Technical Note
Total Factor Productivity: Total factor productivity measures are derived by dividing an index of real
industry output by an index of the combined inputs of labor, capital, and intermediate inputs. The total
factor 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: 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.
Output measures 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).
Combined Inputs: The index of combined inputs is a Törnqvist index of separate quantity indexes of
capital, labor, and intermediate inputs (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
inputs 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 inputs.
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.
Physical capital is composed 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, 2012, and 2017 Annual Capital Expenditures Surveys 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.
Labor Hours: Labor hours are measured as 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
production worker jobs held by wage and salary workers in nonfarm establishments are supplemented
with CPS data on self-employed and unpaid family workers to estimate industry employment. Hours
worked estimates are derived using CES and CPS employment, CES data on the average weekly hours
paid all employees, CPS data on hours of self-employed and unpaid family workers, and ratios of hours
worked to hours paid based on data from both the CPS and the 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.
Intermediate Inputs: The index of intermediate inputs 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.
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.
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 Inputs Intensity: Intermediate inputs intensity is the ratio of
intermediate inputs to hours worked in the production process. Multiplying the change in
intermediate inputs intensity times intermediate inputs' share of combined inputs yields the
contribution of intermediate inputs intensity.
When positive, both the contribution of capital intensity and the contribution of intermediate
inputs 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
inputs intensity indicates that labor productivity growth is being achieved in part through the
substitution of intermediate inputs 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 inputs intensity, and total factor 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 total factor productivity, the
contribution of capital intensity, and the contribution of intermediate inputs intensity may not
precisely equal the rate of change of labor productivity.
Annual Percent Change: The annual percent change is the change in a series from one year to the
next as a percent of the series-value in the previous year. Over a period of more than one year, the
annual percent change is the compound annual growth rate in an index series, or an annualized
average growth rate. Because the change of an index series varies from year to year, the annual
percent change for a long time period reflects the constant rate that can be applied to each year in a
period, from the start to the end, that would give the same total result. It is calculated as (Ending
Value/Starting Value)^(1/Number of Years)-1.
United States Department of Labor
