Technical notes

Technical Notes

Capital Input 

Capital input is 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 include 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 input measures, as are 
owner-occupied residential structures. The aggregate capital input 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 input 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 input is 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 worked data for the 
measures this news release include hours worked for all persons working
in the 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) program, which provides monthly survey 
data on the number of jobs held by and hours paid to wage and salary 
workers in nonfarm establishments, counting a person who is employed by
two or more establishments at each place of employment. Hours of paid time
off are excluded from hours paid 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, hours of
paid time off are excluded using a combination of NCS and Hours at Work 
survey data. Off-the-clock hours are added, yielding hours worked, using 
data from the Current Population Survey (CPS). To estimate the hours of 
farm labor, nonfarm proprietors, and nonfarm unpaid family workers the
CPS data are used. The hours worked of proprietors, unpaid family workers,
and farm employees are derived from the CPS. Hours worked data reflect 
estimates in the March 7, 2024 “Productivity and Costs” news release 
(www.bls.gov/news.release/archives/prod2_03072024.pdf) and a new method 
for estimating hours worked. More information on the method change can be
found at https://www.bls.gov/opub/mlr/2023/article/an-improved-estimate
-of-self-employment-hours.htm.

The estimates of 2023 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 7,
2024 “Productivity and Costs” news release 
(www.bls.gov/news.release/archives/prod2_03072024.pdf). 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.

Combined Inputs

Labor input and capital input 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 input 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 input. 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/productivity/tables/.

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 28, 2024. The estimates of 2023 
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, 2024 “Productivity and Costs” news 
release (www.bls.gov/news.release/archives/prod2_03072024.pdf). 
 
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 input 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/productivity/technical-notes/impact-of-research-and-
development-on-productivity-growth-1989.pdf. 

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/productivity
/highlights/research-and-development-contribution-to-total-factor-
productivity.htm.

Other Information

Detailed information on methods used in this release can be 
found in the BLS Handbook of
Methods. Productivity Measures: Business Sector and Major Sector section at 
www.bls.gov/opub/hom/msp/home.htm.

Comprehensive tables containing more detailed data than are published in this news
release are available upon request at 202-691-5606 or 
at www.bls.gov/productivity/tables.

Industry specific contributions to output are available at
www.bls.gov/productivity/highlights/contributions-of-total-factor-
productivity-major-industry-to-output.htm.

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