Draft -- comments are welcome
Impacts of Information Technology on Productivity and Linkage of the US Economy*
January 30, 2005
The 15th International Input-output Conference 27 June – 1 July 2005 Beijing, P.R.China
This paper examines structural changes in the US economy in the context of interindustry linkages.
Structural changes are studied in terms of factor saving in the input-output accounting which is in concept
equivalent to productivity growth but whose sign of change is opposite. While the conventional growth
accounting has developed to trace detailed industry sources of productivity growth, its methodology
isolates each industry from the rest. On the other hand, the input-output accounting framework has inter-
industry relations as its essential key features and can be extended smoothly to factor saving analysis.
This thesis reaches three conclusions. First, the I-O accounting produces comparable results in
factor saving as in productivity growth. This paper shows the average annual rate of factor saving was -0.91
percent for 1987-1995 and -1.75 percent for 1995-2000. These figures are larger than the rates of
productivity growth based on the growth accounting but the extent of difference is not very large. The fast
growth in factor saving, particularly for the latter period, is not only noticeable in size but also qualitatively
significant in the sense that active output growth was not accompanied by price increases. Second,
Information Technology industries made substantial contributions to reduce inflation as well as to save
factors by supplying cheaper intermediate inputs to the industries. The IT intermediate inputs contribute to
factor saving by -0.20 percent for 1987 to 1996 and -0.41 percent for 1995-2000. Considering the small
size of IT intermediate inputs, the contribution of IT intermediate inputs is significantly large. Third, the
inter-industry context of I-O accounting provides a fertile ground to investigate the role of sectors in factor
saving and output growth. This paper points out that, while the contraction of the manufacturing sector is
taken as a serious problem, the expansion of trade and transportation which function as a partial operation
of the manufacturing sector tends to be overlooked. Furthermore, the manufacturing sector contributes
significantly to factor saving, while the services sector does so to employment, implying their cooperative
relation which is in some sense a division of labor in an economy-wide scale.
* This paper is a revised version of the PhD dissertation paper which was approved by the University of Notre
Dame, IN, USA, in November 2004. The original paper can be downloaded from the library of U. Notre Dame
(http://lib.nd.edu) under the author name “Kim, Seok-Hyeon” or the same title name.
† Associate Research Fellow of Science and Technology Institute, Seoul, South Korea; email:
email@example.com; address: Science and Technology Institute, 395-70 Shindaebang-dong, 26th Fl. Special Construction
Center Bldg. Seoul 156-714, South Korea
The beginning of the 1980s was a gloomy period for the US economy. Financial markets were subject to
continuous upheavals of crunches and crises, and the accumulating deficits both in the government and in
the trade account led to a rather pessimistic scenario of the US economy. Japan’s and Germany’s strenuous
innovations were taken as a serious threat to the competitiveness of the US economy in high-end markets
such as cars and electronics. And the overseas outsourcing of the manufacturing also destabilized the job
market of the US economy and resulted in sizable unemployment and consequently frequent strikes in a
After the painful recovery period of the 1980s, the US economy started to taste the fruits of success
in the 1990s. The government made efforts to break the trend of rising budget deficits and signaled a sign
of a soft landing on the path to a balanced budget. While the trend of the outsourcing of factories and goods
continued, new high-technology businesses continued to start up and discovered a new promising market
and created a new source of wealth. These emerging businesses helped the US to regain its global
leadership in technology. In spite of the contraction of the manufacturing sector, services-providing sectors
continued to expand and contributed to create jobs. Despite the continued trend of the outsourcing of
manufacturing factories, the US economy increased jobs and GDP fast, resulting in a rapid rise of
productivity, and regaining the level of productivity growth of the golden period of the 1960s.
Dazzling innovations, which may appear intuitively obvious as in the information technology (IT)
sector in particular, can not easily be examined in formal economic analysis due to the abstract nature of
technology. Productivity, which can be defined as production capability of a unit factor, has long been the
most important toolkit for capturing the qualitative development of the economy, even before a rigorous
definition was made and a systematic compilation of necessary data started. The first theoretically founded
research of productivity dates back to Solow (1956; 1957), Nobel Laureate. He formulated total factor
productivity (TFP), which is certainly a breakthrough in the analysis of productivity, which was before
rather limited to labor productivity. By including capital as a factor, he defined technological development
as a residual of output growth unexplained by the growth of factors. However, a huge inexplicable residual
in the Solow model stimulated economists to clarify the details of the residual. Solow’s single national
growth accounting was generalized to cover industry-accounting and Solow’s simple concept of total factor
as the combination of labor and capital has become far more sophisticated. In addition to empirical
sophistication of the research, theoretic challenges to Solow’s simple neoclassical formulation have
continued, giving birth to endogenous growth theory, which modifies and elaborates the neoclassical
growth model, thanks to the economists such as Lucas (1988), Romer (1990), and Mankiw (1992), and
Aghion P. and P. Howitt, (1998).
In contrast with the efforts to understand technological progress in the growth accounting
framework, which assumes a certain form of a production function whose legitimacy is subject to questions,
more intuitive approaches have developed as well. Qualitative discourses, from individual case studies of
innovation to technology paradigms of the national economy, have competed with the growth accounting
approach. In this approach, technology is a rather complicated evolutionary process of innovations (Nelson
and Winter 1982). As it is hard to formulate evolution theory into a mathematical framework, birth and
death of business, technological trends, and industries are traced in terms of detailed cases of innovation,
leading firms or industries.
A union of the growth accounting approach and the qualitative discourses can be made at the input-
output (I-O) framework, initiated by Leontief (1951), Nobel Laureate. The Input-output framework
captures the factors (or factors’ share) supplied to each industry. This accounting fairly resembles a
factory’s production schedule that reflects and is constrained by technological potential of production.
Given that it is impossible to account for the current or possible production schedule of all the firms, the
input-output framework is almost the best accounting convention to capture the production schedules or
technological constraints of the economy.
The development of the input-output framework has enriched productivity analysis by tracing
productivity growth of each industry with a comprehensive definition of the factor (encompassing
intermediate inputs as well as capital and labor). Since industries never develop in a uniform way, the
importance of tracing industry-sources of change in output and productivity does not need further emphasis.
A difficulty is that a huge volume of data is needed and the theoretic underpinning for aggregation should
be further refined. Such a daunting task has been challenged by economists such as Jorgenson, Grilliches,
and Erwin (OECD 2001, Measuring Productivity) and resulted in industry-based productivity analysis.
As far as productivity by industry is concerned, the industry-accounting is superb empirically and
theoretically. However, the shortcoming of the growth accounting is still inherent in the industry scale.
Once factors are identified and reflected into the accounting, then each industry is again studied in isolation
from others. If we define more detailed kinds of factors (in particular intermediate inputs), then each
industry-accounting can reflect the inter-industry interaction through intermediate inputs. But the holistic
picture is not yet much visible and only the aggregation result based on a certain formula for which some
assumptions are unavoidable can be presented.
This paper focuses on the inter-industry relation as its key theme. The inter-industry relationship
can be analyzed in two ways. We can study the input structure of each industry as well as the allocation of
each input as a factor across industries. Based on the output multiplier concept which measures all the
outputs (including intermediate inputs) to meet a given basket of final commodities, we can analyze all the
reactions to final demands. The reactions on output initiated by the input structure of an industry is defined
as backward linkage while those results passed through the supply chain of a commodity is defined as
forward linkage. These two linkage concepts are basic instruments to analyze the structural change of the
This paper also utilizes I-O analysis to develop an alternative measurement of productivity growth
or factor saving. Under certain plausible assumptions, it is possible to construct mathematical formula
connecting prime factors (labor and capital) and final expenditures (GDP) by way of the output multiplier.
Conceptually, factor saving which is defined as the tendency of less prime factors to produce a unit final
output is not different from productivity growth except the sign of change. But in order to emphasize the
methodological difference, the term factor saving will be preferred when it is discussed in the framework of
interindustry linkages. And the term productivity will be preferred in the growth accounting. Since the
output multiplier is also the key instrument in measuring backward and forward linkage, not only the final
results of factor saving but also the whole structure of the relations and the change of the structure that lead
to a certain degree of factor saving can be understood. Since technological progress includes a network
aspect of cooperation, the I-O framework can provide quite rich resources for understanding technological
progress or, more neutrally, the structural change of the economy.
As this paper is concerned with a holistic aspect of the economy, many questions will be explicitly
and implicitly raised and answered. But among many themes or questions, the following ones and
consequent answers summarize well the main contribution of this paper.
(1) Can the I-O framework provide an alternative accounting of productivity growth called factor
saving and how is this alternative method related to the conventional growth accounting?
(2) If the development of the economy is not uniform across industries but is led by a certain group
of industries equipped with new technology and with new kinds of products, how can we identify those in a
quantitative framework? And how can we specify the contribution of those industries to the economy or to
other industries? Regarding this question, this paper plans to confirm the notion that intuitively obvious
progress and influence of IT sectors can be comprehensively and precisely captured in the I-O framework.
(3) Can this analysis provide a quantitative framework or view to understand the relation between
goods (more specifically manufacturing) sectors and service sectors? While the tendency of the contraction
of the manufacturing sector and the expansion of the services sector is agreed well to, its implication or the
interpretation is yet controversial. The aforementioned factor saving analysis can contribute to the
understanding of the sectoral relations in terms of the factor saving. This analysis can decompose factor
saving into the detailed sources that are carried through chain relations of intermediate inputs (otherwise
saying forward and backward linkage).
The main body of this paper from section 2 to section 4, followed by Section 5 conclusion, is
organized as follows. Section 2 Performances of the US economy and the IT sector examines the recent
structural change in the US economy focusing on several large sectors and the IT sector. To gain insights
on the US economy, the analysis of output and a prime factor labor and the relationship between them will
Section 3 Industry Productivity and Aggregation provides the method and empirical analysis of
productivity based on the growth accounting. This section can be a simplified version of the recent work
made by Jorgenson, Ho, and Stiroh (2003; 2004) (shortly, JHS) in the sense that the basic data sets are
quite alike and the methodology is almost the same except rather a simplified specification of factors of this
paper. But the classification of industries is more detailed than JHS. Their research serves as a benchmark
to verify the legitimacy of the data and the validity of the results of this paper.
Section 4 Interindustry Linkage and Factor Saving is the main contribution of this paper. Backward
and forward linkage of each industry and factor saving carried through the linkages is analyzed. Since this
section uses almost the same sources of data and classification of industries of section 3, section 4 also
investigate the different empirical implications due to the methodological difference of the growth
accounting and the factor saving analysis.
The research in this paper covers different methodologies, large and small industries, and various
angles to see the inter-industry structure of the US economy. In terms of immense efforts required for such
a task, this paper follows the tradition of Leontief (1951) and Carter (1970). The author believes that the
methodology taken in this paper can shed new light on the progress of the economy and hopes that the
empirical details of this paper may make easy and expedite interindustry analyses.
2 Performances of the US economy and the IT sector
GDP growth by Sector
The BEA (Bureau of Economic Analysis, Department of Commerce)’s Gross Product by Industry (shortly,
GPI) is the most authoritative industry accounts in the US. Based on the SIC of about two-digit depth, the
data provides very detailed accounts of output and factors by industry. For output measurements, GPI
provides both Gross Output (GO) (shipments value or sales in concept) and Gross Product Originating
(GPO or Value Added as GO net intermediate inputs) in both constant and current dollars.1 While the
former is fully utilized in the measurement of productivity as in the next section, the latter is used widely as
a performance index of the economy. In this section where the main concern is the sectoral performance of
the US economy, GPO will be taken as the output measurement.
Since sectoral output GO is a combination of numerous commodities, we need to use constant
dollar output measurements for aggregation of commodities to get quantity measurements. Constant dollar
output measurement of GO in the GPI is based on the Fisher-ideal chain-weight index which is the
geometric average of the Laspeyres and the Paache index. 2 This chain-weight index is introduced to correct
the substitution bias originating from the fixed commodity basket of the Laspeyres or the Paache index. In
the US, the BEA introduced the tenth comprehensive revision of the NIPA (effective at the end of 1995)
with the Fisher chain-type measurements of real output instead of fixed-weight measurements (Landfeld
and Parker 1995, Survey of Current Business (henceforth, Survey)).
The constant dollar measurement of GPO in GPI is based on the double deflation method, which is
in concept deflated GO net deflated intermediate inputs (M).3 However, since some aggregates considered
in this section are not available directly from GPI, they are made by simply adding constant dollar GPOs
available from GPI. A simple addition of chain-weighted outputs is not methodologically robust but if
prices do not vary widely across sectors (which is true for highly aggregated sectors), errors are negligible.
According to GPI, the US economy experienced a long period of expansion from 1982 to 1990 and,
after a short period of downturn in 1991, another expansion from 1991 to 2000 until it reached a downturn
1 GPO provided by the BEA is slightly different from Value added provided by the US CENSUS; that is,
while “other services” (SIC 89) is regarded as intermediate inputs by the BEA, it is not regarded as intermediate inputs
by the CENSUS. Thus, for some industries, GPO can be larger than VA (ESA, 1999, Emerging Digital Economy II,
Appendix to Chapter II)
2 More detailed explanation of quantity measurements of outputs (GO and GPO) is well illustrated in System
of National Accounts 1993 by UN.
3 See Lum and Yuskavage (1997)’s article in Survey published by the BEA for the exact definition of
constant dollar measurement of GPO.
in 2001 as seen in Table 2.1.4 The intertemporal change of an economy is known to be best understood
when it is analyzed by the period from peak to peak (Baumol and McLennan 1985). In a similar vein, the
period of a whole business cycle from trough to trough in this section is adequate to analyze the
intertemporal change of the US economy. Thus the two business cycles, 1982-1991 and 1991-2001, are
taken for intertemporal comparison of the performance of the US economy. But two other periods, 1987-
1995 and 1995-2000, are also taken for the period average of growth; first because in the forthcoming study
of productivity the time span is limited by the coverage of data of prime factors; second because the year
1995-2000 is particularly regarded as the peak of the latest business cycle as in JHS (acronym of Jorgenson,
Ho, and Stiroh 2002, 2003) and in Digital Economy (Department of Commerce, Economics and Statistics
Analysis, 1998, 1999, 2000, 2002, 2003)
Table 2.1 Annual growth rates of real GPO by large sector
4.3 -5.7 4.9 7.8 4.4 6.8 2.3 3.1
7.3 17.4 16.9 2.3 4.9 10.2 4.3
3.8 10.6 2.0 3.8 1.9 5.8 2.0 4.8
3.4 1.0 -1.5 -1.4 -1.5 7.3 2.6 3.4 2.3
3.4 2.7 8.6 9.0 10.2
-2.9 6.0 5.1
4.2 4.7 9.5 3.8 4.0 6.7 3.4 6.3
-0.5 -4.6 -4.4 -1.8 3.4 1.7 1.6 -0.7 0.4
3.0 1.4 1.7 1.8 2.3 4.5 2.1 2.9
2.7 0.9 5.5 1.0 3.7 1.9 2.4 1.9
4.0 7.6 9.4 4.9 5.2 6.2 1.4 2.8
2.7 -1.0 8.9 3.5 4.7 2.3 3.4 3.6
3.6 4.5 4.7 -0.5 5.0 8.2 3.1 3.6
4.4 4.5 8.6 1.3 0.4 9.3 5.9 4.3
4.1 3.7 6.3 2.8 7.2 6.3 4.1 4.1
0.3 -0.6 -5.2 -7.1 -0.2 2.4 2.8 0.9 1.7
Addendum: Period Average
3.4 2.9 5.0 1.2 3.9 5.1 3.4 3.6
3.5 3.0 3.9 2.4 4.1 4.3 2.9 4.2
3.3 2.8 6.0 0.2 3.7 5.8 3.8 3.1
3.2 2.2 5.3 0.7 4.2 5.2 3.4 3.4
2.7 1.3 3.7 1.4 4.1 3.4 2.2 3.1
Source: Author’s compilation based on BEA, Gross Product by Industry.
Notes: Units are percentage. See Appendix Table for classification details. AMC is based on Agriculture, Mining, and
Construction; Md is Manufacturing of durable goods; Mn is Manufacturing of nondurable goods; TCU is Transportation,
Communication, and Utilities, or the SIC E category; Trade is Wholesale and Retail or the SIC F category; FIRE is Finance, Insurance,
and Real estate or the SIC G category. Services is the SIC I category. Gov is government administration and government enterprises.
The former business cycle recorded a 3.5 percent average annual rate of growth. In particular, the
beginning years of the period recorded rapid growths, including an outstanding growth rate of 7.3 percent
in 1984, in comparison with the later years. The recession in 1991 was short in time and mild in degree
with a -0.5 percent growth rate. Particularly, the latter business cycle for 1991-2001 (with a 3.3 percent
average annual growth rate) has been paid a lot of attention because of its quality characterized with low
inflation contributed by the information technology industries. The performance of the economy for the
latter business cycle is concentrated in the period of 1995-2000, recording a 4.0 percent rate of growth.
Since the year 2001 when the economy recorded only a marginal rate of growth, the economy has not yet
showed an undoubted sign of recovery.
4 This observation of business cycles is supported by the NBER’s comprehensive report of business cycle
If we take a look at sectors in the same table above, we can observe that Md, TCU, Trade, and
Services performed better than the economy average for the whole period 1982-2001. In particular, Md
(Manufacturing of Durable Goods) performed the best for 1991-2001, recording the highest growth rate of
6.0 percent; if we narrow down to the period of 1995-2000, the growth rate of Md is even more remarkable
recording 7.9 percent. Such an outstanding performance of Md is largely associated with the fast expansion
of Information Technology (IT) industries. Furthermore, the Trade sector (Wholesale and Retail), which
packages and distributes commodities, shows the highest growth rate of 5.0 percent for 1982-2001 and 8.1
percent for 1995-2000. This fast growth of the Trade sector is also related to the IT sector because a bulk of
IT commodities are distributed by the Trade sector. The three sectors, TCU (Transportation,
Communication, and Utility), FIRE (Finance, Insurance, and Real Estate), and Services, in order of
performance, record about the economy’s average in the growth rate for 1982-2001. Thus we can see that
goods-producing sectors experience divergence within themselves; while Md expands fast, AMC
(Agriculture, Mining, and Construction) and Mn (Manufacturing of Non-Durable Goods) relatively
contract. In particular, Mn records the worst performance in the average annual growth rate for 1982-2001
(1.2 percent) with its performance even worse in the latter business cycle (0.2 percent) than in the former.
Information Technology Industries
The last decade watched the unprecedented phenomena, called “New Economy”, in the US economy which
is characterized with high growth and minimal inflation. Although many issues remain controversial, it is
not of much doubt that IT industries did a great role to the admirable expansion of the economy. A branch
of the US Department of Commerce, ESA (Economics and Statistics Administration), noticed the
importance of IT in the 1990s and has continued to publish annual reports, Digital Economy, from 1998
through 2003, with only one skip in 2001, the year of the 9/11 terror. The first and the second publication
were titled Emerging Digital Economy. The change of the title reflects that over time IT sectors placed
themselves firmly in the economy. It is a rare case that government staffs continue to research about a
single sector with such a deep and broad extent. The importance of IT industries grew both in qualitative
and quantitative measures until 2001 when the economy turned into recession and the IT sector was hurt
with far more extent than the other industries. As the economy started to show a recovery since 2002, the
IT sector did so. But as of 2004, the economy and the IT sector have not shown a clear sign to resume the
success of the last decade.
According to Digital Economy (2002), the post-1995 was particularly outstanding regarding the IT
sector and the economy.5 Productivity grew at an annual average of 2.4 percent for 1995Q4-2001Q3,
5 The growth rates of two representative IT commodities, computer and semiconductors, are based on
hedonic prices, which have been developed by the BEA and adopted into the official data including the Digital
Economy in the measurement of sectoral output growth. Hedonic prices are not purely for actual measurements of
prices, rather a statistical estimation to reflect the rapid advance of quality of the IT products in terms of the calculation
speed of CPUs and the size of memory capability. Thus some criticism was raised about the possibility of the
overestimation of the growth of the IT sector and consequently that of the whole economy. However, according to
Landefeld and Grim (2000, Survey), the average price decline of 33 percent for 1995-1999 based on the hedonic
measurement is not absurd in comparison with the measurements of more quality-adjusted physical units (new
computers of much higher quality are sold at similar or even lower prices than the old ones) or various kinds of other
reaching that level of the golden period of the US economy (an annual average of 2.8 percent for 1948Q4-
1973Q4). In the meantime, productivity growth was only 1.4 percent on average. As a result of the latest
data, more economists such as Solow, who were skeptical about the qualitative supremacy of the US
economy of the mid 1990s, changed their views (Digital Economy, 2003, Executive Summary) and agreed
on the significant role of IT.
Although over the years the classification of IT industries and statistics have been modified and
updated in Digital Economy, the general concept of IT has not changed much. Digital Economy (2002)
defines IT industry as:
the industries that produce, process, and transmit information goods and services as either
intermediate demand (inputs to production of other industries) or as final products (goods and
services bought by consumers, business investors, government or for exports). The selected IT-
producing industries also include those that supply the goods and services necessary for the
Internet and electronic commerce (e-commerce) to operate—i.e., provide the products and services
for the Internet infrastructure. (Appendix to chapter III)
This definition is more or less supportive of the IT industry as “New IT” or the convergence of information
and communication as in Hall and Preston (1988). The IT sector is composed at large of the information
sector (hardware and software/services) which produces and processes digitalized information packets and
the communication sector (equipment/service) which transmits those digital information packets. While
details are not the same, the definition of the IT sector in the following section will succeed the definition
above in concept.
3 Industry Productivity and Aggregation
Methodology of Industry Productivity
Productivity calculation dates back to the neoclassical growth accounting by Solow (1956; 1957) and
Abramovitz (1956). Since Solow’s neoclassical growth accounting is more formally articulated than
Abramovits’s, Solow’s method is popularly cited. While there can be variations of the accounting, the
neoclassical growth accounting is still essentially the same as Solow’s one.
Take a look at the two different formulas for the aggregate economy as follows:
Y = Ka (AL)1-a , 0 < a <1; and
Y = AKa L1-a , 0 < a <1,
where Y, K, L, and A denote output (e.g. GDP), capital, labor, and technology respectively and AL is
called effective labor. In theory, under the assumption of perfect competition in output and factor markets,
a and (1-a) are the marginal rate of capital and the marginal rate of effective labor respectively and at the
same time the share of capital (K) in output and the share of (AL) respectively. This interpretation of a and
(1-a) in terms of share provides an empirical convenience in measuring both parameters. In labor-
augmented technology, technology factor affects the marginal rate of effective labor. Otherwise saying, (1-
a) already reflects technological change over time, which is hard to implement in empirical study. Thus
output-augmented technology is preferred in empirical studies.
By differentiating (3.2), we have
Ỳ = a K̀ + (1 – a) L̀ + À,
where the over-dot denotes the growth rate of the underlying variable. À is defined as productivity growth
in the economy.
The above equation can be used for industry productivity analysis called VA-accounting, if we take
Y as value added (VA) of an industry. However, in an industry scale approach, neglecting the role of
intermediate inputs (called secondary factors in contrast with prime factors such as labor and capital) is not
methodologically recommendable because of their important role in production process. Although GPO is
widely used to show the growth of sectors, GPO records only the final outcomes or the residuals of all
economic activities because GPO is Gross Output (GO) net Intermediate inputs (M). From GPO data, we
cannot see exactly why and how each sector produced such outcome. On the other hand, in the aggregate
economy, the growth accounting including intermediate inputs is methodologically erroneous because in
that case, prime factors (labor and capital) are counted twice, explicitly as themselves and implicitly as the
embodied components of intermediate inputs.
In the industry level, we need to broaden the definition of output as gross output (GO) which is
defined as the sum of intermediate inputs (M) and value added (VA) from each industry. The industry level
approach to the growth accounting can lead to the following equation:
X̀ = vM M̀ + vK K̀ + vL L̀ + À, with vM + vL + vK = 1,
where X is GO and each coefficient has the same meaning as the marginal product of each factor or the
share of each factor in output. All the coefficients sum up to one. Let’s call this equation the GO-
accounting. The GO-accounting is widely accepted to measure official industry productivities by many
countries, including the US whose statistical resources are rich (Note that this accounting needs information
of intermediate inputs and gross outputs).
One example that can contrast the above two accountings is the case of outsourcing. If an industry
or a firm separates one of its divisions and now purchases intermediate inputs from it, then M will get
larger while K and L will get smaller because of the allocated portions to the separated department. In this
situation, intermediate inputs turn out to substitute for prime factors for the original industry. While the
VA-accounting is likely to be insensitive to this substitution because VA may be decreased in proportion as
workers and capital decrease, the GO-accounting can capture the extent of the substitution effect.
Changing the notation of A into T, we can rewrite (3.4) in a translog approximation form (the
logarithmic difference between two discreet values) as follows:
∆Ln Xt = vM ∆Ln Mt + vL ∆Ln Lt + vK Ln∆ Kt + ∆LnTt, with vM + vL + vK = 1.
Under the competitive equilibrium assumption, the coefficient of each factor equals the marginal
product of the factor and is supposed to be the same as the share of returns to the factor in the total expense
for production. Thus in practice, each coefficient is approximated by each factor’s share in output. Value of
gross output or PXX (PX: the price of output) is composed of the following expenditures:
PX X = PM M + PL L + PK K+ B,
where P with the respective subscript denotes the price of output or factor and B is the indirect business tax.
Since B is not the expense that contributed to the production, in determining the shares, the total expense is
taken as PXX – B, similarly as in Jorgenson, Ho, and Stiroh (2002, 2003, shortly, JHS).6 Thus the shares are
vM = PM M / ( PX X – B);
vL = PL L / ( PX X – B);
vK = PK K / ( PX X – B).
In practice, since the Tornqvist index is the measurement of the change of a variable over adjacent periods,
the share is calculated as the average of the shares in two consecutive years.
Considering that productivity growth of an economy is not a uniform process across industries, we need
both industry-level productivity growth and economy-wide productivity growth. This can be completed by
a weighted sum of the industry GO-accountings with Domar-weights, which is adopted by JHS as well.
The Domar weight is the share of each industry’s VA in GDP (wi) divided by the share of each industry’s
VA in its GO (vVi). The Domar weight of each industry i is:
(3.8) wi / vVi
where vVi = vLi + vKi , with vLi + vKi defined as in the GO-accounting before.
The underlying rationale of this weight is to make the Domar-weighted sum of industrial
productivity growths equal the productivity growth of the hypothetically integrated economy where all the
transactions of intermediate inputs disappear. This hypothetically integrated economy is indeed the same as
the one to which VA-accounting applies at an aggregate scale, which can be proven analytically (Domar,
1961; cited from OECD Productivity Manual 2001, Annex 6). The introduction of the share of each
industry’s VA in GDP is easily understandable because we eventually want to calculate each industry’
contribution to the growth of GDP. The denominator part in the Domar-weight can be understood in an
intuitive way as follows. If the economy is composed of two industries A and B whose productivity growth
is one percent respectively and whose share is exactly a half of GDP, the simple average is one percent. If
two industries do not exchange any intermediate inputs, then the simple average is sensible. However, if
industry A provides intermediate inputs to industry B, the productivity gain of A should be added to some
degree to that of B. For B gets benefits of productivity gain by way of better or cheaper intermediate inputs
supplied by A. That is, the GO-accounting reflects a certain degree of productivity growth embodied in
intermediate inputs (M). The degree of reflection should be proportional to the share of intermediate inputs
of GO of industry B and so can be inversely proportional to the extent of VA in GO of industry B.
The Domar-weighted productivity (Tt) constructed from individual productivities (Tti) is in a
6 Indirect Business Tax B is excluded in calculation of shares in JHS. But the OECD’s manual Measuring
Productivity (2001) recommends for splitting the indirect business B proportionately into Labor part and capital part.
The difference between the two is the size of VA and that of GO in current dollar measurements. Consequently, the
coefficient or share for factor is different between the two methods. However, since the size of indirect business for
most industries is not very large in comparison with that of output, the differences in coefficients are not significant.