Multifactor Productivity

Overview

Mission

Two programs develop multifactor productivity data for elements of the U.S. economy. The Major Sector Productivity program develops indexes of multifactor productivity for the private business and private nonfarm business sectors of the economy and for the aggregate manufacturing sector, as well as for 18 3-digit North American Industry Classification System (NAICS) manufacturing industries. The Industry Productivity program develops indexes of multifactor productivity for 86 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads.

Multifactor productivity measures relate output to two or more inputs, depending on the definition of the particular multifactor productivity measure. This contrasts to labor productivity measures, which relate output to a single input, labor.

Comparisons among multifactor productivity measures must be made with an understanding of the underlying definitions used in constructing each measure. The multifactor productivity measures produced by the Bureau use two distinct concepts of real output which are characterized as gross product originating and sectoral output. For private business, private nonfarm business, and international multifactor productivity measures, a gross product originating measure is used. For manufacturing and industry multifactor measures, a sectoral output measure is used.

Background

Description of Measures

The BLS multifactor productivity measures were first introduced in Trends in Multifactor Productivity, 1948-81, Bulletin 2178, September, 1983, and have been updated annually.

Multifactor productivity measures reflect output per unit of some combined set of inputs. A change in multifactor productivity reflects the change in output that cannot be accounted for by the change in combined inputs. As a result, multifactor productivity measures reflect the joint effects of many factors including new technologies, economies of scale, managerial skill, and changes in the organization of production.

Since 1983, the multifactor productivity measurement program has expanded from producing measures for the major sectors of the U.S. economy only (private business, private nonfarm business, and manufacturing sectors) to include multifactor measures for 18 3-digit NAICS manufacturing industries, 86 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads.

In 2006, BLS revised the multifactor productivity measures for the manufacturing sector as a whole and also began reporting multifactor productivity for manufacturing industries at the 3-digit NAICS level. These changes are described in the December, 2006 press release, "Multifactor Productivity Trends in Manufacturing, 2002, 2003, and 2004."

The multifactor productivity indexes for major sectors measure value-added output per combined unit of labor and capital input in private business and private nonfarm business. BLS measures multifactor productivity in total manufacturing and the 18 3-digit NAICS manufacturing industries as output per unit of combined capital (K), labor (L), energy (E), materials (M), and purchased service inputs (S). These are often referred to as the KLEMS inputs. The most recent data for the U.S. private business, private nonfarm business, and manufacturing sectors, including 18 3-digit NAICS manufacturing industries, are available in the Multifactor Productivity Trends and Multifactor Productivity Trends in Manufacturing news releases.

The detailed industry multifactor productivity measures are constructed in a manner similar to the manufacturing sector series, by calculating the ratio of an output index to an input index comprised of a weighted average of employee hours, capital services, and intermediate purchases (including materials and supplies, energy, and purchased services). Inputs are weighted together using cost weights representing each input's share of total output to develop the combined inputs index. Multifactor productivity measures can be thought of as labor productivity measures adjusted to remove the effects of changes in capital per hour and intermediate purchases per hour. MFP data are available as historical time series for 86 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads. The most recent data for the 86 4-digit manufacturing industries are available in the Multifactor Productivity Trends for Detailed Manufacturing Industries news release.

In addition to the multifactor productivity measures, BLS produces measures of labor productivity or output per hour. A change in labor productivity reflects the change in output that cannot be accounted for by the change in hours worked of all persons. Labor productivity or output per hour differs from multifactor productivity in its treatment of capital and labor inputs. Labor productivity measures do not explicitly account for the effects of capital or shifts in the composition of labor. Labor productivity, then, reflects all of the effects that influence multifactor productivity and the effects of changes in the capital available per worker and shifts in the education attainment and work experience of the work force.

Coverage

Annual multifactor productivity indexes are available for the:

Uses

Glossary of Terms

Value-added output is defined as gross output (sales or receipts and other income, plus inventory change) minus intermediate inputs (goods and service inputs purchased from other domestic industries and foreign sources). This is also termed gross product originating, and represents the value that is added by the application of capital and labor to intermediate inputs in converting those inputs to finished products. Further information on this concept of output is available in Measurement of Productivity Growth in U.S. Manufacturing, by William Gullickson, Monthly Labor Review, July 1995, pp. 13-28.PDF

Sectoral output is defined as gross output excluding intra-industry transactions. This measure defines output as deliveries to consumers outside the sector, in an effort to avoid the problem of double-counting that occurs when one establishment provides materials used by other establishments in the same industry. Further information on this concept of output is available in Measurement of Productivity Growth in U.S. Manufacturing, by William Gullickson, Monthly Labor Review, July 1995, pp. 13-28.PDF

The Tornqvist index is a discrete approximation to a continuous Divisia index. A Divisia index is a weighted sum of the growth rates of the various components, where the weights are the component's shares in total value. When a Tornqvist index is used as an approximation to the continuous Divisia index, the growth rates are defined as the difference in natural logarithms of successive observations of the components and the weights are equal to the mean of the factor shares of the components in the corresponding pair of years. The Tornqvist index represents an improvement over constant base-year weighted indexes, because as relative prices of inputs change, the Tornqvist index allows both quantities purchased of the inputs to vary and the weights used in summing the inputs to vary, reflecting the relative price changes. For the labor input measure, the Tornqvist index effectively weights the growth rate of the hours of each group of workers by their share of labor compensation.

Gross product originating in private business equals gross domestic product in the economy less government, private households, and nonprofit institutions. Gross product originating excludes intermediate transactions between businesses.

Real gross domestic product is the output of goods and services produced by labor and property located in the United States. These data are produced by the Bureau of Economic Analysis.

Data

Data Available

Data Sources

Output

For the major sectors (private business and private nonfarm business), manufacturing, and 18 3-digit NAICS manufacturing industries:

Output data are based on series prepared as part of the National Income and Product Accounts by the Bureau of Economic Analysis, U.S. Department of Commerce.

The multifactor productivity measures use two distinct concepts of real output: gross product originating and sectoral output.

For private business and private nonfarm business, output is defined as gross product originating. Gross product originating in private business equals gross domestic product in the economy less government, private households, and non-profit institutions. Gross product originating excludes intermediate transactions between businesses.

In manufacturing, a sectoral output measure, defined as shipments from producers to all purchasers including other producers (except producers within the same industry) plus inventory change, is used. This reflects the increase in output due to the application of capital and labor and intermediate inputs. The primary distinction between the sectoral output measure used by BLS and a more general "gross output" measure is that the BLS sectoral output measure excludes shipments within the same industry. So, BLS measures total manufacturing output as the deflated value of shipments outside of the manufacturing industry.

For the private business and private nonfarm business sectors as a whole, intermediate inputs are an extremely small part of the input structure. As such, they can be considered insignificant to the analysis of productivity growth. This is not true for manufacturing. Examples of the importance of intermediate inputs in manufacturing include the rapid increase in energy prices in the 1970s and the increased use of business services, such as equipment leasing and computer services, all of which have affected productivity measurement.

For the 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads: Manufacturing industry output is measured as sectoral output, the total value, in real terms, of goods and services produced for sale outside the industry. Industry value of production is derived by adjusting industry shipments for changes in inventories and subtracting intra-industry transfers and resales. For air transportation and line-haul railroads, output is measured by aggregating passenger-miles and freight ton-miles with weights based on revenues or operating expenses. Wherever possible, the indexes of industry output are calculated with a Tornqvist formula. This formula aggregates the growth rates of the various industry outputs between two periods, using their relative shares in industry value of production, averaged over the two periods, as weights.

Labor

For the major sectors (private business and private nonfarm business), manufacturing, and 18 3-digit NAICS manufacturing industries:

Hours and employment data are primarily drawn from the BLS Current Employment Statistics (CES) program, which provides monthly survey data on total employment and average weekly hours of production and nonsupervisory workers in nonagricultural establishments. Jobs rather than persons are counted. Weekly paid hours are adjusted to hours at work using data from the National Compensation Survey (NCS). The BLS Hours at Work Survey (HWS) PDF (12K), conducted for this purpose, was used for years prior to 2001. How to view a PDF file. The Office of Productivity and Technology estimates average weekly hours at work for nonproduction and supervisory workers using information from the Current Population Survey (CPS), the CES, and the NCS.

Data from the BLS Current Population Survey are used for farm labor. In the nonfarm sector, the National Income and Product Accounts prepared by the Bureau of Economic Analysis of the Department of Commerce and the CPS are used to measure labor input for government enterprises, proprietors, and unpaid family workers. All series have been adjusted to take into account the activities of dual jobholders.

Labor composition data are largely based on household surveys and the decennial census. For private business and private nonfarm business, the labor input is an aggregate of the hours worked of all persons classified by their education, work experience and gender. This aggregate labor input measure is constructed by aggregating hours at work data for each of 1,008 types of workers classified by their educational attainment, work experience and gender using an annually chained Tornqvist index. The effect of Tornqvist aggregation is to produce a measure of labor input which reflects both changes in total hours of work and changes in the composition of workers. A shift in the work force toward more educated and experienced workers generally results in faster labor input growth. The difference between the growth rate of labor input and total hours at work is defined to be the growth rate of labor composition and it is, loosely, a measure of the change in the skill level of the work force. For all industries or sectors other than private business and private nonfarm business, labor input is identical to total hours at work and does not reflect changes in labor composition.

For the 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads:

The industry labor input measures represent the hours of all persons in the industry. For manufacturing industries, the primary source of industry employment and hours data is the BLS Current Employment Statistics (CES) survey. The CES provides monthly data on the number of total and production worker jobs held by wage and salary workers in nonfarm establishments, as well as data on the average weekly hours of production workers in those establishments. CES data are supplemented with data from the BLS Current Population Survey (CPS) to estimate employment and hours of self-employed and unpaid family workers in each industry. Data from the CPS, together with the CES data, are also used to estimate the historical average weekly hours of nonproduction workers for each industry. CES and CPS data are supplemented or further disaggregated for some industries using data from the BLS Quarterly Census of Employment and Wages (QCEW), the Bureau of the Census, or other sources. Hours of all persons in an industry are treated as homogeneous and are directly aggregated.

For air transportation and line-haul railroads, labor input measures are derived using data primarily from the U.S. Department of Transportation (DOT). For air transportation, annual estimates are based on monthly data from the Bureau of Transportation Statistics (BTS) of DOT. For line-haul railroads, total labor hours for supervisory and nonsupervisory workers are derived using data from the Surface Transportation Board (STB) of DOT and supplemented with data from the Association of American Railroads (AAR). For the railroad industry, the labor input measure includes an adjustment to remove capitalized labor hours in order to avoid double-counting because some capitalized labor costs are embedded in the railroad investment data.

Capital

For the major sectors (private business and private nonfarm business), manufacturing, and 18 3-digit NAICS manufacturing industries:

Capital data are based on measures of equipment and structures, land, and inventories prepared by the Bureau of Labor Statistics from data of the Bureau of Economic Analysis and U.S. Department of Agriculture.

Capital input is measured by the services which flow from the stock of capital. This differs from the stock of capital sometimes used in productivity measurement because not all forms of capital provide services at the same rate. Short lived assets such as a car or computer must provide all of their services in just the few years before they completely depreciate. Office buildings provide their services over decades. So in a year, a dollar's worth of a car provides relatively more services than a dollar's worth of a building. Because of differences in capital services between assets, capital input can increase not only because investment increases the capital stocks, but also if investment shifts toward assets (such as equipment) which provide relatively more services per dollar of capital stock.

For the 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads:

For manufacturing industries, the measure of capital input is based on the flow of services derived from the stock of physical assets. Physical capital is composed of 26 categories of equipment, 2 categories of structures, 3 categories of inventories, and land. Measures of total capital services for each industry are estimated by aggregating capital stocks of individual asset types. Estimates of investment by asset type for each industry are derived using annual capital expenditures for detailed industries from the economic censuses and annual surveys of the Bureau of the Census, in combination with benchmark capital flow tables and annual detailed asset investment by industry from the Bureau of Economic Analysis (BEA). Price changes are removed from the annual investment data before calculating stocks. Price deflators for each asset category are constructed by combining detailed price indexes (mostly BLS Producer Price Indexes) with weights that reflect each industry’s use of individual asset commodities.

The capital stocks for the different assets are combined using weights based on estimated annual rental prices for each asset type, averaged between two time periods. Each rental price reflects the nominal rate of return to all assets within the industry and the rates of economic depreciation and revaluation of the specific asset. Rental prices are adjusted for the effects of taxes.

For air transportation, a weighted index of 44 types of airframes and 34 types of engines is derived from quantities and purchase prices from BTS. For assets other than airframes and engines, capital stocks are calculated as is done for manufacturing industries. Inventories of parts and supplies are also included; the current dollar series is deflated with a weighted cost index based on data from the Air Transport Association (ATA) and BTS. Indexes for aircraft and engines, non-aircraft assets, and parts and supplies inventories are aggregated using cost share weights to derive an overall measure of capital input.

For line-haul railroads, current dollar investment for 10 categories of equipment and 13 categories of structures, obtained from STB and AMTRAK, are deflated with BLS PPIs and deflators based on BEA data. The capital stocks for each of the items are calculated as is done for manufacturing industries. Inventories of materials and supplies are also included. Estimates of investments in land from STB and AMTRAK were deflated with price indexes from BEA.

Intermediate Purchases

For the 18 3-digit NAICS manufacturing industries:

Intermediate inputs (energy, materials, and purchased business services) are obtained from BEA based on BEA annual input-output tables. Tornqvist indexes of each of these three input classes are derived at the 3-digit NAICS level and then aggregated to total manufacturing.

For the 4-digit NAICS manufacturing industries, air transportation, and line-haul railroads:

The index of intermediate purchases is a Tornqvist index of separate quantities of materials, services, fuels, and electricity consumed by each industry. Except for electricity consumed by manufacturing industries, for which direct quantity data are available, quantities are derived by deflating current-dollar values with appropriate price deflators.

For manufacturing industries, nominal values of materials, fuels, and electricity, along with quantities of electricity consumed by each industry are obtained from economic censuses and annual surveys of the Bureau of the Census. To avoid double counting, an adjustment is made to the materials estimates to exclude the value of intra-industry commodity transfers. Purchased business services are estimated using annual industry data and benchmark input-output tables from BEA.

Constant-dollar materials consumed are derived by dividing annual current-dollar industry purchases by an aggregate, weighted price deflator for each industry. Aggregate materials deflators are constructed for each industry by combining producer price indexes and import price indexes from BLS for detailed commodities. The deflators are combined using weights based on detailed commodity-consumed data from the BEA benchmark input-output tables. Aggregate price indexes to deflate purchased business services are constructed in a similar manner using consumer price indexes (CPIs), PPIs, and deflators developed by BEA. The value of fuels consumed by each industry is deflated with a weighted price deflator based on PPIs for individual fuel categories; the weights reflect fuel expenditures by industry from the Energy Information Administration (EIA), U.S. Department of Energy.

For air transportation, detailed cost of materials, services, fuels, and electricity from the BTS were deflated using cost indexes from ATA. For line-haul railroads, intermediate purchases data from STB were supplemented with data from other sources including AAR, AMTRAK, EIA, and the Edison Electric Institute. The nominal values were deflated with producer price indexes from BLS and implicit price deflators calculated from BEA investment data.

Energy

For the 18 3-digit NAICS manufacturing industries:

Intermediate inputs (energy, materials, and purchased business services) are obtained from BEA based on BEA annual input-output tables. Tornqvist indexes of each of these three input classes are derived at the 3-digit NAICS level and then aggregated to total manufacturing.

Materials

For the 18 3-digit NAICS manufacturing industries:

Nonenergy materials input represents all commodity inputs exclusive of fuel (electricity, fuel oil, coal, natural gas, and other miscellaneous fuels) but inclusive of fuel-type inputs used as raw materials in a manufacturing process, such as crude petroleum used by the refining industry. In addition to raw and processed materials, these measures include all incidental commodity inputs such as office supplies, vehicle parts bought for maintenance, and small tools, if these are allowable as current costs for computing business taxes.

For a more complete discussion, please refer to the article "Multifactor Productivity in U.S. Manufacturing," by William Gullickson, Monthly Labor Review, July 1995, pp. 13-27.PDF

For the 4-digit NAICS industries: Materials input is derived from cost of materials data from the Bureau of the Census. Estimates of materials purchased from establishments in the same industry are subtracted. Detailed BLS PPIs are aggregated to produce a deflator to convert materials costs to constant dollars.

Purchased Business Services

For the 18 3-digit NAICS manufacturing industries:

Purchased business services consist of the following nine types: communications; finance and insurance; real estate rental; hotel services; repair services; business services, including equipment rental, engineering and technical services, and advertising; vehicle repair; medical and educational services; and purchases from government enterprises. These services are estimated from published input-output tables. The general approach to these estimates is to take service shares in the value of production from annual input-output tables at the greatest possible level of detail; to obtain service costs by multiplying these shares by the value of production as given in the Census of Manufactures or the Annual Survey of Manufactures; and to deflate these current cost estimates. Prices from many service inputs are available from the BLS price program, from the National Income and Product Accounts, or from private sources.

For a more complete discussion, please refer to the article "Multifactor Productivity in U.S. Manufacturing," by William Gullickson, Monthly Labor Review, July 1995, pp. 13-27.PDF

Reference period

Methodology

The estimation procedures used in constructing the underlying data series and the various multifactor productivity measures are described in the BLS Handbook of Methods, Bulletin 2490, April 1997.

"Productivity Measures: Business Sector and Major Subsectors," Chapter 10 of the BLS Handbook of Methods, pp. 89-102, pertains to multifactor productivity measures for the private business, private nonfarm business, aggregate manufacturing, and manufacturing industries.

"Industry Productivity Measures," Chapter 11 of the BLS Handbook of Methods, pertains to multifactor productivity measures for detailed industries.

The BLS Handbook of Methods is available at a cost of $20.00 from the U.S. General Printing Office and may be ordered by contacting the GPO by mail or phone (202-512-1800) with your request. The GPO stock number for this bulletin is 029-001-03265-0.

The mailing address is:
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P.O. Box 371954
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Research

Labor

Workers differ in their educational attainment and work experience, and both of these factors are believed to contribute to productivity growth. Average levels of educational attainment and work experience have shifted over the past 50 years, as workers have generally become more educated and unusually large cohorts associated with the "baby boom" generation have entered the work force. These shifts in the composition of the work force have added about 0.2% per year to productivity growth between 1948 and 1998, as reported in the May 6, 1998 news release Multifactor Productivity Trends. Labor Composition and U.S. Productivity Growth, 1948-90, BLS Bulletin 2426, December 1993, provides further information on labor composition effects.

Current research seeks to strengthen and extend these measures with longitudinal microdata from the Survey of Income and Program Participation. This survey collects annual data on total work experience, which have been shown to dominate the work experience proxies used in earlier research. The research focuses on incorporation of earnings equation selection bias correction factors, derived from conventional labor supply equations, into the regular procedure with which the index is constructed. Based on this research, labor composition measures will be updated and its impact on productivity growth will be analyzed.

Capital

Research in this area includes an examination of the treatment of inventories in a growth accounting framework, investigation of the role of inventories as an input and the measurement of their contribution to output and productivity.

Research and Development

Investment in research and development (R&D) benefits not only the company undertaking the research but also other firms in the same industry and firms in other industries which purchase research intensive capital or materials. Because R&D benefits firms that did not pay for the research, R&D has a social return not captured by traditional productivity measures. The Impact of Research and Development on Productivity Growth, BLS Bulletin 2331, published in December 1989, investigated the direct effect of R&D on firms within the same industry and found a social direct return of 30 percent and a direct effect on multifactor productivity of 0.15 percent per year.

Current research investigates the indirect effect of R&D on purchasers of research intensive equipment and materials. The project will measure the stocks of R&D embodied within purchases of capital and materials and estimate their impact on productivity. Social indirect rates of return are determined from a variety of methods and the impact of indirect R&D on measured productivity will be determined.

Disequilibrium Effects

The standard productivity model assumes perfect competition and constant returns to scale. Completed research has shown how to modify the standard growth accounting formula for imperfect competition and non-constant returns to scale.

Research is underway to econometrically estimate a cost function for manufacturing and derive annual measures of the degree of scale and imperfect competition. These additional parameters will then be used to measure the impact of imperfect competition and returns to scale on productivity measures. An additional result will be measures of capacity utilization based on differences between short run marginal and average costs.

Infrastructure

Productivity measures the relationship between output and paid inputs. However, some inputs such as R&D and public infrastructure contribute to output even though they are not paid for by the firm directly. Recent academic research has produced widely differing estimates of the impact of public infrastructure (highways, airports, sewers, and related government investment) on productivity. Because government spending can have a stimulative effect on the general economy, state or national models of infrastructure may be misleading.

This research will develop public infrastructure stocks by county for the 1970s and 1980s from the Census of Governments. In turn these data will augment a cost function for manufacturing at the county level. Fixed effects models will also be estimated. The social return to infrastructure and its impact on productivity will be measured.

Publications

On the Internet

News Releases:

Related Documents:

Bulletins and staff papers:

Other Publication Sources

Periodic review articles and special analytical articles in the Monthly Labor Review, including:

Unpublished measures—available on request—containing information on the components of the labor, capital, and output measures prepared as part of the multifactor program.

Last Modified Date: September 23, 2011

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