Summary of methods for the manufacturing sector and manufacturing industries

The manufacturing 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, capital, or any other 
factor of production.  Rather, multifactor productivity is 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 input of labor, capital services, energy, non-energy materials,
and business service inputs.  

The multifactor productivity measures for manufacturing differ in several ways
from those for private business and private nonfarm business in their 
treatment of labor input, output, and classes of factor inputs.  First, 
the manufacturing measure of labor input is a direct aggregate of hours.  
This is in contrast to the major sector measures for which estimates of the 
effects of changing labor composition have been developed. 

Next, the output concept used for multifactor productivity in manufacturing 
is “sectoral output.”  Sectoral output is similar to gross output, but 
excludes shipments from one establishment to another within the same 
manufacturing industry or sector.  In contrast, the output concept used for
private business and nonfarm business is “gross product originating” and is 
similar to “real value added”.  Gross product originating in private business 
equals gross domestic product in the economy less general government,
government enterprises, private households (including the rental value of 
owner-occupied real estate), and non-profit institutions.  Gross product
originating 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.  
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. 

 

The resulting manufacturing multifactor productivity measure compares what is
produced in the manufacturing sector with the inputs used to produce it.  The
comparison excludes flows of intermediate inputs between manufacturing 
establishments from measures of both output and inputs.  However, the 
comparison does include capital service inputs and capital goods produced, 
even when these goods are produced and consumed in manufacturing.    

Multifactor productivity in manufacturing compares "sectoral output" to 
three classes of inputs: 1) hours at work of labor employed within 
manufacturing; 2) capital services employed by manufacturing establishments;
and 3) purchases of energy, materials, and business services from outside 
of manufacturing (intermediates). 

Hours paid of production workers are obtained from the Current Employment
Statistics (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 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
reflect Productivity and Costs data as of the March 5, 2008 news release.
Therefore, it reflects the benchmark revisions to the CES survey and other 
revisions to hours released on February 1, 2008.  The construction of hours 
at work follows the methods used in the private business sector described 
in USDL 08-0410, Multifactor Productivity Trends, 2006, 
http://www.bls.gov/news.release/pdf/prod3.pdf, except that hours in 
manufacturing are directly aggregated and do not include the effects of 
changing labor composition. 

Capital input measures the services derived from the stock of physical 
assets and software.  The assets included are fixed business equipment, 
structures, inventories, and land.  Among equipment, BLS provides additional 
detail for information processing equipment and software (IPES). IPES is 
composed of four broad classes of assets: computers and related equipment, 
software, communications equipment, and other IPES equipment.  Computers and 
related equipment includes mainframe computers, personal computers, printers, 
terminals, tape drives, storage devices, and integrated systems.  Software
is comprised of pre-packaged, custom, and own-account software.  
Communications equipment is not further differentiated. “Other IPES" includes
medical equipment and related instruments, electromedical instruments, 
nonmedical instruments, photocopying and related equipment, and office and 
accounting machinery.  

The aggregate capital input 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 BEA.  
Nonfarm industry detail for land is based on IRS book value data.  
Current-dollar gross product originating (GPO) data, obtained from BEA, are
used in estimating capital rental prices.


In manufacturing, intermediates are the largest input in terms of costs.  
Furthermore, research has shown that substitution among inputs, including 
intermediates, affects productivity change.  Therefore, it is important to 
include intermediates 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 methods, productivity change in manufacturing cannot be 
directly compared with changes in private business or private nonfarm 
business.  

Intermediate inputs (energy, materials, and purchased business services) 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.  As with the sectoral output 
measures, materials inputs are adjusted to exclude transactions between 
establishments within the same sector.

The five input indexes (capital services, hours, energy, materials, and 
purchased business services) are combined using Tornqvist aggregation, 
employing weights that represent each component's share of total costs. 
Total costs are defined as the value of manufacturing sectoral output.  The
index uses changing weights: The share in each year is averaged with the 
preceding year's share.

Multifactor productivity data incorporate NAICS input-output tables and 
revised BEA chain-type price and quantity indexes for intermediate inputs 
(energy, materials, and business services).  See tables at 
http://www.bea.gov/Industry/Index.htm , Gross Domestic Product by Industry. 

BLS built multifactor productivity measures from three-digit NAICS detail.  
Most of the critical data used to calculate these measures were not reported
on a NAICS basis for years prior to 1998.  Detailed GDP by industry data were
available from 1998 forward. But from 1987 to1997, many of the income 
components needed to construct capital rental prices were obtained by applying
1997 SIC-to-NAICS conversion factors to SIC data and adjusting to the 
estimated NAICS totals.  A similar procedure was applied to manufacturing 
inventories, energy, materials, and business services.    Land data were only
available from 1998 to 2004 on a NAICS basis.  As a consequence, land 
estimates from 1987 to 1997 were calculated using a combination of SIC to
NAICS conversion factors and more detailed IRS data.  Data for 2005 and 2006
were extrapolated using detailed IRS data for 2004. 

Comprehensive tables containing additional data beyond the scope of 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.  
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. 
More detailed data can be obtained from our web site at http://www.bls.gov/mfp
or by request at 202-691-5606.