Technical Notes for the manufacturing sector and manufacturing industries

Technical Notes

Capital Services 

Capital services are the services derived from the stock of physical assets 
and software. There are 86 asset types for fixed business equipment and
software, structures, inventories, and land. 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 investments 
in physical assets and software are obtained from the Bureau of Economic 
Analysis (BEA). Data on inventories are estimated using BEA and additional
information from IRS Corporation Income Returns. Nonfarm industry detail
for land is based on IRS book value data.  

Labor Hours 

The construction of the hours measures follows the methodology described 
in USDL 13-0626, Multifactor Productivity Trends, 2011, Hours in 
manufacturing are directly aggregated and do not include the effects of
labor composition. Hours data for the manufacturing multifactor productivity
measures include hours for all persons working in the manufacturing sector
– wage and salary workers, the self-employed and unpaid family workers. 
The primary source of hours data is the BLS Current Employment Statistics 
(CES) survey. Hours paid of production workers are also obtained primarily
from the CES survey. The hours of these employees are then converted to an
at-work basis by using information from the Employment Cost Index (ECI) of
the National Compensation Survey (NCS) and the BLS Hours at Work Survey. 
Hours at work for nonproduction workers are derived using data from the 
Current Population Survey (CPS), the CES, and the NCS. The hours at work 
of proprietors are derived from the CPS.

Hours at work data are based on underlying hours data published in the
February 7, 2013, USDL-13-0192, Productivity and Costs, Therefore,
the data do not reflect the benchmark revisions to the CES and other 
revisions to hours released on March 7, 2013. 

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 3-digit NAICS level and then aggregated to
total manufacturing. Materials inputs are adjusted to exclude 
transactions between establishments within the same sector.

Combined Inputs 

The five input indexes (capital services, hours, 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. 

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. Manufacturing multifactor productivity measures exclude
intermediate inputs between manufacturing establishments from both 
output and inputs. 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 hours, 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 "Measurement of
productivity growth in U.S. manufacturing” in the July 1995 issue of 
the Monthly Labor Review. See  

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Last Modified Date: June 19, 2013