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 April 3, 2014 “Multifactor Productivity
Trends” news release (USDL-14-0529).

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 bill. 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 2013 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 
6, 2014 “Productivity and Costs” news release (USDL-14-0167). The estimate 
of the 2013 labor composition index assumes relative wages across groups 
remain constant between 2012 and 2013 using the Current Population Survey

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 if the price of one factor is less 
than 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. 

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 2012. Additionally, the private nonfarm business sector 
excludes farms from the private business sector, but includes agricultural 
services. Multifactor 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, 2014 but do not reflect the
revised data released by BEA on February 28, 2014. The preliminary estimates
of 2013 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 6, 2014 “Productivity and Costs” news 
release (USDL-14-0167). 
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: July 09, 2014