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 2, 2023 “Productivity and Costs” news release 
(www.bls.gov/news.release/archives/prod2_03022023.pdf) and a new methodology
for estimating hours worked. More information on the methodology change can
be found at www.bls.gov/productivity/technical-notes/labor-productivity-hours
-worked-method-using-ces-all-employee-hours-nov-2022.htm.


The estimates of 2022 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 2, 2023
“Productivity and Costs” news release 
(www.bls.gov/news.release/archives/prod2_03022023.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 23, 2023. The estimates of 2022 
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 2, 2023 “Productivity and Costs” news 
release (www.bls.gov/news.release/archives/prod2_03022023.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 that which is 
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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