Technical Notes for the manufacturing sector and manufacturing industries

Technical Notes

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 NAICS industry
groups 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 hours worked. 

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 hours worked. Hours at
work data reflect Productivity and Costs data as of the February 2, 2017 
“Productivity and Costs” news release (USDL-17-0140). 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.

Additional information concerning data sources and methods of measuring labor 
composition can be found in “Changes in the Composition of Labor for BLS 
Multifactor Productivity Measures, 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 industry level. 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 capture 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  

Table of Contents

Last Modified Date: July 12, 2017