Technical Notes for the manufacturing sector and manufacturing industries

Technical Notes
Beginning with this release, 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 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 4, 2016 
“Productivity and Costs” news release (USDL-16-0209). 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 Cindy Zoghi, 2007,
“Measuring Labor Composition: A Comparison of Alternate Methodologies” and in 
“Changes in the Composition of Labor for BLS Multifactor Productivity Measures”

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 level of manufacturing. 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

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. BLS 
industry output measures for manufacturing industries are constructed using
data from the economic censuses and annual surveys of the Bureau of the 
Census, U.S. Department of Commerce, together with information on price 
changes, primarily from BLS. 

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 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 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  

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Last Modified Date: June 22, 2016