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.

Additional detail on information processing equipment and intellectual property
products are available in table C. 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 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 61 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 www.bls.gov/opub/mlr/2005/06/art3full.pdf. 

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 March 4, 2021 “Productivity and Costs” news release 
(www.bls.gov/news.release/archives/ prod2_03042021.htm).


The estimates of 2020 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 March 4, 2021 “Productivity
and Costs” news release (www.bls.gov/news.release/archives/prod2_03042021.htm).
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. 
These cell estimates are smoothed using a three year moving average to address
missing observations and reduce volatility.

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” (www.bls.gov/mfp/mprlabor.pdf). 

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 www.bls.gov/mfp/mprdload.htm.

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.
Additionally, the private nonfarm business sector excludes farms from the 
private business sector, but includes agricultural services. Total factor 
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 26, 2021. The estimates of 2020 
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 4, 2021 “Productivity and Costs” news 
release (www.bls.gov/news.release/archives/prod2_ 03042021.htm). 
 
Total factor Productivity

Total factor 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, Total factor 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 total factor 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 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 www.bls.gov/mfp/mfparchive.htm. 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 www.bls.gov/mfp/rdtable.pdf.

Other Information

Comprehensive tables containing additional data beyond the scope of this press 
release are available upon request at (202) 691-5606 or 
at www.bls.gov/mfp/mprdload.htm. 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” 
(www.bls.gov/mfp/mfparchive.htm) 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” (www.bls.gov/mfp/mprtech.pdf). General information is available
on the BLS website at www.bls.gov/mfp/mprover.htm. Additional data not 
contained in the release can be obtained at www.bls.gov/mfp. Comprehensive
tables for the private business and private nonfarm business sector can be 
downloaded at www.bls.gov/mfp/mprdload.htm, including data that links 1948-87
SIC data to NAICS data from 1987 forward.