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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

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 prices.

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 February 1, 2018 
“Productivity and Costs” news release (USDL-18-0153). 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” (www.bls.gov/mfp/mprlabor.pdf).

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 http://www.bls.gov/mfp/mprdload.htm.   

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 2016 and earlier years are 
constructed primarily using data from the economic censuses and annual surveys
of the U.S. Census Bureau together with data data on 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 2017 is
estimated based on historical relationships between BLS sectoral output, BLS
price indexes, and data on industrial production from the Federal Reserve

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 http://www.bls.gov/mfp/mprdload.htm. 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 Industries at http://www.bls.gov/mfp/mprtech.pdf. General 
information is available on the BLS Multifactor Productivity website at
http://www.bls.gov/mfp/mprover.htm. Additional data not contained in 
the release can be obtained in print or at http://www.bls.gov/mfp. A 
number of comprehensive tables set up as zip files can be obtained at
http://www.bls.gov/mfp/mprdload.htm. 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 http://www.bls.gov/mfp/mprgul95.pdf.  

Table of Contents

Last Modified Date: April 23, 2019