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 and custom. 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.  Research and 
Development also includes own-account R&D for software which had previously
been classified in software. 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 

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 1996 forward and data from the BLS Hours 
at Work survey, conducted for this purpose, prior to 1990. Between 1990 
and 1995, weekly paid hours are adjusted to hours at work using a combination
of NCS and Hours at Work survey data. 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 6, 2019 “Productivity and Costs” news 
release (USDL-19-0188).

The estimates of 2018 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 6, 2019 “Productivity and Costs” news release (USDL-19-0188). 
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.  The index of hours worked of all persons including 
employees, proprietors, and unpaid family workers, classified by age, 
education, and gender are weighted together using median wages to compute
the labor composition estimates reflecting the different skillset of the
work force. 

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
2017.    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 February 28, 2019. The estimates of 2018 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 March 7, 2019 “Productivity and Costs” news release 
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 labor. 

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 

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 drawn.

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 

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: March 20, 2019