Technical Notes

Capital Services 

Capital services are the services derived from the stock of physical assets
and software. There are 86 asset types for fixed business equipment and 
software, structures, inventories, and land. The aggregate capital services 
measures are obtained by Tornqvist aggregation of the capital stocks for 
each asset type within each of the eighteen manufacturing NAICS industry 
groupings using estimated rental prices for each asset type. Each rental 
price reflects the nominal rate of return to all assets within the industry 
and rates of economic depreciation and revaluation for the specific asset; 
rental prices are adjusted for the effects of taxes. Data on investments in 
physical assets and software are obtained from Bureau of Economic Analysis 
(BEA). Nonfarm industry detail for land is based on IRS book value data.  

Labor Hours 

The construction of the hours measures follows the methodology described in 
USDL 12-0494, Multifactor Productivity Trends, 2010, 
http://www.bls.gov/news.release/archives/prod3_03212012.pdf. Hours in 
manufacturing are directly aggregated and do not include the effects of 
labor composition. Hours data for the manufacturing multifactor productivity
measures include hours for all persons working in the manufacturing sector – 
wage and salary workers, the self-employed and unpaid family workers. The 
primary source of hours data is the BLS Current Employment Statistics (CES) 
survey. Hours paid of production workers are also obtained primarily from 
the CES survey. The hours of these employees are then converted to an at-work 
basis by using information from the Employment Cost Index (ECI) of the 
National Compensation Survey (NCS) and the BLS Hours at Work Survey. Hours
at work for nonproduction workers are derived using data from the 
Current Population Survey (CPS), the CES, and the NCS. The hours at work 
of proprietors are derived from the CPS.  

Hours at work data are based on underlying hours data published in the 
February 2, 2012, USDL-12-0162, Productivity and Costs, 
http://www.bls.gov/news.release/archives/prod2_02022012.pdf. Therefore, the 
data do not reflect the benchmark revisions to the CES and other revisions 
to hours released on March 7, 2012. 

Intermediate Inputs 

In manufacturing, intermediate inputs consist of energy, materials, and 
purchased business services, and represent a large share of production 
costs. Research has shown that substitution among inputs, including 
intermediate inputs, affects productivity change. Therefore, it is 
important to account for intermediate inputs in productivity measures at 
the level of manufacturing. In contrast, the more aggregate productivity
measures compare "value-added" output with two classes of inputs, capital
and labor. Because of these differences in concepts and methodology, 
productivity change in manufacturing cannot be directly compared with 
changes in private business or private nonfarm business.  

Data on intermediate inputs are obtained from BEA based on BEA annual 
input-output tables. Tornqvist indexes of each of these three input 
classes are derived at the 3-digit NAICS level and then aggregated to 
total manufacturing. Materials inputs are adjusted to exclude 
transactions between establishments within the same sector.


Combined Inputs 

The five input indexes (capital services, hours, energy, materials, and
purchased business services) are combined using chained superlative 
Tornqvist aggregation, employing weights that represent each component's
share of total costs. Total costs are defined as the current dollar value
of manufacturing sectoral output.  

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 falls 
relative to the price of 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. 

Sectoral Output 

The output concept used for multifactor productivity in manufacturing is
“sectoral output”. Sectoral output equals gross output (sales, receipts, 
and other operating income, plus commodity taxes plus changes in inventories),
excluding transactions between establishments within the same sector. 
In contrast, the output concept used for private business and private
nonfarm business is “real value added”. Real value added output in private
business equals gross domestic product less general government, government 
enterprises, private households (including the rental value of owner-occupied
real estate), and non-profit institutions. Real value added output excludes 
intermediate transactions between businesses.

The output index for manufacturing is computed using a chained superlative 
index (Tornqvist) of three-digit NAICS industry outputs. Industry output is 
measured as sectoral output, the total value of goods and services leaving 
the industry. Wherever possible, the indexes of industry output are 
calculated with a Tornqvist 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. BLS industry output measures for manufacturing industries are 
constructed 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 BLS. 

Multifactor Productivity 

The manufacturing multifactor productivity measures describe the relationship
between output in real terms and the inputs involved in its production. 
Manufacturing multifactor productivity measures exclude intermediate inputs
between manufacturing establishments from both output and inputs.
Multifactor productivity measures do not account for the specific 
contributions of labor, capital, or intermediate inputs. Rather, they are
designed to measure the joint influences on economic growth of technological
change, efficiency improvements, returns to scale, reallocation of resources
due to shifts in factor inputs across industries, and other factors. The 
multifactor productivity indexes are derived by dividing an output index by
an index of the combined inputs of labor hours, capital services, energy,
non-energy materials, and purchased business services.  

Other information 

Comprehensive tables containing more detailed data than that which is 
published in this press release are available upon request at 202-691-5606 
or at http://www.bls.gov/mfp/mprdload.htm. More detailed information on 
methods, limitations, and data sources of capital and labor are provided 
in BLS Bulletin 2178 (September 1983), Trends in Multifactor Productivity,
1948-81 and on the BLS Multifactor Productivity website under the title 
“Technical Information About the BLS Multifactor Productivity Measures”
for Major Sectors and 18 NAICS 3-digit Manufacturing Industries at 
http://www.bls.gov/mfp/mprtech.pdf. Methods for measuring manufacturing 
multifactor productivity are discussed in "Measurement of productivity 
growth in U.S. manufacturing” in the July 1995 issue of the Monthly Labor
Review. See http://www.bls.gov/mfp/mprgul95.pdf.