Technical Note

Multifactor Productivity:  Multifactor productivity measures for detailed industries are derived by 
dividing an index of real industry output by an index of the combined inputs of labor, capital, and 
intermediate purchases. The multifactor productivity indexes do not measure the specific contributions 
of capital, labor, and intermediate inputs.  Rather, they are designed to reflect the joint influences on 
economic growth of a number of factors, including technological change, returns to scale, improved 
skills of the workforce, better management techniques, or other efficiency improvements.

Output:  Manufacturing industry output is measured as annual sectoral output, the total value, in real 
terms, of goods and services produced for sale outside the industry.  Industry value of production is 
derived by adjusting industry shipments for changes in inventories and subtracting intra-industry 
transfers and resales. For most manufacturing industries, real output is measured by deflating nominal 
value of production, but for some industries physical quantities of output are measured. For air 
transportation and line-haul railroads, output is measured by aggregating passenger-miles and freight ton-
miles with weights based on revenues or operating expenses.

Output measures for manufacturing industries are constructed using data primarily from the economic 
censuses and annual surveys of the Bureau of the Census, U.S. Department of Commerce, together with 
information on price changes chiefly from the Bureau of Labor Statistics (BLS). Output measures for air 
transportation and line-haul railroads are constructed using data primarily from the Bureau of 
Transportation Statistics (BTS) and the Surface Transportation Board (STB), both in the U.S. 
Department of Transportation (DOT), together with information from the Association of American 
Railroads (AAR), AMTRAK, and several other sources.

Combined Inputs:  The index of combined inputs is a Törnqvist index of separate quantity indexes of 
capital, labor, and intermediate purchases (including fuels, electricity, materials, and purchased services). 
The annual growth rates of the various inputs are aggregated using their relative cost shares in total 
industry value of production as weights. The labor weight is based on labor compensation including 
fringe benefits. The weight for intermediate purchases is based on the total cost of materials, fuels, 
electricity, and purchased services. The capital weight is calculated as the value of sectoral production 
minus the costs of labor compensation and intermediate purchases.

Capital Input:  Capital input reflects the flow of services derived from the stock of physical assets. 
Capital services are estimated by calculating productive capital stocks and are assumed to be 
proportional to changes in these capital stocks for each asset. The capital index is a Törnqvist index of 
separate quantity indexes of equipment, structures, inventories, and land.

For manufacturing industries, physical capital is comprised of 26 categories of equipment, 2 categories of 
structures, 3 categories of inventories, and land.  Measures of total capital services for each industry are 
estimated by aggregating the capital stocks of individual asset types. Estimates of investment by asset 
type for each industry are derived using annual capital expenditures for detailed industries from the 
economic censuses and annual surveys of the Bureau of the Census, in combination with benchmark 
capital flow tables and annual detailed asset investment by industry from the Bureau of Economic 
Analysis (BEA). Price changes are removed from the annual investment data before calculating stocks. 
Price deflators for each asset category are constructed by combining detailed price indexes (mostly BLS 
Producer Price Indexes) with weights that reflect each industry’s use of individual asset commodities.

The capital stocks for the different assets are combined using weights based on estimated annual rental 
prices for each asset type, averaged between two time periods. Each rental price reflects the nominal rate 
of return to all assets within the industry and the rates of economic depreciation and revaluation of the 
specific asset. Rental prices are adjusted for the effects of taxes.

For air transportation, a weighted index of 44 types of airframes and 34 types of engines is derived from 
quantities and purchase prices from BTS. For assets other than airframes and engines, capital stocks are 
calculated as is done for manufacturing industries. Inventories of parts and supplies are also included; 
the current dollar series is deflated with a weighted cost index based on data from Airlines for America 
(A4A) and BTS. Indexes for aircraft and engines, non-aircraft assets, and parts and supplies inventories 
are aggregated using cost share weights to derive an overall measure of capital input.

For line-haul railroads, current dollar investment for 10 categories of equipment and 13 categories of 
structures, obtained from STB and AMTRAK, are deflated with BLS PPIs and deflators based on BEA 
data. The capital stocks for each of the items are calculated as is done for manufacturing industries. 
Inventories of materials and supplies are also included. Estimates of investments in land from STB and 
AMTRAK were deflated with price indexes from BEA.

Labor Input:  For manufacturing industries, the primary source of industry employment and hours data 
is the BLS Current Employment Statistics (CES) survey. The CES provides monthly data on the number 
of total and production worker jobs held by wage and salary workers in nonfarm establishments, as well 
as data on the average weekly hours of production workers in those establishments. CES data are 
supplemented with data from the Current Population Survey (CPS) to estimate employment and hours 
of self-employed and unpaid family workers in each industry. Data from the CPS, together with the 
CES data, are also used to estimate the historical average weekly hours of nonproduction workers for 
each industry. CES and CPS data are supplemented or further disaggregated for some industries using 
data from the BLS Quarterly Census of Employment and Wages (QCEW), the Bureau of the Census, or 
other sources. Hours of all persons in an industry are treated as homogeneous and are directly 
aggregated.

For air transportation and line-haul railroads, labor input measures are derived primarily from DOT data. 
For air transportation, annual estimates are based on monthly data from BTS. For line-haul railroads, 
total labor hours for supervisory and nonsupervisory workers are derived from STB data and 
supplemented with data from AAR. For the railroad industry, the labor input measure includes an 
adjustment to remove capitalized labor hours in order to avoid double-counting because some capitalized 
labor costs are embedded in the railroad investment data.

Intermediate Purchases Input:  The index of intermediate purchases is a Törnqvist index of separate 
quantities of materials, purchased services, fuels, and electricity consumed by each industry. Except for 
electricity consumed by manufacturing industries, for which direct quantity data are available, quantities 
are derived by deflating current-dollar values with appropriate price deflators. 

For manufacturing industries, nominal values of materials, fuels and electricity, along with quantities of 
electricity consumed by each industry are obtained from economic censuses and annual surveys of the 
Bureau of the Census. To avoid double counting, an adjustment is made to the materials estimates to 
exclude the value of intra-industry commodity transfers. Purchased business services are estimated using 
annual industry data and benchmark input-output tables from BEA. 

Constant-dollar materials consumed are derived by dividing annual current-dollar industry purchases by 
a weighted price deflator for each industry. Aggregate materials deflators are constructed for each 
industry by combining producer price indexes and import price indexes from BLS for detailed 
commodities.  The deflators are combined using weights based on detailed commodity data from the 
BEA benchmark input-output tables. Aggregate price indexes to deflate purchased business services are 
constructed in a similar manner using consumer price indexes (CPIs), PPIs, and deflators developed by 
BEA. The value of fuels consumed by each industry is deflated with a weighted price deflator based on 
PPIs for individual fuel categories; the weights reflect fuel expenditures by industry from the Energy 
Information Administration (EIA), U.S. Department of Energy.

For air transportation, detailed cost of materials, services, fuels, and electricity from the BTS were 
deflated using cost indexes from A4A. For line-haul railroads, intermediate purchases data from STB 
were supplemented with data from other sources including AAR, AMTRAK, EIA, and the Edison 
Electric Institute. The nominal values were deflated with producer price indexes from BLS and implicit 
price deflators calculated from BEA investment data.

Revisions: This news release incorporates 2010 data and revisions to 2009 data from Annual Survey of 
Manufactures published by the Census Bureau.  This news release also incorporates the annual 
benchmark revisions of the BLS Current Employment Statistics (CES) survey published in February, 
2012. All of the measures for 2010 in this release are preliminary and subject to revision.

Additional Information:  The industries included in this release are classified according to the 2007 
NAICS. While the rates of change reported by BLS in this news release are rounded to one decimal 
place, all industry productivity percent changes are calculated using index numbers rounded to three 
decimal places.

Industry multifactor productivity and related indexes and rates can be accessed by visiting the 
Multifactor Productivity and Costs website at http://www.bls.gov/mfp. Additional data are available 
upon request by calling the Division of Industry Productivity Studies at 202-691-5618 or by sending a 
request by e-mail to dipsweb@bls.gov. Information in this report will be made available to sensory-
impaired individuals upon request. Voice phone: 202-691-5618; TDD message referral phone number: 1-
800-877-8339.

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