Multifactor Productivity Trends for Detailed Industries News Release

For release 10:00 a.m. (EDT) Thursday, June 28, 2018                                                    USDL-18-1059

Technical Information:	(202) 691-5606  •  productivity@bls.gov •  www.bls.gov/mfp 
Media contact:          (202) 691-5902 • PressOffice@bls.gov


                     MULTIFACTOR PRODUCTIVITY TRENDS FOR DETAILED INDUSTRIES - 2016


Multifactor productivity -- defined as output per unit of combined inputs -- rose in 37 of the 86 4-digit 
NAICS manufacturing industries in 2016, the U.S. Bureau of Labor Statistics reported today. This was 
up from 2015, when multifactor productivity increased in 21 manufacturing industries. In 2016, 
multifactor productivity rose in one of the two transportation industries measured (air transportation), 
the same as in 2015.

Of the 12 largest industries, multifactor productivity increased the most in printing and related support 
activities (3.6 percent), as output increased while combined inputs declined. Output growth occurred in 
7 out of the 12 industries. In 5 of these, combined inputs fell or grew at a slower rate than output, 
leading to multifactor productivity growth. However, output fell more than combined inputs in 4 of the 
12 industries, leading to declines in multifactor productivity. In the case of 2 industries (animal 
slaughtering and processing, and motor vehicle parts), increases in output coincided with larger 
increases in combined inputs, causing slight declines in multifactor productivity.

Among all 86 manufacturing industries, 4 industries posted multifactor productivity gains 
greater than 4.0 percent: 

	*  Iron and steel mills and ferroalloys (9.4 percent)
	*  Leather and hide tanning and finishing (7.8 percent)
	*  Alumina and aluminum production (7.3 percent)
	*  Clay products and refractories (4.9 percent)

Multifactor productivity declined by 6.0 percent or more in 5 manufacturing industries in 2016. The 
largest productivity decline occurred in agriculture, construction, and mining machinery (-8.6 percent).

Multifactor productivity moved in opposite directions in the two measured transportation industries: 

	*  Air transportation (0.6 percent)
	*  Line-haul railroads (-0.9 percent)

Multifactor Productivity: Definition and Concepts

Multifactor productivity indexes relate the change in real output to the change in the combined inputs of 
labor, capital, and intermediate purchases (energy, materials, and purchased services) used in producing 
that output. Multifactor productivity is also known as total factor productivity.

A variety of factors that influence economic growth are not specifically accounted for among measured 
inputs, including: technological change, returns to scale, enhancements in managerial and staff skills, 
changes in the organization of production, and other efficiency improvements. Multifactor productivity 
reflects these factors. See the technical note for more information.

Components of Multifactor Productivity Growth: Output and Combined Inputs

In 2016, output increased in 32 manufacturing industries, compared to 46 industries in 2015. Output increased 
by 5.0 percent or more in the following 2 industries in 2016:

	*  Other food products (6.6 percent)
	*  Electric lighting equipment (5.6 percent) 

Combined inputs of capital, labor, and intermediate purchases rose in 28 manufacturing industries in 
2016, compared to 64 industries in 2015. Just under half of the manufacturing industries saw growth in 
hours worked (40 industries), while fewer industries had growth in capital services (35 industries) and 
intermediate purchases (30 industries).

The following industries had the largest increases in combined inputs in 2016:

	*  Agricultural chemicals (6.6 percent)
	*  Footwear (5.6 percent)
	*  Animal slaughtering and processing (5.0 percent)
	*  Petroleum and coal products (4.2 percent) 

In 4 manufacturing industries, multifactor productivity rose more than 3.0 percent despite falling 
output, as combined inputs fell more rapidly. This occurred in: 

	*  Iron and steel mills and ferroalloys (9.4 percent)
	*  Leather and hide tanning and finishing (7.8 percent)
	*  Clay products and refractories (4.9 percent)
	*  Other nonferrous metal production (3.5 percent)

In the air transportation industry, output increased 3.5 percent and combined inputs increased 2.8 
percent in 2016. In line-haul railroads, output fell 4.1 percent and combined inputs decreased 3.2 
percent.

Trends in Multifactor Productivity for Selected Time Periods

Year-to-year movements and long-term trends in industry multifactor productivity may reflect cyclical 
changes in the economy. However, long-term average annual percent changes in multifactor 
productivity are more reliable indicators of historical trends in industry performance.

More industries saw multifactor productivity growth over the long term than the short term. Over the 
long term period from 1987 to 2016, multifactor productivity grew in 53 manufacturing industries, 
compared to only 37 from 2015 to 2016. (See tables 1 and 2.) Over the long term, average annual rates 
of change in multifactor productivity ranged between -2.0 percent and 2.0 percent for nearly all 
manufacturing industries.

In contrast, multifactor productivity declined by 2.0 percent or more in 26 industries in 2016. Only one 
industry (pharmaceuticals and medicines) saw an average annual decline of that magnitude from 1987 to 
2016.

Between 1987 and 2016, the number of manufacturing industries with growth in multifactor productivity 
was highest in 2003 and 2010. These were years of economic growth following recessions. In contrast, 
relatively few manufacturing industries saw multifactor productivity growth in the recession years of 
2001 and 2009.

From 1987 to 2016, multifactor productivity rose in both air transportation and line-haul railroads by an 
average annual rate of 1.3 percent and 1.5 percent, respectively. While both industries posted gains in 
output, productivity grew more in line-haul railroads because its combined inputs showed little change 
over the long term.

Multifactor Productivity as a Source of Labor Productivity Growth

Multifactor productivity measures differ from the BLS labor productivity measures because they 
compare output to the combined inputs of hours worked, capital, and intermediate purchases. Labor 
productivity relates output only to hours worked. Mathematically, an industry’s labor productivity is 
equal to multifactor productivity plus the effects of factor substitution; that is, the combined effects of 
changes in weighted capital services relative to hours worked and weighted intermediate purchases 
relative to hours worked. These factor substitutions are referred to as contribution of capital intensity 
and contribution of intermediate purchases intensity.

Eighty-one out of the 86 manufacturing industries posted gains in labor productivity from 1987 to 2016. 
Among these 81 industries, substitution of intermediate purchases for labor was the leading source of 
labor productivity growth. Growth in the contribution of intermediate purchases intensity 
occurs when firms purchase a greater share of materials instead of using their own labor. Contribution of 
intermediate purchases intensity may also rise when firms substitute contracted labor for payroll labor.

Strong growth in multifactor productivity was the dominant source of labor productivity growth in the 
industries that manufacture computers and electronic products (computer and peripheral equipment, 
semiconductors and electronic components, and communications equipment). Labor productivity growth in the 
measured transportation industries (air transportation and line-haul railroads) was also primarily driven by 
multifactor productivity growth. The remaining manufacturing industries with high average annual growth in 
labor productivity mostly saw greater growth in factor substitution of intermediate purchases for labor.

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					Technical Note

Multifactor Productivity:  Multifactor productivity measures 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 reflect the joint influences on economic growth of a number of factors 
that are not specifically accounted for on the input side, 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 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 based on total capital cost, which 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 24 categories of equipment, 10 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. Additional annual investment data 
comes from the fixed asset accounts from the Bureau of Economic Analysis (BEA). Annual investment 
data is supplemented with the 1997 benchmark capital flow table from the BEA as well as the 2008 and 
2012 Annual Capital Expenditures Survey from the Bureau of the Census. 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 similarly to manufacturing industries. For these assets, a more detailed breakdown of annual 
expenditures on equipment and structures from the BEA is used. 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 similarly to 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, labor hours reflect annual hours worked by all employed 
persons in an industry. Data on industry employment and hours come primarily from the BLS Current 
Employment Statistics (CES) survey and the Current Population Survey (CPS). CES data on the number 
of total and nonsupervisory worker jobs held by wage and salary workers in nonfarm establishments are 
supplemented with CPS self-employed and unpaid family worker data to estimate industry employment. 
Hours worked estimates are derived using CES and CPS employment, CES data on average weekly 
hours paid of nonsupervisory workers, CPS data on hours of supervisory, self-employed, and unpaid 
family workers, and ratios of hours-worked to hours-paid based on data from the BLS National 
Compensation Survey (NCS). For some industries, employment and hours data are supplemented or 
further disaggregated using data from the BLS Quarterly Census of Employment and Wages (QCEW), 
the Census Bureau, or other sources. Hours worked are estimated separately for different types of 
workers and then are directly aggregated; no adjustments for labor composition are made. 

For air transportation, annual labor input estimates are based on monthly employment data from DOT 
supplemented by employment and hours from the CES program and hours from the CPS. For line-haul 
railroads, labor input measures are derived primarily from DOT 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 are 
deflated using cost indexes from A4A. For line-haul railroads, intermediate purchases data from STB are 
supplemented with data from other sources including AAR, AMTRAK, EIA, and the Edison Electric 
Institute. The nominal values are deflated with producer price indexes from BLS and implicit price 
deflators calculated from BEA investment data.

Labor Productivity:  Labor productivity describes the relationship between real output and the labor 
hours involved in its production. These measures show the changes from period to period in the amount 
of goods and services produced per hour worked. Although the labor productivity measures relate output 
in an industry to hours worked of all persons in that industry, they do not measure the specific 
contribution of labor to growth in output. Rather, they reflect the joint effects of many influences, 
including: changes in technology; capital investment; utilization of capacity, energy, and materials; the 
use of purchased services inputs, including contract employment services; the organization of 
production; the characteristics and effort of the workforce; and managerial skill.

Contributions to Labor Productivity:

	Contribution of Capital Intensity:  Capital intensity is the ratio of capital services to hours 
	worked in the production process. Multiplying the change in capital intensity times capital’s 
	share of combined inputs yields the contribution of capital intensity. 

	Contribution of Intermediate Purchases Intensity: Intermediate purchases intensity is the 
	ratio of intermediate purchases to hours worked in the production process. Multiplying the 
	change in intermediate purchases intensity times intermediate purchases’ share of combined 
	inputs yields the contribution of intermediate purchases intensity.

	When positive, both the contribution of capital intensity and the contribution of intermediate 
	purchases intensity represent sources of labor productivity growth. These statistics represent 
	factor substitution in the production process. In other words, positive change in the contribution 
	of capital intensity indicates that labor productivity growth is being achieved in part through the 
	substitution of capital for labor. Likewise, positive change in the contribution of intermediate 
	purchases intensity indicates that labor productivity growth is being achieved in part through the 
	substitution of intermediate purchases for labor.

	Over a given time period, the average logarithmic growth rate of labor productivity will equal the 
	sum of the average logarithmic growth rates of the contribution of capital intensity, the 
	contribution of intermediate purchases intensity, and multifactor productivity. However, because 
	both output and input data are expressed annually, average annual (as opposed to logarithmic) 
	rates of change are calculated. Therefore, the sum of growth rates of multifactor productivity, the 
	contribution of capital intensity, and the contribution of intermediate purchases intensity may not 
	precisely equal the rate of change of labor productivity.

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