Technical Notes

Capital Services

Capital services are the services derived from the stock of physical assets 
and software. There are 86 asset types for fixed business equipment and 
software, structures, inventories, and land. Data on investments in physical
assets are obtained from BEA. Data on inventories are estimated using BEA 
and additional information from IRS Corporation Income Returns. Data for 
land in the farm sector are obtained from 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. 

Among equipment, BLS provides additional detail in tables 5 and 6 on 
information processing equipment and software (IPES). IPES is composed of
four broad classes of assets: computers and related equipment, software, 
communications equipment, and other IPES equipment. Computers and related
equipment includes mainframe computers, personal computers, printers, 
terminals, tape drives, storage devices, and integrated systems. Software 
is comprised of pre-packaged, custom, and own-account software. 
Communications equipment is not further differentiated. Other IPES includes
medical equipment and related instruments, electromedical instruments, 
nonmedical instruments, photocopying and related equipment, and office and 
accounting machinery. 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. 

Labor Input

Labor input in private business and private nonfarm business is obtained
by chained superlative Tornqvist aggregation of the hours at work by all
persons, 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 program (CES). These 
hours paid are then converted to an at-work basis by using information from 
the Employment Cost Index (ECI) of the National Compensation Survey (NCS) 
benchmarked to the Hours at Work Survey. Hours at work for nonproduction and
supervisory workers are derived using data from the Current Population Survey 
(CPS), the CES, and the NCS. The hours at work of proprietors, unpaid family
workers, and farm employees are derived from the Current Population Survey. 
Hours at work data reflect Productivity and Costs data as of the 
February 7, 2013 “Productivity and Costs” news release (USDL-13-0192). 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 Cindy Zoghi, 2007, “Measuring 
Labor Composition: A Comparison of Alternate Methodologies”
http://www.bls.gov/bls/fesacp1121407.pdf.




Combined Inputs 

Labor input and capital services are combined using chained superlative 
Tornqvist aggregation, applying weights that represent each component's 
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 is. 

In a production process, profit maximizing/cost-minimizing firms adjust the
factor proportions of capital and labor if the price of one factor falls 
relative to the price of the other factor; there would be 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. 

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, which accounted for approximately 74 percent of 
gross domestic product in 2011, includes all of gross domestic product except 
the output of general government, government enterprises, non-profit
institutions, the rental value of owner-occupied real estate, and the output
of paid employees of private households. The private nonfarm business sector 
excludes farms but includes agricultural services. All multifactor productivity
measures exclude government enterprises; however government enterprises are 
included in the business and nonfarm business sectors covered by the BLS 
quarterly productivity measures. The output measures are based on the revised
National Income and Product Accounts (NIPA) data released by BEA on 
January 30, 2013. 

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 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
cumulating 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. 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." 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 http://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 
http://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” 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 at 
http://www.bls.gov/mfp/mprtech.pdf. General information is available on
the BLS Multifactor Productivity website at
http://www.bls.gov/mfp/mprover.htm. Additional data not contained in the 
release can be obtained in print or at http://www.bls.gov/mfp. A number of 
comprehensive tables set up as zip files can be obtained at
http://www.bls.gov/mfp/mprdload.htm. Included in the additional data available
in the home page is a zip file containing selected multifactor productivity 
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 sectors.