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Economic News Release
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Technical Notes for the manufacturing sector and manufacturing industries

Technical Notes

BLS includes a measure of the effects of changes in the composition of the
work force for manufacturing sectors and industries. Labor input in 
manufacturing sectors and NAICS industry groups is obtained by chained 
superlative Tornqvist aggregation of the hours at work, classified by 
age, education, and gender with weights determined by each group’s share
of total wages. The labor composition index estimates the effect of 
shifts in the age, education, and gender composition of the work force
on hours worked. 

Capital Services 

Capital services are the services derived from the stock of physical
assets and intellectual property assets. There are 90 asset types for
fixed business equipment, structures, inventories, land, and intellectual
property products. The aggregate capital services measures are obtained
by Tornqvist aggregation of the capital stocks for each asset type within
each of the eighteen manufacturing NAICS industry groupings using 
estimated rental prices for each asset type. Each rental price reflects 
the nominal rate of return to all assets within the industry and rates 
of economic depreciation and revaluation for the specific asset; rental
prices are adjusted for the effects of taxes. Data on investment for 
fixed assets are obtained from BEA. Data on inventories are estimated
using data from BEA and additional information from IRS Corporation Income
Returns. Data for land in the farm sector are obtained from USDA. Nonfarm
industry detail for land is based on IRS book value data. Current-dollar
value-added data, obtained from BEA, are used in estimating capital rental

Labor Input 

Labor input in manufacturing sectors and industries is obtained by chained
superlative Tornqvist aggregation of the hours at work, classified by age,
education, and gender with weights determined by each group’s share of 
total wages. The labor composition index estimates the effect of shifts in 
the age, education, and gender composition of the work force on hours worked.
Hours at work data reflect Productivity and Costs data as of the December 10,
2019 “Productivity and Costs” news release (USDL-19-2143). The growth rate of
labor composition is defined as the difference between the growth rate of 
weighted labor input and the growth rate of the hours.

The growth rate of labor composition in manufacturing may be underestimated 
due to limitations in the source data. The education proxy does not include 
training certifications and licensing. The proxy only includes number of years
of schooling.

Additional information concerning data sources and methods of measuring labor
composition can be found in “Changes in the Composition of Labor for BLS 
Multifactor Productivity Measures, 2014” (

Intermediate Inputs 

In manufacturing, intermediate inputs consist of energy, materials, and
purchased business services, and represent a large share of production costs.
Research has shown that substitution among inputs, including intermediate
inputs, affects productivity change. Therefore, it is important to account 
for intermediate inputs in productivity measures at the industry level. In 
contrast, the more aggregate productivity measures compare "value-added"
output with two classes of inputs, capital and labor. Because of these 
differences in concepts and methodology, productivity change in manufacturing
cannot be directly compared with changes in private business or private 
nonfarm business.  

Data on intermediate inputs are obtained from BEA based on BEA annual 
input-output tables. Tornqvist indexes of each of these three input classes
are derived at the three-digit NAICS level and then aggregated to the 
manufacturing sectors. Materials inputs are adjusted to exclude transactions
between establishments within the same sector.

Combined Inputs 
The five input indexes (capital services, labor, energy, materials, and 
purchased business services) are combined using chained superlative Tornqvist
aggregation, applying weights that represent each component's share of total
costs. Total costs are defined as the current dollar value of manufacturing
sectoral output. Most taxes on production and imports, such as excise taxes,
are excluded from costs; however, property and motor vehicle taxes remain in
total costs. 

Capital Intensity 
Capital intensity is the ratio of capital services to hours worked in the 
production process. The higher the capital to hours ratio, the more capital
intensive the production process is. 

In a production process, profit maximizing/cost-minimizing firms adjust the
factor proportions of capital and labor if the price of one factor falls 
relative to the price of the other factor; there would be a tendency for the 
firms to substitute the less expensive factor for the more expensive one. In
the short run, changes in hours worked are more variable than changes in 
capital services. Changes in hours worked in business cycles can result in 
volatility of the capital intensity ratio over short periods of time. In
the long run an increase in wages relative to the price of capital will 
induce the firm to substitute capital for labor, resulting in an increase
in capital intensity. Rising labor costs are, in fact, an incentive for 
firms to introduce automated production processes. Industry estimates 
of capital to hours ratios can be obtained at  

Sectoral Output 

The output concept used for multifactor productivity in manufacturing is 
“sectoral output”. Sectoral output equals gross output (sales, receipts,
and other operating income, plus commodity taxes plus changes in inventories),
excluding transactions between establishments within the same sector. 
In contrast, the output concept used for private business and private 
nonfarm business is “real value-added”. Real value-added output in private
business equals gross domestic product less general government, government
enterprises, private households (including the rental value of 
owner-occupied real estate), and non-profit institutions. Real value-added 
output excludes intermediate transactions between businesses.

The output index for manufacturing is constructed using a chained 
superlative index (Tornqvist) of three-digit NAICS industry outputs.
Industry output is measured as sectoral output, the total value of goods
and services leaving the industry. The indexes of industry output are 
calculated with the Tornqvist index formula. This index 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. 

Manufacturing industry output measures for 2017 and earlier years are 
constructed primarily using data from the economic censuses and annual
surveys of the U.S. Census Bureau together with data on price changes 
primarily from BLS. These measures have been revised due to new and revised
data from the Bureau of Economic Analysis, used in part to construct 
intra-industry transactions. Manufacturing industry output for 2018 is
estimated based on historical relationships between BLS sectoral output,
BLS price indexes, and data on industrial production from the Federal 
Reserve Board.

Multifactor Productivity 

The manufacturing multifactor productivity measures describe the 
relationship between output in real terms and the inputs involved in
its production. Multifactor productivity measures are not intended to 
capture the specific contributions of labor, capital, or intermediate 
inputs. Rather, they are designed to measure the joint influences on 
economic growth of technological change, efficiency improvements, returns
to scale, reallocation of resources and other factors of economic growth,
allowing for the effects of capital, labor, and intermediate inputs. The 
multifactor productivity indexes are derived by dividing an output index 
by an index of the combined inputs of labor, capital services, energy, 
non-energy materials, and purchased business services.

Other information 

Comprehensive tables containing more detailed data than that which is 
published in this press release are available upon request at 202-691-5606 
or at Industry specific contributions to 
output are available at

More detailed information on methods, limitations, and data sources of capital
and labor are provided in BLS Bulletin 2178 (September 1983), Trends in 
Multifactor Productivity, 1948-81 and on the BLS Multifactor Productivity 
website under the title “Technical Information About the BLS Multifactor 
Productivity Measures” for Major Sectors and 18 NAICS 3-digit Manufacturing

General information is available on the BLS Multifactor Productivity website
at Additional data not contained in the release 
can be obtained in print or at A number of comprehensive 
tables set up as zip files can be obtained at
Methods for measuring manufacturing multifactor productivity are discussed
in the July 1995 issue of the Monthly Labor Review, "Measurement of 
productivity growth in U.S. manufacturing”. See

Table of Contents

Last Modified Date: January 28, 2020