R&D and Real Interest Rate in the US: Theory and Empirics
Constantine Alexandrakis∗
Emory University
September 2003
Abstract. In this paper we investigate the relationship between the long-run real interest rate and the share of
resources devoted to research in the US. In contrast to what is predicted by many R&D-based growth models we
find the two to be positively correlated. We then calibrate a model with endogenous technological change and
examine if it can produce a positive relationship between the two variables. Our results provide an appealing
explanation for the observed low-frequency variations in the share of labor employed in R&D and the long-run real
interest rate, and for the productivity slowdown.
JEL classification: E40, O30, O40, O51
Keywords: R&D, real interest rate, calibration, endogenous growth, productivity slowdown
∗
This paper is based on my doctoral dissertation. I would therefore like to thank my committee members Attiat Ott,
Zheng Liu, and Wayne Gray for extremely valuable comments. I have also benefited from comments by Charles
Evans, Stefan Krause, Bob Chirinko, and Andrew Young. All remaining errors are my responsibility.
1
1.
Introduction
In his testimony to the National Academy of Sciences in December 8, 1999, Harris N. Miller,
President of the Information Technology Association of America, reported that between 1995 and 1998
the Information Technology (IT) sector “contributed one-third of all US economic growth”, and that
investment in IT accounted for “nearly one-half of all business investment”.1 A year earlier, the
Department of Commerce reported that “employment levels for computer systems analysts, engineers, and
scientists more than doubled from 1988-1996”, whereas during the same period “the number of workers
across all occupations in the United States grew by 12 percent.”2 In addition, in the late 1980s and 1990s
the real rate of return to stocks, and the real interest rate paid to bonds, time deposits, and other securities
experienced on average levels much higher than the ones observed in the 1970s and early 1980s. The
purpose of this study is to determine whether an explanation for this simultaneous increase in the shares
of income and labor devoted to the production of new technology and the rate of return to financial assets
can be found within the realm of economic theory.
Addressing this issue becomes even more significant once we consider that the only models
providing a link between the real interest rate and the share of resources devoted to research, R&D-based
growth models, predict a negative relationship between the two. In P. Romer’s (1990) model of
endogenous technological change, when the interest rate is treated as an exogenous parameter, an increase
in the real interest rate leads to a decrease in the share of labor devoted to research and the economic
growth rate.3 Intuitively, because research takes time, an increase in the real interest rate raises the
opportunity cost of devoting resources to research instead of devoting them to a market activity with more
immediate payoffs. In other words, an increase in the real interest rate reduces the present value of the
stream of future profits that a discovery can generate. In addition, because in the model assets supplied by
households serve as an input in the production of capital, a higher interest rate raises the cost of
borrowing for the producers of capital equipment, and thus reduces the profit they can earn at each period
2
from the commercial application of their technological discovery. Both effects tend to eliminate
incentives for individuals to devote resources in research. When the preference side is specified, the
interest rate becomes a function of the subjective discount factor through the Euler equation, and the share
of labor devoted to research becomes decreasing in the subjective discount factor.
Aghion and Howitt’s (1992) model of creative destruction also predicts a negative relationship
between the real interest rate, which Aghion and Howitt treat as exogenous, and the share of resources
devoted to research. Because, however, Aghion and Howitt assume that labor and not assets is the input
that, combined with a patent, is required for the production of capital equipment, an increase in the real
interest rate in this model affects the share of resources devoted to research only by raising the marketdiscount factor. The same is true about Grossman and Helpman’s (1991a, b) quality ladders model, which
also finds the share of resources devoted to research to be decreasing in the real interest rate. When the
preference side is specified, like Romer’s model, Grossman and Helpman’s model finds the share of
resources devoted to R&D to be decreasing in the subjective discount factor.
It is clear that the negative relationship between the real interest rate and the share of resources
devoted to research that is found in all three models stands in strong contrast with the observations laid
out in the beginning of the introduction. Motivated by this fact, we conduct a formal statistical analysis of
the relationship between the real interest rate and the share of resources devoted to research. Moreover,
we raise the question of whether, if in fact the two variables prove to be positively correlated in the data,
the models can provide an explanation for this relationship. The statistical analysis and the subsequent
attempt to answer this question provide some interesting insights about the effect of variations in research
funding on the real interest rate during the last three decades, and on the productivity slowdown observed
in the 1970s. Several conclusions about the effect of specific policies on the rate of economic growth are
also drawn.
The remaining of this paper is organized as follows: In section 2, using US time-series data, we
investigate the relationship between the real interest rate and the share of labor employed in R&D, and
3
between the real interest rate and the share of GDP spent in R&D, for a period covering from 1963 to
1999. We find the relationship between the two variables to be positive for each case. In section 3, we
solve and calibrate a model with endogenous technological change, and compare its steady state
properties with US data. We specifically examine whether the model can explain the correlation between
the real interest rate and the share of resources devoted to research. In section 4 follows a discussion on
whether the explanation provided by the model is consistent with the behavior of other related variables.
The paper ends with a summary of conclusions in section 5.
2.
Real Interest Rate and R&D: The Data
The variables used in our analysis are the share of labor conducting research (RSESH), the real
interest rate, and expenditure in research as a share of GDP (TSHEXP). The variable RSESH was
constructed by dividing the number of research scientists and engineers employed in industrial R&D by
total non-farm employment. Data on non-farm employment were obtained from the Bureau of Labor
Statistics. Data on research scientists and engineers in R&D were taken from the Industrial R&D
Information System (IRIS) of the National Science Foundation (NSF) and are based on an annual survey.
Some important definitions of the survey are the following:
Research and Development: Basic and applied research in the sciences and engineering and the design
and development of prototypes and processes. This definition excludes quality control, routine product
testing, market research, sales promotion, sales service, research in the social sciences or psychology,
and other non-technological activities or technical services.
4
R&D scientists and engineers: The January number of those engaged in research and development full
time, and the full-time equivalent of those working part time in research and development. Scientists and
engineers are defined as persons engaged in scientific or engineering work at a level which requires a
knowledge of physical, life, engineering, or mathematical sciences equivalent at least to that acquired
through completion of a 4-year college course with a major in one of those fields.
The interest rate is defined as the cost for the firms of borrowing assets. Consequently, as a
measure of the real interest rate, the rate of return to equity, and specifically the annual rate of return to
the S&P 500 (R), and the prime rate (PR) are used. Since the reported rate of return is nominal, it was
adjusted for inflation by subtracting from it the percentage change in urban CPI. The data on CPI were
obtained from the Bureau of Labor Statistics. Data on the rate of return to the S&P 500 were taken from
Ibbotson Associates’ 2002 Yearbook and data on the prime rate were taken from the Federal Reserve
Statistical Release. Data on R&D expenditures were obtained from the Science and Engineering
Indicators of the NSF.
Figure 1 reveals that both interest rates are much more sensitive to high frequency shocks than the
fraction of labor engaged in research, or the share of GDP spent in research. Since we are interested in the
relationship between the variables at the steady state we used a simple moving-average smoothing
technique with an 8-year rolling window to reduce the effect of high frequency shocks.4 Figure 2 shows
the behavior of the smoothed series over time. One issue that needed to be addressed was that changes in
the rate of return to the S&P 500 could at least partially be attributed to changes in the risk differential
between investment in equity and investment in a risk-free asset. To account for that factor, a variable
denoted by RADJ was constructed to obtain the real rate of return per unit of risk. RADJ was constructed by
dividing the average real annual rate of return to the S&P 500 in a given period by the standard deviation
during the same period. If the excess return per unit of risk (Sharpe ratio) is relatively constant, then any
changes in RADJ should be attributed to changes in the risk-free interest rate. The correlations reported in
5
Table 1 verify what is evident in Figure 2; the smoothed series for R, RADJ, and PR are significantly and
positively correlated with the smoothed series for RSESH and TSHEXP. Finally, as one would expect,
TSHEXP and RSESH are strongly and positively correlated with each other.
Figure 3 is a graphical representation of two interest rates that are commonly used as proxies for
the risk-free interest rate: The interest rate paid to the 3-month Treasury Bill (TRATE), and that paid to 3month time deposits (CDRATE). The series presented are also smoothed using an 8-year moving average
technique. The data were obtained from the Federal Reserve Board’s Statistical Release. As can be seen,
the series are characterized by the familiar pattern of a decrease during the 1970s and an increase back to
or above their 1960’s levels during the late 1980s and the 1990s. In addition, the correlation coefficient
between RSESH and CDRATE is equal to 0.661, and the correlation coefficient between RSESH and
TRATE is equal to 0.731. In conclusion, changes in risk do not seem to be responsible for the observed
positive correlation between the real interest rate and the share of resources devoted to research.
The next step is to examine if lagged values of the real interest rate have predictive power on the
share of resources allocated to research, or whether the opposite is true. The results from several Grangercausality tests presented in Table 2 show that, when five lags are included, the null hypothesis that the
share of labor employed in the research sector does not Granger-cause the real interest rate is rejected at a
5 percent significance level when the variables R and PR are used, and at a 1 percent significance level
when the variable RADJ is used. On the other hand, in all three cases, the null hypothesis that the real
interest rate does not Granger-cause the share of employment in the research sector cannot be rejected at a
10 percent significance level. These tests suggest that the direction of causality runs from the share of
employment devoted to research to the real interest rate.
When Granger-causality tests between TSHEXP and the three measures of the interest rate are
employed, the results do not support any Granger-causality. However, when non-smoothed series are
used, the null hypothesis that TSHEXP does not Granger-cause RSESH is strongly rejected but the null
that RSESH does not Granger-cause TSHEXP cannot be rejected at a 10 percent significance level. When
6
the smoothed series are used the test supports a two-way causality. The null, however, that TSHEXP
does not Granger-cause RSESH is rejected much more strongly. In conclusion, spending in R&D as a
share of GDP seems to determine the share of labor devoted to research, which in turn determines the real
interest rate.
3.
Real Interest Rate and R&D: The Models
Given our findings, the question that arises is whether an explanation consistent with the
predictions of R&D-based growth models can be provided for the observed co-movement between the
real interest rate and the share of resources devoted to research. To answer this question we solve and
calibrate a simple model economy with endogenous technological change and examine its steady state
properties. The model departs from Romer’s only in the following respects. First, to simplify the model, it
is assumed that labor is homogeneous. Secondly, we use discreet instead of continuous time in order to
make calibration possible. Finally, research and the production of capital durables take place within one
sector.
The economy can be described as follows: There are many identical infinitely lived households.
Production of final goods takes place within a single, competitively behaving firm. Capital goods are
produced by a number of identical research firms. Each research firm is the owner of a patent (blueprint).
At the beginning of each period, taking as given the labor compensation in each sector, the households
allocate their labor endowment between working in the final goods’ sector and conducting research.
Finally, the households decide how much of their income to consume, and how much to save so as to
increase the stock of their assets. The research firms are owned by the households. Each labor hour that a
household contributes to research buys it one share of the new research firm established once a blueprint
is discovered. At the beginning of each period, each research firm that owns a blueprint borrows assets
7
from the households and combines them with the blueprint to produce a number of capital durables of a
specific type. Each research firm has property rights on the use of their blueprint and thus monopoly
power. The final goods’ firm rents at the beginning of each period a certain amount of durables from each
research firm and labor from households, and uses it for the production of final goods. At the end of each
period, the final goods’ firm returns the undepreciated amount of durables to the research firms together
with rental payments for its use. The firm also provides payments to the households for the use of their
labor services. Each research firm returns the undepreciated stock of borrowed assets back to the
households together with a rental payment for its use. The monopoly profits of each research firm are then
divided equally among the shares. A circular flow diagram for this economy is presented in Figure 4.
Given the monopolistic nature of the research firms, the solution of this model economy follows the
decentralized equilibrium approach.
3.1
A Model Economy: Description
Let At denote the number of all different research firms existing at time t, and xjt denote the
number of units of a durable owned and rented out by research firm j in period t. The production function
for final goods is given by
1−α
Yt
Yt = L
At
∑ xα ,
j =1
(1)
jt
where LYt is the amount of labor devoted to the production of final goods at period t. The stock of
blueprints evolves by the following rule:
At +1 = At + ZAt LAt ,
(2)
In equation (2), L At denotes the fraction of labor devoted to the production of new blueprints at time t,
and Z denotes research productivity. A crucial assumption is that technological knowledge incorporated in
8
the stock of durables, At, can be used freely in the production of new blueprints. For each research firm j,
the production function for durables after a discovery has been made is given by
x jt = φ jt ,
(3)
where φ jt denotes the units of assets borrowed from households by research firm j. The net increase in
the number of durables during period t is given by
At +1
At
j =1
j =1
∑ x jt +1 − (1 − δ )∑ x jt ,
(4)
where δ is a depreciation parameter for which it is true that δ ∈ [0,1]. From equations (3) and (4), the
capital market’s clearing condition that sets gross investment equal to saving requires that
At + 1
At
At + 1
At
j =1
j =1
j =1
j =1
∑ x jt +1 − (1 − δ )∑ x jt = ∑φ jt +1 − (1 − δ )∑φ jt +1 ,
(5)
where the left hand-side of equation (5) represents the total number of new durables produced during
period t, and the right hand side of the equation represents the units of assets created during period t. In
the absence of government in the model, savings is defined as the portion of aggregate income not
consumed. Therefore, gross investment can be expressed as:
At + 1
∑x
j =1
At
jt +1
− (1 − δ )∑ x jt = Yt − Ct
(6)
j =1
An aggregate resource constraint requires that:
LYt + LAt = 1
(7)
Equation (7) states that the sum of labor hours employed in both sectors should be equal to the total labor
endowment, which is normalized at 1.
Let WYt denote the hourly wage of labor employed in the final goods’ sector at time t, Pjt denote
the rental price charged by research firm j in period t for its durables, and Dt,t+I denote the market discount
9
factor applied to period t + I at time t so that Dt,t = 1, and Dt,t+I =
t + I −1
∏ (1 + R
n
− δ ) −1 ∀I > 0 , where
n =t
I ∈ N and Rt denotes the real interest rate at time t. The problem for the final goods’ producer is to
maximize a discounted stream of profits taking the production technology, the price for her product and
the prices of inputs at each period as given. Mathematically the producer’s problem can be expressed as
∞
max ∑ Dt ,t + I π yt + I ,
x j , LY
I =0
where π Yt = Yt − WYt LYt −
At
∑P x
j =1
jt
jt
. The price of final goods is used as a numeraire and is set equal to 1.
Given the absence of intertemporal dependency, the solution to this problem is equivalent to the oneperiod profit maximizing solution. The two first-order conditions yield the following two equations:
−α
Yt
WYt = (1 − α ) L
At
∑ xα
j =1
(8)
jt
Pjt = αL1yt−α x αjt −1
(9)
In equation (9), Pjt( x jt ) is the inverse demand function for the durable produced by firm j. Each research
firm faces the problem
∞
max ∑ Dt ,t + I π jt + I ,
x
I =1
where π jt = Pjt x jt − Rtφ jt . The first order condition yields the following equation:
Pjt =
Rt
(10)
α
Substituting Pjt with its equivalent from equation (10) in the inverse demand function in equation (9) and
the profit function, we obtain the following two equations:
10
1
 a 2 1−α
xt =   Lyt
 Rt 
(11)
1−α 
 ⋅ Rt ⋅ xt
 α 
π jt = 
(12)
If all firms can borrow at the same interest rate, the equilibrium price charged and quantity produced will
be the same for all types of durables. Therefore, the subscript j can be dropped and we obtain:
At
At
j =1
j =1
∑ xt = At xt = ∑φt =Atφt
(13)
By setting K t = Atφt and using equation (13), equation (1) becomes
Yt = ( At LYt )1−α K tα ,
(14)
where Kt denotes the total stock of assets available at time t. Equation (14) relates the production of final
goods to the stock of assets. Similarly, by substituting the stock of assets with Kt in equation (6) we
obtain:
K t +1 − (1 − δ ) K t = Yt − C t
(15)
Equations (8), (9), and (12) become respectively:
WYt = (1 − α ) LYt−α At1−α K tα
(16)
Pt = α ( At LYt )1−α K tα −1
(17)
K
 1 − α  Kt
= α (1 − α ) L1Yt−α ( t )α
 Rt
At
 α  At
π jt = 
(18)
It follows that Rt = α ⋅ MPK where MPK stands for the marginal product of assets used in the
final goods’ sector.
11
The value of each blueprint in terms of final goods will be equal to the discounted
stream of profits that it can generate when used in the production of durables. The stream of
profits from renting each type of durables developed at time t is given by:
∞
∑D
I =1
t ,t + I
π jt + I = V jt
Thus, each stock issued in the R&D sector at the end of period t will have a value equal to
∞
At +1 − At
Vjt = A t Z∑ Dt ,t + I π jt + I .
L At
I =1
W At =
(19)
The value of this share is the compensation of each labor hour devoted to research in period t. Due to free
mobility of labor between the two sectors, a no-arbitrage condition requires that
WAt = WYt = Wt .
(20)
Households are assumed to have identical preferences with respect to consumption at every date.
Each household’s labor endowment in period t is set equal to lt . The representative household’s lifetime
utility function at period t is assumed to be of the form:
∞
U t = ∑ θ t ln ct
(21)
t =0
We use θ to denote the subjective discount factor for which it is true that θ ∈ [0,1]. Small case letters
denote individual levels. Each household at time t faces the following budget constraint:
ct + k t +1 − k t = Wt l t + ( Rt − δ ) ⋅ k t
(22)
In mathematical terms, the representative household’s problem can be expressed as
∞
max ∑ θ t ln ct ,
ct , k t + 1
t =0
subject to an infinite series of budget constraints as the one described by equation (22). By setting up the
Langrangian we get:
12
∞
∞
t =0
t =0
λ = ∑ θ t ln ct + ∑ Λ t (Wt lt + Rt kt − ct − kt +1 +(1 − δ )kt )
The first order conditions for optimality require that
λt =
1
ct
(23)
λt
= θ(1 + Rt − δ )
λ t +1
(24)
lim θ t λ t k t +1 = 0
(25)
t →∞
and that the original budget constraint expressed by equation (22) holds. Equation (25) is the usual
transversality condition, and λ t =
Λt
.
θt
In summary, the equilibrium in this economy consists of a set of individual allocations
{ct , kt +1 , lt }t∞= 0 and aggregate allocations {Ct , LYt , LAt , K t +1}t = 0 as well as prices {Pt , Rt ,WAt ,WYt , Λ t }t = 0
∞
∞
that satisfy the following conditions: (i) Taking prices as given, the allocation solves the household’s
problem. (ii) Taking input prices as given, the allocation satisfies the profit maximizing conditions (8) and
(9) in the final goods’ sector. (iii) Taking input prices and the demand function for durables as given, the
allocation satisfies the profit maximizing condition (10) for each research firm. (iv) The aggregate
resource constraints (7) and (15) hold, the no-arbitrage condition (20) is satisfied, and all markets clear so
that ct = C t , lt = 1 , and k t +1 = K t +1 .
3.2
A Model Economy: Solution
According to Kaldor’s (1957) stylized facts, at the steady state, output, technology, capital, and
consumption grow at the same rate, while the interest rate follows a horizontal trend. Therefore, in the
13
absence of stochastic disturbances, the interest rate becomes time invariant, and so does each period’s
profit in the R&D sector. By substituting Rt with R, we can express the market-discounting factor as
Dt ,t + n = ( Dt ,t +1 ) n . The value of each blueprint now becomes:
∞
∞
I =1
I =0
V jt = ∑ ( Dt ,t +1 ) I π A = Dt ,t +1π A ⋅ ∑ ( Dt ,t +1 ) I .
For R > δ , it follows that Dt ,t +1 < 1 and so the above power series converges to
Vt =
Dt ,t +1
1 − Dt ,t +1
π A=
1
πA
R −δ
(26)
Using equations (18) and (26), equation (19) becomes:
W At =
(1 − α )
α
⋅
R
⋅ Z ⋅ Kt
R −δ
(27)
Using equations (16), (20) and (27) we get:
Ly =
R −δ
.
αZ
(28)
Equations (23) and (24) imply:
Ct +1
= θ( R + 1 − δ )
Ct
(29)
Since at the steady state consumption and productivity grow at the same rate, we use equations (2) and
(29) to obtain:
LA =
θ( R + 1 − δ ) − 1
Z
(30)
The resource constraint in equation (7) and equations (28) and (30) imply:
R − δ θ (R + 1 − δ ) − 1
+
=1
αZ
Z
(31)
Finally, using equation (31) to solve for R we get that
14
R=
where ψ =
1
ψ
1
α
Z+
ω
ψ
+ θ , and ω = 1 +
(32)
δ
− θ (1 − δ ) .
α
An examination of equation (32) reveals that the real interest rate, like the share of labor devoted
to each sector, depends on the value of research productivity, Z. Is it possible that Z has experienced
variations during the period under examination? The answer is yes if, in accordance with Aghion and
Howitt, the economy experienced either “a fundamental breakthrough leading to a Schumpeterian wave
of innovations…” or “the exhaustion of a line of research.” (p. 335) Both events would have an impact on
research productivity. In addition, variations in Z could represent changes in government subsidies to the
research sector. (Romer, 1990, p. S96) It is therefore essential to examine the effect that a change in Z
would have on the share of labor devoted to research and the real interest rate. The effect of a change in Z
on the real interest rate is given by:
dR 1
=
dZ ψ
(33)
Since G = θ ( R + 1 − δ ) , the effect of a change in Z on the growth rate is given by:
1
dG
=θ .
dZ
ψ
(34)
Similarly, the effect of a change in Z on the share of labor devoted to research is given by:
 ωθ
 1
dLA
= −
+ θ (1 − δ ) − 1 2
dZ
ψ
Z
(35)
Cleary, whether all three derivatives are simultaneously positive will depend on the parameter values. To
restrict these values we employ the method of calibration.
15
3.3
A Model Economy: Calibration
Following Kydland and Prescott (1982), the income paid to owners of assets is set equal to 36
percent of GNP. This implies a value for alpha of 0.6. Interestingly enough, this value is much higher
than the ones obtained when exogenous growth models are used, and closer to the value estimated by
Romer (1987). Driving this result is the fact that a fraction of the income generated by capital is used to
compensate the researchers responsible for designing these capital durables. In the model, this fraction is
equal to (1 − α ) ⋅ α ⋅ Y . Only the remaining fraction, α 2 ⋅ Y , ends up in the hands of stockholders and
other owners of assets used in the production of final goods. Thus, it seems that calibrated values for the
share of capital in output production based on exogenous growth models understate the contribution of
capital in the production of final output. In addition, because of this fact, using in this model calibrated
values consistent with exogenous growth models might lead to erroneous conclusions. For example, the
mark-up implied by equation (10) is equal to 1.667, only a little higher than most empirical estimates and
far lower than the number reported by Jones and Williams (2000) who used a calibrated value for the
share of capital borrowed from Kydland and Prescott (1991).
According to the NIPA tables, the capital to annual output ratio should be set equal to 2.8. This
implies a net interest rate equal to 0.1285. The annual net growth rate of the model economy, G, is set
equal to 0.02. Based on NIPA tables, the share of investment to GNP is set equal to 0.21. Using the fact
that
I
I Y
= ⋅ , where I represents investment, an estimate for the investment to capital ratio equal to
K Y K
0.075 is obtained. By rearranging the law of motion of capital it is found that δ =
I
− G . This yields an
K
annual depreciation rate equal to 0.055. Substituting these results in equation (29) and solving for theta, a
value for theta equal to 0.95 on an annual basis (or 0.987 on a quarterly basis) is obtained. Using equation
(32) we obtain an estimate of Z equal to 0.1425. In table 3 a summary of the calibrated values of the
16
parameters of the model is presented. The fact that σ is equal to 1 is implied by the log-linearity of the
utility function with respect to consumption, where
1
is the intertemporal elasticity of substitution of a
σ
CRRA utility function.
Given these numbers, the value of equation (33) is 0.382, equation (34) is equal to 0.363, and
equation (35) is equal to 2.737. Thus, for reasonable values of the parameters so that θ , ψ , and Z are
positive, and the bracketed term in equation (35) is negative, the growth rate, the real interest rate, and the
share of labor devoted to research will all be increasing functions of Z. Figure 5 graphs the steady state
values of the key variables corresponding to different levels of Z. Intuitively, the results can be explained
as follows: A change in any parameter that results in a reallocation of inputs towards research will cause
an increase in the rate of technological innovation. Consequently, the demand for assets in order to
transform these new ideas into capital durables will be greater. Households however, will be willing to
accept a steeper consumption path and save more only if there is an increase in the real interest rate. As a
result, as long as savings are not supplied “too inelastically”, the growth rate, the share of labor devoted to
research, and the equilibrium real interest rate determined in the capital market will all increase.
Unfortunately, the match is not perfect. The model predicts that about 14 percent of total
employment should be engaged in research. This number is too high compared to the data according to
which the share of labor employed in industrial research is less than 1 percent of non-farm employment.
Similarly, the ratio of equation (35) to equation (33) tells us that an increase in the share of labor
conducting research by 1 percentage point will increase the real interest rate by approximately 7.2
percentage points. The data suggest that such an increase in the rate of return to equity can be achieved by
an increase in the share of labor conducting research by just a little over 0.1 percentage points.5 Although
this discrepancy can be partially explained by the fact that the data do not include non-industrial research,
the numbers still seem to be “too far” off.
17
In conclusion, the simplified version of Romer’s model examined in this section is consistent
with, and can provide an explanation for the co-movement between the real interest rate and the share of
resources devoted to research that was observed in the data. It does however require significant
improvements as it overstates the share of labor devoted to research that is required to produce long-run
growth consistent with US data, and understates the response of the real interest rate to changes in the size
of that share. On the other hand, because Aghion and Howitt, and Grossman and Helpman assume that
assets are not required in the production or implementation of new technology, their models are not
capable of generating co-movement between the real interest rate and the share of resources devoted in
research, since changes in the rate of technological growth will have no effect on the demand for savings.6
4.
Further Evidence
In the previous section it was argued that variations in the real interest rate are caused by changes
in the rate of technological discovery. If this claim is true, one should expect a change in the real interest
rate to be accompanied by a change in US productivity growth in the same direction. To examine whether
the data support this hypothesis, time series data on US labor productivity for the period covering from
1963 to 1999 are examined. Secondly, Romer’s model suggests that the observed variations in the share
of labor conducting research and consequently the rate of technological discovery must have been caused
by either changes in government subsidies to the research sector, or shocks in research productivity. To
determine whether such shocks are evident in the data, time series data on federal and industrial
expenditure in R&D as a share of GDP are examined.
18
4.1
US Labor Productivity
Figure 6 presents graphically 8-year moving-average smoothed series for US labor productivity
growth rates from 1963 to 1999. The data were obtained from the Bureau of Labor Statistics. One can
easily identify a familiar pattern. Like the other series, productivity growth is also characterized by a
sharp decrease during the 1970s, and an overall increase during the 1980s and the 1990s. However,
although the share of employment conducting research has more than recovered from its sharp decline
that took place between 1963 and 1975, the growth rate of labor productivity has gained back only a
fraction of its pre-1970s levels. This well established fact is referred to as the productivity slowdown. If,
therefore, the post-1979 increase in the real interest rate should be attributed to an increase in the rate of
technological discovery caused by the increase in the share of labor employed in the research sector, why
hasn’t productivity growth also experienced an equivalent increase?
One explanation is that technological innovation affects productivity with a lag, and therefore the
effects from the increase in the size of the R&D sector in the 1980s that began showing in the late 1990s
have yet to be completed. Adams (1990) for example found a 10-year lag between the development of
academic technology and its absorption by industry. This lag may be larger when network externalities or
other sources of uncertainty are present. This hypothesis is supported by the fact that the annual growth
rate of labor productivity increased further and between 2000 and 2002 averaged 2.85 percent per year,
despite the slowdown in GDP growth that was experienced during the same period.7
The second explanation has to do with the difficulties associated with measuring productivity
changes. Baily and Gordon (1988) point out that much of investment in new technology is directed
towards improving convenience, an example being the introduction of ATM’s that allow 24-hour
banking. Although such new technology might reduce transaction costs by reducing, for example, waiting
time at the bank, these effects do not show up in the National Accounts. Griliches (1988, 1994) argues
19
that not only has a large part of investment in new technology gone to improvements in such
“unmeasurable” sectors, but also that the relative importance of these sectors in total production has been
steadily growing. Other measurement issues, ranging from the fact that a large fraction of industrial R&D
is directed towards the government and thus its effects do not show up in productivity measures, to the
fact that the introduction of similar and often cheaper varieties of the same product in the market are
treated as an introduction of new and separate commodities8 can be found in Griliches (1979, 1994).
Taking into account these difficulties, we conclude that the behavior of US labor productivity is roughly
consistent with the hypothesis that changes in the share of labor employed in the research sector, by
affecting the rate of technological innovation, are responsible for the observed variation in the real interest
rate.
4.2
Federal and Industrial Funding of R&D
In an effort to determine whether the productivity slowdown was caused by a decrease in the
productivity of the R&D sector, Griliches (1994) used three-digit SIC data to regress industry level total
factor productivity (TFP) growth rates on R&D investment to sales ratios. The results provided evidence
of a decrease in R&D productivity in the latter half of the 1970s, which Griliches attributed to increased
import competition and the two oil shocks that occurred during that period. According to Griliches, these
shocks were more likely to affect R&D intensive industries such as chemicals and petroleum refining.
These results are puzzling however in light of the fact that the decline in the share of labor employed in
the research sector and the real interest rate began much earlier, in the mid-1960s. If a decrease in
research productivity was not what caused the decrease in the series observed in the late 1960’s and the
1970’s, the only other explanation consistent with the model is a decrease in government funding to
research. In Figure 7, a graphical representation of federal and industrial expenditure on R&D as a
percentage of GDP between 1960 and 2000 can be found. The data were obtained from the Science and
20
Engineering Indicators of the NSF. The behavior of the series is consistent with earlier findings reported
by Stephan (1996), who after examining the same series for the period 1960 to 1993 concluded that
changes in the proportion of GDP spent on R&D “…are driven in large part by decisions made at the
federal level.” (p. 1213)
The series reveal that federal spending on R&D as a proportion of GDP has declined significantly
compared to its 1960s levels, from about 1.8 percent to only 0.8 percent in 2000, with only a short
rebound between 1979 and 1987. In addition, this decline seems to have had its most significant impact
on total spending in R&D from 1964 to 1979. This fact strongly suggests that the observed decrease in the
real interest rate, the share of labor employed in research, and productivity growth that took place from
the mid-1960s until the end of 1970s was mostly caused by the decrease in government funding of R&D
as a percentage of GDP. This explanation does not invalidate the one put forth by Grilliches. It is quite
likely that any effect a decrease in government funding of R&D had on the share of employment in
research and the related variables was prolonged by the two oil shocks that took place in the 1970s.
Highlighting the significant role that government funding has played is important however, since it
provides support for Romer’s argument that the rate of technological change is sensitive to “direct
subsidies that increase the incentive to undertake research.” (p. S99)
Finally, data reported in Figures 2 and 7 indicate that the increase in total expenditure on R&D as
a percentage of GDP that has taken place since 1979 is mostly the result of a rapid increase in industrial
expenditure, which has more than made up for the decrease in federal expenditure. What can explain this
rapid increase? A positive shock in research productivity might be an explanation that deserves further
investigation, especially when one considers the significant advancements, such as the manufacturing of
the first integrated circuit in 1958 and the development of C programming language in 1972, that took
place in the Information and Computer Technology (ICT) sector around that time. There are two channels
through which advancements in ICT could have affected research productivity. First, these discoveries are
exactly the type of breakthroughs that Aghion and Howitt described, which by creating a new line of
21
research could have affected research productivity in the ICT sector significantly. 9 Secondly, several
studies have indicated a continuous significant decrease in the price of computing power since the 1960s,
due mainly to the sharp decline in the price of semi-conductors.10 To the extent that ICT is a significant
input to research, we would expect some of the productivity gains in ICT to spill over to other research
sectors.
5.
Conclusions
Why was the real interest rate so low during the 1970s and so high during the 1990s? Why was
there only a small fraction of resources devoted to research in the 1970s whereas the 1990s were the
decade “the new economy” was born? We have shown that Romer’s model of endogenous technological
change is capable of explaining the co-movement between the two variables, if the observed variation
results from either changes in research productivity that alter the expected return from investing resources
in research, or variations in federal funding of research as a share of GDP. Intuitively, if due to an
increase in the share of resources devoted to research more valuable discoveries per time period are being
made, more assets will be required to produce new types of capital equipment using these discoveries.
Thus, the demand for savings and the equilibrium real interest rate will both increase. Is this explanation
put forth by the model supported by the data? Several Granger causality tests indicated that changes in the
share of labor devoted to research precede changes in the real interest rate. They also supported the
hypothesis that the share of GDP spent on research Granger-causes the share of labor devoted to research.
These results are consistent with the model’s predictions.
Given the above-mentioned findings, an explanation consistent with both the model and the data
for the significant decline in the real interest rate, the share of labor devoted to research, and US labor
productivity that occurred between 1964 and 1979 can be provided. This explanation suggests that the
22
decline was the result of the sharp decrease in federal expenditure on R&D as a share of GDP that took
place from 1964 till 1979. On the other hand, although it is hard to state with certainty what might have
caused the rapid increase in industrial spending on R&D as a fraction of GDP observed after 1979, which
has more than made up for the decline in federal spending and has been followed by an increase in the
share of labor devoted to research and the real interest rate, a positive shock in research productivity
seems to be a very likely candidate. This hypothesis is supported by the fact that a series of technological
breakthroughs in Information Technology took place right before and during the 1960s and 1970s. These
breakthroughs are likely to have increased the productivity of the research sector, although their effect
was delayed by the two oil shocks that took place in the 1970s.
In conclusion, several points can be made. First, from a methodological viewpoint, although
R&D-based growth models developed by Romer (1990), Grossman and Helpman (1991a, b), and Aghion
and Howitt (1992) have been used in the literature interchangeably and regarded as equivalent in terms of
their predictions, Romer’s model seems to have an advantage over the other two, as it can explain part of
the variation in the data that the other two models cannot. However, the model overestimates the fraction
of labor that needs to be devoted to research in order for the economy to grow at rates consistent with US
data, and underestimates the real interest rate’s response to changes in that fraction.
Secondly, both the model and the data suggest that changes in the percentage of GDP used to
subsidize research affect not only the rate of technological change, but also the long-run real interest rate.
The same may be said about any shock that affects the share of resources allocated to research. Thirdly,
countries that devote a higher fraction of their resources to R&D will not only enjoy a higher rate of
technological growth, but will also offer a higher real rate of return to savings at the steady state, therefore
attracting foreign funds. Since most such countries are developed rather than developing, greater
international capital flow, ceteris paribus, is likely to benefit relatively rich countries at the expense of
poor.
23
Finally, the findings support Romer’s claim that government initiatives aimed at increasing the
share of resources devoted to research may lead to faster economic growth. For countries undertaking
such initiatives, free international capital flow may prove to be beneficial. An example of successful
implementation of such policies can perhaps be found in Taiwan who, by establishing National Chiao
Tung University, creating Hsinchu Science-based Industrial Park, and implementing compensation
schedules for researchers that reduced the brain drain and attracted human capital from abroad, has
transformed its economy from one relying on manufacturing of low value-added products to one driven
by a high-technology sector. This transformation is considered by many as the engine behind the high
growth rates observed during the 1980s and 1990s, and the increase in Foreign Direct Investment.11
24
Notes
1. Source: Information Technology Association of America (ITAA),
URL: http://www.itaa.org/govt/cong/c19991208.pdf
2.
Source: Office of Technology Policy, Update, January 1998,
URL: http://www.ta.doc.gov/prel/andii.pdf
3. Romer’s model, as the ones developed by Grossman and Helpman (1991a, b) and Aghion and
Howitt (1992), predict that the level rather than the share of resources used in R&D determines
the technological growth rate. Jones (1995a, b) however demonstrated that this hypothesis is
rejected by US data. Dalgaard and Kreiner (2001) showed that once human capital is incorporated
into the model, the technological growth rate becomes increasing in the share and not level of
resources used in R&D. Our analysis is consistent with their finding.
4. The decision to use an 8-year rolling window was made in order to average out shocks occurring
at business cycle frequency. Burns and Mitchell (1946) define this frequency to be three to five
years.
5. From regressing R on RSESH (Alexandrakis, 2003)
6. Grossman and Helpman, and Aghion and Howitt did examine the effect of changes in research
productivity on the share of recourses devoted to R&D. In both models the interest rate was
unaffected for the reasons listed above.
7. According to the Wall Street Journal, investment in new Internet services that require broadband
connections has been discouraged by the slow rate of adoption of broadband solutions by
households. This delay is often times due to either the higher cost of such connections, or to
technical difficulties associated with the old technology of telephone lines in many geographical
areas. (The Wall Street Journal: 01/08/2003)
25
8. Griliches and Cockburn (1994) showed for example that the treatment of generic drugs as
separate commodities leads to a significant underestimation of productivity growth in the
pharmaceutical sector.
9. Since the discovery of the first integrated circuit in 1958, technological progress in
semiconductors has been rapid. Gordon Moore (1965), a co-founder of Intel Corporation,
predicted that the transistor density on integrated circuits would double every year, and his
revised prediction in 1975 to doubling every 18 months became known as Moore’s Law. This
prediction has been consistent with what we have roughly observed since 1965 and until recent
years.
10. Dale Jorgenson has done extensive work on the impact of advancements in ICT on US
productivity. For a collective volume of his work, see Jorgenson (2002).
11. Chang and Yu (2001)
26
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Chang Chun-Yen and Po-Lung Yu (eds.). (2001). Made by Taiwan, Booming in the Information
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Griliches, Zvi. (1979). “Issues in Assessing the Contribution of R&D to Productivity Growth.” Bell
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Jorgenson, Dale W. (2002). Econometrics, Volume 3: Economic Growth in the Information Age.
Cambridge, MA: MIT Press.
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Jones, Charles I. (1995). “Time Series Tests of Endogenous Growth Models.” Quarterly Journal of
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30
Table 1. Correlation Coefficients
PAIR OF VARIABLES
CORRELATION
R, RSESH
0.8958
RADJ, RSESH
0.8786
PR, RSESH
0.7625
R, TSHEXP
0.5799
RADJ, TSHEXP
0.5964
PR, TSHEXP
0.5723
RSESH, TSHEXP
0.7465
Notes: PR, R, RADJ, RSESH, and TSHEXP represent the moving-average smoothed series of the
prime rate, the rate of return to the S&P 500, the rate of return to the S&P 500 per unit of risk, the
share of labor in R&D, and the share of GDP spent in research respectively.
31
Table 2. Granger Causality Tests
NULL HYPOTHESIS
F-STATISTIC
R does not Granger-cause RSESH
1.3943
RSESH does not Granger-cause R
3.0283**
RADJ does not Granger-cause RSESH
0.7743
RSESH does not Granger-cause RADJ
5.2907***
PR does not Granger-cause RSESH
2.2971
RSESH does not Granger-cause PR
4.1548**
TSHEXPA does not Granger-cause RSESHA
21.0141***
RSESHA does not Granger-cause TSHEXPA
2.0969
RSESH does not Granger-cause TSHEXP
4.7971***
TSHEXP does not Granger-cause RSESH
34.7059***
R does not Granger-cause TSHEXP
2.1663
TSHEXP does not Granger-cause R
0.9270
RADJ does not Granger-cause TSHEXP
1.8684
TSHEXP does not Granger-cause RADJ
0.9950
PR does not Granger-cause TSHEXP
2.3402
TSHEXP does not Granger-cause PR
1.7787
Notes: Asterisks denote rejection at (*) 10 percent significance level, (**)
5 percent significance level, and (***) 1 percent significance level.
Subscript A denotes the use of non-smoothed series (annual frequency).
32
Table 3. Model Parameters: Calibrated values
PREFERENCES
TECHNOLOGY
α
G
δ
Z
σ
θ
0.6
0.02
0.055
0.142
1
0.95
33
40
2.9
30
2.8
20
2.7
10
2.6
0
2.5
-10
2.4
-20
2.3
-30
2.2
2.1
-40
1965
1970
1975
1980
1985
1990
1995
1965
1970
1975
R
1980
1985
1990
1995
1990
1995
TSHEXP
20
.80
18
.75
16
.70
14
.65
12
.60
10
.55
8
.50
6
.45
4
1965
1970
1975
1980
1985
1990
1965 1970
1995
1975
1980
1985
RSESH
PR
Figure 1. Rate of Return to S&P 500 (R), Prime Rate (PR), Share of GDP in Industrial Research
(TSHEXP), and Share of Labor in Industrial Research (RSESH) in percentage
34
20
.75
16
.70
12
.65
8
.60
4
.55
0
.50
-4
1975
1980
1985
1990
1995
.45
1970
1975
1980
R
1985
1990
1995
RSESH
1.6
2.8
2.7
1.2
2.6
0.8
2.5
2.4
0.4
2.3
0.0
2.2
-0.4
1970
1975
1980
1985
1990
2.1
1970
1995
RADJ
6
5
4
3
2
1
0
1980
1985
1980
1985
TSHEXP
7
1975
1975
1990
1995
PR
Figure 2. Smoothed Series: 8-Year Moving Average
35
1990
1995
5
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
1975
1980
1985
1990
1995
1975
CDRATE
1980
1985
1990
1995
TRATE
Figure 3. Real Interest Rate paid to 3-month T-Bills (TRATE), and 3-month Time Deposits (CDRATE):
Smoothed Series
36
Wages
FINAL OUTPUT
SECTOR
INDIVIDUALS
Labor
Profit
Rent
Capital
R&D SECTOR
Figure 4. Circular Flow Diagram
37
Labor, Assets
Figure 5. Model-Generated Steady State Values
38
2 .8
2 .4
2 .0
1 .6
1 .2
0 .8
1970
1975
1980
1985
DLP
Figure 6. Labor Productivity Growth Rate: Smoothed Series
39
1990
1995
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.6
0.8
60
65
70
75
80
85
90
95
00
60
65
70
75
FEDSHEXP
80
85
90
95
00
INDSHEXP
1.6
1.8
1.5
1.6
1.4
1.4
1.3
1.2
1.2
1.1
1.0
0.8
1970
1.0
1975
1980
1985
1990
0.9
1970
1995
1975
1980
1985
1990
1995
INDSHEXP
FEDSHEXP
Figure 7. Federal (FEDSHEXP) and Industrial (INDSHEXP) Expenditure on R&D as a Share of GDP:
Annual Frequency (top) and Smoothed Series
40