Monthly Labor Review • June 2010 3

Imported Inputs and Productivity

Effects of imported intermediate

inputs on productivity

Lucy P. Eldridge

and

Michael J. Harper

Lucy P. Eldridge is a senior economist in the Office of Productivity 

and Technology, Bureau of Labor 

Statistics. Michael J. Harper is 

Associate Commissioner of the 

Office. Email: eldridge.lucy@bls.

gov or harper.mike@bls.gov

A framework for estimating the effects of imported

intermediate inputs on U.S. major-sector labor productivity

is used together with the Solow multifactor productivity

equation to show that private business sector multifactor

productivity may have grown about 0.1 percent

more slowly than what the BLS published series indicates

Offshoring, or offshore outsourcing—the substitution of imported intermediate inputs for domestic 

labor or domestically produced intermediate 

inputs—affects U.S. economic performance. 

The existing framework for measuring productivity does not permit an analysis of 

offshoring; thus, the framework needs to 

be adjusted in order to assess the effects of 

imported intermediate inputs on the U.S. 

economy. The BLS Major Sector Productivity program develops measures of labor productivity for broad sectors of the economy: 

business, nonfarm business, manufacturing, 

and nonfinancial corporations. In addition, the program develops annual indexes 

of multifactor productivity for the private 

business sector, the manufacturing sector, 

and most manufacturing groups. This article 

focuses on BLS productivity measures for 

the private business sector and the manufacturing sector. Productivity measures for 

these two sectors are constructed under different methodologies: the private business 

sector productivity measures use a valueadded output concept, while the manufacturing sector measures use a sectoral output 

approach. This difference in methodology 

influences the effects of imported intermediates on BLS measures of productivity.

In the sections that follow, the private business sector and the manufacturing sector are 

analyzed separately with an eye toward developing a framework for estimating the effects of 

imported intermediate inputs on U.S. majorsector labor productivity. First, the production 

model used to calculate the BLS private business 

sector multifactor productivity measures is expanded to treat imported intermediate inputs as 

an input, rather than as a subtraction from output. Then, the BLS framework for constructing 

manufacturing multifactor productivity is decomposed in order to isolate imported intermediate inputs. For both sectors, the Solow multifactor productivity equation is used to estimate 

the effects on labor productivity of substitution 

between imported intermediate inputs and U.S. 

hours worked.1 The data reveal that growth in 

imported intermediate inputs contributed 14 

percent to the average annual growth in labor 

productivity for the private business sector, and 

23 percent to the average annual growth in labor productivity in the manufacturing sector, 

from 1997 to 2006.2

Data sources

Output. Real output measures used by the 

BLS to construct major-sector productivity 

statistics are produced by the Bureau of Eco-
Imported Inputs and Productivity

4 Monthly Labor Review • June 2010

nomic Analysis (BEA) of the U.S. Department of Commerce. The most widely known measure of aggregate output for the U.S. economy is the gross domestic product 

(GDP): the sum of personal consumption expenditures, 

gross private domestic investment, government consumption expenditures and gross investment, and exports of 

goods and services less imports of goods and services. The 

BEA constructs nominal outputs for detailed components 

of GDP from various data sources, converts the outputs to 

real measures, and then aggregates them to calculate real 

GDP.

As a fundamental part of the national accounts, the 

BEA also distinguishes three primary sectors of GDP: business, household, and government.3

 The business sector accounts for the bulk of national output. The BEA calculates 

business sector output by removing from GDP the gross 

products of general government, private households, and 

nonprofit institutions.4

Ideally, productivity statistics measure the productivity of the U.S. economy at the most aggregate level of 

domestic output—that is, GDP. However, the BLS must 

exclude several activities from aggregate output in order 

to remove potential sources of bias that are specific to the 

measurement of productivity. The real gross products of 

general government, of private households, and of nonprofit institutions are estimated primarily from data on 

labor compensation. Trends in such output measures will, 

by definition, move with measures of input data and will 

tend to imply little or no labor productivity growth. Although these measures are the best available estimates of 

nonmarket components of GDP, including them in measures of the aggregate productivity of the economy would 

bias labor productivity trends toward zero.

The BLS business sector also excludes the gross product 

of owner-occupied housing and the rental value of buildings and equipment owned and used by nonprofit institutions serving individuals.5

 These components are excluded 

because no adequate corresponding labor input measures 

have been developed. To measure multifactor productivity, 

the BLS must further restrict output to the U.S. private business sector, excluding the output of government enterprises. 

Appropriate weights for labor and capital in government 

enterprises are not estimated because subsidies account for 

a substantial portion of capital income; therefore, there is 

no adequate measure of government enterprise capital income in GDP. In 2006, the BLS measure of the U.S. private 

business sector output accounted for approximately 76 percent of the value of GDP.

6

In the manufacturing sector, the BLS measures output 

for productivity statistics differently. Output in the manufacturing sector is defined as the deflated value of production shipped to purchasers outside of the sector, including 

shipments to final users and establishments elsewhere 

within the private business sector. This is a sectoral output 

concept: output is gross output, excluding intrasectoral 

transactions (sales or transfers between establishments 

within the sector); sectoral output represents sales to final 

demand plus intermediate goods sent to other industries. 

The manufacturing multifactor productivity indexes are 

based on sectoral output in an effort to avoid the problem 

of double-counting that occurs when one establishment 

provides materials used by other establishments in the 

same sector.

Labor input. Labor input for the U.S. private business 

sector is measured as total hours actually worked by all 

persons, multiplied by a labor composition index. The 

measure of hours actually worked is based on the sources 

and methods used to measure the quarterly labor productivity of the business sector. The BLS labor composition 

index estimates the effects that shifts in age, education, 

and gender have on labor input growth and multifactor 

productivity growth.

Labor input is based on a jobs concept. The Current 

Employment Statistics (CES) survey is the primary source 

of data used to construct hours for the BLS productivity 

measures.7 Data from the CES survey on average weekly 

hours paid are adjusted to an hours-at-work concept with 

the use of a ratio of hours worked to hours paid.8 Current 

Population Survey (CPS) data on average weekly hours of 

nonproduction and supervisory workers are incorporated 

into the methodology to expand coverage to all employees.9

 To expand sectoral coverage, hours actually worked 

for employees of farms, proprietors, and unpaid family 

workers reported in the CPS are incorporated into the 

labor input measure; remaining data are obtained from 

various sources.10 

Construction of the multifactor productivity labor composition measure begins with estimates of the number of 

hours worked by each type of worker, based on CPS data. 

The BLS assembles data on workers’ hours, classified by 

their educational attainment, age, and gender, using actual 

wage averages for weights. The sum, over all groups, of the 

growth rates of hours, multiplied by the labor cost shares, 

gives the growth in adjusted labor input. Subtracting from 

this the growth in total (unweighted) hours yields the 

growth in labor composition.11 

The same methods are used to construct the labor input 

measure for the U.S. manufacturing sector, except that no 

adjustment is made for labor composition (age, education, 
Monthly Labor Review • June 2010 5

and gender of the workforce) because the CPS sample size 

is too small for that purpose.12

Capital inputs. Capital inputs for private business and 

manufacturing multifactor productivity measures are similar. The BLS capital input measures include assets that are 

owned and operated by a business within the sector; rented 

capital services are included in intermediate inputs. Capital 

input measures the services derived from the stock of physical assets and software. Among the capital input measures 

are fixed business equipment, structures, inventories, and 

land. Financial assets, owner-occupied residential structures, and nonprofit capital are excluded from the capital 

input measures. The aggregate capital input measures are 

obtained by Tőrnqvist aggregation of the capital stocks 

for each type of asset within each of 60 NAICS industry 

groupings; estimated rental prices are used for each type of 

asset. Rental prices reflect the nominal rates of return and 

nominal rates of economic depreciation and revaluation for 

the specific types of assets. Rental prices are adjusted for 

the effects of taxes; rental prices of capital are computed 

for 18 three-digit NAICS industries within manufacturing. 

Data on investments in physical assets are obtained from 

the BEA.

13

Energy, materials, and purchased business services. In the 

manufacturing sector, inputs include intermediate inputs, 

as well as capital and labor inputs. Data on intermediate 

inputs (energy, materials, and purchased business services) are obtained from BEA's annual input-output tables. 

Tőrnqvist indexes of each of these three input classes are 

derived at the three-digit NAICS level and then aggregated to total manufacturing. For manufacturing, materials inputs are adjusted to exclude transactions between 

manufacturing establishments, to maintain consistency 

with the sectoral output concept.14

Nominal values of materials, fuels, and electricity and 

nominal quantities of electricity consumed are obtained 

from economic censuses and annual surveys conducted by 

the U.S. Bureau of the Census. Purchased business services 

are estimated with the use of benchmark input-output tables 

and other annual industry data from BEA. Prices for many 

service inputs are based on the BLS price programs and obtained from the National Income and Product Accounts.

Imported intermediate inputs. The BEA produces import 

matrices as supplementary tables to the annual inputoutput accounts. For each commodity, the import-matrix 

table shows the value of imports of that commodity used 

by each industry. Because such information is not available from most businesses, the estimates must be imputed 

from data available in the annual input-output accounts. 

The imputed import values are based on the assumption 

that each industry uses imports of a commodity in the 

same proportion as the ratio of imports to domestic supply 

of the same commodity. (Domestic supply represents the 

total amount of a commodity available for consumption 

within the United States; it equals domestic output, plus 

imports, less exports.) Using this assumption to calculate 

the estimates implies that whatever variability of import 

usage there is across industries is not based on industryspecific information.15

The BEA provided the BLS with detailed statistics on 

imported intermediates for this article. These data are not 

included in BEA published tables because their quality is 

significantly lower than that of the higher level aggregates 

in which they are included. Compared with these aggregates, the detailed statistics are more likely to be based on 

judgmental trends, on trends in the higher level aggregate, 

or on less reliable source data.16

The BEA data reveal trends in the shares of imported 

intermediate inputs. For all private industries, the share of 

intermediate inputs that is accounted for by imports grew 

from 8 percent in 1998 to more than 10 percent in 2006. 

Chart 1 shows that there was a decline in the share of imports used by private industries around the 2001 recession; 

however, beginning in 2002, the share increased steadily. 

Purchased materials account for the majority of imported 

intermediates, and their share grew steadily, again with a 

slight dip around the 2001 recession. Imported material 

inputs, which accounted for 15 percent of total materials 

used by private industries in 1998, saw their share grow to 

21 percent by 2006.17

Although it was once thought that services were not 

subject to offshoring, there is evidence that service inputs 

are now being imported. Imported service inputs accounted for 1.4 percent of total intermediates used by private industries in 1998 and 1.7 percent in 2006. However, 

imported service inputs accounted for roughly 3 percent 

of all service inputs used by private industries, a percentage that stayed relatively steady from 1998 to 2006. Interestingly, the share of energy inputs that are imported 

appears to be growing: three percent of all energy inputs 

used by private industries were imported in 1998, and 8 

percent were imported by 2006.18 However, imported energy inputs are less than 0.4 percent of total intermediates 

used by private industries.

Looking at the imported intermediate data by industry reveals that the manufacturing sector consumed more 

than 60 percent of all imported intermediates used by 
Imported Inputs and Productivity

6 Monthly Labor Review • June 2010

private industries. For the manufacturing sector, the share 

of intermediate inputs that is accounted for by imports is 

significantly larger than it is for all private industries, and it 

grew at a faster rate. The BLS uses the term sectoral intermediate inputs to denote total intermediates less domestically 

manufactured inputs. Chart 2 shows imported intermediates’ share of sectoral intermediate inputs, as well as the 

import share of total intermediates. The sectoral intermediate inputs for the BLS manufacturing sector are less than 

the total intermediates in the BEA annual input-output 

accounts because intermediates that are purchased from 

other firms within the U.S. manufacturing sector have been 

removed. Therefore, imports’ share of sectoral intermediates 

is greater than imports’ share of total intermediate inputs. 

The sectoral intermediate inputs for the manufacturing sector are 55 percent of the BEA total intermediates.

The data show that 24 percent of sectoral intermediates 

in manufacturing were imported in 1998; the percentage 

grew to almost 34 percent in 2006. Notice in chart 2 that, 

beginning in 2002, there has been a steady increase in the 

share of imported intermediates used by U.S. manufacturing firms relative to sectoral and total intermediates.19 As 

observed for the private business sector, imported materials accounted for the majority of imported intermediate 

inputs. However, service inputs also were imported by the 

manufacturing sector. Imported services’ share of sectoral 

intermediates in the manufacturing sector grew from 1.4 

percent in 1998 to 2.1 percent in 2006, while imported energy’s share grew slightly, from 0.1 percent to 0.3 percent, 

over the same period.

BLS multifactor productivity

Solow model of productivity. It is generally acknowledged 

that technical progress can best be captured with a totalfactor productivity concept. The most common model of 

total-factor productivity is credited to Robert M. Solow. 

First proposed in 1957, the Solow residual model evaluates technical progress as the difference between the 

growth rate of output and the weighted aggregate of the 

growth rates of each factor of production. This measure of 

disembodied technological change evaluates the expansion of the production possibilities frontier without the 

addition of resources. Mathematically, given a production 

function , the growth rate of total-factor productivity A can be written as 

 (1)

where Δ represents a time derivative, Y denotes real aggre-

 Chart 1. Imported intermediate inputs’ share of total intermediates, by type of input, private industries, 

1998–2006

Percent

12.0

11.0

10.0

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

Percent

1998 1999 2000 2001 2002 2003 2004 2005 2006

SOURCE: Bureau of Economic Analysis.

12.0

11.0

10.0

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

Imported energy Imported materials Imported services

 Y = f(X,t)

∑ ∆ ∆ ∆















 = − i i

i i

x

x

Y

Y

A

A β ,
Monthly Labor Review • June 2010 7

as well as all imported intermediate inputs and other domestic intermediate inputs produced outside the sector. 

Consequently, BLS multifactor productivity, ABLS, contains 

only two factor inputs—labor (L) and capital services 

(K)—and can be written as 

 (2)

or

  (3)

where YBLS is BLS real private business sector output, 

dlnABLS denotes the difference in logarithms of ABLS for 

successive years (lnA(BLS,t) – lnA(BLS,t-1)), and the weights 

for labor and capital, wi, are the averages of each factor’s 

nominal cost Ci relative to nominal output YN

BLS in two 

successive years, so that

 (4)

Because of this design, it is impossible to observe the impact of offshoring intermediate inputs on production. To 

incorporate intermediate inputs into the model, a sectoral 

gate output, Xi denotes the ith factor of production, and 

βi

 represents the corresponding elasticity of output. This 

productivity growth model requires well-defined concepts 

of output and inputs that correspond to a specified production process. To construct measures of productivity, a 

discrete approximation for the time derivatives20 must be 

made and cost-minimizing behavior is assumed in order 

to measure the i with cost shares.

BLS multifactor productivity for the private business sector. 

The BLS labor productivity measures for the private business sector compare output, measured as the real gross domestic product of all U.S. businesses, with hours worked 

by all U.S. workers who contribute to the production of 

that output. Real gross domestic product is measured by 

adding all exports and subtracting all imports from domestic final demand. Thus, imported intermediate inputs 

are excluded from the scope of the output measures, and 

as a result, the contribution of the labor hours worked 

overseas that produce the imported intermediate inputs 

also are absent from the analysis of U.S. productivity. The 

output measure used to construct the productivity measure for the private business sector removes the output of 

intermediate inputs produced and used within a sector, 

 Chart 2. Imports’ share of sectoral intermediate inputs and of total intermediates, by type of input, U.S. 

manufacturing, 1998–2006

55.0

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

0.0

1998 1999 2000 2001 2002 2003 2004 2005 2006

Percent Percent

SOURCE: Bureau of Labor Statistics, Bureau of Economic Analysis.

55.0

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

0.0

Imported energy Imported materials Imports’ share of 

total intermediates

Imported services

β ,

BLS

BLS

BLS

BLS

K

K w

L

L w

Y

Y

A

A L K

∆ ∆ ∆ ∆ = − −

d lnABLS = d lnYBLS – wL d lnL –wK d lnK,

.

•





















= +

−

−

= Y

C

Y

C w N

BLS,t

i,t

N

BLS,t

i,t

i L,K

1

1

2

1

,
Imported Inputs and Productivity

8 Monthly Labor Review • June 2010

























= +

−

−

=

Y

C

Y

C

w N

S ,t

j,t

N

S ,t

j,t

( j IE,IM,IS)

1

1

2

1

output concept must be used.

Private business sector multifactor productivity adjusted to 

include imports. Sectoral output removes from the value 

of output only intermediate inputs that are produced elsewhere within the sector, to eliminate double counting. Intermediate inputs that are produced outside of the sector 

(that is, imported intermediates) remain in output.21 To 

bring imported intermediate inputs inside the major-sector 

model framework requires not excluding them as a component of output and including them as a factor input to 

production. With imported intermediate inputs denoted as 

II, the production function becomes YS = f(L, K, II, t) and 

multifactor productivity can be written as 

 (5)

where the factor weights for imported intermediate inputs of energy (IE), materials (IM), and services (IS) are 

defined as 

 (6)

and an output adjustment ratio , used to correct the 

weights on labor and capital, is written as a two-period 

average:

 (7)

Algebraically working through the model yields an adjusted multifactor productivity measure that encompasses 

imported intermediate inputs in both the output and input indexes. Assuming that growth in sectoral output is 

a weighted average of growth in the BLS output measure 

and intermediate imports gives the multifactor productivity growth rate as a scalar of the existing BLS multifactor 

productivity growth rate:

 (8)

Table 1 presents growth rates for the components of 

the multifactor productivity model for the private business sector.22 Notice that imported intermediates grew 

faster than labor and capital in most years, except around 

the 2001 recession. The growth of imported intermediate inputs has an impact on the growth of sectoral output 

trends as well. Sectoral output grew somewhat faster than 

the published value-added output measure for all years 

except 2001 and 2002. The year-to-year growth rates of 

imported intermediates fluctuate quite a bit. Over the 

1997–2006 period, energy and service imports grew faster 

than imported materials. However, because of the small 

share of all imports held by energy and service imports 

in comparison with imported materials, the growth in 

imported materials drove the growth in total imported 

intermediate inputs.

Using BEA estimates of imported intermediate inputs 

yields the adjustment scalar for the private business sector multifactor productivity measures. Table 2 shows the 

results of adjusting the published BLS multifactor productivity data. Notice that, by incorporating the imported 

intermediate inputs into the multifactor productivity 

framework, the annual growth in private business sector 

multifactor productivity is reduced by 0.1 to 0.2 percentage point in all but two of the years shown. 

Substitution of imported intermediates for U.S. labor in the 

private business sector. The effects on labor productivity 

of substitution between imported intermediate inputs and 

U.S. hours worked are estimated with the Solow multifactor productivity equation. The growth in imported 

intermediate inputs, combined with both growth in capital inputs and technical change, directly influences labor 

productivity. Thus, labor productivity can be written as the 

sum of the intensity of each of the other input factors 

(increases in the factor’s quantities relative to domestically 

employed labor):

 (9)

Chart 3 shows the contributions to private business sector 

labor productivity of the remaining nonlabor factor inputs. 

From 1998 through 2002, year-to-year growth in capital 

services accounted for the majority of labor productivity 

growth. Beginning in 2003, capital’s contribution to labor 

productivity declined and was outpaced by multifactor 

productivity growth. Also, beginning in 2004, imported 

intermediate inputs contributed more to labor productivity growth than did capital growth. Again, the influence of 

imported material inputs dominated the contribution of 

all imported intermediate inputs.

The sectoral output approach reveals that, for the 

1997–2006 period, approximately 14 percent (0.37/2.56) 

of labor productivity growth was attributable to growth in 

imported intermediate inputs, 11 percent (0.27/2.56) to 

materials, 3 percent (0.08/2.56) to services, and less than 

0.5 percent (0.01/2.56) to energy. The following tabula-

∑ 















= − − − j L K S S d ln A d lnY θ w d lnL θ w d ln K wj d ln IIj

θ

d lnYS − d ln L =





 



 + − + 

 ∑ 















d ln AS θ wK dlnK− dlnL j wj d ln IIj d ln L

dlnAs = θ dlnABLS •

,





















= +

−

−

Y 1

BLS BLS 1

2

1

N

S ,t

N

,t

N

S ,t

N

,t Y

Y

Y θ •

,

•
Monthly Labor Review • June 2010 9

tion shows the contribution (average annual growth rates) 

of nonlabor inputs and multifactor productivity to labor 

productivity growth in the private business sector over 

that period:23

 Contribution

 to labor productivity

 Factor growth (percent)

 Output per unit of labor (including 

 imports)............................................... 2.56

Multifactor productivity (including 

 imports) ............................................... 1.31

Capital intensity ...................................... .88

 Imported intermediates........................ .37

 Imported materials............................... .27

 Imported services.................................. .08

 Imported energy ................................... .01

BLS multifactor productivity for the U.S. manufacturing sector. As mentioned earlier, BLS productivity measures 

for the manufacturing sector are constructed with the use 

of a sectoral output concept. Therefore, imported intermediates are within the productivity model framework. 

For the multifactor productivity measures, imported 

intermediate inputs are a component of measured output and intermediate inputs. To identify the impact of 

imported intermediates on manufacturing productivity, 

it is not necessary to adjust the measures to include imports; instead, the intermediates must be separated into 

domestic and imported components. This demarcation is 

achieved by using the BEA estimates of imported intermediates, which were provided to the BLS at the industry 

level of detail.

Table 3 presents the year-to-year growth rates and 

the average annual growth for the components of the 

manufacturing multifactor productivity model over the 

1997–2006 period. Notice that in most years labor inputs 

declined and imported intermediates grew faster than 

capital and domestic nonmanufactured intermediate inputs. Prior to the 2001 recession, there was strong growth 

in capital services, imported intermediates, and domestic 

nonmanufactured intermediates. However, as the table 

shows, domestic nonmanufactured intermediates were 

affected by the recession sooner than imported intermediates were. Also, imported intermediates were able to 

rebound after the recession, whereas domestic nonmanufactured inputs shrank through 2004. Over the entire 

1997–2006 period, labor and domestic nonmanufactured 

intermediates inputs declined, while capital services and 

imported intermediates grew.24

Table 4 compares the growth of domestic nonmanufactured intermediate inputs and imported intermediates by type of input. In general, imported intermediates 

showed stronger growth than domestic nonmanufactured 

inputs. It is interesting to note that domestic material inputs (excluding materials purchased from other manufacturing industries) declined in most years, while imported 

materials grew.

Growth of components of private business sector multifactor productivity, alternative output concepts, annual 

percent changes, 1997–2006

[Percent change from previous year]

Year Original 

output

Sectoral 

output

Labor Capital Imported 

intermediates

Imported 

energy

Imported 

materials

Imported 

services

1998.......................... 4.9 5.3 2.3 6.3 10.7 3.8 10.9 10.3

1999.......................... 5.2 5.4 2.7 6.5 8.5 9.2 8.3 9.3

2000.......................... 3.9 4.4 1.0 6.3 9.6 11.2 9.5 9.7

2001.......................... .5 .1 –1.4 4.6 –3.8 –1.9 –5.4 3.8

2002.......................... 1.5 1.4 –1.4 2.9 –.1 –6.5 –1.3 5.5

2003.......................... 3.1 3.1 –.3 2.3 3.1 3.4 4.4 –2.4

2004.......................... 4.3 4.9 1.5 2.3 11.8 27.3 10.3 16.4

2005.......................... 3.7 3.9 1.8 2.5 5.7 13.9 5.6 4.7

2006.......................... 3.2 3.4 2.6 2.7 4.9 2.8 4.7 6.8

Average annual

 percent change,

 1997–2006 ......... 3.4 3.5 1.0 4.0 5.5 6.6 5.1 7.0

Table 1.
Imported Inputs and Productivity

10 Monthly Labor Review • June 2010

relative to nominal output YN in 2 successive years and are 

given by

 (11)

The growth in imported intermediate inputs, combined 

with growth in capital inputs, growth in domestic intermediate inputs, and technical change, directly influence 

labor productivity. Thus, labor productivity can be written 

as the sum of the intensity of each of the other input factors (increases in the factors’ quantities relative to domestically employed labor):

 (12)

In the preceding equation, wDIj denotes the weights on 

domestic intermediates j = E,M,S and wIIj denotes the 

weights on imported intermediates j = E,M,S. 

Chart 5 shows the contributions of nonlabor input factors to the year-to-year growth of manufacturing sector 

labor productivity. Notice that in most years multifactor 

productivity contributed the most to labor productivity 

growth. Notice also that growth in capital services contributed to labor productivity growth prior to 2004, but 

very little thereafter. Imported intermediate inputs made 

a relatively constant contribution to labor productivity 

growth in all years, with the exception of 2001. Over the 

period 1997–2006, multifactor productivity accounted 

for 45 percent (1.79/3.96) of productivity growth and 

imported intermediate inputs accounted for 23 percent 

(.92/3.96). The following tabulation shows the contributions of nonlabor factor inputs to the average annual 

growth of labor productivity in the manufacturing sector 

over the entire period from 1997 to 2006:

 Average annual

 Factor growth (percent)

 Output per unit of labor......................... 3.96

Multifactor productivity ............................. 1.79

Capital intensity ......................................... .64

Domestic intermediates.............................. .65

Imported intermediates.............................. .92

 Imported materials............................... .80

 Imported services................................. .10

 Imported energy................................... .01

THIS ARTICLE DEVELOPS A FRAMEWORK for estimating the effects of imported intermediate inputs on U.S. 

major-sector labor productivity. The production model 

used to calculate the BLS private business sector multifacChart 4 presents the trends in constant-dollar factor input 

costs for the U.S. manufacturing sector. Note that labor represents the highest cost and was constant prior to the 2001 

recession, when it declined together with falling employment 

in manufacturing. Energy and imported services represented 

a very small portion of the overall factor costs in manufacturing and were relatively constant over the 1997–2006 period. 

Interestingly, the cost of imported materials increased over 

the period, while the cost of domestic nonmanufactured 

materials declined. The factor costs of capital services and 

purchased domestic services increased somewhat. 

Substitution of imported intermediates for U.S. labor in the 

manufacturing sector. In this subsection, the effects of 

imported intermediate inputs on labor productivity are 

estimated. The model used by the BLS to measure multifactor productivity for the U.S. manufacturing sector can 

be written as 

 (10)

where YG is real sectoral output for the manufacturing sector; dlnAG denotes the difference in logarithms of AG for 

successive years (lnA(G,t) – lnA(G,t-1)); and the weights for 

labor, capital, energy, materials, and purchased business 

services, wi, are the averages of each factor’s nominal cost 

dlnAG = dlnYG − wL dlnL − wK dlnK

−wE d ln E − wM dln M − wS dlnS

Multifactor productivity growth for the private 

business sector, by alternative treatment of 

imports, annual percent changes, 1997–2006 

[Percent change from previous year]

 Year 

Official BLS

measure

(excludes 

imported 

intermediate 

inputs)

Adjusted

measure

(includes 

imported 

intermediate 

inputs) 

Difference 

(adjusted 

measure

minus

official 

measure)

1998.................................. 1.3 1.2 –.1

1999.................................. 1.3 1.2 –.1

2000.................................. 1.3 1.2 –.1

2001.................................. .1 .1 .0

2002.................................. 1.7 1.5 –.2

2003.................................. 2.6 2.4 –.2

2004.................................. 2.5 2.3 –.2

2005.................................. 1.6 1.5 –.1

2006.................................. .5 .5 .0

Average annual

 percent change,

 1997–2006 ................. 1.4 1.3 –.1

Table 2. G





















= +

−

−

= Y

C

Y

C

w N

G,t

i t

N

G, t

i t

i L K E M S 1

, , 1

2

1

, , , , •

,

∑ ∑ • 



 



  + −



 



 − j j jwDIj dlnDIj dlnL wI I dlnIIj dlnL

− = + + 















d Y d L d A wK d K d L G ln ln ln ln ln G

−
Monthly Labor Review • June 2010 11

tor productivity measures is expanded to treat imported 

intermediate inputs as an input, rather than as a subtraction from output. Once the imported intermediate inputs 

are placed inside the framework, the Solow multifactor 

productivity equation is used to estimate the effects on 

labor productivity of substitution between imported intermediate inputs and U.S. hours worked. Separate effects 

are estimated for imported energy, materials, and services. 

The data show that imports increased as a share of total 

intermediates used by private industries, from 8 percent 

in 1998 to 10 percent in 2006. By including imported 

intermediates in the multifactor productivity model, the 

adjusted private business sector multifactor productivity 

is seen to have grown 0.1 percent to 0.2 percent per year 

more slowly than is indicated by the BLS published series. 

Also, the growth in imported intermediate inputs is estimated to have contributed 14 percent to the average annual growth of labor productivity for the private business 

sector from 1997 to 2006.

On the basis of the analysis presented here, it likely is 

not a good idea to alter the labor productivity model to incorporate imported intermediates, because then the trend 

could be considered biased to the extent that output would 

reflect the growth in imported intermediates while labor 

input would not include the corresponding hours worked 

overseas. However, as is attested to by the aforementioned 

0.1-percent to 0.2-percent less growth than the BLS published series, the role of imported intermediates can be 

meaningfully assessed in the multifactor productivity model. 

Because more than 60 percent of imported intermediate inputs purchased by private industries are used by the 

manufacturing sector, the role of imported intermediates 

in the U.S. manufacturing sector is also evaluated. The BLS

methods for constructing manufacturing multifactor productivity include intermediates in the model framework. 

Therefore, the imported components are isolated to assess 

their impact on labor productivity. The data reveal that, 

over the 1998–2006 period, imported intermediate inputs 

grew as a share of total intermediate inputs. In addition, 

labor inputs and domestic nonmanufactured inputs declined over the entire period while capital services and 

imported intermediates grew. Finally, the analysis shows 

that growth in imported intermediate inputs contributed 

23 percent to the average annual growth in labor productivity in the manufacturing sector.

Questions have been raised concerning whether the 

quantity of imported materials is measured accurately. 

The issue is that foreign imports may provide input of the 

 Chart 3. Labor productivity growth, by contributing input factors, private business sector, annual percent 

changes, 1997–2006

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

–0.5

1998 1999 2000 2001 2002 2003 2004 2005 2006

Percent change

from previous year

Percent change

from previous year

SOURCE: Bureau of Labor Statistics, Bureau of Economic Analysis (unpublished import data).

Imported services Imported materials

Adjusted multifactor productivity

Imported energy

Capital

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

–0.5
Imported Inputs and Productivity

12 Monthly Labor Review • June 2010

same quality at a lower price than domestic products and 

the advantage of substituting foreign for domestic inputs 

may not be reflected in the productivity statistics. Prices of 

imports enter the BLS business sector productivity measures when they are removed from real GDP by the BEA. 

Therefore, the impact of any possible inaccuracy in the 

measurement of import prices on the BLS business sector 

productivity measures would be weighted by the relative 

importance of imported intermediate inputs in measured 

business sector output, which has grown from 8 percent in 

1998 to almost 11 percent in 2006. Prices of imports enter the BLS manufacturing sector multifactor productivity 

model when imports are included in the construction of 

purchased intermediate inputs. Thus, in the manufacturing sector, the impact of any possible inaccuracy in the 

measurement of import prices on the BLS multifactor 

productivity measures would be weighted by the relative 

importance of imports in measured intermediate inputs 

in that sector: 12 percent to 18 percent. Research is being 

carried out on this topic25 both within and outside the 

statistical agencies, but economic analysis has not reached 

a definitive conclusion concerning its importance.

Multifactor productivity and components in the U.S. manufacturing sector, annual percent changes, 1997–2006

[Percent change from previous year]

 Year

Sectoral 

output Labor Capital

Domestic 

intermediates

Imported 

intermediates

Multifactor 

productivity

1998..................................... 5.2 –0.2 5.0 2.3 9.6 2.3

1999..................................... 3.8 –.7 4.1 4.2 7.1 .8

2000..................................... 2.7 –1.3 3.1 –4.1 5.5 3.5

2001..................................... –5.1 –6.5 1.5 –3.0 –4.9 –1.3

2002..................................... –.7 –7.1 .6 –4.4 –2.1 3.7

2003..................................... 1.0 –4.9 .0 –1.3 2.6 2.8

2004..................................... 1.7 –.5 –.6 –5.2 8.7 2.6

2005..................................... 3.7 –1.1 .0 7.7 4.9 .4

2006..................................... 1.8 .6 .5 –2.0 4.3 1.6

Average annual percent 

change, 1997–2006...... 1.5 –2.4 1.6 –.7 3.9 1.8

NOTE: Combined intermediates are constructed as a weighted aggregate of energy, materials, and purchased services.

Table 3.

Comparison of imported and domestic intermediate inputs, by type of input, U.S. manufacturing sector, annual percent 

changes, 1997–2006

 [Percent change from previous year]

 Year

Total 

intermediates Energy Materials Services

Domestic Imported Domestic Imported Domestic Imported Domestic Imported

 1998.................................... 2.3 9.6 –2.5 –7.8 1.9 9.7 3.0 8.5

 1999.................................... 4.2 7.1 .1 .4 3.8 6.6 4.9 15.8

 2000.................................... –4.1 5.5 –5.0 –11.1 –10.1 5.9 –.1 1.5

 2001.................................... –3.0 –4.9 –9.5 –7.0 –6.1 –7.3 –.5 28.5

 2002.................................... –4.4 –2.1 –1.5 –1.2 –8.4 –2.1 –2.5 –1.8

 2003.................................... –1.3 2.6 –6.1 13.0 –4.9 3.2 1.1 –4.2

 2004.................................... –5.2 8.7 –2.2 35.1 –10.0 8.1 –2.9 13.9

 2005.................................... 7.7 4.9 8.1 25.1 7.4 4.6 7.9 6.4

 2006.................................... –2.0 4.3 –6.8 10.7 –7.4 3.9 1.7 8.2

Average annual 

 percent change, 

 1997–2006 ..................... –.7 3.9 –2.9 5.3 –3.9 3.5 1.4 8.1

NOTE: Combined intermediates are constructed as a weighted aggregate of energy, materials, and purchased services.

Table 4.
Monthly Labor Review • June 2010 13

 Chart 4. Input costs for the manufacturing sector, by type, 1998–2006

Billions 

of constant

 2000 dollars

1,200

1,000

800

600

400

200

0

1998 1999 2000 2001 2002 2003 2004 2005 2006

Billions

of constant

2000 dollars

SOURCE: Bureau of Labor Statistics, Bureau of Economic Analysis (unpublished import data).

 Chart 5. Labor productivity growth, by contributing nonlabor input factors, manufacturing sector, annual 

percent changes, 1997–2006

Percent change

from previous year

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

–1.0

–2.0

Percent change

from previous year

1998 1999 2000 2001 2002 2003 2004 2005 2006

SOURCE: Bureau of Labor Statistics, Bureau of Economic Analysis (unpublished import data).

Multifactor

productivity

Domestic intermediate 

intensity

Imported intermediate 

intensity

Capital intensity

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

–1.0

–2.0

1,200

1,000

800

600

400

200

0

Imported energy

Labor

Domestic energy

Imported materials

Capital services

Domestic materials

Imported services

Domestic services
Imported Inputs and Productivity

14 Monthly Labor Review • June 2010

Notes

ACKNOWLEDGMENT: The authors thank Erich Strassner and Robert Yuskavage of the Bureau of Economic Analysis for providing the 

import data necessary for this study. We also thank Steve Rosenthal 

and Randy Kinoshita for helpful comments and assistance. All views 

expressed in this article are those of the authors and do not necessarily 

reflect the views or policies of the Bureau of Labor Statistics. 

1 Robert M. Solow, “Technical Change and the Aggregate Production Function,” Review of Economics and Statistics, August 1957, pp. 

312–20. 

2 Annual input-output tables, as well as data on imported intermediate inputs, from the Bureau of Economic Analysis (BEA) are used in 

the analysis presented. (See Robert E. Yuskavage, Erich Strassner, and 

Gabriel W. Medeiros, “Domestic Outsourcing and Imported Inputs 

in the U.S. Economy: Insights from Integrated Economic Accounts,” 

paper prepared for the World Congress on National Accounts and 

Economic Performance (Arlington, VA, Bureau of Economic Analysis, 

May 15, 2008). 

3 Allan H. Young and Helen Stone Tice, “An Introduction to National Economic Accounting,” Survey of Current Business, March 1985, 

pp. 59–76.

4 The gross product of general government is the sum of government expenditures on compensation of general government employees and the general government consumption of fixed capital, which 

measures the services of general government fixed assets. Government 

expenditures on goods and services purchased from the private sector 

are not excluded from private business sector output. The gross product of private households is the compensation of paid employees of 

private households; the gross product of nonprofit institutions serving 

individuals is the compensation paid to employees of those institutions.

5 This value is measured as the sum of the consumption of fixed 

capital, indirect business taxes, and interest paid.

6 BLS data in this article originate in the multifactor productivity 

program and cover the private business sector, which differs from the 

business sector covered by the BLS quarterly labor productivity program in that the former excludes government enterprises. In addition, 

the multifactor productivity measures are available only on an annual 

basis.

7 The Current Employment Statistics (CES) survey is an establishment survey whose sample is benchmarked annually to levels based on 

administrative records of employees covered by State unemployment 

insurance tax records. Data on employee hours from establishments 

provide consistency with output data from industries and thus are well 

suited to producing industry-level measures. CES data on employment 

and average weekly hours paid for production workers in goods-producing industries and for nonsupervisory workers in service-providing 

industries are the building blocks of labor input.

8 Information from the BLS National Compensation Survey program is used to construct the ratio of hours worked to hours paid. Prior 

to 2000, the annual Hours at Work Survey was used.

9 In August 2004, the BLS introduced this new method of constructing estimates of hours for nonproduction and supervisory workers; see Lucy P. Eldridge, Marilyn E. Manser, and Phyllis F. Otto, 

“Alternative measures of supervisory employee hours and productivity 

growth,” Monthly Labor Review, April 2004, pp. 9–28.

10 Employment counts for employees in agricultural services, forestry, and fishing are reported from the BLS QCEW program and are 

based on administrative records from the unemployment insurance 

system.

11 Additional information concerning data sources and methods 

of measuring labor composition can be found at www.bls.gov/mfp/

mprlabor.pdf and in Labor Composition and U.S. Productivity Growth, 

1948–90, Bulletin 2426 (Bureau of Labor Statistics, December 1993).

12 The BLS is investigating the possibility of constructing labor 

composition estimates for the manufacturing sector productivity 

measures.

13 See “Multifactor Productivity Trends, 2007,” news release 09–

0302 (Bureau of Labor Statistics, March 25, 2009).

14 A nonprofit adjustment is made to intermediate inputs, but not 

to imported intermediates, because it is doubtful that nonprofits use a 

significant amount of imported intermediates. Note, however, that, absent a nonprofit adjustment to imported intermediates, the importance 

of imports may be slightly overstated.

15 Erich H. Strassner, Robert E. Yuskavage, and Jennifer Lee, 

“Imported Inputs and Industry Contributions to Economic Growth: 

An Assessment of Alternative Approaches,” paper presented at the 

Conference on Measurement Issues Arising from the Growth of 

Globalization, Washington, DC, Nov. 6–7, 2009. This study uses International Transaction Account data from the BEA to assess the import comparability assumption. The authors find that real imported 

materials may be understated in the annual input-output accounts. 

However, they indicate that the assumption provides reasonable results at the aggregate level. In another paper presented at the same 

conference (“Evaluating Estimates of Materials Offshoring from 

U.S. Manufacturing”), Robert C. Feenstra and J. Bradford Jensen use 

an alternative method for allocating imported input across industries 

to derive imported intermediates. Comparing the results with the 

BEA import matrix that uses the comparability assumption, Feenstra 

and Jensen find differences between the two approaches and identify 

cells in the input-output table in which the differences are greatest. 

Unfortunately, data limitations prevent them from resolving those 

differences.

16 Notes about the imported intermediate input data are from BEA

documentation that accompanied the data.

17 Imported materials inputs include crude petroleum as a raw material for the refining and coal products industry. The increase in crude 

petroleum prices over the 1998–2006 period could be responsible for 

the increase in imported materials’ share of intermediate inputs used 

by private industries and for the increase in imported materials’ share 

of intermediate inputs in the manufacturing sector.

18 Crude oil is classified as a nonenergy material input to U.S. refineries, rather than an energy input.

19 In 2006, total materials imported by the petroleum industry accounted for 34 percent of material imports by the manufacturing sector. Over the 1997–2006 period, the price of imported intermediates 

for the petroleum industry grew 14 percent, compared with the 4-percent average growth of prices in the manufacturing sector as a whole. 

20 W. Erwin Diewert, “Exact and Superlative Index Numbers,” 

Journal of Econometrics, vol. 4, 1976, pp. 15–145.

21 Evsey Domar, “On the Measurement of Technological Change,” 

Economic Journal, vol. 71, 1961, pp. 709–29. 

22 The time series does not cover the business cycles sufficiently to 

divide the data into subperiods that would allow a meaningful analy-
Monthly Labor Review • June 2010 15

sis. A categorization of the data into subperiods of 1997–2000 and 

2001–2006, as well as 1997–2002 and 2003–2006, and a comparison 

of results revealed a high sensitivity to the years into which the data 

were divided. Accordingly, no subperiod analysis is presented in this 

article.

23 Note that because output has been expanded to include imports, 

labor productivity growth is 2.6 percent per year, rather than 2.4 percent per year.

24 Christopher Kurz and Paul Lengermann, “Outsourcing and U.S.

Economic Growth: The Role of Imported Intermediates,” paper presented at the 2008 World Congress on National Accounts, May 12–17, 

2008, Washington, DC, construct a gross output productivity measure 

in order to keep U.S. manufactured intermediates in the model. The 

Kurz-Lengermann model allows an analysis of the shift from domestic 

to imported intermediate inputs.

25 See, for example, papers presented at the Conference on Measurement Issues Arising from the Growth of Globalization, sponsored 

by the Upjohn Institute, Washington, DC, November 6–7, 2009.