Technical notes

Technical Notes

The simplified methodology for preparing preliminary estimates of MFP is 
outlined in the June 2005 Monthly Labor Review article, “Preliminary 
estimates of multifactor productivity growth” located at This methodology is
applied to both the private nonfarm business and private business 
sectors and measures are calculated only for the most recent year. 
Data for all previous years are identical to the March 26, 2015 
“Multifactor Productivity Trends” news release (USDL-15-0480).

Capital Services  

Capital services are the services derived from the stock of physical
assets and intellectual property assets. Capital services measures 
constructed for the preliminary MFP measures are based on less detail 
only for the most recent year. The preliminary measures consist of 
six 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 preliminary estimates 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.

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. The labor composition index estimates
the effect of shifts in the age, education, and gender composition of the work 
force on the efficiency of hours worked. The preliminary estimates of 2015
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 4, 2016 
“Productivity and Costs” news release (USDL-16-0209). 

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” and in “Changes in the Composition
of Labor for BLS Multifactor Productivity Measures” 

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 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 74 percent of gross domestic product in 2014. 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 Cost
series include them. 

The output measures are based on the National Income and Product Accounts
(NIPA) data released by the Bureau of Economic Analysis (BEA) on January 29,
2016 but do not reflect the revised data released by BEA on February 26, 2016.
The preliminary estimates of 2015 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 February 4, 2016
“Productivity and Costs” news release (USDL-16-0209). 
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.

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Last Modified Date: May 05, 2016