Technical Notes for the manufacturing sector and manufacturing industries

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 Hours 

The construction of the hours measures follows the methodology 
described in USDL 15-0480, Multifactor Productivity Trends, 2013, 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 5, 2015, USDL-15-0157, Productivity and Costs, 
Therefore, the data do not reflect the benchmark revisions to the 
CES and other revisions to hours released on March 5, 2015. 

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: February 16, 2016