What Happens when the Technology Growth Trend Changes? : Transition Dynamics, Capital Growth and the "New Economy

WORKING PAPER SERIES
What Happens when the Technology Growth Trend Changes? :
Transition Dynamics, Capital Growth and the "New
Economy
Michael R. Pakko
Working Paper 2001-020A
http://research.stlouisfed.org/wp/2001/2001-020.pdf
October 2001
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What Happens When the Technology Growth Trend Changes?:
Transition Dynamics, Capital Growth and the “New Economy”
Michael R. Pakko*
Federal Reserve Bank of St. Louis
411 Locust Street
St. Louis, MO 63102
Phone: (314) 444-8564
Fax: (314) 444-8731
E-mail: pakko@stls.frb.org
Working Paper 2001-020A
October 2001
Abstract
The rapid increase in U.S. economic growth during the late 1990s inspired speculation that an
acceleration in the rate of technological progress had given rise to an increase in potential
output growth. This paper considers the transition dynamics associated with such a change
using a general equilibrium framework that incorporates stochastic growth trends. The model
suggests that transition dynamics associated with a shift in the technological growth trend can
have important implications for macroeconomic growth patterns, particularly when
technological change is investment-specific. Simulations of the post-WWII U.S. economy
show that the model’s internal propagation mechanism is capable of explaining a significant
portion of the variation in growth rates over the sample period, particularly for investment,
capital accumulation, and employment.
*This paper has been prepared for the Federal Reserve Bank of New York conference “Productivity Growth: A
New Era?” November 2, 2001. Rachel Mandel provided invaluable research assistance. The views
expressed in this paper are those of the author and do not necessarily reflect official positions of the Federal
Reserve Bank of St. Louis, the Federal Reserve System or the Board of Governors.

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What Happens When the Technology Growth Trend Changes?:
Transition Dynamics, Capital Deepening and the “New Economy”
Introduction
The increase in productivity growth during the late 1990s has raised the issue of
whether a fundamental change has taken place in the U.S. economy. Although many
economists remain skeptical about “new economy” or “new paradigm” theories that have
emerged in this context, the conjecture that there has been a shift in the potential growth
trend has been seriously entertained. Indeed, the issue is often cast in terms of whether
recent trends suggest a return to growth conditions prior to the productivity growth
slowdown that apparently began in the early 1970s.
In this paper, I examine the implications a change in the trend rate of
technological progress in the context of a simple general equilibrium model that
incorporates stochastic growth trends. The model illustrates a potentially important but
often overlooked source of dynamics associated with such a change: the transition
dynamics due to a change in the optimal capital/labor ratio.
Simulations of the model’s responses to growth shocks suggest that long-run
adjustment of the capital stock to changes in underlying growth trends gives rise to
persistence in the model’s dynamics, so that changes in the growth rate of technological
progress may not be clearly manifested in measured productivity data for several years after
the event. Moreover, the inverse relationship between the capital/labor ratio and the
underlying growth trend implicit in the model’s dynamics implies non-monotonic
convergence paths for the growth rates of key macroeconomic variables.
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Another element of many “new economy” stories that has been the subject of
serious macroeconomic investigation is the notion that the productivity gains associated
with recent technological advances are embedded in new forms of capital. In the spirit of
this hypothesis, the model in this paper incorporates a role for capital-embodied, or
investment-specific technological progress.
Simulation experiments show that the transition dynamics associated with a shift in
this type of technology growth can have more dramatic implications for macroeconomic
growth patterns. For a given change in productivity growth, a change in the underlying
trend rate of technology growth displays both slower convergence of productivity and more
variable adjustment dynamics in the growth rates of macroeconomic variables.
To examine the importance of these effect in explaining recent growth U.S. growth
patterns, I take the model to the data by constructing empirical proxies for underlying
technology growth trends and conducting model simulations of the post-WWII U.S.
economy. The results show that the model’s dynamics can explain an important share of
growth fluctuations over the sample period, particularly for investment, capital
accumulation, and employment. The contribution of dynamics associated with
investment-specific technology growth trends is relatively modest, but has important
implications for the outlook for future trends in productivity growth.
Issues and Questions
Figure 1, showing the growth of output per hour in the private business sector, is
typical of the evidence used to illustrate changes in long-run growth trends. For the entire
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postwar sample period, the growth rate of this productivity measure averaged about 2.5%.
However, the average growth rate from 1947 to 1973 was 3.3%, falling to 1.5% for the
period 1973-1995. Recent data (1996-2000) suggest a growth trend has risen to 2.6%. Of
course, such comparisons are quite sensitive to the sample periods selected. Nevertheless,
they illustrate how the data are often parsed to demonstrate the widespread conception that
there is a variable component of the underlying trend rate of productivity growth.
Focusing on the role of new information technologies in the emergence of the “new
economy,” recent growth accounting analyses investigating the notion of a changing
growth trend have been particularly concerned with finding a role for computer-related
productivity gains. For example, Gordon (1999) examines a sectoral decomposition,
finding that most productivity gains in total-factor productivity are in the computer
producing sector. Oliner and Sichel (1994, 2000) consider the importance of computers in
the capital component of their growth accounts, finding an important role for the use of
computers embedded in the growth of capital services. Jorgenson and Stiroh (1999)
explicitly incorporate computer related growth in demand for investment and consumer
durables. Whelan (1999b) adjusts the growth contribution of capital deepening by
modeling the rapid obsolescence of computer hardware, and Kiley (1999) incorporates
investment adjustment costs associated with new technologies into a growth accounting
framework.
In these studies, the nature of the issue being investigated—an apparent
acceleration of productivity growth in the latter half of the 1990s—necessitates analysis
with limited data. As Figure 1 illustrates, however, there is a considerable amount of
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variation in 5-year average rates of productivity growth. Uncovering emerging trend
changes is an inherently difficult endeavor.
To the extent that changes in underlying technology growth trends have
predictable implications for emerging patterns of productivity growth, understanding
these dynamics can be important for interpreting observed changes in growth. The model
examined in this paper suggests one possible source of such patterns, which can be
demonstrated using the comparative statics of a standard Solow growth model.1

An Illustration Using the Solow Growth Model
In the Solow growth model, output is produced using capital and labor with a
constant-returns-to-scale production technology, savings is a constant fraction, s, of
output, and capital depreciates at rate . In the presence of population growth, n and
labor-augmenting technical change, g, the standard capital accumulation equation implies
that capital evolves according to:
∆k = i − k
δ − nk − gk
(1)
where k and i represent per-capita magnitudes of capital and investment (in labor
efficiency units). Setting k=0 in equation (1) defines a locus of feasible steady-state
values for the capital/labor ratio. The savings function, s@f(k) and the equilibrium
condition that savings equals investment then defines a unique steady state.
Figure 2 illustrates this relationship using a familiar textbook diagram, and
demonstrates the effect of an increase in the technological growth rate, from g to gN. In
1See, for example, the popular macroeconomics textbook by Mankiw (1992).
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the initial steady state, the capital/labor ratio is k* . At the higher growth rate, the
equilibrium real rate of return in the economy is higher, so that the optimal marginal
product of capital increases. In the Figure 2, the increase in g is represented as an
increase in the slope of the locus of steady states, resulting in a new long-run equilibrium
that is associated with a higher marginal product of capital and hence a lower
capital/labor ratio, k*N.
The implication of this comparative-statics result for dynamics is that while the
underlying technology growth rate – and hence the long-run growth rate of the economy –
has increased, there will be a transition period in which the declining capital/labor ratio
tends to suppress growth. In this simple model it is unclear how these two opposing
forces might interact during the period of transition, but its basic mechanism provides the
intuition for interpreting the analyses of growth shocks presented in subsequent sections
of this paper.
The basic Solow growth model abstracts from household optimization over
consumption-saving and labor-leisure choices, and its comparative statics fall short of
providing a fully articulated description of dynamics. The model developed in the next
section incorporates intertemporal optimization, endogenous labor/leisure choice, and a
role for investment embodied technological progress, yet it retains much of the
fundamental simplicity of the Solow growth model so as to focus on the dynamics of
capital-transition paths. The first issue to be addressed is how the offsetting forces – long-
run growth and capital accumulation – interact in the dynamics of a plausibly calibrated
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model, both for conventional neutral technological growth shocks and for investment-
specific growth shocks.2
With these insights in hand, I take the model to the data by incorporating a limited-
information setting in which agents infer the underlying growth trend by solving a signal-
extraction problem. This allows for a model-consistent approach to empirically estimating
the perceived trend components of data series for technology growth. Simulating the
model for the post-WWII U.S. economy, I find an important role for capital transition
dynamics in explaining fluctuations in the growth rates of key macroeconomic variables.
A Neoclassical Stochastic-Growth Model
Model Structure
The underlying structure of the model that I examine is quite basic: Consumers
(represented by a social planner) maximize logarithmic utility over consumption and leisure,
∞
max ∑ βt[ln(C ) +
1− N
t
ν ln(
)],
t
t = 0
subject to an overall resource constraint with Cobb-Douglas production:
−
Y = (1− )Z K a N 1
τ
α + T = C + I .
(2)
t
t
t
t
t
t
In equation 2, C , K , N , and I represent consumption, capital, labor, and gross
t
t
t
t
investment, respectively. Z is an index of total-factor, or neutral, productivity. Income is
t
2These basic dynamics are also presented in a previous paper, Pakko (2000), where the focus is
on the role of transition dynamics for conventional growth accounting exercises.
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subject to a tax rate, , with government revenues rebated lump sum via T= Y (taken as
given in the optimization problem).3
In order to incorporate the notion that the productivity-enhancing potential of
recent technological progress is embodied in new capital equipment itself (particularly in
for new information-processing and communications technologies), the model
incorporates a role for investment-specific technological change, as modeled by
Greenwood, Hercowitz and Krusell (1997,2000). Specifically, the capital accumulation
equation is assumed to be:
K
1
(
δ)
(3)
1 =
−
K + Q I
t +
t
t
t
where Q represents an index of the quality of new capital goods. When Q is fixed (and
normalized to one), the model is a standard balanced growth model. Growth in Q is
associated with technological progress that becomes embodied in the quality of the stock
of capital equipment.4
The pair of papers by Greenwood, Hercowitz and Krusell (1997,2000), both of
which focus on this type of investment-embodied technological progress, provide a
convenient context for describing the distinguishing feature of the present analysis. In the
first paper, Greenwood et al investigate the contribution of investment-embodied growth
to overall economic growth in the long run. Following in the tradition of growth-
accounting literature, they consider steady-state implications in terms of averages for the
3Taxes are included in order to incorporate their importance for marginal decision-making
(particularly their effects on the after-tax marginal product of capital and investment), and rebated lump-
sum to abstract from wealth affects associated with taxation.
4Hercowitz (1998) relates this type of model of investment-specific technological change with
the “embodiment” controversy of Solow (1960) and Jorgenson (1966) .
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entire sample period covered by their data. In the second paper, which follows in the
spirit of real-business-cycle analyses pioneered by Kydland and Prescott (1982), Hansen
(1985) and King, Plosser and Rebelo (1988a), they examine the cyclical implications of
Q-shocks in terms of deviations of model variables from a long run trend, where the trend
is identified and removed by the application of a Hodrick-Prescott filter. The H-P filter
removes slow-moving, low-frequency components of the data, implicitly allowing for a
trend that is variable over time. In this paper, my focus is on that variation in longer-run
underlying growth rates. That is, the model incorporates a role for stochastic growth
trends.5
The stochastic growth aspect is modeled by assuming that each of the technology
variables, Z and Q, can be decomposed into trend and cyclical components as
Z = G v
and
Q = G v
t
zt
zt
t
qt
qt
(4)
where
G
γ
+
,
,
1 =
G
i = z q
it
it
it
The represent growth rates of the underlying trends, while and
are stationary
i
zt
qt
cyclical components that reflect transitory shocks to technology. The latter pair of
technology variables are associated with the stationary shocks commonly assumed in the
real business cycle literature. The focus here is on the idea that the trend variables are
also subject to stochastic variation.
5Examples of similar approaches to modeling stochastic growth in a computable general
equilibrium framework include King, Plosser and Rebelo (1988b); and King and Rebelo (1993).
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