Technical Note

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 a few 
detailed industries physical quantities of output are measured. 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). 
	
	For air transportation and line-haul railroads, annual real output is measured by aggregating freight ton-
miles and passenger-miles. For air transportation, data on passenger-miles and freight ton-miles from the Bureau 
of Transportation Statistics (BTS), U.S. Department of Transportation (DOT), are combined using revenue 
weights from that source. For line-haul railroads, data on freight ton-miles and passenger miles from the Surface 
Transportation Board (STB) of DOT, the Association of American Railroads (AAR), and AMTRAK are 
aggregated using operating expenses from those sources as weights.  
	
	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.
	
Combined Inputs

	The index of combined inputs is a Tornqvist index of separate quantity indexes of labor, 
capital, and intermediate purchases.  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 the value of net production minus
the values 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 capital stocks; changes in the stocks are assumed to be proportional to 
changes in capital services for each asset.  For the manufacturing industries, physical capital is composed of
26 categories of equipment, 2 categories of structures, 3 categories of inventories, and land. 
	
	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 for calculating the relative efficiency of an asset at different ages. 
       
	For manufacturing industries, estimates of investment by asset type are derived using annual capital 
expenditures from the economic censuses and annual surveys of the Bureau of the Census, along with estimates 
of asset detail by industry from the capital flow tables of 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 PPIs) with weights from the BEA capital 
flow tables that reflect each industry's use of individual asset commodities. 
      
	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, current dollar capital 
stocks are calculated with the perpetual inventory method. Inventories of parts and supplies are also included; 
the current dollar series is deflated with a weighted cost index based on data from the Air Transport Association 
(ATA) 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, were deflated with BLS producer price indexes and deflators based on
BEA data.  An estimate of capitalized hours was removed from the labor input measure in order to avoid
double-counting, because some capitalized labor costs are embedded in the railroad investment data. The perpetual
inventory method was used to calculate capital stocks for each of the items. Inventories of materials and supplies
are also included.  Estimates of investments in land from STB and AMTRAK were deflated with price indexes from BEA.  
       
	The index of aggregate capital input for each manufacturing and transportation industry is calculated as 
an annually-chained Tornqvist 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

	For manufacturing, the industry labor input measures represent the hours paid to wage and salary 
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 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. 
	
	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 measures use the same source data as that used in the labor 
productivity series which includes an adjustment to remove capitalized labor hours. 

Intermediate Purchases Input

	The index of intermediate purchases is constructed as a Tornqvist index of separate 
quantities of materials, 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 and 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 benchmark input-output 
tables and other annual industry data BEA.  
      
	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 (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 ATA.  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.