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 total wages. 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 2014
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 5, 2015 “Productivity and
Costs” news release (USDL-14-0157). 

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, 2013” 

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 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


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 2013. 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 30, 2015 but do 
not reflect the revised data released by BEA on February 27, 2015. 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 5, 2015
“Productivity and Costs” news release (USDL-15-0157). 
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: June 23, 2015