Chapter 10.
Productivity Measures: Business Sector and Major Subsectors

Data Sources and Estimating Procedures

Output per hour measures
Output. Real gross domestic product in the business and nonfarm business sectors is the basis of the output components of the major sector labor productivity and multifactor productivity measures. These output components are based on and are consistent with the National Income and Product Accounts (NIPA), including the gross domestic product (GDP) measure, prepared by the Bureau of Economic Analysis (BEA) of the U.S. Department of Commerce⁶.

Real business sector output is an annual-weighted (Fisher-Ideal) index. It is constructed from the gross domestic product (GDP) excluding the following outputs: General government, nonprofit institutions, paid employees of private households, and the rental value of owner-occupied dwellings. These same exclusions are made when calculating current dollar output for the sector. The business sector thereby excludes many activities where it is difficult to draw inferences on productivity from NIPA output measures. Such inferences would be questionable mainly because the output measures are based largely on incomes of input factors. The farm sector, which is subject to unique external forces, also is excluded to yield the nonfarm business sector, the principal focus of many productivity studies. Nonfinancial corporate output is similar to that of the business sector but also excludes unincorporated businesses and those corporations which are depository institutions, nondepository institutions, security and commodity brokers, insurance carriers, regulated investment offices, small business offices, and real estate investment trusts.

Annual manufacturing indexes for both the quarterly labor productivity and KLEMS multifactor productivity measures are constructed by deflating the current-dollar industry value of production provided by the U.S. Bureau of the Census with data from BEA. These deflators are constructed by BEA by combining data from the BLS producer price program and other sources. The industry shipments are aggregated using annual weights, and intrasector transactions are removed⁷. Quarterly manufacturing output measures are based on the index of industrial production prepared monthly by the Board of Governors of the Federal Reserve System, adjusted to be consistent with the annual indexes of manufacturing sector output prepared by BLS.

Labor input. The primary source of hours and employment data is the BLS Current Employment Statistics (CES) program, which provides monthly survey data on total employment and employment and average weekly hours of production and nonsupervisory workers in nonagricultural establishments. Jobs rather than persons are counted, so that multiple jobholders are counted more than once.

The CES data are based on payroll records from a sample of establishments in which the probability of sample selection is related to the establishment size. Data on employment, hours, and earnings are collected monthly; the reference period for these data is the payroll period including the 12th of the month. (The CES methods are described in chapter 2.) Establishment data are published monthly in Employment and Earnings.

Because CES data include only nonfarm wage and salary workers, data from the Current Population Survey (CPS) are used for farm employment. In the nonfarm sector, the CPS is also used for proprietors and unpaid family workers. Government enterprise hours are developed from the National Income and Product Accounts estimates of employment and CPS data on average weekly hours.

Separate estimates for employment and hours paid are developed for each major sector, converted to an hours-at-work basis. The labor input of employees of nonprofit corporations are estimated based on data from the Commerce Department's Bureau of the Census and Bureau of Economic Analysis and subtracted from the totals for each major sector. Hours of labor input are treated as homogeneous units; no distinction is made among workers with different skill levels or wages.

For nonmanufacturing sectors, employment and average weekly hours are computed from the CES, CPS, and NIPA sources. Although CES data on average weekly hours refer only to nonsupervisory workers, it is assumed for the computation of hours that the length of the workweek in each nonmanufacturing industry is the same for all wage and salary workers.

In manufacturing, separate measures for production and nonproduction workers' hours are derived and aggregated to the manufacturing total. Employment and average weekly hours for production workers and employment for nonproduction workers are taken directly from CES data. Average weekly hours for nonproduction workers were developed from BLS studies of wages and supplements in manufacturing which provide data on the regularly scheduled workweek of white-collar employees.

In the CES, weekly hours are measured as hours paid rather than hours at work. The Hours at Work Survey is used to convert the hours paid of nonagricultural production and nonsupervisory employees to an hours-at-work basis.⁸ Hours at work exclude all forms of paid leave, but include paid time to travel between job sites, coffee breaks, and machine downtime. This survey of about 5,500 establishments has collected quarterly and annual ratios of hours at work to hours paid since 1981.⁹ (See BLS form 2000P1 in the printed edition of the Handbook of Methods for a sample data collection form for manufacturing industries. Form 2000N1 is a virtually identical form for nonmanufacturing industries and is not reproduced.) Ratios are developed for each 2-digit SIC industry within manufacturing and for each 1-digit SIC industry outside of manufacturing.

Unpublished data and one-time surveys have been used to extend the annual ratios back to 1947 as well as develop ratios for nonproduction and supervisory workers.¹⁰ The quarterly ratios are not currently used in the quarterly measures of labor input. Instead, a quadratic minimization formula devised by Frank Denton is used to generate quarterly ratios.¹¹

The resultant quarterly measures are used to convert the paid hours of nonfarm employees to an hours-at-work basis. The estimates of hours of farm workers, proprietors, unpaid family workers, employees of government enterprises, and paid employees of private households are collected on an hours-at-work basis. These hours are only adjusted to include information on those persons who are employed but not at work during the survey week.

Compensation and labor costs. BEA develops employee compensation data as part of the national income accounts. These quarterly data include direct payments to labor—wages and salaries (including executive compensation), commissions, tips, bonuses, and payments in kind representing income to the recipients—and supplements to these direct payments. Supplements consist of vacation and holiday pay, all other types of paid leave, employer contributions to funds for social insurance, private pension and health and welfare plans, compensation for injuries, etc.

The compensation measures taken from establishment payrolls refer exclusively to wage and salary workers. Labor cost would be seriously understated by this measure of employee compensation alone in sectors such as farm and retail trade, where hours at work by proprietors represent a substantial portion of total labor input. BLS, therefore, imputes a compensation cost for labor services of proprietors and includes the hours of unpaid family workers in the hours of all employees engaged in a sector. Labor compensation per hour for proprietors is assumed to be the same as that of the average employee in that sector for measures found in the BLS news release, "Productivity and Costs."

Multifactor productivity measures
Major sectors. The multifactor productivity indexes for major sectors measure output per combined unit of labor and capital input in private business and private nonfarm business. The output measures for private business and private nonfarm business are similar to the Fisher-Ideal indexes of output for business and nonfarm business except that output of government enterprises is omitted. Estimates of the appropriate weights for labor and capital in government enterprises cannot be made because subsidies account for a substantial portion of capital income.

Labor input for the multifactor productivity measures in these sectors begins with hours at work data similar to the hours in the quarterly labor productivity program with two principle differences. First, the hours of employees of government enterprises are excluded. Second, the hours at work for each of 1,008 types of workers classified by their educational attainment, work experience and gender are aggregated using an annually chained (Tornqvist) index. The growth rate of the aggregate is therefore a weighted average of the growth rates of each type of worker where the weight assigned to a type of worker is its share of total labor compensation. The resulting aggregate measure of labor input accounts for both the increase in raw hours at work and changes in the skill composition (as measured by education and work experience) of the work force.¹²

Capital inputs for the multifactor productivity measures are computed in accordance with a service flow concept for physical capital assets—equipment, structures, inventories, and land. Capital inputs for major sectors are determined in three main steps: 1) A very detailed array of capital stocks is developed for various asset types in various industries; 2) asset-type capital stocks are aggregated for each industry to measure capital input for the industry; and 3) industry capital inputs are aggregated to measure sectoral level capital input.

The asset detail consists of 28 types of equipment, 22 types of nonresidential structures, 9 types of residential structures (owner-occupied housing is excluded), 3 types of inventories (by stage of processing), and land. BLS measures of capital stocks for equipment and structures are prepared using NIPA data on real gross investment. Real stocks are constructed as vintage aggregates of historical investments (in real terms) in accordance with an "efficiency" or service flow concept (as distinct from a price or value concept). The efficiency of each asset is assumed to deteriorate only gradually during the early years of an asset's service life and then more quickly later in its life. These "age/efficiency" schedules are based, to the extent possible, on empirical evidence of capital deterioration. Inventory stocks are developed using data from the NIPA. Farm land input is based on data from the Economic Research Service of the U.S. Department of Agriculture. A benchmark for nonfarm land is estimated by applying a land-structure ratio based on unpublished estimates by the Bureau of the Census to BLS estimates of the value of structures. This benchmark is extrapolated using gross stocks of structures calculated from Bureau of Economic Analysis investment data. The resulting nonfarm land data series is allocated to industries based on Internal Revenue Service data on book values of land.¹³

For each industry (the BLS procedures are applied to 57 industries in the private business sector corresponding, approximately, to the 2-digit SIC level), these measures of capital stocks are aggregated using a Tornqvist chain index procedure (described below). The weight for each asset type is based on the share of property income estimated to be accruing to that asset type in each industry averaged over 2 years. Property income in each industry is allocated to asset types by employing estimates of the "implicit rental prices" of each asset type.¹⁴ The implicit rental price concept is based on the neoclassical theory of the firm and provides a framework for deriving weights for asset-type capital stocks. Because some asset types tend to deteriorate much more quickly than others and because of tax rules specific to asset types, the real economic cost of employing a dollar's worth of stock varies substantially by asset type.

At the sector level, aggregate capital input is obtained by further chained (Tornqvist) aggregation of each industry's capital input using each industry's two-period average share of total capital income as weights.

Once the sector's capital input is measured, total input is computed by aggregating capital and labor. For each input, the weight is the input's share of total costs and is derived from NIPA data on the components of nominal gross product originating (GPO) by industry. At both the sector and the industry levels, labor costs are measured as compensation to employees (wages, salaries, and supplements) plus a portion of noncorporate income.¹⁵ Most other components of nominal GPO are assigned to capital.¹⁶ The exception is those indirect taxes which are not assigned either to capital or labor (notably sales and excise taxes). Thus total cost is less than GPO by an amount equal to these taxes. Labor and capital shares in total cost are computed and then used in the aforementioned aggregation of capital and labor.¹⁷ Finally, major sector multifactor productivity indexes are calculated as the ratio of output to input.

Manufacturing industries. Multifactor productivity indexes for aggregate manufacturing and for 20 manufacturing industries also measure output per unit of input. In this case, input is a weighted aggregate of capital, labor, energy, nonenergy materials, and purchased business services inputs.¹⁸

For these multifactor productivity manufacturing measures, output is the deflated value of production, adjusted for inventory change, shipped to purchasers outside of the industry and not just final users. Hence, it differs from the output measures used for the major sector multifactor productivity indexes. Capital is measured as it is for the major sector multifactor productivity indexes; rental prices of capital are computed for each industry. However, labor is measured as a direct summation of hours at work rather than as the Tornqvist index method used in the major sector multifactor productivity measures.

The inclusion in the industry multifactor productivity measures of all intermediate inputs—energy, nonenergy materials, and purchased business services—is consistent with the use of total value of production as the output measure. Energy input is constructed using data on the price and quantity of fuels purchased for use as heat or power. Nonenergy materials input includes all commodity inputs exclusive of fuels but inclusive of fuel-type inputs used as raw materials in manufacturing. The measures of purchased business services are constructed using price and value data on services purchased by manufacturing industries from service industries. Data sources used in constructing these three inputs include input-output tables, surveys of establishments in manufacturing and other industries, and price indexes.

Total input is computed from components as a Tornqvist chain index number series. The weight for each input is its share in total input cost. The multifactor productivity industry measures are available for 1949 to the present.

Footnotes
⁶ A detailed description of the methods and procedures for estimating GNP and GDP in current and constant dollars is given in Carol S. Carson, "GNP: An Overview of Sources Data and Estimating Methods," Survey of Current Business, July 1987, pp. 103-26. Also see Methodology Paper No. 1 "Introduction to National Income Accounting" (Bureau of Economic Analysis, 1985). The current chain-type annual-weighted quantity measures are discussed in Allan H. Young, "Alternative Measures of Change in Real Output and Prices," Survey of Current Business, April 1992, pp. 32-48. These official introduction of these measures into the National Accounts is discussed in J. Steven Landefeld and Robert P. Parker, "Preview of the Comprehensive Revision of the National Income and Product Accounts: BEA's New Featured Measures of Output and Prices," Survey of Current Business, July, 1995, pp. 31-38. Derivation of business sector output is discussed also in Jerome A. Mark, "Measuring Single-Factor and Multifactor Productivity, Monthly Labor Review, December 1986, pp. 3-11.
⁷ A discussion of manufacturing output measures is given in William Gullickson, "Measurement of productivity growth in U.S. manufacturing," Monthly Labor Review, July 1995, pp. 13-28.
⁸ Kent Kunze, "A New BLS Survey Measures the Ratio of Hours Worked to Hours Paid," Monthly Labor Review, June 1984, pp. 3-7.
⁹ The sample design and universe of establishments for the Hours at Work survey are essentially the same as those used in the Current Establishments Statistics program. The response rate has ranged from 70 to more than 80 percent including responses obtained through computer assisted telephone interviews.
¹⁰ A description of the hours at work ratios for the period 1948 through 1988 can be found in Mary Jablonski, Kent Kunze, and Phyllis Flohr Otto, "Hours at Work: A New Base for Productivity Statistics," Monthly Labor Review, February 1990, pp. 17-24.
¹¹ See Frank T. Denton, "Adjustment of Monthly and Quarterly Series to Annual Totals: An Approach Based on Quadratic Minimization," Journal of the American Statistical Association, March 1971, pp. 99-102. This method is also used to produce quarterly ratios prior to 1981.
¹² See Labor Composition and US Productivity Growth, 1948-90 for a complete description of Tornqvist aggregation of hours.
¹³ These methods are described in detail in Trends in Multifactor Productivity, 1948-81, appendix C.
¹⁴ The rental price formula and related methodology and data sources are described in Trends in Multifactor Productivity, 1948-81, appendix C. The rental price formulas described in this publication have been modified to eliminate large fluctuations due to inflation in new goods prices. Research on this issue is reported by Michael J. Harper, Ernst R. Berndt and David O. Wood, "Rates of Return and Capital Aggregation Using Alternative Rental Prices," in Dale W. Jorgenson and Ralph Landau, Technology and Capital Formation, 1989, MIT Press, pp. 331-37.
¹⁵ Noncorporate income is allocated to labor and capital costs in each year using the following assumption: Initially self-employed persons are assumed to receive the same hourly compensation as employees and the rate of return to non-corporate capital is assumed to be the same as in the corporate sector. Based on these assumptions, the resultant income of proprietors is adjusted to match proprietors income reported in the GPO data by scaling proportionately the hourly compensation of the self-employed and the noncorporate rate of return. This treats any apparent excess or deficiency in noncorporate income neutrally with respect to labor and capital.
¹⁶ Capital costs are the sum of 1) the balance of noncorporate income, 2) corporate profits, 3) net interest, 4) rental income, 5) adjusted capital consumption allowance, 6) inventory valuation adjustments, and 7) portions of indirect taxes assumed to be associated with capital (notably motor vehicle and property taxes), 8) the sum of business transfers and government subsidies.
¹⁷ Excluding these indirect business taxes from the calculation of factor shares has the effect of assuming the incidence of these taxes are neutral with respect to capital and labor income.
¹⁸ An explanation of the methods and some results are presented in William Gullickson and Michael J. Harper, "Multifactor Productivity in U.S. Manufacturing, 1949-83," Monthly Labor Review, October 1987, pp. 18-28.

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