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 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 the efficiency of hours worked. 

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” 

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 the efficiency
of hours worked.  Hours at work data reflect Productivity and Costs data as
of the February 5, 2015 “Productivity and Costs” news release (USDL-15-0157).
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.  

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 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. 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 measure 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

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: July 28, 2015