FRBNY Economic Policy Review / March 2001 37
What Drives
Productivity Growth?
n 1995, the U.S. economy started to experience a strong
resurgence in labor productivity growth. After growing only
1.3 percent per year from 1973 to 1995, labor productivity
growth jumped to 2.5 percent from 1995 to 1999 (see chart).1
This striking revival has hardly gone unnoticed, with
academics, policymakers, and the financial press hotly debating
competing explanations. Some commentators emphasize rapid
capital accumulation and the recent investment boom, others
point to deeper factors like fundamental technological change
in high-tech industries, and still others argue that cyclical
forces provide the primary explanation.2
This debate about the forces driving the U.S. economy
mirrors a larger debate between the neoclassical and new
growth theories regarding the sources of economic growth.
Economists have long disagreed about this vital question, and
the recent U.S. productivity revival presents an opportune
backdrop to review this debate.
In the neoclassical view, broadly defined capital
accumulation drives growth in the short run, but capital
eventually succumbs to diminishing returns, so long-run
productivity growth is entirely due to exogenous technical
progress. The new growth theory, however, moves beyond this
unsatisfying conclusion, arguing that productivity growth can
continue indefinitely without the elixir of exogenous, and
entirely unexplained, technical progress. Either by avoiding
Kevin J. Stiroh is a senior economist at the Federal Reserve Bank
of New York.
An earlier version of this article was written for Industry Canada while the author
was part of the Program on Technology and Economic Policy, Harvard University,
Cambridge, Massachusetts. The author thanks Mun Ho, Dale Jorgenson, Kenneth
Kuttner, Frank Lee, Charles Steindel, Lauren Stiroh, and two anonymous referees
for helpful comments on an earlier draft, Mike Fort and Amir Sufi for excellent
research assistance, and Industry Canada for financial support while the author
was in the Program on Technology and Economic Policy. The views expressed
are those of the author and do not necessarily reflect the position of the
Federal Reserve Bank of New York or the Federal Reserve System.
• Neoclassical and “new growth” theories offer
alternative explanations for productivity and
output growth.
• In the neoclassical view, exogenous
technical progress drives long-run productivity
growth since broadly defined capital
suffers from diminishing returns. In contrast,
the new growth models yield long-run
growth endogenously, either by avoiding
diminishing returns to capital or by
explaining technical progress
internally.
• Despite their differences, both views help
to explain the recent rise in U.S. productivity
growth. The methodological tools
developed by neoclassical economists
provide a means to measure the rate of
technical progress, while the models of
the new growth economists can provide
an internal explanation for technical
progress.
Kevin J. Stiroh
I
2 What Drives Productivity Growth?
diminishing returns to capital or by explaining technical
change internally, this framework offers an economic
explanation for sustained productivity and output growth.
Despite these divergent conclusions, the neoclassical and
new growth frameworks both contribute to our understanding
of the growth process. Using traditional neoclassical methods,
for example, Jorgenson and Stiroh (2000) and Oliner and
Sichel (2000) show that a combination of accelerating technical
progress in high-tech industries and the resultant investment in
information technology (IT) are driving recent productivity
gains in the United States. This type of neoclassical analysis
clearly illustrates what happened to the U.S. economy. It
cannot, however, explain why technical progress accelerated in
high-tech industries; this is a job left to the new growth
theorists. In this sense, each theory makes a significant
contribution to our understanding of productivity growth. The
sophisticated methodological tools developed by neoclassical
economists enable us to measure the rate of technical change,
while the sophisticated models of the new growth theorists
provide an internal explanation for the sources of technical
change. In the next section, I compare these alternative views
and discuss the useful role of each.
One important theme, common to both views, is that
investment is a fundamental part of the growth process.
Investment, moreover, may be defined broadly to include any
expenditure that provides productive payoffs in the future;
therefore, measures of human capital and research and
development (R&D) expenditures are now routinely included in
productivity analyses. Indeed, even the concept of tangible capital
is not static—the U.S. national accounts now treat software
expenditures as an investment good since software code is a
durable asset that contributes to production over several years.
In addition to this broadening of the investment concept, an
important part of the measurement process is the recognition
of the enormous heterogeneity of investment. For example, the
productive impact of investment in information technology
may be quite different from that of investment in structures. By
disaggregating investment and accounting for these
differences, economists can accurately gauge the productive
impact of input accumulation and thus isolate and gauge the
extent of technical change. In this article, I outline several
major conceptual and methodological issues related to
measuring production inputs and technical progress correctly.
The differences between neoclassical and new growth
theories also have a direct bearing on several specific topics that
have recently generated considerable interest. Later in this
article, I address two relevant issues. In particular, I present a
resolution to the computer productivity paradox and review
the renewed embodiment controversy. These topics are
important in their own right, and they illuminate the ongoing
debate over the sources of productivity and output growth.
Productivity Growth from the
Neoclassical and New Growth
Perspectives
Economic growth theory has enjoyed a revival in recent years,
with questions about the sources of productivity growth high on
the list of scholars, policymakers, and the business press. The
academic growth literature has bifurcated, however, into
arguments for two competing views—a neoclassical and a new
growth view.3
This section presents stylized models from each
perspective and discusses the strengths and weaknesses of each.
Broadly defined investment—which includes expenditures
on tangible assets, education, training, and other human
capital accumulation, as well as research and development—
plays a pivotal role in both frameworks, although investment’s
precise impact on productivity growth differs. Benefits from
investment may accrue only internally to the economic agent
that actually makes the investment, or the benefits may spill
over more broadly to others in the economy. As a preview of
the discussion, the idea that broadly defined capital generates
primarily internal and diminishing returns is the hallmark of
the neoclassical view, differentiating it from the new growth
theory’s focus on external and constant (or increasing) returns.
This leads to contrasting views of the investment-productivity
nexus and the potential for long-run growth.
-2
-1
0
1
2
3
4
5
1959-73 73-90 90-95 95-99
U.S. Labor Productivity Growth, 1959-99
Percent
Source: U.S. Department of Labor, Bureau of Labor Statistics.
Note: Both series refer to annual nonfarm business productivity.
Annual growth rate
6 Annual average growth
rate for subperiod
FRBNY Economic Policy Review / March 2001 39
The World of Neoclassical Growth
The standard neoclassical growth model is well known and will
be reviewed here only briefly. Seminal papers by Solow (1956,
1957) formalized the neoclassical model, integrated theory
with national account data, and formed the basis for much of
applied growth analysis.
The Basic Neoclassical Model
The link between output, , and capital services, , labor
input, , and labor-augmenting (Harrod-neutral) technical
progress, , is given by the familiar aggregate production
function
(1) ,
where the neoclassical production function is typically
assumed to have constant returns to scale, positive and
diminishing returns with respect to each input, and marginal
products of each input that approach zero (infinity) as each
input goes to infinity (zero).
Investment enters through the capital accumulation
equation, which governs the relationship between investment
in tangible assets, , and capital stock, , via the perpetual
inventory relationship
(2) ,
where is depreciation and can either be determined
endogenously by profit-maximizing firms or assumed to be
some fixed proportion of output.
Note that the production function includes a measure of
capital services, , while the perpetual inventory equation
defines the capital stock, . These two capital concepts are
closely linked but differ according to compositional changes in
aggregate investment. In the simplest neoclassical world with
one investment good, the two concepts are identical, but in a
world with many heterogeneous types of investment goods,
they differ. For example, a shift in investment toward high-tech
equipment with large marginal products leads capital services
to grow more quickly than capital stock. This important
distinction is discussed in detail later in this article.
The striking implication of the neoclassical model is that, in
the long run, per capita output and productivity growth are
driven entirely by growth in exogenous technical progress and
they are independent of other structural parameters like the
savings rate.4
If the savings rate and investment share increase,
for example, the long-run level of productivity rises but the
long-run growth rate eventually reflects only technical
progress. In this sense, the neoclassical growth model is not
Y K
L
T
Yt f Kt Tt Lt = ( ) , ⋅
I S
St ( ) 1 – δ St – 1 I + t = ⋅
δ It
K
S
really a model of long-run growth at all since productivity
growth is due to exogenous and entirely unexplained technical
progress. Nonetheless, the neoclassical model has proved to be
a useful tool for understanding the proximate factors that
contribute to output and productivity growth.5
Solow (1957) provides an explicit methodology for
measuring the rate of technical progress under the neoclassical
assumptions of competitive factor markets and input
exhaustion when technology is Hicks-neutral and output is
modeled as . In this case, the rate of Hicksneutral technical progress equals the famous Solow residual, or
total factor productivity (TFP) growth. This is defined as the
difference between output growth and the share-weighted
growth rates of primary inputs (capital and labor) as
(3) ,
where represents a first difference, is capital’s share of
national income, is labor’s share of national income, the
standard neoclassical assumptions imply , and
time subscripts are dropped for ease of exposition.6
Under the same assumptions, one can identify the sources
of average labor productivity (ALP) growth, defined as output
per hour worked, . Transforming equation 3 yields
(4)
,
where lowercase letters are per hour worked.
Growth in ALP, , depends on three factors. The first is
capital deepening, , which captures the increase in capital
services per hour. The second is the growth in labor quality,
which measures substitution toward workers with higher
marginal products and is defined as the difference between the
growth of labor input and the growth of hours worked
. The third is the growth in TFP, , defined
in equation 3, which captures the impact of technical change
and other factors that raise output growth beyond the
measured contribution of inputs.
If the neoclassical assumptions fail to hold, however, the
Solow residual will not measure only technical change. Other
factors that affect the Solow residual include distortions from
imperfect competition, externalities and production spillovers,
omitted inputs, cyclical fluctuations, nonconstant returns to
scale, and reallocation effects. If there are increasing returns to
scale but no technical change, for example, input shares will
not equal output elasticities and one would estimate a positive
Solow residual even though there is no technical change. While
this may confound the interpretation of the Solow residual as a
pure technology measure, it remains a useful indicator of the
underlying technological forces. Basu and Fernald (1997), for
example, report a high correlation between a traditional Solow
Yt At f Kt Lt = ⋅ ( ) ,
∆lnA = ∆ln v Y – K∆lnK – vL∆lnL
∆ vK
vL
vK v + L = 1
Y H⁄
∆lny = ∆lnY – ∆lnH
vK∆ln v k = + + L( ) ∆lnL – ∆lnH ∆lnA
∆lny
∆lnk
( ) ∆lnL – ∆lnH ∆lnA
40 What Drives Productivity Growth?
residual and a more sophisticated index of technology that
controls for market imperfections. Moreover, they argue that
the Solow residual is an important welfare measure, even when
it is not a measure of pure technical change.
Applications of the Neoclassical Model
Jorgenson and Stiroh (2000) use equations 2-4 in a traditional
growth accounting analysis to study the sources of U.S.
economic growth. They conclude that investment in tangible
assets has been the dominant source of growth over the past
four decades, while the contribution of technical progress as
measured by the Solow residual has been relatively modest.
From 1959 to 1998, output grew 3.63 percent per year,
reflecting 1.59 percent annual growth in hours and 2.04 percent
growth in labor productivity (Table 1). Labor productivity
growth reflects the contributions of capital deepening (1.10
percentage points per year), labor quality (0.32 percentage point
per year), and TFP growth (0.63 percentage point per year).
Thus, accumulation of tangible assets and human capital
(measured as labor quality gains) has been an important part of
U.S. output and productivity growth over the past four decades.
For the late 1990s, Jorgenson and Stiroh (2000) find that
both an acceleration of TFP and rapid capital accumulation
contributed to the recent U.S. productivity revival. For the
1995-98 period, estimated TFP growth of 0.99 percent per year
was nearly three times as fast as it was during the 1973-95
period. Although the neoclassical model cannot really explain
why TFP accelerated, it is nonetheless an important result since
faster technical progress drives long-run productivity growth.
Indeed, faster TFP growth is now incorporated into the rapid
medium-run growth projections made by the Congressional
Budget Office (2000).
Gauging the relative importance of capital deepening and
technology has also been an important part of the debate
surrounding the performance of the Asian newly industrialized
countries (NICs). Krugman (1994), Young (1995), and Collins
and Bosworth (1996) use this type of traditional neoclassical
analysis to evaluate the potential for long-run growth in the NICs.
All three conclude that broadly defined capital accumulation, as
opposed to exogenous technical progress (measured as TFP
growth), was the primary engine of growth for the NICs, and thus
they are pessimistic about future growth prospects. Again, it is the
neoclassical implication—that only technical change drives longrun productivity growth—that makes this distinction so
important. These findings have led to a sharp debate over the
relative importance of capital accumulation and TFP growth as
sources of growth in these economies.7
These two applications of neoclassical growth accounting help
to explain the proximate factors driving growth in the United
States and in the NICs, although the conclusions must be kept in
the proper perspective. As stressed by Hulten (1979), this
methodology yields a valid measure of the rate of technical
change if neoclassical assumptions hold, but also tends to
understate the economic importance of it. For example, in a
simple neoclassical model, faster technical change induces higher
output, saving, investment, and capital accumulation, so part of
historical capital accumulation itself is due to technical change in
a deeper sense. It must be stressed, however, that the goal of
growth accounting is to quantify the contribution of accumulated
inputs correctly so that the rate of technical progress can be
accurately measured. Modern growth accounting is more about
measuring technical change than explaining it.
Table 1
Sources of U.S. Output and Productivity Growth, 1959-98
1959-98 1959-73 1973-90 1990-95 1995-98
Growth in output (Y) 3.63 4.33 3.13 2.74 4.73
Growth in hours (H) 1.59 1.38 1.69 1.37 2.36
Growth in average labor productivity (Y/H) 2.04 2.95 1.44 1.37 2.37
Contribution of capital deepening 1.10 1.49 0.91 0.64 1.13
Contribution of labor quality 0.32 0.45 0.20 0.37 0.25
Contribution of aggregate total factor productivity 0.63 1.01 0.33 0.36 0.99
Source: Jorgenson and Stiroh (2000).
Notes: Decomposition of labor productivity growth is based on equation 4 in the text. All values are average annual percentages.
FRBNY Economic Policy Review / March 2001 41
Moving beyond the Neoclassical Model
The appealing simplicity and intuition of the neoclassical
framework have made it the backbone of applied work on
productivity and economic growth.8
Despite this popularity,
however, several shortcomings make the standard neoclassical
model not entirely satisfactory. First, early studies attributed
the vast majority of labor productivity growth to exogenous
forces.9
Then, in the 1970s and 1980s, the neoclassical model
failed to offer a persuasive explanation for important U.S.
productivity trends like the post-1973 productivity slowdown.
Second, since capital accumulation is subject to diminishing
returns, steady-state growth in per capita variables inevitably
grinds to a halt without exogenous technical progress. Finally,
the international data did not seem to fit with the basic
neoclassical model in terms of observed differences in income,
capital shares and rates of return, and convergence
properties.10 These shortcomings led to several lines of
subsequent research on the relationship between investment
and productivity growth.
One approach, originated by Jorgenson and Griliches
(1967) and summarized in Jorgenson (1996), remained firmly
embedded in the neoclassical tradition and sought to develop
better measures of investment, capital, labor, and other
omitted inputs in order to reduce the magnitude of the
unexplained residual. This approach did not seek to explain the
origins of technical progress but rather to reduce its
importance as an empirical explanation of growth. I return to
the details of this work later. The second direction was the
endogenous growth literature, to which I now turn.
The World of Endogenous Growth
The endogenous or new growth theory was developed to move
beyond the neoclassical model by providing an endogenous
mechanism for long-run productivity growth, either by
removing the diminishing returns to capital or by explaining
technical change as the result of specific actions. This literature
is quite varied, and alternative explanations focus on many
factors like different production structures, the dynamics of
competition, innovation, increasing returns, and production
spillovers. The following discussion describes a representative
endogenous growth model.11
A Simple Endogenous Growth Model
A primary motivation for developing endogenous growth
models was the desire to avoid the neoclassical implication
that only exogenous technical progress drives long-run
productivity growth. Indeed, one can simply assume a constant
marginal product of capital as in the so-called “AK” models in
which output is a linear function of capital, .12 In this
case, long-run productivity growth can continue, and any
change in the level of technology or savings rate leads to a longrun change in productivity growth.
Romer (1986), in a classic paper that sparked the new
growth theory, provided a mechanism and corresponding
economic explanation for why capital might not suffer from
diminishing returns. In particular, Romer focused on the
possibility of external effects as research and development
efforts by one firm spill over and affect the stock of knowledge
available to all firms. Firms face constant returns to scale to all
yt Ak = t
private inputs, but the level of technology, , varies, depending
on the aggregate stock of some privately provided input
(5) ,
where an subscript represents firm-specific variables, is
the aggregate stock of knowledge, and time subscripts are
dropped.13
The exact nature of the spillover is not particularly
important for the aggregate properties of the model, and
economists have identified several alternative channels. For
instance, Arrow (1962) emphasizes “learning-by-doing,” in
which investment in tangible assets generates spillovers as
aggregate capital increases; past gross investment proxies for
experience and determines A(.).
14 Alternatively, Romer (1986)
essentially models A(.) as a function of the stock of R&D, Lucas
(1988) models A(.) as dependent on the stock of human
capital, and Coe and Helpman (1995) argue that A(.) also
depends on the R&D stock of international trading partners.
The key point is that there may be constant (or increasing)
A
Yi A R( ) f Ki Li Ri = ⋅ ( ) , ,
i R
A primary motivation for developing
endogenous growth models was
the desire to avoid the neoclassical
implication that only exogenous technical
progress drives long-run productivity
growth.
42 What Drives Productivity Growth?
returns to accumulated inputs at the aggregate level, and thus
the generation of long-run endogenous growth.15
The existence of production spillovers raises a significant
empirical question that has generated a vast literature. If
investment of any type—tangible assets, human capital, or
R&D—generates benefits to the economy that are not
internalized by private agents, then this suggests that there are
multiple long-run growth paths and that there are specific policy
implications. Since investment may be too low from society’s
point of view, spillovers open a role for government intervention
such as investment tax credits or research and development
grants. R&D spillovers, in particular, have attracted considerable
attention in the new growth literature, and I review the
microeconomic evidence on them later.
Macro Evidence of Endogenous Growth
One aggregate implication of early endogenous growth models
is a “scale effect,” in which productivity growth increases with
the size of the economy. Larger economies devote more
resources to R&D and knowledge production is available to all,
so technology should grow more rapidly. In addition, this
suggests that government policy, in the form of taxes or
subsidies that increase resources allocated to knowledge
production or investment, can raise long-run growth.
In a pair of influential studies, however, Jones (1995a,
1995b) strongly rejects this scale effect and finds little
relationship between policy variables and long-run growth.
There is no obvious relationship between the number of
scientists and engineers employed in R&D activities and U.S.
TFP growth (Jones 1995a), nor has there been persistent
acceleration in growth in countries belonging to the
Organization for Economic Cooperation and Development,
even as investment shares rose dramatically (Jones 1995b).
Over a very long horizon, however, the evidence of a scale effect
is somewhat stronger; Kremer (1993) argues that productivity
and population growth are highly correlated with initial
population levels, as scale effects imply.
This influential critique has led to several alternatives to
remove the link between scale and growth found in
endogenous growth models.16 Jones (1995a), for example,
presents a model of “semi-endogenous” growth, in which longrun growth still reflects firms’ R&D choices, but is independent
of government policies such as investment tax credits or R&D
subsidies. Scale or policy variables affect the levels of output
and productivity but not long-run growth rates. The key factor
determining long-run growth in this semi-endogenous growth
model remains the degree of external returns in the R&D
process, which delivers endogenous growth and provides the
critical distinction from the neoclassical model.
In more recent work at the macro level, Jones and Williams
(1998) formalize the macroeconomic impact of increasing
overall returns due to various external effects related to R&D.
They calibrate their model and estimate that optimal
investment in R&D is two to four times actual investment in
the United States. This work suggests an important role for
R&D but remains consistent with the empirical refutation of
the macro R&D models in Jones (1995a, 1995b).
Expanding the Investment Definition
I now turn to several broad measurement issues that directly
affect how these types of models are implemented and
evaluated. Over the years, sophisticated tools have been
developed to measure inputs properly, and the definition of
investment has been expanded beyond tangible assets. By
quantifying substitution between heterogeneous tangible assets
and explicitly recognizing investment in human capital,
research and development, and public infrastructure,
economists have made considerable methodological advances
in the understanding of productivity growth. These
improvements are now well-accepted and are part of the
toolkits of most applied productivity analysts; for example, the
official U.S. TFP estimates of the Bureau of Labor Statistics
(2000a) account for asset substitution, human capital, and
R&D.
These advances are also relevant to the debate between the
neoclassical and new growth views. From the neoclassical view,
improved measurement of inputs allows technical progress to
be more accurately assessed. From the new growth view,
constant returns may be more realistic for broader definitions
of capital. The degree of economy-wide returns to accumulated
inputs—diminishing returns in the neoclassical world and
constant (or increasing) returns in the new growth world—
remains the fundamental difference between the two views of
economic growth, and this is conceptually independent of how
broadly capital is defined or measured. Simply including
additional inputs like human capital or R&D capital is not
enough to generate endogenous growth if broadly defined
capital still faces diminishing returns.
Finally, many of these methodological advances have been
implemented within neoclassical growth accounting analyses.
As mentioned above, the primary goal of these studies is to
develop better measures of inputs and a more accurate estimate
of technical progress. It is not, as is often assumed, to show that
FRBNY Economic Policy Review / March 2001 43
there is no technical progress. Careful growth accounting
analyses purge the transitory impact of investment and input
accumulation to leave behind a more precise estimate of the
growth rate of technical progress.
Heterogeneous Tangible Assets
An important insight, first implemented by Jorgenson and
Griliches (1967), is that one must account for the vast
heterogeneity of capital inputs. A dollar spent on new
computer equipment, for example, provides more productive
services per period than a dollar spent on a new building. By
explicitly recognizing these types of differences, one can
estimate a “capital service flow” that is appropriate for the
production function in equation 1.
Aggregate capital service flows are estimated by using assetspecific “user costs” or “rental prices” to weight each
heterogeneous asset and to account for substitution between
them. As firms respond to changing relative prices—for
example, by substituting toward high-tech equipment and
away from structures—a larger portion of investment is in
assets with relatively high marginal products, and the capital
service flow rises.17 The difference between capital service flows
and capital stock is called “capital quality” by some authors and
reflects the changing composition of investment toward assets
with higher marginal products.18
Jorgenson and Stiroh (2000) provide estimates of this
decomposition between capital stock and capital quality. As
shown in Table 2, capital stock accumulation has been the
dominant force behind the growth in capital services in the
United States, accounting for 1.32 of the 1.77 percentage
point growth contribution of capital for the 1959-98 period.
For the most recent period, the contribution of capital
quality has increased markedly as firms steadily responded
to changing relative prices and substituted toward high-tech
equipment. Gordon (1999a) examines a longer time period,
dating back to 1870, and concludes that quality adjustments
of capital and labor inputs have been important sources of
long-run growth in the United States.
The evidence shows that one must use a capital services
methodology to quantify the role of capital accumulation
correctly and to isolate technical progress. Failure to account
for ongoing substitution understates the contribution of input
accumulation and overstates the TFP residual from equation 3.
Thus, this type of careful measurement of capital services is
critical to obtaining accurate measures of technical progress
and understanding long-run growth.
Human Capital
A second important extension of the capital concept is the
explicit inclusion of the contribution of changes in labor
quality. Economists have long recognized the importance of
investments in human beings; and expenditures on education,
job training, labor migration, and health care all increase the
quality of human labor, enhance productivity, and are rightly
called investments.19
Griliches (1960), Denison (1962), and Jorgenson and
Griliches (1967) pioneered the use of wage data to weight
heterogeneous workers and construct constant-quality indexes
Table 2
Growth Contribution of Capital and Labor Inputs, 1959-98
1959-98 1959-73 1973-90 1990-95 1995-98
Contribution of capital services (K) 1.77 2.07 1.62 1.20 2.17
Contribution of capital stock 1.32 1.66 1.22 0.77 1.23
Contribution of capital quality 0.45 0.40 0.41 0.43 0.95
Contribution of labor input (L) 1.23 1.25 1.17 1.18 1.57
Contribution of labor hours 0.92 0.80 0.97 0.81 1.32
Contribution of labor quality 0.32 0.45 0.20 0.37 0.25
Source: Jorgenson and Stiroh (2000).
Notes: Growth contribution of capital quality equals the difference between the contribution of capital services and capital stock. Growth contribution of
labor quality equals the difference between the contribution of labor input and labor hours. See the text for details. All values are average annual percentages.
44 What Drives Productivity Growth?
of labor input. Similar to the treatment of capital, this
approach captures substitution between different types of labor
and results in a flow of labor inputs appropriate for the
production function analysis of equation 1. In contrast, a
simple sum of hours worked by heterogeneous workers ignores
this type of compositional change.20
Using the framework in equations 3 and 4 and again defining
labor quality as the difference in the growth of labor input and
unweighted hours, Jorgenson and Stiroh (2000) estimate that
labor quality growth accounted for nearly 15 percent of labor
productivity growth for the 1959-98 period (Tables 1 and 2).
Similarly, the Bureau of Labor Statistics (1999b) attributes onethird of U.S. nonfarm labor productivity growth from 1990 to
1997 to labor composition effects. Again, failure to account for
these quality changes overstates historical TFP growth.
Looking at the impact of human capital from a different
perspective, Mankiw, Romer, and Weil (1992) include
investment in human capital in an augmented Solow growth
model to examine cross-country differences in growth.
Employing a Cobb-Douglas specification for aggregate
output, they explicitly model human capital as a
determinant of output as
(6) ,
where is the stock of human capital.21
Mankiw, Romer, and Weil (1992) use educational
attainment to proxy for human capital accumulation. They
find that this extended neoclassical model fits the data well in
terms of the growth convergence predictions and the estimated
output elasticities. The authors conclude that the augmented
Solow model in its neoclassical form is consistent with the
international evidence. In contrast, Lucas (1988) incorporates
human capital in a growth model but explicitly includes an
external spillover effect in the spirit of new growth theory.
Although these studies differ in their approach and
questions—Jorgenson and Stiroh (2000) show labor quality to
be an important contributor to U.S. productivity growth, and
Mankiw, Romer, and Weil (1992) find human capital to be a
good predictor of cross-country income differences—both
emphasize the importance of accounting for human capital
accumulation. By correctly identifying and measuring
accumulated inputs, this extension of the neoclassical model
allows for a better understanding of the growth process.
Research and Development
Knowledge creation through explicit research and
development activities is a third extension of the capital
Y Kα H β ( ) AL 1 – α – β =
H
accumulation process that deserves special attention. R&D,
broadly defined as investment in new knowledge that improves
the production process, has been the focus of considerable
research activity. There is still some debate, however, over
whether R&D is best viewed as a neoclassical factor of
production or if it is best viewed as a source of spillovers as in
the endogenous growth models.
It is straightforward to think of R&D as just another form of
capital in which firms choose to invest. In this sense, R&D is
not fundamentally different from investment in tangible
capital. Griliches (1973, 1979), for example, argues that it is
reasonable to view the primary impact of R&D investment in a
neoclassical sense since returns accrue internally. Firms
presumably invest in R&D to improve their own production
processes and to raise profits, so any spillover effects are
secondary and unintended consequences.
While it is conceptually straightforward to treat R&D as a
neoclassical factor of production with diminishing returns,
Griliches (1995), Hall (1996), and Jorgenson (1996) all
emphasize the practical difficulty in measuring the growth
contribution of R&D because of thorny measurement
problems and a lack of adequate data. Hall (1996) points out
that R&D is often associated with product improvements, and
the measured impact of R&D therefore depends critically on
how price deflators are constructed and how output is deflated.
In addition, one must estimate an appropriate depreciation
rate to calculate the productive stock of R&D capital.
Despite these problems, many studies have attempted to
measure the direct impact of R&D.22 As an example of the
typical approach, Griliches (1995) presents a skeletal model of
R&D that is a straightforward extension of the neoclassical
framework:
(7) ,
where is a vector of standard inputs, such as capital and
labor, and is a measure of cumulative research effort.
Studies of this type typically have found that R&D capital
contributes significantly to cross-sectional variation in
productivity. It is important to emphasize that equation 7
examines the relationship between firm or industry productivity
and its own R&D stock. In the equation, R&D is treated as a
conventional neoclassical capital input with internal rewards.
Others, however, argue that R&D capital is fundamentally
different from tangible and human capital. Knowledge capital
appears to be noncompetitive since many producers can use
the same idea simultaneously, and the returns may be hard to
appropriate due to potential production spillovers. This
difference is what makes R&D capital an important part of the
endogenous growth models discussed earlier.23 As emphasized
by Romer (1994) and Basu (1996), the distinction between
ln a t Y = ( ) + ++ β lnX γ lnR ε
X
R
FRBNY Economic Policy Review / March 2001 45
internal and external benefits drives the difference in returns to
capital that delineates the role of research and development in
the neoclassical and the new growth theories.
There seems to be some confusion, however, about what
constitutes a true production spillover and what is really a
more conventional measurement problem. Griliches (1995,
p. 66) defines a production (knowledge) spillover as “ideas
borrowed by research teams of industry from the research
results of industry .” This is quite distinct from situations in
which transaction prices do not fully reflect the marginal
benefit of the innovation (for example, see Bresnahan [1986],
Bartelsman, Caballero, and Lyons [1994], and Keller [1998]).
Similarly, Hall (1996) discusses how competition may lead to
lower prices for goods of innovative firms. Rather than
measuring spillovers in Griliches’ sense, these gains to
innovation reflect the inaccuracy of prices that do not
adequately capture changes in the quality dimension.24 While
there are daunting practical difficulties, if all attributes and
i
j
quality characteristics could be correctly priced, then increased
quality or variety of intermediate inputs would not be
measured as productivity spillovers.
If true productivity gains do spill over to other firms,
however, one channel for endogenous growth is opened. The
microeconomic evidence suggests that R&D spillovers may
exist,25 but a wide variation in results and conceptual
difficulties suggest that some caution is warranted. Griliches
(1995), for example, points out that the impact of R&D in
industry analyses is not greater than in firm analyses (as the
presence of spillovers implies) and warns, “in spite of a number
of serious and promising attempts to do so, it has proven very
difficult to estimate the indirect contribution of R&D via
spillovers to other firms, industries and countries” (p. 83).
Given the poor quality of the data and methodological
problems discussed earlier, it is difficult to draw definitive
conclusions from these studies.
Public Infrastructure
A final extension of the investment concept worth noting is
public infrastructure investment. In a series of influential and
controversial studies, Aschauer (1989a, 1989b, 1990) argues that
core infrastructure investment is an important source of
productivity growth and that the sluggish productivity
performance of the 1970s can be largely attributed to a slowdown
in public investment. These claims led to a wide-ranging debate
about policy implications and possible methodological problems
such as potential biases from common trends, omitted variables,
and potential reverse causality.26
Independent of any methodological concerns, the primary
impact of government capital is conceptually the same as that
of tangible capital and depends on proper measurement.27 In a
standard neoclassical growth accounting framework with only
private inputs, any impact from government capital would be
mismeasured as TFP growth. In this sense, government capital
is just another accumulated input that is often missed and thus
contributes to an overstatement of true technical change. As
long as diminishing returns to all capital exist, the neoclassical
implications hold.
Alternatively, Barro (1990) suggests that government
services generate constant returns to broadly defined capital
and lead to endogenous growth. In this view, government
capital differs from private capital, and the real question is
whether long-run constant returns to scale exist across broadly
defined capital.28
The recent results of Fernald (1999) shed some light on this
question. He shows that investment in roads contributed
substantially to productivity prior to 1973, but he also suggests
that new investment in roads offers a normal or even zero
return at the margin. That is, the original interstate highway
system improved productivity, but a second one would not.
While not an exact test, this seems more consistent with the
neoclassical view of diminishing returns of capital than with
the endogenous growth view.
Recent Productivity Controversies
I now move to a discussion of two current and important
issues relating to investment, productivity, and growth.
Both are concerned with understanding the sources of
productivity growth and draw on the neoclassical and
endogenous growth theories described above. In particular, I
offer a resolution to the computer productivity paradox and
review the renewed embodiment controversy.
The distinction between internal and
external benefits drives the difference
in returns to capital that delineates the
role of research and development in the
neoclassical and the new growth theories.
46 What Drives Productivity Growth?
The Computer Productivity Paradox
Over the past few decades, investment in high-tech equipment,
particularly computers, exploded, but aggregate productivity
growth remained sluggish through the mid-1990s. This
apparent contradiction—the so-called computer productivity
paradox of the 1980s and early 1990s—disappointed many
observers and initiated a broad research effort at both the
macro and micro levels. More recently, however, productivity
growth has accelerated sharply (see chart); I argue that this
pattern is entirely consistent with neoclassical explanations of
capital accumulation and technical progress.29
The defining characteristic of the information technology
revolution is the enormous improvement in the quality of
computers, peripherals, software, and communications
equipment. As epitomized by Moore’s Law—the doubling of
the power of a computer chip every eighteen months—each
generation of new computers easily outperforms models
considered state-of-the-art just a few years earlier. The constantquality deflators employed by the U.S. Bureau of Economic
Analysis translate these massive quality improvements into
increased real investment and real output and show annual price
declines of 18 percent over the past four decades.30
How does this IT phenomenon fit within the neoclassical
framework? To address this question, it is critical to distinguish
between the use and the production of IT.31 Information
technology is both an output from the IT-producing industries
and an input to the IT-using industries, so there are two effects.
The massive quality improvements in IT contribute to faster
productivity growth in the IT-producing industries and faster
input accumulation in the IT-using industries. Thus, the
neoclassical model predicts rapid capital deepening and ALP
growth in IT-using industries, and technical progress and TFP
growth in the IT-producing industries. This fundamental
distinction is apparent in Solow (1957), but often has been
overlooked in discussions of the computer productivity paradox.
IT Use, Capital Deepening, and Productivity
Growth
Consider the productivity of firms and industries that invest in
and use information technology. Following the neoclassical
framework in equation 4, strong IT investment contributes
directly to ALP growth through traditional capital deepening
effects. In the case of IT, this reflects rapid growth in capital
services and, until recently, a small income share. Over the past
four decades, however, U.S. firms have continued to respond to
large price declines by investing heavily, particularly in
computer hardware, and rapidly accumulating IT.
As long as relative prices continued to fall, it was inevitable
that IT inputs would eventually make a large contribution to
growth. Indeed, recent estimates by Jorgenson and Stiroh
(2000), Oliner and Sichel (2000), and Whelan (2000) indicate
substantial increases in the growth contributions from
computers and other IT capital. Jorgenson and Stiroh (2000),
as reported in Table 3, estimate that the contribution of
computer hardware increased from 0.19 percentage point
per year for the 1990-95 period to 0.46 percentage point for
1995-98; Oliner and Sichel (2000) report an increase from
0.25 for 1990-95 to 0.63 for 1996-99.32 Both agree that IT
capital accumulation has been an important part of the
acceleration in U.S. productivity since 1995.
Table 3
Growth Contribution of Information Technology and Other Assets, 1959-98
1959-98 1959-73 1973-90 1990-95 1995-98
Contribution of capital services (K) 1.77 2.07 1.62 1.20 2.17
Other capital 1.45 1.89 1.27 0.80 1.42
Computer hardware 0.18 0.09 0.20 0.19 0.46
Computer software 0.08 0.03 0.07 0.15 0.19
Communications equipment 0.07 0.06 0.08 0.06 0.10
Source: Jorgenson and Stiroh (2000).
Notes: A growth contribution is defined as the share-weighted real growth rate of the asset as in equation 3 in the text. All values are average annual
percentages.
FRBNY Economic Policy Review / March 2001 47
This historical record on IT capital accumulation appears
entirely consistent with the neoclassical model. Massive input
substitution and rapid capital accumulation during the 1990s
have led to an aggregate growth contribution that is now quite
large. Prior to that, the contribution was modest because the
stock of IT was small. Only in the late 1990s, after a major
information technology investment boom, were there enough
information technology inputs to have a substantial impact on
growth and labor productivity at the aggregate level.
Despite the straightforward relationship and mounting
aggregate evidence, the empirical evidence on computers
and ALP growth across industries has been mixed. Gera, Gu,
and Lee (1999), McGuckin, Steitwieser, and Doms (1998),
McGuckin and Stiroh (1998), and Steindel (1992) find a
positive impact, while Berndt and Morrison (1995) report a
negative impact. Morrison (1997) finds overinvestment in
high-tech assets for much of the 1980s. The microeconomic
evidence for firms is somewhat stronger. For example,
Brynjolfsson and Hitt (1993, 1995, 1996), Lehr and
Lichtenberg (1999), and Lichtenberg (1995) typically
estimate returns to computers that exceed other forms of
capital.
On the surface, exceptionally high returns to IT suggest
effects found in some endogenous growth models. The
findings of large gross returns, however, are also quite
consistent with the neoclassical model—computers must
have high marginal products because they obsolesce and
lose value so rapidly. Computers have a low acquisition
price, but rapid obsolescence makes them expensive to use
and a high return is needed as compensation. This is exactly
the type of asset heterogeneity for which the user-cost
methodology was designed. In addition, Brynjolfsson and
Yang (1997) suggest that much of the “excess returns” to
computers actually represent returns to previously
unspecified inputs such as software investment, training,
and organizational change that accompany computer
investment.
Note that the neoclassical framework predicts no TFP
growth from IT use since all output contributions are due to
capital accumulation. Computers increase measured TFP
only if there are nontraditional effects like increasing
returns, production spillovers, or network externalities, or if
inputs are measured incorrectly. The nontraditional effects,
if present, would move the IT revolution into the world of
new growth theory. The evidence, however, is not very
strong. Siegel and Griliches (1992) and Siegel (1997)
estimate a positive impact of computer investment on TFP
growth across U.S. industries, while Berndt and Morrison
(1995) and Stiroh (1998a) do not. Working with aggregate
data, Gordon (2000) finds no evidence of computer-related
spillovers in the late 1990s. In sum, there does not appear to
be compelling evidence for nontraditional effects from IT
that lead outside of the neoclassical model.
IT Production and Technical Progress
Now consider the productivity of firms and industries that
produce IT assets. These sectors are experiencing fundamental
technical progress—the ability to produce more output in the
form of faster processors, expanded storage capacity, and
increased capabilities from the same inputs—that should be
measured directly as industry TFP and lead to higher ALP
growth (equations 3 and 4). This affects both industry and
aggregate productivity.
The data are quite clear that fundamental technical
progress, measured as TFP growth, is a driving force in the
production of these new high-tech assets. The Bureau of Labor
Statistics (1999b), Jorgenson and Stiroh (2000), Oliner and
Sichel (2000), and Stiroh (1998a) all report strong industry
TFP growth in the high-tech producing industries. Moreover,
much of the acceleration in aggregate U.S. productivity growth
after 1995 can be traced to accelerations in the pace of technical
progress—measured as faster relative price declines in these
high-tech industries.33
This notion that technical progress in specific industries
drives aggregate productivity is hardly new and is consistent
with the broad neoclassical framework. As early as Domar
(1961), economists recognized that aggregate TFP growth
reflects technical progress among component industries.
Accelerating technical progress in key industries can then drive
aggregate productivity through both a direct TFP contribution
and induced capital accumulation as relative prices change.
Only in the late 1990s, after a major
information technology investment boom,
were there enough information
technology inputs to have a substantial
impact on growth and labor productivity at
the aggregate level.
48 What Drives Productivity Growth?
Alternative Explanations
The preceding discussion still leaves open the question of why
even ALP growth remains sluggish in some computer-intensive
sectors like finance, insurance, real estate, and services. Since
computers are highly concentrated in service sectors, where
output and productivity are notoriously hard to measure,
Diewert and Fox (1999), Griliches (1994), Maclean (1997), and
McGuckin and Stiroh (1998) suggest that measurement error
plays a role in the remaining computer productivity paradox
for certain IT-using industries.
A second common explanation is that computers are still
relatively new and it may just be a matter of time until they
fundamentally change the production process and usher in a
period of faster productivity growth throughout the economy.
David (1989, 1990) draws a parallel between the slow
productivity benefits from electricity and those from
computers. Triplett (1999a), however, cautions against such
analogies, arguing convincingly that the massive declines in
computer prices, and hence the diffusion patterns, are
unprecedented. Moreover, computers are no longer really a
new investment—the first commercial purchase of a UNIVAC
mainframe computer was in 1954, and computer investment
has been a separate entity in the U.S. national accounts since
1958.34 This critical mass and delay hypothesis is beginning to
lose credibility as an explanation for low productivity in certain
computer-intensive industries.
A final explanation is simply that computers are not that
productive in some industries. Anecdotes abound of failed
systems, lengthy periods of downtime, unwanted and
unnecessary “features,” and time-consuming upgrades—
all of which can reduce the productivity of computer
investment.35
IT and the New Economy
Despite some lingering questions, the computer productivity
paradox appears to be over. Aggregate productivity growth is
strong, and IT-producing industries are showing rapid TFP
growth. Moreover, the IT revolution and the “new economy”
appear to be largely a neoclassical story of relative price declines
and input substitution. Technical change in the production of
information technology assets lowers the relative price, induces
massive high-tech investment, and is ultimately responsible for
the recent productivity revival.
These benefits, however, accrue primarily to the producers
and users of IT, with little evidence of large spillovers from
computers. That is, we see TFP growth in IT-producing
industries and capital deepening elsewhere. Of course, the
neoclassical model provides no explanation for why technical
progress may have accelerated in high-tech industries in recent
years. Perhaps models of endogenous innovation and
competition can provide an answer.
The Renewed Embodiment Controversy
The discussion so far has focused on the modern neoclassical
framework and new growth models as explanations of
productivity growth. An alternative perspective, however, argues
that technological progress is “embodied” in new machinery and
equipment, as opposed to being a more pervasive force that
affects the production of all goods and services. In challenging
papers, Greenwood, Hercowitz, and Krusell (1997) and
Hercowitz (1998) recently brought this debate back to center
stage and reopened the embodiment controversy.
This debate is important since it helps us to understand the
precise roles of technology and investment in the growth
process. By better understanding these issues, such as whether
technology is driving the recent investment boom, one may be
able to implement more effective policies. Moreover, there are
clear implications associated with how real aggregate output
should be measured that directly affect how the economy is
viewed. For example, Greenwood et al. (1997) disagree with the
current practice of adjusting the output of investment goods,
such as computers, for quality improvements. As noted in the
previous section, gains in the production of computers have
been a major part of the productivity revival of the 1990s and
excluding them would substantially change our perception of
the U.S. economy.
The embodiment idea goes back at least to Solow (1960), who
suggests that technical change is embodied in new investment
goods, which are needed to realize the benefits of technical
Technical change in the production of
information technology assets lowers the
relative price, induces massive high-tech
investment, and is ultimately responsible
for the recent productivity revival.
FRBNY Economic Policy Review / March 2001 49
progress. In response, Jorgenson (1966) shows this to be no
different conceptually from the neoclassical view of disembodied
technical change with the calculation of investment price deflators
responsible for apparent differences. If new vintages of capital have
different productive characteristics, the appropriate constantquality deflators attribute output and productivity growth to input
accumulation and not to technical progress. Hulten (1992)
shows how failure to account for improved characteristics of
recent vintages of investment goods suppresses capital
enhancements into the traditional TFP residual.
There seems to be general agreement that different vintages of
capital inputs need to be adjusted for quality change in order to
understand and quantify the sources of growth. A second
conclusion of Jorgenson (1966), however, is that investment as an
output must also be measured in quality-adjusted units; Hulten
(2000) discusses potential measurement errors when investment is
not measured in such units. While this methodology has been
integrated into the U.S. national accounts—where constantquality deflators are used for investment goods like computer
hardware and software to calculate real GDP—it plays a central
role in the renewed embodiment debate.
Greenwood et al. (1997) and Hercowitz (1998) argue
explicitly against adjusting investment output for quality
change, preferring to measure real investment output in units
of consumption. As motivating evidence, Greenwood et al.
report that the relative price of equipment in the United States
has fallen 3 percent per year in the postwar era, while the
equipment-to-GDP ratio increased dramatically. They
calibrate a balanced growth path and attribute 60 percent of
postwar productivity growth to “investment-specific
technological change” that is conceptually distinct from capital
accumulation and disembodied (Hicks-neutral) technological
change. A clear implication, they argue, is that constant-quality
price indexes are appropriate only for deflating investment
inputs, not for deflating investment as an output.36
It is essential, in my view, that both investment outputs and
capital inputs be measured consistently in quality-adjusted
units, as currently employed in the U.S. national accounts. The
key point is that improved production characteristics of new
investment cohorts are themselves produced and rightly
considered output. Although a rigorous theoretical model is
beyond the scope of this article, it is useful to sketch out a
defense of this position.
Consider a simple two-sector, neoclassical model like the
one outlined in the earlier discussion of the computer
productivity paradox. One sector produces computers and one
sector uses computers; both use neoclassical production
functions. Can this explain the motivating evidence cited by
Greenwood et al.? The answer is clearly yes. Disembodied
technical change in the computer-producing industry
(measured as industry-level TFP) reduces the marginal cost of
producing computers and lowers prices. Profit-maximizing
firms elsewhere in the economy respond to the relative price
change, substitute between inputs, and rapidly accumulate
computers. Thus, one would observe falling relative prices and
rising investment shares in a traditional neoclassical world with
purely disembodied technical change in one sector.
Greenwood et al. appear to need investment-specific technical
change since they focus on a one-sector model in which
consumption, equipment investment, and construction
equipment are produced from the same aggregate production
function. This effectively imposes perfect substitutability between
investment and consumption goods and requires investmentspecific technical change to explain relative price changes. In a
multisector neoclassical model like the one proposed by Domar
(1961) and implemented by Jorgenson et al. (1987), investmentspecific technical change is not needed since disembodied
technical progress can proceed at different rates in different
industries and generate the observed relative price changes.37
What does this say about the appropriate deflation of
investment goods? In this example, the answer clearly depends on
what one believes the computer-producing sector actually
produces. High-tech industries expend considerable resources in
the form of investment, R&D, and labor to produce better, faster,
and more powerful products. Indeed, the hedonic literature on
computers is based on the idea that the computer-producing
industry creates computing power measured as a bundle of
productive characteristics, rather than as computer boxes or
units.38 If computing power measured in quality-adjusted
efficiency units is the appropriate measure of industry output, and
I believe it is, then internal accounting consistency requires that
aggregate output also be measured in quality-adjusted units.
Finally, and perhaps more fundamentally, the neoclassical
model at its most basic level is a model of production and not
of welfare. This too implies that output must be a measure of
produced characteristics in terms of quality-adjusted units,
rather than consumption forgone. The embodiment approach,
in contrast, confounds the link between the sources of growth
An alternative perspective [to the
neoclassical and new growth models]
argues that technological progress is
“embodied” in new machinery and
equipment.
50 What Drives Productivity Growth?
(labor, capital, and technology) and the uses of growth
(consumption and investment goods) that constitute
separate views of production and welfare.
Conclusion
This article provides a broad overview of the link between
investment and productivity in two alternative views—the
neoclassical and new growth models. Although the models
emphasize different aspects of productivity growth, they both
contribute to our understanding of the growth process.
The key distinction between the neoclassical and new growth
theories concerns the aggregate returns to capital and the
implications for long-run productivity growth. In the
neoclassical world, capital (broadly defined to include all
accumulated inputs) suffers from diminishing returns, and
productivity growth is ultimately determined by exogenous
technical progress. In the world of endogenous growth, there
can be constant returns to capital that generate long-run
growth in per capita variables. Although both views attempt to
explain growth, they focus on different aspects and need not be
mutually exclusive. Neoclassical economists developed
sophisticated measurement tools to identify technical progress
accurately by removing the transitory impact of input
accumulation; new growth theorists developed sophisticated
growth models to explain the evolution of technology as a result
of the actions of economic agents. Both contributions are
important.
Attempts to understand recent changes in the U.S. economy
illustrate this complementarity. Aggregate productivity growth
has accelerated in the past few years due to a combination of
accelerating technical progress in high-tech industries and
corresponding investment and capital deepening. This type of
neoclassical analysis clearly explains what happened to the U.S.
economy. To explain why it happened, we need to focus on the
incentives and actions of the firms that actually invest,
innovate, and create the new capital and knowledge that are
driving the U.S. economy. This is the domain of the
endogenous growth framework. Thus, both approaches make
important contributions to our understanding of the economic
growth process.
Endnotes
FRBNY Economic Policy Review / March 2001 51
1. Labor productivity is defined as real output per hour worked. These
estimates are for the U.S. nonfarm business sector from the Bureau of
Labor Statistics (2000b) and are consistent with the revised GDP data
after the benchmark revision in October 1999.
2. See, for example, Jorgenson and Stiroh (2000), Oliner and Sichel
(2000), Gordon (1999b, 2000), and Parry (2000).
3. See Jorgenson (1996) for a discussion of the growth theory revival,
Barro and Sala-i-Martin (1995) for a thorough analysis of the
neoclassical framework, and Aghion and Howitt (1998) for a detailed
review of different strands of new growth theory. The terms “new
growth” and “endogenous growth” are used interchangeably
throughout this article.
4. The Solow model assumes labor is fully employed so per capita
income and labor productivity growth coincide.
5. The neoclassical model has also been used extensively to examine
cross-country differences in the growth and level of output. This vast
body of literature is not discussed here; see Barro and Sala-i-Martin
(1995) for references and Mankiw (1995) for a summary of the
strengths and weaknesses of the neoclassical model in this context.
6. Under the neoclassical assumptions, an input’s elasticity equals its
share of nominal output since the marginal product of an input equals
its factor price, for example, the wage rate for labor and the rental price
for capital.
7. Hsieh (1997, 1999), Rodrick (1997), and Young (1998b) provide
recent views on this controversy.
8. Stiroh (1998b) reports that the long-run projection models used by
various U.S. government agencies—for example, the Social Security
Administration, the Congressional Budget Office, the Office of
Management and Budget, and the General Accounting Office—are all
firmly embedded in this neoclassical tradition.
9. Solow (1957), for example, estimates that nearly 90 percent of
per capita income growth is due to technical progress.
10. See Mankiw (1995), particularly pp. 280-9.
11. My working definition follows Segerstrom (1998), who defines
endogenous growth models as those in which “the rates of
technological change and economic growth are endogenously
determined based on the optimizing behavior of firms and
consumers” (p. 1292). Hulten (2000) identifies noncompetitive
markets, increasing returns to scale, externalities, and endogenous
innovation as the key aspects of the new growth theory.
12. Technically, long-run growth in per capita variables exists under
constant returns to all accumulated inputs. Note that in the simplest
AK model like this one, represents a constant level of technology, in
contrast to the general production functions in the text.
13. These simplifications follow Romer (1994), who summarizes the
evolution of endogenous growth models. One alternative mechanism
is to allow for increasing returns at the level of individual firms.
However, this approach is inconsistent with perfect competition. See
Aghion and Howitt (1998) for a discussion. In addition, there are
aggregation concerns when moving from a firm to an aggregate
production function.
14. Note that Arrow (1962) does not explicitly derive a model of
endogenous growth. In his model, growth eventually stops if
population is held constant.
15. Barro (1990) achieves endogenous growth in a model with
constant returns to capital and government services together, but
diminishing returns to private capital alone. DeLong and Summers
(1991, 1992, 1993), although not modeling endogenous growth, argue
that equipment investment yields large external benefits in the spirit of
Arrow (1962).
16. See, for example, Jones (1995a), Kortum (1997), Segerstrom
(1998), and Young (1998a). Jones (1999) reviews.
17. An asset’s rental price reflects the opportunity cost of buying
the asset, depreciation, and any capital gains or losses on the asset.
High-tech equipment experiences more rapid depreciation and
smaller capital gains than structures, so equipment must have a
correspondingly higher marginal product and service price. See Hall
and Jorgenson (1967) for the original derivation and Jorgenson and
Stiroh (2000) for a recent application and details.
18. Note that capital quality in this framework does not reflect
increased productive power from a particular asset. These gains, such
as the enhanced performance of more recent vintages of computers,
are handled by the investment deflator, which translates nominal
investment into larger quantities of real investment. I provide details
later in this article.
A
52 What Drives Productivity Growth?
Endnotes (Continued)
19. Mincer (1958, 1974), Shultz (1961), and Becker (1962) are early
examples; Griliches (1996) provides a summary of the early work on
human capital. As early as 1961, the similarities between investments in
tangible capital and human capital such as tax incentives, depreciation,
pricing imperfections, and the primarily internal benefits of human
capital investments were discussed by Schultz (1961, pp. 13-5).
20. This methodology provides an index of aggregate human capital
that changes as the composition of the labor force changes. The key
assumption is that the quality of a particular type of labor—for
example, a person of a given age, education, experience—is constant
over time. Ho and Jorgenson (1999) provide methodological details.
21. Note that Mankiw, Romer, and Weil (1992) explicitly assume
there are diminishing returns to accumulated inputs, ,
which places the model squarely in the neoclassical tradition.
22. Good et al. (1996), Griliches (1994, 1995), and Hall (1996) provide
detailed surveys of the empirical literature.
23. Hall (1996) offers a number of reasons why R&D might lead to
production spillovers such as reverse engineering, migration of
scientists and engineers, and free dissemination of public R&D.
Grossman (1996, particularly pp. 86-8) emphasizes the differences
between R&D capital and tangible capital.
24. See Griliches (1992) for a discussion of this distinction.
25. Good et al. (1996) state that “most of these recent studies point in
the direction that there is some effect of R&D spillovers on the
productivity growth of the receiving industry or economies” (p. 39).
Griliches (1992) states that “in spite of many difficulties, there has
been a significant number of reasonably well-done studies all pointing
in the same direction: R&D spillovers are present, their magnitude
may be quite large, and social rates of return remain significantly
above private rates” (p. S43).
26. The conference proceedings in Munnell (1990) explore this issue.
Aaron (1990) is a good example of important critiques of the Aschauer
findings. Gramlich (1994) and Binder and Smith (1996) provide more
recent reviews.
27. Measurement problems may be more severe for government
capital because there are no markets for many types of such capital,
which makes estimation of user costs difficult.
α + β < 1
28. One obvious difference between private and public investment is
the financing mechanism. For example, the typical argument for
government infrastructure investment is a traditional public-good
argument that prevents returns from being recouped by the investor,
which can lead to underprovision of the good. Gramlich (1990)
discusses this in detail.
29. Brynjolfsson and Yang (1996) summarize earlier empirical work,
Sichel (1997) provides a broad analysis of the impact of computers,
and Triplett (1999a) presents a detailed critique of common
explanations for the productivity paradox. Ultimately, one would like
to answer a difficult counterfactual question—how fast would labor
productivity have grown in the absence of computers?—but this is
very difficult indeed. For example, the explosion of computing power
occurred roughly contemporaneously with the well-known
productivity slowdown, and one must distinguish the productivity
impact of computers from the host of factors examined in that
context. See Federal Reserve Bank of Boston (1980), Baily and Gordon
(1988), Baily and Schultze (1990), and Wolff (1996) for a few
examples of the extensive literature on the productivity slowdown.
30. There is strong agreement that adjusting the output of computers
for quality change is appropriate, but there are dissenting views.
Denison (1989) argues specifically against constant-quality price
indexes for computers.
31. See Baily and Gordon (1988), Stiroh (1998a), Gordon (2000),
Jorgenson and Stiroh (2000), and Oliner and Sichel (2000) for details
on this fundamental distinction. This discussion is also relevant to the
discussion of the renewed embodiment controversy below.
32. These empirical differences primarily reflect the time periods and
output concepts. See Oliner and Sichel (2000) for details.
33. As an important caveat, Triplett (1996) shows that one must
incorporate quality adjustments for all inputs to correctly allocate TFP
across sectors to specific high-tech industries. His results suggest that
falling prices of computers are in large part due to enormous technical
progress in the production of semiconductors, a crucial intermediate
input to computer production. See Oliner and Sichel (2000) for recent
estimates.
34. Gordon (1989) provides a history of the early evolution of
computers.
Endnotes (Continued)
FRBNY Economic Policy Review / March 2001 53
35. Gordon (2000) summarizes this pessimistic view. Kiley (1999)
presents a formal model of how computer investment could lower
productivity due to large adjustment costs.
36. Reported relative price changes are based on Gordon (1990) and
extended forward. This is a puzzling appeal to evidence, however,
since the goal of Gordon’s monumental effort was to develop better
output price measures and he explicitly states, “both input price and
output price indexes treat quality change consistently” (p. 52).
Moreover, this approach assumes no quality change in consumption
goods, so measured relative price changes are more accurately thought
of as the relative rate of technical change between these two.
37. In their introduction, Greenwood et al. (1997) seem to agree; they
view their motivating facts as evidence of “significant technological
change in the production of new equipment” (p. 342). Although they
do calibrate a simple two-sector model, it is not fully integrated with
their empirical work on the sources of growth and they reject it as an
unreasonable explanation of balanced growth rates.
38. See Triplett (1989) for a survey.
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The views expressed in this article are those of the author and do not necessarily reflect the position of the Federal Reserve Bank
of New York or the Federal Reserve System. The Federal Reserve Bank of New York provides no warranty, express or
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