is our assumption, for which we bine service price and quantity indexes and buildings, too!) while Okun [67] have no explicit evidence, that our by class of asset into an overall capital suggested a nonlinear relationship be- measure of utilization measures not service price index and potential service tween the two. It appeared to us that only the utilization of power-driven quantity index, again as Divisia index the unemployment of capital can be equipment but also the fraction of

Table 11.—Potential Gross Private Domestic Capital Input, 1950-62 (Constant Prices of 1958)

Corporate Corporate Noncorporate Noncorporate Household Household Private domestic Private domestic capital input, capital input, capital input, capital input, capital input, capital input, capital input, • capital input, Year quantity index price index quantity index price index quantity index price index quantity index price index (billions of 1958 (1958=1.000) (billions of 1958 (1958=1.000) (billions of 1958 (1958=1.000) (billions of 1958 (1958=1.000) dollars) dollars) dollars) dollars)

i960 47.3 1.027 34.9 0.894 39.0 0.845 121.2 0.930 1951 49 9 1 103 36 6 1 029 43 8 848 129.9 .999 1952 53 3 1 Oil 37 6 968 46 6 938 137.2 .977 1953. 55.5 1 004 38.3 .939 48.7 .939 142. 2 .967 1954. 57.7 .970 38.9 .930 51.6 .969 147.9 .961 1955.. 59.0 1 141 39.5 .937 54.3 .989 152.5 1.037 1956 61.9 1.101 40.3 .864 58.7 1.011 160. 7 1.101 1957 65.3 1.076 30.7 .909 61.6 1.003 167.5 1.009 1958 67 8 1 000 41.2 1 000 64 1 1 000 173.1 1.000 1959. 68.7 1.154 41.6 .925 65.5 1.067 175.8 1.067 1960. . 70.9 1.119 42.2 .890 68.4 1.121 181.7 1.066 1961 . . 73.4 1.110 42.8 .938 70.9 1.137 187.5 1.079 1962 . ' 75.2 1. 211 43.2 1.025 72.9 1. 171 191.7 1.151

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average estimated change in utiliza- calendar time that establishments or this to all industrial and agricultural tion (per annum) between 1939 and plants are in actual operation. That is, equipment and structures and also to machine-hours per week are interpreted structures and equipment in the service 1954, we overestimated the former. as a proxy for total hours per week industries. There is some scattered The estimates used in this paper (also operated by an establishment or in- evidence that the hours operated per taken from Christensen and Jorgenson) dustry. This, of course, is not an week by various retail establishments solve this problem by adding a cyclical unambiguous concept, but it does ex- have increased in recent years. adjustment to the previously computed plain why we were and still are willing secular one. The benchmark years are to apply this estimated utilization rate 4.2. Measurement of relative utilisa- now used only to derive the ratio of not only to equipment but also to tion installed horsepower to potential capi- buildings. We are also willing, for lack In measuring the change in utiliza- tal. This ratio is assumed to change of any better evidence, to extrapolate tion between 1945 and 1954 by the slowly and is interpolated linearly between benchmarks. Installed horse- power is then estimated as the product Table 12.—Relative Utilization of Electric Motors, U.S. Manufacturing, 1962 of this ratio and our index of potential

][ndexes, 1954=1.00() flow of (business) capital services. The Total fixed ratio of electric power consumed by Industry ° Horsepower of Total electricity Utilization* assets weight • motors to this estimate of installed electric motors b consumption « horsepower is our new measure of re- (1) (2) (3) (4) lative utilization. The resulting series 20.. 1.420 1.539 1.084 0.103 grows at a significantly lower rate, 0.54 21 1.446 1.794 1.241 .004 22 1. 155 1.229 1.064 .036 percent per year, during the 1950-62 24 1.543 1.289 .835 .023 25 _ _ _ 1.247 1.438 1.153 .008 period than the utilization index used 26 1.616 1.624 1.005 .070 in our original study (which rose at 10.6 27 . . 1.833 2.385 1.301 .034 28 _- ---- _ _ . _ . _ 1.552 1.769 1.140 .122 percent per year). 29 1.537 1. 765 1. 148 .069 30 1.554 1.579 1.016 .024 Denison suggests that the weighting 31 1.158 1.335 1.153 .004 of utilization estimates for industry 32 1. 529 1.447 .944 .055 33 . 1.289 1.394 1.081 .165 groups should be done by something 34 1.289 1.488 1.154 .049 35 and 36 1.344 1. 713 1.275 .119 other than the total horsepower of 37 1.173 1.505 1. 283 .076 electric motors. Since we use it as a 38 1.234 2.187 1.773 .012 39 and 19 1.082 1.336 1.235 014 proxy for the utilization of all capital, Total/ 1.386 1.567 1.131 the appropriate weights would be Total weighted * 1.135 estimates of the value of capital services a "Two digit" manufacturing industries. Industry 23 <* Utilization: column 2/cclumn 1. at the two-digit level. The closest we apparel, excluded because no horsepower figures were asked e 1962 fixed assets weights computed from 1964 Annual Sur- for in 1954. vey of Manufactures [6], M 65 (AS)—6. can come to it is to use weights based ^Horsepower of electric motors from 1963 Census of Manu- /Numbers differ from Table X in Jorgenson and Griliches factures [7], "Power Equipment in Manufacturing Industries [60], because no allowance cculd be made at the two-digit on the of total fixed assets as of December 31,1962", MC 63 (1)—6, table 2. level for electricity consumption in nuclear energy installa- «Electricity, total purchased and generated minus sold, tions. The comparable utilization index for total manufac- in 1962. Recomputing our estimates from 1963 Census of Manvjactures [7], "Fuels and Electric turing allowing for this is 1.111. Energy Consumed in Manufacturing Industries: 1962". MC «S (column 3Xcolumn 4)/0.987, where 0.987=S column 4. separately for each two-digit industry 63 (1)—7, table 3. and then weighting them with these weights doesn't really change the num- Table 13.—Equipment Utilization Indexes, Mining Industries, 1963 (1954=100) bers significantly (see table 12). If Horsepower Electricity Utilization Depreciable anything, it makes them slightly higher. of electric consumption b index e assets Industry motors a weights d The same is also true for mining during (1) (2) (3) (4) the 1954 to 1963 period (see table 13). The resulting weighted utilization index Metal mining 111. 3 175. 0 157.2 0.246 is still quite high and of the same order Anthracite 42.4 51.7 122.0 '.014 of magnitude as the manufacturing Bituminous coal . 99.4 134.5 135.3 « .134 one (if allowance is made for the Oil and gas 224. 0 229.6 102.5 .432 cyclical difference between 1963 and Nonmetallic minerals 152 2 156 9 103.1 .174 1962). We conclude, therefore, that the unweighted figures we used are rather Total mining 126 6 149 3 117 9 close to what the weighted figures Adjusted f 117. 6 would have been had we computed Weighted . s 120.7 them. « 1963 Census of Mining [8], Chapter 7, table 1. • Total "coal mining" weight allocated on the basis of 1954 Thus, except for the over-estimate * 1963 Census of Mining [8], Chapter 6, table 1; purchased data for total capital given in Creamer [22], table B-ll, p. 318. and used. /Adjusted for a small implied change in percentage of of the rate of change of utilization from c Column 2/column 1. electric power used by electric motors (from 93.5 to 93.3) us- <* From U.S. Internal Revenue Service, 1968 Statistics of ing the 1945 percentages given by Foss [33] and the 1954 and 1945 to 1954, our estimates appear to Income [55], Corporation Income Tax Returns, table 37, col. 1963 total electricity consumption as weights. 3, p. 264. * S (column 3 x column 4). be reasonably good estimates of the May 1972 SUEVEY OF CURRENT BUSINESS 75

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Table 14.—Selected Utilization Measures 4.3. Actual and potential capital services Cotton broad Cotton-system Manmade fiber woven goods: spindle hours broadwoven Average loom per spindle goods: Average Year hours per loom in place b loom hours per The index of relative utilization used in place « loom in place ° in this paper is given in table 15. Since the value of the capital service flow as 1947 ...... - _ . 5 042 5 074 5 220 1948 -- 5,161 5 305 5 408 1949 4 689 4 433 4 991 we have measured is independent of the 1950 5 547 5 048 5 532 rate of utilization, we define a price and 1951 5 276 5 823 5 045 1952 5 046 4 919 4 970 quantity index of actual capital serv- 1953 5 579 5 513 5 240 1954 5,431 5 141 4 802 ices as price and quantity indexes of 1955 _ - _ 5,658 5 501 5 326 potential capital services, divided and 1956 .- 5,837 5,783 5 036 1957 ------5,425 5,512 5 463 multiplied, respectively, by our index 1958 5 499 5 311 5 397 1959 6 114 5 853 5 718 of relative utilization. Price and quan- 1960 6,145 6,216 5 844 1961 6,020 5,830 5 717 tity indexes of actual capital services 1962 -_- . _ . ' . ._ 6, 061 6,283 6 042 1963 6,124 6, 074 6, 105 for corporate and noncorporate sectors 1964 . - _ 6,450 6,243 6,412 and price and quantity indexes of actual 1965 ----- . . 6,741 6,489 6,513 capital services for the private domestic Rates of growth, percent per year: 1950-62 0.8 1.8 0.7 economy for 1950-62 are also presented 1947-65 1.6 1.4 1.7 in table 15. ° Computed from various issues of Current Industrial average hours per loom per week from the American Textile Reports [12], series M22T.1 and M22T.2. 1947-1953: Looms Manufacturers Institute [2], for manmade fibers based on To provide the basis for comparison in place are averages of quarterly data as of the end of the looms in place at the end of 1964. quarter; 1954-64: Looms in place are averages of beginning & Bureau of the Census, Cotton Production and Distribution of sources of growth of capital input and of year figures; 1965 for cotton broadwoven goods ex- [11], page 37. This is a more variable series, since the denom- trapolated on the basis of averages of monthly data on inator is available only once during each year. with those for labor input, we present data on capital stock, potential service rate of utilization of electric motors in the residential housing, land, and inven- flow per unit of capital stock, and the manufacturing. Similar estimates were tories components by this measure of relative utilization of capital in table 16. presented for mining in table 13. An . Until better evi- Capital stock is a Divisia index of capi- entirely different set of estimates, based dence comes along, however, we are tal stock for each class of asset—con- on actual machine-hours worked for willing to hazard the very strong sumers7 durables, nonresidential struc- three textile subindustries, is presented assumption that the capacity utilization tures, producers' durables, residential in table 14. They, too, indicate an of all business equipment and structures structures, nonfarm inventories, farm upward trend in utilization in the post- may be approximated by our estimate inventories, and land. The potential World War II period of about the of capacity utilization of power-driven service flow per unit of capital stock same order of magnitude. Thus, there equipment in manufacturing (and min- is the ratio of the quantity of potential is something in these data. They are ing) . Business equipment and structures gross private domestic capital input measuring something, at least as far account for about 46 percent of our as the utilization of electic motors in total capital input. Applying this to from table 11 to the index of capital manufacturing and mining is concerned. the reduced rate of growth in utilization stock. The relative utilization of capital Given our data, it was an error on leads to a utilization adjustment on is the ratio of the quantity of actual to our part (and on the part of those who the order of 16 percent of our previous potential gross private domestic capital preceded us on this path) to adjust adjustment. input.

Table 15.—Actual Gross Private Domestic Capital Input, 1950-62 (Constant Prices of 1958)

Corporate capital Corporate capital Noncorporate Noncorporate Private domestic Private domestic Index of input, quantity input, price capital input, capital input, capital input, capital input, relative Year index index quantity index price index quantity index price index utilization (biUions of 1958 (1958=1.000) (billions of 1958 (1958=1.000) (billions of 1958 (1958=1.000) (1958=1.000) dollars) dollars) dollars)

1950 49.5 0.981 35.9 0.870 124.1 0.908 1.065 1951 ....- _ . 53.2 1.034 37.9 .991 134. 5 .965 1.092 1952 . „ 55.2 .977 38.5 .947 139.7 .959 1.046 1953 59.4 .938 39.8 .903 147. 4 .932 1.098 1954 58.4 .958 39.3 .920 148.9 .955 1. 020 1955 63.5 1.061 41 2 .896 158.6 .996 1.105 1956 . . 66.6 1.024 42.1 .827 167. 1 .971 1.105 1957 68.4 1.027 41.9 .883 171.9 .983 1.065 1958 . 67.8 1. 000 41.2 1. 000 173.1 1. 000 1.000 1959 73 6 1 078 43 4 .887 182.5 1.028 1.092 1960 76 3 1 040 44 2 .850 189 0 1. 024 1.098 1961 78 2 1 042 44 5 902 194 1 1.043 1.085 1962__ 83.0 1 097 46.0 962 202.3 1. 091 1. 137

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Table 16.—Gross Private Domestic Capital Input, 1950-62 (Constant Prices of 1958) race-region category and about 1 per-

Private domestic Potential capital Relative utilization cent to the changing mix of these Year capital stock input per unit of of capital categories. In this case, a more de- (billions of 1958 capital stock (1958=1.000) dollars) (percent) tailed quality calculation for men produced a higher correction than the 1950. _ . . 964.6 0.126 1.024 1951 1021 4 127 1 035 simple overall measure used by us. 1952 1068 5 128 1. 018 All this is just intended to indicate our 1953 „• .._.,.„_ 1100. 3 .129 1.037 1954 1134 6 130 1 007 belief that if we had developed a 1955 _ - 1163. 2 . 131 1. 040 really detailed age-sex-race-region-edu- 1956 1213 9 132 1 040 1957 1255 5 133 1 026 cation correction, it would as likely as 1958 - . 1287 9 134 1 000 not result in a higher rate of growth of 1959 _. 1305. 8 135 1 038 1960 1341 4 135 1 040 labor input than was estimated by us 1961 1373 9 136 1 035 originally. 1962 1399. 1 137 1 055 5.2. Hours of work Up to this point we have proceeded on the assumption that hours per man changed at the same rate for all cate- 5. Measurement of Labor Input gories of labor. If this is not the case, a more detailed labor input index is called for. The rate of growth in total labor should be measured by S.I. Introduction effect on our estimates.29 There has The labor input series used in this been, however, an increase in the paper have also been borrowed from proportion of women in the labor Chris tensen and Jorgenson. They are force. We investigated the magnitude very similar to our original series of an appropriate adjustment for this, where nt is the number of workers in except for the correction of an error using data on the average shares of the ith category, ht are the hours per in our original persons engaged series men and women in total earnings man worked by men in this category, (it did not contain unpaid family during the years 1958-64, and the and workers) and the use of quality adjust- number of men and women employed ments as extended by Griliches.27 The in 1950 and 1958. The resulting adjust- Christensen-Jorgenson series add Ken- ment is somewhat smaller but of the is the share of the ith category of labor drick's estimates of unpaid family same order of magnitude as that in total labor payments (w^wage per reported by Denison for 1950-62.30 workers to the QBE data on full-time hour and yi=wihi= total earnings per equivalent employees and proprietors We also attempted to estimate a man-year). ^ Adding and subtracting to arrive at a total persons engaged more detailed quality adjustment for .N/N and H/H, the rate of growth in measure. Total man-hours in the private men for the 1950-60 period, allowing total employment and the rate of domestic sector are also based on for changes in education, age, race, 28 growth in average hours worked per Kendrick's series. and region (South and non-South). The man, respectively, we can write Christensen and Jorgenson incorpo- basic data for this calculation were rate our original adjustment for the taken from Miller's monograph [65] quality of the labor force based on the and the associated Census volumes and changing distribution of the labor force refer to the population of men "with by years of school completed. They do income'7, between the ages of 25 and not adjust, however, for the changing 65. For this population, using the age-sex distribution of the labor force. average of 1950 and 1960 income An examination of the underlying labor shares as weights, a straight education force data indicates that there has been adjustment using average incomes by little relevant change in the age dis- education for the population as a tribution of the employed in the whole leads to an estimated 8.7 percent 1950-62 period. There has been some improvement in "quality." Using sep- where ei=nt/N is the relative fraction relative increase in the number of arate weights by region, race, age, and of employment accounted for by the young people in the labor force which education leads to an estimated 12 ith category and m^hi/H is its rel- has been largely counterbalanced by a percent rise in total labor quality, of ative employment intensity (per year). decline in the proportion of older which about 11 percent is due to the E/E is then the rate of growth of (above 65) employees. A pure age average improvement in the educa- average labor "quality" per man while adjustment would have a very minor tional distribution within each age- M/M is the rate of growth in the May 1972 SUEVEY OF CURRENT BUSINESS 77

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relative quality of the average hour. In the 1950 and 1960 Censuses of Popula- This, however, is somewhat of an over- our original computations we left out tion [9, 10] were not cross-classified by estimate, since during the 1950-60 the M/M term, assuming that all hours education and hence we cannot con- period (the only one for which we have changed proportionately. To the extent struct a comparable M/M index. Some data) a similar measure of "quality" that there has been a secula- idea, however, of the direction and of weeks worked deteriorated at about lar improvement in the employment cTrder of magnitude of such an adjust- —0.04 percent per year (see table 18). experience of the educated versus ment can be gathered from scattered That is, while the decline of hours was uneducated, our index actually under- data on hours worked by occupation. relatively smaller for some of the estimates the "quality" improvement These are summarized in table 17 and "higher quality" categories, this was in the total labor force. imply about a 0.2 percent rate of counterbalanced to some extent by the Unfortunately, the published data on growth per annum in the quality of the improved annual employment experi- hours and weeks worked per man from average hour during the 1950-65 period. ence of several of the less well paid occupations. On net we would estimate Table 17.—Average Hours Worked Per Week by Employed Persons at Work M/M ^0.16, which if multiplied by the average labor share would more than Occupation 1950 « 1960° 1960 & 1965 * 1959 counterbalance (0.11 versus —0.09) the weights e estimated decline in overall quality of the labor force due to the increased Total 44.6 43.2 40.5 40.5 participation of females. Professional, technical, and kindred 44.1 46.9 41.3 41.4 .167 Many of these adjustments are small Farmers and farm managers 60.0 54.2 52.0 52.1 .031 Managers, etc., except farm 51.7 49.3 49.5 49.4 .192 and well within the range of possible Clerical and kindred __ 41.3 40.8 37.6 37.4 .062 error in the data. We conclude, never- Sales workers 45.1 42.9 38.2 37.8 .077 theless, that our original estimate of Craftsmen, etc ______41.6 42.1 41.0 42.3 .214 Operatives and kindred ______42.0 42.2 40.3 41.2 .169 the rate of growth of total labor input Private household workers 40.8 32.8 26.6 24.1 .003 stands up rather well under reexamina- Service workers except private household 44.7 41.9 38.7 37.8 .037 tion and that a more thorough and Farm laborers and foremen 48.5 43.2 39.3 39.4 .007 Laborers except farm and mine 39.3 37.1 35.9 35.5 .041 detailed analysis would in all likelihood result in a higher rather than lower 0 Employed males. 1950 data computed from table 5, page 42, of Finegan [30], The separate figures for self-employed and wage and salary workers were averaged using the numbers given in 1950 Census of Population [9], Occupational Characteristics, figure. tables 14 and 15. The 1960 data are from 1960 U.S. Census of Population [10], Occupational Characteristics, table 13. Average hours for farm and service workers estimated for 1950 using Finegan's procedures. Both average hours figures are for the Census survey week. & All persons at work, annual average, from Bureau of Labor Statistics, Special Labor Force Reports [16], 14 and 69. 5.3. Price and quantity of labor 6 Computed from data on mean earnings of males 18 to 64 years of age and on the number of such males with earnings in services 1959, from 1960 U.S. Census Population [10], Occupation by Earnings and Education. The service weight allocated between private household workers and other workers using median incomes from the Occupational Characteristics volume. Bate of growth of quality of average hours per man: The assumption that effective labor per annum services are proportional to the stock hit HTt . 1950-60 _ 2.30 6723 Wi hit-i HTI-I' 1960-65 _ ___.79 .16 of labor is obviously incorrect. On the other hand the assumption that effective Table 18.—Average Weeks Worked by Males in the Experienced Civilian Labor Force0 labor services can be measured directly from data on man-hours is equally in- correct, as Denison [24] has pointed out. Occupation 1949 1959 The intensity of effort varies with the

Total 45.1 45.6 number of hours worked per week, so that effective labor input can be Professional 46.9 47.6 measured accurately only if data on Fanners and farm managers 47.4 47.7 man-hours are corrected for the effects Managers 48.6 49.6 of variations in the number of hours per Clerical 46.7 46.5 man on effective labor input. Denison Sales workers 46.0 46.3 [26] suggests that the stock of labor Craftsmen, _ 45.4 46.2 provides an upper bound for effective Operatives 44.1 44.9 labor services while the number of Private household workers 41.7 37.4 man-hours provides a lower bound. He Service, except private household 44.7 37.4 estimates effective labor input by Farm laborers - 40.2 38.6 correcting man-hours for variations in Laborers, except farm 41.0 39.7 labor intensity. We employ Denison's correction for intensity, but we apply "Average for those who worked in the particular year. Computed from the Occupational Characteristics volumes of the 1950 and 1960 Censuses of Population [9,10]. Midpoints used: 50-52: 51; 40-49: 45; 27-39: 33; 14-26: 20; and 1-13: 7. this correction to actual hours per man Rate of growth of quality of average week worked, using weights from table 17, can be computed as follows: rather than potential hours per man, as in our original study. Our current measure of labor services 78 SURVEY OF CURRENT BUSINESS May 1972

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Table 19.—Private Domestic Labor Input, 1950-62 data on labor input—number of per- sons engaged, educational attainment Educational Private domestic Private domestic Private domestic Private domestic attainment per hours per person Effective labor labor input, labor input, per person, and hours per person—are Year persons engaged person (index) (thousands per input per hour quantity index price index (millions) (1958=1.000) year) (1958=1.000) (billions of 1958 (1958=1.000) presented in table 19. The correspond- dollars) ing data on capital input—capital stock, potential service flow per unit of 1950 52. 972 0.948 2.197 0.978 228. 8 0.683 1951 55. 101 .954 2.185 .981 239.0 .742 stock, and the relative utilization of .980 241.7 .782 1952 55. 385 .960 2.187 capital—are presented in table 15. 1953 56. 226 .965 2.159 .986 245.2 .827 1954 54. 387 .971 2.139 .990 237.4 .846 The index of educational attainment per 2.161 .986 245.9 .880 1955 55. 718 .977 person provides an adjustment of 1956 56. 770 .982 2.151 .988 251.6 .930 1957 56.809 .988 2.121 .995 251.5 .978 persons engaged for the aggregation 2.099 1.000 245.1 1.000 1958 55. 023 1.000 bias that results from combining dif- 1959 56. 215 1.012 2.122 .995 254.9 1.042 1960 56. 743 1.020 2.126 .994 259.6 1.074 ferent types of labor into an un- 1961 56. 211 1.028 2.110 .998 258.1 1.103 weighted aggregate. Similarly, capital 1962 57. 078 1.036 2. 117 .996 264.6 1.144 stock is an unweighted aggregate; the index of potential capital services per unit of the capital stock provides an is based on the stock of labor as meas- implicit in private domestic labor com- adjustment for aggregation bias. Po- ured by persons engaged, adjusted for pensation is also given in table 19. It tential capital services must be adjusted effective hours per person and for would obviously be desirable to incor- for relative utilization to obtain the changes in the composition of the labor porate additional aspects of labor force actual flow of capital services. We con- force by educational attainment. The composition in adjusting the stock of struct price and quantity index num- cost of labor services index is calcu- labor for quality change. It would also bers of factor input by combining lated by dividing total labor compensa- be desirable to adjust the number of Divisia indexes of labor and capital tion by the quantity index of labor hours per man for changes in the rela- input into a Divisia index of total services. The number of persons en- tive number of hours worked by persons factor input. Price and quantity in- gaged, the index of quality change, differing in educational attainment. But dexes for 1950-62 are given in table 20. actual hours per worker, effective labor as outlined above, this would require The relative share of property compen- input per man-hour, and the quantity a data base that is much more sation for the same period is also given of labor input for 1950-62 are given in detailed than anything currently in table 20. table 19. The price of labor services available. To provide a detailed accounting for the sources of growth in real factor input, we can separate the growth of quantity indexes of labor and capital input into the growth of the stock, 6. growth in the quantity of input due to shifts in composition of such unweighted aggregates as persons engaged and cap- ital stock or "quality change",31 and 6.1. Introduction economy we combine estimates of growth in relative utilization. The Total factor productivity is defined labor and capital input. The basic growth in labor input is the sum of as the ratio of real product to real factor input, or equivalently, as the ratio of the price of factor input to the product Table 20.—Gross Private Domestic Factor Input, 1950-62 (Constant Prices of 1958) price. Growth in total factor produc- Gross private domestic factor Gross private Property compen- tivity has a counterpart in growth of the Year input, quantity domestic factor sation, relative index input, price index share price of factor input relative to the price (billions of 1958 (1958=1.000) (percent) of output. We may define a Divisia dollars) index of total factor productivity, say 1950 350 0 0 768 0 419 P, as: 1951 371 3 827 423 1952 379.8 .850 .415 1953 .. _ 391 5 869 404 log *-= log _ log 1954 385 6 .889 .414 rt__i x t__i - 1955 404.3 .926 .422 1956 418 7 947 410 where F is the quantity index of total 1957. . 423 4 .980 .407 product and X is the quantity index of 1958 418.2 1.000 .414 1959 437 4 1 036 414 total factor input. I960.. 448.5 1.053 .410 To obtain an estimate of real factor 1961 452 0 1 077 .415 input for the U.S. private domestic 1962 466.5 1.122 .422

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growth in the number of persons services for sectors distinguished by used.33 Denison also adjusts man-hours engaged, the quality of the labor force, legal form of organization in order to for changes in labor efficiency that and the effective number of hours per provide a more detailed representation accompany changes in hours per man.34 person. The growth in capital input is of the tax structure. These differences Solow uses unweighted man-hours, , the sum of growth in capital stock, the have an important impact on the omitting the effects of changes in the quality of capital, and relative utiliza- estimate of total factor productivity. composition of the labor force on the tion. Geometric average annual rates quantity of labor input.35 Kendrick of growth for 1950-62 are given for 6.2. Alternative measures of adjusts labor and capital input for each component of the growth of labor productivity change changes in the industrial composition and capital input in table 21. To provide a basis for comparison of of labor force and capital stock.36 our estimate of total factor produc- However, changes within an industial Table 21.—Sources of Growth in Factor tivity with estimates that result from sector due to shifts in composition are Input, 1950-62 alternative conventions for the measure- not included in his measures of real [Annual percentage rates of growth] ment of real factor input, we present a factor input. 1. Capital input: number of variants based on alternative We present measures of total factor a. Stock 3.14 accounting conventions. We begin with productivity based on potential service b. Quality change..__.._ _-_.. . 70 c. Relative utilization .25 an estimate of total factor productivity flows and o^ stocks of labor and capital 2. Labor input: based on the actual flow of labor and in table 22. The first variant on our a. Stock . .63 capital services. We compare this esti- estimate of total factor productivity b. Quality change.- .7*5 c. Relative utilization '.___ —.16 mate with alternatives based on poten- omits the relative utilization adjustment tial flows of labor and capital services for capital, the second the relative and on stocks of labor and capital. utilization adjustment for labor; the Price and quantity indexes of output The services of consumers' durables and second variant is based on potential are given above in table 3. The index producers' durables used by institutions service flows for both labor and capital of total factor productivity for 1950-62 are allocated directly to final demand so input. The third variant omits the corresponding to the quantity index of that growth in the quantities of these quality adjustment for capital, while output from table 3 and the quantity services does not affect growth of total the fourth omits the quality adjust- index of gross private domestic factor factor productivity. Similarly, the serv- ment for labor, providing a stock meas- input from table 20 is given in table 22. ices of owner-occupied dwellings and ure of total factor productivity. Two The conventions for measurement of institutional structures are allocated final variants provide combinations of factor services underlying our concept directly to final demand. alternative measures of labor input of gross private domestic factor input Kendrick and Solow use a stock with the stock measure of capital. were employed in our original study. concept of capital input, measuring The fifth combines actual labor input Our revised estimates, based on those neither changes in relative utilization with the stock of capital, while the of Christensen and Jorgenson, differ nor changes in the quality of capital sixth combines unweighted actual man- in two significant respects: First, we services due to changes in the compo- hours with capital stock, It is obvious have converted the index of relative sition of the capital stock.32 Denison from a comparison of the alternative utilization to an annual basis and weights persons engaged by an index of estimates of total factor productivity reduced the scope of adjustments of labor quality that incorporates the given in table 22 that the results are potential flows of capital services for effects of growth in educational attain- highly sensitive to the choice of con- changes in relative utilization. Second, ment but differs in a number of impor- ventions for measuring real factor input we have measured the flow of capital tant respects from the index we have The effects of varying the convention

Table 22.—Total Factor Productivity, 1950-62 (1958=1.000)

Actual labor Potential labor Potential labor Actual labor Unweighted Year Labor and services; and capital services; Labor and services; man-hours; capital services potential services capital stock capital stock capital stock capital stock capital services

1950 . 0.939 0.948 0.961 0 935 0.906 0 922 0.882 1951 946 960 971 949 923 938 .902 1952 .949 956 967 949 927 938 .904 1953 ._ - .968 .982 .990 .974 .954 : .966 .938 1954 ., .974 .977 .982 .969 .953 .964 .942 1955 1 006 1 022 1 031 1 020 1 006 1 012 989 1956 994 1 010 1 018 1 Oil 1 001 1. 004 .986 1957 998 1 009 1 012 1 009 1 002 1 006 .996 1958 1 000 1 000 1 000 1 000 1 000 1 000 1. 000 1959____ 1.019 1.034 1 038 1 039 1 046 1.035 1. 039 1960 1. 019 1.036 1 040 1 043 1 056 1.039 1.048 1961 1.031 1.046 1 048 1 054 1 072 1.053 1. 068 1962 1. 062 1.086 1.088 1 097 1 120 1.094 1. 114

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are summarized for the period 1950-62 1950-62. The resulting estimates of the that total factor productivity grows at in table 23; geometric average annual distribution of the growth of real 1.37 percent per year, not adjusted for rates of growth are given for each product between growth in real factor intensity of demand. We find that es- variant of total factor productivity. input and total factor productivity are timates of real factor input based on comparable to those of Solow's earlier our data suggest that total factor pro- Table 23.—Growth in Total Factor study. On the basis of our data and ductivity grows at the average rate of Productivity, 1950-62 Solow's conventions total factor pro- 1.44 percent per year while real factor [Average annual rates of growth] ductivity grows at the average rate of input grows at 2.03 percent per year. 1.96 percent per year while real factor The discrepancy between estimates 1. Actual labor and capital services ...._._____ 1.03 2. Actual labor services; potential capital services.-__ 1.14 input grows at 1.51 percent per year. based on our conventions, given in 3. Potential labor and capital services 1.04 Our estimates, given in table 24, are table 23, and those based on capital 4. Potential labor services; capitalstock _ ___ 1.34 that total factor productivity grows at stock and actual labor input is ac- 5. Labor and capital stock ___ 1.78 6. Actual labor services; capital stock 1.44 1.03 percent per year and real factor counted for almost entirely by our 7. Man-hours and capital stock _ _ 1.96 input at the rate of 2.42 percent per adjustments of the measure of capital year. input for quality change and relative We also present estimates of real utilization. Denison has incorporated 6,3. Sources of U.S. economic factor input based on capital stock and about half the growth in real factor growth, 1950-62 actual labor input, which provide the input over and above the growth of best approximation to the conventions capital stock and actual man-hours Finally, to evaluate the relative im- adopted by Denison [28]. Denison finds into his estimates of real factor input. portance of growth in real factor input and growth in total factor productivity as sources of , we con- sider the relative proportion of growth in real factor input. Geometric average 7. Major Issues in Growth Accounting annual rates of growth are given for real product and real factor input for 1950- 62 in table 24. The relative proportion of growth in total factor productivity 7.1. Introduction approach, and our own approach. We in the growth of real product is also Denison has examined our approach have concentrated on the period provided. to productivity measurement in his 1950-62 employed by Denison in his We find that the growth in real factor paper, "Some Major Issues in Produc- most recent study, Why Growth Rates input predominates in the explanation tivity Analysis: An Examination of Differ [28]. For convenience of the of the growth of real product for the Estimates by Jorgenson and Griliches" reader we follow the order of topics in Denison's paper [25]. period 1950-62. These findings are di- [25]. Denison's detailed examination of rectly contrary to those of Abramovitz our estimates contributes significantly 7.2. Scope of product to the definition of unresolved issues We begin our examination of the [1], Kendrick [61, 62] and Solow [70] in the measurement of total factor pro- issues raised by Denison with an anal- in earlier studies of productivity change. ductivity. This contribution is especial- ysis of the effects of the concept of real We have estimated real factor input on ly valuable in view of the underlying product on the measurement of pro- the basis of capital stock and actual agreement between our objectives and ductivity change. Denison regards both man-hours, the conventions used by Denison's objectives in his pathbreaking gross and net product measures as Solow and subsequently adopted by studies of productivity change [26, 28]. legitimate for productivity analysis,37 Arrow, Chenery, Minhas, and Solow [3], Although the basic agreement between our objectives in productivity measure- but gives priority to the net product ment and Denison's is reassuring, im- measure: "Insofar as a larger output Table 24.—The Relative Importance of Pro- is a proper goal of society and objective ductivity Change, 1950-62 portant differences in methods of meas- of policy, it is net product that measures [Average annual rates of growth] urement and in substantive conclusions remain. the degree of success in achieving this Gross private domestic product: We have attempted to indicate the goal. Gross product is larger by the Heal product 3.47 quantitative magnitude of disagreement value of capital consumption. There is Real factor input. _.____. 2.42 no more reason to wish to maximize between Denison's estimates of total Capital input: capital consumption—the quantity of Stock 1.30 factor productivity and ours by rework- Quality change .30 capital goods used up in production— Relative utilization. .11 ing our estimates in order to provide a Labor input: than there is to maximize the quan- Stock .37 direct comparison among the results of Quality change. .44 tity of any other intermediate prod- Relative utilization .___• -.10 three different approaches to the meas- uct . . ,"38. Total factor productivity 1.03 urement of total factor productivity— The first problem with Denison's Relative proportion of productivity change .30 the conventional approach, Denison's argument is that the difference be- May 1972 SURVEY OF CURKENT BUSINESS 81

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tween gross product and net product solute contribution of productivity represent gross value added from the is equal to depreciation, while the change is the same for gross product producers' point of view we suppose for quantity of capital goods used up in from the producers' point of view, gross simplicity that tax depreciation and production is equal to replacement. product at factor cost, and net product. economic depreciation are the same. Depreciation is equal to replacement if The difference between gross product Under this simplifying assumption the and only if the decline in efficiency of from the producers' point of view and price of capital services may be capital goods is geometric. Under gross product at factor cost is indirect written:42 Denison's characterization of decline in taxes on factors of production, such as efficiency, depreciation is not equal to property taxes. These taxes appear as replacement, so that Denison's argu- part of both output and input and leave ment is internally contradictory. 39 the absolute contribution of productiv- where p is the (before-tax) rate of This contradiction can be removed by ity change unaffected. The difference return, /* the rate of depreciation, and defining net product as gross product between gross product and net product less depreciation. r the rate of indirect taxation of is depreciation. Depreciation also ap- property. The accounting identity may In the estimates of productivity pears as part of both output and input, then be rewritten: change given in Section 6 above, the leaving the contribution of productivity decline in efficiency of capital goods change unaffected. Problems that arise is assumed to be geometric so that in measuring the depreciation compo- - K+pLL. depreciation and replacement are equal. nent of gross capital input also arise in Our product measure is gross product measuring depreciation to convert gross Identifying the change in the aggre- from the producers' point of view. product to net product. The data gate quantity of output with the sum Under our assumptions, Denison's argu- required for measurement of gross of changes in consumption and invest- ment justifying net product as a product product from the producers' point of ment goods output, evaluated at cur- measure is irrelevant to productivity view, gross product at factor cost, and rent prices, and defining the change in measurement. Net product is associated net product are identical. aggregate input similarly, the absolute with precisely the same measure of The absolute contribution of produc- contribution of productivity change the absolute contribution of produc- tivity change to the growth of real may be represented in the form : tivity change as gross product from output is the difference between changes the producers' point of view. Deni- in output and changes in input, both - K-pLL son's argument provides no basis for evaluated at current prices ; this is equal discriminating between net and gross to the difference between changes in the To obtain corresponding measures of product as a basis for productivity prices of output and input, each measurement. Furthermore, the meas- the contribution of productivity change multiplied by the corresponding quan- for alternative concepts of social prod- ure of the absolute contribution of tity: productivity change is the same for uct, we first derive gross product at our measure of gross product and for qY-pX=pX-qY. factor cost by subtracting the value of gross product at factor cost, the gross property taxes from both sides of the product concept Denison prefers for The relative contribution of productiv- basic accounting identity, obtaining : productivity analysis.40 ity change, say PjPj is obtained by The contribution of productivity dividing the absolute contribution by change may be expressed as the absolute the value of output (or input) : amount of growth in real product Defining the absolute contribution of accounted for by changes in produc- P=qY~pX=g_Y pX=Y X productivity change as before we tivity.41 This contribution is equal to P~ qY ~~qY pX Y X obtain: the difference between period to period changes in real product and changes in Dividing output between consump- real factor input. The contribution of tion and investment goods and input productivity change may be expressed between capital and labor services, the relative to any of the alternative identity between the value of output concepts of real product, gross product and the value of input may be written: from the producers' point of view, which is identical to the contribution gross product at factor cost, and net of productivity change for gross prod- product. Alternative measures of rela- uct from the producers' point of tive productivity change differ only in where O and / are quantities of con- view. the concept of real product employed, sumption and investment goods and Second, we derive net product by not in the measure of the absolute K and L are quantities of capital and subtracting the value of depreciation contribution of productivity change. labor input. The corresponding prices from both sides of the identity given We first demonstrate that the ab- are denoted gc, g/, pK, and pL. 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ure covers the private domestic econ- quantities [F/] of the m components. omy, incorporating the services of Differentiating the value of output durables used by households and insti- totally with respect to time and divid- tutions along with the services of ing both sides by total value, The resulting measure of the absolute structures used in this sector. Our contribution of productivity change is original product measure did not include the same as for gross value added: the services of durables used by house- holds and institutions. Denison covers the entire national economy. Our re- weights [wt] are the relative shares of vised product measure provides for a the value of the ith output: more satisfactory treatment of indirect taxes. It also treats durables sym- metrically with structures in the house- hold sector. We define the price and quantity in- To reconcile our revised product dexes of output as weighted averages of measure with Denison's it would be- We conclude that the measure of rates of growth of prices and quan- necessary to exclude the services of productivity change in absolute terms tities of individual components: is the same for all three concepts of durables used by households and in- real product we have considered — stitutions and to eliminate indirect gross product from the producers' taxes and depreciation at replacement point of view, gross product at factor cost. The product of government and rest of the world sectors would have to cost, and net product. The absolute obtaining Divisia price and quantity be added. None of these changes would 43 contribution of productivity change indexes. Rates of growth of the Divisia alter our estimate of the absolute con- may be expressed relative to any indexes of prices and quantities add up tribution of productivity change. Any measure of output. Alternative meas- to the rate of growth of the value (factor ures of relative productivity change difference in percentage rates of growth reversal test) and are symmetric in differ in the concept of output of total factor productivity would be different directions of time (time re- employed as a standard of comparison, due to the product measure relative to versal test). A Divisia index of Divisia but not in the measure of the absolute which productivity change is expressed. indexes is a Divisia index of the contribution of productivity change. The more comprehensive the product components. measure the less the relative rate of The absolute contribution of pro- For application to data for discrete growth of total factor productivity ductivity change has the important points of time an approximation to the associated with any absolute contri- property that the contribution to the continuous Divisia indexes is required. bution of productivity change. To ad- growth of the economy as a whole is Price and quantity index numbers just estimates of the relative growth of the sum of contributions to the growth originally discussed by Fisher [31] have total factor productivity based on our of individual sectors. This property is been employed for this purpose by data to a net national product basis, maintained for measures of output of Tornquist [74]: an economic sector that include inter- percentage rates of growth should be multiplied by the ratio of gross product mediate goods purchased from other log qt — log g,_! = t [log g_it — sectors, as in interindustry studies. to net national product in each period. log Si,«-i], Intermediate goods appear as real A similar adjustment can be made to convert relative rates of growth of total log Yt - log Fw , [log F« - output in the sector of origin and real log F _J, input in the sector of destination. factor productivity to any other prod- M uct measure. Changes in the output of intermediate where the weights wit are arithmetic goods cancel out in any measure of averages of the relative shares in the 7.3. Index numbers the contribution of productivity change two periods, to the economy as a whole*. To separate flows of product and In our original estimates we used factor outlay into prices and quantities, gross product at market prices; we now we introduce price and quantity index employ gross product from the pro- numbers. As an example, suppose that A discrete Divisia index of discrete ducers' point of view, which includes there are m components to the value of output, Divisia indexes is a discrete Divisia indirect taxes levied on factor outlay, index of the components. Divisia index but excludes indirect taxes levied on numbers for discrete time are also sym- 2F=2lF1+2aFa+ . . . +

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of price and quantity is approximately product at market prices included sales that differ in legal form of organization equal to the change in the logarithm of and excise taxes and customs duties in —corporate, noncorporate, and house- the value (factor reversal). It is con- the earnings of capital. Our present holds and institutions. We assume, venient to have the product of price estimates include only taxes levied on following Christensen and Jorgenson and quantity indexes equal to the income from property. This measure of [19], that the rates of return on all value of transactions, so that we con- capital earnings is the appropriate one, assets held within a given sector are the struct discrete Divisia price indexes as given our concept of gross product from same. Property income in the corporate the value in current prices divided by the producers7 point of view. The im- sector is subject to both corporate and the discrete Divisia quantity index. plied weights for labor and capital meet personal income taxes. Noncorporate The estimates of Chris tensen and Denison's objections to our original property income is subject only to the Jorgenson [19, 20] are based on a differ- treatment of indirect business taxes.47 personal income tax. The property ent discrete approximation to Divisia income of households and institutions index numbers from that employed in 7.5. Weights for components of is subject to neither tax. This new, more our original estimates; the results are capital and land detailed, asset classification enables us essentially unaffected for the period The major difference between our to meet a number of valid objections 1950-62. Denison's estimates are based measure of total factor input and Denison has raised to our original 48 on an alternative discrete approxi- Denison's is in the assignment of rela- treatment of the tax structure. mation. The three approximations ap- tive weights to components of land Our new estimates incorporate the pear to produce essentially similar re- and capital input. An ideal measure tax structure for property income in a sults. Our approximation satisfies both of capital input is strictly analogous more satisfactory way than our original time reversal and, approximately, factor to an ideal measure of labor input. estimates. Property taxes are separated reversal tests for index numbers. Both measures combine rates of growth from other earnings from capital and of individual components into an over- treated as tax deductible for income 7.4. Capital and labor weights all rate of growth, using relative shares tax purposes. Depreciation for tax The value of labor input includes of the individual components as purposes is incorporated at its present labor compensation of employees and weights. While factor shares for com- value for the lifetime of an asset, so that the self-employed. Our estimates of the ponents of labor can be estimated from the effects of accelerated depreciation labor compensation of the self-einployed data on and employment, factor are simultaneous with the adoption of are based on the assumption that aver- shares for components of capital must the depreciation provisions of the age labor compensation of the self- be imputed from accounting data on Internal Revenue Act of 1954. Our employed in each sector is equal to total property income. The problem for revised estimates also incorporate the investment tax credit adopted in 1962. average labor compensation of full-time productivity measurement is to provide equivalent employees in each sector. a practical method for carrying out this The rate of the investment tax credit and the rate of the corporate income tax This method of imputation of the labor accounting imputation. Our method of are effective rates, measured from compensation of the self-employed is imputation is described in detail in Sec- national accounting data. only one of many that have been pro- tion 3 above. Denison incorporates part of the tax posed. Our original method did not sep- Our original estimates, like those of structure implicitly by excluding prop- arate labor and property components of Denison, distinguished alternative capi- tal inputs by class of asset. For the erty taxes from his measure of social noncorporate income by industrial product. This procedure is equivalent sector. Our new method, discussed in private domestic economy we dis- tinguished among five categories of to our treatment of property taxes detail by Ghristensen [18], has the effect assets—land, residential structures, for the purposes of measuring absolute of allocating a larger share of factor nonresidential structures, equipment, productivity change. Denison's esti- outlay to capital, overcoming Denison's mates do not take explicit account of 44 and inventories. For this sector of the objection to our original method. The economy Denison distinguishes be- direct taxation of income from property. resulting rates of return in corporate tween residential and nonresidential He distinguishes among property in- and noncorporate sectors are essentially land; otherwise the breakdown of come in housing, agricultural, and all the same, taking into account the effect assets is the same. Neither of these other sectors of the economy, but this of the corporate income tax. The re- breakdowns is fully satisfactory for the breakdown of the economy does not coincide with the breakdown associated vised allocation of noncorporate income incorporation of the effects of the tax with the structure of taxation of prop- seems to us to be superior to our original structure on property income. 45 erty income. The availability of data allocation and to Denison's allocation. In our revised estimates inventories on property income by legal form of Second, the concept of gross product are allocated between farm and non- organization from the U.S. national from the producers' point of view en- farm sectors and consumers' durables accounts makes it possible to improve ables us to eliminate an error in our are introduced as a new and separate on Denison's treatment of property original allocation of indirect tax lia- class of assets. Each of the seven classes income and on our original estimates. bility.46 Our original concept of gross of assets is then allocated among sectors We conclude that Denison's classifica- 84 SURVEY OF CURRENT BUSINESS May 1972

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tion of assets, like our original classifica- taken into account in allocating pro- pattern of the service flow. We assume tion, fails to capture differences in perty income among capital assets and, that the relative efficiency of the ith direct taxation of property income for implicitly, among individual wealth investment good may be described by a enterprises that differ in legal form of holders. The changes in the value of sequence of nonnegative numbers, organization. Denison's estimates of assets that enter individual and national property income fail to incorporate wealth accounts must be consistent depreciation for tax purposes and the with the property income attributed to investment tax credit in a satisfactory those assets in individual and national Denison points out, correctly, that way. income accounts. The use of real rates a capital input measure depends on the The rates of return included in our of return is necessitated by internal relative efficiency of capital goods of capital service prices are real rates of consistency of the complete system of different ages: return rather than nominal rates of national accounts. Capital gains should In principle, the selection of a return. Nominal rates are assumed to be incorporated into the allocation capital input measure should de- be the same for all assets within a of property income among classes of pend on the changes that occur in given sector. Real rates differ by assets. Denison is in error, not only the ability of a capital good to differentials between rates of growth in failing to take capital gains into contribute to net production as of asset prices for different classes of account in measuring income from the good grows older (within the assets. The allocation of property land, but in omitting capital gains in span of its economic life). Use of income among asset classes depends on measuring income from other assets.51 net stock, with depreciation com- differentials among rates of growth We conclude that Denison's proposed puted by the straight line formula, of prices. If all asset prices are growing allocation of property income among would imply that this ability drops at the same rate, real rates of return assets is inconsistent with the integra- very rapidly — that it is reduced by are the same for all assets within tion of property income into indi- one-fourth when one-fourth of the service life has passed, and by each sector. Denison objects to the vidual and national accounts for saving use of real rates of return on the nine-tenths when nine-tenths of and wealth. the service life has passed. Use of grounds that price changes in assets Finally, Denison defends Kendrick's other than land are always unantici- gross stock would imply that this 49 exclusion of depreciation on the grounds ability is constant throughout the pated. His proposed procedure would 55 amount to ignoring differentials among that Kendrick uses net product and net service life of a capital good. assets other than land and to setting earnings from capital in measuring Denison argues, further, that: 52 the differential between land and other total factor productivity. Actually, I believe that net value typically assets equal to the rate of growth of Kendrick employs both net and gross declines more rapidly than does land prices. For the 1950-62 period measures of output and uses net earn- the ability of a capital good to land prices grow more rapidly than ings for allocating property income for contribute to production. . . . On other asset prices, but there is sub- both, which is the error we originally the other hand, the gross stock assumption of constant services stantial in the price of struc- pointed out.53 Denison is in error in tures and producers' durables. On the throughout the life of an asset is asserting that we recommend the inclu- extreme. 56 other hand the price of farm inven- sion of depreciation in weights for the tories actually falls. It is clear that Under our assumption, that decline in analysis of net product and in associat- Denison's proposed procedure, or his efficiency is geometric: ing himself with Kendrick's weighting actual practice of ignoring differential 54 rates of inflation,50 introduces distor- scheme. tions in the allocation of property The most serious problem with Under Denison's gross stock assump- income among asset classes. Denison's treatment of depreciation is tion relative efficiency is constant over A serious accounting problem arises the lack of consistency between depre- the economic lifetime of the equipment : in attempting to integrate Denison's ciation as it enters his measure of real proposed allocation of property income product and the corresponding treat- dtr=i, (T-O,I, . . ., r,-i), among assets into national accounts ment of capital assets in his measure of for saving and wealth. Changes in the real factor input. In Section 3.2 above where Tt is economic lifetime of the value of national wealth are equal to we have outlined a perpetual inventory ith investment good. Under Denison's saving plus capital gains from the method for measurement of deprecia- net stock assumption, efficiency de- revaluation of assets. Saving is equal clines linearly to labor income less consumption plus tion and capital assets based on the property income less depreciation. assumption that the service flow from an investment good declines geometri- diT=l-~r These definitions hold for individual JL i wealth holders as well as for the cally. To describe Denison's method, economy as a whole. Capital gains we must generalize our treatment to from the revaluation of assets must be alternative assumptions about the time where TFT is the rate of decrease in May 1972 SURVEY OF CURRENT BUSINESS 85

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efficiency of the ith investment good with weights given by the mortality depreciation is equal to replacement, from period to period. distribution: that is, if and only if decline in efficiency Capital stock at the end of the period, is geometric. r-f-1 say Kit, is the sum of past investments, Denison measures capital consump- say {Iit t-T} each weighted by its relative r=t+l s=t+l tion allowances on the basis of Bulletin efficiency: F lives and the straight line method.58 For geometric decline in efficiency Under the assumption that relative depreciation is proportional to the asset efficiency (Denison's "ability to con- price: T = 0 tribute" to production) declines lin- early, this estimate corresponds to re- With a geometric decline in efficiency placement rather than depreciation. To we obtain the capital stock measures Depreciation and replacement must measure net product Denison reduces used in Section 3 above. With con- be carefully distinguished in order to gross product by his estimate of capital stant relative efficiency we obtain preserve consistency between the treat- consumption allowances.59 Since his Denison's gross stock measure; with ment of capital services and the estimate of capital consumption allow- linear decline in relative efficiency, we treatment of capital assets. Deprecia- ances is a measure of replacement, this obtain Denison's net stock measure. In tion is a component of the price of procedure employs the incorrect defini- Denison's study, Sources of Economic capital services. The value of capital tion of net product as consumption Growth [26], gross stock is employed as services is equal to property income, plus investment less replacement. This a measure of capital input. In Why including depreciation. Replacement is inappropriate measure of net product Growth Rates Differ [28, p. 141] an the consequence of a reduction in the is reduced by labor compensation to arithmetic average of gross stock and efficiency of capital assets or, in obtain property income net of capital net stock is employed; the implied Denison's language, the ability of a consumption allowances. Thus, Deni- relative efficiency of capital goods is an capital good to contribute to produc- tion. The value of depreciation is son's measure of property income is also average of constant and linearly de- equal to the value of replacement if and net of replacement rather than de- clining relative efficiency, only if decline in efficiency is geometric : preciation. This erroneous measure is » allocated among capital inputs to obtain d

£** — / , and replacement pervades Denison's of an arithmetic average of gross and treatment of real product, real factor net stock as a measure of capital input. input, and capital stock. The first As indicated above, this measure of where : indication of this confusion is Denison's capital input implies that efficiency definition of net product: "Net product declines linearly up to the end of an measures the amount a nation consumes asset's economic lifetime; at that point For geometric decline in efficiency, plus the addition it makes to its capital half the asset's "ability to contribute" replacement requirements are propor- stock. Stated another way, it is the to production remains so that all the tional to capital stock, amount of its output a nation could remaining decline in efficiency takes consume without changing its stock place in one year. Denison's measure of of capital." 57 The correct definition of capital consumption allowances by the net product is gross product less straight-line method fails to measure Turning to asset and service prices, depreciation; this is the definition either replacement or depreciation. We the price of the ith asset is equal to the suggested by Denison's second state- conclude that Denison's treatment of discounted value of future services: ment quoted above. The first state- capital consumption allowances in the ment defines net product as gross measurement of net product and net

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factor input. A similar problem arises vestment.64 Geometric decline in ef- Denison registers disagreement with in Denison's earlier study, Sources of ficiency has been employed in the study this approach to the problem of quality Economic Growth [26]. There gross of depreciation on capital goods by change;71 in fact, our view of this product is employed as a measure of Cagan, Griliches, and Wykoff.65 This problem is identical to Denison's. 60 capital input. Denison's measure of assumption has been tested by Hall, If it were possible to implement our capital consumption allowances cor- who finds no effect of the age of a capi- original suggestion that different vin- responds to replacement rather than tal good in the determination of de- tages of capital goods be weighted in depreciation so that his measures of net preciation as measured from the prices measuring capital input by their mar- 66 product and net factor input are in- of used capital goods. The power of ginal products, this would not have the consistent with his measure of capital these tests is not high and some contrary effect of incorporating '' embodied'' 67 input. evidence is presented by Griliches. technical progress, as Denison [25, p. We assume that the decline in effi- Nevertheless, the weight of the evidence 26] suggests. In fact the position ciency of capital goods is geometric; suggests that Denison's treatment of attributed to us by Denison, the use under this assumption depreciation and capital could be radically simplified and of "unmeasured" quality change to replacement are equal, so that the made internally consistent by adopting correct capital input for changes in inconsistencies in Denison's procedure our assumption of geometric decline in quality by vintage, is precisely the outlined above do not arise. If we were efficiency of capital goods. Any alterna- position we originally rejected [60, p. to assume that the decline in efficiency tive assumption about the decline in 260]. Of course implementation of our is linear, as in Denison's arithmetic efficiency requires redefinition of Deni- suggestion would require data on serv- average of net and gross stock, depre- son's measures of replacement, depre- ice prices by vintage at each point of ciation would be measured differently ciation, and capital stock to make them time. from replacement. The first step would consistent. be to estimate the value of capital assets A conceptual issue that can be clari- 7.6. Measurement of capital and of each age at each point of time as the fied at this point is the role of disaggre- land discounted value of future capital serv- gation in the measurement of real Our estimates of the value of land ices. This is the definition of net stock product and real factor input. Our 61 are revised considerably from the Gold- suggested by Denison, but not the original presentation included an exten- smith estimates employed in our orig- definition used in his measure of net sive discussion of two alternative con- inal paper.72 While we have assumed stock, which is net of replacement cepts of "quality change" in produc- 62 68 that nonresidential land has remained rather than net of depreciation. The tivity analysis. We indicated that constant, this assumption could be second step would be to estimate de- quality change in the sense of "aggre- improved upon. There are scattered preciation on capital goods of each age gation error" should be eliminated by data on types of land, their relative by discounting the mortality distribu- disaggregating product and factor input value, and the changing composition tion, as indicated above in the definition measures so as to treat distinct prod- D of land actually in use in the private of depreciation q . The third step would ucts and factors as separate commodi- it economy. Very little of the investment be to obtain total depreciation as the ties wherever possible. The term quality related to shifts of land from one cate- sum over all types of capital goods and change is often used in a different gory of use to another is captured in all ages. Only at this point would it sense. Estimates of quality change are the standard investment series. Some be possible to measure net product as sometimes made by attributing changes of these investments are directly ex- gross product less depreciation. in productivity to changes in the qual- pensed and others are government sub- It is clear that the selection of an ity of a particular factor without sidized. A rough measure of the effects appropriate assumption about the de- disaggregation. cline in efficiency of capital goods is both A particularly graphic example of of shifts in the use of land to higher valued urban uses from 1945 to 1958 important and difficult. We selected inappropriate use of quality change can be constructed from Goldsmith's geometrically declining efficiency on the occurs in the analysis of the "vintage" data. Land input rises 1.4 percent per basis of its convenience and consistency model of capital. The correct measure year by this measure.73 If this figure with scattered empirical evidence. The of quality change across vintages would were extrapolated to the 1950-62 period available evidence arises from two require data on the price and quantity it would raise our estimated growth of sources—studies of replacement invest- of capital services for each vintage at total factor input by 0.14 percent per ment and studies of depreciation in each point of time. Aggregation over year. the market prices of capital goods. vintages could then be carried out in Geometric decline in efficiency has been the same way as any other type of Our estimates of the stocks of inven- employed by Hickinan and by Hall and aggregation and biases due to quality tories and depreciable assets are based Jorgenson in studies of investment.63 change could be eliminated.69 In the on those of OBE. Estimates of depreci- This assumption has been tested by absence of the required data, produc- able assets for corporate and noncor- Meyer and Kuh, who find no effect of tivity change itself has been employed porate sectors are based on the OBE the age distribution of capital stock in to estimate the quantity of capital Capital Goods Study [49]. Our perpetual the determination of replacement in- input corrected for quality change.70 inventory estimates of stocks of resi- May 1972 SUEVEY OF CURRENT BUSINESS 87

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dential structures and durables used by (2) they are extrapolated too widely, in the quality of capital. Nor is there households are based on methods simi- from electric motors in manufacturing any evidence that this has been already lar to those employed in the Capital to " e very thing "; counted in the contribution of labor Goods Study. The main difference be- (3) they are misused by not allowing or inventory input. For example, the tween our estimates of capital stock and for double counting, i.e., these changes ratio of inventories to shipments in Denison's is in our use of declining bal- are due to other inputs and hence have manufacturing has remained virtually ance depreciation. Denison uses a mix- already been measured; unchanged between 1947 and 1965.78 ture of the one-hoss-shay and the (4) they are misinterpreted as an From our point of view, the main 74 straight-line method, which gives rise increase in input rather than an difficulty with the capacity utilization to the problems in maintianing internal advancement in knowledge. adjustment is that it is not articulated consistency among depreciation, re- We have reviewed our adjustment for well with our theory and measurement placement, and capital stock outlined relative utilization in Section 4 above. of capital services and their rental above. Our revised estimates differ very sub- prices. We lack an explicit theory of Our original estimates of capital input stantially from our original estimates. capacity utilization. It is either a were based on price indexes that at- In the original estimates we estimated disequilibrium phenomenon, or is re- tempted to correct for various biases the contribution of utilization to the lated to differential costs of working in the deflators emplo}^ed in the U.S. explanation of growth in total factor people and machines at different hours national accounts. Since a positive bias productivity at 0.58 percent per year. of the day and different days of the in the investment goods price index By reducing the scope of the adjust- year. Neither case fits well into the results in underestimation of the growth ment to business structures and equip- equilibrium, all - prices - are - equalized, of both product and capital input, ment and by incorporating annual esti- framework of national income accounts. correction of biases does not affect mates of horsepower or capacity, we One possible basis for such a theory is estimates of total factor productivity have reduced the contribution of utili- to make depreciation a function of substantially. Our present estimates, zation to 0.11 percent per year for the utilization. Thus, industries wheie ma- based on those of Christensen and Jor- period 1950-62. This may be contrasted chines worked a higher number of genson [19, 20] are conservative in the with Denison's estimate of —0.04 per- hours per year would have a higher choice of price deflators. We use na- cent per year for the same period. rate of depreciation. In such a world, tional accounts deflators except for Denison points out that we do not a mix change such as discussed by structures; for both residential and discuss the "sources" of changes in Denison would show up as an increase nonresidential structures we employ utilization rates and wonders if there in aggregate capital input, with the OBE "constant cost 2" as a price de- has been some double counting. We do weight of industries with higher 6's flator. 7S We also incorporate both asset not see why the possibility of a change increasing in the total. And from our and investment deflators for inventories, in machine-hours per year per machine point of view, this would be a correct overcoming another of Denison's objec- is more mysterious than a change in interpretation of the data. An economy tions to our original estimates.76 Finally, man-hours per man-year. Obviously, that succeeded in recovering its capital we did not replace the producers' dura- there is a need for an explanation of in a shorter period would in fact ex- ble equipment price index by the com- the sources of such changes and an perience a growth in output, and our parable consumers' durable series, a analysis of the prospects for additional measure would provide an "explana- practice Denison objects to but which such changes in the future. Although we tion" for it. we have defended above.77 Thus, there have not provided such an explanation, The issue whether this growth should is no practical difference between the we did point out and localize what may be attributed to "advances in knowl- price series we use and those recom- be an important source of observed edge" or to increase in "inputs", is mended by Denison. growth in output. An attribution of ultimately a semantic one. What is 7.7. Utilization adjustment growth to investment, education, re- important is to know whence it has come, not what its name is. We don't Denison directs his strongest criti- search and development, economies of think it very fruitful to put utilization cisms, and correctly so, against what is scale, or capacity utilization is always probably the weakest link in our chain. just the beginning of a relevant line of into the "advances in knowledge" cate- gory because (a) the latter is already a While we have accepted most of his analysis. But that is as far as one can criticism, we still believe tha't the go within the framework of national "residual" category and throwing some- question posed by our utilization ad- income accounting. A more "causal" thing more into it will just muddle up justment is interesting, the numbers analysis requires different models, tools, its meaning further, and (b) the types used are not all that bad, and some- and data. of change which are likely to be the thing has been learned from this As to the actual points enumerated sources of the increased rates of utiliza- tion, be they institutional or a con- exercise. by Denison, we see no evidence that Denison's criticisms can be sum- the sources of such utilization changes sequence of changing relative marized under the following headings: have already been counted in the other of machine versus human time, are (1) the basic numbers are faulty inputs. There is no evidence that our only very vaguely and probably mis- (because of cyclical and weighting rather faulty machinery price deflators leadingly related to the ideas associated problems); have allowed for such improvements with the concept of "advances in 88 SUEVEY OF CUEEENT BUSINESS May 1972

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knowledge". In any case, our contribu- results of Christensen and Jorgenson depreciation and replacement. Part of tion was to isolate and identify a [20], our original estimates [60], and the unexplained residual between our potentially important source of growth. Denison's estimates [28]. At this point version of Denison's estimate of total Since we have not really "explained" it is useful to compare these alternative factor productivity and his own is it, and we agree that this is the im- estimates and to attempt a reconcili- accounted for by his separation of portant next task, we are unwilling to ation among them; a partial reconcilia- assets among those held by housing, argue too much over "naming" it. We tion is given in table 25. From this agricultural, and all other sectors of the find it more convenient to work within comparison it is apparent that our new economy. This separation goes part a broader definition of "input," mini- estimates represent a compromise be- of the way toward a satisfactory treat- mizing thereby the role of the amor- tween our original position and Deni- ment of the tax structure, but should phous "residual." But we concede that son's position. Referring to table 25, be replaced, in our view, by a break- the same questions can be also asked in we may now summarize our conclusions. down by legal form of organization. a different language. From an empirical point of view the In revising our original computations greatest differences among our original we have made a number of conservative 7.8. Labor input estimates, our revised estimates, and assumptions and did not correct for Our methods for measuring labor Denison's estimates are in the adjust- some obvious errors in the data where input are similar to Denison's, except ment for utilization of resources. Deni- the data base for such adjustments that Denison reduces the observed son estimates that the utilization of appeared to be too scanty. This is income differentials among components resources declines between 1950 and particularly true of the deflators of of the labor force classified by years of 1962. We estimate that utilization capital expenditures that we used and school completed to allow for the increased, but by considerably less of our measure of land input. More correlation between education and than we originally suggested. The research is needed on these and on the "ability." At the same time, Denison revision in our adjustment for relative magnitude and sources of changes in also makes an adjustment for the utilization accounts for 0.47 percent utilization rates, on capital deteriora- increase in the length of the school per year of the total discrepancy of tion and replacement rates, and on the year over time. We have made neither 0.73 percent per year between our changing characteristics of the labor of these adjustments and have come original estimate of the rate of growth force. out to about the same numbers as of total factor productivity and our While better data may decrease Denison, indicating that these two revised estimate. further the role of total factor pro- adjustments just about cancel out. From a conceptual point of view the ductivity in accounting for the observed Elsewhere one of us has argued that greatest difference among alternative growth in output, they are unlikely Denison's "ability" adjustment may procedures is in the allocation of income 79 to eliminate it entirety. It is probably be too large. Thus, if we had made from property among its components. impossible to achieve our original a smaller ability adjustment and had Except for our assumption that replace- program of accounting for all the accepted Denison's "days per school ment requirements should be estimated sources of growth within the current year" adjustment our total labor input by the double declining balance for- conventions of national income ac- would probably grow somewhat faster mula, our estimates of capital stock counting. But this is no reason to accept over most of this period. for each class of assets are very similar the current estimates of total factor Our labor input measure is very to Denison's estimates. Our estimates productivity as final/Their residual similar to Denison's. Careful examina- of capital input differ very substantially nature makes them intrinsically un- tion of the issues raised by Denison from his due to differences in treatment of satisfactory for the understanding of leads us to the conclusion that our the tax structure for property income, actual growth processes and useless for original estimate of labor input can be the use of real rates of return rather policy purposes. left unchanged. This estimate has been than nominal rates for each class of To make further progress in explain- incorporated into our measure of total assets, and the use of declining balance ing productivity change will require the factor productivity, but with a relative extension of such accounts in at least weight that differs due to changes in Table 25.—Reconciliation of Alternative Estimates of Growth in Total Factor three different directions: (1) allowing our method for allocating noncorporate Productivity, 1950-62 rates of return to differ not only by income between labor and capital. (percent per year) legal form of organization but also by We have also corrected the error of Denison, adjusted for utilization, his data . 1.41 industry and type of asset; (2) in- omitting unpaid family workers from Denison's utilization adjustment —0.04 corporating the educational sector into our estimates of persons engaged; this Denison, unadjusted, his data.- _'_ . 1.37 a total economy-wide accounting frame- leaves the final results unaffected. Unexplained difference.__. .-- .07 Denison, unadjusted, our data 1.44 work; and (3) constructing measures of * 7.9. Conclusions and suggestions for Capital input: research (and other intangible) capital further research Quality change and incorporating them into such pro- We have summarized the differences Our utilization adjustment. .11 ductivity accounts. Jorgenson- Griliches, adjusted, revised 1.0 among our estimates of the rate of Revision in utilization adjustment .47 To allow rates of return to differ growth of total factor productivity for Other revisions .26 among industries and assets would re- the period 1950-62, based on the Jorgenson-Griliches, adjusted, original _ _ - .3 quire a much more detailed data base May 1972 SURVEY OF CURRENT BUSINESS 89

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than is currently available and would occupation, and education should be develop measures of investment in introduce the notion of disequilibrium incorporated into the labor input research and development.81 The final (at least in the short and intermediate measure. step is to develop data on the stock of runs) into such accounts. Such a frame- The basic accounting framework accumulated research. A similar ac- work would be consistent with a more should also be expanded to incorporate counting problem arises for advertising general view of sources of growth 80 and investment in human capital along expenditures, also currently treated as would introduce explicitly the chang- with investment in physical capital. a current expenditure. ing industrial composition of output as Investment in human capital is pri- Both education and investment in one such source. marily a product of the educational research and development are heavily In measuring labor input, OBE data sector, which is not included in the subsidized in the United States, so that on persons engaged should include esti- private domestic sector of the economy. private costs and returns are not equal mates of the number of unpaid family In addition to data on education al- to social costs and returns. The effects workers, such as those of Kendrick [61, ready incorporated into the national of these subsidies would have to be 62]. 'Estimates of man-hours for dif- accounts, data on physical investment taken into account in measuring the ferent components of the labor force and capital stock in the educational effects of human capital and accumu- should be compiled on a basis consistent sector would be required for incorpora- lated research on productivity in the with data on persons engaged as Kend- tion of investment in human capital private sector. If the output of research rick has done. Although Denison [28] into growth accounting. activities is associated with external has given additional evidence in sup- Another issue for long-term research benefits in use, these externalities would port of his adjustment of labor input is the incorporation of research and not be reflected in the private cost of for intensity of effort, a satisfactory development into growth accounting. investment in research. Some way must treatment of this adjustment requires At present research and development be found to measure these externalities. data on income by hours of work, hold- expenditures are treated as a current Once such measures are developed and ing other characteristics of the labor expenditure. Labor and capital em- the growth accounts expanded accord- ingly, this would result in a significant force constant. Until such data become ployed in research and development departure from the conventions of na- available it may be best to exclude this activities are commingled with labor tional accounting, more far-reaching adjustment from the measure of real and capital used to produce marketable than the departures contemplated in labor input incorporated into the na- output. The first step in accounting for our original paper. A new accounting tional accounts. Quality adjustments for research and development is to develop system is required to comprehend the labor input based on such characteris- data on factors of production devoted whole range of possible sources of tics of the labor force as age, race, sex, to research. The second step is to economic growth.

Footnotes

1. Estimates of real capital input are presented in [19]; estimates 9. This allocation is described by Christensen and Jorgenson [20], of total factor productivity are given in [20]. Our original estimates pp. 297-301. are presented in [47, 60]. 10. A derivation of prices of capital services is given by Hall and 2. Christensen and Jorgenson [19], pp. 314-319. Jorgenson [52, 53] for continuous time. Christensen and Jorgenson [19] have converted this formulation to discrete time, added property 3. Denison [26], pp. 35-87, and Griliehes [43], pp. 1414-1417. taxes, and introduced alternative measurements for the tax parameters. 4. Accounts are given by Christensen and Jorgenson [20]. Similar formulas have been developed by Coen [21]. 5. All references to data from the U.S. national income and product 11. The perpetual inventory method is discussed by Goldsmith [36] accounts are to The National Income and Product Accounts of the and employed extensively in his Study of Saving [38] and more recent United States, 1929-1965, Statistical Tables, A Supplement to the Survey studies of U.S. national wealth [34, 35, 37]. This method is also used of Current Business, August 1966, henceforward NIP [66]. in the OBE Capital Goods Study [49] and in the study of capital stock for the United States by Tice [73]. 6. Self-employed persons include proprietors and unpaid family wor kers. The method for imputation of labor compensation of the 12. Denison [28], p. 140. self -employed that underlies our estimates is discussed in detail by Ch ristensen [18]. Alternative methods for imputation are reviewed by 13. Detailed evidence on the quality of the price quotations underly- Kravis[63]. ing the WPI is presented by Flueck [32]. 7. Kendrick [61, 62]. Office of Business Economics data on nonfarm proprietors and employees are from NIP [66], tables 6.4 and 6.6. 14. See Gordon [39] for additional evidence supporting this position. 8. Christensen and Jorgenson [20] assume that the statistical dis- 15. The A.T. & T. structures index uses American Appraisal Com- crepancy reflects errors in reporting property income rather than labor pany indexes with essentially negligible productivity adjustments since income. 1955. 90 SUEVEY OF CUEEENT BUSINESS May 1972

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16. Gordon's "final Price of Structures" index rises by 11 percent 31. "Quality change" in this sense is equivalent to aggregation bias. less between 1950 and 1965 than the constant cost 2 deflator See Gor- For further discussion, see Jorgenson and Griliches [60], especially don [40], table A-l, pp. 427-428. Gordon errs, in a paper published a pp. 259-260. year later than ours, in failing to notice that the final version of our paper did not incorporate the Bureau of Public Roads index as a 32. Kendrick [62], pp. 252-289, and Solow [70], p. 315. deflator but used the more representative but still imperfect OBE constant cost 2 index. 33. Denison [26], especially pp. 67-72. 17. The imputation of the value of services from owner-occupied dwellings and structures is imputed by this method in the U.S. national 34. Dension [26], especially pp. 35-41. accounts. NIP [66], table 7.3. 35. Solow [70], p. 315. 18. See footnote 6.

19. This division of the private domestic economy follows the U.S. 36. Kendrick [62], especially pp. 252-289. national accounts; see NIP [66], table 1.13. Other sectors included in the accounts are government and rest of the world. 37. Denison [25], p. 4.

20. These data were provided by the Office of Business Economics. 38. Denison [25], p. 2. 21. Christensen and Jorgenson [20] assume that errors in reporting property income occur mainly in noncorporate business. 39. See Section 7.5 below for further discussion.

22. Christensen and Jorgenson [20] assume that business transfer 40. Denison [27], fn. 1, p. 2. payments are taken mainly from corporate income. 41. The absolute contribution of productivity change is discussed 23. Alternative provisions for the investment tax credit are discussed by Denison [25], pp. 2-3. by Hall and Jorgenson [52]. 42. See Hall and Jorgenson [52]; see also [53]. We assume here 24. Christensen and Jorgenson [19] assume that no depreciation is that the decline in efficiency of capital goods with age is geometric so taken during the year of acquisition of an asset. that capital consumption allowances are proportional to capital stock. If decline in efficiency is not geometric, capital consumption 25. Formulas for the present values of depreciation deductions are: allowances are not proportional to capital stock and depreciation is not equal to replacement. Since Denison assumes that decline in straight-line: efficiency is linear rather than geometric [28, p. 140], serious difficulties arise in preserving internal consistency in his accounts for gross product, net product, factor input, and capital stock. See Section 7.5 below for further discussion. sum of the years' digits:

I 1 [ I i i I. 43. The interpretation of Divisia indexes is discussed by Solow r*L r(*+l) V 1+r/ J [70], Richter [68], and Jorgenson and Griliches [60].

where r is the discount rate and t is the lifetime of assets allowable for 44. Denison [25], p. 4. tax purposes. Depreciation practices have adapted to the use of accelerated methods only gradually, as Wales [75] has demonstrated. 45. Denison [25], p. 4, bases his allocation of noncorporate income 26. The appropriate rate of return for this purpose is the long-term on relative shares in the nonfinancial corporate sector. This procedure expected rate of return; 10 percent is close to the average of corporate has the effect of ignoring the impact of the corporate income tax. For after-tax rates of return for the period 1929-67. See Christensen and further discussion, see Christensen [18]. Jorgenson [19], table 5, pp. 312-313. 46. See Denison [25], p. 5. 27. Griliches [45], pp. 77-78. 28. See footnote 7. 47. In fact, our revised estimates can be regarded as solving the problem of simultaneously incorporating both property taxation and 29. See for example [13], p. 7, where it is estimated that the quality the corporate income tax posed by Denison as follows: of men deteriorated by less than 1 percent over the 10 year period For one tax classified as indirect, that on real property, this between 1956 and 1966 due to changes in their age distribution. assumption [that the tax be included in the earnings of capital] may be preferable. Indeed, in the context of considering the effect 30. Index Numbers; 1958=100 of taxes on the allocation of resources among sectors of the econ- Men Women Total Weighted total omy, I have myself suggested that one should not consider the 1964_ 107.7 120.8 112.1 110.2 impact of the corporate income tax, which bears only on the 1950_ 99. 1 81. 9 93.8 95. 7 corporate sector, without simultaneously considering the property tax, which bears most heavily on the principal noncorporate The weights used were 0.805 for males and 0.195 for females. The sectors of the private economy: housing and farming [25, p. 5]. share of men in total earnings was 0.81 in 1958 and 0.80 in 1964. These figures imply a —0.13 percent per year decline in the quality of the labor force due to the increase in the female population. Given our 48. Denison [25], pp. 6-13. average labor share, this would imply a — 0.09 percent contribution to the rate of growth of total input. These numbers are taken from [14]. 49. Denison [25], p. 8. May 1972 SUKVEY OF CURRENT BUSINESS 91

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50. Denison [25], p. 8, suggests adjusting the weight of land, but not 73. Our calculations are based on data from Goldsmith [35], that of other capital, for inflation. His actual procedure [26, 28] for table A-13: allocating property income ignores the effects of inflation for all assets. In constant prices (1947-49 == 100) Average (1945- Denison [25], p. 8, argues that: 58) relative Their [our] idea is that current asset values are proportional to weight in total Category of private land 1945 1958 Rate of change value of private the discounted value of the anticipated stream of earnings per year 1945-58 land and capital gains .... (1) (2) (3) (4) He then states that prices of depreciable assets ... are firmly anchored to the present and present Agricultural.- 53.8 52.9 -0.15 0. 40 production costs of capital goods and are not affected by capital Residential 31.3 44.6 2.77 .28 gains. Actually, the contradiction between our view and his is only apparent. Nonresidential 47. 7 64.6 2.37 .33 From the point of view of producers of capital goods the prices are Forests 6.4 6.9 .60 .04 anchored to present production costs. From the point of view of purchasers of capital goods these prices are related to the discounted NOTE.—Rate of growth of private stock of land per year=S [column 3Xcolumn 4]=1.38. value of future earnings, including capital gains or losses. Thus prices are simultaneously anchored to the current price level and to an- 74. Denison [19] employs OBE estimates of inventory stocks [25], ticipations of future earnings. p. 13; we have employed the same estimates of inventory stocks. We also incorporate estimates of stocks of depreciable assets from the 51. Denison [25], pp. 8, 13, acknowledges the possibility that his OBE Capital Goods Study [49]. Although Denison did not employ results could be improved by taking capital gains into account in these estimates, he indicates that: measuring earnings from land. Had the OBE study been completed, I would have used OBE capital stock series based on Bulletin F lives, on the use of the 52. Denison [25], p. 13. Winfrey distribution for retirements, and on the use of the OBE "price II" [25, p. 14]. 53. Jorgenson and Griliches [60], p. 257. See Kendrick [61, 62]. This accords with our estimates except for the use of the Winfrey distribution. 54. Denison [25], p. 13. 75. See [49]. 55. Denison [28], p. 140. 76. Denison [25], pp. 12-14. 56. Denison [28], p. 140. 77. Denison [25], p. 16. 57. Denison [28], p. 14. 78. There is also some confusion about the measurement of marginal 58. Denison [28], p. 351. contributions in some of Denison's examples. These examples seem to imply that if higher skill workers are required to run new machines, the 59. Denison [28], p. 14. contribution of such machines cannot be measured separately and is already included in the contribution of labor input. But this is clearly 60. Denison [26], pp. 112-113. wrong.

61. Denison [28], p. 140. 79. Griliches [45] and [48].

62. Denison [28], p. 351. 80. See Johnson [57] for an outline of a similar position. 63. Hickman [54], pp. 223-248; Hall and Jorgenson [52], pp. 28-31. 81. See Griliches [46] for further discussion of this topic and for some Many other references could be given. Geometrically declining order of magnitude estimates, efficiency is the standard assumption in econometric studies of invest- ^___mtfm__M______MMMM_*_»___^ ment behavior. 64. Meyer and Kuh [64], pp. 91-94. References 65. Cagan [17], pp. 222-226; Griliches [42], pp. 197-200; Wykoff [76], pp. 171-172. [1] M. Abramovitz, Resource and Output Trends in the United States since 1870, Occasional Paper 63, New 66. Hall [51], pp. 19-20. York, National Bureau of Economic Research, 1950. 67. Griliches [41], pp. 121-123 and 129-131. [2] American Textile Manufacturers Institute, Textile Highlights, various monthly issues. 68. Jorgenson and Griliches [60], pp. 259-260; see also [44]. [3] K. J. Arrow, H. B. Chenery, B, Minhas, and R. M. 69. Jorgenson and Griliches [60], p. 260. Solow, "Capital-Labor Substitution and Economic Efficiency/' Review of Economics and Statistics, Vol. 43, 70. See Solow [69, 71]; for an interpretation of the resulting measure August 1961, pp. 225-250. of capital input, see Jorgenson [59]. [4] K. J. Arrow, "Optimal Capital Policy, the Cost of 71. Denison [25], p. 26. Capital, and Myopic Decision Rules/' Annals of the Institute of Statistical Mathematics, Vol. 16, 1964, pp. 72. For a detailed discussion, see Christenson and Jorgenson [19], p. 296. 21-30. May 1972 92 SUEVEY OF CURRENT BUSINESS

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[5] Y. Barzel, "The and Technical Statistics Section of the American Statistical Association, Change in the Steam-Power Industry/7 Journal of 1961, pp. 271-279. , Vol. 72, April 1964, pp. 133-150. [24] E. F. Denison, "Measurement of Labor Input: Some [61 Bureau of the Census, Annual Survey of Manufactures, Questions of Definition and the Adequacy of Data," Washington, D.C., U.S. Government Printing Office, in Conference on Research in Income and Wealth, various annual issues. Output, Input, and Productivity Measurement, Studies [7] _—_? Census of Manufactures, 1963, Washington, in Income and Wealth, Vol. 25, Princeton, Princeton D.C., U.S. Government Printing Office. University Press, 1961, pp. 347-372. [8] , Census of Mining, 1963, Washington, D.C., [25] —', "Some Major Issues in Productivity Analysis: U.S. Government Printing Office. 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