Technical notes

Technical Notes

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.
Data on investment for fixed assets are obtained from the Bureau of Economic
Analysis (BEA). Data on inventories are estimated using information from BEA
and the Internal Revenue Service (IRS) Corporation Income Returns. Data for 
land in the farm sector are obtained from the U.S. Department of Agriculture 
(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.

BLS provides additional detail in table C on information processing equipment
and intellectual property products. Information processing equipment is 
composed of three broad classes of assets: computers and related equipment,
communications equipment, and other information processing equipment. 
Computers and related equipment includes mainframe computers, personal 
computers, printers, terminals, tape drives, storage devices, and integrated
systems. Communications equipment is not further differentiated. Other 
information processing equipment includes medical equipment and related 
instruments, electromedical instruments, nonmedical instruments, photocopying
and related equipment, and office and accounting machinery. Intellectual 
property products are composed of three broad classes of assets: software,
research and development, and artistic originals. Software is comprised of
pre-packaged, custom, and own-account software. Research and development 
is creative work undertaken to increase the stock of knowledge for the 
purpose of discovering or developing new products or improving existing 
ones. Artistic originals include theatrical movies, long-lived television
programs, books, music, and other forms of entertainment. Structures include
nonresidential structures and residential capital that are rented out by 
profit-making firms or persons.

Financial assets are excluded from capital services measures, as are 
owner-occupied residential structures. The aggregate capital services 
measures are obtained by Tornqvist aggregation of the capital stocks for 
each asset type within each of 60 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. Current-dollar capital costs can be 
defined as each asset’s rental price multiplied by its constant-dollar 
stock, adjusting for capital composition effects. 

Capital services measures constructed for the most recent year are
preliminary and are based on less detail than the rest of the series.
These measures consist of 6 asset types as opposed to the 90 asset types
for fixed business equipment, structures, inventories, land, and intellectual
property products included in estimates for all previous years. The assets 
included in the most recent year are structures, fixed business equipment, 
intellectual property products, inventories, rental residences, and land.
Investments, depreciation, and capital income are estimated for each of these
six aggregates. Capital services are calculated by a chained superlative 
Tornqvist index combining stocks of the six asset categories, weighted by 
capital income shares. See the June 2005 Monthly Labor Review article, 
“Preliminary estimates of multifactor productivity growth” located at 

Labor Input 

Labor input in private business and private nonfarm business is obtained 
by a chained superlative Tornqvist aggregation of the hours worked, 
classified by age, education, and gender with weights determined by each
group’s share of the total wage bill. Hours paid of employees are largely
obtained from the Current Employment Statistics (CES) program. Weekly paid
hours are adjusted to hours worked using data from the National 
Compensation Survey (NCS) for 2001 forward and data from the BLS Hours
at Work survey, conducted for this purpose, for earlier years. Hours 
worked for nonproduction and supervisory workers are derived using data
from the Current Population Survey (CPS), CES, and NCS. The hours worked
of proprietors, unpaid family workers, and farm employees are derived from
the CPS. Hours worked data reflect estimates in the February 2, 2017
“Productivity and Costs” news release (USDL-17-0140).

The estimates of 2016 hours worked for the private nonfarm business and 
private business sectors are extrapolated from the hours worked reported
in the nonfarm business and business sectors, respectively, in 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
of all persons. 

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” 

Combined Inputs

Labor input and capital services are combined using chained superlative 
Tornqvist aggregation, applying weights that represent each component's 
average share of total costs. The chained superlative Tornqvist index uses
changing weights; the share in each year is averaged with the preceding 
year's share. Total costs are defined as the value of output less a portion
of taxes on production and imports. 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 becomes. 

In a production process, profit-maximizing/cost-minimizing firms adjust 
the factor proportions of capital and labor when the price of one factor
is less than the other factor; there is 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

Value-Added Output

Private business sector output is a chain-type, current-weighted index
constructed after excluding from gross domestic product (GDP) the 
following outputs: general government, nonprofit institutions, private 
households (including owner-occupied housing), and government 
enterprises. This release presents data for the private business and 
private nonfarm business sectors. The private business sector accounted
for approximately 75 percent of GDP in 2015. Additionally, the private 
nonfarm business sector excludes farms from the private business sector,
but includes agricultural services. Multifactor productivity measures 
exclude government enterprises, while the BLS quarterly Productivity 
and Costs series include them. 

The output measures are based on the National Income and Product 
Accounts (NIPA) data released by BEA on January 27, 2017. The 
estimates of 2016 output for the private nonfarm business and private
business sectors are extrapolated from the output reported in the 
nonfarm business and business sectors, respectively, in the February 2, 2017
“Productivity and Costs” news release (USDL-17-0140). 
Multifactor Productivity

Multifactor productivity measures describe the relationship between output
in real terms and the inputs involved in its production. They do not 
measure the specific contributions of labor or capital, or any other 
factor of production. Rather, multifactor productivity is designed to
measure the joint influences of technological change, efficiency 
improvements, returns to scale, reallocation of resources, and other 
factors on economic growth, allowing for the effects of capital and 

The multifactor productivity indexes for private business and private
nonfarm business are derived by dividing an output index by an index 
of combined inputs of capital services and labor input. The output 
indexes are computed as chained superlative indexes (Fisher Ideal indexes)
of components of real output.

Research and Development

The stock of research and development in private nonfarm business
is derived by aggregating different vintages of constant dollar 
measures of research and development expenditures and allowing for
depreciation. Current dollar expenditures for privately financed 
research and development are obtained from annual issues of Research
and Development in Industry published by the National Science 
Foundation. BLS develops price deflators and estimates of the rate 
of depreciation.

The research and development data in the private nonfarm business 
sector presented here show the effect of spillovers from economic 
units that conduct research and development. BEA publishes measures 
of research and development investments in each industry that include
estimates of the direct returns to firms conducting such research and 
development activities. By combining the direct returns to firms conducting
research and development with the spillover effect of other firms, a 
picture of the total overall effects of research and development can be

Further description of these data and methods can be found in BLS Bulletin
2331 (September 1989), "The Impact of Research and Development on 
Productivity Growth" at BLS measures 
of year-to-year contributions of research and development to the private
nonfarm business sector and measures of the stock of research and
development are available at
Other Information

Comprehensive tables containing additional data beyond the scope of 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” ( General information is available
on the BLS website at Additional data not 
contained in the release can be obtained at Comprehensive
tables can be downloaded at, including data 
that links 1948-87 SIC data to NAICS data from 1987 forward. This file
includes data for the private business and private nonfarm business sector. 

Table of Contents

Last Modified Date: November 08, 2017