Economic News Release

Technical Notes for the manufacturing sector and manufacturing industries

Technical Notes
Beginning with this release, historical data for multifactor productivity in
all sectors and industries reflect several important changes and revisions to
the data sources used to develop these series. In "Preview of the 2013 
Comprehensive Revision of the National Income and Product Accounts: Changes
in Definitions and Presentations,” Survey of Current Business, March 2013, 
and the 2014 Comprehensive Revision of the Industry Economic Accounts, the 
Bureau of Economic Analysis (BEA) described several important changes to the
national and annual industry accounts. Principal changes include the 
introduction of research and development and artistic originals as fixed 
investment, the capitalization of ownership transfer costs of residential 
fixed assets, and revisions to the annual industry accounts.
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 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 14-0529, Multifactor Productivity Trends, 2012, 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 6, 2014, USDL-14-0167, Productivity and Costs, Therefore, the 
data do not reflect the benchmark revisions to the CES and other revisions 
to hours released on March 6, 2014. 

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 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

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.
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. 

Table of Contents

Last Modified Date: August 21, 2014
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