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Economic News Release
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Technical Notes for the manufacturing sector and manufacturing industries


Capital Services: Capital services are the services derived from the stock of 
physical assets and software.  Capital services asset detail consists of 44 
types of equipment, 28 types of structures, 3 categories of inventory, 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 Bureau of Economic Analysis (BEA).  Nonfarm industry detail for land is 
based on IRS book value data.  

Labor Hours: The construction of the hours measures follows the methods used 
in the private business sector described in USDL 10-1171, Multifactor 
Productivity Trends, 2008, , 
except that 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 June 3, 
2010, Productivity and Costs news release.  Therefore, the data reflect the 
benchmark revisions to the CES and other revisions to hours released on 
February 5, 2010.  Data in this release do not reflect the comprehensive 
revision to the National Income and Product Accounts (NIPA) released by the 
Bureau of Economic Analysis of the U.S. Department of Commerce on July 30, 

Intermediate Inputs: In manufacturing, intermediate inputs are 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 Tornqvist 
aggregation, employing weights that represent each component's share of total 
costs.  Total costs are defined as the value of manufacturing sectoral output.  

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 nonfarm 
business is “real value added”.  Real value added output in private business 
equals gross domestic product in the economy 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 computed 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. Wherever possible, the indexes of industry output are calculated with
a Tornqvist formula. This 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.  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 does not measure the specific contributions 
of labor, capital, or any other factor of production.  Rather, multifactor 
productivity is designed to measure the joint influences on economic growth 
of technological change, efficiency improvements, returns to scale, 
reallocation of resources due to shifts in factor inputs across industries, 
and other factors.  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  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: October 30, 2020