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L * . 3 ' . Trends in MuSifactor Produciwitfg 1948=81 T /y f U.S. Department of Labor Bureau of Labor Statistics September 1983 S£T 2 1 1 9 8 3 .INDUSTRY AND SCIENCE Bulletin 2178 - 'a y t o n & M o n tg o m e r y r LABOR PRODUCTIVITY P u b lic Co' Library of Congress Cataloging in Publication Data Main e n try under t i t l e : Trends in m u ltif a c to r p r o d u c tiv ity , I 9U8- 8I 0 ( B u lle tin / U«S0 D epartm ent o f L abor, Bureau o f Labor S t a t i s t i c s ; 2178) "This stu d y was p re p a red by th e B u reau ’s O ffice o f P r o d u c tiv ity and Technology" — Pref* In c lu d e s b ib lio g r a p h ic a l r e f e r e n c e s 0 1* I n d u s t r i a l p r o d u c tiv ity - - U n ite d S t a t e s —S t a t i s t i c s * I . U n ited S t a t e s * Bureau o f Labor S t a t i s t i c s 9 O ffice o f P r o d u c tiv ity and Technology* II* S e r ie s : B u lle tin (U nited S ta te s * Bureau o f Labor S t a t i s t i c s ) ; 2178* HCUO*I52T73 1983 338f *06 f 0973 83- I 8835 Trends in SluSSifaetor Productivity,1948-81 U.S. Department of Labor Raymond J. Donovan, Secretary Bureau of Labor Statistics Janet L. Norwood, Commissioner September 1983 Bulletin 2178 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402, Stock no. 029-001-02758-3 ■ One of the principal functions of the Bureau of Labor Statistics is to inform policymakers on the utilization of the Nation’s resources, particularly as this affects the well-being of U.S. workers. Thus an important part of the Bureau’s work is the study of productivity, which is directly related to real income, price stability, employ ment, and the competitiveness of U.S. goods and serv ices in world markets. The major purpose of this bulletin is to present new bls annual indexes of multifactor productivity for pri vate business, private nonfarm business, and manufac turing for the period 1948 through 1981. These indexes incorporate capital in addition to labor inputs and are therefore more inclusive measures of productivity than the more familiar bls measures of output per hour of all persons. The indexes, including revisions, will be pub lished annually. The bulletin also presents for the first time bls annual measures of output per unit of capital service inputs for the three sectors. In addition, the bulletin presents revised, updated in dexes of the bls quarterly measures of output per hour of all persons in the business, nonfarm business, and m anufacturing sectors for the period 1947 through 1982. It also includes revised annual indexes of real product per hour of all persons in the total private economy beginning in 1909. (Government enterprises are included in the productivity indexes for the business sectors but not in those for private business.) The bulle tin also includes appendixes describing the methodology and basic data employed in constructing the bls produc tivity measures. Previously, a comprehensive descrip tion of the methodology and data sources used to con struct the output per hour measures was published in Trends in Output per M an-hour in the Private Economy, 1909-1958, Bulletin 1249 (1959). The bls measurement of multifactor productivity and output per unit of capital is in keeping with recommen dations of the Panel to Review Productivity Statistics set up by the National Academy of Sciences and chaired by Professor Albert Rees. The panel’s recommendations, published in 1979 by the National Academy of Sciences in Measurement and Interpretation of Productivity, were: “ . . . that the Bureau of Labor Statistics experiment with combining labor and other inputs into alternative measures of multifactor productivity, (p.14) “ . . . that government agencies make use of available esti mates of real capital stocks to develop ratios of output per unit of capital in order to determine the savings that have been achieved over time in physical capital per unit of out put.” (p .ll) The new measures presented in this bulletin are the first of a series of measures of multifactor productivity that bls will be producing. Future work will include multifactor productivity measures by major sector based on gross output and inputs of energy, materials, and purchased services as well as capital and labor services. In addition, bls will be developing measures showing changes in the composition of the labor force, invest ment in research and development, capacity utilization, economies of scale, and resource allocation in order to see how these factors have influenced the growth of multifactor productivity. This study was prepared by the Bureau’s Office of Productivity and Technology under the direction of Jerome A. Mark, Associate Commissioner, and under the direct supervision of William H. Waldorf, Chief of the Division of Productivity Research, who also pre pared the text. Kent Kunze prepared appendixes A and F; William Gullickson was responsible for appendix B; Michael Harper and Steven Rosenthal for appendix C; Lawrence J. Fulco for appendix D; and Kent Kunze and Leo Sveikauskas, appendix E. The staff of the Bureau of Economic Analysis, U.S. Department of Commerce, provided helpful comments in their review of the manuscript. Material in this publication is in the public domain and, with appropriate credit, may be reproduced without permission. ©©mtemts Summary of findings ............................................................................................................................................. Private business sector ................................................................................................................................... Private nonfarm business sector ................................................................................................................... Manufacturing sector ..................................................................................................................................... Chapter I. Page 1 1 2 2 Introduction ....................................................................................................................................... 3 Chapter II. Output per hour of all persons in the business sector .................................................................. Cyclical movements in output per hour ....................................................................................................... Trends in output per hour ............................................................................................................................. Post-1948 growth rates ................................................................................................................................. The long term: 1909-81 5 5 5 9 10 Chapter III. Multifactor productivity in the private business sector ............................................................. Trends in multifactor productivity ............................................................................................................... Capital per hour of all persons ..................................................................................................................... Relationship between capital per hour and factor prices ........................................................................... 16 16 16 21 Chapter IV. Sources of change in multifactor productivity ............................................................................ Intersectoral shifts ......................................................................................................................................... Changes in labor force composition ............................................................................................................. Capacity utilization......................................................................................................................................... Research and development ........................................................................................................................... Hours at work versus hours paid ................................................................................................................. Summary ......................................................................................................................................................... 25 25 25 27 29 31 31 Appendix A. The multifactor productivity model ........................................................................................... 33 Appendix B. Real output measures: Methodsand sources ............................................................................... Business sector ............................................................................................................................................... Farm sector ..................................................................................................................................................... Manufacturing sector ..................................................................................................................................... 35 35 37 37 Appendix C. Capital input and capital andlabor shares ................................................................................... Measurement of capital stocks by assettype ............................................................................................... Aggregation of capital stocks by asset type ............................................................................................... Capital and labor income shares ................................................................................................................... Examination of the measures ....................................................................................................................... Sensitivity analysis ......................................................................................................................................... Summary ......................................................................................................................................................... 39 40 49 52 53 56 58 Appendix D. Hours of all persons: Methodsand so u rces................................................................................. Nonmanufacturing ......................................................................................................................................... Manufacturing ................................................................................................................................................. Farm ................................................................................................................................................................. Government enterprises ................................................................................................................................. Nonprofit institutions ..................................................................................................................................... 66 67 67 67 68 68 v 0 ® [n ite B itS “ 0 © E n 3 in y @ d ] Page Appendix E. Comparison of base-year-weighted and Tornquist index numbers of multifactor productivity Annual percent changes ................................................................................................................................. Average annual rates of growth ................................................................................................................... 69 69 69 Appendix F. Comparison of multifactor measures ......................................................................................... Output ............................................................................................................................................................. Labor input ..................................................................................................................................................... Capital input ................................................................................................................................................... Aggregation ........................................................................... Labor and capital shares ............................................................................................................................... 73 73 76 76 79 79 Charts: 1. 2. 3. 4. 5. 6. 7. 8. 9. C - l. C-2. F - l. F-2. F-3. F-4. Tables: 1. 2. 3. 4. 5. Real hourly compensation and productivity in the business sector, 1947-82 ................................ Business sector: Output per hour, output, and hours, quarterly, 1948-82 ...................................... Nonfarm business sector: Output per hour, output, and hours, quarterly, 1948-82 ...................... Manufacturing sector: Output per hour, output, and hours, quarterly, 1948-82 ............................ Output per hour, 1909-82 ..................................................................................................................... Private business sector: Output per hour of all persons, output per unit of capital, and multifactor productivity, 1948-81 ....................................................................................................................... Private nonfarm business sector: Output per hour of all persons, output per unit of capital, and multifactor productivity, 1948-81 .................................................................................................. Manufacturing sector: Output per hour of all persons, output per unit of capital, and multifactor productivity, 1948-81 ....................................................................................................................... Output per unit of capital and rate of capacity utilization in manufacturing, 1948-81 .................. General forms of an efficiency function .............................................................................................. Cohort efficiency function for gross stocks with a truncated normally distributed discard function ............................................................................................................................................... Output for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick, 1948-81 ............................................................................................................................................... Labor input for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick, 1948-81 ................................................................................................................ Capital input for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick, 1948-81 ................................................................................................................................................... Multifactor productivity for the most aggregate sector measured by b l s , Denison, Jorgenson, and Kendrick, 1948-81 ................................................................................................................................. Rates of growth in output per hour of all persons between business cycle peaks in the business and nonfarm business sectors, 1948IV to1981 III ......................................................................... Rates of growth in output per hour of all persons, output, and hours by major sector, 1948-81 .................................................................................................................................................... Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82 .................................................................................................................................................... Output per hour, output, and hours inthe total private sector, 1909-82 ......................................... Rates of growth in output per hour of all persons, capital per hour, the contribution of capital, and multifactor productivity by major sector,1948-81 vt 4 6 7 8 11 17 18 19 29 42 43 75 78 78 9 9 12 15 (SooDSents— Continued Tables— Continued 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Page Labor and capital shares of total income by major sector, 1948-81 ................................................ Relationship between changes in rates of growth in capital services per hour and changes in relative factor prices in the private business sector, 1948-81 ...................................................... Private business sector: Productivity and related measures, 1948-81 .............................................. Private nonfarm business sector: Productivity and related measures, 1948-81 .............................. Manufacturing sector: Productivity and related measures, 1948-81 ................................................ Contribution of intersectoral shifts in labor to rates of growth in multifactor productivity in the private business sector, 1948-81 .......................................................................................................... Percent distribution of the labor force by years of school completed, by sex, 1948, 1973, and 1981 .......................................................................................................................................................... Adjustments to hours measures for changes in composition of labor input .................................... Rates of growth in multifactor productivity in manufacturing, unadjusted and adjusted for utilization of physical capital, 1948-81 Rates of growth in the ratio of hours at work to hours paid, private nonfarm business and manufacturing sectors, selected periods, 1952-81 .............................................................................. B - l. Relationship between gross national product and the product, 1981 C -l. C-2. C-3. C-4. C-5. Summary of methods and data sources used to measurecapital andmultifactor productivity . . . . Illustration of a perpetual inventory calculation for afictional type ofasset ........................................ Types of assets and service life assumptions ........................................................................................... Weighted sum of differences between hyperbolicefficiencypatterns andsimulated data .................... Manufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948- 81 ................................................................................................................................................ Farm sector: Shares in total income used to aggregatelaborand capitalinputs, 1948-81 Nonfarm-nonmanufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948-81 Private business sector: Growth rates including and excluding selected assets from published measures, 1948-81 ................................................................................................................................. Private nonfarm business sector: Growth rates including and excluding selected assets from published measures, 1948-81 ................................................................................................................ Manufacturing sector: Growth rates including and excluding selected assets from published measures, 1948-81 ................................................................................................................................. Sensitivity of multifactor productivity measure to relative efficiency assumptions, private business sector, 1949-81 ...................................................................................... Sensitivity of capital services measure to relative efficiency assumptions, private business sector, 1949- 81 ................................................................................................................................................ C-6. C -l. C-8. C-9. C-10. C -ll. C-12. bls vii 21 22 23 24 25 26 26 31 measure of private business sector gross Private business sector, 1948-81: C - 13. Real capital input ........................................................................................................................................ C-14. Productive capital stock .............................................................................................................................. C-15. Shares in current capital cost .................................................................................................................... C - l 6. Ratio of capital services to productive stock .......................................................................................... C - l 7. Gross real investment .................................................................................................................................. C-18. Price of new capital goods ........................................................................................................................ C-19. Rate of depreciation .................................................................................................................................... 20 39 41 43 44 54 55 57 57 58 59 60 60 60 61 61 61 61 Contents— Continued Tables— Continued Page Private nonfarm business sector, 1948-81: C-20. Real capital input .................................................................................................................................... C-21. Productive capital stock .......................................................................................................................... C-22. Shares in current capital cost ................................................................................................................ C-23. Ratio of capital services to productive stock ...................................................................................... C-24. Gross real investment ........................................................ C-25. Price of new capital goods .................................................................................................................... C-26. Rate of depreciation ................................................................................................................................ Manufacturing sector, 1948-81: C-27. Real capital input .................................................................................................................................... C-28. Productive capital stock ........................................................................................................... C-29. Shares in current capital cost ................................................................................................................ C-30. Ratio of capital services to productive stock ...................................................................................... C-31. Gross real investment .............................................................................................................................. C-32. Price of new capital goods .................................................................................................................... C-33. Rate of depreciation ................................................................................................................................ D -l. E - l. E-2. E-3. E-4. F - l. F-2. F-3. F-4. F-5. F-6. F-7. F-8. Sources of employment and hours data used in labor input measures for bls productivity series, private business sector ....................................................................................................................... Private business sector: Annual percent change in multifactor productivity under different index number methods, 1949-81 Private nonfarm business sector: Annual percent change in multifactor productivity under different index number methods, 1949-81 .......................................................................................... Manufacturing sector: Annual percent change in multifactor productivity under different index number methods, 1949-81 Rates of growth of multifactor productivity under different index number methods by major sector, 1948-81 Computation of output measures by bls, Denison, Jorgenson, and Kendrick ................................. Indexes and rates of growth of output for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick, 1948-81 ...................................................................................................... Indexes and rates of growth of labor input for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick, 1948-81 ................................................................................. Computation of labor input measures by bls, Denison, Jorgenson, and Kendrick ......................... Indexes and rates of growth of capital input for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick, 1948-81 ...................................................................................... Computation of capital input measures by bls, Denison, Jorgenson, and Kendrick ....................... Labor’s share for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick, 1948-81 ................................................................................................................................................... Indexes and rates of growth of multifactor productivity for the most aggregate sector measured by bls, Denison, Jorgenson, and Kendrick, 1948-81 viii 62 62 62 63 63 63 63 64 64 64 65 65 65 65 66 70 71 73 74 76 77 77 77 79 S u m m a ir f © f F in d in g s per year. During this period, capital inputs rose by 3.5 percent per year and hours of all persons by 0.9 percent, so that the rate of growth of capital services per hour (i.e., capital intensity) was 2.5 percent annually. This growth in capital per hour, when weighted by capital’s share of total income, indicates that increased capital in tensity contributed 0.9 percentage point—or roughly 40 percent—to the growth in output per hour. Multifactor productivity—the remainder—grew at an average annu al rate of 1.5 percent. This rate of growth in multifactor productivity means that the U.S. economy produced about 65 percent more in 1981 than in 1948 from the same quantity of labor and capital resources. The American economy experienced a historically high rate of growth in productivity measured by output per hour during the quarter century 1948-73; however, the rate fell sharply in the following decade. There are a host of factors that could have caused these divergent trends: Changes in the amount of capital per worker, changes in technology, shifts in the composition of the work force, differences in effort per hour worked, changes in capacity utilization, increases in the cost of energy, and other factors. This bulletin presents a recently constructed measure of productivity—multifactor productivity— which quan tifies the effects of changes in the amount of capital per unit of labor (i.e., capital intensity), one of the most im portant sources of growth of output per hour of all per sons. The new measure adds to existing bls measures of productivity; it represents the Bureau’s first step in try ing to quantify the contributions of a number of major factors underlying the movements in productivity. The index of multifactor productivity measures annu al change in output per unit of combined labor and capi tal input. This is mathematically equivalent to sub tracting the effects of annual rates of change in capital per hour from the annual rates of change in output per hour of all persons. Thus, the multifactor productivity measure differs from the familiar bls measure of output per hour of all persons in that it excludes the effects of capital intensity. Comparing the two productivity series indicates how much of the growth or falloff in the tradi tional measure of output per hour was due to changes in capital per hour and how much was due to a combina tion of the other factors— i.e, changes in technology, shifts in the composition of the labor force, changes in capacity utilization, and so on. In addition, the multifactor productivity index can be interpreted as one of a number of indicators of the eco nomic progress of the U.S. economy because it shows the growth in output that has been obtained from a given amount of resources (capital and hours of labor), or, conversely, the reduction over time in the quantity of these resources used to produce a unit of output. Output per unit of capital services exhibited marked fluctuations between 1948 and 1981, but there was little or no apparent trend over the period as a whole. Thus, there was no measured saving in the amount of capital used to produce a unit of output over the more than three decades. In the latter part of the period, between 1973 and 1981, there was a decrease in output per unit of capital services, but this represented a change from the peak of one cycle to the trough of a later one, not a slowdown in the long-term trend. The long-term average annual growth rate in output per hour, however, combines a high rate of growth (3.0 percent) between 1948 and 1973 with a much slackened one (0.8 percent) from 1973 to 1981. A small part of this falloff— 0.3 percentage point—was the result of a slowdown in the annual rate of growth of capital per hour. The remainder— 1.9 percentage points— came from a slowdown in multifactor productivity growth: Between 1973 and 1981, output per unit of combined capital and labor input rose by only 0.1 percent per year compared with 2.0 percent during 1948-73. The slowdown in the rate of growth of capital per hour after 1973 reflects a decline in the rate of substitu tion of capital for labor. From 1948-73 to 1973-81, the average annual rate of growth of capital inputs in the private business sector decreased somewhat, whereas the growth rate of hours of all persons doubled. This de cline in the rate of substitution of capital for labor after 1973 was largely associated with a change in relative factor prices: Historically, the price of capital has de clined relative to the price of labor (average hourly compensation); during 1973-81, the average annual rate of decline in the price of capital relative to labor com Private business sector From 1948 to 1981, the period mainly covered in this bulletin, the growth of output per hour of all persons in the private business sector, which accounts for about 76 percent of gross national product, averaged 2.4 percent 1 pensation was only half as great as in the earlier period, 1948-73. Comparisons with earlier decades in this century for which reasonably comparable bls data are available in dicate that the average annual rate of growth in output per hour of all persons during 1948-73 was about the same as in the two decades 1918-28 and 1938-48. But the annual growth rate during 1973-81 was the lowest during any decade since 1909-18, when there was ap parently no change in productivity. Many factors have influenced the movements in the bls measure of multifactor productivity. Judging from estimates made by bls and private scholars, about 40 percent of the long-term growth rate can be explained; the rest remains unexplained. Of the 1.5 percent per year growth in multifactor productivity from 1948 to 1981, about 0.6 percentage point can be explained by (1) shifts of labor from the farm to the nonfarm sector (0.1 percentage point); (2) changes in the composition of the work force, mainly due to more education per worker (0.4 percentage point); (3) growth of research and development ( r & d ) expenditures (perhaps 0 .2 per centage point); and (4) a reduction in hours worked rel ative to hours paid (—0.1 percentage point). Changes in utilization of physical capital appear to have had little or no effect on the long-term rate of growth of productiv ity. These same underlying factors explain an even smaller fraction of the 1.9 percent per year falloff in m ultifactor productivity growth from 1948-73 to 1973-81. About 0.4 percentage point is accounted for by (1) the virtual end of the shift of labor from the farm to the nonfarm sector (0.2 percentage point); (2) a slow down in the rate of growth of r & d (perhaps 0.1 percent age point); and (3) a decrease in hours worked relative to hours paid (0.1 percentage point). Changes in the composition of the work force took place at about the same rate before and after 1973 and therefore did not contribute to the slowdown. Measures of changes in the utilization of physical capital are not available for the private business sector as a whole; but judging from comparisons for manufacturing, changes in capacity utilization could have been an im portant factor contributing to the productivity falloff. However, even if this additional factor were included, the fraction of the falloff left unexplained would probably still be large. productivity growth was about the same in private nonfarm business as in private business as a whole. This is not surprising since the private nonfarm business sector constitutes about 95 percent of the private business sec tor. Between 1948 and 1981, output per hour of all per sons in private nonfarm business grew at an average an nual rate of 2.0 percent. Increases in capital input per hour contributed about 0.7 percent per year to the growth of output per hour. M ultifactor productiv ity—output per unit of combined labor and capital input—grew at an average annual rate of 1.3 percent. The annual rate of growth of output per hour of all persons dropped from 2.5 percent in 1948-73 to 0.6 percent during 1973-81, a slowdown of 1.9 percent per year. There was also a slowdown in the rate of growth of capital intensity, but this only contributed 0.2 per centage point to the falloff in output per hour. Multi factor productivity grew by 1.7 percent per year before 1973 but did not increase after that. That is, from 1973 to 1981, the growth in output came solely from in creases in combined labor and capital inputs; in effect, the same quantity of resources produced the same amount of output in 1981 as it did almost a decade earlier. Manufacturing sector Productivity trends in manufacturing were similar to those in private business and private nonfarm business. But while the falloff in output per hour in the other two sectors was associated with slower rates of growth in capital inputs per hour after 1973, this was not the case in manufacturing. From 1948 to 1981, output per hour of all persons in m anufacturing increased by 2.6 percent per year; growth in capital intensity contributed about 0.8 per centage point; and multifactor productivity contributed the remainder, 1.8 percentage points. The growth in multifactor productivity in manufacturing was signifi cantly faster than in private business and, particularly, private nonfarm business. The average annual rate of growth in output per hour of all persons decreased from 2.9 percent during 1948-73 to 1.5 percent from 1973 to 1981. The growth of capital per hour accelerated between the two periods and, as a result, the falloff in output per hour was less than if there had been no rise in capital intensity. Con sequently, the falloff in multifactor productivity was also greater than that for output per hour. Specifically, there was a 1.8 percent per year slowdown in the rate of growth of multifactor productivity after 1973. Private noefarm business sector Although the numbers are different, the pattern of 2 Chapter l„ SrutrodyetoBi One of the major issues now facing the U.S. economy is the marked slowdown in productivity during the last decade. Between 1973 and 1982, the average annual rate of growth in output per hour of all persons in the business sector was only one-fourth the rate during the earlier postwar period, 1948 through 1973. The slow down was pervasive: Each of the major sectors—manu facturing, farming, and nonfarm-nonmanufacturing— experienced lower rates of growth in output per personhour during the last decade, bls publishes annual in dexes of productivity for 116 industries, and 80 percent of these showed productivity slowdowns after 1973.1 These slower growth rates are a major source of con cern because productivity is important in determining national economic well-being. Productivity gains ac count for most of the increases in real compensation, so the slowdown means a retarded growth in the American standard of living. Chart 1 shows that, for the business sector, changes in hourly compensation adjusted for movements in consumer prices virtually paralleled those in output per hour of all persons, including the slow down after 1973. In addition, gains in productivity can contribute to price stability. Productivity increases help to offset the effects of increases in hourly compensation on unit la bor cost which, in turn, are closely associated with changes in prices. By moderating price rises, productiv ity gains also contribute to the U.S. balance of trade by making the Nation’s goods and services more competi tive in world markets, bls comparisons of productivity growth in 11 countries (the United States, Canada, 8 Western European countries, and Japan) show that, be tween 1960 and 1981, the average annual rate of growth in U.S. output per employee-hour in manufacturing was substantially below that of any of the other countries and only half as large as the combined average for the 10 foreign countries.12 Like the United States, all of the other countries experienced a falloff in productivity growth in manufacturing after 1973 but, except for Can ada, their post-1973 productivity growth rates remained substantially above that of the United States. The Cana dian and U.S. annual productivity growth rates were virtually the same from 1973 to 1981. Although the more familiar productivity measures re late output to hours of all persons engaged in a sector, they do not measure the specific contributions of labor, capital, or any other factor of production. Rather, they reflect the joint effects of many influences including changes in capital services, technology, level of output, utilization of capacity, the organization of production, managerial skill, and the composition and effort of the work force. The new measure of multifactor productivity intro duced in this bulletin relates output to inputs of both capital and labor and, therefore, includes more inputs than the bls productivity index of output per hour of all persons. Since it incorporates capital inputs, the multi factor productivity measure is intended to reflect all of the same influences as the labor productivity measure discussed in the previous paragraph except for changes in capital services. The bls is currently developing and reviewing measures of capacity utilization, composition of the labor force, investment in research and develop ment, and other factors in order to determine their influ ence on movements in multifactor productivity. The next chapter discusses the bls quarterly indexes of output per hour of all persons and reviews trends and cyclical movements in these series since 1947, the first year for which the data are available. These quarterly measures are for the business sector, which includes government enterprises; the discussions in the succeed ing chapters related to multifactor productivity are based on annual data and cover private business, which excludes government enterprises. Chapter III discusses the new b l s index of m ultifactor productivity, its changes, and how these relate to changes in output per hour of all persons and output per unit of capital input. Chapter IV reviews sources of change in multifactor productivity and their implications for the growth of productivity and the slowdown since 1973. The bulletin also includes six technical appendixes. Appendix A discusses the conceptual framework underlying the multifactor productivity measures; appendixes B, C, and D explain the methodology and basic data sources used in measuring output, capital inputs, and hours of all persons; appendix E presents a comparison of the re sults of using a Tomquist (changing weight) index versus a fixed weight index; and in appendix F, the new bls multifactor productivity measures are compared with those constructed by other researchers. 1Productivity Measures for Selected Industries, 1954-81, Bulle tin 2155 (Bureau of Labor Statistics, December 1982). 2Patricia Capdevielle, Donato Alvarez, and Brian Cooper, “ In ternational Trends in Productivity and Labor Cost,” Monthly La- bor Review, December 1982, pp. 3-14. International comparisons are made in terms of output per employee-hour in manufacturing to achieve comparability of the series for each country. 3 Chart 1. Real hourly compensation and productivity in the business sector, 1947-82 (Index, 1947 = 100) 1947 1952 1957 1962 4 1967 1972 1977 1982 ©Ihaptteir DQ= O utput per H our o f All [Persons on tin® B usiness SeeSor adjusting output, employment, and average weekly hours in the farm sector for changes in weather and other conditions. Therefore, the analysis of cyclical movements focuses on both the business and nonfarm business sectors. Output per hour in the nonfarm business sector rose consistently in all of the eight postwar expansions (chart 3) because output grew significantly faster than hours of all persons. The business sector exhibited the same pat tern during the expansionary phases of the cycles. During the contractions, however, the movements in aggregate output per hour were not consistent. In the nonfarm business sector, output per hour did not decline during the first five recessions, but it did during the last two. The percentage decreases in hours were greater than those in output during the first five recessions whereas, in the succeeding two contractions, hours de clined relatively less than output. This was also the pat tern in the business sector. In sum, during each of the postwar cyclical expan sions, hours of all persons showed significantly smaller relative increases than output, so that output per hour grew. However, during the contractions, hours some times fell relatively more and sometimes relatively less than output, so that labor productivity rose in some re cessions but declined in others.2 This suggests, among other things, that there is no simple, constant lag be tween hours and output at the aggregate level. There are many determinants of output per hour. Over time, changes in some of these result in cyclical move ments in the series, while others have more gradual ef fects and give rise to trends. For exam ple, rapid changes in output, coupled with lags in hiring or laying off workers, and changes in the utilization of the ex isting capital stock are likely to cause cyclical move ments in output per hour. On the other hand, changes in such factors as capital per unit of labor, labor force composition, technology and its diffusion, and shifts of resources among sectors are likely to result in changes in the long-term trend of output per hour. This chapter reviews movements since 1947 in the bls quarterly indexes of output per hour of all persons in the business, nonfarm business, and manufacturing sectors and attempts to separate the trends from cyclical patterns. The trends are then used to date and gauge the extent of the productivity slowdown. Although cyclical movements in output per hour help to explain cyclical changes in unit labor costs, profits, and prices, which tend to retard both contractions and expansions during the business cycle, the relationships between output per hour and costs are not discussed in this bulletin.1 Cyclical movements in output per hour Charts 2, 3, and 4 show quarterly changes in output per hour of all persons (seasonally adjusted) for the business, nonfarm business, and manufacturing sectors from the first quarter of 1947 (1947 I) through the fourth quarter of 1982 (1982 IV); the index numbers charted are given in table 3 at the end of this chapter. The shaded areas in the charts indicate periods of con traction in general business activity; the cyclical peaks and troughs are those designated by the National Bureau of Economic Research. Quarterly movements in the business sector are less clear than movements in the nonfarm subsector because of difficulties in seasonally Trends in output per hour The three charts showing quarterly movements in out put per hour of all persons in business, nonfarm busi ness, and manufacturing all indicate a definite slow down in the rate of growth of productivity since early 1973, a shift now well established. There is, however, some question about whether the productivity slowdown actually started earlier, perhaps in 1965 or 1966. In orThor Hultgren based on industry data. He found that “ manhours in the aggregate usually do not rise and do not fall by as great a per centage as output.’’ See Thor Hultgren, “ Changes in Labor Cost During Cycles in Production and Business,’’ Occasional Paper 74 (New York, National Bureau of Economic Research, 1960), p. 8. The difference between Hultgren’s conclusions and those offered here, which are based on broad aggregates, may be due in part to changes in the product mix during cyclical contractions. 'See Wesley C. Mitchell, Business Cycles and Their Causes (Berkeley, University of California Press, 1941); and Geoffrey H. Moore and John Cullity, “ Trends and Cycles in Productivity, Unit Costs, and Prices: An International Perspective,’’ paper presented at the Conference on International Comparisons of Productivity and Causes of the Slowdown held by the American Enterprise Institute, Washington, Sept. 30, 1982. 2These results are somewhat at variance with those reported by 5 Chart 2. Business sector: Output per hour, output, and hours, quarterly, 1948=82 (Index, 1947 = 100) 6 Chart 3. Nonfarm business sector: Output per hour, output, and hours, quarterly, 1948=82 (Index, 1947 = 100) 7 Chart 4. iHianufactyring sector: Output per hour, output, and hours, quarterly, 1948=82 (Index, 1947 = 100) 8 der to see this, long-term trends have to be separated from cyclical and random fluctuations. One method of highlighting the long-term trends is to compare rates of growth in output per hour of all per sons at peaks of business activity. Since these are at the same stage of the business cycle, there is a presumption that utilization of capital and labor is also “ roughly” the same. These peak-to-peak comparisons for the busi ness and nonfarm business sectors show that, although the annual growth rate in productivity differed among periods, the only clearly evident slowdown occurred af ter 1973 (table l) .3 The productivity growth rate in the business sector during the initial period, 1948 IV— 1953 III, was unusually high (3.7 percent) and reflects a sharp rise in farming. There was a productivity slow down in the subsequent period, 1953 III— 1957 III, but this was not as large or as prolonged as the one after 1973. In sum, the peak-to-peak comparisons of growth rates in output per hour of all persons based on quarterly data confirm that the slowdown began in early 1973; they do not reveal any falloff before then.4 For this reason, the analyses of the slowdown in this bulletin are based only on a comparison of the periods before and after 1973. Table 2. Rates of growth in output per hour of all persons, output, and hours by major sector, 1948-81 (Percent per year, compounded) 1948 IV -1953 III ............................. 1953 111-1957 III ............................. 1957 111-1960 II ............................. 1960 11-1969 IV ............................. 1969IV -1973 IV ........................... 1973IV -1980 I ............................... 1980 1-1981 III ............................... Nonfarm business 3.7 2.1 2.8 2.9 2.6 0.8 1.1 2.6 1.4 2.8 2.5 2.4 0.6 0.9 Slowdown (1) (2) (3) (3)-(2) Business:1 Output per h o u r ........... Output .......................... Hours ......................... 2.4 3.3 0.9 2.9 3.7 0.7 0.8 2.2 1.4 -2.1 -1 .5 0.7 Nonfarm business:1 Output per h o u r........... Output .......................... Hours .......................... 2.0 3.4 1.4 2.5 3.8 1.3 0.6 2.1 1.5 -1.9 -1 .7 0.2 Manufacturing: Output per h o u r ........... Output .......................... Hours .......................... 2.6 3.3 0.7 2.9 4.0 1.1 1.5 1.2 -0 .2 -1.4 -2.8 -1 .3 During the three decades from 1948 to 1981, output per hour of all persons in the business sector of the economy grew at an average annual rate of 2.4 percent. (Table 2 presents a summary of the quarterly and annu al data provided in table 3.) This was significantly higher than the rate in nonfarm business (2.0 percent) because of a high rate of growth of output per hour in farming. During the same three decades, the annual rate of growth in output per hour in manufacturing (2.6 per cent) was slightly higher than in the business sector but substantially higher than in nonfarm business, apparent ly because of slower rates of growth of productivity in nonfarm-nonmanufacturing activities. Coincidentally, output grew at virtually the same annual rate in the three sectors (about 3.3 percent) during the three decades. The highest rate of growth in hours of all persons oc curred in nonfarm business, specifically in nonfarm nonmanufacturing . 1Cyclical peaks are those designated by the National Bureau of Economic Research. Source : Table 3. 3Peter Clark also used peak-to-peak growth rates in order to date the slowdown in labor productivity up to 1973 II, the latest period for which the data were then available. For the period after that, he developed an econometric model based on a lagged response of la bor inputs (hours) to output. His model assumes that the structure of the lag is constant throughout the postwar period but, as earlier analysis in the text shows, there was no constant lag during busi ness contractions. Also, about one-half of the slowdown (0.8 per cent per year) that Clark found for 1965 II— 1973 II compared with 1955 IV— 1965 II for the business and nonfarm business sectors based on earlier bls data has “ disappeared” in subsequent statis tical revisions. See Peter K. Clark, “ Capital Formation and the Re cent Productivity Slowdown,” Journal of Finance, June 1978, pp. 1965-75. 4In addition, comparison of average annual rates of growth in the index itself, measured between peaks, indicates that, to the extent that there was a slowdown in the series prior to 1973, it was small. 1973-81 Post-1948 growth rates (Percent per year, compounded) Business 1948-73 ’ Includes government enterprises. Source : Table 4. Table 1. Rates of growth in output per hour of all persons be tween business cycle peaks in the business and nonfarm busi ness sectors, 1948 IV to 1981 IBS Period1 1948-81 Sector and measure The quarters in which the output per hour series peaked were 1950 IV, 1966 II, and 1973 II. The average yearly growth rate in the business sector declined from 2.9 percent in 1950 IV— 1966 II to 2.6 percent in 1966 II— 1973 II, only 0.3 percentage point; for the nonfarm business sector the decline in the rate of growth between the same two periods was from 2.4 percent to 2.2 percent, only 0.2 percentage point. The results are virtually the same based on growth rates computed between 3-quarter averages of output per hour centered on the 3 peak quarters. These growth rate differen tials are all well within the range of variation of those shown in ta ble 1 for the periods before 1973 IV. The comparisons in this foot note begin with 1950 IV because the sharp rise in productivity prior to that quarter reflects the sharp rise in farming during the Korean War (see charts 2 and 3). Other analysts, relying on annual data, have placed the beginning of the productivity slowdown in the mid- 1960’s. 9 Comparisons of the annual growth rates in the two pe riods 1948-73 and 1973-81 show the dimensions of the productivity slowdown during the last decade. In the business sector, output per hour of all persons grew at a yearly rate of only 0.8 percent from 1973 to 1981, slightly more than one-fourth the 2.9 percent growth rate between 1948 and 1973. This reflects a sharp drop in the annual rate of growth of output (1.5 percent) cou pled with a significant increase in the rate of growth of hours (0.7 percent). Part of the productivity slowdown resulted from shifts of output and employment from in dustries with higher to those with lower levels of output per hour. Nonfarm business experienced a similar slowdown in productivity after 1973. The annual rate of growth of output per hour fell from 2.5 percent during 1948-73 to 0.6 percent during 1973-81. This reflects a somewhat larger drop in the rate of growth of output (1.7 percent) and a significantly smaller slowing of the rate of growth in hours than in the business sector. The annual rate of growth in hours in nonfarm business (1.3 percent) dur ing 1948-73 was substantially larger than in the busi ness sector (0.7 percent) because of the large shift of workers from farm to nonfarm activities. The growth rates for hours in the two sectors were about the same during 1973-81, which indicates that the major shift of labor out of farm ing was essentially com pleted by 1973.5 In manufacturing, the average annual growth rate in output per hour was 1.5 percent during 1973-81 com pared with 2.9 percent in 1948-73, a falloff of 1.4 per cent per year. In contrast to the other two sectors, the slowdown in manufacturing reflects decreases in the an nual growth rates of both output (2.8 percent) and hours (1.3 percent). In fact, hours declined by 0.2 percent per year from 1973 to 1981 whereas they grew by 1.1 per cent in the earlier period, 1948-73. sThe proportion of all persons in the business sector engaged in farming was 15.5 percent in 1948, 7.3 percent in 1965, 4.7 percent in 1973, and 3.5 percent in 1981. Since output per hour is lower in the farm than in the nonfarm sector, the smaller decrease in the per centage after 1965 compared with the period from 1948 to 1965 partially accounts for the small slowdown in labor productivity be tween 1965 and 1973 noted earlier. 6The private economy is defined as gross national product ex cluding general government. As measured in the National Income and Product Accounts, the output of the business sector accounts for between 85 and 90 percent of output of the private economy. See appendix B for a detailed discussion of the relationship between gross national product and business output and some of the problems in using the broader concept for productivity measurement. The long term: 1909-81 bls also maintains an annual series on output per hour of all persons in the private economy for the period 1909-47.6 This series was linked to the bls measure of output per hour of all persons in the business sector in order to review long-term movements in productivity (chart 5 and table 4). This makes it possible to broadly judge U.S. long-term progress in productivity and to see whether there was a similar slowdown prior to 1948. In 1981, output per hour of the average American worker was about 4V2 times as much as it was in 1909. This averages out to a long-term yearly rate of growth of 2.5 percent. The annual rates of growth varied sub stantially among the seven decades. The differential movements largely reflected major events such as the two World Wars, the Great Depression, and various recessions. Comparisons of the pre- and post-1948 experience show that the average annual rate of growth in output per hour during 1948-73 was about the same as during the two decades 1918-28 and 1938-48. Two earlier pe riods also were marked by low productivity growth: 1909-18, when there was virtually no change in output per hour, and 1929-38, when productivity increased only 1.6 percent per year. However, these two periods of little or no productivity growth differ from the 1973-81 experience: The post-1973 productivity falloff was associated with a 3.0 percent annual rate of growth in output whereas in 1909-18 output grew by only 1.5 percent per year, and in 1929-38 there was virtually no growth in output. 10 Chart 5. Output p®r hour, 1009=82 (Index, 1 9 09= 100) 11 Table 3. Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82 (Index, 1977=100) Nonfarm business sector Business sector Manufacturing sector Output Hours of all persons Output per hour of all persons Output Hours of all persons 49.9 49.4 49.9 49.9 50.3 34.0 33.6 33.9 33.9 34.5 68.1 68.0 67.9 67.9 68.7 42.4 41.6 42.2 42.6 43.1 33.9 33.5 33.7 33.6 34.7 79.9 80.5 79.9 78.8 80.4 80.7 80.7 80.2 81.1 80.8 52.0 51.0 52.2 51.9 52.8 36.0 35.3 36.1 36.1 36.5 69.2 69.3 69.0 69.6 69.1 45.1 43.7 44.9 45.6 46.0 35.8 35.2 35.7 36.2 36.1 79.4 80.6 79.4 79.5 78.3 36.5 36.8 36.4 36.6 36.1 78.1 79.6 78.8 77.5 76.3 53.1 52.6 52.9 53.7 53.1 35.3 35.8 35.3 35.4 34.9 66.6 67.9 66.7 66.0 65.7 46.9 46.5 46.9 47.4 46.8 33.9 35.0 33.7 34.0 33.1 72.4 75.2 71.9 71.6 70.7 50.4 49.3 50.1 50.9 51.3 39.8 37.7 39.2 40.8 41.4 78.9 76.5 78.3 80.1 80.8 56.3 55.1 56.1 56.8 57.1 38.6 36.4 38.1 39.7 40.3 68.7 66.1 67.8 70.0 70.6 49.4 47.5 49.2 50.5 50.3 38.6 34.6 37.5 40.8 41.7 78.2 72.9 76.2 80.7 82.9 1951 .................... I .................... II .................. Ill .................. IV ................ 51.8 50.8 51.1 52.6 52.7 42.1 41.4 41.8 42.4 42.7 81.3 81.5 81.7 80.8 81.1 57.2 56.5 56.4 57.8 58.3 41.1 40.6 40.9 41.4 41.7 71.9 71.9 72.4 71.6 71.6 51.1 51.0 51.1 50.8 51.4 43.0 43.2 43.6 42.5 42.8 84.2 84.7 85.3 83.6 83.3 1952 .................... I .................... II .................. Ill .................. IV ................ 53.5 52.6 53.6 53.8 53.9 43.5 42.9 43.1 43.4 44.6 81.4 81.6 80.4 80.6 82.7 58.6 58.1 58.6 58.6 58.9 42.5 42.0 42.1 42.3 43.7 72.6 72.2 71.8 72.2 74.3 52.0 51.6 51.4 52.0 53.1 44.5 43.7 43.0 43.9 47.3 85.4 84.6 83.6 84.5 89.1 1953 .................... I .................... II .................. Ill .................. IV ................ 55.2 54.6 55.3 55.5 55.5 45.4 45.4 45.8 45.5 44.8 82.2 83.2 82.8 82.0 80.7 59.5 59.2 59.6 59.8 59.6 44.3 44.4 44.8 44.5 43.6 74.5 75.0 75.2 74.3 73.3 52.9 52.9 52.8 53.3 52.6 47.5 48.1 48.3 48.0 45.6 89.8 91.0 91.6 90.0 86.6 1954 .................... I .................... II .................. Ill .................. IV ................ 56.1 55.0 55.5 56.5 57.3 44.6 44.2 43.9 44.6 45.5 79.5 80.3 79.2 78.9 79.5 60.4 59.6 59.9 60.8 61.2 43.4 43.1 42.9 43.4 44.4 71.9 72.3 71.7 71.3 72.4 53.7 52.5 53.4 54.2 54.8 44.1 44.0 43.8 43.7 45.0 82.1 83.7 81.9 80.8 82.1 1955 .................... I .................... II .................. Ill .................. IV ................ 58.3 58.0 58.6 58.5 58.3 48.1 46.8 47.9 48.6 49.1 82.5 80.8 81.7 83.0 84.2 62.8 62.2 62.9 63.2 62.8 47.0 45.8 46.8 47.5 47.9 75.9 73.5 74.4 75.2 76.3 56.4 56.0 56.6 56.6 56.4 48.9 47.2 49.0 49.2 50.0 86.6 84.3 86.6 87.0 88.6 1956 .................... I .................... II .................. Ill .................. IV ................ 58.9 58.6 58.7 58.7 59.7 49.3 49.0 49.3 49.2 49.8 83.7 83.7 84.0 83.7 83.4 62.9 62.5 63.0 62.9 63.3 48.3 47.9 48.4 48.1 48.8 76.8 76.6 76.8 76.5 77.0 56.0 56.0 56.0 55.5 56.5 49.2 49.5 49.2 48.2 50.0 87.9 88.4 87.9 86.8 88.6 1957 .................... I .................... II .................. Ill .................. IV ................ 60.4 60.1 60.3 60.3 60.8 49.8 50.0 50.0 50.0 49.3 82.5 83.3 82.8 82.9 81.1 64.0 63.7 63.8 64.1 64.4 48.9 49.1 49.0 49.1 48.4 76.4 77.0 76.8 76.6 75.1 57.1 57.2 57.1 57.7 56.5 49.5 50.6 49.9 49.9 47.4 86.5 88.5 87.4 86.4 83.8 1958 .................... I .................... 62.3 61.1 61.7 62.6 63.8 49.0 48.1 48.0 49.2 50.9 78.8 78.8 77.8 78.6 79.8 65.5 64.1 65.2 65.8 67.1 48.0 47.0 47.0 48.1 49.8 73.2 73.3 72.1 73.1 74.2 56.9 55.3 56.0 57.5 58.9 45.2 44.3 43.5 45.5 47.5 79.4 80.1 77.6 79.1 80.7 Year and quarter Output Hours of all persons Output per hour of all persons 43.7 43.6 43.8 43.6 43.8 35.0 34.9 34.9 34.9 35.5 80.2 80.0 79.6 80.1 81.0 1948 .................... I .................... II .................. Ill .................. IV ................ 46.0 45.0 46.4 45.9 46.7 37.2 36.3 37.3 37.2 37.7 1949 .................... I .................... II .................. Ill .................. IV ................ 46.7 46.3 46.1 47.2 47.3 1950 .................... I .................... II .................. Ill .................. IV ................ Output per hour of all persons 1947 .................... I .................... II .................. Ill .................. IV ................ II ................ Ill .................. IV ................ 12 Table 3. Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82— Continued (Index, 1977=100) Manufacturing sector Nonfarm business sector Business sector Output per hour of all persons Output Hours of all persons Output Hours of all persons Output per hour of all persons Output Hours of all persons 64.3 64.3 64.4 63.9 64.4 52.6 52.0 53.4 52.4 52.7 81.9 80.9 82.8 82.0 81.8 67.7 67.6 68.4 67.3 67.6 51.8 51.0 52.6 51.7 51.8 76.5 75.5 76.9 76.7 76.7 59.6 59.7 60.8 58.9 59.1 50.5 49.9 52.3 49.9 49.8 84.7 83.6 86.0 84.7 84.4 1960 .................... I .................... II .................. Ill .................. IV ................ 65.2 65.9 65.1 64.8 64.9 53.5 54.0 53.7 53.4 52.8 82.0 81.8 82.4 82.4 81.4 68.3 68.7 68.2 68.1 68.1 52.5 53.2 52.8 52.4 51.8 77.0 77.4 77.3 76.9 76.1 60.0 60.9 59.8 59.6 59.7 50.7 52.8 51.1 50.1 48.6 84.4 86.7 85.5 83.9 81.4 1961 .................... I .................... II .................. Ill .................. IV ................ 67.3 65.5 67.4 67.8 68.9 54.4 52.9 53.9 54.6 56.0 80.8 80.8 80.0 80.6 81.3 70.3 68.7 70.1 70.7 71.8 53.5 51.9 53.0 53.8 55.2 76.1 75.6 75.6 76.1 76.9 61.6 59.5 61.1 62.5 63.4 50.7 47.8 49.9 51.6 53.4 82.3 80.4 81.7 82.6 84.2 1962 .................. I .................... II .................. Ill .................. IV ................ 69.9 69.1 69.3 70.3 71.2 57.4 56.7 57.2 57.7 58.0 82.1 82.1 82.5 82.1 81.5 72.8 72.4 72.0 72.9 73.9 56.6 55.9 56.3 56.9 57.3 77.8 77.2 78.2 78.0 77.5 64.3 63.8 63.5 64.3 65.6 55.1 54.1 54.7 55.3 56.1 85.6 84.8 86.1 86.0 85.6 1963 .................. I .................... II .................. Ill .................. IV ................ 72.5 71.4 72.2 73.1 73.5 59.9 58.6 59.6 60.4 61.0 82.6 82.1 82.6 82.6 82.9 75.1 74.1 74.9 75.7 76.0 59.1 57.8 58.8 59.6 60.2 78.7 78.0 78.5 78.7 79.2 68.9 67.0 68.8 69.3 70.4 59.6 57.6 59.5 60.1 61.3 86.5 85.9 86.5 86.8 87.0 1964 .................. I .................... II .................. Ill .................. IV ................ 75.6 75.0 75.2 76.1 76.5 63.5 62.1 63.0 64.0 64.7 83.9 82.9 83.8 84.1 84.7 78.1 77.2 77.8 78.7 78.7 62.8 61.5 62.4 63.3 64.1 80.5 79.7 80.2 80.5 81.4 72.3 71.3 72.1 72.6 73.0 63.9 62.2 63.5 64.5 65.3 88.4 87.2 88.1 88.9 89.4 1965 .................. I .................... II .................. Ill .................. IV ................ 78.3 77.4 77.6 78.7 79.7 67.8 66.3 67.3 68.0 69.6 86.6 85.7 86.7 86.4 87.4 80.5 79.4 80.0 80.7 81.9 67.2 65.6 66.7 67.4 69.1 83.5 82.6 83.4 83.4 84.4 74.5 73.7 74.5 75.1 74.8 69.8 67.8 69.2 70.5 71.6 93.6 92.0 92.8 93.9 95.7 1966 .................. I .................... II .................. Ill .................. IV ................ 80.7 80.5 80.4 80.8 81.2 71.5 71.0 71.2 71.8 72.1 88.6 88.1 88.6 88.8 88.8 82.5 82.4 82.2 82.5 82.9 71.2 70.5 70.8 71.6 71.9 86.3 85.5 86.2 86.7 86.7 75.3 75.3 75.4 75.5 75.4 75.1 73.7 75.1 75.8 76.1 99.8 97.8 99.6 100.4 101.0 1967 .................... I .................... II .................. Ill .................. IV ................ 82.5 81.3 82.5 82.8 83.6 73.1 72.1 72.6 73.4 74.4 88.6 88.6 88.0 88.6 89.0 84.0 82.9 83.9 84.4 85.1 72.7 71.7 72.3 73.0 73.9 86.5 86.5 86.1 86.5 86.9 75.3 74.7 75.0 75.1 76.5 75.0 74.8 74.2 74.5 76.4 99.6 100.1 99.0 99.2 99.9 1968 .................... I .................... II .................. Ill .................. IV ................ 85.3 84.4 85.0 85.8 85.9 76.8 75.3 76.4 77.6 78.1 90.1 89.2 89.8 90.4 91.0 86.8 86.0 86.7 87.2 87.2 76.6 77.8 88.2 87.2 87.9 88.7 89.2 78.0 77.5 78.1 78.0 78.4 79.1 75,0 76.2 77.3 78.9 79.4 80.3 101.4 100.4 101. 0 101 .8 102. 4 1969 .................... I .................... II .................. Ill .................. IV ................ 85.5 85.3 85.5 85.5 85.3 79.0 78.8 79.1 79.4 78.8 92.5 92.4 92.5 92.9 92.4 86.5 87.1 86.7 86.4 86.2 78.8 78.5 78.9 79.1 78.7 91.1 90.2 91.0 91.6 91.3 79.3 79.5 79.1 79.5 79.3 81.7 81.6 81.7 82.3 81.3 103.1 102.7 103.3 103.6 102. 6 1970 .................... I .................... II .................. Ill .................. IV ................ 86.2 85.0 85.8 87.3 86.8 78.4 78.3 78.4 79.0 77.9 91.0 92.2 91.4 90.5 89.7 86.8 85.5 86.6 88.0 87.1 78.0 78.0 78.0 78.7 77.3 89.8 91.2 90.1 89.4 88.8 79.1 77.6 78.6 79.6 80.6 77.0 78.4 77.5 77.0 75.1 97.3 101.0 98.6 96.7 93.2 Output per hour of all persons 1959 .................... I .................... II .................. Ill .................. IV ................ Year and quarter 13 77.7 Table 3. Output per hour, output, and hours of all persons by major sector, annual and quarterly, 1947-82— Continued (Index, 1977=100) Manufacturing sector Nonfarm business sector Business sector Output Hours of all persons Output per hour of all persons Output Hours of all persons 89.7 88.9 89.2 90.4 90.4 80.3 79.2 79.7 80.6 81.6 89.5 89.1 89.4 89.1 90.2 83.9 82.3 83.6 84.5 85.5 78.7 77.3 78.4 78.7 80.3 93.7 93.9 93.8 93.1 94.0 93.2 92.3 92.7 93.3 94.3 93.0 91.4 92.4 93.6 94.7 85.8 83.4 85.0 86.5 88.5 92.3 91.3 91.9 92.4 93.5 88.2 86.1 87.0 88.7 90.9 86.2 82.5 84.7 86.9 90.9 97.8 95.8 97.4 97.9 100.0 91.8 91.5 91.5 91.6 92.4 96.8 95.6 96.5 97.2 97.7 95.3 96.1 95.3 94.9 94.9 91.7 91.3 91.5 91.8 92.2 96.2 95.0 96.0 96.7 97.2 93.0 92.3 93.3 93.8 92.5 95.9 94.3 96.2 96.8 96.4 103.2 102.1 103.1 103.2 104.1 92.5 92.8 92.8 92.2 92.0 89.9 90.9 90.7 89.8 88.3 97.3 98.0 97.8 97.4 96.0 92.9 93.8 93.0 92.4 92.3 89.8 91.0 90.5 89.7 88.1 96.7 97.0 97.2 97.1 95.4 90.8 90.0 91.0 91.7 90.3 91.9 92.9 92.8 93.3 88.5 101.2 103.2 102.0 101.8 98.1 1975 .................... I .................... II .................. Ill .................. IV ................ 94.5 92.1 94.6 96.0 95.7 88.2 85.7 87.2 89.5 90.3 93.3 93.0 92.1 93.2 94.4 94.7 92.4 94.7 96.2 95.8 89.8 85.4 86.7 89.0 90.0 92.7 92.4 91.5 92.5 94.0 93.4 88.4 92.0 96.6 96.4 85.4 80.9 82.7 88.1 89.9 91.4 91.5 89.8 91.2 93.2 1976 .................... I .................... II .................. Ill .................. IV ................ 97.6 97.2 97.6 97.9 98.0 93.8 92.9 93.5 94.0 94.6 96.0 95.6 95.8 96.1 96.6 97.8 97.1 98.0 98.2 97.9 93.7 92.7 93.5 94.1 94.5 95.8 95.4 95.4 95.8 96.5 97.5 96.2 97.4 97.9 98.3 93.6 92.1 93.2 94.2 94.9 95.9 95.7 95.7 96.1 96.5 1977 .................... I .................... II .................. Ill .................. IV ................ 100.0 99.4 99.6 100.9 100.5 100.0 97.0 99.5 101.5 102.0 100.0 97.6 99.9 100.6 101.5 100.0 99.3 99.9 100.6 100.4 100.0 97.0 99.6 101.4 102.0 100.0 97.7 99.7 100.8 101.6 100.0 99.0 99.9 100.4 100.5 100.0 96.9 99.8 101.2 102.1 100.0 97.9 99.8 100.8 101.6 1978 .................... I .................... II .................. Ill .................. IV ................ 100.6 100.4 100.7 100.6 100.8 105.5 102.7 105.5 106.2 107.4 104.9 102.2 104.8 105.5 106.6 100.6 100.4 100.8 100.6 100.8 105.7 102.7 105.8 106.4 107.8 105.0 102.3 105.0 105.8 106.9 100.8 99.8 100.4 101.2 101.8 105.3 102.0 104.7 106.5 108.1 104.5 102.1 104.3 105.2 106.2 1979 .................... I .................... II .................. Ill .................. IV ................ 99.6 100.4 99.8 99.3 99.1 107.8 108.0 107.5 108.0 107.9 108.2 107.6 107.7 108.7 108.8 99.3 100.3 99.4 98.9 98.8 108.0 108.2 107.6 108.0 108.0 108.7 107.9 108.2 109.2 109.2 101.5 101.5 101.5 101.1 102.0 108.2 108.9 108.0 108.0 107.9 106.6 107.3 106.4 106.9 105.8 1980 .................... I .................... II .................. Ill .................. IV ................ 98.9 99.3 98.2 98.9 99.4 106.2 107.9 104.7 105.3 107.0 107.4 108.7 106.6 106.5 107.7 98.5 98.8 97.6 98.4 99.2 106.3 107.9 104.6 105.3 107.3 107.9 109.3 107.2 107.0 108.2 101.7 102.6 100.5 100.3 103.7 103.6 107.8 101.6 99.9 105.0 101.8 105.1 101.1 99.6 101.3 1981 .................... I .................... II .................. Ill .................. IV ................ 100.7 100.7 100.7 101.0 100.3 108.9 109.1 109.1 109.6 107.8 108.1 108.3 108.3 108.5 107.4 99.9 100.4 100.1 100.0 99.1 108.6 109.2 109.0 109.1 107.1 108.7 108.8 108.9 109.1 108.0 104.6 105.2 105.1 105.1 103.0 105.9 106.7 107.5 107.4 102.0 101.2 101.4 102.3 102.2 99.0 1982 .................... I .................... II .................. Ill ......... IV ................ 101.0 100.1 100.4 101.3 102.0 106.4 106.3 106.4 106.7 105.9 105.4 106.2 106.0 105.3 103.9 99.9 99.3 99.5 100.4 100.4 105.8 106.0 106.1 106.3 104.9 105.9 106.7 106.6 105.9 104.5 103.6 102.4 102.6 104.4 104.7 96.5 98.2 97.0 96.6 94.2 93.2 95.9 94.5 92.5 90.0 Output Hours of all persons Output per hour of all persons 89.2 88.7 88.6 89.9 90.0 80.7 79.9 80.2 81.0 82.0 90.5 90.0 90.5 90.0 91.1 1972 .................... I .................... II .................. Ill .................. IV ................ 92.4 91.0 92.2 92.6 94.0 86.1 84.0 85.4 86.4 88.6 1973 .................... I .................... II .................. Ill .................. IV ................ 94.7 95.6 94.8 94.3 94.5 1974 .................... I .................... II .................. Ill .................. IV ................ Output per hour of all persons 1971 .................... I .................... II .................. Ill .................. IV ................ Year and quarter 14 Table 4. Output per hour, output, and hours in the total private sector, 1909-82 (Index, 1977=100) Output per hour of all persons Output Hours 1909 ............................. 22.0 13.4 61.0 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 23.2 22.1 22.7 22.7 22.0 21.9 22.2 21.5 22.7 23.6 13.8 14.1 14.9 15.0 14.3 14.1 15.3 15.1 15.9 16.0 59.4 63.8 65.8 66.2 65.1 64.4 69.0 70.4 69.9 67.7 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 22.8 23.0 25.1 26.3 26.8 28.1 28.9 29.0 28.8 30.3 15.7 14.2 16.7 18.8 18.7 20.4 21.6 21.5 21.6 23.1 68.6 61.8 66.4 71.5 69.9 72.4 74.8 74.3 75.0 76.4 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 28.9 28.8 27.3 26.8 29.6 31.0 32.9 32.9 33.7 35.1 20.6 18.9 15.9 15.5 16.8 18.5 21.0 22.3 20.9 22.9 71.3 65.6 58.3 57.7 56.5 59.6 63.9 67.9 62.1 65.2 1940 1941 1942 1943 1944 ............................. ............................. ............................. ............................. ............................. 36.5 38.9 39.2 40.2 42.8 24.9 28.7 31.2 33.1 34.8 68.2 73.8 79.5 82.3 81.2 Year Year 15 Output per hour of all persons Output Hours 1945 1946 1947 1948 1949 ............................. ............................. ............................. ............................. ............................. 44.6 43.1 42.9 45.3 46.2 34.2 33.3 33.8 35.8 35.4 76.7 77.3 78.7 79.1 76.6 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 49.7 51.1 52.9 54.6 55.8 57.9 58.5 60.2 62.2 64.1 38.6 40.8 42.3 44.1 43.6 47.1 48.4 49.1 48.6 52.0 77.7 79.9 79.9 80.8 78.2 81.3 82.7 81.6 78.2 81.2 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 65.1 67.4 69.9 72.4 75.4 78.0 80.4 82.1 84.7 85.1 53.2 54.2 57.2 59.6 63.1 67.3 71.0 72.8 76.4 78.8 81.6 80.4 81.8 82.4 83.7 86.3 88.4 88.7 90.2 92.5 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. ............................. 86.0 89.0 92.0 94.3 92.7 94.8 97.7 100.0 100.7 100.1 78.3 80.7 85.9 91.3 90.0 88.7 94.1 100.0 105.4 108.1 91.1 90.7 93.3 96.8 97.1 93.6 96.3 100.0 104.7 108.0 1980 ............................. 1981 ............................. 1982 ............................. 99.8 101.5 101.8 107.2 109.8 107.7 107.4 108.2 105.8 Chapter SDL Multsfactor Prodyetiwiy in the Prowat© Busines® Seetor As indicated earlier, the aggregate measure of output per hour of all persons reflects many influences, such as the amount of capital per unit of labor, shifts in re sources among industries and sectors, composition of the work force, capacity utilization, and the organiza tion of production. This chapter looks at the influence of one of these— capital per hour of all persons. The bls index of multifactor productivity, which measures output per unit of combined labor and capital, is, in fact, an index of output per hour of all persons adjusted for the influence of capital per hour. The chapter also reviews trends in output per unit of capital services, which indicate the savings realized over time in the use of physical capital per unit of output. As previously in dicated, the analyses in this and the following chapters are based on the private business and private nonfarm business sectors, which exclude governm ent enterprises.1 trends in this measure during the period as a whole. This means that there were no apparent long-term sav ings in the amount of capital services required to pro duce a unit of output. The short-term fluctuations in output per unit of capital are primarily an indication of changes in capacity utilization, the result of cyclical movements in aggregate demand.2 Capacity utilization is discussed in the next chapter as one of the factors af fecting movements in multifactor productivity. Capital per hoar of all persons Tables 8, 9, and 10 and charts 6, 7, and 8 show the annual indexes of multifactor productivity in addition to those for output per hour and output per unit of capital services for private business, private nonfarm business, and manufacturing during the period 1948 to 1981. Sev eral trends are immediately evident from the charts. First, in each of the three sectors, output per hour grew at a faster rate than multifactor productivity. This, as shown later, reflects the growth of capital per unit of la bor. Second, multifactor productivity, like output per hour, experienced a marked slowdown in the rate of growth after 1973 in all three sectors. Third, short-term fluctuations in multifactor productivity generally moved in the same direction as those in output per hour; for ex ample, in 1981, both output per hour and multifactor productivity rose in all three sectors but multifactor pro ductivity indexes rose relatively less. The charts also show that, although output per unit of capital exhibited marked short-term fluctuations be tween 1948 and 1981, there were no clearly evident The growth in capital intensity— i.e., the amount of capital inputs per person-hour— is one of the major causes of the growth in output per hour during the three decades as a whole. Between 1948 and 1981, output per hour of all persons in the private business sector grew at an average annual rate of 2.4 percent, and this was as sociated with a 2.6 percent yearly growth rate in capital intensity. The growth rate of capital per hour multiplied by capital’s share of total output measures its contribu tion to the growth in output per hour (table 5). (Table 6 shows the capital and labor shares of total income for 1948-81.) Capital’s contribution was 0.9 percent per year, or nearly 40 percent of the growth rate in output per hour between 1948 and 1981. Multifactor productiv ity, which measures output per combined unit of capital and labor, grew at a yearly rate of 1.5 percent; this is the residual obtained by subtracting the contribution of capital per hour from the growth rate of output per hour.3 In the private nonfarm sector, capital per hour of all persons grew at an average annual rate of 2.2 percent from 1948 to 1981, somewhat less than in the business sector because of the large rise in capital-intensive pro duction in farming. The increase in nonfarm capital in tensity contributed 0.8 percent per year, or 40 percent, to the 2.0 percent annual rate of growth of output per hour. Multifactor productivity grew at a significantly slower annual rate in private nonfarm business (1.3 per cent) than in business; this, too, reflects the technologi- 'In 1981, output of government enterprises accounted for 2 per cent of total business output. 2The index of output per unit of capital input in the manufactur ing sector is closely correlated with the Federal Reserve Board in dex of capacity utilization for total manufacturing. The correlation coefficient between the two series was about 0.9 during the years 1948-81. 3See appendix A for a discussion of the multifactor productivity model and the conceptual relationships among the different variables. Trends in nraltifactor productivity 16 Chart 6. Private business sector: Output per hour of all persons, output per unit of capital, and muitifaotor productivity, 1048=81 (Index, 1498 = 100) 17 Chart 7. Private nonfarm business sector: Output per hour of aiS persons, output per unit of capital, and multifactor productivity, 1948-81 (Index, 1 948= 100) 18 Chart 8. Manufacturing sector: Output per hour of all persons, output per unit off capital, and muStiffaetor productivity, 1948-81 (Index, 1 948= 100) 19 Table 5. Rates of growth in output per hour of all persons, capital per hour, the contribution of capital, and multifactor productivity by major sector, 1948-81 productivity during 1973-81 was 0.1 percent compared with 2.0 percent during 1948-73, a falloff of 1.9 percent per year. In the private nonfarm business sector, there was no growth in m ultifactor productivity during 1973-81, whereas it grew by 1.7 percent per year dur ing 1948-73. The zero growth rate for 1973-81 means that all of the increase in output during the period came from increases in capital inputs and hours of labor. The slowdown experienced in manufacturing was markedly different than in the other two sectors. In manufacturing, capital per hour grew at a faster annual rate (4.2 percent) after 1973 than during the earlier peri od (2.4 percent). Consequently, it did not contribute to the slowdown in output per hour but rather increased 0.4 percent per year, which helped to offset the 1.8 per cent falloff in the growth rate for multifactor productiv ity after 1973.4 In sum, the growth in capital per hour contributed a (Percent per year, compounded) Sector and measure Private business:1 Output per hour of all per sons ................................... Capital per h o u r.................... Contribution of capital to out put per hour2 ...................... Multifactor productivity3 ......... Private nonfarm business:1 Output per hour of all per sons ................................... Capital per h o u r.................... Contribution of capital to out put per hour2 ...................... Multifactor productivity3; ....... Manufacturing: Output per hour of all per sons ................................... Capital per h o u r.................... Contribution of capital to out put per hour2 ...................... Multifactor productivity3 ......... 1948-81 1948-73 1973-81 Slowdown (3)-(2) (2) (3) (1) 2.4 2.6 3.0 2.8 0.8 1.8 -2 .2 -1 .0 0.9 1.5 1.0 2.0 0.7 0.1 -0 .3 -1 .9 2.0 2.2 2.5 2.3 0.6 1.2 -1 .9 -0 .6 0.7 1.3 0.8 1.7 0.6 0.0 -0 .2 -1 .7 2.6 2.8 2.9 2.4 1.5 4.2 -1 .4 1.8 0.8 1.8 0.7 2.2 1.1 0.4 0.4 -1 .8 Table 6. Labor and capital shares of total income by major sector, 1948-81 (Percent) ’ Excludes government enterprises. 2Growth of capital per hour weighted by capital’s share of total output. 3Output per unit of combined labor and capital input. Private business cal “ revolution” in U.S. agriculture during the postWorld War II years, which both facilitated and resulted from the reallocation of labor to nonfarm occupations. Manufacturing experienced the highest average annu al rate of growth (2.8 percent) in capital per hour among the three major sectors between 1948 and 1981. How ever, the growth in capital intensity contributed only 0.8 percent per year to the 2.6 percent per year growth in output per hour. Multifactor productivity grew by 1.8 percent per year during the period. A slowdown in the growth of capital per hour contrib uted somewhat to the slowdown in the growth of output per hour after 1973 in the private business and private nonfarm business sectors—but not in manufacturing. In the private business sector, the average rate of growth of capital per hour was 1.0 percent per year lower after 1973 than before. This contributed 0.3 percent per year to the slowdown in output per hour. In the private non farm sector, the annual growth rate in capital intensity was 0.6 percent lower after 1973, and this contributed 0.2 percent per year to the falloff in output per hour in that sector. Most of the slowdown in output per hour in the two sectors was associated with decreases in the annual rates of growth of multifactor productivity. In the private business sector, the annual rate of growth in multifactor 4A small percentage of the post-1973 rise in the bls capital input measures represents spending for pollution abatement which is not reflected in the output measures. Based on estimates made by the Private nonfarm business Labor Capital Labor Capital Manufacturing Year Labor Capital 1948......... 1949......... 62.2 64.2 37.8 35.8 62.7 65.0 37.3 35.0 68.1 67.0 31.9 33.0 1950......... 1951......... 1952......... 1953......... 1954......... 1955......... 1956 ......... 1957......... 1958 ......... 1959......... 61.3 61.8 64.8 66.4 66.1 63.3 63.9 64.6 64.6 63.5 38.7 38.2 35.2 33.6 33.9 36,7 36.1 35.4 35.4 36.5 62.7 62.3 64.2 65.8 65.8 62.8 63.4 64.2 64.2 63.1 37.3 37.7 35.8 34.2 34.2 37.2 36.6 35.8 35.8 36.9 65.6 66.1 68.3 69.4 69.6 67.1 69.4 69.7 70.6 68.3 34.4 33.9 31.7 30.6 30.4 32.9 30.6 30.3 29.4 31.7 1960......... 1961......... 1962......... 1963 ......... 1964......... 1965......... 1966 ......... 1967......... 1968 ......... 1969......... 63.6 62.9 62.2 61.4 61.6 60.9 61.8 62.5 62.9 64.5 36.4 37.1 37.8 38.6 38.4 39.1 38.2 37.5 37.1 35.5 63.3 62.7 62.2 61.4 61.7 61.2 62.1 62.8 63.1 64.7 36.7 37.3 37.8 38.6 38.3 38.8 37.9 37.2 36.9 35.3 69.6 69.3 68.6 67.5 67.2 65.8 67.1 68.4 68.4 70.4 30.4 30.7 31.4 32.5 32.8 34.2 32.9 31.6 31.6 29.6 1970......... 1971......... 1972......... 1973 ......... 1974......... 1975 ......... 1976 ......... 1977......... 1978 ......... 1979......... 65.8 65.0 65.6 65.0 66.4 63.8 63.9 63.3 64.3 65.4 34.2 35.0 34.4 35.0 33.6 36.2 36.1 36.7 35.7 34.6 65.8 65.0 65.8 65.3 66.4 64.2 64.4 63.7 64.9 66.0 34.2 35.0 34.2 34.7 33.6 35.8 35.6 36.3 35.1 34.0 72.3 70.1 70.1 71.2 74.1 71.1 70.1 70.0 71.0 73.2 27.7 29.9 29.9 28.8 25.9 28.9 29.9 30.0 29.0 26.8 1980......... 1981......... 65.5 64.6 34.5 35.4 66.3 65.3 33.7 34.7 75.7 74.8 24.3 25.2 Bureau of Economic Analysis, U.S. Department of Commerce, capital inputs for pollution abatement in manufacturing, where the impact was greatest, grew about 0.2 percent per year between 1973 (Continued) 20 sizable fraction—between 30 and 40 percent— to the longer term growth, from 1948 to 1981, in output per hour of all persons in private business, private nonfarm business, and manufacturing. It also accounted for a small proportion of the post-1973 slowdown in output per hour in private business and private nonfarm busi ness, but not in manufacturing. Thus, most of the long term growth— as well as the post-1973 slowdown—in output per hour in the three major sectors was associ ated with movements in multifactor productivity. The next chapter reviews some of the factors that have influ enced the movements in multifactor productivity. Table 7. Relationship between changes in rates of growth in capital services per hour and changes in relative factor prices in the private business sector, 1948-81 (Percent per year, compounded) Measure Relationship between capital per hour and factor prices In a competitive economy, changes in the amount of capital per unit of labor reflect, among other things, the behavior of firms trying to minimize their total produc tion costs as relative prices of these factors change. Thus, increases in the price of labor relative to the price of capital services induce firms to shift production tech niques from less to more capital-intensive methods. Table 7 shows average annual rates of change of capital per hour (the substitution of capital for labor inputs) and average annual changes in the relative prices of capital and labor for the private business sector. During the pe riod 1948-81 as a whole, the average annual rate of growth of inputs of capital services (3.5 percent) was substantially greater than that for hours of all persons (0.9 percent). This was probably partly in response to the slower rise in the price of capital services (3.4 per cent) than in labor services (6.4 percent). That is, the 2.6 percent average annual growth in capital per hour discussed in the previous section may partially reflect a response to a 3.0 percent per year decline in the price of capital services relative to the price of labor inputs (av erage hourly compensation).5 Comparisons of the subperiods before and after 1973 indicate that the slowdown in the rate of growth of capi tal per unit of labor can largely be explained by the changes in the relative prices of the two factors. As shown in the previous section, the average annual rate 1948-73 1973-81 (1) (2) (3) Factor inputs: Capital services ........... Hours of all persons .. . Capital per hour . .. 3.5 0.9 2.6 3.6 0.7 2.9 3.2 1.4 1.8 -0 .4 0.7 -1.1 Factor prices: Capital services1 ......... Labor2 ........................... Relative price3 . . . . 3.4 6.4 -3 .0 2.3 5.7 -3 .4 7.2 8.9 -1 .7 4.9 3.2 -1 .7 Ratio: Capital per hour to relative factor prices............. 0.9 0.9 1.1 0.2 11mplicit price of capital services in the private business sector. 2Hourly compensation of all persons in the private business sector. Numerical (absolute) value of the ratio of the price of capital services rela tive to hourly compensation of all persons. of growth of capital per hour of all persons dropped from 2.9 percent in 1948-73 to 1.8 percent in 1973-81. This was the result of a slowdown in the rate of growth of capital inputs coupled with a doubling in the annual rate of increase in hours. The falloff in the growth in capital intensity after 1973 coincided with a slowdown in the rate of decline in the price of capital services rela tive to hourly compensation. Between 1973 and 1981, the price of capital relative to labor declined 1.7 percent per year, half as fast as the 3.4 percent annual rate of decline during the earlier period, 1948-73. The bottom row of table 7 shows the numerical (abso lute) value of the ratio of the average annual rate of growth of capital per hour (the capital-labor ratio) to the average annual rate of growth of the price of capital rel ative to the price of labor.6 The numerical value of the ratio was 0.9 for the period 1948-81 as a whole; but, more interestingly, it appears to have been fairly stable between the two periods— 0.9 during 1948-73 and 1.1 during 1973-81. This suggests that most of the slow- (Continued) and 1981, the same rate as between 1960 and 1973. Thus, the capi tal inputs for pollution abatement appear to have had little effect on the slowdown in productivity; in long-term growth, the overstate ment of the contribution of capital inputs to the annual growth rate of “ measured” output per hour would be less than 0.1 percentage point. It should also be noted that the equipment can affect produc tivity in other ways. For example, the pollution abatement invest ment may embody a less or possibly more efficient technology than the existing one; it may require additional labor inputs, or it may raise worker efficiency if it results in a cleaner and healthier workplace. 5The measures of quantity and price of labor services used in this bulletin are based on hours of all persons and average hourly com pensation and, therefore, do not take account of changes in the composition of the labor force resulting from the growth in the 1948-81 Change, 1948-73 to 1973-81 (3)-(2) amount of human capital (e.g., education) per worker. However, this does not affect the broad conclusions in the text because ad justing the series for quality changes would lower the annual rate of growth of capital per unit of labor and the decline in the ratio of the price of capital to the price of labor by the same percentage. 6The ratio is a crude estimate of the (negative) value of the elas ticity of substitution between capital and labor. The estimate is crude because it ignores technological change, changes in the prod uct mix, and other factors that could affect the capital-labor ratio. It also does not take into account lags between changes in relative factor prices and the capital-labor ratio. For one of many studies on the theory and empirical measurement of the elasticity of substitu tion, see Murray Brown, On the Theory and Measurement of Tech nological Change (Cambridge, Mass., Cambridge University Press, 1966). 21 Table 8. Private business sector: Productivity and related measures, 1948-81 Productivity Period Output per hour of all persons Output per unit of capital Inputs Multifactor productivity1 Output1 2 Hours of all persons3 Capital4 Combined units of labor and capital inputs5 Capital per hour of all persons Index, 1977=100 1948 .................... 1949 .................... 45.3 46.0 99.2 93.6 60.1 59.4 36.8 36.1 81.3 78.6 37.1 38.6 61.3 60.8 45.6 49.1 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 49.7 51.2 52.9 54.6 55.6 57.8 58.5 60.0 61.8 63.9 98.7 100.2 99.4 100.7 96.3 100.9 100.0 97.9 94.3 99.3 63.6 65.1 66.3 68.0 67.8 70.7 71.0 71.6 72.0 74.9 39.5 41.8 43.2 45.1 44.4 47.9 49.2 49.7 48.9 52.5 79.5 81.8 81.8 82.6 79.8 82.9 84.2 82.9 79.0 82.1 40.0 41.8 43.5 44.9 46.1 47.5 49.2 50.7 51.9 52.9 62.1 64.3 65.2 66.4 65.5 67.8 69.3 69.4 67.8 70.0 50.4 51.1 53.2 54.3 57.7 57.3 58.5 61.2 65.6 64.4 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 64.8 67.0 69.6 72.3 75.4 78.1 80.4 82.3 85.1 85.3 98.4 98.0 101.2 102.6 105.2 107.8 108.0 104.9 105.5 103.7 75.4 76.9 79.7 82.0 84.9 87.6 89.3 89.6 91.7 91.3 53.3 54.2 57.2 59.7 63.3 67.6 71.3 72.9 76.7 78.9 82.2 80.9 82.2 82.7 84.0 86.7 88.7 88.6 90.1 92.5 54.1 55.3 56.6 58.2 60.2 62.8 66.1 69.6 72.7 76.1 70.7 70.5 71.8 72.9 74.6 77.2 79.9 81.4 83.7 86.5 65.8 68.4 68.8 70.4 71.6 72.4 74.5 78.5 80.7 82.3 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 86.1 89.2 92.4 94.7 92.4 94.5 97.6 100.0 100.6 99.6 98.6 98.1 101.0 103.0 96.5 91.9 96.1 100.0 101.8 100.3 90.2 92.2 95.2 97.5 93.8 93.6 97.1 100.0 101.0 99.9 78.3 80.6 86.0 91.8 89.9 88.0 93.7 100.0 105.5 107.8 90.9 90.4 93.2 96.9 97.2 93.1 95.9 100.0 104.9 108.3 79.4 82.2 85.2 89.1 93.1 95.7 97.5 100.0 103.6 107.5 86.8 87.5 90.4 94.1 95.8 94.0 96.5 100.0 104.4 108.0 87.4 91.0 91.5 92.0 95.8 102.8 101.6 100.0 98.8 99.3 1980 .................... 1981 .................... 98.8 100.6 95.3 95.0 97.6 98.6 106.2 108.8 107.4 108.2 111.3 114.5 108.8 110.3 103.6 105.8 Compound annual percent change 1948-73 ............... 1973-81 ............... 3.0 0.8 0.2 -1 .0 2.0 0.1 3.7 2.2 0.7 1.4 3.6 3.2 1.7 2.0 2.9 1.8 1948-81 ............... 2.4 -0.1 1.5 3.3 0.9 3.5 1.8 2.6 10utput per unit of combined labor and capital inputs. 2Gross domestic product originating in the sector, in constant dollars. 3Paid hours of all employees, plus the hours of proprietors and unpaid fam ily workers engaged in the sector. 4A measure of the flow of capital services used in the sector. 5Hours of all persons combined with capital input, using labor and capital shares of output as weights. S ou r c e : See appendixes B, C, and D. 22 ; Table 9. Private nonfarm business sector: Productivity and related measures, 1948-81 Inputs Productivity Period Output per hour of all persons Output per unit of capital Multifactor productivity1 Output2 Hours of all persons3 Capital4 Combined units of labor and capital inputs5 Capital per hour of all persons Index, 1977=100 1948 .................... 1949 .................... 51.2 52.3 98.1 92.8 64.6 64.2 35.6 34.9 69.6 66.8 36.3 37.7 55.1 54.4 52.2 56.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 55.6 56.6 58.0 59.0 59.9 62.3 62.5 63.6 65.1 67.4 98.4 100.6 99.7 100.9 96.2 100.9 100.1 98.0 94.0 99.5 68.2 69.5 70.4 71.5 71.0 74.1 74.0 74.3 74.3 77.5 38.3 40.9 42.2 44.1 43.2 46.8 48.2 48.7 47.8 51.6 69.0 72.2 72.8 74.7 72.1 75.1 77.0 76.6 73.4 76.6 39.0 40.6 42.4 43.7 44.9 46.4 48.1 49.7 50.8 51.9 56.2 58.8 60.0 61.7 60.8 63.2 65.1 65.6 64.3 66.6 56.5 56.3 58.2 58.5 62.3 61.7 62.5 64.9 69.3 67.7 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 67.9 70.0 72.5 74.9 77.8 80.3 82.2 83.8 86.7 86.4 98.4 97.9 101.3 102.6 105.5 108.1 108.7 105.3 106.0 104.1 77.6 78.9 81.7 83.8 86.7 89.2 90.7 90.7 92.9 92.1 52.3 53.3 56.4 58.9 62.7 67.0 71.0 72.5 76.5 78.7 77.0 76.1 77.8 78.6 80.5 83.5 86.4 86.5 88.2 91.1 53.2 54.4 55.7 57.4 59.4 62.0 65.3 68.9 72.1 75.6 67.5 67.5 69.0 70.3 72.3 75.1 78.3 79.9 82.3 85.4 69.1 71.5 71.6 73.0 73.8 74.2 75.7 79.6 81.7 83.0 1970 .................... 1971 .................... 1972 .................... 1973-.................... 1974 .................... 1975 .................... 1976 .................... 1977 .................... 1978 .................... 1979 .................... 86.8 89.7 93.0 95.3 92.9 94.7 97.8 100.0 100.6 99.3 98.6 98.0 101.1 103.2 96.5 91.7 96.1 100.0 101.9 100.0 90.7 92.4 95.7 97.9 94.1 93.6 97.2 100.0 101.1 99.6 77.9 80.1 85.8 91.7 89.7 87.6 93.6 100.0 105.7 108.0 89.7 89.3 92.2 96.2 96.6 92.5 95.7 100.0 105.1 108.7 78.9 81.8 84.8 88.8 93.0 95.6 97.4 100.0 103.7 107.9 85.9 86.7 89.7 93.6 95.4 93.6 96.3 100.0 104.6 108.4 88.0 91.5 92.0 92.3 96.3 103.3 101.8 100.0 98.7 99.2 1980 .................... 1981 .................... 98.4 99.8 95.1 94.4 97.3 97.9 106.2 108.5 108.0 108.8 111.7 115.0 109.2 110.9 103.4 105.7 3.6 3.3 3.6 2.1 2.1 2.1 2.3 1.7 2.2 Compound annual percent change 1948-73 ............... 1973-81 ............... 1948-81 ............... 2.5 0.6 2.0 0.2 -1.1 -0.1 1.7 0.0 1.3 3.9 2.1 3.4 See footnotes for table 8. 23 1.3 1.5 1.4 Table 10. Manufacturing sector: Productivity and related measures, 1948-81 Productivity Period Output per hour of all persons Output per unit of capital Inputs Multifactor productivity1 Output2 Hours of all persons3 Capital4 Combined units of labor and capital inputs5 Capital per hour of all persons Index, 1977=100 1948 .................... 1949 .................... 45.1 46.9 94.4 86.0 56.2 56.0 35.8 33.9 79.4 72.4 37.9 39.5 63.7 60.6 47.8 54.5 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 49.4 51.1 52.0 52.9 53.7 56.4 56.0 57.1 56.9 59.6 94.9 99.6 95.7 98.6 89.2 95.8 92.5 89.6 80.5 89.2 59.9 62.3 62.2 63.5 62.3 65.9 64.8 65.1 62.8 67.0 38.6 43.0 44.5 47.5 44.1 48.9 49.2 49.5 45.2 50.5 78.2 84.2 85.4 89.8 82.1 86.6 87.9 86.5 79.4 84.7 40.7 43.2 46.4 48.2 49.5 51.0 53.2 55.2 56.2 56.6 64.5 69.1 71.4 74.8 70.8 74.2 75.9 76.0 71.9 75.4 52.1 51.3 54.4 53.7 60.2 58.8 60.5 63.8 70.7 66.9 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 60.0 61.6 64.3 68.9 72.3 74.5 75.3 75.3 78.0 79.3 88.0 86.9 92.9 98.3 102.4 107.3 108.7 101.1 101.1 100.5 67.0 68.0 71.5 76.3 79.8 82.8 83.7 81.8 83.7 84.6 50.7 50.7 55.1 59.6 63.9 69.8 75.1 75.0 79.1 81.7 84.4 82.3 85.6 86.5 88.4 93.6 99.8 99.6 101.4 103.1 57.5 58.3 59.2 60.7 62.4 65.1 69.2 74.2 78.2 81.3 75.6 74.6 77.0 78.2 80.0 84.3 89.8 91.7 94.4 96.6 68.2 70.9 69.2 70.1 70.6 69.5 69.3 74.5 77.1 78.9 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 .................... .................... .................... .................... .................... .................... .................... .................... .................... .................... 79.1 83.9 88.2 93.0 90.8 93.4 97.5 100.0 100.9 101.6 91.8 92.4 99.9 108.2 99.6 89.4 96.1 100.0 101.5 99.5 82.3 86.0 91.1 96.8 93.0 92.2 97.1 100.0 101.0 101.0 77.0 78.7 86.2 95.9 91.9 85.4 93.6 100.0 105.3 108.2 97.3 93.7 97.8 103.2 101.2 91.4 95.9 100.0 104.4 106.5 83.9 85.2 86.4 88.6 92.2 95.5 97.4 100.0 103.8 108.8 93.6 91.5 94.7 99.1 98.8 92.6 96.4 100.0 104.2 107.2 86.2 90.9 88.3 85.9 91.1 104.4 101.5 100.0 99.4 102.1 1980 .................... 1981 .................... 101.7 104.5 90.0 87.5 98.6 99.9 103.6 105.9 101.8 101.3 115.1 121.1 105.1 106.0 113.1 119.5 Compound annual percent change 1948-73 ............... 1973-81 .............. 2.9 1.5 0.6 -2 .6 2.2 0.4 4.0 1.2 1.1 -0 .2 3.5 4.0 1.8 0.9 2.4 4.2 1948-81 ............... 2.6 -0 .2 1.8 3.3 0.7 3.6 1.6 2.8 See footnotes for table 8. down in the growth of capital per hour after 1973 was the result of the change in relative factor prices—the markedly slower rate of decline in the ratio of the price of capital to the price of labor. If the ratio (0.9) for the 1948-81 period as a whole was, in fact, the same in both subperiods, the smaller rate of decline in the price of capital relative to that of labor (1.7 percent per year) would alone have accounted for about 80 percent of the slowdown in the growth of the capital-labor ratio after 1973.7 7Econometric estimates based on a model derived from the constant-elasticity-of-substitution production function relating the capital-labor ratio to relative factor prices and including dummy variables indicates an elasticity of substitution of 0.9 for the period 1948-81 as a whole. There was no statistically significant differ ence in the elasticity between 1948-73 and 1973-81. The qualifica tions discussed in the previous footnote also apply here. Part of the slowdown in the rate of substitution of capital for labor after 1973 may also reflect the sharp increases in energy prices that began in that year. Dale Jorgenson and others have estimated that energy and physical capital are complementary, whereas energy and labor are substitutes in production. This implies that the sharp rise in energy prices in 1973 (and 1979) would have induced firms to decrease their investment and to increase their employment more than they otherwise would have done. Such an energy-induced substitution of capital for labor would be reflected in the figures in table 7 and, to that extent, the effect of change in relative factor prices on the slowdown in capital intensity would be overstated. See Dale W. Jorgenson, “ Energy and the Future of the U .S. Econom y,’’ Wharton Magazine, Vol. 3 (Summer 1979), pp. 15-21. 24 C hapter SW. B ourses ©f C hange in M ultifaetor IProduetawity This chapter reviews several of the statistically ob servable sources of change in multifactor productivity to see how they have influenced long-run growth in pro ductivity and the slowdown after 1973. These sources include (1) intersectoral shifts in resources, (2) selected changes in labor force composition, (3) changes in ca pacity utilization, (4) research and development ( r & d ) , and (5) changes in hours at work relative to hours paid. Tabie 11. Contribution of intersectoral shifts in labor to rates of growth in multifactor productivity in the private business sector, 1948-81 (Percent per year, compounded) Item Multifactor productivity ......... Contribution of intersectoral shifts of la b o r...................... Multifactor productivity ad justed for intersectoral shifts of labor ............................... Intersectoral shifts Multifactor productivity is increased when labor and capital shift to sectors where they are more productively employed. The most dramatic shift of resources during the period 1948-81 was from the farm to the nonfarm sector. In 1948, persons engaged in farming accounted for about 16 percent of the total engaged in the private business sector; by 1973, the proportion had dropped to 5 percent; and by 1981, to about 4 percent.1 Capital also moved from the farm to the nonfarm sector during the post-World War II period. As in the case of labor, the shift was virtually completed by the mid-1960’s. 1948-73 (2) 1973-81 Slowdown (3) - (2) (3) 1.5 2.0 0.1 -1 .9 0.1 0.2 0.0 -0 .2 1.4 1.8 0.1 -1 .7 Changes in labor force composition The b l s measures of multifactor productivity are based on hours of all persons engaged in the private business sector, which assumes that workers are homo geneous with respect to skills. As a result, the shifts from less to more skilled labor because of increased ed ucation or on-the-job training are not reflected in the b l s measure of labor input but instead contribute to growth in multifactor productivity.3 Table 11 shows the contribution of intersectoral shifts in labor to the growth rates of multifactor productivity in the private business sector.2 Because of data limita tions, resource reallocation effects reflect only shifts among the three major sectors— farm, manufacturing, and nonfarm-nonmanufacturing. Over the total period, 1948-81, the reallocation of labor, mainly from the farm to the nonfarm sector, contributed 0.1 percent per year to the average annual growth rate of multifactor productivity. Intersectoral shifts in labor contributed 0.2 percentage point to the growth rate of multifactor pro ductivity betwen 1948 and 1973; but it was not a con tributing factor after 1973. Thus, 0.2 percentage point of the 1.9 percent slowdown in multifactor productivity growth after 1973 in the private business sector resulted from the fact that there were no longer large numbers of workers moving from farm to nonfarm activities. Historically, the change in the composition of the la bor force has been one of the most important sources of growth in m ultifactor productivity. This includes, among other things, changes in the amount of formal education and on-the-job training per worker, in the age-sex distribution of the labor force, and in the occu pational and industry mix of employment. Three of these compositional changes are discussed in this sec tion: The amount of education per worker, which is by far the most important; the age-sex composition of the work force; and increases in the efficiency of an hour’s work resulting from the secular decline in average weekly hours. Education is generally viewed as one of the major factors affecting the productivity of labor. Over the last three decades, the amount of schooling of U.S. workers 'The shift was largely completed by 1965; in that year, the num ber engaged in farming accounted for only 7 percent of all persons engaged in private business. The importance of farm output also declined—from about 6 percent of business output in 1948 to 3 per cent in 1973. 2The contributions from intersectoral shifts in capital are not in cluded in table 11 because they are already reflected in the b l s 1948-81 (1) m e a su re o f cap ital p e r h o u r a n d , hence, accounted f o r in th e bls m e a s u r e o f m u l t i f a c t o r p r o d u c t i v it y s h o w n in th e ta b le . 3For a detailed review of the issues in measuring the effects of changes in the composition of labor inputs on productivity, see Kent Kunze, “ Evaluation of Work-Force Composition Adjust ment,” in National Academy of Sciences, Measurement and Inter pretation of Productivity (Washington, n a s , 1979). 25 has increased dramatically.4 The proportion of the labor force with at least 1 year of college rose from 12 percent in 1948 to 36 percent in 1981; the proportion with 1 to 4 years of high school rose from 47 percent to 55 percent; and the fraction in the lowest education group, those with only 8 or fewer years of schooling, dropped from 41 percent to 8 percent (table 12). There was also a marked rise between 1948 and 1981 in the percentage of students who completed 4 years of high school. The pic ture was generally the same for men and women. Table 13 shows Denison’s estimates of average annu al growth rates in the amount of education per worker during the periods discussed in this bulletin; it also in cludes his estimates of the growth in efficiency of an hour’s work resulting from the decline in the average workweek, and an index of average annual change in the age-sex composition of total hours.5 The numbers in the last three columns of the table show the contribution of each of these factors to the growth in the bls measure Table 13. Adjustments to hours measures for changes in composition of labor input1 Annual growth rate Item 1948-81 1948-73 1973-81 1948-81 1948-73 1973-81 T otal......... Amount of education............. Efficiency of an hour’s work3 .. Age-sex composition ............. Elementary Total Less 5-8 than years 5 years High school 4 years 1-3 years 4 years or more Total: 1948 . . . . 1973 . . . . 1981 . . . . 100.0 100.0 100.0 7.5 2.0 1.2 33.5 11.6 6.7 19.8 18.6 14.9 27.2 39.4 40.9 6.9 14.2 17.9 5.2 14.1 18.3 Men: 1948 . . . . 1973 . . . . 1981 . . . . 100.0 100.0 100.0 8.8 2.4 1.5 35.7 13.1 7.9 20.2 18.6 15.4 23.1 35.8 37.5 6.6 14.5 17.4 5.7 15.6 20.3 Women: 1948 . . . . 1973 . . . . 1981 . . . . 100.0 100.0 100.0 4.4 1.4 .8 28.0 9.2 5.1 18.8 18.6 14.2 37.3 45.2 45.5 7.5 13.8 18.6 4.0 12.0 15.7 S ources : Data for 1948 from Edward F. Denison, Accounting for United States Economic Growth, 1929-69 (Washington, The Brookings Institution, 1974). Data for 1973 and 1981 from Labor Force Statistics Derived from the Current Population Survey: A Databook, Vol. 1, Bulletin 2096 (Bureau of La bor Statistics, September 1982). — 0.4 0.4 0.4 0.7 0.6 0.7 0.4 0.4 0.5 0.2 0.2 0.1 0.1 0.1 0.1 -0.2 -0.2 -0.3 -0.1 -0.1 -0 .2 He also makes some adjustment for differences in ability and socioeconomic status. Similarly, Denison’s annual index showing changes in the agesex composition of the work force is based on a weighted distribu tion of total hours worked in the business sector by age and sex. The weights are relative hourly earnings of the different demo graphic groups. For a discussion of the methodology used in arriving at these estimates, see Denison, Accounting for United States Economic Growth, 1929-69. 6The b l s measures of m ultifactor productivity employ a Tornquist index number formula which involves changing weights; however, labor’s share for the private business sector was fairly stable between 1948 and 1981—about 65 percent of total output— so that the use of a fixed weight does not significantly affect the results. 4The literature on human capital (including education) and its im plications for productivity is too extensive to cite here. For a recent attempt to measure the stock of human capital, see John W. Kendrick, The Formation and Stocks of Total Capital, National Bureau of Economic Research (New York, Columbia University Press, 1976) and the literature cited there; for an earlier review of the relationship, see Zvi Griliches, “ Notes on the Role of Educa tion in Production Functions and Growth Accounting,’’ in W. Lee Hansen, ed., Education, Income, and Human Capital, Studies in Income and Wealth No. 35, National Bureau of Economic Research (New York, Columbia University Press, 1970). 5Edward F. Denison kindly made these estimates available to us. Denison’s index of the amount of education is based on a weighted distribution of full-time-equivalent business employment by years of schooling and sex. The weights are relative earnings for 1959 standardized for age, race, region, and farm-nonfarm employment. — of multifactor productivity based on the bls weight for labor’s share (65 percent).6 The amount of education per worker is, by far, the most important single source of the measured changes in the composition of labor input. Denison’s estimates in dicate that the amount of education per person in the la bor force grew at an average annual rate of 0.7 percent between 1948 and 1981. This was only 0.2 percentage point lower than the annual growth rate of hours of all persons; it means that quality enhancement in the work force from increased education grew nearly as much as the quantity of “ raw” labor inputs measured by total hours of all persons. When weighted by the bls estimate of labor’s share of total output, Denison’s estimate shows that the growth in education per worker contrib uted about 0.4 percent per year to the annual rate of growth of the bls measure of multifactor productivity between 1948 and 1981. Changes in the amount of edu cation per worker did not contribute to the falloff in the growth rate of multifactor productivity after 1973 and, judging from Denison’s estimates, may even have added nearly 0.1 percentage point to growth. Average weekly hours in the private business sector declined from 42.5 in 1948 to 38.4 in 1973 and to 36.7 College 1-3 years — 1Based on Edward Denison’s estimates rounded to a tenth of a percentage point. See Denison, Accounting for United States Economic Growth, 1929-69, and his Accounting for Slower Economic Growth: The United States in the 1970’s (Washington, The Brookings Institution, 1979). Contribution to multifactor productivity is equal to the annual growth rate multipled by the bls estimate of labor’s share (0.65). efficiency of an hour’s work as affected by changes in hours due to intragroup changes and specified intergroup shifts. Table 12. Percent distribution of the labor force by years of school completed, by sex, 1948,1973, and 1981 Labor force group and years Contribution to multifactor productivity2 26 using an index showing changes in the age-sex compo sition of the labor force. This index declined about 0.2 percent per year between 1948 and 1981, which implies that changes in the age-sex composition of the labor force reduced the annual rate of growth of the bls meas ure of multifactor productivity by 0.1 percentage point during the period. The rate of decline in the age-sex composition index appeared to be slightly higher after than before 1973 and thus may have contributed slightly (less than 0.1 percent per year) to the productivity slow down. That is, it offset the equally slight positive effect from the increased amount of education per worker. In sum, based on Denison’s estimated growth rates and bls weights, the total combined changes in the composition of labor inputs accounted for about 0.4 per centage point of the 1.5 percent annual growth rate in multifactor productivity between 1948 and 1981.8 The compositional changes in the work force, considered as a whole, had virtually no effect on the productivity slowdown after 1973. in 1981. These declines reflect both decreases in aver age hours worked within sectors and the shift of labor from the farm to the nonfarm sector, where average weekly hours tend to be shorter. Denison has also esti mated changes in the efficiency of an hour’s work re sulting from those intrasectoral changes in average weekly hours and intersectoral shifts in labor. Accord ing to his measure, the efficiency of an hour’s work due to the combination of these two sources rose about 0.2 percent per year between 1948 and 1981. Multiplying this by the bls estimate of labor’s share indicates that the contribution of the shorter workweek added 0.1 per cent per year to the growth of multifactor productivity during the period. The contribution was apparently the same before and after 1973, so that changes in efficien cy from the shorter workweek were not a factor in the productivity slowdown. Work experience, like schooling, is a major compo nent of the composition of the labor force that influ ences multifactor productivity. Unfortunately, data are not available for directly measuring changes in the aver age work experience of the total work force, so re searchers have had to develop a measure from available data that is closely associated with the desired one. The measure generally used is an index showing changes in the age-sex composition of the labor force.7 For exam ple, teenagers entering the labor force for the first time probably have little or no work experience and, conse quently, an increase in their relative importance tends to reduce the average amount of experience per worker. The measure is stratified by sex because, in general, women tend to have less work experience than men of the same age, either because they enter the labor force later after raising children or because they temporarily leave the labor force to raise children. Between 1948 and 1981, the proportion of the civil ian labor force between 16 and 24 years of age in creased from 19.5 percent to about 23 percent; over the same time period, the proportion of women in the civil ian labor force rose from about 29 percent to 43 percent. Both of these shifts tended to have a dampening effect on the average number of years of work experience of the labor force during the period. Denison, like others, has tried to estimate the changes in the average amount of experience of labor inputs by Short-term fluctuations in aggregate demand result in cyclical changes in the utilization of capital and labor, and these too are reflected in the bls m easures of multifactor productivity. This is evident from looking at the cyclical fluctuations in multifactor productivity be tween 1948 and 1981 (charts 6, 7, 8), and it is perhaps most clearly seen in the 1973-75 recession. Multifactor productivity in each of the three sectors declined from a peak in 1973, bottomed out in 1975, and recovered in 1976. These changes paralleled those in output per unit of capital, which also reflects utilization of the capital stock. To some extent, the labor inputs are adjusted to cur rent production needs by firms hiring and laying off workers and by changing the number of weekly hours worked. However, to the extent that labor is a quasifixed factor and there is labor hoarding, firms tend to underutilize (overutilize) the work force during periods of recession (expansion), and this is reflected in the bls measures of multifactor productivity. In the case of capital, firms mainly adjust their inputs to meet changes in their short-run production needs by changing the utilization of existing stocks.9 The magni- 7That is, the index showing changes in the age-sex composition of the labor force is used as a proxy for changes in the average amount of work experience per person. 8In the formulation of “ growth accounting,’’ the growth of out put is related to the growth of inputs of labor, capital services, and other factors. Labor inputs are generally measured by combining hours of all persons and the compositional changes in the labor force, and the growth rate of this aggregate is then weighted by la bor’s share of the total output in order to determine its contribution to the growth of output. The figures in the text suggest that these combined labor inputs contributed 1.0 percent per year to the rate of growth of output in the private business sector between 1948 and 1981; of this, 0.6 percentage point came from hours of all persons and 0.4—or 40 percent—from the effects of changes in the compo sition of the work force. 9The Tornquist index number formula used to construct the b l s measure of capital stock implicitly adjusts, to some degree, for changes in the utilization of capital. For a theoretical discussion of this implicit ex post adjustment, see Charles R. Hulten, “ Produc tivity Change, Capacity Utilization, and the Sources of Efficiency Growth,” b l s Working Paper 137 (Bureau of Labor Statistics, June 1983). Capacity utilization 27 tude of the adjustments for the utilization of capital in puts is therefore likely to be larger than that for labor. Unfortunately, there is at present no generally ac cepted way to adjust the labor and capital input series in the private business or nonfarm business sectors for changes in capacity utilization resulting from fluctua tions in aggregate demand. The approach used in this bulletin has been to calculate growth rates between cy clical peaks as designated by the National Bureau of Economic Research (see chapter II), but it is not clear that the rates of utilization of the capital stock were the same at each peak; it is equally problematical for labor utilization.10* The Federal Reserve Board ( f r b ) indexes of capacity utilization for total manufacturing can be used to sug gest the effects of changes in resource utilization on the b l s measures of multifactor productivity in the manu facturing sector.11 It is important to stress that the ad justments are only suggestive because different pub lished measures of capacity utilization yield somewhat different results and, to some unknown extent, the b l s multifactor productivity measure implicitly incorporates adjustments for changes in resource utilization.12 Table 14 compares the growth rates for the b l s multi factor productivity measure for total manufacturing un adjusted and adjusted for capacity utilization based on the f r b index. This was done by adjusting the b l s annu al measures of capital inputs in manufacturing by the f r b annual indexes of capacity utilization in that sector. 1From table 3. 2Average annual rates of growth of capacity utilization weighted by capital’s share of total output. 3Multifactor productivity minus the contribution of utilization of physical capital. According to the f r b index, the rate of capacity utiliza tion in manufacturing in 1948 was only slightly higher than in 1981 and, as a consequence, the average annual rate of change was virtually zero. For 1948-81 as a whole, the average annual rate of growth in the adjusted multifactor productivity measure is the same as the unadjusted one. The results, however, do suggest that some of the productivity slowdown after 1973 may be explained by changes in capacity utilization. The f r b index shows that the rate of capacity utilization rose from 82.5 per cent in 1948 to 87.6 percent in 1973 and then fell to 78.5 percent in 1981. The figures based on the adjusted capital inputs indicate that the increase in capacity utili zation before 1973 added 0.1 percent per year to the an nual growth rate in the b l s (unadjusted) measure of multifactor productivity during 1948-73, and that the decrease in capacity utilization after 1973 reduced it by 0.3 percent per year during 1973-81. Thus, multifactor productivity adjusted for changes in capacity utilization grew at an average annual rate of 0.7 percent in 197381 compared with 2.1 percent in 1948-73. This slow down of 1.4 percent per year in the adjusted measure is 0.4 percentage point lower than the 1.8 percent per year falloff registered by the b l s (unadjusted) series. In sum, these tentative calculations suggest that changes in capacity utilization may have accounted for a significant fraction of the post-1973 falloff in manufac turing productivity, but that a large fraction probably still remains unexplained. The parallel cyclical move ments of multifactor productivity in the three major sec tors (charts 6, 7, and 8) also suggest that these general conclusions for manufacturing might be true for the pri vate business and private nonfarm business sectors as well. Finally, it is interesting to note the virtually parallel fluctuations in the f r b index of capacity utilization for total manufacturing and the b l s measure of output per unit of capital input in the sector (chart 9). During the period 1948-81 as a whole, the association between the two indexes was close; about 80 percent of the total var iation in output per unit of capital input could be “ ex plained” by variations in capacity utilization.13 10Arthur Okun and Robert Solow made relative utilization of la bor and capital functions of the unemployment rate and used the same measure to adjust both inputs simultaneously. Denison pains takingly measures the “ effects” of varying intensity of demand on output per unit of input as a function of the ratio of nonlabor earn ings to national income of corporations and he, too, applies the same measure of utilization rates to labor and capital. See A.M. Okun, “ Potential GNP: Its Measurement and Significance,” Pro ceedings of the Business and Economics Statistics Section of the American Statistical Association, 1962, pp. 98-104; R.M. Solow, “ Technical Change and the Aggregate Production Function,” Re view of Economics and Statistics, (August 1957), pp. 312-20; and Denison, Accounting for United States Economic Growth. u The main reason for using the Federal Reserve Board indexes rather than other measures of capacity utilization is their availabili- ty for the total period, 1948-81. 12For a review of the issues, see Frank de Leeuw, Lawrence R. Forrest, Jr., Richard D. Raddock, and Zoltan E. Kenessey, Meas ures of Capacity Utilization: Problems and Tasks (Washington, Board of Governors of the Federal Reserve System, July 1979). 13The two measures are not wholly independent because the f r b measure of capacity utilization is at least partially based on meas ures of output and capital stock, albeit not the b l s series. Also, the b l s measures of output per unit of capital input for both the private business and private nonfarm business sectors exhibit equally high correlations with the f r b index of capacity utilization in manufac turing. On the face of it, this would indicate that the large fluctua tions in the b l s series of output per unit of capital largely reflect changes in capacity utilization and hence fluctuations in aggregate demand. Table 14. Rates of growth in multifactor productivity in manu facturing, unadjusted and adjusted for utilization of physical capital, 1948-81 (Percent per year, compounded) Item Multifactor productivity1 ....... Contribution of utilization2 ... Adjusted multifactor productivity3 ................................. 1973-81 (3) Slowdown (3) - (2) 1948-81 (1) 1948-73 (2) 1.8 0.0 2.2 0.1 0.4 -0.3 -1 .8 -0 .4 1.8 2.1 0.7 -1 .4 28 Chart 9. Output per unit ©fi capita! and rate ©f capacity utilization in manufacturing, 1948=81 (Index, 1948= 100) Note: Shaded areas indicate recessions. ured in constant prices as gross investment in the capital stock of technical knowledge, and this raises a number of very difficult conceptual and empirical problems.14 It is, therefore, not surprising that present knowledge about the contribution of r & d to the long-term growth of multifactor productivity and its falloff in the 1970’s is limited. Total r & d expenditures as a percentage of g n p , a measure of “ research intensity,” declined from 2.7 per cent in 1961 to 2.3 percent in 1973; there was virtually no change in the rates between 1973 and 1980. The total figures include r & d expenditures by the U.S. Govern ment for defense, the atomic energy program, and space exploration, and there has been some question about the degree to which these government r & d outlays affect measured productivity in the private business sector of the Economy.15 Private r & d expenditures (which ex- Research and development Additions to the stock of knowledge that yield tech nological improvements in production are generally viewed as one of the major sources of growth in multi factor productivity. Research and development ( r & d ) expenditures that contribute to this new knowledge have consequently been a major area of research for ex plaining the growth in productivity. In addition, the slowdown in the rate of growth of r & d during the 1970’s focused attention on its possible role in the pro ductivity slowdown. Unfortunately, the relationship between r & d expend itures and multifactor productivity is one of the most difficult and, perhaps, more intractable areas of produc tivity research. The analysis used to relate r & d to multifactor productivity treats r & d expenditures meas 14Some of the more obvious problems are: (1) determining the relevant r & d expenditures that affect multifactor productivity; (2) r & d expenditures measure the cost of inputs, not the value of the output of knowledge; (3) there is no appropriate deflator for r & d presently available and researchers have generally used the g n p de flator; (4) the difficulty of measuring the length and structure of the lag between r & d outlays and their impact on multifactor productiv ity; (5) the meaning and measurement of depreciation and obsoles cence of the r & d capital stock; (6) determining the spillover effects (externalities) of r & d among industries using the products of the industry undertaking the r & d as well as between defense and space exploration projects and the private business sector; and (7) the usual quality problems in the price series used to deflate the value of the products embodying the improved technology. For a review of these and other conceptual and empirical issues in relating r & d expenditures to multifactor productivity, see Z. Griliches, “ Issues in Assessing the Contribution of Research and Development to Eco nomic Growth,’’ Bell Journal of Economics. Spring 1979, pp. 92-116. 15Nestor Terleckyj found no correlation between governmentcontract r & d (other than for agriculture) and the productivity of the industries conducting it. He also found that the indirect effects on (Continued) 29 elude outlays by the three government agencies) as a percentage of g n p actually rose from 1 .2 percent in 1961 to 1.4 percent in 1973 and to 1.6 percent in 1980.16 These comparisons suggest that, to the extent that changes in research intensity contributed to the post-1973 falloff in productivity, the effect was small. At present, there is no generally accepted measure of the r & d stock over time which can be used to evaluate the impact of research on national multifactor produc tivity growth over the 1948-81 period.17 Cross-section studies based on data for different industries in the 1950’s and 1960’s indicate research intensity had a pos itive influence on productivity growth in these periods. This is true for both the direct effects for the industries conducting the research and the indirect effects on the industries that purchased capital and materials with r & d content. Griliches, for example, estimated that r & d contributed 0.3 percentage point to the growth of multi factor productivity based on a study for the mid-1960’s; but he also noted that this was probably a maximum.18 The findings based on cross-section analyses for the 1970’s are mixed; they depend upon the particular sample used and the level of aggregation of the data.19 The estimates made by different researchers on the contribution of R&D to the slowdown in multifactor productivity between the 1960’s and 1970’s range from less than 0.1 percentage point (Denison)20 to about 0.2 percentage point (Kendrick, Clark, and Griliches)21 and between 0.2 and 0.4 percentage point (Scherer).22 It might, perhaps, be concluded from these results that the slowdown in the rate of growth of r & d contributed to the post-1973 slowdown in multifactor productivity, but the effect was probably small, perhaps on the order of 0.1 percentage point. This and the earlier cited estimate of 0.3 percentage point for the 1960’s reported by Griliches suggest that, over the longer term, r & d ’ s con tribution to the annual rate of growth of multifactor pro ductivity averaged between 0.2 and 0.3 percentage point. (Continued) productivity of industries purchasing goods from the industries con ducting the government-contract r & d were weak or nonexistent. See Nestor E. Terleckyj, Effects o f r & d on the Productivity Growth of Industries: An Exploratory Study," Report No. 140 (Washington, National Planning Association, December 1974). Griliches omits r & d expenditures by the Defense Department, the Atomic Energy Commission, and the National Aeronautics and Space Administration, in order to arrive at an estimate of “ expend itures with probable effects on measured private productivity.” Government r & d outlays by these three agencies accounted for half of the total r & d expenditures in 1970. See Zvi Griliches, “ Re search Expenditures and Growth Accounting,” in B.R. Williams, ed., Science and Technology in Economic Growth (London, 1973) table 3.1, p. 75. ,6Civilian r & d expenditures accounted for about 70 percent of total r & d outlays in 1980 compared with 62 percent in 1973 and 44 percent in 1961. However, even this series is not appropriate for determining the relationship of r & d to multifactor productivity be cause it includes research outlays by government, universities, colleges, other nonprofit institutions, and even consumer product research by profitmaking firms, that do not affect the amount of in puts required to produce a unit of output included in the b l s meas ures. See Griliches, “ Research Expenditures,” pp. 74—77, and Denison, Accounting for Slower Economic Growth: The United States in the 1970’s (Washington, The Brookings Institution, 1979), p. 124. 17John Kendrick has developed a time series for the stock of r & d capital beginning in 1929. Based on this, he estimated that between 1948 and 1978, the growth of R & D capital contributed about 0.8 percentage point per year to the growth of multifactor productivity (i.e., his total factor productivity). This is about 3 times as large as estimates made by Griliches and others based on cross-section anal ysis. Kendrick obtains this result because his measure of the stock of R & D capital includes total r & d , both government and privately financed, and, as pointed out in the text and footnote 15, most government-financed r & d has little or no effect, directly or indi rectly, on measured multifactor productivity. See John W. Kendrick, “ Why Productivity Growth Rates Change and Differ,” in Herbert Giersch, ed., Towards an Explanation of Economic Growth, Symposium 1980 (Tubingen, J.C.B. Mohr (Paul Sieback), 1981), and Edwin Mansfield’s Comment. 18Griliches, “ Research Expenditures,” pp. 59-83; Terleckyj, Effects of r & d on Productivity Growth; and Leo Sveikauskas, “ Technological Inputs and Multifactor Productivity Growth,” Re view of Economics and Statistics, May 1981, pp. 275-82. I9For example, Griliches, using more aggregate data, found that the growth in productivity was much less sensitive to r & d intensity in manufacturing in the 1970’s than in the 1960’s and that the 1970’s estimate was not significantly different from zero. Taken at face value, this would imply that developments in r & d were a ma jor cause of the slowdown in productivity during the 1970’s. How ever, in his later studies with associates using more disaggregated data, he found that r & d continued to have a positive effect on multifactor productivity in manufacturing during the 1970’s. See Zvi Griliches, “ r & d and the Productivity Slowdown,” American Economic Review, May 1980, pp. 343-48; Kim B. Clark and Zvi Griliches, “ Productivity Growth and r & d at the Business Level: Results from the p i m s Data B a se,” Working Paper No. 916 (Cambridge, Mass., National Bureau of Economic Research, June 1982); and Zvi Griliches and F. Lichtenberg, “ r & d Productivity Growth at the Industry Level: Is There Still a Relationship?” Working Paper No. 850 (Cambridge, Mass., National Bureau of Economic Research, February 1982). Clark and Griliches point out that the p i m s data base is not a representative sample of firms in any given sector; but, interestingly, their estimate of the direct rate of return for the firms in the p i m s data base (18-20 percent) is about the same as the one estimated by Griliches and cited earlier. Clark and Griliches conclude that about 10 percent of the decline in multifactor productivity for the firms in the p i m s data base can be attributed to a reduction in their R&D-to-sales ratio. 20Edward F. Denison, “ Accounting for Slower Economic Growth: An Update,” paper prepared for the Conference on Inter national Comparisons of Productivity and Causes of the Slowdown held by the American Enterprise Institute, Washington, Sept. 30, 1982, p. 25. 21John W. Kendrick, “ Survey of the Factors Contributing to the Decline in U.S. Productivity Growth,” in The Decline in Produc tivity Growth, Conference Series No. 22 (Boston, Federal Reserve Bank of Boston, June 1980); and Clark and Griliches, “ Productivi ty Growth and r & d at the Business Level.” 22F.M. Scherer, “ r & d and Declining Productivity Growth,” (Continued) 30 Hours at work versus hours paid percent per year between 1952 and 1977. Thus, ad justing the b l s measure of hours paid to an hours-atwork concept would reduce the average annual rate of growth of labor inputs by 0.1 percent per year during that 15-year period and, consequently, raise the annual rate of growth of multifactor productivity by somewhat less than 0.1 percent.25 The average annual rate of de cline in the ratio was 0.2 percent in 1972-77 compared with 0.1 percent during 1952-72, which suggests that the decline in hours at work relative to hours paid con tributed to the falloff in the b l s measured productivity growth, but only minimally. The estimate for manufacturing suggests that the ef fects of the increase in hours paid relative to hours at work on measured multifactor productivity growth in that sector are somewhat larger than for private nonfarm business but still quite small. For all employees in man ufacturing, the annual rate of decline between 1952 and 1977 in the ratio of hours at work to hours paid aver aged 0.2 percent, so that the annual growth rate of mul tifactor productivity in manufacturing would be in creased by somewhat more than 0.1 percentage point if it were adjusted to an hours-at-work concept of labor inputs. The evidence on the measured contribution to the falloff in the productivity growth rate is unclear: The es timates for production workers which are based on the new b l s survey data for 1981 indicate that the rate of decline in the ratio of hours at work to hours paid re mained constant (0.2 percent per year) between 1968 and 1981 and therefore did not affect the measured falloff in productivity during the 1970’s. The estimates for all employees, however, show a possible 0.1 per centage point difference in the contribution to the fall off. In any case, to the extent that the declining ratio of hours at work to hours paid was a contributing factor to the measured slowdown, its effects were small. The b l s series on labor inputs is based on hours paid for rather than at work and therefore includes paid vacations and sick leave. Conceptually it would be more appropriate to use a measure of hours of work but the necessary data are not now available. In order to help rectify this problem, b l s started a survey in 1981 which will make it possible in the future to adjust the hours measure to a more appropriate one, hours at work.23 Prior to the new survey, the b l s used two sources of information in order to experiment with possible adjust ments of hours paid to obtain an hours-at-work measure. One source, which was mainly used internally, em ployed estimates on leave practices and tenure of em ployees to calculate vacation time. These estimates were used to compute ratios of hours at work to hours paid in the private nonfarm business and manufacturing sectors during the years 1952-66. The other source of informa tion was a biennial survey conducted by the Bureau of Labor Statistics between 1968 and 1977.24 In this sur vey, annual measures of both hours at work and hours paid were collected for office and nonoffice workers in the private nonfarm business and manufacturing sectors. Table 15 shows average annual rates of growth of the ratio of hours at work to hours paid for selected years based on the 1981 survey findings and estimates from the two earlier sources. The estimates for all employees in private business show that the ratio decreased by 0.1 Table 15. Rates of growth in the ratio of hours at work to hours paid, private nonfarm business and manufacturing sec tors, selected periods, 1952-81 (Percent per year, compounded) Employee group and period Private nonfarm business Manufacturing All employees: 1952-77 ................................... 1952-72 ........................... 1972-77 ........................... -0.1 -0.1 -0 .2 -0 .2 -0.1 -0 .3 Production workers: 1968-81 ................................... 1968-72 ........................... 1972-81 ........................... (1) (1) (1) -0 .2 -0 .2 -0 .2 Summary This chapter reviewed several of the many factors that have influenced the movements in the b l s measure of multifactor productivity since 1948. While these have helped to explain a part of the longer term annual growth rate and its fallo ff after 1973, the part left unexplained remains large. 1Not available. Sources : 1952-66, unpublished bls study; 1968-77, Employer Expendi tures for Employee Compensation Survey; 1981, Hours Worked Survey (cov ers production and nonsupervisory workers only). (Continued) American Economic Review, May 1983, pp. 215-18. 23The new survey, conducted annually, collects both quarterly and annual data on hours at work and hours paid for production and nonsupervisory workers. Approximately 4,000 establishments are surveyed, representing the private nonagricultural business sector of the U.S. economy. Adjustments are calculated for the major groups (1-digit sic) and for the 2-digit industries within the manu facturing sector. The data collected refer to the previous year. Most of the data are tabulated from payroll records. Findings from the initial survey in 1981 indicate that the measures are reliable and consistent with prior expectations. Estimates of hours at work will also be available in the future on a quarterly basis. 24Employer Expenditures for Employee Compensation Survey. These series have not been published but are discussed in “ Report of the b l s Task Force on Hours Worked’’ (Bureau of Labor Statis tics, March 1976). 25The contribution of the decline in the ratio to multifactor pro ductivity growth is measured by multiplying the annual rate of de cline by labor’s share of total output (0.65). 31 Between 1948 and 1981, multifactor productivity in the private business sector grew at an average rate of 1.5 percent per year. During this period, intersectoral shifts of labor, particularly from the farm to the non farm sector, contributed 0.1 percentage point to the pro ductivity growth rate. Based on Denison’s estimates, changes in the composition of the work force, mainly from increased education per worker, contributed an ad ditional 0.4 percentage point. Available information suggests that there was only a small difference in the rate of capacity utilization and that it probably had no significant effect on the long-term growth rate. Judging from G rilich es’ estim ates for the m id-1960’s and 1970s’s, r & d may have contributed about 0.2 percent age point to the annual growth rate in multifactor pro ductivity during the period. The sparse data available relating hours at work to hours paid show that the use of hours paid rather than the more appropriate hours-atwork concept in the bls measure of hours of all persons reduced the measured productivity growth rate by 0.1 percentage point. Adding the influences of these five sources indicates that, together, they explain about 0.6 percentage point of the 1.5 percent annual growth rate of multifactor productivity in the private business sec tor. That is, they explain about 40 percent of the total long-term growth rate; about 60 percent remains unex plained. The longer term trend was interrupted after 1973: The average annual rate of growth of multifactor productivi ty in the private business sector declined from 2.0 per cent in 1948-73 to 0.1 percent in 1973-81, a falloff of 1.9 percent per year. The shift of workers out of farm ing into the nonfarm sector had virtually come to an end by 1965, and this contributed 0.2 percentage point to the productivity slowdown from the earlier to the later periods. Changes in the work force occurred at about the same rate in the two periods and therefore had no ef fect on the falloff. The slowdown in the growth of r & d during the 1970’s contributed only to a small degree to the productivity falloff, possibly only about 0.1 percent age point. Using hours paid rather than hours at work in measuring total hours of all persons could have contrib uted another 0.1 percentage point to the measured pro ductivity slowdown. Adding the effects of these four sources indicates that, together, they contributed about 0.4 percentage point—or about 20 percent—to the 1.9 percent per year slowdown in multifactor productivity in private business. Unfortunately, data are not available for measuring changes in capacity utilization for the pri vate business sector. However, the analysis of the man ufacturing sector strongly suggests that changes in the rates of capacity utilization could account for a signifi cant fraction of the unexplained portion of the produc tivity slowdown in private business. But, even with this additional adjustment, the percentage left unexplained would probably still be large.26 26For analyses of other possible sources contributing to the pro ductivity slowdown besides those discussed in this chapter, see Edward F. Denison, “ The Interruption of Productivity Growth in the United States,’’ Economic Journal, Vol. 93, March 1983, pp. 1-22; and Kendrick, “ Survey of the Factors Contributing to the Decline in U.S. Productivity Growth.” 32 Appendix A, TGi® MuStiactoir Prodyetiwiitf Model puts which are delivered to final demand or, as conven tionally stated, the aggregate value added. In accord ance with this measure of output, only the primary inputs, labor and capital, are measured and included in the framework. Thus both output and input measures are net of interindustry flows of goods and services. In the b l s series on multifactor productivity, labor is measured as total hours, and capital is measured as the value of services rendered by the stock of capital.1 The general framework for the measurement of multifactor produc tivity comes directly from the economic theory of pro duction.2 In this approach, a production function is pos tulated as follows: The new measures of multifactor productivity pre sented in this bulletin not only extend the scope of pro ductivity analysis by the inclusion of more than one fac tor but also incorporate a number of recently developed measurement techniques. Many theoretical difficulties in the measurement of aggregate inputs and of produc tivity growth have been addressed over the last 20 years. As a result, fewer restrictive assumptions are needed in order to measure and aggregate inputs. Now much more general (flexible) functions relating inputs have been developed. Furthermore, index numbers based on discrete data on prices and quantities of the in puts and output of production have been shown to be consistent with these more flexible aggregation functions. Although econometric methods can be used to identi fy the structure of production, index numbers enjoy several advantages for measuring productivity. Index numbers avoid the errors inherent in a stochastic speci fication on a limited sample size. Estimates of produc tivity based on index numbers provide reliable and time ly estimates of productivity change. This appendix describes in detail how the new meas ures of multifactor productivity are constructed and how they relate to the older measures of output per hour. The appendixes that follow provide detailed descriptions of the separate factors: Output, capital input, and labor in put (hours). A multifactor productivity measure is similar to a single-factor productivity measure in that it is computed as the ratio of output to input. In the case of the multifactor measure, the input is an index of several factors. In this bulletin, multifactor productivity is de fined as value-added output per unit of combined labor and capital input. Real output is a function of the quan tities of real capital and real labor inputs used and the technological structure. Output is measured as net of its intermediate inputs. It is the sum of the industries’ out Q (t)= A(t)f[K(t),L(t)] where: Q (t) = real output, K (t) = real capital input, L (t) = real labor input, A (t) = index of (neutral) technological progress or multifactor productivity. Taking the logarithmic differential of equation (A .l) with respect to time yields: Q/Q = A/A + sk K/K + Si L/L. (A.2) The dot notation refers to the change in the factor over time; hence, Q/Q represents the growth rate of output. Similarly, K/K is the growth rate of capital and L/L is the growth rate of labor. The weights, sk and s1? are the output elasticities of the factor inputs. Assuming com petitive factor markets and constant returns to scale, the weights equal the relative cost shares of the individual factors in total cost (income):3 o o o will reflect both scale effects and technological change. See Mi chael Denny, Melvyn Fuss, and Leonard Waverman, “ The Meas urement and Interpretation of Total Factor Productivity in Regu lated Industries, with an Application to Canadian Telecommunica tions,” in Productivity Measurement in Regulated Industries, Thomas C. Cowing and Rodney E. Stevenson, eds. (New York, Academic Press, 1981). 1See appendixes B, C, and D for detailed explanations and meas ures of output, capital input, and labor input, respectively 2The methodology described in this appendix can be easily ex tended to different measures of output- and to additional factor inputs. 3If the function does not exhibit constant returns to scale, A/A (A. 1) 33 PkK(t) The index I(t) is a Tornquist index, which is consist ent with a “ translog” production function.6 The advan tage of the general translog form over the more com monly used Cobb-Douglas function (which is a special case of the translog) is that it has fewer restrictive prop erties. In particular, the translog function allows the elasticities of substitution among inputs to vary as input proportions vary whereas the Cobb-Douglas does not. This generally is a major improvement over index forms which use constant-base-year-weighted index numbers. This improvement amounts to recognizing that input factor prices and quantities observed in a given year are most relevant for computing weights in that year. Con stant weights mean relative use of inputs is held con stant even if there are significant price changes in the factor inputs. For example, if the price of capital were to increase sharply relative to labor costs, enterprises would be likely to begin using relatively more labor (work more hours, or work more shifts) and relatively less capital (possibly by reducing investment expansion plans). In this scenario, two changes take place: The relative price of capital increases, and the relative quan tity used decreases. The two changes have opposite ef fects on cost shares or weights. When base-year weights are used, only the quantity change is reflected; in Tornquist weights, both changes are included. Turning to the relationship between the traditional measure of output per hour and multifactor productivity, it can be shown that the rate of growth of output per hour can be separated into the rate of growth of multifactor productivity and the contribution of changes in capital services per hour. Subtracting the growth in labor input (L/L) from both sides of equation (A.2) and some further algebraic manipulation yields the follow ing equation: Sk = ------------------PkK(t) + PlL(t) PiL(t) s, = ------------------PkK(t) + piL(t) Si + sk = 1 PkK(t) + piL(t) = current-dollar output = PqQ(t). where: pk = price of capital services (the rental price) Pi = price of labor (hourly compensation) pq = price of output (the value-added de flator) . Equation (A.2) is the basic measurement relationship for multifactor productivity growth. It expresses the growth in output as equal to a weighted average of the growth in capital and labor inputs plus the growth in o multifactor productivity (A/A). Or, after rearranging o terms, the growth rate of multifactor productivity (A/A) can be measured as the growth rate of the ratio of output to inputs.4 Hence A(t), productivity in time (t), is: A(t) = Q(t)/I(t) (A.3) where I(t) is the aggregate index of inputs. This index is computed using discrete annual estimates of prices and quantities. It is the weighted average of the growth rates of the separate inputs. For each time period, the change in I is calculated as: o + wlt In (L(t)/L(t—1)) (A.4) o o o sk it + sk t-1 2 (A.5) Wkt - - S1 t + Si t-1 2 (A.6) Wit =■ (A.7) The left side of equation (A.7) is the rate of change of the ratio (Q/L), output per hour; the right side of the equation is the sum of multifactor productivity growth (A/A) and capital’s share times the rate of change of the ratio of capital services to hours (i.e., the contribution of changes in the capital-labor ratio). This is the rela tionship that is used to analyze the changes in output per hour in chapter III. where the weights are averages of the relative cost shares of the input factor for the given and previous year:5 4See Charles R. Hulten, “ Divisia Index Numbers,” Econo metrics, Vol. 41, No. 6, 1973, pp. 1017-25; and Marcel K. Richter, ‘‘Invariance Axioms and Economic Indexes,” Economet rics, Vol. 34, No. 4, 1966, pp. 739-55. s The weights for a Tornquist index are defined as arithmetic av erages of the cost shares. The geometric average is used for compu tational convenience. Numeric differences between these methods are slight and considered insignificant. o Q/Q - L/L = A/A + sk (K/K - L/L). In (I(t)/I(t—1)) = wkt In (K(t)/K(t—1)) 6This consistency is shown by W.E. Diewert, ‘‘Exact and Super lative Index Numbers,” Journal of Econometrics, May 1976, pp. 115-45. The translog production function was formulated by L. R. Christensen, D. W. Jorgenson, and L.J. Lau, ‘‘Transcendental Logarithmic Production Frontiers,” Review of Economics and Sta tistics, February 1973, pp. 28-45. 34 B. Real Output Measures Methods and Sources These components of g n p were excluded from the b l s measure of output used for productivity measurement This appendix describes the methodology and data sources employed in preparing the real output series for the b l s measures of productivity presented in this bulle tin. These include output measures for the business, nonfarm business, and manufacturing sectors which are used in the more familiar measures of output per hour of all persons. The output measures used in the multifactor productivity indexes are for the private business sector and exclude the output of government enterprises. Real output for the farm sector is also measured; it is sub tracted from the business output totals in order to obtain the output measures for the nonfarm business sector. The measures of real output employed in the b l s pro ductivity indexes are derived from data on gross nation al product ( g n p ) published in the National Income and Product Accounts ( n i p a ) by the Bureau of Economic Analysis ( b e a ) , U.S. Department of Commerce. Several important components of the gross national product measures are excluded in order to obtain indexes of out put which are appropriate for measuring productivity. This appendix explains the reasons for these exclusions. It also describes the concepts and methods underlying the measures for the farm and manufacturing sectors. Table B-1. Relationship between gross national product and the BLS measure of private business sector gross product, 1981 Amount (billions of 1972 dollars) Percent Total: Gross national product1 ........................ $1,502.6 100 Excluded from bls private business gross product: ..................................... 349.6 23 Output originating in: General government2 ...................... Owner-occupied housing3 ................ Rest of the world2 ........................... Households and institutions2 4 ......... Statistical discrepancy2 .................... Government enterprises6 ................ 156.0 100.2 25.4 52.1 -0 .9 22.0 10 7 2 3 (5) 1 1,147.3 76 1,133.2 75 Equals: BLS private business gross product Value of output deflated by output price indexes................................................. Business sector The business sector is the largest aggregate for which productivity measures are presented in this bulletin. Output of the sector can be briefly described as all ac tivities of for-profit business establishments engaged in production in the United States. It is based on concepts underlying the n i p a measures of g n p . 1 Table B -l shows the relationship of the b e a measure of g n p and the b l s measure of private business output in 1981 (1972 prices). The value of output in the private business sector accounted for 76 percent of g n p . The 24 percent of g n p not included comprised general govern ment; output of the “ rest of the world” ; output of household workers and of nonprofit institutions; output imputed to the housing services of owner-occupied housing; and the statistical discrepancy.2 Nonresidential structures1 ................ Services furnished without payment by financial intermediaries, except life insurance carriers7 .................. Other ................................................ 51.6 4 19.6 1,062.0 1 71 Value of output deflated by index of wage rates and materials prices .................. 14.1 1 12.9 1 1.3 (5) Personal consumption expenditures (part)8 .......................................... Producers’ durable equipment (part)9 ............................................ ’ Table 1.2 in Survey of Current Business, July 1982. 2Table 1.6 in Survey of Current Business, July 1982. 3Table 1.21 in Survey of Current Business, July 1982, and unpublished detail for farms. Comprises $98.9 billion of nonfarm and $1.3 billion of farm housing. 4Includes unpublished bea measures of nonprofit real estate rental value. 5Less than 0.5 percent. 6Table 6.2 in Survey of Current Business, July 1982. 7Table 2.5 in Survey of Current Business, July 1982. 8Estimate provided by the Bureau of Economic Analysis, U.S. Department of Commerce, from unpublished detail underlying table 2.5 in Survey of Cur rent Business, July 1982. Comprises life insurance and commercial and vo cational schools. 9Table 5.7 in Survey of Current Business, July 1982. Comprises ships and boats. 'For a description of the concepts, methodology, and sources of data underlying the n i p a , see Carol S. Carson and George Jaszi, “ The National Income and Product Accounts of the United States: An Overview,’’ Survey of Current Business, Vol. 61, February 1981, pp. 22-34; “ Revised Estimates of the National Income and Product Accounts,’’ Survey of Current Business, Vol. 62, July Item 1982, and National Income, 1954 Edition: A Supplement to the Survey of Current Business. 2The statistical discrepancy is the difference between g n p and the charges against g n p . It arises because g n p and the charges against g n p are estimated independently, and each is subject to measurement errors. 35 because (1) no adequate corresponding labor or capital input measure can be developed for these components of the nipa or (2) the gross product measures for the com ponent are based on labor inputs, implying constant out put per unit of labor input. The specific reasons for excluding each of these com ponents will be discussed in turn. Before doing so, it is important to note that only about 1 percent of private business output (measured in 1972 prices)—the remain der after the exclusions from gnp—was based on real output measured by deflating current-dollar output by an index of labor and materials inputs.3 This clearly does not represent a serious problem in measuring real output for the private business or private nonfarm business sector. The output of general government has been excluded since the bls measures of output per hour were first in troduced in 1959. This exclusion is due to the manner in which constant-dollar real output is measured in the nipa . In the accounts, general government output is de rived by moving base-year compensation by changes in total hours of governm ent employees adjusted for changes in grade level. This virtually assumes that pro ductivity remains constant, since changes in output are essentially proportional to changes in hours. Although this is not the only area in the national accounts where, for lack of data, output change is equated with labor in put change, it is by far the largest single sector where this occurs. In addition, the proportion of employment accounted for by government (including military) has increased significantly since 1950. bls excludes the rest-of-the-world sector because there are no corresponding labor or capital input data. The current value of output of the rest-of-the-world sec tor is equal to payments to factors (labor and capital) abroad owned by U.S. residents, less payments to fac tors in the United States owned by foreigners. Hence, a dividend paid to a foreigner is a negative entry and a wage received by an American employee in a foreign country is a positive entry. Since it is not possible to identify domestic labor or capital inputs associated with this output, the rest-of-the-world sector is excluded. Output imputed to owner-occupied dwellings is also excluded from the aggregate productivity measure be cause there is no measure available for the labor input of homeowners. In the nipa , an imputation is made for the rental value of owner-occupied homes. This imputa tion treats homeownership as a business providing hous ing services which are sold to the homeowner in his ca pacity as tenant. The output of this service is estimated as the amount for which owner-occupied homes could be rented, less maintenance, insurance, and like ex penses of the homeowner. Since no comparable labor input data are available for the activity of homeowner ship, the product of owner-occupied homes is excluded from the output estimates for productivity purposes. The output measure for private households is ex cluded because real output in this sector is measured by labor input. The household industry refers to domestic employees, and current value of output is measured in the nipa by the compensation of domestic employees. Real output is measured by deflating this compensation by the Consumer Price Index for housekeeping and home maintenance services, which is essentially an in dex of hourly compensation. This assumes that output per employee is constant over time. Nonprofit institutions are also excluded because real output is measured essentially by labor inputs. Current value of output is measured using employee compensa tion. The bea method of deflation used for nonprofit or ganizations is somewhat more complex than that used for private households. Nevertheless, real output of nonprofit institutions is essentially measured by deflat ing the employee compensation series by an index of compensation per full-time-equivalent employee. These measures have serious limitations for productivity meas urement, and this sector is consequently excluded from the private business sector. The “ statistical discrepancy” is the difference be tween gnp estimates measured from the product and in come ( “ charges against gnp ” ) sides of the accounts. Government enterprises—the U.S. Postal Service, other Federal enterprises such as the Tennessee Valley Authority, and State and local enterprises such as Staterun liquor stores—are excluded for two reasons. First, it would be especially difficult to measure capital inputs in this sector because in the nipa , structures and durable equipment used by these enterprises are treated as final sales to general government, rather than as investments of the enterprises. Government enterprises thus show no capital cost associated with plant and equipment. The second reason concerns the measurement of income from capital (i.e., property income). In these enter prises, capital and labor are combined in multifactor productivity measurement, and this requires the use of labor and capital income shares as weights. Satisfactory data are available on compensation of employees; how ever, the data on income from capital are unsuitable be cause these enterprises are subsidized by the govern ment and the pricing of output reflects these subsidies. Thus, estimating property income as the residual of value of output minus labor compensation would seri ously understate capital’s share of output. measured by labor input.” That is, it accounted for only 1.3 per cent of private business output (.01 divided by .76). 3Table B -l shows that, within the 76 percent of GNP used to calculate the b l s measure of private business output (in 1972 prices), only 1 percentage point was accounted for by “ output 36 Farm sector The measure of output used in the b l s index of multi factor productivity for private nonfarm business is ob tained by subtracting real output of the farm sector from private business real output. The measure for real farm output is the b e a estimate of “ gross farm product’’ in constant (1972) prices.4 b e a , in turn, bases its measures on estimates of farm income and expenses prepared by the U.S. Department of Agriculture ( u s d a ) employing data collected by the u s d a and benchmarked periodical ly to statistics from the Census of Agriculture. The b e a measure of gross farm product is derived by the “ double-deflation” value-added procedure. Using this method, the current values of output and purchases of intermediate goods and services by the industry are first deflated by appropriate price deflators. The de flated figures for purchased goods and services are then subtracted from the deflated value of output; the residu al is industry product originating (value added) in con stant prices.5 B ea farm output includes cash receipts from farm marketings, net Commodity Credit Corporation loans, rental value of farm dwellings, home consumption of farm products, other farm income, and changes in in ventories. Receipts from farm marketing of crops and livestock are obtained by summing monthly estimates based on quantities sold and market prices, or, in the case of poultry and dairy products, directly from pro duction reports. Sales of approximately 150 items are covered, accounting for 90 percent of farm income. All sales of crops are covered, including seed and feed sold to other farmers; livestock sold to other farms in the same State are excluded from both sales and expenses. Farm sales of forest products are included in the crop totals. Constant-dollar estimates of farm output are obtained by deflating each of the current-dollar components sepa rately. Constant-dollar farm marketings are obtained for the following categories of farm products: Food and feed grains; oil bearing crops; tobacco; cotton; vegeta bles; potatoes, sweet potatoes, and beans; fruit; other crops; meat animals; dairy products; poultry and eggs; wool; and other livestock. Deflators are aggregated from 150 “ prices received by farmers” collected by the u s d a . Food and fuel consumed on farms are deflated by the same u s d a prices received by farms or appropriate n i p a personal consumption expenditure deflators. Intermediate goods and services purchased include all M anufacturing sector The computation of real output in manufacturing fol lows the double-deflation method discussed above for the farm sector.6 In the n i p a , the output measures for manufacturing are prepared in two steps: (1) A deflator is obtained by dividing Census current-dollar value added by constant-dollar value added; and (2) this defla tor is applied to the b e a measure of gross product originating in manufacturing. Current-dollar value added in the first stage is derived from data from the Censuses and Annual Surveys of Manufactures on the value of manufacturing production, less the cost of ma terials, less the estimated value of business service in puts. Constant-dollar value added is the deflated value of production, less the deflated value of material inputs, less an estimate of the deflated value of service inputs. The b e a gross product data to which the value-added deflators are applied are the sum of factor and nonfactor charges, compiled independently for 2-digit Standard Industrial Classification (sic) industries in the n i p a . The underlying deflation of the value of output and of mate rial inputs is done at the most detailed level of industry possible. 4For a description of the method and sources used by b e a to measure gross farm product in the n i p a , see Shelby W. Herman, “ The Farm Sector,’’ Survey of Current Business, Vol. 58, Novem ber 1978, pp. 18-26. The annual figures in current and constant prices appear in tables 1.18 and 1.19, respectively, in the July is sues of the Survey. Conceptually, the sum of gross product originating (value added) for all industries is equal to g n p . This is so in both current and constant dollars. However, in practice, the equality in constant prices may not hold because of errors of measurement. 6B ls used the same method for manufacturing in the 1950’s. See Trends in Output per Man-Hour and Man-Hours per Unit o f Output—Manufacturing, 1939-53, Report 100 (Bureau of Labor Statistics, 1955). production costs incurred by the farm operator, such as feed, seed, fertilizer, contract labor, machine hire, and rent paid to nonoperator landlords. Estimates of most expenses are based on information from u s d a surveys of farm production expenses. Constant-dollar estimates are prepared by b e a by separately deflating 13 expense components, using appropriate indexes from among the “ prices paid by farmers” published by u s d a . The difference between b e a farm output and interme diate purchased goods and services is gross farm prod uct in current dollars, the n i p a measure of farm value added, or the contribution of the farm sector to currentdollar g n p . Equivalently, on the income side, gross farm product comprises factor incomes (employee com pensation, net interest, noncorporate income, corporate profits) plus nonfactor costs (capital consumption allow ances, indirect business taxes), less subsidies to farm ers. These components of g n p originating on farms are estimated concurrently with the farm output and pur chases data. Similarly, the difference between the deflated value of farm output and the deflated cost of intermediate goods and services purchased is equal to real farm gross product, or the contribution of the farm sector to real GNP. 37 Manufacturing output. Value of shipments and changes in inventories are prepared for 4-digit sic industries in manufacturing.7 These data have been collected since 1949 and published in the benchmark Censuses and An nual Surveys of Manufactures in generally the same form. There have been periodic revisions to the sic af fecting both product and industry classifications. Large revisions took place in 1958 and 1972, causing some es tablishments in 4-digit Census industries to be moved across 2-digit lines. In most cases, the effect of these classification revisions at the 2-digit industry level is small or even trivial. The deflation of value of shipments and changes in inventories is done by b e a using the b l s product class indexes, which are groupings of highly detailed pro ducer price indexes into the “ 5-digit” product catego ries reported in the Annual Survey of Manufactures. This tabulation of prices was published in the late 1950’s as part of the Census of M anufactures for benchmarking purposes, and it has been maintained ever since.8 About 54 percent of the product classes in man ufacturing are covered by b l s product price indexes. Another 38 percent are covered by related b l s price in dexes. Price series for most of the remainder are con The current cost of materials is deflated to obtain the real quantity of materials inputs for double-deflation purposes. Deflators are constructed by b e a using b l s producer prices (mainly the 5-digit product-class defla tors) and weights based on the b e a input-output tables of the U.S. economy for the years 1947, 1958, 1963, 1967, and 1972. The tables provide a complete list of material inputs for each industry for those years, from which weights are computed for the aggregation of ma terials prices. Weights are interpolated between tables; for years after the most recent input-output table, weights remain constant. 7The classification of products and establishments in the b l s pro ductivity program follows the scheme established by the Office of Management and Budget in its Standard Industrial Classification Manual, 1972 edition. Under this system, related products or serv ices are grouped together in categories denoted by a code of up to 7 digits, depending on the breadth of the category. Thus, a 7-digit code is assigned to a relatively narrowly specified group of prod ucts, and a 2-digit code to a broad area such as fabricated metal products (sic 34). Every establishment reporting data to the Census Bureau or the b l s is assigned the 4-digit code in which its most im portant product, in terms of value of shipments, falls. 8These indexes were constructed jointly by the Board of Gover nors of the Federal Reserve System, the Bureau of Labor Statistics, and the Bureau of the Census. They were published in United States Census of Manufactures, 1954, Vol. IV: Indexes of Produc tion (Bureau of the Census, 1958). structed as weighted averages of indexes of material in put and labor costs. Cost o f materials, containers, and supplies. The current cost of materials inputs is collected by the Census Bu reau and published in the Annual Survey of Manufac tures and the Census of Manufactures. All purchased materials are included, with the exception of those bought for resale without further processing. All fuels and office supplies are included; items treated as capital investment are excluded. 38 Appendix C. Capfel Input and Capital and Latoir Slhaires two stages in developing the aggregate measures are de scribed in section II. Section III discusses the method used to measure capital and labor income shares. Sec tion IV examines the capital input measures and capital and labor shares of income. Section V reports on the sensitivity of capital input and multifactor productivity measures to the inclusion of inventories and land and to alternative “ efficiency” functions. The final section summarizes the discussion and concludes with the de tailed tables of capital input measures by major type of asset for the private business, private nonfarm business, and manufacturing sectors. Table C -l provides a con venient guide and summary of the procedures used to generate the b l s capital measures (steps 1-7) as well as of the additional work needed to measure multifactor productivity (steps 8-10). Capital input, defined as the services from physical assets, is measured for each of three subsectors of the U.S. private business sector—manufacturing, farm, and nonfarm-nonmanufacturing. These measures are then aggregated to the three published sectors: Private busi ness, private nonfarm business, and manufacturing. This appendix presents a detailed discussion of how capital is measured and of how the capital and labor cost shares used to weight the respective input measures are determined. The capital measures are constructed in three major stages. First, stocks are estimated for 47 type of assets; this is discussed in section I. Second, rental prices are estimated for each type of stock. Third, assets are ag gregated using shares based on rental prices. These last Table C-1. Summary of methods and data sources used to measure capital and multifactor productivity— Continued 1. Obtain real invest ment data for depre ciable assets Investment in: a. equipment b. structures c. rental residential capital 2. Allocate investment data to major sectors Investment by asset type by sector (manufacturing, farm, nonfarm nonmanufacturing) 3. Determine age/efficiency functions for each type of asset 4. Perform vintage ag gregation Methods used and detail in which step is performed Data item obtained or constructed Step Weights reflecting the declining services of an asset type cohort as it ages Real stocks of depreciable assets by type by sector Data source a. 20 asset types b. 14 asset types c. 9 asset types a.-c. National Income and Product Ac counts (nipa)1 a. asset detail allocated using: b. sectoral investment totals proportional to c. historical data cross-classified by asset detail and sector a. step 1 A hyperbolic form using: a. an average service life estimate b. normal distribution of discards c. a shape determined using empirical evi dence Perpetual inventory method: Real historical investments weighted by age/efficiency functions b . NIPA C. NIPA a. nipa b . NIPA c. Hulten and Wykoff2 a. steps 2 and 3 a. stock of inventories b. stock of farm land c. stock of land in manufactur ing and nonfarm-nonmanu facturing a. by stage of processing in manufacturing b. regional services weighted using rental prices c. proportional to structures using benchmark land estimate a. nipa b. U.S. Department of Agriculture c. Manvel3 6. Construct rental prices Implicit rental value of the services of a unit of each type of asset in each sector a. rental price formula estimated using data on capital stocks and data on payments to capital a. Christensen and Jorgenson4; steps 4 and 5; nipa 7. Aggregate assets Measure of real capital input in each sector Tomquist index of asset capital stocks using rent al prices to determine weights 5. Measure nondepreci able assets See footnotes at end of table. 39 a. steps 4, 5, and 6 labile C—1. Summary of methods and data sources used to measure capital and muitifactor productivity—Continued Step 8. Constm ct cost shares Data item obtained or constructed Methods used and detail in which step is performed Shares of labor and capital inputs in the value of each sector’s output Based on: a. em ployees’ labor compensation b. corporate capital payments and c. proprietors’ income allocated to labor and capital using d. em ployee com pensation per hour and e. corporate rate of return to capital e. based on step 6 Tom quist index of: a. labor and b. capital in each sector using c. cost shares as weights d. Tom quist index of com bined input across sectors using factor shares in value of output b. step 7 c. step 8 d. shares based on 9. Combine inputs a .- c . measures of com bined la bor and capital input by sector (manufacturing, farm, nonfarm -nonm an ufacturing) d. m easures of combined input for private business, nonfarm business 10. Compute multifactor productivity Reported for private business, nonfarm business, manufacturing Ratio of: a. output to b. input Data source a .- c . NIPA d . BLS a . BLS nipa a. nipa b. step 9 ’Bureau of Economic Analysis. 2Shares were reconciled to functions reported in Charles R. Hulten and Frank C. Wykoff, “The Estimation of Economic Depreciation Using Vintage Asset Prices: An Application of the Box-Cox Power Transforma tion,” Journal of Econometrics, 1981, pp. 367- 96; and in C. R. Hulten and F. C. Wykoff, “The Measurement of Economic Depreciation,” in C. R. Hulten, ed., Depreciation, Inflation and the Taxation of Income from Capital (Washington, The Urban Institute Press, 1981), pp. 81-125. benchmarks based on estimates from Allan D. Manvel, “Trends in the Value of Real Estate and Land, 1956-1966,” in Three Land Re search Studies (Washington, National Commission on Urban Problems, 1966). 4Formula used to measure rental prices derived by Laurits R. Christensen and Dale W. Jorgenson, “The Measurement of U.S. Real Capital Input, 1929-1967,” Review of Income and Wealth, Vol. 15, No. 4, 1969, pp. 293-320. L ileasuremain! of Capital Stoeks by Asset Type Conceptually, the wealth stock represents the present value of all future services embodied in existing assets. Unlike the productive stock, the wealth stock does not directly influence productivity but indicates the current market value of all new and used capital goods. The wealth stock is needed to estimate depreciation, which is used in m easuring the im plicit rental prices for capital. This section is concerned with the framework used to construct the bls capital measures.1 A central concept in this framework is that of the “ productive” capital stock, or the stock measured in efficiency units. Con ceptually, the productive stock represents the amount of new investment which would be required to produce the same capital services actually produced by existing as sets of all vintages. Thus, total current services from as sets of all vintages are proportional to the productive stock. It is this measure of capital stock which is direct ly associated with productivity. The measurement of the productive stock involves vintage aggregation, which requires historical data on real investm ent and an “ age/efficiency ” function that describes the pattern of services that capital goods supply as they age. In addition, this section discusses the measurement of the “ wealth” stock of physical capital, or the stock measured in terms of the market price of used assets. Vintage aggregation Each type of stock is computed by the perpetual in ventory method. The stock at the end of a period is equal to a weighted sum of all past investment, where the weights are the asset’s efficiency (defined below) as of a given age. Mathematically, the productive stock Kt, at the end of the period t is given by: K t = X T= t s T- t l 2 t - T where It is investment in period t and st is the efficiency function. pp. 292-320. An extensive discussion of this topic, together with references to the literature, may be found in W.E. Diewert, “ Ag gregation Problems in the Measurement of Capital,” in Dan Usher, ed., The Measurement of Capital (Chicago, The University Press, 1980)pp. 433-528. ’The model used to measure capital stock was developed in Rob ert E. Hall, “ Technical Change and Capital from the Point of View of the Dual,” Review of Economic Studies, January 1968, pp. 35-46. The model was used empirically in Laurits R. Christensen and Dale W. Jorgenson, “ The Measurement of U.S. Real Capital Input, 1929-1967,” Review of Income and Wealth, Vol. 15, 1969, (C.l) 40 Table C-2. Illustration of a perpetual inventory calculation for a fictional type of asset Item Gross new investment.................................................................... Contribution of goods of a givpn age to year-end stock: Age 0 ...................................................................................... 1 ........................................................................................ 2 ........................................................................................ 3 ........................................................................................ 4 ........................................................................................ 5 ........................................................................................ Year-end stock (weighted sum of past investments).................... Change in stock since previous y e a r............................................ Equals gross investment......................................................... Minus efficiency losses of all vintages.................................. Age/efficiency function 1.0 .9 .7 .4 .1 .0 The efficiency function is a schedule which indicates the quantity of services provided by an asset of a given age relative to a new asset of the same type. This func tion is generally assigned a value of 1.00 when the asset is new and declines as the asset ages, eventually ap proaching or reaching zero. Consequently, investments in the more distant past contribute less to current output. Illustration of perpetual inventory method. Table C-2 illustrates the perpetual inventory method for a hypo thetical asset with a 5-year service life. The cells of the matrix of contributions to the capital stock are calcula ted as the product of two values. The first value is the age/efficiency function for an asset of the given age (column 1). The second is the gross investment made the given number of years ago. The contribution of a given year’s investment to the stock can be tracked through the successive years as it ages. This is done by following a diagonal downward and to the right. One example is marked with asterisks. The total stock in a given year is equal to the sum of contributions from past investments. It changes from year to year to reflect new gross investments net of accruing efficiency losses. These losses cannot be cal culated without knowing the distribution of past invest ments. Only in the case of geometric decay are they equal to a constant percentage of the stock. In order to measure the first year’s stocks, it is neces sary to collect historical investment data extending back as long as the life of the asset. The U.S. Commerce De partment’s estimates of investment go back as far as 1820 for some types of structures. The same procedures are used for each of 43 types of depreciable assets in order to obtain the b l s measures of capital. Each type of asset has a different efficiency function depending on its expected life and on whether it is a structure or a type of equipment. The year-end stocks are then averaged with the previous year-end stock to estimate the services contributed by a given 2For a criticism of this approach, see Martin S. Feldstein and Mi chael Rothschild, “ Towards an Economic Theory of Replacement 1971 1972 1973 1974 1975 1976 1977 1978 100 120 150 200 100 200 220 250 100* 120 90* 150 108 70* 200 135 84 40* 100 180 105 48 10* 200 90 140 60 12 0* 502 59 200 141 220 180 70 80 15 0 565 63 220 157 250 198 140 40 20 0 648 83 250 167 443 type of asset during the year. Average stocks of differ ent asset types are then aggregated using a Tornquist in dex. In this procedure, rental prices are used to con struct the weights for assets of different types by different sectors. Age/efficiency function In general, the relationship between the economic ef ficiency of an asset and its age is very complex and de pends on the particular type of asset as well as on a host of other factors such as the level of economic activity, relative input prices, interest rates, and technological developments. To further complicate matters, it is very difficult if not impossible to “ observe” or directly measure quantity of capital services. The standard prac tice among economists is to represent the pattern of services as a capital good ages by using an efficiency function as defined above. This pattern of services is proportional to the rental income, in constant prices, which the good is capable of generating. Use of an efficiency function involves strong assump tions. First, the quantity of capital services from a par ticular type of asset is assumed to be a function of its age.2 Second, the pattern does not respond to any fac tors other than age, remaining fixed over time. In view of these restrictive assumptions, the validity of using an efficiency function to represent capital services remains a major issue, particularly as it relates to the applicabil ity of microeconomic assumptions to aggregate data. Several general forms have been employed by re searchers. These are illustrated in chart C - l. Use of the gross stock or “ one hoss shay” form assumes that the asset exhibits no loss of services until it suddenly ex pires. A light bulb is perhaps the best example of this. The three other forms are “ net” of some loss of serv ices during their lives. The straight-line form exhibits the same loss of services each year. The concave form exhibits gradual losses early in the life of an asset, and more rapid losses as it ages. The convex form exhibits Investment,’’ E c o n o m e tr ic a , May 1964, pp. 393-424. Several attempts have been made to address the effi ciency function issue by observing used asset prices.8 A relationship is postulated between the efficiency of a used asset and its market price relative to a new asset. In a dynamic model where the firm minimizes costs over all time periods, the market price of an asset will equal the discounted (rental) value of the stream of fu ture services that the asset embodies. This duality be tween efficiency and price also determines the relation ship between the (assum ed) form of the efficiency function and the pattern of prices as the asset ages. Thus, observations of used asset prices may be em ployed indirectly to infer the form of the efficiency function.9 The most intensive empirical study of used asset prices done to date is by Hulten and Wykoff.10 In a 5-year project recently completed for the Treasury De partment, Hulten and Wykoff collected extensive data on prices of used assets and fitted them econometrically to various mathematical forms. Their published findings make use of a very general function, the “ Box-Cox” function. Thus, rather than assume either a convex or concave form, they employed a function which can be either convex or concave depending on the sample data. The gross, straight-line, and geometric shapes are spe cial cases of the Box-Cox function so that it can be used to statistically test each of these cases. Hulten and Wykoff reject each of these three special forms of the age/price function. Their results, in particular, rule out the geometric form and the one hoss shay (gross capital stock) for most types of assets. They did, however, find that the typical age/price profile of an asset was convex. In order to obtain a summary measure of depreciation for each type of asset, Hulten and Wykoff fitted “ best geometric approximations” ( b g a ) to their Box-Cox esti mated prices. These were determined by regressing the logarithms of the Box-Cox estimated prices against age and time. The results indicated no consistent trend in rapid early service losses followed by more gradual losses of the remaining efficiency. Practitioners have adopted a wide variety of solutions to the problem of selecting an appropriate efficiency function. John Kendrick prefers a gross stock form.3 A concave form is used by Edward Denison4 and was used in the past by b l s . 5 Dale Jorgenson and his associates have used the convex geometric form.6 Edward Miller points out that, since obsolescence as well as deteriora tion must be removed as an asset ages, a straight-line or even convex form may be best.7 Both Kendrick’s and Denison’s work is based on capital stock data computed by b e a . Chart C-1. General forms of an efficiency function 3John W. Kendrick, The Formation and Stocks of Total Capital, National Bureau of Economic Research (New York, Columbia Uni versity Press, 1976). 4Edward F. Denison, Accounting for Slower Economic Growth: The United States in the 1970’s (Washington, The Brookings Insti tution, 1979). 5Capital Stocks for Input-Output Industries: Methods and Data, Bulletin 2034 (Bureau of Labor Statistics, 1979). 6See, for example, Barbara M. Fraumeni and Dale W. Jorgenson, “ The Role of Capital in U.S. Economic Growth, 1948-1976,” in George von Furstenberg, ed., Capital, Efficiency and Growth (Cambridge, Mass., Ballinger Publishing Co., 1980), pp. 9-250. 7Edward M. Miller, Capital Aggregation for Productivity Meas urement and Other Purposes, Working Paper No. 34 (Houston, Jesse H. Jones Graduate School of Administration, Rice Universi ty, May 1983). 8For a discussion of problems in empirically determining the form of the efficiency function, see Michael J. Harper, “ The Meas urement of Productive Capital Stock, Capital Wealth, and Capital Services,” Working Paper No. 128, (Bureau of Labor Statistics, 1982). 9This is perhaps most simply illustrated in the special case of the geometric form. If the efficiency function is a geometric form (i.e., a convex form in which efficiency declines by the same percent each year), then the price pattern is also geometric so that deprecia tion (i.e., the rate of decline in price) occurs at the same constant rate as the efficiency loss. This “ self duality” property is pos sessed only by the geometric form. 10The work is presented in Charles R. Hulten and Frank C. Wykoff, “ The Estimation of Economic Depreciation Using Vintage Asset Prices: An Application of the Box-Cox Power Transforma tion,” Journal of Econometrics, 1981, pp. 367-96; and in C.R. Hulten and F.C. Wykoff, “ The Measurement of Economic Depre ciation,” in C.R. Hulten, ed., Depreciation, Inflation and the Taxation of Income from Capital (Washington, The Urban Institute Press, 1981), pp. 81-125. 42 Wykoff data using a hyperbolic functional form resulted in an efficiency function which declines initially at onehalf the straight-line depreciation rate for equipment, and at one-fourth the straight-line rate for structures. Since formula (C.2) is applied to broad types of as sets, each of which represents a variety of capital goods, a distribution of lives was assumed. This was done by constructing a “ cohort” efficiency function which is a weighted average of efficiency functions cal culated using formulas (C.2) and various specific ages. The weights are determined by a discard density func tion. Chart C-2 illustrates a cohort efficiency function for an assumed average life of L years with a truncated normally distributed density function of retirement ages ranging from 0.5 to 1.5 times L. the age/price profile over time; the age coefficients rep resent an estimate of the average rate of depreciation. After carefully considering the alternatives, b l s de cided to use a concave efficiency form (slow decline during the earlier years), and to determine its shape using available empirical evidence. The assumption of a concave form was settled on because of the cursory ob servation that many capital assets do not tend to decay rapidly during their intital years. In addition, members of the b l s Business Research Advisory Council can vassed their organizations and reported similar experi ences with the capital assets owned by the firms they represent. The mathematical form used for the age/efficiency re lationship is the hyperbolic function: st = (L - t) / (L - j8t) st = O where st L t and /3 is to vary. 0<t<L t>L Table C-3. Types of assets and service life assumptions (C.2) Type of asset is the relative efficiency of a t-year-old asset is the service life is the age of the asset the parameter allowing the shape of the curve Nonresidential equipment Furniture and fixtures .......................... Fabricated metal products .................. Engines and turbines........................... Tractors ................................................ Agricultural machinery (except tractors) In this formula, a value of (3 equal to zero corre sponds to a straight-line efficiency pattern, while a value of /3 equal to one is consistent with the one hoss shay. The mean service lives, L, are the b e a estimates shown in table C-3. In experiments described shortly, it was determined that the best statistical fit to the Hulten- Construction machinery (except tractors) ............................... Mining and oilfield machinery ................................................. Metalworking machinery........................................................... Special industry machinery ..................................................... General industrial, including materials handling equipment.. . Office, computing, and accounting machinery Service industry machinery ........................... Electrical machinery........................................ Trucks, buses, and truck trailers.................... Autos .............................................................. Aircraft .................. Ships and boats .. Railroad equipment Instruments ........... Other equipment... Cfoart C-2. Cohort efficiency function for gross stocks with a truncated normally distributed discard function (Two standard deviations correspond to one-half of the mean service life, L) Life (in years) 21 8 17 9 10 16 16 14 8 10 14 9 10 16 22 25 11 11 Nonresidential structures Industrial buildings.............................................. Commercial buildings ........................................ Religious buildings.............................................. Educational buildings.......................................... Hospital and institutional buildings .................... 27 36 48 48 48 Other nonfarm nonresidential buildings Railroad structures............................... Telephone and telegraph structures . .. Electric light and power structures Gas structures ..................................... 31 51 27 30 30 Other public utility structures................................................... Farm nonresidential buildings .................................................. Petroleum, gas, and other mineral drilling and exploration .. . All other private nonresidential structures............................... 26 38 16 31 Residential assets Tenant-occupied nonfarm: 1- to 4-unit structures (additions) ......... 1- to 4-unit structures (new).................. Structures of 5 units or more (new) Structures of 5 units or more (additions) Mobile hom es........................................ Residential equipment............................ Tenant-occupied farm: 1- to 4-unit structures (new).................. 1- to 4-unit structures (additions) ......... Mobile hom es........................................ 43 15 18 80 40 65 32 16 11 80 40 16 b l s selected a somewhat flatter truncated normal dis tribution ranging from 0.02 to 1.98 times L. (Two standard deviations correspond to 0.98 times the mean service life.) Thus, formula (C.2) was computed repeat edly for each asset type, with L varying between 0.02 and 1.98 times the mean service life. The results of these computations were then added together, weighted by a discrete approximation to the normal density func tion, to produce a cohort efficiency function. The value 0.98 was chosen in order to conform to the empirical observation by Hulten and Wykoff that assets are occa sionally found which are considerably older than the BEA-estimated average service lives and also to take ac count of the fact that a few assets are accidentally de stroyed when new. The final step in estimating the cohort age/efficiency function was to obtain estimates of (3, the parameter that determines the shape of the hyperbolic function (C.2). As previously noted, these were estimated using the Hulten and Wykoff fitted Box-Cox price functions. Spe cifically, the following equation was used to generate dual price functions for selected values of /3:11 Table C-4. Weighted sum of differences between hyperbolic efficiency patterns and simulated data Value of /3 parameter1 Type of asset 0.5 0.75 1.00 (one hoss shay) S tr u c tu r e s Retail (prices)2 ................ Offices (prices) ............... Warehouses (prices) . . . . Factories (prices) ........... 0.956 .394 .229 1.173 0.803 .324 .203 1.001 0.630 0.432 .217* .258 .189* .210 .796 .538 0.268* .421 .483 .139* .309 .003* .063 .133* .155 .359 E q u ip m e n t Tractors (prices) ............. Light trucks (efficiency)2 . Heavy trucks (efficiency) . .523 .224 .023 .467 .139 .008* .399 .058 .011 *=closest fitting (3 parameter. 1Statistics presented are the weighted sum of squared differences between the dual to the presumed hyperbolic function and the fitted Box-Cox function. Weights are the Box-Cox function itself. 2Price comparisons were done between price functions which were dual to assumed hyperbolic forms and simulated price series using price parameters based on Hulten and Wykoff's fitted Box-Cox price functions. Efficiency com parisons were done directly between efficiency patterns and a miles per year proxy for truck efficiency. See text for complete descriptions of data and com parison statistics. X ;= t s* (1 - r) T- 1 pt = 0.00 0.25 (straight line) ---------------------------------------------------------- X ;=o s* (1 - r) T (C.3) justed for discards (mean service life of 8 years, nor mally distributed between 0 and 16 years) and compared directly to the presumed efficiency pattern using the same error comparison statistics described in footnote 12. These steps were repeated for light and heavy trucks.13 The comparison statistics for the seven sets of trials are shown in table C-4. The lowest value, indicating the best fit, is marked with an asterisk for each trial. For structures, one hoss shay was best in two cases, while relatively high j3 values of 0.50 and 0.75 were best in one case each. For equipment, one comparison (trac tors) was made on the basis of price, while two compar isons (trucks) were made directly between efficiency functions. One hoss shay was best for tractors, while (3 values of 0.75 and 0.25 were best for light and heavy trucks, respectively. One of Hulten-Wykoff’s important results is that structures depreciate very slowly compared to equip ment during the initial years, even considering their longer lifetime. The trial comparisons are consistent with a somewhat higher (3 value (slower decay) for structures. Also, as indicated earlier, the Hulten and where pt is the price of a t-year-old asset relative to a new one st * is the cohort efficiency function and r is real discount rate assumed to be .04. The values of f3 selected were 0.0 (straight-line effi ciency loss), 0.25, 0.5, 0.75, and 1.0 (one hoss shay). The three intermediate forms correspond to increasing degrees of concavity for the hyperbolic function (C.2). The simulated dual price functions for each of the five values of (3 was compared with the Hulten-Wykoff fitted Box-Cox function. The estimate of (3 chosen was the one that resulted in the best fit.12 This same proce dure was used to estimate values of (3 for four different types of structures and one type of equipment (tractors). In addition, efficiency functions were compared di rectly to a proxy for the services provided by trucks. This proxy was constructed from the Census Bureau’s Truck Inventory and Use Survey (1977). Estimates of the total number of trucks and total truck miles were ob tained for each of 12 model years. Miles per year were then computed for each model year as a proxy for the services provided by the fleet of trucks still in service by age. Finally, this miles per year variable was ad- weights are the heights of the Box-Cox function so as to put more weight on the newer assets which, in fact, constitute a greater portion of the stock for each type of asset. 13Other factors, particularly maintenance costs and type of driv ing, would also affect relative efficiency. However, adjustments for such factors would be difficult to construct accurately even if data were available. n This is simply a discount formula, which assumes that the pur chase price of an asset equals the real discounted rental value of the stream of all future services that the asset will generate. ,2Two statistics were used to determine the best fit between the simulated dual price functions and the Hulten and Wykoff Box-Cox prices: (1) the coefficient of determination; and (2) a weighted sum of squared errors between the dual and Box-Cox prices where the 44 Meal gross investment Besides an efficiency function, the other element re quired to perform vintage aggregation in equation (C .l) is historical data on real gross investment. This section discusses the methods and sources of data used to meas ure the stocks of depreciable assets and to estimate the price deflators for new durable goods. It also describes the sources and methods used to construct stocks of in ventories and land. Estimates of investment are available from bea for a variety of asset categories, in both historical and con stant dollars. Constant-dollar investment is based on historical-dollar investment deflated by bea in detailed categories. Equipment is deflated principally by using bls Producer Price Indexes (ppi). Structures are deflated by indexes of residential prices, highway construction prices, and construction cost indexes.15 Historicaldollar investment estimates are developed at bea from survey data and are assigned to detailed asset categories using a “ capital flows table” based on U.S. Census Bu reau surveys of industry. Annual investment from bea is available by major sector, by tenure group, by legal form of organization, and by asset class. Major sectors include manufactur ing, farm, and nonfarm-nonmanufacturing. The calcula tions described below are conducted separately for each of these three sectors. The tenure grouping applies only to residential capital and refers to whether housing is owner- or tenant-occupied, bls measures exclude all owner-occupied housing, but include tenant-occupied housing, since private business sector output includes rental housing. Legal form of organization comprises several subdivisions. The major split is between corpo rate and noncorporate. The noncorporate sector, in turn, can be divided into sole proprietorships, partnerships, tax-exempt cooperatives, and nonprofit institutions. The bls measures do not use these detailed subdivisions. With respect to investment data, the only separate sub groups by legal form of organization is nonprofit insti tutions, since these are excluded from the business sec tor data. How ever, bea net stock figures for the corporate and noncorporate sectors are used to estimate corporate factors for the rental price computations. The final and most detailed breakout available from bea is by type of asset. The major bea asset types are equipment and structures. Since residential capital is al most entirely structures, aggregates are presented for three major groups of capital assets: Nonresidential equipment, nonresidential structures, and total residen tial capital. This procedure makes it possible to show nonresidential fixed capital for those interested in the effect of excluding residential capital (see tables C-8 and C-9 in the last section of this appendix). Each major asset category is divided into more spe cific types. Table C-3 in the previous section lists the 20 types of equipment, 14 types of structures, and 9 types of residential capital, bls applies the perpetual in ventory calculation separately for each type of asset. Performing the calculation in greater asset detail allows the stock measures to reflect changes in the distribution of service lives. Lack of such detail can bias the stock measures through two mechanisms—through changes in the asset composition of current-dollar investment and through differences in the growth rates of the prices of the various assets. In the present study, such asset detail is maintained not only during the perpetual inventory calculation, but also during rental price computation, al lowing use of asset-specific estimates of the effects of tax laws, depreciation, and price inflation. bea has estimated investment data as far back as pos sible (in some cases as early as 1820) to ensure that the perpetual inventory has been through one full life cycle by 1948, the initial year for which the bls measures capital. This is necessary to avoid measurement bias that would tend to overstate the rate of growth of capital. The following subsections specify which nonresiden tial and residential investment data are used in the bls application of the perpetual inventory method. Several steps are taken to ensure that detailed investment data are fully consistent with the most recent totals available from bea . 14It is also important to note that the “ best geometric averages’’ computed by Hulten and Wykoff are equally consistent with their data. That is, given the current state of knowledge, there is no empirical basis for choosing between the hyperbolic and geometric forms. The choice is then up to the researcher, and, clearly, differ ent researchers have different preferences. The concluding section of this appendix reports on a sensitivity analysis based on alterna tive assumptions about the form of the age/efficiency function for the measurement of the growth of both the capital stock and multifactor productivity. 15A more detailed discussion is presented in the Survey of Cur rent Business, August 1974. Wykoff tests reject the one-hoss-shay specifications. On the basis of these considerations and the experiments re ported above, the estim ate of (3 used in the age/efficiency functions for structures is 0.75; and the estimate of (3 used in age/efficiency functions for equip ment is 0.50. To summarize, the age/efficiency function used in the bls measures of the productive stock of capital by asset type is the hyperbolic form. The choice of this form is a “ prior” based on cursory observations and informal discussions with businessmen. The average lives used are those estimated by bea . The estimates of the /3 pa rameters for structures (0.75) and equipment (0.50) are consistent with the Hulten-Wykoff evidence on used as set prices.14 ( b g a ’s ) 45 Nonresidential investment, bea has provided historical data by detailed asset type cross-classified by major sec tor. This includes constant-dollar investment by asset type for residential and nonresidential equipment and structures in three sectors: Farming, manufacturing, and nonfarm-nonmanufacturing. This historical detail is re vised each time there is a benchmark revision of the Na tional Income and Product Accounts (nipa ). Updates and revisions for more aggregate totals are available from bea annually. The annual updates include con stant-dollar and current-dollar investment data by asset type and sector. The bea updates also include revisions to all series used to estimate corporate shares. In gener al, the cross-classified data are adjusted at bls to corre spond to revisions in the asset type investment totals using the biproportional matrix model (or “ ras” mod el).16 Furthermore, updates of the cross-classified detail are estimated from asset type and sectoral totals for the new year by applying the biproportional model to a ma trix starting with the cross-classified data for the most recent year available. Essentially, it is a method of creating a matrix which is consistent with known row and column sums and as consistent as possible with cross-classified data from a second source. After constant-dollar investment is allocated by asset type and sector, current-dollar investment is estimated for each category. This is done by m ultiplying the constant-dollar figures by price deflators. Separate de flators are estimated for each asset type, but are as sumed to be the same in all sectors for a given asset type. In effect, the output deflator for the producing in dustry is assumed to apply to all purchasers. Deflators are estimated in two steps. First, currentdollar investment figures supplied by bea are divided by corresponding constant-dollar figures for each asset type. Second, these initial estimates of the deflators are scaled to equal 1.00 in 1972. This step is necessary be cause some adjustments done by bea affect 1972 cur rent-dollar investment and constant-dollar investment differently. These adjustments reflect transfers of prop erty, including business purchases of secondhand gov ernment assets, sales by business to foreigners, transfer of residential capital from farm to nonfarm status, pur chases of residential capital by government for demoli tion, sales of passenger cars to the public by rental firm s, and conversions of residential capital from tenant- to owner-occupied status. These adjustments are reflected in the bls constant-dollar investment series. Within nonfarm-nonmanufacturing, an adjustment is made to remove nonprofit institutions from investment estimates for equipment, structures, and residential cap ital. These are removed from capital in order to be con sistent with the output and labor data in the private busi ness sector; output measures available from the nipa are based largely on labor inputs. Specific asset categories likely to contain nonprofit assets are isolated based on information from bea . For structures, nonprofit investment is assumed to be a fixed percentage of investment in four asset categories: Reli gious buildings (100 percent), educational buildings (98 percent), hospitals (95 percent), and other nonfarm nonresidential buildings (30 percent). Since initial bls estimates of total nonprofit investment based on these percentages overestimate the bea figure, the difference is reallocated among educational buildings, hospitals, and nonfarm nonresidential buildings to ensure consist ency with the most recent bea total. For equipment, total investment by nonprofit institu tions reported by bea is allocated to four equipment as set types: Furniture and fixtures, office machinery, trucks, and autos. In this study, the allocation is made in such a way that, when nonprofit institutions have been subtracted from these four categories, the relative proportions of the four asset types are unaffected. ,6The biproportional model is discussed by Michael Bacharach in “ Estimating Non-Negative Matrices from Marginal Data,’’ Inter national Economic Review, 1965, No. 6, pp. 294-310. Residential investment. Since private business sector output excludes owner-occupied housing, the only resi dential investment series included in bls capital meas ures are tenant-occupied farm and nonfarm residential housing. Tenant-occupied nonfarm investment is as signed to the nonfarm-nonmanufacturing sector; farm investment, to the farm sector. Constant-dollar residential nonfarm investment in structures is available for five types of assets (table C-3). Equipment is available for only a single asset type. Constant-dollar residential farm investment is available for structures for three asset types. Since current-dollar totals were not available for the five types of tenant-occupied nonfarm structures, deflators are de termined for total nonfarm residential investment. These deflators are then multiplied by each of the five asset classes to determine estimates of current-dollar invest ment for the five categories. Although stock estimates exist for tenant-occupied farm structures in recent years, bea has assumed new investment in this category to be zero since 1967 to en sure that their stock estimates decline as quickly as their benchmark data indicate. Proxies are therefore needed for bls to calculate deflators for the three asset types in cluded in this category. Prices for new and additional tenant-occupied 1- to 4-unit farm structures are assumed to equal the ratio of current- to constant-dollar owneroccupied farm structures of this size. Prices for tenantoccupied farm mobile homes are assumed to equal the ratio of current- to constant-dollar investment in owneroccupied farm mobile homes. 46 annual level. For the manufacturing sector, data are available from bea on inventories by stage of process ing. The stages are materials and supplies, work in process, and finished goods. Within manufacturing, bls works with the disaggregate bea inventories to reflect this detail. The rationale for including all types of in ventories in a capital measure is that all represent a cost and all can contribute to the orderliness of the produc tion process. A number of additional adjustments to residential in vestment data are made before the perpetual inventory method is applied. These include a reallocation involv ing nonfarm structures after 1970, an adjustment to make less detailed updates conform with the categories for which historical data are maintained, and, finally, the extraction of nonprofit investment from residential assets. First, an adjustment is made by bea to represent the large number of condominium conversions during the 1970’s. The adjustment—to total constant-dollar invest ment for nonfarm residential structures—has the effect of gradually moving condominiums from new tenantoccupied to new owner-occupied nonfarm structures during the years after 1970. During the years 1970-74, this reallocation is not reflected in the data by asset type cross-classified by major sector. The reallocation for condominiums is applied entirely to new tenantoccupied nonfarm structures of 5 units or more. Smaller differences between the bls sum of invest ment for the five structure asset types and the structures total received from bea occur for years where condo miniums are not an issue. As in the case of nonresidential capital, these small differences occur because the more detailed data are obtained from a listing to which revisions are not frequently made. In the bls measures, the most recent totals are imposed, and any discrepancy between totals and detail is distributed proportionally to the five categories of detail. Also, totals are updated to include new years before complete detail is available. Again, totals for updated years are allocated in propor tion to detail from the most recent year for which it is available. Finally, investment in residential capital by nonprofit institutions is removed. Total residential nonprofit fig ures are available from bea , but asset detail for this sec tor is not. Such investment occurs mainly in three asset types: New 1- to 4-unit structures, new structures of 5 units or more, and nonhousekeeping structures (a resi dential asset type not included in the private business sector). All nonhousekeeping structures are considered nonprofit institutions. Therefore, they are subtracted from total residential nonprofit constant-dollar invest ment. The amount left over is then removed proportion ally from the other two asset types. Inventories. Estimates of inventories in current and constant dollars are published in the Survey of Current Business for the three major sectors. Since the pub lished figures are end-of-period estimates, and since the concept of a productive input would be the average level during the year, an average of the end-of-quarter figures is computed in order to better approximate the average Land. Estimation of the quantity and rental price of land is important to the measurement of growth in mul tifactor productivity for the private business sector, es pecially for the farm and nonfarm-nonmanufacturing sectors. Besides the fact that land is a productive input in its own right, it is important to assign it a share in capital income when determining the rates of return and rental prices for all capital inputs. Unfortunately, the measurement of land poses several difficulties, the most serious of which is the scarcity of data for the manufac turing and nonfarm-nonmanufacturing sectors. Fortunat ely, land represents a smaller share of capital here than in the farm sector, where data are available. In the farm sector, data published by the U.S. Depart ment of Agriculture include land in farms (acreage), to tal current-dollar value of land plus buildings, and total current-dollar value of buildings alone, bls calculates a benchmark total value of land by subtracting the total value of buildings from the total value of land and buildings in 1972. This benchmark is extrapolated using an unpublished index of the quantity of land services provided by V. Eldon Ball of the Department of Agri culture. Ball derived this as a Tornquist index of region al land estim ates using rental prices to determine weights. Rental prices are estimated from actual rental transactions observed in the various regions. These measures are ideal from a conceptual viewpoint, be cause they are aggregated considering the apparent dif ferences in efficiency of land in different regions. Also, the weights used in this aggregation are based on direct observation of the rental market for land rather than on the implicit methods used for most rental prices in this study. In order to estimate land in manufacturing and non farm-nonmanufacturing, structures are multiplied by a land-structures ratio. The first step toward deriving an estimate of real land stocks for the manufacturing and nonfarm-nonmanufacturing sectors is to relate estimates of structures by Manvel to the bls data on capital effi ciency and wealth.17 This is done by using 1966 ratios of land to structure values based on Manvel’s work and applying these ratios to the bls estimates of the value of structures in 1966 results in benchmark land estimates. 17Use was made of data published in Allan D. Manvel, “ Trends in the Value of Real Estate and Land, 1956-1966,” Three Land Research Studies (Washington, National Commission on Urban Problems, 1968). 47 function and is the appropriate concept of capital inputs to use for productivity measurement. This section describes the com putation of the “ wealth” stock, which is based on the age/price func tion, equation (C.3). The wealth stock represents the sum of money (in base-period prices) which could be generated by selling all vintages of an asset at prevailing real prices. The wealth stock is used to estimate depre ciation, which is used in computing rental prices. The wealth stock, like the productive stock, is com puted by the perpetual inventory method; it too adds past investments using weights which decline with the age of the asset. However, in the case of the wealth stock, the weights are based on the age/price function rather than the age/efficiency function (C.2). Mathemat ically, the vintage aggregation equation used to compute the wealth stock is: Manvel’s land estimates are not used directly because the structures estimate on which they are based does not conform to bls structures. This is due to differences in sectoral definitions and in the technique used by Manvel to arrive at his benchm ark. By employing a ratio, M anvel’s work is used to extrapolate from the bls benchmark. The current-dollar stock of structures in 1966 consistent with bls data is calculated by reflating detailed constant (1972) dollar stocks of structures (in value or wealth terms) by each asset’s investment price deflator in 1966. Current- and constant-dollar asset stocks are then aggregated for each of three categories: Manufacturing, nonresidential nonfarm-nonmanufactur ing, and residential nonfarm-nonmanufacturing. Bench marks for 1966 for land are then calculated by multiply ing these 1966 structure values by ratios of land to structures. Each categ o ry ’s stock of structures is multiplied by a corresponding 1966 ratio. The ratio for manufacturing is based on Manvel’s estimates of indus trial structures and land; for nonresidential nonmanufac turing, on his estimates of total commercial and indus trial property; and for residential land, on his estimates of urban residential property. The linking of current- and constant-dollar land value growth rates to structures requires selection of an appro priate structures concept for extrapolation. Although stocks net of depreciation (losses in value) are used to benchmark land quantities, gross stocks of structures (i.e., based on one-hoss-shay efficiency patterns) are used to extrapolate them. Also, reflated gross stocks are used to extrapolate estimates of the current-dollar value of land. This tends to remove a bias that could be intro duced into land quantity and value estimates from the depreciation of structures. In effect, bls assumes that the real value of land cannot be a function of the depre ciation of the building standing on it. The extrapolation is done separately for manufacturing and for the resi dential and nonresidential business parts of nonfarm nonmanufacturing, since separate benchmarks are avail able for each. These are then aggregated to represent a total nonfarm-nonmanufacturing stock of land. Defla tors are then calculated by dividing the current-dollar land stock by the constant-dollar stock for the manufac turing and nonfarm-nonmanufacturing sectors. wt = s ; =tpT_t i2t_T where pt is the asset’s age/price function and It is investment in period t. The age/price series for pt are obtained from equation (C.3). The real gross investment data for the It are the same as those used to construct the productive capital stock; the sources and methods for these data are de scribed above. Equation (C.4) shows that the wealth stock measures the value represented by all existing assets. It thus rep resents the present value of all future service embodied in existing capital assets because of the relationship be tween efficiency and price discussed earlier.18 The de cline in the wealth stock from one period to the next, before adding in new investment, is a measure of depre ciation. Depreciation represents the amount of money in the current period needed to m aintain the stock of wealth at its current level. This information is used to estimate rental prices discussed below. Timing of investment and output Both the productive and the wealth stocks are yearend estimates and include all changes occurring during the year, such as new investment, accruing efficiency loss, and depreciation. These changes do not, in gener al, have their full impact on output during the year in question. For example, an increment of investment put in place on January 1 may have an impact on output during the entire year. Investment put in place July 1 can only affect output during the second half of the year, and December investment can contribute almost nothing to current-year output. Since the investment fig ures received from bea count investment at the time it is finished and ready to use, it seems reasonable to count about half of a given year’s new investment, efficiency loss, and depreciation towards the annual average meas- Wealth stock The discussion up to this point has been mainly con cerned with the computation of the “ productive” capi tal stock by asset type. The productive stock, as shown by equation (C .l), is based on the asset’s age/efficiency 18The wealth stock and the productive stock coincide in the spe cial case where the age/efficiency function is one of geometric decay. (c.4) 48 to be charged in order to cover costs of p dollars’ worth of an asset. For example, if d = 0.10 and the real inter est rate is 0.04, the owner would have to charge $.14 in rent in order to cover expenses on a $1 asset. At the end of a year, he could sell what was originally a $1 asset for $.90 and pay the bank 4 cents interest due, breaking even. Inflation in the price of new assets and tax laws com plicate the derivation of the rental price. Hall and Jorgenson19 derived the expression: ures of stocks. Therefore, a half-year convention is used in the bls measures. A given year’s output is matched to the arithmetic mean of the current year-end stock and the year-end stock for the previous year. Thus, capital services are assumed proportional to the annual average productive stock of a given asset. These averages are used to compute the Tornquist index of real capital in put (appendix E) and the index of real factor input in the multifactor productivity measures. On the other hand, depreciation during the year is computed from the yearend stocks of wealth in order to reflect the losses of value from the beginning to the end of the year. As previously indicated, vintage aggregation is done separately for each of the 43 depreciable asset types listed in table C-2. Time series are generated repre senting the productive stock, the wealth stock, real de preciation, gross new real investment, and the price de flator of new capital goods. Each of these is computed by asset for each of the three major subsectors of the private business sector. (1 - utzt - et) (ptrt + ptdt - Apt) + Pt*t ct = 1 - ut (C.6) where Ut Zt et rt dt SL Aggregation of Capital Stocks by Asset Type Pt <1 After the productive capital stock for each type of as set is computed, the next major step is to combine these different stocks in order to obtain the aggregate meas ures of capital input for the private business, private nonfarm business, and manufacturing sectors. The pro ductive stocks are aggregated by asset type using im plicit rental prices as weights. The method and data sources used to construct the rental prices are described below. The Tornquist formula is used for the aggrega tion; this is defined in appendix F, where it is compared with other methods of aggregation. xt The data sources for and derivation of these variables are discussed below. All of the variables on the right side of expression (C.6) except for the rate of return, rt, are derived from these sources. Before the rental prices are computed, expression (C.6) is used to solve for an implicit rate of return rather than using a market interest rate.20 Computing the internal rate of return is necessary to empirically implement (C.6) because the rate of capi tal gain is frequently greater than market interest plus depreciation. The procedure would result in some nega tive rental prices if the market interest rate were used. In order to obtain the implicit rate of return, the rental price, ct, is multiplied by the capital stock, Kt, and this product is set equal to capital (i.e., nonlabor) income reported in the n i p a . The following equation for rt, the implicit internal rate of return, is derived by substituting ct from equation (C.6) in the product ct Kt: Mental price (user cost) off capital The “ implicit rental price” or “ user cost” of capital is based on the neoclassical principle that inputs should be aggregated using weights that reflect their marginal products. The assumption used to formulate the rental price expression is that the purchase price of a capital asset equals the discounted value of the stream of serv ices (and, hence, implicitly the rents) that the asset will provide. Disregarding inflation and taxes, the rental price, c, would be c = p (r + d) IS the corporate income tax rate is the present value of $ 1 of tax deprecia tion allowances is the effective rate of the investment tax credit is the nominal rate of return on capital is the average rate of economic deprecia tion is the deflator for new capital goods is revaluation of assets due to inflation in new goods prices is the rate of indirect taxes. Yt - rt = - Kt (ptdt - Apt) (1 - utzt —et) / (1 — ut) ----------------------------------------------------------Ktpt (1 - utzt - et) / (1 - Ut) (C.5) (C.7) Where p is the price of the asset, r is a rate of return, and d is the rate of depreciation. In terms of equation (C.5), c represents the amount of rent that would have where Yt is capital income and Kt is productive capital stock. Expression (C.6) is computed separately by bls for 19Robert E. Hall and Dale W. Jorgenson, “ Tax Policy and Investment Behavior,’’ American Economic Review, Vol. 57, June 1967, pp. 391-414. 20The method used to obtain the implicit rate of return was derived in Christensen and Jorgenson, “ The Measurement of U.S. Real Capital Input.” i 49 each type of asset and rt is computed jointly for all as sets. By solving for rt, nipa capital income, Yt is exact ly allocated to capital assets. That is, the rental prices, Ci, are determined by solving for the rate of return such that: Y t = Si citK it. (C.8) Hence, cit Kit/Kt is the share of capital income allocated to the i th asset in year t.21 Computation of rental prices for capital requires esti mates of capital income and several tax rates. Data on capital income are available in the nipa. For the corpo rate sector, a comprehensive set of categories of capital income is available for each major sector—profits, net interest, capital consumption allowances, transfers, in direct business taxes, and inventory valuation adjust ments. These components are aggregated to obtain a measure of the current value of corporate capital income. Data for measuring capital income for noncorporate capital are incomplete. This is because proprietors’ in come in the nipa is not differentiated between wage and salary income (labor) and profits (capital income). This is a difficulty not only for estimating noncorporate rent al prices, but also for determining noncorporate capital and labor income shares, a problem which is addressed below. Noncorporate rental prices are determined by as suming that they are equal to corporate rental prices for each type of asset. Corporate rental prices are deter mined after estimating the corporate portion of each type of productive capital asset. These percentage esti mates are based on ratios of corporate to total net bea stocks for equipment, structures, and residential capital in the farm , m anufacturing, and nonfarm nonmanufacturing sectors. The most closely corre sponding share is multiplied by the bls estimate of the total productive stock for an asset type in each year in order to determine the corporate productive stock of the asset. This is the estim ate of corporate kt used in estimating the internal rate of return in equation (C.7). Deflators are calculated for new investment goods based on the ratio of current- to constant-dollar invest ment for each asset. The rate of depreciation is the ratio of the real value of depreciation to the real wealth stock. The real value of depreciation equals real investment minus the increase in the wealth stock. The effective rate of indirect taxes is assumed to be equal for all as sets, and is defined as total indirect taxes in the sector divided by the total stock of wealth. Estimates of the effective rate of the investment tax credit for each type of capital for each year are also re quired. The strategy used by bls to estimate effective credit rates for each of 21 equipment categories is to consider historical credit laws and to assume a distribu tion of useful tax lives associated with the average serv ice lives used.22 In estimating effective tax credit rates, bls attempts to account for all the special features of the law, except those related to the profitability tests and carryover rules. Therefore, the rental price formulation is used in such a way as to assume that all marginal investment decisions are made by firms which are operating at a profit for tax purposes. Although this is restrictive, it is preferable to the alternative of using actual allowances claimed, which reflect historical decisions as well as in centives in the current period. The first step in the procedure is to estimate, for each type of equipment, the percentage of the maximum allowable rate which is applicable.23 For this purpose, service lives for tax purposes are assumed to be normal ly distributed about the mean service life, with the dis tribution cut off before 0.5 times the mean life and after 1.5 times. Although we assume lives are more widely dispersed for the purpose of vintage aggregation, a more truncated distribution of service lives is used for tax purposes. The full amount of the credit is assumed to have been claimed for that portion of the distribution of service lives over 8 years, % credit for that between 6 and 8 years, and V3 credit for lives under 6 years. The procedure is repeated for each asset type for the post-1970 period, when 5 and 7 years are the appropri ate cutoffs. Since the smallest mean service life is 8 years, no portion of any of the distributions falls in the range where no credit is allowed (less than 3 years). Next, these initial estimates are multiplied by the rate of the maximum allowable credit for the year in ques tion. In years where the credit was suspended by Con gress for part of the year, estimates are multiplied by the percentage of days in the year in which the credit was in effect. The result is an asset-specific estimate of Since the direct data reflect complex rules on profits tests and carryovers and carrybacks, the volume of credits tends not to re spond proportionally to changes in new investment. Thus, the ratio of the volume of credits taken in a year to nominal new investment is a poor indicator of marginal incentives. For example, in 1970 the credit was totally suspended for new investment, and yet substan tial credits were claimed against that y ea r’s taxes because of carryovers from earlier years. 23The procedure used is similar to the methods used by others, such as Patrick J. Corcoran and Leonard G. Sahling, “ The Cost of Capital: How High Is It?’’ Federal Reserve Bank of New York Quarterly Review, 1982, Summer, pp. 23-31. 2‘The farm sector is handled somewhat differently with respect to determining the asset shares in capital income. This exception will be discussed together with the handling of farm proprietor’s capital-labor income shares at the conclusion of this section of the appendix. 22 Data on investment tax credits actually claimed are available for corporations by detailed industry group in the U.S. Treasury Department’s Statistics of Income. The difficulty with this direct source is that actual credits claimed reflect the complexities of the tax laws concerning credits. The rental price expression is meant to represent the price incen tives afforded firms on a marginal decision to buy new capital. 50 nipa . produces estimates of capital costs, by type of cost, for 2-digit industries. Data collected include capital consum ption allow ances, profits (before and after taxes), net interest, business transfer payments, and in direct business taxes. Since the work on capital costs is based on the corporate sector, data specific to that sec tor are collected. Each component is obtained separately for the corporate portions of manufacturing, farm, and nonfarm-nonmanufacturing. The noncorporate sector is excluded from this cost work because detailed noncor porate income data are unavailable. As discussed earlier, noncorporate rental prices are assumed to be equal to corporate rental prices for each specific type of asset in each major sector. A majority of the series are obtained from informa tion provided by bea containing the “ 14 components” of income. From this source, bls obtains estimates, by 2-digit industry, of corporate capital consumption al lowances, corporate profits, total business transfer pay ments, and indirect business taxes. Using this data, in direct taxes and transfers are allocated to the corporate sector in proportion to corporate shares in the stock of corporate and noncorporate depreciable assets. These shares are based on bea measures of net capital stock. Capital consumption allowances exclude adjustments. Total net corporate interest and corporate profits tax lia bility are obtained from table 1.13 in the Survey of Cur rent Business. Corporate profits before and after tax by industry are obtained from tables 6.21 and 6.23 of the same publication. Net corporate interest by sector is ob tained from the bea staff. As discussed earlier, the bea work on the measure ment of capital stock is the source for the gross invest ment data for the bls major sector capital measures. Al though bls computes stocks by type of asset for each major sector (manufacturing, farm, and other), it does not do so separately for corporate and noncorporate stocks. Estimates of the corporate breakout are needed, however, to estimate rental prices. Cost data are used as a basis for rental prices in the corporate sector. Noncor porate rental prices are then set equal to corporate rental prices at a disaggregate level. This equality assumption, in effect, excludes from the bls measures any capital composition adjustment based on legal form of organi zation., Differences between corporate and noncorporate rental prices could be used as the basis for a significant composition adjustment because the relative size of the noncorporate sector has declined steadily over time. However, the composition adjustment might mistakenly imply that capital input is growing faster than it would if the trend were absent. Since rental prices must be calculated for the corpo rate sector alone, estimates of the corporate stock of 24In this approach, the rental price expression is used to investi gate the effects of inflation, working through the tax system, on in vestment incentives. See Dale W. Jorgenson, and Martin A. Sullivan, “ Inflation and Corporate Capital Recovery,” in Hulten, ed., Depreciation, Inflation and Taxation of Income fr o m Capital, pp. 171-237. the marginal incentive associated with the investment tax credit for that year. The rental price formulation, equation (C.6), also re quires an estimate of the present value of $ 1 of depreci ation deductions, zt. This is the portion of investment expenses which can be recovered in capital consumption allowances after discounting these allowances for nomi nal interest charges. This value is generally less than 1, since deductions are based on historical purchase prices. This value is generally lower for longer lived assets be cause the deductions must be more severely discounted. It is assumed that all firms elected straight-line depre ciation prior to 1954, double declining balance with switchover to straight line for 1954-80, and the acceler ated capital recovery system (acrs) beginning in 1981. For each depreciation pattern and for each type of asset, an allowable stream of deductions for $ 1 of new invest ment is calculated. This stream is based on the assumed average service lives used for computing capital input and a normally distributed retirement pattern. Then, that stream is discounted using the average long-term bond rate in effect during a given year. Therefore, the esti mates of the present value of $ 1 of depreciation used by bls vary not only by type of asset but also from year to year as a function of changing interest rates. Finally, equation (C.6) requires an estimate of the corporate income tax rate, Ui. The traditional way of estimating this rate is to compute the ratio of total cor porate profits tax liability to before-tax total profits. Such a rate presumably reflects an aggregate of tax rates actually paid during the year including the effect of those companies which faced losses. In such an ap proach, no attempt is made to differentiate the effective tax rate by type of asset. The difficulty is that this aver age tax rate is not conceptually appropriate for the rental price expression. In this expression, the tax rate should reflect the marginal incentives afforded investors in new capital by current tax laws and it should be specific to the type of asset. B ls follows an approach suggested by Jorgenson and Sullivan.24 They use the statutory tax rate for their esti mate of ut in equation (C.6)—the marginal rate faced by a profitable firm. Using the rental price formulation, (C.6), they derive an expression for an “ effective” rate in terms of the statutory tax rate (ut), the effective rate of investment credits (et), the present value of $1 of de preciation (zt), and the other variables in the rental price expression. Since ut, et, and zt are distinguished by as set type, this effective rate reflects the asset-specific ef fects of each of these aspects of the tax law. Capita! costs The main source of data on capital cost is the bea C. R. 51 prietors’ income by assuming either that proprietors and unpaid family workers earn the same wage as employees or that corporate and noncorporate capital yield the same rate of return. Unfortunately, the two methods of imputation applied together generally overestimate the nipa measures of proprietors’ income. Rather than select one imputation over the other, the two methods are initially employed simultaneously, and the results are reconciled at a later stage. First, an imputation is made for noncorporate income by assigning proprietors and unpaid family workers the same average wage received by paid employees, and then adding to that an imputation of capital income by assigning noncorporate capital the same rental price as corporate capital.25 This imputation is compared to noncorporate income in the nipa . (Noncorporate income includes proprietors’ income, noncorporate capital con sumption allowances, and a portion of indirect business taxes.) The imputation is adjusted to equal the reported noncorporate income by multiplying the wages of pro prietors and unpaid fam ily workers and the noncorporate rate of return by a single scalar which equates the imputed and nipa totals. Thus, noncorporate wages and the rate of return to capital are scaled back proportionally to determine proprietors’ capital and la bor shares. It should be noted that the scalar is applied only to the rate of return on capital, not to the entire rental price. Thus, the noncorporate rates of economic depreciation, asset revaluation, and indirect taxes are held equal to the corporate sector. The rationale for this treatment is that these other ele ments are exogenous for the self-employed. The selfemployed can willingly accept lower wages and returns to their capital in exchange for the greater degree of independence—or for some other reason. However, their preference is unlikely to affect factors like eco nomic depreciation or inflation. Tables C-5 through C-7 illustrate the effects of this procedure. Two exceptions are made to the methods outlined above for allocating capital income in the farm sector. During the period studied, farm land prices consistently increased faster than the deflators for other capital in puts. In terms of the rental price equation (C.6), the capital gains (Ap) on land frequently exceeded the rate of return, which was presumed equal for all assets. To maintain the assumption that the rates of return were equal for all asset types would imply that land frequent ly had a negative rental price and a negative income share. Such a situation makes little sense and would in validate a Tornquist index based on these “ shares.” each asset type in each sector are required, be a net stocks are used to derive corporate stocks for each asset. bea provides corporate stocks broken out by sector and year for equipment, structures, and residential capital. In each sector and in each major asset category (that is, equipment, structures, and residential capital), the ratio of corporate capital stock to total capital stock is com puted based on the bea net stock estimates. Using these ratios, bls proportionally allocates stock estimates for more detailed asset types to the two legal forms, the corporate and noncorporate sectors. Aggregation procedure As indicated in the introduction to this section, the Tornquist procedure is used to combine the capital stock series by asset type described in the previous section using the rental price described in this section to derive weights. The resulting indexes are the BLS-derived ag gregate measures of capital service inputs. The capital input index for the private business sector is, in effect, a weighted sum of the percent changes in capital stocks by asset type where the weights are averages of the re spective rental prices for the current and past year. The capital input measures for private nonfarm business and manufacturing are similarly aggregated. Appendix E contains a discussion of the Tornquist in dex number formula. Capital input indexes by broad class of asset are presented for each of the three major sectors at the end of this appendix. @ 11. Capital and Labor Income Shares The other major methodological issue addressed in this appendix concerns the calculation of capital and la bor income shares. These shares are used to weight the labor and capital inputs in order to obtain the combined input measure. Data are available in the nipa for employee compen sation and for corporate capital income. Corporate capi tal income is defined by bls to include unadjusted before-tax profits, corporate capital consumption allow ances, corporate net interest payments, corporate inven tory valuation adjustments, and a portion of indirect business taxes. Corporate capital income is used to de termine the corporate rental price for each type of asset as outlined in the previous section. However, the nipa report only a single figure for proprietors’ income, which reflects returns to both labor and capital. Since data are available on hours of proprietors and unpaid family workers, and on noncorporate capital stock, it is possible to develop an implicit capital-labor split of pro 25For the purposes of this analysis, the income of employees of proprietors is excluded from noncorporate income. The assumption made implies that, while proprietors can accept a lower wage and rate of return than corporations, they do not have the same control over the wages of their employees. Therefore, employees of propri etors are assumed to have the same wage as other employees and no further adjustment to their wage is made. Adjustment is made only by changing proprietors’ wages and the rate of return to noncor porate capital. 52 This difficulty with high capital gains on farm land is well known. Doll and Widdows26 point out that farmers have often made a large portion of their income in the form of capital gains on land which occur at rates in ex cess of the general inflation rate. Sometimes the effect is so large that farmers with little equity in their land are forced to take out increasing mortgages against the ever larger land values to maintain a positive cash flow. Because of this situation, capital-labor income shares and asset type income shares cannot be reasonably esti mated based on the model described above. Instead, shares of capital assets in farm capital income are esti mated as follows. First, rental prices for each type of asset are assigned using an assumed real rate of return (4 percent) plus the asset’s depreciation rate. Then, an estimate of total farm capital income is computed as a sum of terms, each term being the productive stock of an asset type times its assigned rental price. Next, each asset is assigned a share in total capital income based on the share of its term in the sum. Finally, these assigned shares are used to weight the various productive stocks to compute real capital input as a Tornquist index of the asset type stocks. Since these assigned prices are not controlled to any income or cost estimate, the estimate of capital income derived in this way is not used in determining farm cap ital and labor income shares. Instead, total capital in come is assumed to equal corporate capital income in the n i p a plus an estimate of noncorporate capital in come. The noncorporate capital income estimate is as sumed equal to the noncorporate productive stock times the ratio of the corporate capital income to the corporate productive stock. Farm proprietors’ wages are initially computed by equating them with employees’ wages in the same man ner as for the nonfarm sectors. Wages are also imputed to unpaid family workers at the same rate on the as sumption that they receive compensation for their serv ices in unmeasured forms. This imputation is compared to total n i p a noncorporate income after noncorporate capital income is subtracted. The imputation is adjusted by multiplying the wages of proprietors and unpaid fam ily workers by a scalar which equates the imputed and BEA-reported totals. Measures of total capital input and multifactor pro ductivity were presented in the main body of this bulle tin. In this section, capital measures are given in more detail. The three sectors for which measures are pre sented are private business, private nonfarm business, and manufacturing. These reflect calculations which were done separately for manufacturing, farm, and nonfarm-nonmanufacturing. Sets of tables at the end of this appendix present annual figures for equipment, structures, rental residential capital, inventories, and land, as well as the total for all types of assets. The discussion in this appendix will be directed mainly at the private business sector, tables C-13 through C-19. However, much of the discussion applies equally to the private nonfarm business sector (C-20 through C-26) and the manufacturing sector (C-27 through C-33). Referring to table C-13, one can examine the annual percent changes in the private business capital measure. With two minor exceptions, every component exhibits positive growth in every year. Steady growth is not sur prising in light of the growth of the economy, but the uniformity of growth, even during business downturns, exemplifies the rather static nature of capital as meas ured. The main contributor to the measure is a stock es timate, which is determined by historical investments net of efficiency loss (which is assumed to occur at a small, predetermined rate). New gross investment (table C-17 ) is added to the stock each year, and accruing ef ficiency losses are removed. Gross investment is rela tively volatile but has always been great enough to off set efficiency losses. Large positive and negative fluctuations in the growth of investment result in more modest changes in the rate at which capital inputs in crease (C-13). Analogous observations apply to the pri vate nonfarm business and manufacturing sectors. Referring again to table C -1 3 , a clear pattern emerges when comparing the growth rates of various as set types. Equipment consistently grows faster than structures which, in turn, generally grow faster than res idential capital, inventories, or land. In other words, there has been a long-term shift in the composition of capital towards depreciable assets, particularly the shorter lived equipment. This shift in the overall capital measures is captured by the use of rental prices to weight capital assets during aggregation. The effect of the shift on the capital input measures can be judged by comparing the growth of capital input for all assets (ta ble C-13) with that of an index of the direct aggregate of productive stocks (table C-14). Table C-16 shows the index of the ratio of capital input to productive stock, which is sometimes referred to as the capital “ composition effect.’’ Clearly, the shift toward shorter lived assets has caused a steady and significant increase in capital services per unit of stock. This is because equipment yields its services more quickly than struc tures and hence is assigned a larger weight. Also, the decline in this effect since 1973 reflects in part the low er revaluation of equipment. Presumably, investment 26John P. Doll and Richard Widdows, “Imputing Returns to Production Assets in 10 U.S. Farm Production Regions ’, Eco- nomic Research Service Staff Report No. ACES820703 (U.S. Department of Agriculture, July 1982). B¥. Examination of the Measures 53 Table C-5. Manufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948-81 Year 1948 ............................................................ 1949 ............................................................ Ratio adjusting proprietors’ wages and rate of return to noncorporate capital (1) Total adjusted labor share (2) 0.9338 .8215 Breakdown of adjusted labor share Breakdown of adjusted capital share Employees Proprietors Corporate Noncorporate (3) (4) (5) (6) 0.681 .670 0.662 .652 0.019 .017 0.307 .317 0.012 .014 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .8745 .9372 .8341 .7492 .6353 .5482 .7744 .6118 .4618 .3043 .656 .661 .683 .694 .696 .671 .694 .697 .706 .683 .640 .645 .668 .681 .685 .662 .681 .686 .698 .678 .016 .016 .014 .013 .011 .009 .013 .010 .008 .005 .329 .326 .304 .293 .290 .315 .295 .291 .280 .302 .014 .013 .014 .014 .014 .015 .010 .012 .014 .015 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .3087 .2207 .2285 .2591 .3340 .3078 .3956 .3595 .3596 .4244 .696 .693 .686 .675 .672 .658 .671 .684 .684 .704 .691 .689 .683 .671 .668 .654 .666 .680 .680 .699 .005 .004 .004 .004 .004 .004 .004 .004 .004 .005 .290 .292 .301 .313 .317 .331 .320 .307 .308 .290 .014 .015 .013 .012 .012 .011 .009 .008 .008 .006 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .4384 .3991 .4232 .4679 .6396 .5130 .3756 .4206 .4756 .5160 .723 .701 .701 .712 .741 .711 .701 .700 .710 .732 .717 .697 .696 .706 .734 .705 .697 .695 .704 .726 .005 .004 .004 .005 .007 .006 .004 .005 .006 .007 .272 .294 .294 .284 .256 .287 .294 .297 .288 .266 .005 .005 .006 .004 .002 .003 .004 .003 .003 .001 1980 ............................................................ 1981 ............................................................ .4744 .4423 .757 .748 .750 .742 .007 .006 .243 .250 .000 .002 composition is skewed toward equipment sufficiently so that $1 of new equipment no longer yields much more current services than new structures. A further point can be made about the composition ef fect (table C-16). Since each major asset category is ag gregated from subcategories of asset types with different rental prices (i.e., with different depreciation rates and for different sectors), a composition effect exists within each major category. The equipment effect is positive every single year, indicating a pervasive trend toward the shorter lived types of equipment. In contrast, the structures effect is often negative, indicating a slow trend toward longer lived forms of structures. The in ventory and land effects reflect mainly intersectoral shifts. The land effect is persistently positive due to the relative growth of nonfarm land compared to farm land. The size of these composition effects demonstrates the results of measuring capital services as a detailed array of assets rather than at a more aggregate level. Table C-5 reports the shares of the major asset cate gories in total capital costs. Table C-18 shows the price index for new investment goods. Table C-19 shows the depreciation rates used in the rental price formulation. These are averages for more detailed rates used for indi vidual assets. Capital and labor income shares In this section, the computation of the capital and la bor shares of income is illustrated. As discussed earlier in this appendix, an estimation procedure is required to allocate proprietors’ income between labor and capital, basically a two-step process. The first step is to approx imate labor compensation using employee compensation per hour times proprietors’ hours and to approximate capital compensation assuming the corporate and non corporate rental price of capital to be equal. The second step is to adjust the capital and labor compensation fig ures so that they equal the reported figures for proprie tors’ income. 54 farm noncorporate capital earns the same rate of return as corporate capital; any shortfall or excess in proprie tors’ income is attributed as a differential in the wage of proprietors compared to that of corporate employees. The farm adjustment is usually, but not always, less than 1.00. The most notable exceptions are in 1973 and 1974, when new farm subsidies were introduced. Columns 3 through 6 in each table divide total income into shares arising from employees’ labor, proprietors’ labor, corporate capital, and noncorporate capital. These allow the reader to observe the relative impor tance of the noncorporate portion of each sector. Non corporate enterprises are very important in the farm sec tor, but relatively small in manfuacturing. Tables C-5, C-6, and C-7 refer to the manufactur ing, farm, and nonfarm-nonmanufacturing portions of the private business sector, respectively. In each table, column 1 illustrates the adjustment made; in manufac turing (C-5) and in nonmanufacturing (C-7), this col umn indicates the factor by which “ first” estimates of proprietors’ wages and the rate of return to noncorporate capital had to be multiplied to “ control” their associ ated values to the n i p a proprietors’ income figure. The most significant observation is that this adjustment is less than 1.00 and thus involves decreasing the “ first” estimates in both sectors, more so in manufacturing. For the farm sector (table C-6), this adjustment is applied only to the proprietors’ wage rate. It is assumed that Table C-6. Farm sector: Shares in total income used to aggregate labor and capital inputs, 1948-81 Ratio adjusting proprietors’ wages and rate of return to noncorporate capital (1) Total adjusted labor share (2) 1948 ............................................................ 1949 ............................................................ 0.8113 .6410 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ............................................................ ............................................................ ............................................................ ......... ................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Year Breakdown of adjusted labor share Breakdown of adjusted capital share Employees Proprietors Corporate Noncorporate (3) (4) (5) (6) 0.575 .550 0.134 .157 0.441 .393 0.009 .010 0.416 .440 .5247 .8418 1.0341 1.0148 .8625 1.0482 1.0622 1.0423 1.1399 .9735 .441 .559 .717 .749 .696 .719 .726 .728 .714 .721 .148 .133 .138 .141 .140 .148 .149 .157 .149 .169 .294 .427 .579 .608 .556 .571 .577 .571 .565 .552 .012 .010 .007 .007 .009 .009 .009 .010 .011 .012 .547 .431 .276 .244 .295 .272 .264 .262 .275 .267 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ 1.1544 1.0336 .8919 .9097 .7304 .7372 .7176 .7894 .7108 .8283 .694 .662 .626 .608 .581 .536 .528 .549 .551 .580 .165 .170 .174 .179 .197 .176 .169 .176 .181 .173 .529 .492 .452 .429 .385 .360 .358 .372 .370 .407 .014 .016 .019 .021 .023 .026 .027 .027 .031 .033 .293 .322 .355 .371 .396 .438 .445 .425 .418 .388 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .9040 .9965 1.1333 1.7150 1.7130 1.1699 .8853 .7957 .9261 1.1645 .646 .644 .603 .586 .643 .520 .508 .492 .458 .503 .179 .169 .153 .113 .139 .147 .179 .191 .167 .154 .467 .474 .450 .473 .503 .373 .329 .301 .292 .349 .030 .033 .039 .043 .039 .054 .057 .061 .067 .063 .323 .323 .358 .371 .319 .426 .434 .447 .475 .434 1980 ............................................................ 1981 ............................................................ .5538 .7343 .401 .425 .190 .175 .211 .250 .077 .074 .522 .501 55 Table G -7. Wonfarm-nonmanufacturing sector: Shares in total income used to aggregate labor and capital inputs, 1948-81 Year 1948 ............................................................ 1949 ............................................................ Ratio adjusting proprietors’ wages and rate of return to noncorporate capital (1) Breakdown of adjusted labor share Total adjusted labor share (2) Breakdown of adjusted capital share Employees Proprietors Corporate Noncorporate (3) (4) (5) (6) 0.6757 .9515 0.595 .639 0.495 .494 0.100 .146 0.230 .226 0.175 .135 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .8382 .7442 .8747 .9272 .9144 .7483 .6493 .7129 .7232 .7061 .610 .599 .617 .635 .635 .600 .597 .609 .606 .600 .488 .497 .502 .510 .508 .500 .508 .509 .503 .503 .122 .101 .115 .125 .127 .101 .089 .100 .103 .098 .237 .233 .230 .227 .231 .243 .240 .240 .243 .248 .153 .168 .154 .138 .134 .157 .162 .152 .151 .151 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .5950 .5620 .5569 .5166 .5824 .5985 .6439 .6848 .7060 .7512 .596 .590 .585 .579 .585 .584 .592 .595 .600 .615 .512 .510 .509 .511 .509 .509 .515 .518 .522 .532 .085 .080 .076 .068 .076 .075 .077 .078 .079 .083 .249 .252 .257 .258 .260 .264 .265 .265 .265 .262 .155 .158 .158 .163 .155 .152 .143 .140 .135 .122 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ ............................................................ .7551 .7715 .8716 .6931 .6910 .6564 .6904 .6548 .7435 .7282 .625 .625 .637 .624 .628 .611 .616 .608 .621 .627 .543 .540 .544 .550 .555 .543 .546 .541 .545 .552 .082 .085 .093 .073 .073 .068 .070 .066 .075 .074 .258 .262 .262 .258 .257 .274 .271 .276 .275 .268 .117 .113 .102 .118 .115 .115 .113 .117 .104 .106 1980 ............................................................ 1981 ............................................................ .7196 .7117 .624 .613 .551 .544 .072 .069 .272 .279 .104 .108 ¥= Sensitivity AmaSysis It is apparent that the final measure of multifactor productivity is only mildly reduced by excluding any of these assets, with the largest difference being 0.2 per cent per year when land, inventories, and residential as sets are all excluded. This is due partly to the fact that capital enters the multifactor measure only after being multiplied by capital’s income share (roughly 0.35 dur ing the two periods). The capital input measures are in creased by up to 0.8 percent a year during 1973-81 by the exclusion of land, inventories, and the residential component. Thus, exclusion of these components from a capital measure would lead to attributing more growth of output per hour of all persons to capital per hour and less to multifactor productivity. The difference is great er in the recent period (1973-81) than in the earlier one (1948-73). Therefore, failure to include these assets would result in attributing less of the slowdown in out put per hour to capital per hour and more to other sources. The differences, however, would be small; about 0.1 percentage point. The effects on the unweighted productive stock of not The effects of two major issues concerning the meas ures of capital and multifactor productivity are explored in this section. These are: (1) The choice of assets to in clude as capital input, and (2) the mathematical form of the efficiency function. Table C-8 shows growth rates during two major peri ods for multifactor productivity, capital input, and the distribution of capital input into the growth in the pro ductive stock and the composition effect. The figures are for the private business sector; similar comparisons for private nonfarm business and manufacturing are shown in tables C-9 and C-10, respectively. The first column shows the actual figures published by b l s . The succeeding columns indicate what the results would be for a more restricted list of assets. The alternatives are computed using the same capital and labor income shares, and the same rental prices of capital for individ ual assets. The other four columns exclude selected as set types. 56 stock) efficiency, straight-line efficiency (both with the same asset lives as the hyperbolic calculation), and with geometric decay using Hulten and Wykoff’s “ best geo metric approximation” ( b g a ) rates of efficiency decline to construct the efficiency function. Table C - l l presents annual rates of change and com pound growth rates for selected periods for the resulting private business multifactor productivity measures. It is evident that the method selected has little effect on the final measure of multifactor productivity, for year-toyear changes or over a long time period. The largest variation in the measure for any one year appears to be 0.4 percent (1966), while the largest effect on the long er term growth rate is 0.1 percent. Table C-12 presents the same information for private business capital input, which is more sensitive to the ef ficiency assumption than is multifactor productivity. Table C-8. Private business sector: Growth rates including and excluding selected assets from published measures, 1948-81 (Percent per year, compounded) All assets excluding: Land, inven tories, and residential Land Inven tories Resi dential 1.5 2.0 0.1 1.5 1.9 0.1 1.5 2.0 0.1 1.4 1.9 0.1 1.3 1.8 -0.1 Quantity of capital services:3 1948-81 ........... 1948-73 ........... 1973-81 ........... 3.5 3.6 3.2 3.6 3.7 3.4 3.4 3.5 3.3 3.7 3.8 3.5 4.0 4.1 4.0 Productive capital stock:4 1948-81 ........... 1948-73 ........... 1973-81 ........... 2.6 2.6 2.7 3.2 3.3 3.2 2.6 2.5 2.8 2.8 2.8 2.9 3.8 3.8 3.7 Composition effects:5 1948-81 ........... 1948-73 ........... 1973-81 ........... 0.8 1.0 0.5 0.4 0.5 0.2 0.9 1.0 0.5 0.9 1.0 0.6 0.3 0.3 0.2 Measure and period All assets1 Multifactor productivity:2 1948-81 ........... 1948-73 ........... 1973-81 ........... Output per unit of capital input: 1948-81 ........... 1948-73 ........... 1973-81 ........... Table G-9. Private nonfarm business sector: Growth rates in cluding and excluding selected assets from published meas ures, 1948-81 (Percent per year, compounded) -0.1 0.2 -1.0 -0.3 0.0 -1 .2 -0.1 -0.2 -1 .0 -0 .4 -0.1 -1 .3 All assets excluding: -0 .7 -0.3 -1 .7 1 Equipment, structures, rental residential capital, inventories, and land. 2Output per unit of combined labor and capital inputs where the com bined input is a weighted average of capital and labor (hours of all per sons) inputs. The respective weights are capital’s share (approximately 35 percent during the period) and labor’s share (approximately 65 per cent during the period). Aggregate productive capital stocks by asset type weighted by rental prices. 4Aggregate productive capital stocks by asset type, unweighted. 5Ratio of weighted to unweighted aggregate productive stocks. including all the assets are even greater than on capital input; the difference was as much as 1.2 percentage points in 1948-73. This is because the composition ef fect is greater when more assets are included. It is ap parent from the tables that much of the composition ef fect comes from inclusion of land, a factor which has a relatively low rental price and slow growth rate. The second group of comparisons looks at the sensi tivity of the multifactor productivity and capital input measures to the assumption about the form of the effi ciency function. In order to do this, all steps in the measurement process were repeated using alternative as sumptions about efficiency, including tracing through all of the implications for the rates of depreciation, rent al prices, rates of return, and so on. Besides the hyper bolic form which was selected for the b l s measures, calculations were made using one-hoss-shay (gross Resi dential Land, inven tories, and residential Measure and period All assets1 Land Inven tories Multifactor productivity:2 1948-81 ........... 1948-73 ........... 1973-81 ........... 1.3 1.7 0.0 1.2 1.6 0.0 1.3 1.7 0.0 1.2 1.6 -0.1 1.1 1.5 -0 .2 Quantity of capital services:3 1948-81 ........... 1948-73 ........... 1973-81 ........... 3.6 3.6 3.3 3.7 3.7 3.4 3.5 3.6 3.4 3.8 3.9 3.6 4.0 4.1 4.0 Productive capital stock:4 1948-81 ........... 1948-73 ........... 1973-81 ........... 3.2 3.2 3.1 3.4 3.4 3.2 3.1 3.1 3.1 3.5 3.6 3.3 3.8 3.9 3.7 Composition effects:5 1948-81 ........... 1948-73 ........... 1973-81 ........... 0.3 0.4 0.2 0.3 0.3 0.2 0.4 0.4 0.2 0.3 0.3 0.2 0.2 0.2 0.2 Output per unit of capital input: 1948-81 ........... 1948-73 ........... 1973-81 ........... -0.1 0.2 -1.1 -0 .2 0.1 -1 .2 -0.1 0.3 -1 .2 -0 .4 -0.1 -1 .4 -0 .6 -0 .2 -1 .8 1Equipment, structures, rental residential capital, inventories, and land. 2Output per unit of combined labor and capital inputs where the com bined input is weighted average of capital and labor (hours of all per sons) inputs. The respective weights are capital’s share (approximately 35 percent during the period) and labor’s share (approximately 65 per cent during the period. Aggregate productive capital stocks by asset type weighted by rental prices. 4Aggregate productive capital stocks by asset type, unweighted. 5Ratio of weighted to unweighted aggregate productive stocks. 57 Table C-10. Manufacturing sector: Growth rates including and excluding selected assets from published measures, 1948-81 VI. Summary The b l s measures of capital input have been con structed to represent the flow of services attributable to the stock of physical assets. Stocks are measured by a perpetual inventory calculation to estimate relative serv ice flow, by detailed asset type, from assets of different vintages. The perpetual inventory method employs a hy perbolic efficiency function in which services decline relatively slowly during the early years of an asset’s life and more quickly later. A slower hyperbolic form is used for structures than for equipment, because compar isons between the age/price profiles consistent with various hyperbolic forms and the Hulten-Wykoff re search on used asset prices indicated that this distinction was appropriate. Rental prices are constructed by as suming that the value of a new asset equals the dis counted stream of services it will provide. Rates of re turn in the rental price expression are derived from asset stocks and from the n i p a data on the components of income. Labor and capital income shares used to aggregate the two inputs are based on employee compensation and corporate capital income figures from the n i p a and also on a procedure which allocates proprietors’ income to labor and capital. In the private nonfarm sector, this al location reduces both noncorporate labor’s compensa tion per hour and capital’s rate of return after having initially assumed that these variables are equal to their corporate sector counterparts. In the farm sector, where proprietorship is the dominant legal form of organiza tion, corporate capital is assumed to earn the noncorpo rate rate of return, with the residual of proprietors’ in come being attributed to labor. Extensive detail is presented in the following tables, C-13 through C-33. For each major asset and in each sector, there are measures of capital input, productive capital stock, the asset’s share in capital income, and in dexes showing the effects of changes in the composition of assets over time. Sensitivity analysis indicates that capital measures are somewhat sensitive to the inclusion of land, inventories, and residential capital and to the pattern of efficiency assumed. However, multifactor productivity measures are much less sensitive because the capital measures are weighted by capital’s share (approximately equal to 35 percent). These issues have only relatively small effects on the conclusions which can be drawn about multifac tor productivity growth and the post-1973 slowdown. (Percent per year, compounded) All assets excluding: Land and Inventories inventories Measure and period All assets1 Land Multifactor productivity:2 1948-81 ....... 1948-73 ....... 1973-81 ....... 1.8 2.2 0.4 1.7 2.2 0.3 1.8 2.2 0.3 1.7 2.2 0.2 Quantity of capital services:3 1948-81 ....... 1948-73 ....... 1973-81 ....... 3.6 3.5 4.0 3.7 3.5 4.1 3.5 3.3 4.3 3.7 3.4 4.5 Productive capital stock:4 1948-81 ....... 1948-73 ....... 1973-81 ....... 3.3 3.1 3.7 3.4 3.3 3.8 3.2 3.0 3.9 3.4 3.1 4.1 Composition effect:5 1948-81 ....... 1948-73 ....... 1973-81 ....... 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.4 0.4 0.3 0.3 0.4 Output per unit of capital input: 1948-81 ....... 1948-73 ....... 1973-81 ....... -0 .2 0.6 -2 .6 -0.3 0.5 -2 .8 -0 .2 0.7 2.9 -0 .3 0.6 -3.1 ’ Equipment, structures, inventories, and land. 2Output per unit of combined labor and capital inputs where the com bined input is a weighted average of capital and labor (hours of all per sons) inputs. The respective weights are capital’s share (approximately 35 percent during the period) and labor’s share (approximately 65 per cent during the period). Aggregate productive capital stocks by asset type weighted by rental prices. Aggregate productive capital stocks by asset type, unweighted. 5Ratio of weighted to unweighted aggregate productive stocks. However, the practical difference between efficiency as sumptions is again small. The largest annual variation is 1.2 percent (1966), and the largest for a time period is 0.5 percent. It is interesting that the widest differences are between gross and straight-line methods. A case in point is 1967, when these two differed by 0.9 percent age point, while the hyperbolic and geometric results differed by only 0.3 percentage point. The close con formity of the hyperbolic and the b g a series is due in large part to the fact that both were selected for their conformity to the age/price profiles measured by Hulten and Wykoff. 58 Table C-11. Sensitivity of multifactor productivity measure to relative efficiency assumptions, private business sector, 1949-81 Table C-12. Sensitivity of capital services measure to rela tive efficiency assum ptions, private business sector, 1949-81 (Percent change) (Percent change) BLS (hyperbolic) Period Hulten/Wykoff (best geometric approximation) Gross (one hoss shay) Straight line Period BLS (hyperbolic) Hulten/Wykoff (best geometric approximation) Gross (one hoss shay) Straight line 1949 ....... -1.1 -1 .0 -1 .0 -1 .2 1949 ....... 4.0 3.5 3.5 4.2 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 7.2 2.4 1.8 2.6 -0 .4 4.4 0.3 0.9 0.7 4.0 7.4 2.5 2.0 2.8 -0 .3 4.4 0.4 1.0 0.8 4.1 7.2 2.5 1.8 2.5 -0 .5 4.3 0.4 0.9 0.5 3.9 7.1 2.2 1.8 2.6 -0 .4 4.3 0.2 0.8 0.7 4.1 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 3.7 4.4 4.2 3.1 2.7 3.1 3.6 3.1 2.2 2.0 3.3 4.0 3.8 2.5 2.3 3.0 3.5 2.9 1.8 1.8 3.6 4.0 4.2 3.3 3.1 3.3 3.5 3.2 2.5 2.4 3.8 4.7 4.3 3.0 2.6 3.2 3.9 3.3 2.1 1.8 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 0.6 2.0 3.6 2.9 3.6 3.1 1.9 0.3 2.4 -0 .5 0.5 1.9 3.6 2.8 3.6 3.1 2.0 0.4 2.5 -0 .4 0.6 1.9 3.6 2.9 3.7 3.3 2.2 0.5 2.5 -0 .4 0.6 1.9 3.6 2.8 3.5 3.0 1.8 0.2 2.3 -0 .5 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 2.4 2.2 2.3 2.9 3.4 4.3 5.3 5.3 4.6 4.7 2.8 2.3 2.4 3.1 3.4 4.2 5.1 5.0 4.3 4.4 2.5 2.3 2.3 2.8 3.1 3.8 4.6 4.8 4.3 4.4 2.5 2.2 2.4 3.2 3.2 4.7 5.8 5.7 4.8 4.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... -1 .2 2.2 3.3 2.4 -3 .8 -0 .2 3.8 3.0 1.0 -1.1 -1 .0 2.3 3.4 2.4 -3 .7 -0.1 3.8 3.0 1.0 -1.1 -1.1 2.1 3.2 2.4 -3 .8 -0 .3 3.6 2.9 1.0 -1 .2 -1 .2 2.2 3.3 2.3 -3 .8 -0 .2 3.9 3.1 1.0 -1 .2 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 4.3 3.5 3.6 4.6 4.5 2.7 1.9 2.6 3.6 3.7 3.9 3.1 3.4 4.4 4.3 2.4 1.7 2.5 3.6 3.5 4.3 3.7 3.9 4.6 4.5 3.0 2.2 2.8 3.7 3.8 4.4 3.4 3.6 4.6 4.6 2.5 1.6 2.5 3.7 3.8 1980 ....... 1981 ....... -2 .2 1.1 -2 .2 1.1 -2 .3 1.0 -2 .2 1.1 1980 ....... 1981 ....... 3.6 2.9 3.3 2.6 3.8 3.1 3.5 2.7 1948-65 .. 1965-73 .. 2.2 1.3 2.3 1.4 2.3 1.4 2.2 1.3 1948-65 . . 1965-73 .. 3.1 4.5 3.0 4.2 3.1 4.3 3.3 4.6 1948-73 .. 1973-81 .. 2.0 0.1 2.0 0.2 2.0 0.1 1.9 0.2 1948-73 .. 1973-81 .. 3.6 3.2 3.4 3.0 3.5 3.4 3.7 3.1 1948-81 .. 1.5 1.6 1.5 1.5 1948-81 .. 3.5 3.3 3.5 3.6 59 Table C-13. Private business sector: Real capita! input, 1948-81 All assets Period Equip ment Struc tures Table C-14. Private business sector: Productive capital stock, 1948-81 Rental residential capital (Index, 1977=100) Inven tories Land Period Index, 1977=100 All assets Equip ment Struc tures 47.6 48.7 27.6 30.1 41.2 42.1 Rental residential capital Inven tories Land 68.0 68.1 37.6 37.8 76.8 77.3 1948 ....... 1949 ....... 37.1 38.6 24.9 27.4 43.8 44.8 61.9 62.2 34.6 34.7 57.0 57.6 1948 ....... 1949 ....... 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 40.0 41.8 43.5 44.9 46.1 47.5 49.2 50.7 51.9 52.9 29.5 31.5 33.4 35.1 36.5 38.0 39.8 41.5 42.5 43.2 45.6 46.6 47.7 48.9 50.2 51.9 53.8 55.7 57.5 59.1 62.8 63.3 63.5 63.8 64.1 64.6 65.1 65.5 66.0 66.8 35.3 39.5 42.7 43.7 43.3 44.2 46.8 48.2 47.8 48.6 58.1 58.6 59.1 59.7 60.5 61.6 62.8 64.1 65.3 66.4 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 49.7 51.1 52.4 53.4 54.2 55.3 56.7 57.9 58.8 59.7 32.0 34.1 35.9 37.6 39.1 40.5 42.1 43.6 44.6 45.2 43.0 44.0 45.0 46.1 47.4 48.9 50.8 52.7 54.3 55.9 68.5 68.8 68.8 68.9 69.0 69.2 69.5 69.7 70.0 70.6 38.8 42.6 45.5 46.4 46.3 47.2 49.3 50.5 50.4 51.3 77.8 78.1 78.5 79.0 79.6 80.2 80.9 81.2 82.0 82.6 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 54.1 55.3 56.6 58.2 60.2 62.8 66.1 69.6 72.7 76.1 44.1 44.9 45.8 47.1 49.1 51.9 55.8 59.9 63.5 67.5 60.8 62.5 64.2 65.8 67.5 69.7 72.4 75.2 78.0 80.8 67.9 69.0 70.5 72.5 74.8 76.9 78.6 79.9 81.4 83.5 50.9 52.0 53.4 55.9 58.2 61.2 65.8 71.1 75.5 79.3 67.2 68.5 70.0 71.7 73.5 75.6 77.8 79.9 82.0 84.3 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 60.6 61.6 62.9 64.5 66.4 68.7 71.5 74.4 77.1 79.9 46.1 46.9 47.8 49.1 51.0 53.8 57.5 61.4 65.1 69.1 57.5 59.4 61.3 63.2 65.2 67.7 70.7 73.7 76.6 79.7 71.4 72.3 73.7 75.7 77.9 79.9 81.6 82.8 84.1 86.1 53.4 54.5 55.9 58.4 60.6 63.4 67.5 72.2 76.0 79.4 81.7 82.0 82.7 83.5 84.8 85.9 87.2 88.4 89.5 90.9 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 79.4 82.2 85.2 89.1 93.1 95.7 97.5 100.0 103.6 107.5 71.4 74.6 77.9 82.8 88.4 92.6 95.9 100.0 105.7 112.6 83.5 86.0 88.5 91.4 94.4 96.8 98.4 100.0 102.1 104.6 85.7 87.9 91.3 95.0 97.1 98.0 98.8 100.0 101.5 103.2 82.4 84.8 87.6 90.9 94.9 95.6 96.4 100.0 105.3 109.2 86.6 88.8 91.1 93.6 95.7 97.3 98.7 100.0 101.7 102.2 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 82.6 85.0 87.5 90.7 94.1 96.3 97.9 100.0 103.1 105.9 72.9 75.9 79.1 83.8 89.1 93.1 96.1 100.0 105.6 112.3 82.7 85.4 88.0 91.0 93.9 96.3 98.1 100.0 102.2 104.9 88.1 90.0 92.6 95.6 97.5 98.3 99.0 100.0 101.4 103.0 82.2 84.4 87.1 90.8 94.9 96.6 97.2 100.0 104.7 108.4 92.2 93.6 94.9 96.5 98.2 99.3 99.5 100.0 101.0 99.3 1980 ....... 1981 ....... 111.3 114.5 119.1 124.5 107.4 110.6 104.8 106.1 109.9 110.6 105.8 108.2 1980 ....... 1981 ....... 109.6 112.5 118.5 123.8 107.7 110.9 104.4 105.6 109.2 110.0 104.0 105.7 Percent change from preceding year 1949 ....... 4.0 9.7 2.4 0.6 0.3 1.0 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 3.7 4.4 4.2 3.1 2.7 3.1 3.6 3.1 2.2 2.0 7.8 6.9 6.0 5.0 4.0 4.1 4.6 4.3 2.6 1.6 1.8 2.1 2.3 2.5 2.7 3.4 3.7 3.6 3.3 2.8 0.9 0.7 0.3 0.4 0.6 0.7 0.7 0.6 0.8 1.3 1.7 12.0 8.2 2.3 -0.7 1.9 5.8 3.0 -0.7 1.7 0.9 0.8 0.8 1.1 1.3 1.7 2.0 2.0 2.0 1.7 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 2.4 2.2 2.3 2.9 3.4 4.3 5.3 5.3 4.6 4.7 2.1 1.9 2.0 2.9 4.1 5.8 7.4 7.3 6.1 6.3 2.9 2.8 2.6 2.5 2.6 3.3 3.9 3.8 3.7 3.7 1.5 1.7 2.2 2.9 3.1 2.8 2.3 1.7 1.9 2.6 4.7 2.1 2.6 4.8 4.1 5.2 7.5 8.1 6.1 5.0 1.2 1.9 2.3 2.3 2.6 2.8 2.9 2.7 2.6 2.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 4.3 3.5 3.6 4.6 4.5 2.7 1.9 2.6 3.6 3.7 5.8 4.4 4.5 6.3 6.7 4.8 3.5 4.3 5.7 6.5 3.4 3.0 2.9 3.2 3.4 2.5 1.6 1.6 2.1 2.5 2.6 2.6 3.8 4.1 2.2 0.9 0.9 1.2 1.5 1.7 3.9 3.0 3.2 3.9 4.4 0.7 0.8 3.7 5.3 3.7 2.7 2.6 2.6 2.7 2.2 1.8 1.4 1.3 1.7 0.5 1980 ....... 1981 ....... 3.6 2.9 5.8 4.5 2.7 3.0 1.5 1.3 0.6 0.6 3.5 2.3 <4 Table C-15. Private business sector: Shares in current capital cost, 1948-81 Compound annual rate of growth 1948-81 .. 3.5 5.0 2.8 1.6 3.6 2.0 1948-73 .. 1973-81 .. 3.6 3.2 4.9 5.2 3.0 2.4 1.7 1.4 3.9 2.5 2.0 1.8 60 Period All assets Equip ment Struc tures Rental residential capital 1948 ....... 1949 ....... 1.000 1.000 0.291 .334 0.265 .340 0.220 .099 0.138 .136 0.085 .091 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .379 .345 .345 .443 .417 .364 .312 .400 .328 .442 .350 .219 .296 .301 .347 .333 .232 .271 .356 .294 .125 .180 .132 .103 .089 .135 .191 .142 .120 .110 .030 .197 .156 .088 .061 .070 .174 .108 .076 .082 .116 .059 .072 .065 .086 .098 .090 .080 .120 .073 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .402 .403 .380 .376 .353 .335 .374 .354 .362 .429 .318 .311 .313 .296 .306 .306 .282 .295 .309 .258 .126 .102 .111 .124 .111 .114 .112 .105 .097 .105 .085 .072 .095 .107 .119 .125 .129 .136 .123 .128 .069 .113 .101 .098 .111 .121 .103 .111 .110 .080 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .425 .416 .427 .411 .433 .222 .297 .313 .370 .370 .264 .274 .306 .295 .238 .268 .352 .306 .255 .269 .102 .088 .035 .121 .219 .128 .090 .120 .106 .127 .123 .137 .120 .066 .047 .159 .105 .129 .144 .093 .086 .085 .112 .107 .063 .222 .155 .133 .125 .142 1980 ....... 1981 ....... 1.000 1.000 .349 .284 .275 .301 .126 .100 .098 .147 .153 .168 Inven tories Land Table C-16. Private business sector: Ratio of capital services to productive stock, 1948-81 Table C-18. Private business sector: Price of new capital goods, 1948-81 (Index, 1977=100) (Index, 1977=100) Period All assets Equip ment Struc tures Rental residential capital Inven tories Land Period All assets Equip ment Struc tures Rental residential capital Inven tories Land 33.3 35.0 30.2 30.2 35.8 36.8 45.5 42.3 18.2 19.3 1948 ....... 1949 ....... 77.9 79.2 90.4 90.9 106.3 106.4 91.0 91.4 91.8 91.6 74.2 74.4 1948 ....... 1949 ....... 28.8 29.4 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 80.5 81.7 83.0 84.0 84.9 85.9 86.8 87.7 88.2 88.6 92.2 92.5 93.0 93.3 93.4 93.8 94.5 95.1 95.4 95.6 106.2 106.0 106.0 105.9 105.9 106.1 106.0 105.8 105.9 105.9 91.7 92.0 92.2 92.6 93.0 93.3 93.7 94.0 94.3 94.7 90.8 92.6 93.9 94.1 93.7 93.7 94.8 95.4 94.8 94.8 74.7 75.0 75.2 75.6 76.1 76.7 77.7 78.9 79.6 80.5 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 30.4 33.3 34.7 35.2 35.2 35.8 38.2 39.6 40.8 41.1 36.4 39.6 41.8 41.5 41.8 42.7 47.9 49.1 52.2 51.0 30.7 34.7 35.9 36.8 36.2 36.1 40.0 41.9 41.6 41.6 38.0 39.5 40.5 41.4 42.2 42.9 43.3 43.8 44.5 44.5 47.3 48.6 46.1 46.0 45.6 45.3 47.4 48.9 50.2 49.2 19.2 21.8 23.8 24.4 24.4 25.2 26.3 27.7 28.9 30.5 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 89.3 89.7 89.9 90.3 90.7 91.4 92.4 93.5 94.4 95.3 95.6 95.7 95.8 95.9 96.2 96.6 97.0 97.4 97.6 97.7 105.7 105.3 104.8 104.2 103.6 103.0 102.4 102.0 101.8 101.4 95.1 95.4 95.6 95.8 96.0 96.2 96.4 96.6 96.8 97.0 95.4 95.5 95.5 95.7 96.0 96.5 97.4 98.6 99.3 99.8 82.3 83.5 84.7 85.8 86.7 87.9 89.2 90.3 91.6 92.7 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 41.7 41.6 42.0 42.5 43.3 44.5 46.1 47.9 50.0 53.1 51.5 51.5 51.5 51.5 51.9 53.2 53.8 55.8 57.8 59.8 41.6 41.4 41.3 41.8 42.3 43.1 44.9 46.7 48.5 52.6 44.5 44.4 44.4 44.0 44.5 45.3 46.5 48.5 51.1 54.6 49.7 49.6 49.6 49.5 49.6 50.9 51.8 52.4 53.9 56.5 31.6 31.6 32.6 33.6 35.1 36.4 38.7 40.8 43.0 45.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 96.1 96.7 97.4 98.2 99.0 99.3 99.6 100.0 100.5 101.5 98.0 98.2 98.5 98.9 99.1 99.5 99.8 100.0 100.1 100.3 101.0 100.7 100.5 100.4 100.5 100.6 100.3 100.0 99.9 99.8 97.3 97.7 98.6 99.4 99.6 99.7 99.8 100.0 100.1 100.3 100.2 100.5 100.5 100.2 100.0 99.0 99.2 100.0 100.6 100.7 93.9 94.9 96.0 97.0 97.4 98.0 99.1 100.0 100.6 103.0 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 56.2 59.6 63.4 68.5 79.2 87.2 92.8 100.0 109.5 122.5 62.9 65.4 67.2 68.8 75.0 87.2 93.5 100.0 105.9 114.5 56.9 61.4 65.1 69.8 82.6 91.5 94.4 100.0 111.4 125.9 58.4 63.4 71.6 76.3 81.2 87.4 94.3 100.0 110.9 122.5 58.2 60.3 64.0 73.1 85.0 90.2 94.6 100.0 109.8 124.5 48.4 51.4 55.2 61.1 75.1 81.3 89.0 100.0 110.5 125.9 1980 ....... 1981 ....... 101.6 101.8 100.6 100.6 99.7 99.8 100.4 100.5 100.6 100.5 101.7 102.3 1980 ....... 1981 ....... 136.6 147.4 124.7 134.7 141.5 153.4 135.0 148.4 140.3 146.8 142.8 155.3 Table C-17. Private business sector: Gross real investment, 1948-81 Table C-19. Private business sector: Rate of depreciation, 1948-81 (Index, 1977=100) (Percent per year) Period All assets Equipment Structures Rental residential capital 1948 ............... 1949 ................ 40.9 34.7 37.2 29.4 51.4 47.1 37.8 38.7 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ................ ................ ................ ......... ................ ................ ............... ................ ................ ................ 37.8 39.3 38.1 40.7 40.1 45.0 46.7 47.5 42.0 46.1 32.3 34.6 33.0 34.9 33.1 36.5 37.5 38.8 32.5 36.3 48.9 51.9 51.7 56.2 57.7 66.2 71.2 70.3 64.4 66.6 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ 48.4 48.7 53.2 56.4 61.8 70.9 76.8 74.4 78.6 84.8 37.8 36.6 40.4 43.5 49.6 57.6 66.0 64.2 67.6 73.0 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ................ ................ ................ ................ ................ ................ ................ ................ ................ ................ 81.4 80.0 88.9 101.6 97.2 85.2 89.0 100.0 113.9 121.1 1980 ................ 1981 ................ 119.1 122.9 Period All assets Equipment Structures Rental residential capital 1948 ................ 1949 ............... 3.229 3.463 11.930 12.382 5.772 5.741 2.218 2.247 51.0 37.9 36.3 38.6 40.9 46.7 43.6 45.2 50.3 64.0 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ............... ............... ............... ............... ................ ............... ............... ............... ............... ............... 3.529 3.613 3.730 3.803 3.897 3.941 3.954 3.997 4.093 4.108 12.535 12.729 12.955 13.043 13.222 13.245 13.366 13.412 13.651 13.661 5.700 5.660 5.638 5.609 5.587 5.540 5.498 5.474 5.480 5.469 2.264 2.295 2.323 2.348 2.373 2.392 2.416 2.442 2.463 2.475 72.0 73.5 76.8 76.4 82.0 97.4 102.1 99.5 101.9 107.7 63.2 74.6 91.2 109.4 107.4 101.8 86.0 78.1 98.7 115.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ................ ................ ................ ............... ............... ............... ............... ................ ............... ............... 4.115 4.136 4.140 4.145 4.167 4.187 4.236 4.333 4.394 4.451 13.716 13.806 13.779 13.753 13.666 13.523 13.376 13.461 13.465 13.451 5.445 5.425 5.399 5.386 5.358 5.302 5.257 5.236 5.215 5.188 2.494 2.502 2.497 2.483 2.476 2.477 2.495 2.516 2.524 2.532 70.6 68.8 77.6 92.5 93.7 81.7 87.3 100.0 116.0 122.6 104.3 100.4 104.3 114.4 109.1 95.7 94.7 100.0 110.1 118.4 100.8 114.5 144.5 143.8 84.9 78.8 83.3 100.0 108.5 116.4 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ............... ................ ............... ............... ............... ............... ............... ............... ............... ................ 4.537 4.603 4.640 4.691 4.809 4.970 5.041 5.098 5.152 5.259 13.593 13.727 13.726 13.644 13.742 14.042 14.118 14.117 14.075 14.150 5.181 5.184 5.175 5.152 5.150 5.181 5.215 5.241 5.254 5.262 2.558 2.578 2.589 2.616 2.681 2.740 2.784 2.818 2.849 2.879 119.0 121.2 122.6 131.6 105.6 104.2 1980 ................ 1981 ................ 5.410 5.516 14.339 14.465 5.271 5.277 2.917 2.949 61 Table C-21. Private nonfarm business sector: Productive capital stock, 1948-81 Table C-20. Private nonfarm business sector: Real capital input, 1948-81 Index, 1977=100) All assets Period Equip ment Struc tures Rental residential capital Inven tories All assets Equip ment Struc tures Rental residential capital Inven tories Land 1948 ....... 1949 ....... 40.2 41.2 26.6 28.9 41.0 41.9 64.5 64.8 33.7 33.8 49.6 50.1 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 42.2 43.7 45.0 46.0 47.0 48.2 49.8 51.3 52.3 53.4 30.4 32.3 34.1 35.7 37.2 38.7 40.3 42.1 43.1 43.8 42.6 43.6 44.5 45.6 46.9 48.4 50.3 52.3 54.0 55.5 65.2 65.7 65.8 66.0 66.2 66.5 66.8 67.2 67.6 68.3 34.8 38.6 41.4 42.2 42.0 42.8 45.3 46.6 46.3 47.1 50.8 51.5 52.1 52.9 53.8 54.9 56.2 57.6 58.8 60.1 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 54.8 56.1 57.6 59.5 61.6 64.2 67.5 70.7 73.8 77.1 44.8 45.7 46.7 48.1 50.0 52.8 56.6 60.6 64.3 68.5 57.2 59.1 61.0 62.9 65.0 67.6 70.7 73.7 76.7 79.8 69.2 70.2 71.8 73.9 76.2 78.4 80.2 81.5 83.0 85.1 49.4 50.5 51.8 54.3 56.7 59.8 64.4 69.6 73.9 77.7 61.5 63.0 64.7 66.6 68.6 70.8 73.4 75.8 78.2 80.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 80.3 83.0 85.9 89.5 93.2 95.7 97.5 100.0 103.5 107.3 72.5 75.6 79.0 83.8 89.2 93.2 96.1 100.0 105.7 112.6 82.9 85.7 88.4 91.3 94.3 96.6 98.3 100.0 102.1 104.6 87.2 89.2 92.0 95.2 97.2 98.1 98.9 100.0 101.5 103.2 80.7 83.0 85.7 89.4 93.8 95.6 96.3 100.0 105.4 109.3 83.5 86.0 88.7 91.6 94.4 96.4 98.2 100.0 102.1 104.5 1980 ....... 1981 ....... 110.7 114.1 119.1 124.9 107.4 110.6 104.8 106.1 110.2 111.1 107.2 110.0 Land Period Index, 1977=100 1948 ....... 1949 ....... 36.3 37.7 24.7 26.9 43.9 44.9 60.6 61.0 33.8 33.9 49.7 50.4 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 39.0 40.6 42.4 43.7 44.9 46.4 48.1 49.7 50.8 51.9 28.8 30.6 32.5 34.2 35.6 37.1 39.0 40.7 41.9 42.6 45.6 46.6 47.6 48.8 50.1 51.8 53.7 55.7 57.5 59.1 61.7 62.3 62.5 62.9 63.3 63.8 64.3 64.7 65.2 66.1 34.5 39.0 42.2 43.1 42.8 43.6 46.2 47.6 47.3 48.0 51.0 51.7 52.3 53.1 54.0 55.0 56.4 57.7 59.0 60.2 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 53.2 54.4 55.7 57.4 59.4 62.0 65.3 68.9 72.1 75.6 43.5 44.4 45.3 46.7 48.6 51.5 55.4 59.5 63.2 67.2 60.8 62.5 64.2 65.8 67.5 69.7 72.5 75.2 78.0 80.9 67.1 68.3 69.9 71.9 74.2 76.3 78.1 79.5 81.0 83.2 50.4 51.4 52.8 55.3 57.7 60.7 65.3 70.7 75.1 78.9 61.6 63.1 64.8 66.6 68.6 70.9 73.4 75.8 78.2 80.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 78.9 81.8 84.8 88.8 93.0 95.6 97.4 100.0 103.7 107.9 71.2 74.4 77.8 82.8 88.4 92.6 95.9 100.0 105.8 112.8 83.6 86.1 88.6 91.5 94.5 96.9 98.4 100.0 102.0 104.5 85.4 87.6 91.0 94.9 97.1 97.9 98.8 100.0 101.5 103.3 82.1 84.5 87.3 90.6 94.8 95.5 96.3 100.0 105.5 109.3 83.6 86.1 88.8 91.8 94.4 96.5 98.2 100.0 102.1 104.6 1980 ....... 1981 ....... 111.7 115.0 119.5 125.1 107.4 110.5 104.9 106.3 111.0 110.7 107.2 110.1 Percent change from preceding year 1949 ....... 3.7 8.8 2.3 0.8 0.2 1.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 3.5 4.2 4.3 3.2 2.8 3.3 3.7 3.3 2.3 2.0 7.1 6.5 6.1 5.1 4.2 4.3 4.9 4.6 2.8 1.7 1.7 2.1 2.2 2.5 2.7 3.4 3.8 3.6 3.3 2.8 1.2 0.9 0.4 0.5 0.7 0.8 0.8 0.7 0.8 1.3 1.7 13.0 8.3 2.3 -0.8 1.9 6.0 3.1 -0.8 1.7 1.2 1.4 1.3 1.5 1.6 2.0 2.4 2.5 2.2 2.1 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 2.6 2.3 2.4 3.0 3.5 4.4 5.4 5.4 4.7 4.8 2.2 2.0 2.1 3.0 4.2 5.9 7.5 7.4 6.2 6.4 2.9 2.8 2.6 2.5 2.6 3.3 3.9 3.8 3.7 3.7 1.6 1.7 2.3 2.9 3.2 2.9 2.3 1.7 1.9 2.7 4.8 2.1 2.6 4.8 4.2 5.3 7.6 8.3 6.2 5.1 2.2 2.5 2.7 2.8 3.0 3.3 3.5 3.3 3.2 3.4 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 4.5 3.6 3.7 4.7 4.7 2.8 1.9 2.7 3.7 4.0 5.9 4.5 4.6 6.4 6.8 4.9 3.5 4.3 5.8 6.6 3.4 3.0 2.9 3.2 3.4 2.5 1.6 1.6 2.0 2.4 2.7 2.6 3.9 4.2 2.3 0.9 0.9 1.2 1.5 1.7 3.9 3.0 3.3 3.9 4.6 0.7 0.8 3.9 5.5 3.7 3.4 3.1 3.1 3.3 2.9 2.2 1.8 1.8 2.1 2.4 1980 ....... 1981 ....... 3.5 3.0 5.9 4.7 2.7 3.0 1.6 1.3 0.7 0.6 Table C-22. Private nonfarm business sector: Shares in current capital cost, 1948-81 Period All assets Equip ment Struc tures Rental residential capital Inven tories Land 1948 ....... 1949 ....... 1.000 1.000 0.285 .328 0.276 .361 0.235 .101 0.141 .142 0.063 .069 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .374 .337 .339 .442 .414 .360 .307 .398 .324 .442 .375 .226 .306 .309 .360 .342 .236 .275 .365 .300 .131 .191 .136 .105 .090 .138 .196 .145 .123 .112 .021 .206 .161 .089 .061 .071 .178 .109 .076 .082 .098 .040 .059 .055 .075 .090 .084 .073 .112 .064 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .401 .402 .379 .375 .352 .333 .374 .353 .361 .431 .326 .318 .321 .302 .312 .313 .288 .301 .315 .262 .129 .104 .114 .127 .114 .117 .115 .108 .099 .108 .085 .072 .096 .108 .121 .127 .132 .139 .125 .130 .059 .104 .091 .087 .101 .110 .090 .100 .099 .068 2.6 2.7 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .427 .418 .430 .416 .438 .218 .297 .314 .374 .374 .268 .278 .312 .303 .242 .274 .361 .313 .261 .275 .105 .090 .035 .126 .227 .134 .093 .123 .110 .132 .124 .139 .122 .064 .045 .163 .107 .131 .147 .094 .076 .076 .102 .091 .048 .211 .142 .118 .108 .125 2.4 2.5 2.3 1980 ....... 1981 ....... 1.000 1.000 .352 .285 .282 .039 .131 .104 .099 .151 .136 .151 Compound annual rate of growth 1948-81 .. 1948-73 .. 1973-81 .. 3.6 3.6 3.3 5.0 5.0 5.3 2.8 3.0 2.4 1.7 1.8 1.4 3.7 4.0 2.5 62 Table C-23. Private nonfarm business sector: Ratios of capital services to productive stock, 1948-81 Table C-25. Private nonfarm business sector: Price of new capital goods, 1948-81 (Index, 1977=100) (Index, 1977=100) All assets Equip ment Struc tures Rental residential capital Inven tories Land 1948 ....... 1949 ....... 33.8 34.1 33.5 35.2 29.9 30.0 35.3 36.5 43.0 40.9 31.8 32.0 100.4 100.4 100.4 100.4 100.3 100.3 100.3 100.3 100.3 100.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 35.5 38.4 39.6 40.2 40.2 40.7 43.9 45.2 45.9 45.5 36.7 40.0 42.2 41.9 42.1 43.3 48.6 49.9 53.0 51.7 30.6 34.6 35.9 36.8 36.2 36.1 40.1 41.9 41.7 41.7 37.7 38.9 40.0 41.1 41.9 42.5 43.0 43.5 44.3 44.3 45.2 46.4 45.6 46.0 46.3 47.4 49.3 50.1 50.3 49.8 32.6 35.9 37.1 37.9 37.6 38.1 41.0 42.4 42.3 42.5 101.9 101.8 101.8 101.9 101.6 101.4 101.4 101.6 101.7 101.6 100.1 100.1 100.1 100.1 100.1 100.0 100.0 100.0 100.0 100.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 45.8 45.5 45.4 45.6 46.0 46.9 48.2 50.0 51.9 55.2 52.2 52.1 52.1 52.0 52.4 53.8 54.3 56.3 58.3 60.2 41.8 41.5 41.4 41.8 42.3 43.1 44.8 46.6 48.3 52.4 44.3 44.3 44.3 44.0 44.4 45.2 46.4 48.4 51.0 54.5 49.8 49.7 49.6 49.7 50.0 50.7 51.7 52.5 53.9 56.1 43.3 42.4 42.3 42.5 42.8 43.4 45.1 46.8 48.6 52.6 97.9 98.2 99.0 99.7 99.8 99.8 99.9 100.0 100.1 100.1 101.6 101.8 101.8 101.4 101.1 99.9 99.9 100.0 100.0 100.0 100.1 100.1 100.2 100.2 100.1 100.0 100.0 100.0 100.0 100.0 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 58.8 62.6 66.1 70.5 81.1 89.1 93.9 100.0 109.4 122.0 63.3 66.2 67.6 69.2 75.2 87.4 93.7 100.0 105.7 114.1 56.8 61.2 64.9 69.6 82.3 91.3 94.4 100.0 111.5 125.9 58.4 63.5 71.8 76.5 81.3 87.5 94.4 100.0 110.8 122.4 58.4 60.1 62.3 68.7 83.1 88.9 94.0 100.0 108.1 123.8 56.7 61.4 65.2 70.7 85.5 89.0 93.1 100.0 111.9 126.2 100.1 100.2 99.9 99.7 100.1 100.1 1980 ....... 1981 ....... 135.4 146.4 124.0 133.8 141.4 153.6 134.9 148.4 139.7 148.4 141.0 153.0 All assets Equip ment Struc tures Rental residential capital Inven tories Land Period 1948 ....... 1949 ....... 90.3 91.3 92.7 93.1 107.1 107.2 93.9 94.2 100.4 100.2 100.3 100.4 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 92.3 93.0 94.2 94.9 95.7 96.3 96.7 96.9 97.2 97.2 94.5 94.9 95.4 95.7 95.7 96.1 96.6 96.9 97.1 97.2 107.1 107.0 106.9 107.0 106.9 107.0 106.8 106.5 106.5 106.5 94.6 94.9 95.0 95.3 95.6 95.9 96.1 96.3 96.5 96.8 99.1 100.8 102.0 102.2 102.0 102.0 102.0 102.1 102.1 102.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 97.1 96.9 96.7 96.5 96.4 96.5 96.9 97.4 97.7 98.0 97.1 97.0 97.0 97.0 97.2 97.5 97.8 98.2 98.2 98.1 106.3 105.8 105.2 104.6 103.9 103.2 102.5 102.0 101.7 101.3 97.1 97.2 97.4 97.4 97.3 97.4 97.4 97.5 97.6 97.7 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 98.3 98.6 98.8 99.3 99.8 99.9 99.9 100.0 100.2 100.6 98.2 98.3 98.5 98.8 99.0 99.4 99.8 100.0 100.1 100.2 100.8 100.5 100.3 100.1 100.2 100.3 100.1 100.0 100.0 99.9 1980 ....... 1981 ....... 100.9 100.9 100.3 100.2 99.9 99.9 Period Table C-24. Private nonfarm business sector: Gross real investment, 1948-81 Table C-26. Private nonfarm business sector: Rate of depreciation, 1948-81 (Index, 1977=100) (Percent per year) Period All assets Equipment Structures Rental residential capital Period All assets Equipment Structures Rental residential capital 1948 1949 ..................... ..................... 39.1 32.4 34.5 26.1 51.3 46.8 37.8 38.7 1948 1949 ..................... ..................... 4.183 4.384 11.788 12.258 5.851 5.831 2.206 2.234 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 35.7 37.7 36.7 39.8 39.4 44.5 46.9 47.8 41.5 45.5 29.1 32.1 30.9 33.1 31.6 35.0 36.9 39.3 30.9 34.9 48.7 52.2 51.8 57.2 59.0 68.5 73.8 73.2 66.7 68.0 51.0 37.9 36.3 38.6 40.9 46.7 43.6 45.2 50.2 64.0 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 4.453 4.498 4.573 4.639 4.732 4.764 4.798 4.845 4.939 4.930 12.381 12.530 12.732 12.805 12.974 12.999 13.107 13.166 13.451 13.484 5.800 5.766 5.752 5.726 5.705 5.655 5.609 5.582 5.587 5.578 2.251 2.282 2.310 2.335 2.359 2.377 2.401 2.427 2.448 2.459 1960 ..................... 1961 ..................... 1962 ..................... 1963 ..................... 1964 ..................... 1965 ..................... 1966 ..................... 1967 ..................... 1968 ..................... 1969 ..................... 48.7 48.8 53.4 56.5 62.3 71.4 77.3 74.5 79.6 86.2 37.2 35.7 39.5 42.4 48.8 56.6 65.1 63.1 67.4 73.2 74.4 75.9 79.1 78.8 85.0 101.6 106.6 103.1 106.1 112.2 63.2 74.6 91.2 109.4 107.4 101.8 86.0 78.0 98.7 115.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 4.919 4.932 4.909 4.889 4.874 4.866 4.878 4.945 4.977 5.018 13.536 13.653 13.638 13.631 13.548 13.418 13.272 13.366 13.346 13.337 5.553 5.531 5.504 5.489 5.459 5.397 5.347 5.323 5.299 5.269 2.478 2.485 2.479 2.463 2.456 2.456 2.475 2.496 2.504 2.512 ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 82.4 80.8 90.5 102.6 97.8 84.5 88.4 100.0 114.4 122.2 70.6 68.5 77.8 92.3 93.6 80.5 86.3 100.0 116.3 123.5 108.1 103.8 108.8 118.3 112.0 96.5 95.0 100.0 110.8 120.4 100.8 114.5 144.5 143.8 84.9 78.8 83.3 100.0 108.5 116.4 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... 5.101 5.165 5.184 5.212 5.310 5.459 5.527 5.571 5.628 5.744 13.493 13.643 13.647 13.584 13.693 14.017 14.103 14.096 14.057 14.133 5.261 5.264 5.252 5.228 5.228 5.263 5.304 5.336 5.355 5.365 2.538 2.559 2.571 2.599 2.665 2.726 2.770 2.804 2.837 2.867 1980 ..................... 1981 ..................... 121.7 126.2 121.4 124.4 126.6 136.6 105.6 104.2 1980 ..................... 1981 ..................... 5.896 6.006 14.316 14.441 5.372 5.376 2.905 2.937 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 63 Table C-27. Manufacturing sector: Real capital input, 1948-81 Period All assets Table C-28. Manufacturing sector: Productive capital stock, 1948-81 (Index, 1977=100) Equipment Structures Inventories Land Inventories Land 1948 ... 1949 ... 41.0 42.4 27.9 30.3 60.0 61.8 35.9 35.4 60.8 62.2 1950 1951 1952 1953 1954 1955 1966 1957 1958 1959 .. . ... ... ... ... ... ... ... .. . .. . 43.3 45.9 48.5 50.2 51.1 52.3 54.6 56.6 57.3 57.8 31.9 34.0 36.3 38.4 40.4 42.2 44.2 46.5 47.8 48.1 62.7 63.7 65.0 66.1 67.1 68.7 70.7 72.6 74.3 75.2 35.6 40.8 45.8 47.4 46.7 46.6 49.7 51.4 50.2 50.4 63.0 63.9 65.0 65.9 66.8 68.2 69.9 71.5 73.0 74.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ... ... . .. ... ... ... ... ... ... ... 58.8 59.7 60.6 62.1 63.7 66.1 69.9 74.6 78.6 81.7 48.5 49.0 49.5 50.4 52.1 55.0 59.3 64.1 68.1 71.3 76.0 77.0 78.0 79.1 80.2 81.8 84.5 87.7 90.5 93.0 52.7 53.8 55.2 57.9 60.0 62.8 67.5 74.0 79.4 83.1 74.8 75.8 76.9 78.0 79.2 80.7 83.1 85.9 88.5 90.7 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ... ... ... ... ... ... ... ... . .. ... 84.2 85.6 86.6 88.7 92.2 95.5 97.5 100.0 103.4 107.8 74.2 76.2 78.3 81.4 86.0 90.9 95.1 100.0 105.8 113.0 95.1 96.3 97.0 97.6 98.5 99.2 99.5 100.0 100.7 102.1 85.7 86.3 86.3 88.4 93.5 97.7 98.6 100.0 103.4 107.5 92.8 94.3 95.3 96.2 97.4 98.4 99.2 100.0 101.0 102.5 1980 ... 1981 ... 113.0 118.1 122.4 132.7 103.8 105.5 110.9 112.6 104.2 106.0 All assets Period Index, 1977=100 1948 1949 .... ....... 37.9 39.5 27.0 29.5 62.1 63.9 36.6 36.1 60.8 62.2 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 40.7 43.2 46.4 48.2 49.5 51.0 53.2 55.2 56.2 56.6 31.3 33.4 35.7 37.7 39.6 41.4 43.4 45.8 47.0 47.3 64.9 65.7 66.6 67.8 68.9 70.7 72.0 73.0 74.7 75.6 36.3 41.5 46.6 48.3 47.6 47.5 50.7 52.3 51.2 51.3 63.0 63.9 65.0 65.9 66.8 68.2 69.9 71.5 73.0 74.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 57.5 58.3 59.2 60.7 62.4 65.1 69.2 74.2 78.2 81.3 47.8 48.3 49.0 50.0 51.8 54.9 59.3 64.4 68.3 71.3 76.4 77.6 78.6 79.7 80.6 82.1 84.7 87.9 90.7 93.2 53.7 54.7 56.2 58.9 61.0 63.9 68.7 75.3 80.7 84.4 74.8 75.8 76.9 78.0 79.2 80.7 83.1 85.9 88.5 90.7 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ..... ....... ....... ....... 83.9 85.2 86.4 88.6 92.2 95.5 97.4 100.0 103.8 108.8 73.9 75.5 77.3 80.4 84.9 90.0 94.6 100.0 106.0 113.4 95.2 96.4 97.0 97.6 98.5 99.2 99.5 100.0 100.7 102.1 87.1 87.6 87.5 89.6 94.3 97.6 98.6 100.0 103.4 107.5 92.8 94.3 95.3 96.2 97.4 98.4 99.2 100.0 101.0 102.5 1980 1981 ....... ....... 115.1 121.1 123.6 135.3 103.8 105.5 111.2 112.9 104.2 106.0 1949 ....... 4.0 9.3 3.0 -1 .4 2.4 1950 1952 1953 1954 1955 1956 1957 1958 1959 ....... ....... ....... ....... ....... ....... ....... ....... ....... 3.2 7.5 3.7 2.7 3.1 4.3 3.8 1.7 0.8 6.0 7.0 5.6 5.1 4.5 4.9 5.4 2.7 0.5 14.6 1.5 1.7 1.6 2.7 1.9 1.3 2.3 1.3 0.5 12.3 3.6 -1.5 -0 .2 6.6 3.3 -2 .2 0.4 1.3 1.7 1.5 1.4 2.0 2.5 2.4 2.1 1.3 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 1.6 1.4 1.6 2.4 2.9 4.2 6.3 7.2 5.4 3.9 1.1 1.1 1.3 2.1 3.6 5.9 8.2 8.5 6.1 4.3 1.1 1.5 1.4 1.3 1.2 1.9 3.2 3.8 3.2 2.7 4.4 1.9 2.7 4.9 3.6 4.7 7.5 9.6 7.2 4.6 1.1 1.4 1.4 1.4 1.5 2.0 2.9 3.4 3.0 2.6 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....... ....... ....... ....... ....... ....... ....... ....... ....... ....... 3.2 1.6 1.4 2.6 4.1 3.5 2.0 2.7 3.8 4.8 3.6 2.2 2.4 3.9 5.6 6.0 5.1 5.7 6.0 7.0 2.2 1.2 0.7 0.6 0.9 0.7 0.3 0.5 0.7 1.3 3.1 0.6 -0.1 2.4 5.2 3.5 1.0 1.5 3.4 4.0 2.3 1.6 1.1 1.0 1.2 1.1 0.8 0.8 1.0 1.5 1980 1981 ....... ....... 5.8 5.2 9.0 9.4 1.7 1.7 3.4 1.6 1.7 1.7 Structures Table C-29. Manufacturing sector: Shares in current capital cost, 1948-81 Percent change from preceding year (Index, 1977=100) All assets Equipment Structures Inventories Land 1948 ... 1949 ... Period 1.000 1.000 0.356 .340 0.350 .371 0.248 .248 0.045 .041 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ... ... ... ... ... ... . .. ... ... ... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .444 .388 .397 .436 .433 .369 .449 .446 .431 .448 .427 .179 .300 .356 .388 .452 .156 .298 .394 .337 .053 .433 .272 .158 .118 .082 .401 .220 .117 .168 .076 .000 .030 .050 .060 .097 -.006 .036 .057 .048 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ... ... ... ... ... ... ... ... ... ... 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .466 .488 .450 .457 .429 .400 .425 .426 .443 .526 .340 .321 .311 .269 .279 .292 .272 .268 .277 .215 .146 .151 .195 .238 .248 .254 .254 .262 .234 .236 .047 .040 .044 .036 .044 .055 .049 .045 .046 .022 ... ... ... ... ... .. . . .. .. . ... .. . 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .543 .508 .480 .522 .635 .273 .349 .406 .476 .514 .224 .219 .266 .264 .273 .345 .365 .272 .199 .215 .213 .248 .212 .169 .046 .306 .198 .260 .286 .225 .020 .024 .042 .045 .046 .076 .088 .063 .040 .045 1.000 1.000 .541 .391 .237 .294 .174 .245 .048 .070 1948-81 . .. 3.6 5.0 1.6 3.5 1.7 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1948-73 . .. 1973-81 . .. 3.5 4.0 4.5 6.7 1.8 1.0 3.5 2.9 1.9 1.2 1980 ... 1981 . . . Compound annual rate o f growth Equipment 64 Table C-30. Manufacturing sector: Ratio of capital services to productive stock, 1948-81 Table C-32. Manufacturing sector: Price of new capital goods, 1948-81 (Index, 1977=100) (Index, 1977=100) Inventories Land 29.1 28.8 41.6 39.0 29.2 28.8 32.9 36.5 37.7 38.0 38.4 39.9 44.5 46.4 48.3 48.5 29.4 35.7 37.0 37.1 36.0 32.8 39.6 41.3 40.2 39.1 44.4 45.4 44.5 45.2 45.6 47.4 49.4 50.1 50.2 49.1 29.4 35.7 37.0 37.1 36.0 32.9 39.7 41.4 40.2 39.1 44.8 44.7 44.9 45.6 46.6 47.7 49.4 51.2 52.9 56.0 49.4 49.7 50.1 50.4 51.1 52.4 53.9 55.9 57.7 59.6 38.7 38.3 38.5 39.9 41.5 42.7 44.8 47.0 48.9 53.7 49.4 49.2 49.0 48.9 49.2 49.7 50.8 51.5 52.9 55.1 38.7 38.4 38.6 40.0 41.5 42.7 44.9 47.0 49.0 53.7 ... ... ... ... ... ... ... ... ... ... 59.6 62.7 65.0 69.2 80.7 90.3 93.9 100.0 107.7 120.3 62.6 65.1 66.4 68.2 74.3 87.6 93.6 100.0 105.4 114.4 58.8 64.1 67.5 73.3 86.6 94.6 94.3 100.0 111.0 126.8 57.7 59.3 61.0 66.1 81.3 89.0 93.8 100.0 107.2 121.4 58.8 64.1 67.5 73.3 86.6 94.6 94.3 100.0 111.0 126.8 1980 . . . 1981 ... 133.6 142.5 123.7 132.8 142.5 150.6 137.8 148.3 142.5 150.6 All assets Equipment Structures Inventories Land Period 1948 ... 1949 ... 92.7 93.1 96.9 97.4 103.4 103.4 101.9 101.9 100.0 100.0 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ... ... ... ... ... ... ... ... ... ... 93.9 94.2 95.7 96.0 96.8 97.5 97.4 97.6 98.0 98.0 98.1 98.3 98.4 98.2 98.0 98.1 98.3 98.3 98.4 98.3 103.4 103.1 102.6 102.6 102.6 103.0 101.9 100.5 100.5 100.5 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 101.9 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ... ... ... ... ... ... ... ... ... ... 97.8 97.8 97.7 97.8 98.0 98.4 98.9 99.4 99.5 99.5 98.5 98.7 98.9 99.1 99.4 99.7 100.1 100.4 100.4 100.0 100.6 100.7 100.8 100.7 100.6 100.4 100.3 100.3 100.3 100.2 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ... ... ... .. . ... ... ... ... ... .. . 99.6 99.6 99.7 100.0 100.1 100.0 99.9 100.0 100.3 100.9 99.6 99.1 98.8 98.7 98.8 99.1 99.6 100.0 100.2 100.4 1980 ... 1981 ... 101.8 102.5 101.0 102.0 Period All assets Equipment 1948 ... 1949 . . . 32.8 32.2 30.1 31.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ... ... ... ... .. . ... ... ... ... ... 34.2 38.6 39.4 39.8 39.5 39.0 43.8 45.3 45.3 44.6 101.8 101.7 101.7 101.7 101.7 101.7 101.7 101.7 101.6 101.6 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ... ... ... ... ... ... ... . .. ... ..., 100.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 101.5 101.5 101.5 101.4 100.8 99.8 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 100.0 100.0 100.2 100.3 100.0 100.0 Structures Table C-33. Manufacturing sector: Rate of depreciation, 1948-81 Table C-31. Manufacturing sector: Gross real investment, 1948-81 (Percent per year) (Index, 1977=100) Structures Period All assets Equipment Structures Period All assets Equipment 1948 .......................... 1949 .......................... 48.1 36.3 36.1 27.4 102.6 76.8 1949 ......................... 1949 ......................... 4.961 5.243 11.423 11.916 5.628 5.629 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 .......................... ......................... .......................... .......................... .......................... .......................... .......................... .......................... ......................... ......................... 35.2 43.7 42.8 43.3 44.2 47.0 52.5 53.2 42.1 39.5 28.3 35.3 35.1 35.7 37.1 35.2 42.6 43.1 31.5 32.5 66.6 82.0 77.8 77.8 76.6 100.9 97.5 99.6 90.2 71.7 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... 5.374 5.268 5.250 5.328 5.469 5.570 5.535 5.596 5.788 5.830 12.149 12.149 12.295 12.411 12.494 12.651 12.610 12.666 13.041 13.201 5.639 5.608 5.611 5.623 5.639 5.593 5.598 5.599 5.634 5.687 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ......................... .......................... .......................... .......................... ......................... .......................... .......................... ......................... .......................... ......................... 44.1 43.6 46.3 49.6 56.4 69.4 81.7 83.7 75.1 77.8 35.5 34.3 37.5 41.0 48.9 59.8 70.0 71.3 64.1 66.8 83.5 86.1 86.5 89.0 90.8 113.4 135.1 140.1 125.1 127.8 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... 5.794 5.822 5.810 5.778 5.765 5.747 5.723 5.736 5.800 5.794 13.299 13.459 13.505 13.527 13.411 13.188 12.975 12.978 13.160 13.099 5.711 5.748 5.788 5.823 5.856 5.842 5.802 5.777 5.796 5.810 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... 73.3 65.5 73.2 79.2 94.6 86.0 89.5 100.0 106.5 126.1 64.0 58.3 68.7 75.3 90.9 84.6 87.6 100.0 105.2 125.6 115.6 98.4 93.6 96.9 111.4 92.6 98.5 100.0 112.0 128.2 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... ......................... 5.841 5.926 5.961 5.995 5.959 6.052 6.166 6.255 6.364 6.419 13.140 13.242 13.141 13.072 12.869 12.952 12.992 12.956 13.047 12.968 5.854 5.925 5.988 6.031 6.055 6.118 6.165 6.199 6.208 6.198 1980 ......................... 1981 ......................... 141.0 147.2 143.7 149.8 128.8 134.9 1980 ......................... 1981 ......................... 6.566 6.821 12.976 13.174 6.201 6.178 65 Appendix 0= [Ktouirs ©A All Persons Methods and Sources sources of data on employment and average weekly hours by sector and occupation used in the bls produc tivity measures are summarized in table D - 1. Two sources of monthly information are used: The Current Employment Statistics program survey and the Current Population Survey. The Current Employment Statistics survey collects data for the employees of all nonagricultural establishments; hence it is often called the “ establishment survey.” The Current Population Survey obtains its information through household inter views and is called the “ household survey.” Information collected in the establishment survey is regularly published in the B and C tables of Employ- The traditional bls measures of output per hour of all persons and the new multifactor productivity measures of output per unit of combined labor and capital input use the same measures of labor input, except that the new productivity series excludes hours in government enterprises. Hours of labor represent about two-thirds of the combined labor and capital inputs in the new multifactor measures, and are the only input counted in the traditional productivity series. Using information gathered in monthly surveys, the Bureau of Labor Sta tistics aggregates measures of employment and average weekly hours at the 2-digit sic level to major sector di visions for use in these two productivity series. The T a b le D-1. Sources o f em ploym ent and hours data used in labor input measures fo r BLS p ro d u c tiv ity series, private business sector Employment Sector and occupation Average weekly hours Directly collected Percent of private business hours (1982) Estab lishment survey House hold survey Estab lishment survey House hold survey T o ta l.............................................................. 100 N o n m a n u f a c t u r i n g ............................................................ 69 Employees: All employees .......................................... Production workers ................................. Nonproduction workers ......................... 58 NA NA Self-employed: Proprietors and partners ....................... Unpaid family workers ........................... 11 1 M a n u f a c t u r in g ...................................................................... 27 Employees: All employees .......................................... Production workers ................................. Nonproduction workers ......................... 26 18 9 Self-employed: Proprietors and partners ........................ 1 X X 4 3 X X 2 (1) X X X X ............................................................ Farmers and farm managers ........................ Farm laborers and supervisors: Paid workers ............................................ Unpaid family workers ........................... A g r ic u lt u r e X X X Assumed to be equal to average weekly hours for production workers X X X X X X X Estimates based on data from the bls survey of employer expenditures for employee compensation, and production-worker average weekly hours. NA = not available. 1Less than 0.5 percent. No t e : Detail may not add to totals due to rounding. Not directly collected 66 total hours in the private business sector. Data are col lected for production workers in mining, construction workers in construction, and for nonsupervisory work ers in transportation and public utilities, wholesale and retail trade, finance, insurance, and real estate, and business and personal services. Since employment is collected for all employees and for nonsupervisory workers, supervisors’ employment can be computed by subtraction. Average weekly hours are collected for nonsupervisory workers only. For the purposes of pro ductivity measurement, the average weekly hours of su pervisory workers are assumed to be equal to those of nonsupervisory employees in the industry. Self-employed and unpaid family workers in nonman ufacturing occupations contribute an additional 11 per cent of private business hours. Information on the em ployment and average weekly hours for these workers is collected directly in the household survey. merit and Earnings. Measures of employment and aver age weekly hours are collected for persons on the payrolls of approximately 180,000 establishments dur ing the pay period which includes the 12th of the month. Since the hours are payroll hours, the measure includes paid leave time in addition to time spent at the work site. Persons who appear on the records of more than one establishment during the survey week are counted more than once, whether this results from mul tiple jobholding or job changes. Since several categories of workers are outside the scope of the establishment survey, additional informa tion is obtained from the household survey. These in clude self-employed individuals, farmers and farm workers, employees of private households, and unpaid family workers. Measures based on this survey are pub lished in the A tables of Employment and Earnings. Monthly interviews are conducted in about 60,000 households to gather information on the labor force sta tus and hours at work for the noninstitutional civilian population during the week including the 12th of the month. In this survey, multiple jobholders are counted only once, and all of their hours are assigned to the in dustry at which they worked most during the survey pe riod. Only hours at work are counted; if a paid holiday occurs during the survey week, only 32 hours are re ported even if 40 hours’ pay is received. For practical purposes, the hours data used in the bls productivity measures are hours paid rather than hours at work. This is so because about 85 percent of total pri vate business hours are taken from the establishment survey, which collects information on hours paid; only 15 percent comes from the household survey, which collects data on hours at work (table D -l). In general, hours of all persons are computed by mul tiplying employment by average weekly hours at the 2-digit sic level each month. These weekly values are converted to annual rates by multiplying them by 52. Seasonal factors are computed using a time span and method which correspond to the procedure for seasonal ly adjusting output used by the Bureau of Economic Analysis of the U.S. Department of Commerce. This avoids influencing productivity measures through the use of different seasonal adjustments to the numerator and denominator of the productivity ratios. The seasonally adjusted results are summed to totals for private business, private nonfarm business, and manufacturing; quarterly averages are computed from three monthly levels. Annual averages are computed based on 12 months of data. Year-to-year changes are computed by comparing annual averages, rather than December to December movements. M anufacturing The hours of all persons engaged in the manufactur ing sector account for about 27 percent of private busi ness hours. Employment data are collected for produc tion and related w orkers, and for all em ployees. Average weekly hours are collected only for production workers; average weekly hours of nonproduction work ers are estimated based on information compiled in the bls survey of employer expenditures for employee com pensation and from production-worker average weekly hours. The self-employed in manufacturing make up a very small proportion of the sector. Information on their em ployment and average weekly hours is obtained directly from the household survey. Farm Information on labor inputs in the farm sector comes from the household survey. Data are collected for farm ers and farm managers, unpaid family workers, and paid farm workers. The number of farm proprietors is as sumed to be equal to the number of farmers and farm managers reported in the labor force data; average weekly hours for self-employed persons in the labor force “ agriculture” sector, which includes agriculture services as well as farm, are used to compute hours for farm proprietors. The number of 14- and 15-year-old unpaid family workers on farms is assumed equal to the number of unpaid family workers in this age group in “ agriculture” ; average weekly hours at work for agri cultural unpaid family workers age 16 and over are used to compute hours of all unpaid family workers. Employees on farms are represented in the household data as “ paid workers.” Employment levels of workers over 16 are available directly; those of 14- and 15-yearolds are estimated by subtracting 14- and 15-year-old unpaid family workers on farms (estimated as described Nonmanufacturing Employees of establishments not engaged in manu facturing or agriculture account for about 58 percent of 67 Nonprofit institutions above) from all farm workers in this age group; average weekly hours for wage and salary workers at work in agriculture age 16 and over are used to compute hours for all employees on farms. In order to bring employment data drawn from the es tablishment survey into conformity with the business sector concepts, employees of firms owned by nonprofit institutions are removed. Using b e a compensation data, factors are obtained by 2-digit sic, representing the frac tion of employment associated with nonprofit institu tions. Hours of employees in nonprofit institutions are computed by dividing compensation expenditures of nonprofit firms by hourly industry compensation; these hours estimates are then divided by the average weekly hours appropriate to each industry to obtain employment in nonprofit institutions. The ratio of nonprofit employ ment to employment for the industry as a whole is the factor used to obtain monthly estimates of employment for nonprofit institutions from total industry employ ment in the monthly establishment survey. The latest available factor is used until new b e a annual data are available. Government enterprises Hours for government enterprises are measured by first establishing quarterly employee totals for Federal, State, and local government enterprises and then ap plying these employment levels to average weekly hours of all government workers, available from the house hold survey. The quarterly employee levels are obtained by extrapolating annual b e a measures of government enterprise employment using Post Office and State and local government noneducational employment from the establishment survey as indicators for Federal and State and local enterprises. Average weekly hours for govern ment workers, from the household survey, are used for governm ent enterprises. The governm ent class-ofworker category includes all civilian employees. 68 Appendix E„ Com parison of Base-year-weighted and Tornquist Denoted IMymlbors of Multifaotor Productivity The measures of multifactor productivity introduced in this bulletin are computed using a Tornquist index aggregation procedure. Since this is the first time bls has used this index number formula, a comparison was made of the results of this method and the more com monly used method of base-year weighting. This appen dix presents the findings of this comparison . As shown in appendix A, the index of aggregate in puts (labor and capital) is constructed from a weighted average of the growth rates of the separate inputs. The weights are an average of the relative cost shares of the input for the given and previous years. For a base-yearweighted index, the cost shares are held constant over the period of time. For this comparison, both an index using one set of weights for the complete series and an index using different weights for subperiods (hereafter referred to as a shifted base-year-weighted index) were constructed. For the constant-base-year-weight series, the 1972 cost shares were used, as this is the base year for the output index (gnp). A s with the Tornquist index, the indexes of inputs for the base-year weighting meth od were calculated for the most disaggregated level pos sible. The detailed assets were aggregated to the corre sponding sector level, and these sectors were then aggregated to conform to the final indexes. Hence, a single asset (commercial buildings, for example) within different sectors has different weights. Annual percent changes Tables E - l through E -3 show the annual percent changes of multifactor productivity for the three pub lished sectors (private business, private nonfarm busi ness, and m anufacturing) as calculated using the Tornquist index method, shifted base-year weights, and the same (1972) base-year weights for the complete series. Also shown are the differences in the percent changes for each method. Tornquist vs. shifted base-year index. With the excep tion of a few years (1952 and 1965), there is little dif ference between the annual percent changes calculated using the Tornquist method and the shifted base-year in dex for the private business and private nonfarm busi ness sectors. For the manufacturing sector, there are more years where the differences are large, and the magnitudes are also greater than for the other sectors. For all three sectors, the differences were virtually all negative prior to 1958, and almost all were positive and smaller after 1958. This indicates that, prior to 1958, multifactor productivity grew faster based on the shifted base-year-w eighted index, than on the Tornquist method. Tornquist vs. base-year index. The differences in the annual percent changes between the Tornquist index and the 1972 base-year-weighted indexes follow somewhat different patterns from the com parisons discussed above. The differences are greater in value for the pri vate business and nonfarm business sectors, but not as large as for the manufacturing sector. Average annual rates of growth Table E -4 presents the average annual growth rates for the com plete series, 1948-81, and the two subperiods 1948-73 and 1973-81. For the whole peri od, there is a significant difference in results of the dif ferent methods for each of the three sectors. The aver age annual growth rate based on the Tornquist index is 1.5 percent for private business, 1.3 percent for private nonfarm business, and 1.8 percent for manufacturing. Using shifted base-year weights, the annual growth rates for the sectors are 1.7 percent, 1.5 percent, and 2.0 percent, respectively. And, using 1972 base-year weights, the annual growth rates are 1.3 percent for pri vate business, 1.0 percent for private nonfarm business, and 1.6 percent for manufacturing. In all sectors, the annual rate of growth based on the Tornquist index lies between the shifted base-year index and the 1972 baseyear index. The average annual growth rates for the two sub periods are less affected than those for the total period by the use of the different index number formulas. For 1973-81, the difference in growth rates is at most 0.1 percent. For the earlier period, differences are still pres ent between the Tornquist method and the 1972 baseyear-weighted method, but there is little difference be69 tween the Tornquist and shifted base-year method. Thus, the measured productivity slowdown after 1973 is not significantly changed by using shifted base-year weights rather than the Tornquist method. 1The following base-year weights were used for the subperiods: 1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights, 1969-73; and 1973 weights, 1973-81. 70 Table E -2 . Private nonfarm business sector: Annual percent change in m ultifactor productivity under different index number methods, 1949-81 Shifted base-year weights1 (2) Year Tornquist (1) Difference, (1)-(2) (3) 1972 base year (4) Difference, (1)-(4) (5) 1949 ........................................................................................ - 0 .6 -0 .3 - 0 .3 -1 .2 0.6 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ 6.2 2.0 1.2 1.5 - 0 .6 4.4 -0.1 0.4 6.5 2.2 1.7 1.8 -0 .3 4.7 0.1 0.7 0.3 4.5 - 0 .3 - 0 .2 - 0 .5 - 0 .3 - 0 .3 - 0 .3 - 0 .2 - 0 .3 -0 .3 -0 .2 5.7 1.4 1.1 1.2 - 1 .0 4.0 - 0 .6 0.0 - 0 .2 4.0 0.5 0.6 0.1 0.3 0.4 0.4 0.5 0.4 0.2 0.3 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ....................................................................................... ....................................................................................... 0.1 1.7 3.5 2.5 3.5 2.9 1.7 0.0 0.1 0.0 2.4 -0 .8 1.7 3.4 2.4 3.3 2.5 1.5 0.1 2.3 - 1 .0 -0 .3 1.2 3.1 2.3 3.1 2.4 1.3 -0 .1 2.2 -1 .1 0.4 0.5 0.4 0.2 0.4 0.5 0.4 0.1 0.2 0.3 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ....................................................................................... ........................................................................................ ........................................................................................ ....................................................................................... ....................................................................................... ....................................................................................... ........................................................................................ ........................................................................................ ....................................................................................... ........................................................................................ -1 .6 2.0 3.5 2.3 - 3 .9 - 0 .5 3.8 2.9 1.1 -1 .5 - 1 .7 1.9 3.5 2.3 -3 .9 - 0 .6 3.7 2.8 1.1 - 1 .4 0.2 0.1 -0 .1 - 1 .8 1.9 3.5 2.3 -4 .0 -0 .6 3.2 2.7 1.0 -1 .5 1980 ........................................................................................ 1981 ........................................................................................ -2 .3 0.7 -2 .3 0.7 0.0 0.0 - 2 .3 0.7 0.0 0.0 4.3 0.0 1The following base-year weights were used for the subperiods: 1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights, 1969-73; and 1973 weights, 1973-81. 71 0.1 0.1 0.2 0.4 0.2 -0 .1 0.1 0.2 0.1 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.0 0.0 0.0 0.1 0.1 0.1 0.2 0.1 0.0 0.0 Table E-3. Manufacturing sector: Annual percent change in m ultifactor productivity under different index number meth ods, 1949-81 Shifted base-year weights1 (2) Year Tornquist (1) Difference, (1)-(2) (3) 1972 base year (4) Difference, (1 )- (4) (5) 1949 ........................................................................................ - 0 .4 0.4 - 0 .8 - 0 .7 0.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ 7.1 3.9 -0.1 2.1 -2 .0 5.8 - 1 .6 0.4 - 3 .4 6.6 7.2 4.3 0.9 2.3 - 1 .5 6.1 - 1 .2 0.8 -3 .1 6.5 -0 .1 - 0 .4 - 1 .0 -0 .2 -0 .5 0.3 - 0 .4 - 0 .4 - 0 .3 0.1 6.7 3.6 0.2 1.8 -2 .2 5.6 -1 .8 0.2 - 3 .6 6.5 0.4 0.3 -0 .3 0.3 0.2 0.2 0.2 0.2 0.1 0.1 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ .................................................................................... .. ........................................................................................ ........................................................................................ ........................................................................................ 0.1 1.5 5.1 6.7 4.6 3.7 1.2 -2 .3 2.4 1.0 -2 .7 0.0 1.5 5.0 6.7 4.5 3.4 0.9 -2 .1 2.4 0.9 -2 .8 0.1 0.0 0.1 0.0 0.1 0.3 0.3 -0 .2 0.0 0.1 0.1 0.0 1.4 5.0 6.7 4.5 3.5 1.0 -2 .3 2.3 0.9 -3 .0 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.0 0.1 0.1 0.3 1971 1972 1973 1974 1975 1976 1977 1978 1979 ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ ........................................................................................ 4.5 6.0 6.3 -3 .9 -0 .9 5.3 3.0 1.0 -0 .1 4.5 5.9 6.2 -4 .0 -1.1 5.2 2.9 1.1 0.0 0.0 0.1 0.1 0.1 0.2 0.1 0.1 -0 .1 -0 .1 4.3 5.9 6.3 -4 .1 -1 .5 5.2 .2.9 1.1 0.0 0.2 0.1 0.0 0.2 0.6 0.1 0.1 -0 .1 -0.1 1980 1981 ....................................................................................... ....................................................................................... - 2 .4 1.4 -2 .5 1.4 0.1 0.0 - 2 .6 1.3 0.2 0.1 1The following base-year weights were used for the subperiods: 1948 weights for 1948-59; 1959 weights, 1959-69; 1969 weights, 1969-73; and 1973 weights, 1973-81. Table E-4. Rates o f grow th o f m u ltifa c to r p ro d u c tiv ity un d e r d iffe r e n t in d e x n u m b e r m e th o d s by m a jo r s e c to r, 1948-81 (Percent per year, compounded) Sector and method 1948-81 1948-73 1973-81 Private business: Tornquist............................................ Shifted base-year weights ............. 1972 base-year weights ................ 1.5 1.7 1.3 2.0 2.0 1.7 0.1 0.2 0.1 Private nonfarm business: Tornquist............................................ Shifted base-year weights ............. 1972 base-year weights ................ 1.3 1.5 1.0 1.7 1.8 1.4 0.0 0.0 0.0 Manufacturing: Tornquist............................................ Shifted base-year weights ............. 1972 base-year weights ................ 1.8 2.0 1.6 2.2 2.3 2.1 0.4 0.3 0.3 72 Appendix F„ C©mparss©iii ©f iiyltifaet© r Measures Table F-1. Computation of output measures by BLS, Denison, Jorgenson, and Kendrick This appendix compares the b l s m easures of m ultifactor productivity with those calculated by Edward Denison, Dale Jorgenson, and John Kendrick. These authors have been making estimates of productiv ity growth for many years and each has contributed sig nificantly to the understanding of productivity measure ment. The comparisons are drawn from the authors’ latest published studies.1 The comparisons made within each of the following sections are subject to qualification: First, only the ma jor differences in methodology and classification are discussed; second, the authors’ latest published work may not incorporate the latest data revisions because of publication lags. The comparisons are made on the basis of each of the separate factors used in the measurement of productiv ity—output, capital input, and labor input. Also in cluded are the method of aggregation and the allocation of shares for the input factors. While not all aspects of productivity measurement fit precisely into these cate gories, they capture the major issues. Measure GNP ............................................... Less: Statistical discrepancy................ Owner-occupied housing ........... Tenant-occupied housing........... Rest of the world ........................ General government .................. Government enterprises............. Nonprofit institutions .................. Household sector........................ Capital consumption allowances............................... Business transfer payments................................. Indirect business ta xe s............... Federal indirect business taxes ................................... State and local indirect business taxes .................. Plus: Services of consumer durables .. Services of durables held by institutions............................... Net rent on institutional real e sta te ...................................... Capital stock ta x ......................... Business motor vehicle taxes........................................ Other business taxes ................ Subsidies less surplus of government enterprises (Federal, State, and local)........................................ Output The various authors include different factors in their output measures. These are explained below and com pared in table F - 1. The b l s measure of output for multifactor productivi ty encom passes the private business sector of the economy. This definition represents the privately owned, profit-oriented enterprises in the economy. The measure for this sector is derived from the gross nation al product ( g n p ) measure. Specifically, private business output is equal to g n p less: - X X X X X X X X X X X X X X X Kendrick X X X X X X X X X X X X X X X X X X X X X X X X X X This output measure was 76 percent of g n p in 1972. (The Bureau of Economic Analysis used 1972 as its constant-dollar base year for output measurement.) Denison measures output for the nonresidential busi ness sector. While the coverage is similar to the b l s measures, Denison starts from national income ( n i ) i n stead of GNP. s ta tis tic a l d iscrep a n cy o w n e r-o c c u p ie d h o u s in g rest o f the w o rld general g o v e rn m e n t g o v e rn m e n t enterprises n o n p ro fit in s titu tio n s h o u seh o ld sector. counting for Capital,” both in George von Furstenberg, ed., Capi tal, Efficiency and Growth (Cambridge, Mass., Ballinger Pub lishing Co., 1980); and John Kendrick and Elliot S. Grossman, Productivity in the United States (Baltimore, The Johns Hopkins University Press, 1980). Kendrick’s and Grossman’s data are up dated quarterly in Multiple Input Productivity Indexes (Houston, The American Productivity Center). ’Edward F. Denison, Accounting for Slower Economic Growth: the United States in the 1970’s (Washington, The Brookings Insti tution, 1979), and “ Accounting for Slower Economic Growth: An Update,” paper presented at the Conference on International Com parisons of Productivity and Causes of the Slowdown held by the American Enterprise Institute, Washington, Sept. 30, 1982; Bar bara M. Fraumeni and Dale F. Jorgenson, “ The Role of Capital in U.S. Economic Growth, 1948-1976,” and Dale Jorgenson, “ Ac BLS Denison Jorgenson 73 is equal to ni - gnp less: statistical discrepancy capital consumption allowances business transfer payments indirect business taxes. Nonresidential business output is equal to - For 1972, Kendrick’s measure was 84 percent of g n p in current dollars. Table F-2 lists the indexes and long term growth rates for each of the output measures de scribed above. The measures are also depicted in chart F - l. As is evident from the chart, there is little difference over the postwar period in any of the output measures. Denison’s measure is the lowest; however, all the growth rates are about the same. For most of the period, Jorgenson’s measure is the highest, but his growth rates differ from Denison’s by only 0.2 percent over the 1948-73 period. ni less: owner-occupied housing rest of the world general government nonprofit institutions household sector tenant-occupied housing. This measure of output was 76 percent of ni and 62 per cent of gnp in 1972. The major differences between the b l s and Denison measures of output are that he includes government enterprises and excludes capital consump tion allowances (depreciation), business taxes and trans fers, and tenant-occupied housing. Jorgenson’s measure of output encompasses the sec tor labeled gross private domestic product. In general, this measure covers all private concerns including households and nonprofit institutions. In order to calcu late output for this sector, services from the capital stock of households and nonprofit institutions are esti mated. The income generated by these services is then estim ated and added to the basic output measure. Hence, Jorgenson’s measure of output is larger than any of the others. For 1972, his output measure was over 92 percent of gnp . It is calculated by subtracting from gnp : - Table F-2. Indexes and rates of growth of output for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948-81 Period rest of the world general government Federal indirect business taxes State and local business taxes; services of consumer durables services of durables held by institutions net rent on institutional real estate capital stock tax business motor vehicle licenses business property taxes other business taxes. Kendrick’s measure of output is derived directly from the industry measures of output computed from the 14 component gross product originating (gpo) measures. Theoretically, the gpo measures by industry should be equal to the published gnp . In practice, however the gpo measure falls short of the gnp by a slight but signif icant amount. This measure is approximately equal to the gnp less the same factors which b l s subtracts: - Jorgenson Kendrick 1948 ........................ 1949 ........................ 42.8 42.0 44.4 43.0 39.3 39.6 43.2 42.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 45.9 48.6 50.3 52.5 51.5 55.7 57.2 57.8 56.8 61.0 47.2 50.1 51.7 54.0 52.5 57.0 58.3 58.7 57.3 61.9 43.5 46.5 48.1 50.4 49.9 53.7 54.9 55.8 55.9 59.2 46.3 49.0 50.6 52.7 51.7 55.9 57.3 57.9 57.0 60.1 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 61.9 63.0 66.5 69.4 73.6 78.6 82.9 84.8 89.2 91.7 62.7 63.6 67.3 70.4 74.8 80.2 84.8 86.2 90.5 92.8 60.4 61.9 65.5 68.1 71.9 76.5 81.3 83.5 87.5 90.5 62.2 63.2 66.7 69.6 73.8 78.8 83.1 84.9 89.2 91.9 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 91.0 93.7 100.0 106.6 104.4 102.3 108.9 116.2 122.6 125.3 91.1 93.7 100.0 107.0 103.8 100.6 107.5 115.1 121.7 124.1 90.5 94.1 100.0 106.4 105.4 104.7 111.0 117.7 123.7 127.1 91.1 93.9 100.0 106.7 104.6 102.7 109.2 116.0 121.5 124.9 1980 ........................ 1981 ........................ 123.4 126.5 120.8 123.8 126.4 129.3 124.1 126.5 Rate of growth (annual percent change) statistical discrepancy owner-occupied housing rest of the world general government government enterprises nonprofit institutions household sector. Denison Index, 1972=100 and adding: - BLS 1948-73 .................. 1973-81 .................. 3.7 2.2 3.6 1.8 4.1 2.5 3.7 2.2 1948-81 .................. 3.3 3.2 3.7 3.3 Sources: Bureau of Labor Statistics; Edward F. Denison, Accounting for Slower Economic Growth: The United States in the 1970's (Washington, The Brookings Institution, 1979); Dale F. Jorgenson, Harvard University, Cambridge, Mass.; John F. Kendrick, in Multiple Input Productivity Indexes, Vol. 3, No.1, September 1982 (Houston, The American Productivity Center). 74 Chart F-1. Output for the most aggregate sector measured by B IS , Denison, Jorgenson, and Kendrick, 1948=01 (Index. 1948= 100) Chart F-2. Labor input for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948=81 (Index. 194 8= 100) 75 Labor input Table F-3. Indexes and rates of growth of labor input for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948-81 A detailed explanation of b l s ’ s measure of labor in put is provided in appendix D. Labor input is a measure of hours paid derived from the b l s Current Employment Statistics program (establishment survey) supplemented with data from the Current Population Survey ( c p s ) . Es timates are made for nonproduction and supervisory workers’ average weekly hours. The hours are measured to correspond to the output coverage indicated above for b l s . The only difference between the labor input meas ure for the multifactor productivity and output per hour measures is the exclusion of hours for the government enterprise sector from the multifactor measures. Table F-3 shows the indexes and growth rates of labor input as calculated by b l s , Denison, Jorgenson, and Kendrick. Denison computes the level of employment based on both the c p s estimates and changes from establishment surveys. This is done to develop a measure based on persons rather than jobs, unlike the b l s measure of la bor input. Employment is then multiplied by average hours adjusted to an hours-worked rather than an hourspaid concept. Denison further adjusts the labor input measure for changes in the age, sex, and educational composition of the work force. Adjustments are also made for changes in the mix of part-time and full-time employment. The changes in age, sex, and education cause this measure of labor input to grow significantly faster than the b l s measure. Jorgenson measures labor input starting with the b e a measures of hours worked, at the 2-digit sic level. These measures are developed from b l s establishment surveys, household surveys, and other studies for ad justment to an hours-worked measure. For each 2-digit industry, Jorgenson estimates the proportion of hours worked disaggregated by age, sex, education, occupa tion, and class of worker (self-employed versus employ ee). The proportions are estimated from the decennial census and c p s published data using a multiproportional assumption for all categories of hours. Changes in the levels of each category over time are weighted by the estimated relative compensation to compute a weighted growth rate of labor input. While the procedure and de tail of categories are different from Denison’s approach, as can be seen in table F-4, the results are quite similar at the aggregate level. Kendrick uses the same measure of labor input as b l s . Chart F-2 clearly shows the distinction between the various input measures. Denison’s and Jorgenson’s have much higher levels and much higher rates of growth due to the adjustment for composition of the la bor force. Most of the growth in the adjustment for composition is the result of the increase in educational Period Denison Jorgenson Kendrick Index, 1972=100 1948 ........................ 1949 ........................ 87.3 84.3 76.7 74.0 70.3 67.7 88.6 83.8 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 85.3 87.8 87.7 88.7 85.7 87.0 90.3 89.0 84.8 88.2 76.2 79.9 81.6 83.2 80.6 83.2 84.3 83.8 80.8 83.8 70.3 73.5 74.2 75.5 73.0 75.6 77.2 76.6 74.5 77.6 84.8 87.3 87.4 88.2 85.3 88.5 89.9 88.5 84.6 87.0 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 88.3 86.8 88.2 88.7 90.2 90.3 95.2 95.1 96.7 99.3 84.0 83.6 85.2 85.9 87.6 90.4 93.1 94.2 96.2 98.5 78.7 78.3 80.5 81.8 83.5 86.7 90.1 91.2 93.5 96.8 88.1 86.7 88.1 88.7 90.1 92.9 95.2 95.1 96.7 99.3 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 97.6 97.0 100.0 104.0 104.3 99.9 103.0 107.3 112.6 116.2 97.4 97.3 100.0 104.5 105.4 102.6 105.6 109.6 115.0 119.3 95.8 96 3 100.0 105.1 105.8 102.7 106.7 111.9 118.4 123.7 97.6 97 1 100.0 103.9 104.3 100.1 102.9 107.1 112.3 116.1 1980 ........................ 1981 ........................ 115.3 116.1 119.2 120.8 124.8 127.5 115.3 116.2 Rate of growth (annual percent change) 1948-73 .................. 1973-81 .................. 0.7 1.4 1.2 1.8 1.6 2.4 0.6 1.4 1948-81 .................. 0.9 1.4 1.8 0.8 Sources: See table F-2. attainment.2 The Kendrick and gether at the lower level. bls measures move to Capital input Appendix C provides a detailed explanation of the method used for capital measurement by b l s . The meth ods of the other authors are also discussed at some length in that appendix. Briefly, b l s has constructed a measure of the annual net stock of capital for each ma jor sector (farm, manufacturing, nonfarm-nonmanufac turing) from data on equipment and structures, using a 2See Denison, Accounting for Slower Economic Growth, pp. 160-169. BLS 76 Table F-4. Computation of labor input measures by BLS, Denison, Jorgenson, and Kendrick Measure BLS Denison Jorgenson Table F-5. Indexes and rates of growth of capital input for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948-81 Kendrick Period Hours paid........................... Hours w orked...................... X X X X X X X X X X X X X Jorgenson Kendrick Index, 1972=100 X variable decay function. Assets are aggregated using a weighted average of the growth rates of the separate as sets. The weights are equal to the relative service prices, or user prices, of the different assets. The esti mates for each of the sectors are aggregated to the pub lished measures. Included in the capital input measure are estimates for the quantities of land and inventories, which are also weighted by their respective user prices. The annual flows of services of capital are assumed pro portional to the annual stocks of capital; this assumption is used by the other authors as well. Denison constructs his estimates of capital input di rectly from the b e a estimates of net and gross capital stock, b e a net capital stock is based on straight-line de preciation; gross capital includes no depreciation or de cay. Both measures are based on asset prices rather than rental prices. Denison combines the two measures of stocks, weighting gross by 0.75 and net by 0.25. Jorgenson’s construction of capital input begins with estimates of investment for equipment and structures, land, and inventories all classified by 46 industry group ings and 4 different legal forms of organization. As de scribed in appendix D, b l s has generally followed Jorgenson’s method of capital measurement. The major difference is in the decay function: Jorgenson uses a constant decay rate and b l s uses a variable decay rate. Another major difference is that b l s focuses on asset detail of capital and Jorgenson concentrates on industry detail. Kendrick uses the gross capital stocks of equipment and structures estimated by b e a for their wealth ac counts. He adds measures of land and inventories, as do the other researchers. Table F-5 displays the different measures of capital input. Chart F-3 also shows how the capital measures differ. The Jorgenson measure is the highest and also has the fastest rate of growth. Kendrick’s measure, on the other hand, is the lowest. The Denison and b l s measures move similarly. Table F-6 summarizes the procedures of the various research ers in computing their capital input measures. Denison X Plus adjustments for: A g e ................................... S e x ................................... Education.......................... Occupation ...................... Industry ........................... Employee versus selfemployed...................... Full- versus part-time workers ........................ BLS 1948 ........................ 1949 ........................ 43.6 45.3 42.1 43.4 35.8 38.3 48.5 49.3 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 47.0 49.0 51.1 52.6 54.1 55.8 57.8 59.6 60.9 62.0 44.8 47.5 49.8 51.3 52.5 54.1 56.2 57.9 59.1 60.5 40.0 42.9 95.4 47.1 49.1 50.8 53.7 56.1 58.2 59.2 50.9 52.7 54.0 55.2 56.3 58.4 60.1 61.8 63.0 64.8 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 63.5 64.9 66.4 68.3 70.6 73.7 77.5 81.6 85.4 89.3 62.1 63.7 65.4 67.6 70.0 73.1 77.2 81.5 85.3 89.4 61.3 63.1 64.6 66.8 69.5 72.6 76.7 81.2 85.0 89.0 66.5 68.5 70.1 72.2 74.8 77.8 81.1 84.3 87.5 91.0 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 93.2 96.5 100.0 104.6 109.3 112.3 114.4 117.4 121.6 126.2 93.1 96.4 100.0 104.7 109.8 113.0 115.6 119.4 124.5 129.8 93.2 96.3 100.0 105.3 111.5 115.5 117.6 121.3 126.6 132.7 93.8 96.7 100.0 104.3 107.8 110.2 113.3 117.1 121.0 125.5 1980 ........................ 1981 ........................ 130.7 134.4 134.1 138.3 138.3 141.6 129.4 133.0 Rate of growth (annual percent change) 1948-73 .................. 1973-81 .................. 3.6 3.2 3.7 3.5 4.4 3.8 3.1 3.1 1948-81 .................. 3.5 3.7 4.3 3.1 Sources: See table F-2. Table F-6. Computation of capital input measures by BLS, Denison, Jorgenson, and Kendrick Characteristic Weights: Asset prices......... Rental prices....... Aggregation of assets: Fixed weighted ... Variable weighted........... 77 BLS (hyperbolic decay function) Denison (3 parts gross; 1 part net) Jorgenson (geometric) X X X X X X X Kendrick (gross) X Chart F-3. Capita! Input for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948=81 (Index, 1948= 100) 400 350 300 250 200 150 100 50 Chart F-4. Muitif actor productivity for the most aggregate sector measured by BLS, Denison, Jorgenson, and Kendrick, 1948=81 (Index, 1948 = 100) 78 Aggregation Table F-7. Labor’s share for the most aggregate sector meas ured by BLS, Denison, Jorgenson, and Kendrick, 1948-81 The b l s procedure for aggregating the inputs (labor and capital) to form a combined input is a variable weighted index method, called a Tornquist index. It is formed by taking a weighted average of the growth rates of the individual inputs. The weights are averages of the given year’s and previous year’s relative cost share for each of the inputs. Labor’s share is total labor compen sation divided by current-dollar output; capital’s share is property income divided by current-dollar output, or 1 minus labor’s share. The above procedure is also the one used by Denison and Jorgenson. Kendrick, on the other hand, computes a weighted average of the indexes of the various inputs, not the growth rate. Furthermore, he holds the weights (the cost shares) constant for different periods: 1948 shares are used for the period 1948-59; 1959 shares for the period 1959-69; 1969 shares for 1969-73; and 1973 shares for the period 1973 and after. This method is much more restrictive than the method used by b l s and the others in that it assumes that the relationship be tween output and the different inputs remains constant with respect to relative changes in the input prices. That is, increases in the price of one input would not cause a change in the usage of that input. (Percent) Labor aed capital shares The major difference, however, among the different measures of productivity is not the method of aggrega tion as much as it is the definition and construction of the shares (both labor and capital). Table F-7 shows the annual labor shares used by b l s , Denison, Jorgenson, and Kendrick. The primary reasons for the differences are (1) the output measure, (2) the procedure used to al locate proprietors’ income (which contains both returns from labor and capital) between returns to labor and re turns to capital, and (3) treatment of capital consump tion allowances. Denison measures output net of capital consumption allowances, b l s , Jorgenson, and Kendrick include capital consumption allowances in output and also as part of the cost of capital in the production of output. Hence, in these measures, income from capital is a larger share of output than in Denison’s measure. Jorgenson further estimates the capital services and re turns to these services for the household and nonprofit institutional sectors. These estimates further increase his measure of capital’s share. Proprietors’ income is derived from both returns to capital and returns to labor. In order to compute the la bor and capital shares, proprietors’ income has to be al located between the two different sources. The method developed by b l s is described in appendix D. Briefly, for the manufacturing and nonfarm nonmanufacturing sectors, b l s assumes the corporate rates of return for proprietors’ capital and employee compensation per hour for proprietors’ labor and applies the resulting Year BLS Denison Jorgenson Kendrick 1948............................... 1949 ............................... 62.2 64.2 78.3 78.2 61.9 61.7 63.9 63.9 1950............................... 1951............................... 1952............................... 1953............................... 1954............................... 1955............................... 1956............................... 1957............................... 1958 ............................... 1959............................... 61.3 61.8 64.8 66.4 66.1 63.3 63.9 64.6 64.6 63.5 78.1 78.6 79.4 79.8 80.3 80.9 81.2 81.3 81.7 82.0 60.0 59.3 60.1 61.6 59.9 59.4 60.9 61.4 59.5 59.9 63.9 63.9 63.9 63.9 63.9 63.9 63.9 63.9 64.3 64.3 1960............................... 1961............................... 1962............................... 1963 ............................... 1964............................... 1965 ............................... 1966 ............................... 1967............................... 1968 ............................... 1969 ............................... 63.6 62.9 62.2 61.4 61.6 60.9 61.8 62.5 62.9 64.5 81.9 81.6 81.3 80.6 79.8 79.2 79.1 79.2 79.9 80.7 60.1 59.3 58.9 58.7 58.4 57.1 56.9 57.7 58.3 58.8 64.3 64.3 64.3 64.3 64.3 64.3 64.3 64.3 64.3 65.1 1970............................... 1971............................... 1972............................... 1973............................... 1974............................... 1975............................... 1976............................... 1977............................... 1978............................... 1979............................... 65.8 65.0 65.6 65.0 66.4 63.8 63.9 63.3 64.3 65.4 81.5 82.0 82.3 82.5 82.7 82.7 82.6 82.7 82.8 82.3 60.3 59.1 57.9 57.2 59.6 58.6 58.0 57.0 57.4 58.5 65.1 65.1 65.1 68.8 68.8 68.8 68.8 68.8 68.8 68.8 1980............................... 1981............................... 65.5 64.6 83.0 83.2 60.1 60.7 68.8 68.8 Sources: See table F-2. prices to proprietors’ capital and labor services (hours). Since the sum of these estimates more than exhausts the reported proprietors’ income, these initially estimated payments to each factor are proportionately reduced so that the sum is equal to the n i p a estimates of proprie tors’ income. For the farm sector, the corporate rate of return to capital is imputed to the farm capital. The cap ital income is then calculated and subtracted from the proprietors’ income, the remainder being the labor income. Denison allocates proprietors’ income in a similar manner. The major difference is that business sector rates of return to capital and compensation per hour are applied to the farm sector’s hours and capital. The com puted income is then reduced by a constant ratio for all the factors, both labor and tangible assets. Jorgenson, on the other hand, imputes the corporate rate of return of capital to proprietors’ capital for each sector. This imputation is made at a more detailed in dustry level than that used by b l s or Denison. Capital income is then subtracted from proprietors’ income and the residual is allocated to labor income at the industry level. This method of allocation further increases capi 79 tal’s share relative to labor’s because very little is left of proprietors’ income after subtracting capital income. Kendrick imputes the employee hourly compensation to proprietors and the self-employed for the base years for which he computes weights. The imputed hourly compensation is multiplied by estimated proprietors’ hours and added to labor compensation to obtain labor’s share. Capital’s share is obtained by subtracting labor’s share from unity. Table F -8 lists the indexes and average annual growth rates of multifactor productivity calculated by b l s and other researchers. The implications of the dif ferent methods are readily apparent from the table and from chart F-4. The growth in output for the period 1948-73 is almost the same for each of the different methods but the growth in productivity is different: The differences arise because of the definitions of the inputs and the definition of the factor shares. Jorgenson’s method attributes most of the growth of output to the growth of inputs; therefore productivity growth is the smallest for his measure. Kendrick, on the other hand, attributes more growth of output to produc tivity growth than to input growth. The two major rea sons are that he uses a gross rather than a net capital stock measure and also because he, like b l s , uses an unweighted hours measure for labor input, which has a slower rate of growth. Because the level of the gross capital stock measure is, in general, much higher than the net measure, the additional increment from annual investment does not increase the stock relatively as much. Hence his measure of capital services grows much more slowly during an expansion than a measure using net stocks.3 The b l s and Denison measures of multifactor produc tivity lie between Jorgenson’s and Kendrick’s measures. The reasons for this are different, however. As pointed out above, Denison’s method of output measurement (net of capital consumption) shifts the weight towards labor and away from capital. However, even after ad justing for changes in composition, labor does not grow as fast as capital, so the slower growing input has the much larger weight, b l s does not make the adjustment for labor force composition, but attributes a larger share of growth to the faster growing input (capital) and coincidentially obtains almost the identical total input growth as Denison. Table F-8. Indexes and rates of growth of multifactor produc tiv ity fo r the m ost aggregate se cto r m easured by BLS, Denison, Jorgenson, and Kendrick, 1948-81 BLS Period Denison Kendrick Index, 1972=100 1948 ........................ 1949 ........................ 63.1 62.3 63.1 62.5 73.2 73.6 57.5 57.8 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 66.8 68.4 69.6 71.4 71.2 74.3 74.5 75.2 75.7 78.7 66.7 67.5 67.9 69.5 69.0 72.7 73.2 73.7 73.8 77.3 77.6 78.6 79.1 80.8 80.4 83.5 82.5 82.8 83.1 85.2 62.0 63.7 65.5 67.4 67.7 70.4 70.8 72.0 73.1 74.4 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 79.2 80.7 83.7 86.1 89.2 92.0 93.8 94.1 96.3 95.8 77.7 78.8 81.9 84.5 88.0 91.4 93.6 93.3 95.6 95.5 85.1 86.5 89.1 90.5 92.9 95.0 96.4 96.0 97.3 96.7 76.2 78.0 80.6 83.2 86.3 89.2 91.5 92.5 95.1 94.8 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ ........................ 94.7 96.8 100.0 102.4 98.5 98.3 102.0 105.0 106.1 104.9 94.0 96.3 100.0 102.5 98.2 96.9 100.8 104.2 105.3 103.6 95.5 97.7 100.0 101.2 97.5 97.1 99.9 101.8 101.7 99.9 94.4 96.7 100.0 102.5 99.3 99.5 102.8 105.6 105.6 104.9 1980 ........................ 1981 ........................ 105.2 103.6 100.4 101.4 97.2 97.2 103.7 104.1 Rate of growth (annual percent change) 1948-73 .................. 2.0 2.0 1.3 2.3 1973-81 .................. 1948-81 .................. 0.1 1.5 -0.1 1.4 -0 .5 0.9 0.2 1.8 Sources: See table F-2. 3In the short run, gross capital can also grow faster than net capital when the investment rate is declining. Jorgenson 80 Bureau ©f Labor Statistics Regional O ffices Region IV 1371 Peachtree Street, N.E. Atlanta, Ga. 30367 Phone: (404) 881-4418 Regions VSI and VSII 911 Walnut Street Kansas City, Mo. 64106 Phone: (816) 374-2481 Region SS Suite 3400 1515 Broadway New York, N.Y. 10036 Phone: (212) 944-3121 Region V 9th Floor Federal Office Building 230 S. Dearborn Street Chicago, III. 60604 Phone: (312) 353-1880 Regions SX and X 450 Golden Gate Avenue Box 36017 San Francisco, Calif. 94102 Phone: (415) 556-4678 Region ISS 3535 Market Street P.O. Box 13309 Philadelphia, Pa. 19101 Phone: (215) 596-1154 Region VI Second Floor 555 Griffin Square Building Dallas, Tex. 75202 Phone: (214) 767-6971 Region fi 1603 JFK Federal Building Government Center Boston, Mass. 02203 Phone: (617) 223-6761
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