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Economic News Release
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Technical note

Technical Note


        Industry output is measured as sectoral output, the total value, in real terms, of 
goods and services produced for sale outside the industry. For most manufacturing 
industries, real output is measured by deflating nominal value of production, but for a few 
detailed industries within the petroleum refining, cement, iron and steel, and aluminum 
industries it is measured by physical quantities of output.  Industry value of production is 
derived by adjusting industry shipments for changes in inventories and subtracting intra-
industry transfers and resales.  Wherever possible, the indexes of industry output are 
calculated with a Törnqvist formula. This formula aggregates the growth rates of the 
various industry outputs between two periods, using their relative shares in industry value 
of production, averaged over the two periods, as weights. 
        Industry output measures for manufacturing are constructed primarily using data 
from the economic censuses and annual surveys of the Bureau of the Census, U.S. 
Department of Commerce, together with information on price changes primarily from 

Combined Inputs 

	The index of combined inputs is a Törnqvist index of separate quantity measures 
of labor, capital, and intermediate purchases inputs.  The growth rates of the various 
inputs are aggregated using their average relative cost shares in industry value of 
production as weights.  The labor weight is based on the total value of labor 
compensation, including fringe benefits.  The intermediate purchases weight is based on 
the total value of materials (adjusted to remove intra-industry transactions), fuels, 
electricity, and purchased services.  The capital weight is a residual calculated as the 
value of net production minus the value of labor compensation minus the value of 
intermediate purchases.

Capital Input

	The measure of capital input is based on the flow of services derived from the 
stock of physical assets. Physical capital is composed of 26 categories of equipment, 2 
categories of structures, 3 categories of inventories, and land. Capital services are 
estimated by calculating capital stocks; changes in the stocks are assumed to be 
proportional to changes in capital services for each asset.  

	Capital stocks are calculated using the perpetual inventory method, which takes 
into account the continual additions to and subtractions from the stock of capital as new 
investment and retirement of old capital occur.  The perpetual inventory method 
measures stocks at the end of a year equal to a weighted sum of all past investments, 
where the weights are the asset’s efficiency relative to a new asset. A hyperbolic age-
efficiency function is assumed to calculate the relative efficiency of an asset at different 
        Estimates of investment by asset type are derived from annual capital 
expenditures by industry from the economic censuses and annual surveys of the Bureau 
of the Census, U.S. Department of Commerce, along with estimates of asset detail by 
industry from the capital flow tables of the Bureau of Economic Analysis.  

        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 PPIs) with weights from the BEA capital flow tables that reflect the 
industry’s use of individual asset commodities. 

        The index of aggregate capital input for each industry is an annually chained 
Törnqvist quantity index.  To construct the index, the growth rates of the stocks of each 
type of asset are aggregated using weights that are the average of each asset type’s cost 
share in successive years.  The asset costs are estimated by multiplying the asset stocks 
by implicit rental prices.

Labor Input

        The industry labor input measures represent the hours of all workers in the 
industry. The primary source of data on employment and hours is the BLS Current 
Employment Statistics (CES) survey, which provides monthly data on the number of jobs 
held by wage and salary workers employed directly in nonfarm establishments. The CES 
survey also provides data on the average weekly hours of production and nonsupervisory 
workers in these establishments. 
        Data from the BLS Current Population Survey (CPS) are used to supplement the 
CES data. The Division of Industry Productivity Studies (DIPS) estimates the average 
weekly hours of nonproduction workers for each industry using data from the CPS 
together with the CES data. The hours of all workers are treated as homogeneous and are 
directly aggregated. 
Intermediate Purchases Input
        The measures of intermediate purchases input is constructed as a Törnqvist aggregate 
of separate quantities of materials, services, fuels, and electricity consumed by each 
industry. Except for electricity, for which direct quantity data are available, quantities are 
derived by deflating current-dollar values with appropriate price deflators. 

        Nominal values of materials, fuels and electricity and quantities of electricity 
consumed by each industry are obtained from economic censuses and annual surveys of 
the Bureau of the Census, U.S. Department of Commerce.  Purchased business services 
are estimated using benchmark input-output tables and other annual industry data from 
the Bureau of Economic Analysis, U.S, Department of Commerce.  

        To avoid double counting, the materials estimates exclude the value of intra-industry 
purchases. Estimates of materials purchased from other establishments within the industry 
are subtracted from the gross measure of materials costs.

        Constant-dollar materials consumed are derived by dividing annual current-dollar 
industry purchases by a weighted price deflator for each industry. Materials deflators are 
constructed for each industry by combining detailed producer price indexes and import price 
indexes from BLS 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.

        Annual total fuels consumed by each industry are also deflated with weighted 
price deflators.  Producer price indexes for individual fuel categories are weighted 
together with weights reflecting detailed fuels expenditures by industry from the Energy 
Information Administration, U.S. Department of Energy.

Additional Information

        The multifactor productivity measures in this news release include data on 
industry output, capital expenditures and cost of materials and fuels from the 2005 
Annual Survey of Manufactures of the Bureau of the Census, U.S. Department of 
Commerce, along with data from the 1997 benchmark IO tables and capital flow tables of 
the Bureau of Economic Analysis, U.S. Department of Commerce.  Employment and 
hours data from the BLS Current Employment Statistics survey reflect the annual 
benchmark revision published in February 2007.  The output and labor input measures 
included in this release are the same as those used in the labor productivity measures for 
four-digit manufacturing industries released April 19, 2007.

        Tables containing multifactor productivity and related indexes for the 
manufacturing industries included in this release are accessible on the Multifactor 
Productivity website at   More detailed data and 
information is available upon request by sending an email to or by 
calling the Division of Industry Productivity Studies (202-691-5618).

Material in this report is in the public domain and, with appropriate credit, may be used 
without permission.  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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Last Modified Date: October 30, 2020