ï»¿ WPS6017
Policy Research Working Paper 6017
R&D and Aggregate Fluctuations
Erhan ArtuÃ§
Panayiotis M. Pourpourides
The World Bank
Development Research Group
Trade and Integration Team
March 2012
Policy Research Working Paper 6017
Abstract
The research and development (R&D) sector is technology shocks are important in driving aggregate
considered one of the main driving forces of sustainable output fluctuations. After taking nominal innovations
growth in the long run. The sector, however, also shows into consideration, such as shocks in monetary policy and
excessive volatility which raises interesting questions inflation, capital investment-specific shocks explain 70
regarding the sources of this volatility as well as the percent of fluctuations of R&D investment, while R&D
nature of the relation between the sector and aggregate technology shocks explain 30 percent of the variation
fluctuations. Using data from the United States Bureau in the output of the non-R&D sector. Technology
of Economic Analysis and National Science Foundation, innovations jointly explain most of the variation of
we show that technology innovations are the main output in the R&D sector and 78 percent of the variation
source of fluctuations in R&D investment while R&D of output in the rest of the economy.
This paper is a product of the Trade and Integration Team, Development Research Group. It is part of a larger effort by
the World Bank to provide open access to its research and make a contribution to development policy discussions around
the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be
contacted at eartuc@worldbank.org.
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Produced by the Research Support Team
R&D and Aggregate Fluctuationsâ‡¤
Erhan ArtuÂ¸â€ c Panayiotis M. Pourpouridesâ€¡
World Bank Cardiâ†µ Business School
& Central Bank of Cyprus
March 28, 2012
Abstract
The research and development (R&D) sector is considered one of the main driving
forces of sustainable growth in the long run. The sector, however, also shows excessive
volatility and is one of the important sources of macroeconomic ï¬‚uctuations. Using
data from the United States Bureau of Economic Analysis and National Science Foun-
dation, we show how signiï¬?cant technology innovationsâ€™ contributions are to improve
sector productivity and the e ciency of physical capital. After taking nominal inno-
vations into consideration, such as shocks in monetary policy and inï¬‚ation, capital
innovations explain 70 percent of ï¬‚uctuations of real investment in R&D, while pro-
ductivity innovations in the R&D sector explain 30 percent of the variation in the
output of the non-R&D sectors. Technology innovations explain most of the variation
of output in the R&D sector and 78 percent of the variation of output in the rest of
the economy. Although the R&D sector is relatively small, it has a signiï¬?cant impact
on the ï¬‚uctuations of aggregate output.
JEL Classiï¬?cation Codes: C13; C32; C68; E32; O3
Keywords: Cycles; Productivity Shocks; Investment-speciï¬?c Shocks; R&D; VAR
â‡¤
The views in this paper are the authors and not those of the Central Bank of Cyprus, the Eurosystem,
the World Bank Group, its Executive Directors or the governments they represent. We would like to thank
Raymond Wolfe (National Science Foundation) for information and help with the data and Jane Zhang for
her editorial comments. All errors are our own.
â€
The World Bank, Development Economics Research Group (Economic Policy), 1818 H Street, NW,
Washington DC 20433, USA, Email: eartuc@worldbank.org.
â€¡
Cardiâ†µ Business School, Cardiâ†µ University, Aberconway Building, Colum Drive, Cardiâ†µ, CF10
3EU, UK, E-mail: pourpouridesp@cardiâ†µ.ac.uk and Economic Research Department, Central Bank
of Cyprus, 80 Kennedy Avenue, P.0. Box 25529, 1395 Nicosia, Cyprus, E-mail: PanayiotisPour-
pourides@centralbank.gov.cy.
1
1 Introduction
Investment in research and development (henceforth R&D) as well as employment in the
R&D sector exhibit substantial ï¬‚uctuations relative to those of aggregate production and
aggregate employment. Moreover, contrary to the Schumpeterian view, R&D appears to be
procyclical in the data. These facts raise interesting questions regarding the sources of the
excessive volatility and the nature of the relation between the R&D sector and aggregate
ï¬‚uctuations. The purpose of this paper is to examine the impact of shocks on the R&D sector
as well as the contribution of the sector to annual ï¬‚uctuations. Speciï¬?cally, we identify
sectoral productivity shocks as well as capital investment-speciï¬?c shocks by employing a
Vector Autoregression (VAR) whose shock structure is disciplined by a stochastic general
equilibrium model.
Using annual data from the US for the period prior to 2008, we ï¬?nd that capital
investment-speciï¬?c shocks play the largest role in driving the ï¬‚uctuations of R&D invest-
ment while R&D productivity shocks aâ†µect considerably the ï¬‚uctuations of output in the
non-R&D sector. Our analysis suggests that not only sources listed under R&D expendi-
tures contribute to the stock of R&D. While there can be direct additions to the stock of
R&D within the R&D sector (identiï¬?ed from R&D expenditures), there can also be costly
transfers from the non-R&D sector contributing to the stock of R&D. We show that the cost
of the transfer is inversely related to positive R&D shocks. Thus, an improvement in R&D
productivity may induce a transfer of sources from the non-R&D sector as investment in the
stock of R&D which then augments the production of the non-R&D output. Our calibration
suggests that at the steady state such transfers are positive. Consequently, despite the fact
2
that the size of the R&D sector is small, R&D speciï¬?c shocks have a signiï¬?cant impact on
aggregate ï¬‚uctuations. Our ï¬?ndings conï¬?rm Ouyangâ€™s (2011) proposition that technology
shocks are a cause of the procyclicality of R&D. The evidence suggests that R&D produc-
tivity shocks and capital investment-speciï¬?c shocks not only explain a considerable portion
of output variation in the R&D and non-R&D sectors but they also produce responses of
the same sign for the outputs of the two sectors.
In their seminal work, Kydland and Prescott (1982) and Long and Plosser (1983) empha-
size the role of neutral technology shocks as the main source of business cycle ï¬‚uctuations.
Since then, the real business cycle (RBC) approach has been put forward to explain various
business cycle phenomena. Greenwood, Hercowitz and Krusell (2000), make a distinction
between the aggregate-sector (neutral) technology shocks and capital investment speciï¬?c
shocks that improve the e ciency of newly produced capital.1 The calibration of their
equilibrium model implies that capital investment-speciï¬?c shocks account for 30 percent
of output ï¬‚uctuations. Fisher (2006), estimates a VAR using long-run restrictions derived
from an equilibrium model and ï¬?nds that neutral and investment-speciï¬?c shocks combined
account for 44-80 percent of outputâ€™s short-run ï¬‚uctuations. His ï¬?ndings suggest that capi-
tal investment-speciï¬?c shocks matter more than neutral technology shocks for business cycle
ï¬‚uctuations. The identiï¬?ed technology shocks from the existing RBC literature might be,
to some extent, the result of R&D activities which were not modeled explicitly. It is also
possible that some technology innovations emerging from R&D sectors are not well captured
by the aggregate Solow residual and the real price of capital investment.
1
Investment speciï¬?c shocks are identiï¬?ed from variations in the real price of capital investment.
3
Comin and Gertler (2006), stress the signiï¬?cance of R&D in generating medium-run ï¬‚uc-
tuations. They consider an endogenous growth model where R&D generates new specialized
intermediate goods which enhance the production of ï¬?nal goods. They allow for R&D in
both the capital good and the consumption good sectors. Their model is impressively suc-
cessful in capturing the ï¬‚uctuations of basic macroeconomic variables but does less well in
generating the ï¬‚uctuations of R&D observed in the data.2 In our model, we decompose
aggregate production into two sectors, the R&D sector and the non-R&D or consumption-
good sector. We incorporate the stock of R&D as a distinct input in the production function
adopting Grilichesâ€™ (1979) proposition. Physical capital is mobile between sectors but with
a cost. Fluctuations are driven by three types of shocks: two types of sectoral productivity
shocks and capital investment-speciï¬?c shocks. To quantify the impact of R&D on aggregate
ï¬‚uctuations we ï¬?rst estimate a VAR using seven post-war annual time series. Following
Fisher (2006), the shocks are identiï¬?ed by imposing long-run restrictions which are justiï¬?ed
by the theoretical model. Data on R&D are only available at the annual frequency. Thus,
following Comin and Gertler (2006), we focus our analysis on those frequencies. As shown
by Comin and Gertler, information extracted from annual data regarding medium-run ï¬‚uc-
tuations is virtualy the same as that extracted from quarterly data. The plausibility of the
empirical impulse responses are assessed by comparing them with the theoretical ones which
are generated by the simple equilibrium model.
Previous work by Butler and Pakko (1998) calibrates an endogenous growth model where
R&D drives the level of labor augmenting technology which in turn aâ†µects the production of
2
As noted by the authors, this could be due to measurement errors in the data.
4
the ï¬?nal good. They assume that business cycles are triggered by a shock speciï¬?c to R&D and
a shock that aâ†µects the production of the ï¬?nal good. The speciï¬?cation of technological change
is a modiï¬?ed discrete-time version of Jonesâ€™ (1995) R&D model with duplication externalities,
while physical capital is used only in the production of the ï¬?nal good. They demonstrate
a
that R&D shocks improve the persistence of the dynamics of output and productivity. FÂ´tas
(2000), also demonstrates the ability of an R&D-based model to generate persistence in the
dynamics of output by considering an extension of Shleiferâ€™s (1986) model where the ï¬‚ow of
ideas is endogenous. Maliar and Maliar (2004), develop an R&D-based model of stochastic
endogenous growth where the consumption good, physical capital and increments in R&D
stock are produced by the same technology. In their model, a unit of the ï¬?nal good can be
costlessly transformed into either a unit of R&D stock, a unit of consumption good or a unit
of physical capital. Business cycles are driven by labor augmenting technical progress which
depends, to a large extent, on the stock of R&D. Their model is successful in matching several
business cycle facts and in accounting for the asymmetry in the shape of business cycles. It
predicts, however, that R&D moves countercyclically which is at odds with observations in
the data. Barlevy (2007), addresses this issue by arguing that R&D might be procyclical
because of a dynamic externality inherent to R&D.3
Braun and Nakajima (2009) examine the cyclical pattern of R&D using an endogenous
growth model which consists of three separate interrelated production sectors: R&D, capital
equipment and consumption. As in Butler and Pakko, the production of R&D output is a
3
The idea is based on the fact that a ï¬?rm cannot prevent rival ï¬?rms from exploiting its innovation as
time passes. Since the prospect of a gain during expansions of the economy is greater, there is an incentive
for ï¬?rms to invest more on R&D during those times where proï¬?ts are high.
5
function of labor only. The production of equipment is a function of both capital and labor as
well as the stock of R&D and business cycles are driven by changes in the level of technologies
of the consumption and equipment sectors. Although their model can reproduce most of the
observed variation in output, the impact of technology shocks in the equipment sector on
output is found to be negligible. The latter stands in contrast to the ï¬?ndings of Greenwood
et al. (2000), Fisher (2006) and Altig et al. (2011) who model capital investment-speciï¬?c
shocks as shocks which aâ†µect the marginal e ciency of investment. In our model, capital is a
factor of production in both the R&D and non-R&D sectors, and only a fraction of the output
in the R&D sector is used as increment for the stock of R&D. There is a distinct technology
shock which aâ†µects productivity in the R&D sector while capital investment-speciï¬?c shocks
are modeled as shocks to the marginal e ciency of investment.
Our analysis designates that capital investment-speciï¬?c shocks constitute the main source
of ï¬‚uctuations in R&D investment as they account for 70 percent of its variation. The em-
pirical impulse response function indicates that a one percent positive shock in the real price
of capital investment induces an immediate one percent decline in R&D investment. The
shock induces further declines in R&D investment the following years, reaching 2.5 percent
the 6th year from the date of the shock. Our analysis suggests that improvements in pro-
ductivity in the R&D sector induce a considerably positive impact on the output of the
non-R&D sector to the extent that a one percent improvement in productivity in the R&D
sector leads to a 4 percent increase in the output of the non-R&D sector 6 years after the
occurence of the shock. The variance decomposition implies that R&D productivity shocks
explain 30.2 percent of the variation of output in the non-R&D sector, which exceeds the
6
impact of 19.7 percent of own sector productivity shocks. Non-R&D productivity shocks on
the other hand play a smaller role in driving the ï¬‚uctuations of output in the two sectors.
We ï¬?nd that technology shocks joinly explain 92.3 percent and 78.5 percent of the varia-
tion of output in the R&D and non-R&D sectors, respectively. Among the three shocks,
capital investment-speciï¬?c shocks cause the biggest impact on hours for both sectors. The
ï¬?ndings conï¬?rm Ouyangâ€™s (2011) claim that technology shocks are important factors of the
procyclicality of R&D since capital investment-speciï¬?c and R&D productivity shocks, being
the main sources of output volatility in the two sectors, induce output responses of the same
sign. The combined eâ†µect of technology shocks on hours is 46.1 percent for the R&D sector
and 56.4 percent for the non-R&D sector.
Excluding the R&D sector as a separate sector in the model and treating R&D solely
as an expense according to the NIPA deï¬?nitions, we show that capital investment-speciï¬?c
shocks and neutral technology shocks explain 40.2 percent and 33.3 percent of the variation
of output, respectively. These estimates are not too far from ï¬?ndings of previous studies
which use quarterly data (e.g. Fisher, 2006, Altig et al, 2011). The exercise also signiï¬?es
that if the R&D sector is excluded from the model and R&D is not treated as investment,
the eâ†µect of technology shocks on hours is overstated to some extent. Speciï¬?cally, the eâ†µect
of technology shocks on aggregate per capita hours in the simple model is 68.8 percent as
opposed to 46.1-56.4 percent in the model with two sectors and R&D investment.
The rest of the paper is organized as follows. Section 2 reviews the relevant literature
and presents some empirical evidence to underline the signiï¬?cance of R&D on ï¬‚uctuations.
Section 3 lays out the theoretical framework while section 4 presents the stationary equilib-
7
rium, illustrates the identiï¬?cation of the structural shocks and presents theoretical impulse
response functions. Section 5 describes the econometric approach in estimating the VAR
and section 6 discusses the data. Section 7 presents and analyzes the empirical results from
the VAR model. Section 8 concludes.
2 R&D and Aggregate Fluctuations
Indubitably, investment in R&D constitutes the main engine of endogenous growth. There
is an enormous literature exploring the links between R&D and economic growth, both em-
pirically and theoretically.4 Schumpeter (1939), was probably the ï¬?rst to formalize the idea
of innovations as generators of business cycle ï¬‚uctuations. In his view, innovations which are
produced exogenously lead to permanent improvements in the production technology and
thereby, promote economic development and stimulate cyclical ï¬‚uctuations. The empirical
literature which relates R&D with ï¬‚uctuations has been relatively more limited. Lach and
Schankerman (1989) ï¬?nd that both R&D activities and capital investment are aâ†µected by a
common shock which has very persistent eâ†µects. They provide evidence that R&D expendi-
tures Granger-cause investment in physical capital after a short lag.5 Geroski and Walters
(1995) examine innovations in the UK and argue that the procyclical variation in innovation
contributes signiï¬?cantly to the procyclical variation in productivity growth. They conclude
that although aggregate demand aâ†µects innovation activity, it plays only a modest role as
opposed to aggregate supply.
4
Among others, see the work of Lucas (1988), Romer (1990), Grossman and Helpman (1991), Aghion and
Howitt (1992), Griliches and Lichtenbergand (1984) and Stokey (1995).
5
Similar ï¬?ndings are reported by Lach and Rob (1996).
8
One issue in the literature is that there are no good measures of the contribution of
R&D to technological improvements as they are reï¬‚ected by the ï¬‚uctuations of aggregate
production. Patents might be an indicator of the inventive activity but they are not very
explicit about the degree of the eâ†µect of R&D on macroeconomic ï¬‚uctuations. Griliches
(2000) argues that patent applications are usually taken early during research processes
in expectation of long run gains. As a result, there is lag between granting a patent and
actual innovation. Lach and Schankerman (1989) point out that advancements in science
and technology have a direct impact on R&D spending.6 We argue that potential shocks
identiï¬?ed from ï¬‚uctuations of R&D expenditures (investment) reï¬‚ect precicely technological
innovations resulting from R&D activities. Griliches (1979) proposes the introduction of the
stock of knowledge, approximated by past R&D expenditures, as an input in the production
function. This idea is also implemented by Doraszelski and Jaumandreu (2007), who assume
a linear accumulation equation for the stock of knowledge in order to estimate production
functions and retrieve productivity and its relation with R&D at the ï¬?rm level.
Throughout our analysis, we use US data on investment in R&D, adjusted GDP and
employment for R&D activities. The data on R&D investment and adjusted GDP is provided
in the satellite account which is developed jointly by the Bureau of Economic Analysis
(BEA) and the National Science Foundation (NSF). Data on domestic employment of R&D-
performing companies is provided by NSF.7 As shown in ï¬?gure 1, R&D investment is on
average 2.7 percent of nominal GDP and is characterized by the peaks of the mid 1960s,
6
Work by Rosenberg (1969, 1974), Pakes and Schankerman (1984) and Grilinches, Hall and Pakes (1988)
also stresses the importance of past technological improvements as factors of current R&D.
7
In adjusted GDP, contrary to GDP reported in NIPAs, R&D is treated as investment rather than
expense. An extensive discussion about the data on R&D investment is presented in section 6.
9
the mid 1980s and the early 2000s and the trough of the late 1970s. The shadowed bars
correspond to the NBER recessions. The ï¬?gure suggests that there is no clear pattern in
the behavior of the share during major recessions.8 Overall, R&D appears to be mildly
procyclical as the correlation coe cient between the growth rate of real investment in R&D
and real GDP is 0.53. Evidence against the Schumpeterian view on the cyclicality of R&D
a
is also presented in previous studies (e.g. FÂ´tas, 2000, Barlevy, 2006, Comin and Gertler,
2006). Ouyang (2011), ï¬?nds that the procyclicality of R&D holds even when one controls
for aggregation eâ†µects. To do so, she considers an annual panel of (company ï¬?nanced) R&D
expenditures and output for 20 US manufacturing industries. She argues that technology
shocks is a key factor in explaining the procyclicality of R&D and concludes by noting that
future research should investigate this matter, exploring further the response of R&D to
technology shocks.
Figure 2 compares the growth rate of real R&D investment with the growth rate of
adjusted aggregate real GDP. The ï¬?gure indicates that occasionally, the growth rates of
R&D investment and aggregate output exhibit similar swings but clearly the former is much
more volatile than the latter, especially during the 1990s onward. Figures 3 and 4 plot
the growth rate of output against employment, separately for the R&D sector and the rest
of the economy (net of R&D).9 Figure 3 shows that the growth rate of employment in
the R&D sector is substantially more volatile than the growth rate of R&D investment,
and occasionally exhibits very diâ†µerent swings than the latter. This is not the case in the
8
While the share is increasing during the recessions of the 1960â€™s and the 1980â€™s, it is decreasing during
the two recessions of the early and mid 1970â€™s and mainly decreasing during the recession of early 2000.
9
Output and employment in the non-R&D sector are deï¬?ned as aggregate real adjusted GDP minus
real investment in R&D and aggregate employment minus employment of R&D performing companies,
respectively.
10
non-R&D sector (ï¬?gure 4) where the growth rates of employment and output are highly
correlated and exhibit a similar level of volatility. Not only is there a diâ†µerence in the
behavior of output and employment within sectors, there is also a diâ†µerence in the behavior
of employment between sectors. This diâ†µerence is evident in ï¬?gure 5 which shows that the
correlation between employment in the R&D sector and employment in the non-R&D sector
is quite low (correlation coe cient of -0.27), while employment volatility in the former is
substantially higher than that in the latter. Table 1 quantiï¬?es these observations by reporting
volatilities of aggregate employment and aggregate output vs volatilities of R&D employment
and R&D investment. In particular, the growth rate of R&D investment is more than twice
as volatile as the growth rate of real GDP while the growth rate of employment in R&D-
performing ï¬?rms is four times more volatile than the growth rate of aggregate employment.
What types of structural shocks cause the high volatility in the R&D sector? Is there
a statistically signiï¬?cant link between the R&D sector and ï¬‚uctuations in the rest of the
economy? If so, what is the degree of contribution of the R&D sector in driving aggregate
ï¬‚uctuations? This paper attempts to shed some light on these matters within the context
of an economic model which motivates three long-run identifying restrictions.
3 Economic Model
There are two productive sectors in the economy: the consumption good sector and the R&D
sector. The consumption sector produces good YCt , which can be directly consumed, Ct or
11
invested in the production of capital goods, ICt :
YCt Ct + ICt . (3.1)
Output, YCt , is produced via the constant-returns to scale production function
YCt = At (Rt )â†µ1 (KCt )â†µ2 (HCt )1 â†µ 1 â†µ2
, (3.2)
where At is a measure of the sectorâ€™s technology, KCt denotes the sectorâ€™s beginning of period
t capital stock, HCt is labor employed in the sector and 0 < â†µi < 1. Input Rt is the stock of
R&D which augments the production of the ï¬?nal good. It evolves according to the following
law of motion:
Rt+1 = (1 R ) Rt + Dt , (3.3)
where Dt is an increment to the R&D stock and 0 < R ï£¿ 1. The growth rate of At is
stochastic and denoted by xAt = At /At 1 .
The R&D sector produces good YRt which can be used in the production of the consump-
tion good via Dt or invested in the production of capital goods, IRt :
YRt Dt + IRt . (3.4)
How Dt is determined is discussed below and in the following section. Output, YRt , is
12
produced via the constant-returns to scale production function
YRt = Jt (KRt ) (HRt )1 , (3.5)
where Jt is a shock speciï¬?c to the R&D sector, KRt denotes the sectorâ€™s period t capital
stock, HRt is labor and 0 < < 1. The stochastic growth rate of Jt is denoted by xJt .
Only units of investment from the consumption-good sector correspond to units of aggre-
gate investment on a one-to-one basis. The units of investment in capital of the R&D sector
are converted to units of investment of the consumption-good sector before new capital is
produced. Speciï¬?cally, a time t unit of investment from the R&D sector corresponds to ï£¿âŒ…t
units of consumption-good investment, where ï£¿ > 0 is scale parameter. In addition, capital
is mobile across sectors but not on a one-to-one basis. A unit of consumption-good capi-
tal corresponds to 1/ï£¿âŒ…t units of R&D-good capital. It follows that aggregate investment,
It > 0, and aggregate capital stock, Kt > 0, are expressed as
It = ICt + ï£¿âŒ…t IRt ,
(3.6)
Kt = KCt + ï£¿âŒ…t KRt .
The accumulation equation for the stock of capital is given by
Kt+1 = (1 K ) Kt + Zt I t , (3.7)
where Zt represents the time-t state of the technology for producing capital and 0 < K ï£¿ 1.
The stochastic gross growth rate of Zt is denoted by xZt . E ciency requires that (3.1) and
13
(3.4) hold with equality. Then, using the capital accumulation equation and (3.6) we can
write the economyâ€™s budget constraint as follows:
P Kt K t + PRt Dt + Ct = YCt + PRt YRt ,
where K t denotes the additional units of capital at the end of period t; K t âŒ˜ Kt+1
(1 K ) Kt . The budget constraint is similar to that assumed by Acemoglu and Zilibotti
(2001) in which investment in physical capital and investment in R&D are diâ†µerentiated.
Unlike the Acemoglu and Zilibotti model we assume that only part of R&D output is used in
the production of the consumption good. The price of the consumption good is the numeraire
and P Kt and PRt are the relative prices of capital and R&D, respectively. P Kt equals 1/Zt
and PRt equals ï£¿âŒ…t . Technology âŒ…t is deï¬?ned as a function of technologies At , Jt and Zt and
its exact functional form is derived and discussed in the following section.
The economy is inhabited by a representative household which consists of two members.
One of the members is employed in the consumption-good sector while the other is employed
in the R&D sector. The preferences of the household are deï¬?ned over the householdâ€™s
aggregate consumption, Ct , and the leisure of its two members, LCt and LRt ,
u (Ct , LCt , LRt ) = ln Ct + 'C ln LCt + 'R ln LRt , (3.8)
where Lit = 1 Hit for i = C, R and 'C , 'R > 0.10 Then, the Pareto optimal equilibria are
10
The speciï¬?cation of the utility function implies that labor is speciï¬?c to each sector and it is not mobile
across them. This feature of the model can be justiï¬?ed by evidence provided by Jovanovic and Mo tt (1990)
that workers move mostly within sectors rather than across sectors. In general, it is di cult to justify ï¬‚ows
from and especially to the highly specialized R&D sector. Even if we allow perfect labor mobility across the
14
obtained from the central planning problem where the representative household maximizes
its expected lifetime utility
1
X
t
E0 u (Ct , LCt , LRt ) , (3.9)
t=1
subject to (3.1), (3.2), (3.3), (3.4), (3.5), (3.6) and (3.7). The agent chooses Ct , HCt , HRt ,
Kt+1 , Rt+1 , ICt , IRt , Dt as well as the time t allocation of capital between the two sectors,
KCt and KRt .
b
Let xt = dxt /x denote the percentage deviation of xt from its nonstochastic steady state.
The processes that drive the exogenous shocks are given by the following vector autoregressive
process
b b
xqt = â‡¢q xqt 1 + "qt , for q = A, Z, J
(3.10)
2
where |â‡¢q | < 1, "qt â‡ iid 0, q with E ("pt , "qt ) = 0 for any q 6= p.
4 Stationary Equilibrium and Identiï¬?cation
The equilibrium in this economy is described by constraints (3.1) and (3.4), the accumula-
tion equations for the stock of R&D, (3.3), and capital, (3.7), and the following optimality
conditions:
â‡¢ ï£¿
1 1 K YCt+1
1 = Et + â†µ 2 Zt , (4.1)
xCt+1 xZt+1 KCt+1
Ct 1 â†µ1 â†µ2 YCt
= , (4.2)
1 HCt 'C HCt
two sectors by assuming a representative agent allocating her time between working in the consumption-good
sector, working in the R&D sector and leisure, the results of the next section will still hold. In either case,
the VAR analysis that follows does not depend on whether labor is mobile or immobile across sectors.
15
Ct 1 YRt
= ï£¿âŒ…t , (4.3)
1 HRt 'R HRt
YCt YRt
â†µ2 = , (4.4)
KCt KRt
â‡¢
1 â†µ1 YCt+1
1 = Et + (1 R ) xâŒ…t+1 , (4.5)
xCt+1 ï£¿âŒ…t Rt+1
where xCt = Ct /Ct 1 and xâŒ…t = âŒ…t /âŒ…t 1 . Condition (4.1), is the optimal condition for next
period capital stock. Conditions (4.2) and (4.3) correspond to the optimal choice for work
eâ†µort in the consumption-good and the R&D sector, respectively. Condition (4.4) determines
the optimal allocation of capital across sectors while condition (4.5) determines the optimal
choice for next period stock of R&D.
We identify the three technology shocks by considering their eâ†µects over the long-run.
As we have shown in the previous section, the real price of investment is equal to the inverse
of investment-speciï¬?c technological progress.11 As in Fisher (2006), the model derives the
identifying assumption that in the long-run the real price of investment is only aâ†µected by
investment-speciï¬?c shocks. We would like to stress that we do not rule out the possibility of
R&D-based innovations that improve the e ciency of capital. The argument is that R&D
technological innovations do not aâ†µect the real (relative) price of investment in the long-run
due to the fact that in the long-run those innovations reduce both the nominal price of
capital investment and the aggregate nominal price (numeraire), leaving the long-run price
ratio unaâ†µected.12 This implication follows from the assumed segregation of the R&D and
capital sectors that is justiï¬?ed from the fact that R&D is typically conducted in separate
11
See also Hornstein and Krusell (1996), Greenwood, Hercowitz and Krusell (2000), Cummins and Violante
(2002) and Fisher (2006).
12
In the empirical part of section 5, R&D-based innovations aâ†µect the real price of capital investment only
in the short-run.
16
sectors. Potential long-run eâ†µects of R&D-based improvements in the e ciency of capital
are captured by the permanent eâ†µects of R&D shocks on production.
The identiï¬?cation of shocks speciï¬?c to the R&D sector follows from the assumption that
shocks speciï¬?c to the consumption-good sector do not aâ†µect the R&D sector in the long-run.
The latter enables us to scale the trending variables, eliminating steady state growth. The
optimality conditions can then be expressed in terms of stationary variables. Consequently,
we establish the following proposition.
Proposition: The resource constraints (3.1) and (3.4), the accumulation equations for the
stock of R&D, (3.3), and capital, (3.7), and the optimality conditions (4.1)-(4.5), can
be expressed in terms of only parameters and the stationary variables yCt , yRt , kCt , kRt ,
kt , iCt , iRt , ct , dt , rt , xA , xJ , xZ , HCt and HRt , where
e e e
yCt = YCt /Xt , yRt = YRt /Xt , kCt = KCt /Xt Zt , kRt = KRt /Xt Zt , kt = Kt /Xt Zt ,
e e
iCt = ICt /Xt , iRt = IRt /Xt , ct = Ct /Xt , dt = Dt /Xt and rt = Rt /Xt
1 1 â†µ1 â†µ2
with Xt = (Jt ) 1 (Zt ) 1 e
, Xt = (At ) 1 â†µ2
(Xt ) 1 â†µ2
(Zt ) 1 â†µ2 e
and âŒ…t = Xt /Xt .
As we show further below, the proposition implies intuitive relationships between the
relative price of R&D and the stochastic processes At and Jt . The proposition also implies
that at the steady state the non-stationary variables YRt , KRt , IRt , Dt and Rt are aâ†µected
1
e
only by Jt and Zt . Let the growth rates of Xt and Xt be denoted by et = (xJt ) 1 (xZt ) 1
1 â†µ1 â†µ2
e
and et = (xAt ) 1 â†µ2
(et ) 1 â†µ2
(xZt ) 1 â†µ2
, respectively. Then, at the steady state, variables YRt ,
IRt , Dt and Rt grow at the rate et e
1, variables YCt , ICt and Ct grow at the rate et 1,
17
variable KRt grows at the rate et xZt e
1 and variables KCt and Kt grow at the rate et xZt 1.
The stochastic processes have an eâ†µect on the relative price of R&D which in turn aâ†µects
the distribution of resources between the consumption-good sector and the R&D sector. The
relative (real) price of R&D can be written as ï£¿âŒ…t = ï£¿ (At )âŒ§âŒ…,A (Jt )âŒ§âŒ…,J (Zt )âŒ§âŒ…,Z , where âŒ§âŒ…,A ,
âŒ§âŒ…,J and âŒ§âŒ…,Z are the elasticities of the relative price of R&D with respect to the stochastic
growth rates A, J and Z:
1 (1 â†µ1 â†µ2 ) â†µ2 (1 â†µ1 )
âŒ§âŒ…,A = , âŒ§âŒ…,J = , âŒ§âŒ…,Z = .
1 â†µ2 (1 ) (1 â†µ2 ) (1 ) (1 â†µ2 )
Clearly the eâ†µects of sector productivity shocks A and J on the relative price are positive
and negative, respectively. Any positive (negative) eâ†µect on R&D resulting from an increase
(decrease) in A is mitigated by the increase (decrease) in the relative price. Over the long-
run however, A shocks have no eâ†µect on R&D. On the other hand, the sign of the eâ†µect of
Z on the relative price depends on whether â†µ2 is greater or smaller than (1 â†µ1 ).13
From the economyâ€™s budget constraint it is evident that it is possible to transfer units of
output from the consumption-good sector to the R&D sector and vice versa; e.g. a unit of
output from the consumption good sector corresponds to 1/PRt units of investment in the
stock of R&D. Then, a positive productivity shock in the R&D sector ("Jt > 0) increases
investment in the stock of R&D not only because the same quantities of inputs produce
more output in the R&D sector but also because R&D becomes relatively cheaper as the
13
The higher the share of capital in R&D-sector output the more beneï¬?cial for the R&D sector are improve-
ments in investment-speciï¬?c technological progress. Likewise, the higher the share of capital in consumption-
sector output the more beneï¬?cial for the consumption-good sector are improvements in investment-speciï¬?c
technological progress.
18
relative (real) price of R&D (PRt ) decreases. In other words, a positive R&D shock facilitates
the conversion of units of output from the consumption-good sector into R&D stock. The
latter coupled with anticipation of future gains from R&D motivates the transfer of sources
towards the R&D sector. This means that part of ICt can be invested in the stock of R&D
(i.e. ICt > It ). Among others, the latter can be thought of as sources increasing human
capital. Thus, a positive R&D shock may induce a ï¬‚ow of sources from the consumption-
good sector to the R&D sector (as a contribution to the stock of R&D) to the extent that
Dt > YRt which implies that IRt < 0 while It > 0. Note that those transferred sources may
not be explicitly identiï¬?ed as R&D from the national accounts because they are not listed
under R&D expenditures. Therefore, despite the small size of the specialized R&D sector,
R&D shocks may cause a signiï¬?cant variation in the output of the non-R&D sector, and as
a result in aggregate output.
Calibration and the Theoretical Impulse Response Functions
We calibrate the model and present theoretical impulse responses to the shocks prior
to the empirical analysis. As in Fisher (2006), those responses do not constitute a tool of
identiï¬?cation of the shocks, but help us to motivate the analysis of the following section by
assessing the plausibility of the responses identiï¬?ed from the data. One way to determine
that the empirical impulse responses are correctly identiï¬?ed is by showing that under rea-
sonable model parameter values the theoretical and the empirical responses exhibit a similar
behavior.
To be consistent with the relative magnitudes of the sectors we observe in the data, we
19
set the steady state share of R&D in total output to 3 percent.14 In addition, we set the
steady state growth rates of output in the R&D and non-R&D sectors equal to the average
annual growth rates observed in the data over the sample period that is, (e 1 =) 3.6 percent
e
and (e 1 =) 1.8 percent, respectively. The share of labor in the consumption-good sector,
(1 â†µ1 â†µ2 ), is set to 0.64 while the shares of R&D, â†µ1 , and capital, â†µ2 , are set to 0.10
and 0.26, respectively.15 The discount factor, , is chosen to be 0.95 which is a value tyically
used for annual frequencies. The steady state, xZ , is set to 1.02 which corresponds to the
average annual gross growth rate of the inverse of the real price of investment observed in
the data over the sample period. The annual depreciation rate, K, is choosen to be 0.10
which is consistent with the quarterly value of 0.025 used by Fisher (2006) and Altig et
al. (2011). The weights of leisure in the utility function, 'C and 'R , are normalized to
unity.16 The persistency parameters â‡¢A , â‡¢Z and â‡¢J are all set to 0.65 which corresponds to
a value of 0.87 in the quarterly frequency. Since the R&D sector is labor intensive, we set
the share of labor, (1 ), in the output of the sector to 0.9.17 As noted by Hall (2007), and
previously by Griliches (2000), the measurement of depreciation of R&D assets is the central
unsolved problem in the measurement of the returns to R&D. Hall argues that determining
14
Note that real aggregate output can be written as Yt = YCt + ï£¿âŒ…t YRt which can be expressed as
ï£¿(yRt /yCt ) = (Yt /YCt ) 1. The latter is introduced as an additional equation in the system of steady state
equations so that the set of parameter values are consistent with a steady state ratio of Y /YC equal to 1.03.
15
Those values lie within the range of values typically used in the literature examining aggregate produc-
tion, and imply a reasonably small share of R&D in the production of the non-R&D sector. The baseline
behavior of the impulse response functions are robust around those values.
16
The restriction on the relative size of YC and YR also controls for the relative size of hours despite the
fact that we normalize 'C and 'R to unity. Our benchmark calibration implies a ratio of steady state hours,
HR /HC , of 7.6 percent.
17
Most previous papers assume that R&D output is produced only by labor (e.g. Butler and Pakko, 1998,
Braun and Nakajima, 2008). We allow for, at least, a small share of capital. The results are robust around
this share value.
20
the appropriate depreciation rate of R&D is di cult, if not impossible.18 In this paper, we
calibrate the model assuming two diâ†µerent values for the depreciation rate, R = 0.5 and
= 0.8. The scale parameter ï£¿ is pinned down at the steady state by the steady state
equations. It is worth noting that the calibration implies that at the steady state there is a
positive transfer of resources from the non-R&D sector as a contribution to the stock of R&D
(in addition to the contribution of the R&D sector). The parameter values are summarized
in table 2.
Figure 6, plots the response of output and hours in each sector to one percent positive
productivity shock in the R&D sector. The responses of output suggest that technology
shocks in the R&D sector have a long-run impact on the production of both sectors. The
response of R&D output is always positive while the response of output in the consumption-
good sector is positive after the ï¬?rst period, under R = 0.8. For the lower depreciation
rate, the output of the consumption-good sector responds positively only after the fourth
period indicating that the impact of an R&D shock becomes positive faster, the higher the
depreciation rate. This is due to the fact that a lower depreciation rate of R&D creates an
incentive for the agents to work relatively less. The lower depreciation rate induces a loss
in the consumption utility which is compensated by a gain in leisure utility. Although a
lower R&D depreciation rate induces a lower output than that of a higher depreciation rate,
the underlying utility level of the household can be the same under the two regimes. The
response of hours to a positive shock is positive when the inter-temporal substitution eâ†µect
18
According to Hall, the di culty lies on at least two reasons. First, on the fact that at the micro level,
the depreciation rate is endogenous to the behavior of each ï¬?rm and its competitors, and second, on the
fact that it is extremely di cult to determine the lag structure of R&D in generating returns. For a further
discussion see Hall (2007).
21
dominates the wealth eâ†µect, and negative when the reverse holds. While the households are
willing to exploit the gain from saving by substituting inter-temporally away from leisure
today toward consumption in the future, they also tend to decrease work eâ†µort as they feel
wealthier (wealth eâ†µect). Figure 6 indicates that the response of hours in the R&D sector is
always positive only if the depreciation rate is high. The response of hours in the non-R&D
sector is always negative, and smaller in magnitude the higher the depreciation rate.
Figure 7 displays the responses of output and hours to a negative capital investment-
speciï¬?c shock. The deterioration of investment-speciï¬?c technology always induces negative
responses in both sectors. In this case, the inter-temporal eâ†µects caused by the Z-shock
clearly dominate the wealth eâ†µects. This result is also found in Fisher (2006) and Altig et
al. (2011) who studied an aggregate sector economy. For the same reason as in the case of
a productivity shock in the R&D sector, the responses to an investment-speciï¬?c shock are
larger for a lower R&D depreciation rate. Likewise, ï¬?gure 8, shows that the responses of
output and hours to a positive productivity shock in the non-R&D sector are positive at all
times, indicating the dominance of inter-temporal substitution eâ†µects.
5 VAR Estimation
We embed our identifying assumptions and the structure of our economic model as restric-
tions on the parameters of the following VAR:
Cyt = 1 yt 1 + 2 yt 2 + Â·Â·Â· + p yt p + "t , (5.1)
22
where yt is a vector of time t variables, "t is a vector of time t structural shocks, with
a diagonal variance-covariance matrix E ("t "0t ) = âŒƒ, and C is a matrix that contains the
contemporaneous relations of the variables in yt (with ones in the diagonal). To sum up,
the long-run restrictions imposed on the VAR are the following:
Restriction 1 : Only capital investment-speciï¬?c shocks aâ†µect the real price of investment
in the long-run.
Restriction 2 : Only capital investment-speciï¬?c shocks and R&D shocks aâ†µect labor pro-
ductivity in the R&D sector in the long-run.
Restriction 3 : Only capital investment-speciï¬?c shocks, R&D shocks and consumption-
sector shocks aâ†µect labor productivity in the consumption-good sector in the long-run.
The assumption that capital investment-speciï¬?c technological change is the unique source
of the secular trend in the real price of capital investment goods is commonly used by
previous studies (Fisher, 2006, Altig et al., 2011). The presence of capital as a factor of
production in both sectors justiï¬?es the fact that capital investment-speciï¬?c shocks aâ†µect
labor productivities in both sectors in the long-run. The rest of the assumptions follow
from the fact that production in the non-R&D sector is explicitly augmented by the stock of
R&D while the reverse does not hold. The latter is due to the fact that the level of output
in the non-R&D sector does not have a direct impact on R&D activities. Note that these
arguments hold only in the long-run; in the short and medium run productivity shocks in
the non-R&D sector aâ†µect production in the R&D sector.
23
We deï¬?ne yt as [ ln (PKt /PGDP t ), ln (YRt /HRt ), ln (YCt /HCt ), ln HRt , ln HCt , â‡¤t ]0 where
âŒ˜1 L with L being the lag operator, PKt is the nominal price of capital investment
and PGDP t is the GDP price index. Following Fisher (2006), vector â‡¤t , which consists of the
inï¬‚ation rate and the nominal interest rate, is included in order to capture potential eâ†µects
of monetary policy. Let "t = ["1t , "2t ]0 where "1t = ["Zt , "Jt , "At ]0 and "2t = [ "Rt , "Ct , "It ,
"IN t ]0 . Following Fisher (2006), each regression row of (5.1) is estimated sequentially. The
ï¬?rst equation of (5.1) is
â‡£ âŒ˜ â‡£ âŒ˜ â‡£ âŒ˜
PK PK Y
ln PGDP
= P + PP (L) ln PGDP
+ P R (L) ln HR +
R t
t t 1 (5.2)
â‡£ âŒ˜
Y
P RH ln (HRt ) + P CH ln (HCt ) + PC (L) ln HC + P â‡¤ (L) â‡¤t + "Zt .
C t
As indicated by Fisher (2006), restriction 1 is equivalent to imposing a unit root in each of
the lag polynomials associated with ln (YRt /HRt ), ln (YCt /HCt ), ln (HRt ), ln (HCt ) and
â‡¤t . Doing so, the coe cients of (5.2) become Pi (L) = e P i (L) (1 L) and the regression
is rewritten as
â‡£ âŒ˜ â‡£ âŒ˜ â‡£ âŒ˜
ln PK
PGDP
= P + PP (L) ln PK
PGDP
+ e P R (L) 2
ln YR
HR
+
t t 1 t
â‡£ âŒ˜
e P RH ln (HRt ) + e P CH ln (HCt ) + e P C (L) 2
ln YC
+ (5.3)
HC
t
e P â‡¤ (L) â‡¤t + "Zt .
Since investment-speciï¬?c shocks are not orthogonal to the variables on the right hand side,
ordinary least squares will give inconsistent estimates. According to our economic model the
exogenous shock "Zt is uncorrelated with variables at t 1. Consequently, N lags of variables
2 2
ln (YRt /HRt ), ln (YCt /HCt ), ln (HRt ), ln (HCt ) and â‡¤t are used as instruments.
24
According to restriction 2, only R&D shocks and investment speciï¬?c shocks have an
impact on labor productivity in the R&D sector in the long-run. This amounts to imposing
unit roots on ln (YCt /HCt ), ln (HRt ), ln (HCt ) and â‡¤t and thereby the second equation of
(5.1) reduces to
â‡£ âŒ˜ â‡£ âŒ˜ â‡£ âŒ˜
YR YR PK
ln HR
= YR + RR (L) ln HR RP +ln PGDP (L) +
t t 1 t 1
â‡£ âŒ˜
e RRH ln (HRt ) + e RCH ln (HCt ) + e RC (L) 2 ln HC +
Y (5.4)
C t
e Râ‡¤ (L) â‡¤t + âœ“R "Zt + "Jt ,
b
b
where "Zt denotes the estimated residuals of (5.3). We include the estimate of "Zt as an
b b
instrument in the regression to ensure that "Jt will be orthogonal to "Zt . As in the previous
2
case, to estimate (5.4), we use N lags of variables ln (YCt /HCt ), ln (HRt ), ln (HCt )
and â‡¤t as instruments.
Having estimates for {"Zt } and {"Jt } what is left is to estimate technology shocks speciï¬?c
to the non-R&D sector, {"At }. Restriction 3 states that only shocks in "1t aâ†µect productivity
in the consumption good sector in the long-run. Imposing the appropriate unit roots on the
independent variables, the third equation of (5.1) reduces to
â‡£ âŒ˜ â‡£ âŒ˜ â‡£ âŒ˜
YC YC PK
ln HC
= YC + CC (L) ln HC
+ CP (L) ln PGDP +
t t 1 t 1
â‡£ âŒ˜
e CRH ln (HRt ) + e CCH ln (HCt ) + CR (L) Y
ln HR + (5.5)
R t 1
e Câ‡¤ (L) b b
ln (â‡¤t ) + âœ“CZ "Zt + âœ“CJ "Jt + "At ,
b b
where "Zt and "Jt are estimates of the shocks from the previous regressions. Equation (5.5)
is estimated using N lags of variables ln (HRt ), ln (HCt ) and â‡¤t as instruments.
25
Note that system (5.1) can be written as
0 10 1 0 10 1 0 1
11 12
B C11 C12 C B y1t C B (L) (L) C B y1t 1 C B "1t C
B 3x3 3x4 C B 3x1 C B 3x3 3x4 C B 3x1 C B 3x1 C
@ A@ A=B
@
CB
A@
C+@
A A, (5.6)
C21 C22 y2t 21
(L) 22
(L) y2t 1 "2t
4x3 4x4 4x1 4x3 4x4 4x1 4x1
where y1t = [ ln (PKt /PGDP t ) , ln (YRt /HRt ) , ln (YCt /HCt )]0 and y2t = [ln HRt , ln HCt ,
â‡¤t ]0 . Notice that the coe cients C11 , C12 , 11
(L) and 12
(L) are derived by unravelling
the estimates from (5.3), (5.4) and (5.5). Therefore, the ï¬?rst three equations of the system
are exactly identiï¬?ed. On the contrary, the last four equations of (5.6) cannot be identiï¬?ed
because the structural error "2t cannot be identiï¬?ed separately from the reduced form error
1
(C22 ) "2t . Nevertheless, the shocks in "2t can be identiï¬?ed up to a particular transforma-
tion. It can be shown that there is a family of observational equivalent parametarizations of
the structural form where the responses of y2t to the shocks in "1t are invariant. To see this,
let â‡¥ be the following orthonormal matrix:
0 1
B I 0 C
â‡¥ = B 3x3
@
C,
3x4
A
0 âœ“
4x3 4x4
where I denotes the identity matrix and âœ“ is an orthonormal matrix. Premultiplying both
sides of (5.6) by â‡¥, the last four equations can be written in reduced form as
1 1 1
y2t = C22 21
(L) y1t 1 + C22 22
(L) y2t 1 C22 C21 y1t + âœ?2t , (5.7)
26
1
where = âœ“C22 b
and âœ?2t = âœ“"2t . Let C22 be an estimate of C22 and "2t be the correspond-
b
e b
ing ï¬?tted disturbances. An alternative estimate of C22 is C22 = âœ“C22 with corresponding
â‡£ âŒ˜ 1
b e b
disturbances "2t = âœ“b2t . The estimates C22 and C22 ï¬?t the data equally well. If C22
e " is
lower triangular then the last two equations in (5.6) can be estimated sequentially using the
â‡£ âŒ˜ 1
residuals of the previously estimated equations. Suppose that C22 b is not lower trian-
b
gular. Since C22 is nonsingular, there exist an orthonormal matrix âœ“ and a lower triangular
b b
matrix R such that C22 = âœ“0 R. It follows that âœ“C22 = R is lower triangular, which im-
â‡£ âŒ˜ 1
b
plies that b = C22 âœ“0 is lower triangular. Consequently, the fourth equation in (5.6) is
b b b b
estimated using "Zt , "Jt and "At as regressors to ensure orthogonality with "Rt and the ï¬?fth
b b b b
equation is estimated using "Zt , "Jt , "At and "Rt as regressors to ensure orthogonality with
b
"Ct . The sixth and the seventh equations are estimated in a similar way. All four equations
are estimated by IV, using N lags of yt as instruments.
6 Data
In this section we provide extensive analysis on the measurement of R&D investment as well
as description of the other variables (and their components) used in the empirical analysis.
6.1 Measuring R&D Output
Measuring the output of R&D activity is a challenge because there is neither an observable
market price nor a reported quantity of output for R&D. The latter is mainly produced
by ï¬?rms for internal use. A commonly used measure of R&D activity is expenditures in
27
R&D which constitute an investment that pays oâ†µ in the long run. Currently, expenditures
on R&D are not included as investment in GDP in the o cial accounts but instead they
are treated as current period expenditures. Treating R&D as investment rather than as
intermediate expenditures results in important changes to the calculation of GDP. In BEAâ€™s
National Income and Product Account (NIPA), business R&D expenditures are included
as intermediate rather than ï¬?nal expenditures which means that they are not added up
in deriving GDP. Other expenditures in R&D which are included in the calculation of the
GDP cannot be separately identiï¬?ed from other components reported in the NIPA tables.19
Although those expenditures are included in GDP, they are not treated as investment which
means that they are not subject to depreciation.
In 2006, the Bureau of Economic Analysis (BEA) jointly with NSF launched an R&D
satellite account to explore investment in R&D and its larger economic eâ†µects. The BEA-
NSF R&D satellite account provides a measure of the value of R&D output and adjusted
GDP by transforming R&D expenditures into measures of real investment.20 The nominal
value of R&D is the sum of the costs of the R&D activity of both private and government
organizations. Private organizations consist of businesses such as private universities and
colleges, private hospitals, charitable foundations, other nonproï¬?t institutions serving house-
holds and most Federally Funded Research and Development Centers (FFRDC). Government
organizations consist of the Federal Government, state and local governments (excluding uni-
19
Expenditures on R&D by government and nonproï¬?t institutions are included in consumption expendi-
tures; Federal purchases of R&D, expenditures on in-house R&D performed by the federal government and
state and local purchases of R&D are included in government consumption; Spending on R&D by foun-
dations and non-proï¬?t institutions serving households are included in personal consumption expenditures;
R&D services are also included in exports and imports while the cost of patents for the use of R&D are
included in royalties and licencing fees. For more information refer to Mataloni and Moylan (2007).
20
BEA plans to formally incorporate R&D spending as investment into its core accounts around 2013.
28
versities and colleges), public universities and colleges, and FFRDCs administered by state
and local governments (primarily public universities and colleges). The BEA prepares all es-
timates of current-dollar R&D investment by ï¬?rst compiling data available from the various
NSF surveys and then adjusting these data to be statistically and conceptually consistent
with BEA deï¬?nitions in the NIPA tables.
Real R&D investment is derived by deï¬‚ating detailed current-dollar expenditures by
appropriate price indexes. Two price indexes are constructed and utilized in the satellite
account: an input price index and an aggregate output-based price index. The input price
index is based on an aggregation of detailed price indexes for the inputs used to create R&D
output. As noted by Lee and Schmidt (2010), this index is a good measure of the impact of
inï¬‚ation on R&D inputs but less appropriate in measuring R&D output because it does not
account for productivity growth; it makes the assumption that real output grows at the same
rate as real inputs. On the other hand, the aggregate output-based index indirectly reï¬‚ects
the movement of R&D output prices. In particular, it is a weighted average of the output
prices of other products produced by 14 R&D-intensive industries with weights corresponding
to each industryâ€™s share of annual business R&D investment. There are two issues related
to this index. First, it is inï¬‚uenced by factors that are unrelated to R&D which aâ†µect prices
of other products produced by the same industries. Second, before 1987, it was constructed
based on only the top ï¬?ve industry R&D performers because detailed industry investment
measures were unavailable.21 Despite those issues, the output-based price index is the best
price measure available capturing productivity growth in R&D-intensive industries and thus,
21
For more details about the index refer to Okubo et al. (2006) and Lee and Schmidt (2010).
29
it is used throughout our analysis to deï¬‚ate nominal R&D investment.
6.2 Other Variables Used in the Analysis
In the empirical analysis we employ US annual data for the period 1959-2007. We use annual
frequencies because R&D investment and total employment of R&D performing companies
are reported only at annual frequencies. Moreover, data on R&D investment and employment
are available only after 1959 and 1958, respectively. The former are obtained from the BEA-
NSF R&D satellite account while the latter are from the NSF annual survey.22 Our sample
excludes the turbulent period after 2007.
Total hours worked in each sector are deï¬?ned as the number of employed multiplied by
average hours worked during the reference year. While data on aggregate average hours
worked are available, data on individual hours that correspond to workers employed in
the R&D sectors are not reported. In our benchmark speciï¬?cation, HRt is computed as
employment in the R&D sector multiplied by per capita hours in the nonfarm business
sector divided by a population measure that refers to population over 16 years old (US Census
Bureau).23 To compute hours in the consumption-good sector, we ï¬?rst compute employment
in the sector as employment in the nonfarm business sector minus employment in the R&D
sector. Then, HCt is computed as employment in the sector multiplied by per capita hours in
22
The NSF reports data on domestic employment by R&D performing companies which does not include
universities and government. Although there are various statistics for employment from NSF surveys, there
are di culties in constructing an aggregate measure of R&D employment series. First, there are no complete
data for all years of our sample and second, it is unclear which of the participants in the surveys are actually
involved in performing R&D activities. Given those issues and since R&D investment by universities and
government constitutes, on average, only 20 percent of total R&D investment we approximate aggregate
employment for R&D by the domestic employment of R&D performing companies.
23
Altig, Christiano, Eichenbaum and Linde (2011) compute their measure of aggregate per capita hours
in the same way. Nonfarm business hours and employment are published by the Bureau of Labor Statistics.
30
the nonfarm business sector, divided by the population measure. Consequently, the diâ†µerence
in the variation of HRt over HCt is due to variation in employment.24 Figure 9 displays the
annual growth rate of total hours versus the annual growth rate of total employment. As
the ï¬?gure shows, the two series are highly correlated displaying similar ï¬‚uctuations which
suggests that employment is the main driving force of total hours. For this reason, we also
present alternative measures of HRt and HCt , computed simply as employment divided by
population.25
As in Fisher (2006), the price index of capital investment, PK , corresponds to the price
of total investment and is constructed with the equipment deï¬‚ator and the NIPA (National
Income and Product Accounts) deï¬‚ators for residential and nonresidential structures, con-
sumer durables and government investment. The equipment deï¬‚ator was constructed by
Gordon (1990) for the years up to 1980 and was extended by Cummins and Violante (2002)
for the years up until 2000. We extend the Gordon-Cummins-Violante index further to 2007
using the pattern of NIPA investment price series. The rest of the data were taken from the
NIPA tables. The price index, PGDP t , used to deï¬‚ate the price of capital investment is the
implied deï¬‚ator from chained real GDP. Aggregate output in the consumption good sector
is nominal GDP net of R&D investment as reported in the BEA-NSF satellite account, de-
ï¬‚ated by the implied GDP deï¬‚ator. Outputs YRt and YCt are obtained by dividing real R&D
investment and real aggregate output in the consumption good sector by the population
24
Previous studies also indicate that most variation in total hours is due to variation in employment than
variation in individual hours (e.g. Hansen (1985), Castro and Coen-Pirani (2008)), especially at annual
frequencies.
25
The theory could also be summarized by an indivisible labor model a la Hansen (1985) and Rogerson
(1988). In that case, the optimality conditions for labor supply in the theoretical model would be slightly
diâ†µerent but the main theoretical arguments would remain unaâ†µected.
31
measure.26 The interest rate is measured by the eâ†µective federal funds rate and the inï¬‚ation
rate is deï¬?ned as the growth rate of the consumer price index.
In practice, labor productivities and the real price of capital investment are nonstationary.
To overcome this problem, we follow the common practice of ï¬?rst diâ†µerencing. The measures
of per capita hours also exhibit some nonstationarity. This feature is also documented in
Ä±, Ä±
previous studies that examine quarterly data (e.g. GalÂ´ 1999, Francis and Ramey, 2005, GalÂ´
and Rabanal, 2005, and Fisher, 2006). The nonstationarity of per capita hours is even more
evident at annual frequencies. As Fisher (2002) points out, the appropriate way to include
per capita hours into the analysis is a matter of some controversy. Christiano, Eichenbaum
and Vigfusson (2003) provide an extensive discussion on the treatment of per capita hours
in the VAR. In this paper, we stationarize the hours measures by removing a linear trend
from the log series. As in Collard and Dellas (2007), this approach avoids the criticism of
Christiano et al. (2003), that hours should not be diâ†µerenced. Using hours in levels or
ï¬?rst-diâ†µerences produces conï¬?dence intervals for hours and other variables that diverge to
inï¬?nity as the horizon increases.
7 Empirical Results from the VAR
In this section we discuss our results from the estimated VAR. With quarterly data, four
is the common choice for the number of lags which adequately captures the medium-run
dynamics in the data.27 This corresponds to one lag at annual frequencies. The one year lag
26
Aggregate real output in the consumption-good sector is deï¬?ned as aggregate nominal output net of
R&D investment divided by the implicit GDP deï¬‚ator from the BEA-NSF satellite account.
27
For instance, see Christiano, Eichenbaum and Evans (2005), Altig, Christiano, Eichenbaum and Linde
(2005) and Fisher (2006).
32
is also a preferable choice given the short size of the available sample. In what follows, ï¬?rst
we examine the dynamic responses of outputs and hours of work to a productivity shock in
the R&D sector, a productivity shock in the consumption-good sector and an investment-
speciï¬?c shock. Second, we examine the contribution of each of the three shocks and the
R&D sector to the overall variability of the macroeconomic variables.
7.1 Impulse Response Functions
Figure 10 displays impulse response functions to a one standard deviation positive produc-
tivity shock ("Jt ) in the R&D sector. The two dashed lines correspond to a 90 percent
conï¬?dence interval computed by non-parametric bootstrap. The size of the conï¬?dence in-
tervals are not very diâ†µerent from conï¬?dence intervals of similar studies with quarterly data
(e.g. the 95 percent conï¬?dence intervals for neutral shocks in Altig et al., 2011). When the
shock occurs, the output of the R&D sector increases instantly by 0.5 percent, and continues
to increase till the peak of 1.4 percent in the sixth year from the date of the occurence of the
shock. The response of output in the consumption-good sector becomes signiï¬?cantly positive
and increasing after the second year following the occurance of the shock, reaching a peak
of 0.5 percent in the sixth year following the occurance of the shock.28 Hours in the R&D
sector exhibit a small increase in response to the sectoral productivity shock, followed by a
decrease and eventually by an increase. The sign of the response however is not statistically
signiï¬?cant, at least for the ï¬?rst four periods. Hours in the consumption-good sector exhibit
28
Notice that the initial small and statistically insigniï¬?cant eâ†µect of the R&D productivity shock on the
output of the consumption-good sector is consistent with the structure of our economic model in which
shocks speciï¬?c to the R&D sector do not have a direct contemporaneous eâ†µect on the consumption-good
sector output.
33
a gradual increase which is clearly statistically signiï¬?cant, in terms of sign, after the third
period following the occurence of the shock.
Figure 11 displays impulse response functions to a one standard deviation positive shock
in the real price of capital investment. The latter is equivalent to a one standard devia-
tion negative shock in investment-speciï¬?c technology Zt (i.e. a negative, "Zt , shock that
decreases Zt ). The negative (positive) shock in Zt causes a statistically signiï¬?cant prolonged
decrease (increase) in output in the R&D sector. R&D output decreases instantly by 1 per-
cent and continues to decrease with a peak decline of 2.5 percent over the period displayed.
The positive shock in the real price of investment causes a statistically signiï¬?cant decline in
hours in the R&D sector. Speciï¬?cally, a 1 percent increase in the real price of investment
causes a sharp decline in work eâ†µort of almost 2 percent. The response of hours continues to
remain below its initial level over the period displayed but diminishes gradually. Those re-
sponses indicate the big impact of changes in investment-speciï¬?c technology on ï¬‚uctuations
of R&D activity. Output in the consumption-good sector responds negatively to a negative
investment-speciï¬?c shock with an initial response of 0.2 percent which is marginally statis-
tically signiï¬?cant. Hours in the consumption-good sector do not respond instantly to the
shock but decline gradually reaching a trough of 0.3 percent. The negative response of hours
is only marginally statistically signiï¬?cant throughout the period displayed. Note that the
decrease in R&D output and hours in response to the shock is much larger which suggests
that the R&D sector is relatively more sensitive to changes in investment speciï¬?c technol-
ogy than the consumption-good sector. In other words, an improvement in the technology
producing physical capital induces a considerable increase in R&D activity.
34
Figure 12 displays impulse response functions to a one standard deviation positive pro-
ductivity shock, "At , speciï¬?c to the consumption-good sector. The impulse response of output
in the consumption-good sector is positive and hump-shaped. The response reaches a peak
of 1 percent in the fourth period following the occurance of the shock. While the initial
response of the hours worked in the consumption-good sector is negative and statistically
insigniï¬?cant, it becomes positive in the second period and statistically signiï¬?cant in the
fourth period onward. The response of output in the R&D sector is negative in the ï¬?rst two
periods but marginally statistically signiï¬?cant only in the ï¬?rst one. The response becomes
positive after the third year but remains statistically insigniï¬?cant in terms of the sign.29
7.2 Variance Decompositions
The qualitative similarities between the theoretical and empirical impulse responses functions
provide some conï¬?dence that the structural shocks are correctly identiï¬?ed. In this subsection,
we discuss the contribution of the sectoral productivity shocks and the investment-speciï¬?c
shocks to annual ï¬‚uctuations in economic activity. We evaluate the contribution of each
shock to the overall variability of the variables in our analysis by presenting two sets of
variance decompositions. The ï¬?rst set corresponds to the direct contributions of the three
shocks. In this set, variance decompositions are computed by non-parametric simulations of
the VAR model. The fractions of variances are obtained in simulation blocks in which we
only keep active a single shock while the variances of the rest are set equal to zero. Figure
29
The empirical impulse response functions are roughly consistent with most of the main dynamics gen-
erated by the economic model. We would like to stress that although the model has potential to generate
responses closer to the empirical ones, both in terms of magnitute and size if enriched with more core features,
its role in this paper remains auxiliary.
35
13 displays the distributions of the variance decompositions for output and hours of work in
each sector. The generated distributions draw an informative picture of the accuracy of the
estimated contributions of the shocks. Median values of variance decompositions along with
90 percent conï¬?dence intervals are reported in table 3 (means are close to medians).
Productivity shocks speciï¬?c to the R&D sector explain almost 20 percent of the variability
of output in the sector and only 4.4 percent of the variability of the sectorâ€™s working hours.
Our estimates indicate that despite the fact that the R&D sector is small relative to the
overall economy, the impact of R&D productivity shocks on the output of the non-R&D
sector is quite large. In particular, R&D productivity shocks account for 30.2 percent of
the variance of output in the non-R&D sector. They also explain a non-negligible portion
of the variance of hours in the non-R&D sector in the order of 16.7 percent. Our analysis
shows that shocks to investment-speciï¬?c technology are crucial to the variability of R&D
investment, being the main driving force of output ï¬‚uctuations as they explain 69.9 percent
of its variance. In addition, these types of shocks explain 39.1 percent of the variance of
the hours worked in the R&D sector. The impact of investment-speciï¬?c shocks on the
variance of output in the consumption-good sector is also considerable, but not as large as
it appears to be in the R&D sector. Speciï¬?cally, shocks to investment-speciï¬?c technology
explain 35.4 and 31.1 percent of the variability of the non-R&D sector output and hours,
respectively. Our results suggest that productivity shocks in the non-R&D sector play only
a minor role in driving the ï¬‚uctuations of output and hours in the two sectors. The largest
fraction explained by consumption-good sector productivity shocks is 13.7 percent for the
output of the sector. As regards the variability of labor productivities, the highest fraction
36
in the R&D and non-R&D sectors is attributed to investment-speciï¬?c shocks by 56 and 38.4
percent, respectively.
The three technology shocks jointly explain 92.3 percent and 78.5 percent of the variance
of outputs in the R&D sector and the rest of the economy, respectively. Ouyang (2011)
argues that technology shocks are important factors in explaining the procyclicality of R&D.
Our results conï¬?rm this claim since the main sources of output volatility in the two sectors,
capital investment-speciï¬?c and R&D productivity shocks, induce output responses of the
same sign. Furthermore, technology shocks, jointly explain a moderate proportion of the
variance of hours which is in the order of 46.1 percent and 56.4 percent in the R&D sector
and the consumption-good sector, respectively. Table 4 displays variance decompositions
when the R&D sector is not modeled as a separate sector and R&D is not treated as invest-
ment. In this case, aggregate output correponds to the GDP reported in the NIPA tables
while hours correspond to aggregate per capita hours.30 These results show that under this
speciï¬?cation of the model, investment-speciï¬?c shocks and neutral productivity shocks ex-
plain 40.2 and 33.3 percent of the variability of NIPA output while the combined eâ†µect of
technology shocks is 90.3 percent; this result is not too diâ†µerent from ï¬?ndings of previous
studies that used quarterly data.31 The combined eâ†µect of technology shocks on productiv-
ity and hours increases signiï¬?cantly compared to the model where there is a separate R&D
sector and R&D is treated as investment than solely as an expense.
In the second set of results (tables 5 and 6), we compute variance decompositions of the
30
In the model of section 3, the R&D channel is closed when â†µ1 = 0.
31
Altig et al. (2011), ï¬?nd that capital investment-speciï¬?c shocks explain 41 percent of the variation of
output while neutral technology shocks explain 11 percent for the period 1982:1-2008:3. Fisher (2006), ï¬?nds
that investment-speciï¬?c shocks explain 42-67 percent of the variation of output while neutral technology
shocks explain 8-33 percent for the period 1955:1-2000:4.
37
forecast error. The numbers in parentheses correspond to 90 percent bootstrapped conï¬?dence
intervals. Although the connection between forecast error decompositions and contributions
to cycles is not as direct as that reported in tables 3 and 4, the former roughly conï¬?rm
the latter regarding the impact of shocks. Over a horizon of 1 to 12 years, investment
speciï¬?c shocks explain a fraction of 44.7 to 69.3 percent of the variance of the forecast error
of R&D output while the fraction is increasing with the horizon. Likewise, productivity
shocks in the R&D sector explain 18.3 to 30.6 percent of the variation of the output forecast
error in the R&D sector. The fraction of forecast error variance for the consumption-good
sector output to R&D productivity shocks ranges from 1.2 percent, 1 period ahead, to 35.2
percent, 12 periods ahead. Those decompositions suggest that in the long run, technology
shocks (jointly) explain all the variation of the forecast error of output in both sectors. The
estimates also indicate that capital investment-speciï¬?c shocks explain most of the variation
of the forecast error variance of hours in both sectors. Note that when R&D is neither
treated as investment nor as a separate sector then the joint impact of technology shocks
on the forecast error variance reduces. Speciï¬?cally, over the horizon of 12 years, technology
shocks jointly explain up to 78.8 percent of the variation of the forecast error of NIPA GDP
as opposed to the 100 percent for the two outputs in the extended model.
Tables 7 to 10 display variance decompositions when the alternative measure of labor is
used. Compared to the benchmark case, the impact of capital investment-speciï¬?c shocks
on outputs increases slightly to 73.5 percent for R&D output and 44.8 percent for the
consumption-good sector output. The impact of R&D productivity shocks on the output of
the non-R&D sector reduces to 18.2 percent while the combined eâ†µect of technology shocks
38
on the non-R&D output reduces to 61 percent. The impact of capital investment-speciï¬?c
shocks on labor reduces to 27.3 percent in the R&D sector and 17.4 percent in the non-R&D
sector while the combined eâ†µect of technology shocks on labor in the non-R&D sector reduces
to 35.3 percent. These results show that even under the extreme assumption of constant
individual hours, the signiï¬?cant eâ†µects of R&D and capital investment-speciï¬?c shocks on the
output of the non-R&D sector and R&D investment remain.
8 Conclusion
In this paper we examine sources of the excessive volatility in the R&D sector as well as
the role and contribution of the sector to aggregate ï¬‚uctuations. In doing so, we consider
the eâ†µects of productivity and capital investment-speciï¬?c shocks in the R&D and non-R&D
sectors using a VAR and data from the BEA-NSF satellite account for the period 1959-
2007. The shocks are identiï¬?ed by imposing long-run restrictions which are justiï¬?ed by
a two-sector general equilibrium model. We show that introducing exogenous changes in
sectoral productivities, in addition to investment-speciï¬?c technical change, into an RBC
model motivates three long-run identifying restrictions. First, the model predicts that the
change in capital investment-speciï¬?c technology is the unique source of the secular trend
in the real price of capital investment goods. Second, changes in capital investment-speciï¬?c
technology along with changes in R&D-speciï¬?c technology are the only sources of permanent
shocks to labor productivity in the R&D sector. Third, changes in productivity in the R&D
sector and capital investment-speciï¬?c technology along with changes in technology in the
non-R&D sector are the only sources of permanent shocks to labor productivity in the non-
39
R&D sector. With those restrictions imposed on the VAR, the three technology shocks are
exactly identiï¬?ed.
Our estimates suggest that capital investment speciï¬?c shocks play the largest role in
driving the ï¬‚uctuations in the R&D sector while the impact of the R&D sector on aggregate
ï¬‚uctuations is substantial given its relative size. Speciï¬?cally, after controling for real and
nominal factors, capital investment-speciï¬?c shocks explain 70 percent of ï¬‚uctuations of R&D
investment while productivity shocks in the R&D sector explain 30 percent of the variation
of output in the non-R&D sector. We ï¬?nd that technology shocks can jointly explain almost
all the variation of output in the R&D sector and 78 percent of the variation of output in the
rest of the economy. Our ï¬?ndings also conï¬?rm Ouyangâ€™s (2011) proposition that technology
shocks are key factors in explaining the procyclicality of R&D.
40
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43
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0 0
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0 0
20 1
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(grey) and R&D employment (black)
20 3
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Figure 1 - Share of R&D investment in
20 4
20 4 0
0 20 5
20 5 0
0 20 6
07
20 6
07
Figure 3 - Growth rates of real R&D investment
44
-0,02
-0,01
-0,05
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
-0,1
0
0,05
0,1
0,15
19 19
6 6
19 0 19 0
6 6
19 1 19 1
6 6
19 2 19 2
6 6
19 3 19 3
6 6
19 4 19 4
6 6
19 5 19 5
6 6
19 6 19 6
6 6
19 7 19 7
6 6
19 8 19 8
6 6
19 9 19 9
7 7
19 0 19 0
7 7
19 1 19 1
7 7
19 2 19 2
7 7
19 3 19 3
7 7
19 4 19 4
7 7
19 5 19 5
7 7
19 6 19 6
7 7
19 7 19 7
7 7
19 8 19 8
7 7
19 9 19 9
8 8
19 0 19 0
8 8
19 1 19 1
8 8
19 2 19 2
8 8
19 3 19 3
8 8
19 4 19 4
8 8
years
years
19 5 19 5
8 8
19 6 19 6
8 8
19 7 19 7
8 8
19 8 19 8
8 8
19 9 19 9
9 9
19 0 19 0
9 9
19 1 19 1
9 9
19 2 19 2
9 9
19 3 19 3
9 9
19 4 19 4
9 9
19 5 19 5
9 9
19 6 19 6
9 9
19 7 19 7
9 9
19 8 19 8
9 9
20 9 20 9
0 0
20 0 20 0
0 0
20 1 20 1
[51] Stokey, N.L., 1995. R&D and growth. Review of Economic Studies 62 (3), 469-489
0 0
output and net of R&D employment
20 2 20 2
0 0
20 3 20 3
(black) and adjusted real GDP (grey)
0 0
20 4 20 4
0 0
20 5 20 5
0 0
Figure 4 - Growth rates of net of R&D real
20 6 20 6
07 07
Figure 2 - Growth rates of real R&D investment
0,1
0,2
0,3
0
-0,3
-0,2
-0,1
19
0
-0,06
-0,04
-0,02
0,02
0,04
0,06
0,08
19 6
6 19 0
19 0
the R&D sector
6 6
19 1 19 1
6 6
19 2 19 2
6 6
19 3 19 3
6 6
19 4 19 4
6 6
19 5 19 5
6 6
19 6 19 6
6 6
19 7 19 7
6 6
19 8 19 8
Figure 6 - Theoretical responses
6 6
19 9 19 9
to a positive productivity shock in
7 7
19 0 19 0
7 7
19 1 19 1
7 7
19 2 19 2
7 7
19 3 19 3
7 7
19 4 19 4
7 7
19 5 19 5
7 7
19 6 19 6
7 7
19 7 19 7
7 7
19 8 19 8
7 7
19 9 19 9
8 8
19 0 19 0
8 8
19 1 19 1
8 8
19 2 19 2
8 8
19 3 19 3
8 8
45
19 4 19 4
8 8
years
years
19 5 19 5
8 8
19 6 19 6
8 8
19 7 19 7
8 8
19 8 19 8
8 8
19 9 19 9
9 9
19 0 19 0
9 9
shock
19 1 19 1
9 9
19 2 19 2
9 9
19 3 19 3
9 9
19 4 19 4
9 9
19 5 19 5
9 9
19 6 19 6
9 9
19 7 19 7
9 9
19 8 19 8
9 9
20 9 20 9
0 0
20 0 20 0
0 0
20 1 20 1
0 0
20 2 20 2
0 0
20 3 20 3
0 0
Figure 7 - Theoretical responses
20 4 20 4
to a negative investment-speciÃ–c
0 0
20 5 20 5
0 0
20 6 20 6
07 07
Figure 9 - Growth rates of total hours (grey) and employment (black)
Figure 5 - Growth rates of employment in the non-R&D (black) and R&D (grey) sectors
the consumption-good sector
Figure 8 - Theoretical responses
to a positive productivity shock in
Figure 10 - Response of levels to a positive Figure 11 - Response of levels to a negative
productivity shock in the R&D sector [- - - , investment-speciÃ–c shock [- - - , 90% conÃ–dence
90% conÃ–dence interval] interval]
Figure 12 - Response of levels to a positive Figure 13 - Distributions of variance
productivity shock in the consumption-good decompositions
sector [- - - , 90% conÃ–dence interval]
46
Table 1 - Volatilities of growth rates: Annual US data 1959-2007
real adj. GDP total employment R&D investment R&D employment
Volatility 1.95 1.75 4.01 7.01
Table 2 - Model parameter values
value value value value
ï€‹1 0.1 ï€• 0.1 ï€šJ 0.65 e
e 1.018
ï€‹2 0.26 'C 1 ï€šA 0.65 ï€Ž R 0.5 or 0.8
ï€”ï€ƒ 0.42 or 0.40 'R 1 xZ 1.02
ï€ŽK 0.1 ï€šZ 0.65 e 1.036
ï€ƒ
Each value of ï€” corresponds to the parameterization under each value of ï€Ž R .
Table 3 - Contribution of shocks to Ã¡uctuations (percent)
Productivity Hours Output
Shocksï€ŸSectors R&D C -sector R&D C -sector R&D C -sector
Investment 56 38.4 39.1 31.1 69.9 35.4
(39,69.8) (14.6,60) (19.1,56.9) (11.7,49.4) (53.1,80.1) (12.3,58.5)
R&D 12.8 23 4.4 16.7 19.7 30.2
(6.5,22.5) (9.5,42.8) (1.2,12.1) (7.5,27.4) (11.4,33.8) (15.1,47.9)
C -speciÃ–c 1 12.5 3.2 7.4 1.2 13.7
(0.3,3.2) (5.1,33.9) (0.9,9.2) (2.7,14.7) (0.4,3.1) (7,25.8)
All Technology 74 79 46.1 56.4 92.3 78.5
(56.4,84.3) (58.6,89.8) (27,62.6) (35.5,71) (82.6,96.3) (54.8,89.9)
Table 4 - Contribution of shocks to Ã¡uctuations (percent)
without an R&D sector and shocks
Productivity Hours Output
Investment 39.9 33.3 40.2
(10.5,66.9) (9.9,55.2) (14,66.5)
Neutral 31.1 13 33.3
(12.2,68) (4.7,25.8) (17.9,55.4)
All Techology 85.8 68.8 90.3
(56.5,96) (47.6,84.1) (73.8,97)
47
Table 5 - Forecast error decompositions of the output growth rate (percent)
R&D Output C-sector Output with R&D Output without R&D
Year C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. All Tech.
1 12.8 44.7 18.3 75.8 9.4 11.4 1.2 22 11.7 13.1 24.8
(0.2,36.6) (13.0,58.6) (0.6,46.7) (40.7,88.3) (0.1,41.1) (0.2,31) (0,15.6) (5.1,57.7) (0.1,50.2) (0.3,36.6) (3.5,63.4)
2 1.8 58.3 25.2 85.3 41.5 24.7 14.9 81.1 0.3 22.6 22.9
(0.0,20.9) (19.1,72.9) (2.8,48.5) (47.6,94.6) (5.5,65.1) (0.9,49.0) (0.3,38.2) (32.9,92.4) (0,28.7) (0.5,49.5) (3.4,60.3)
3 0 56.9 34.0 91 51.6 18 29 98.6 11.8 35.7 47.4
(0.0,9) (23.1,73.1) (8.7,55.7) (60.1,97) (21.4,72.0) (0.8,42.2) (5.2,46.8) (70.3,98.5) (0.1,44.5) (2.0,62.4) (9.9,78.3)
6 0.4 61 36.4 97.8 46.5 16.1 36.5 99.1 53.7 25 78.8
(0,5.1) (30.5,76.2) (16.5,59.2) (80.6,99.4) (21.2,73.3) (0.4,42.0) (10.2,55.8) (83.3,99.7) (6.9,74.4) (0.9,53.6) (30.5,89)
12 0 69.3 30.6 100 42.4 22.4 35.2 100 15.6 36.3 51.9
(0,0.9) (43.6,81.5) (17.1,53.7) (96.2,100) (19.2,76.2) (0.6,50.8) (7.8,55.3) (94.2,100) (0.4,73.7) (0.3,58.4) (12.1,87.4)
ï€€ The numbers in parenthesis correspond to bootstrapped 90% conÃ–dence intervals.
48
Table 6 - Forecast error decompositions of hours (percent)
R&D Hours C-sector Hours with R&D Hours without R&D
Year C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. R&D All Tech. Neutral Invest. All Tech.
1 1.5 39.1 0.4 41 6.6 0.1 0.9 7.6 5.8 6.5 12.3
(0,8.7) (22,51.7) (0,6) (26.3,55.5) (0.1,25.7) (0,14.7) (0,16.1) (2.3,35.8) (0.1,22.2) (0.1,23.8) (2,34.5)
2 10.6 33.1 0.8 44.5 1.8 31.1 4.5 37.4 1.4 23.8 25.2
(0.2,34.6) (2.5,59.9) (0.0,19.4) (17.8,71.6) (0,23.3) (0.5,56.6) (0,30.8) (9,72.2) (0,31.1) (0.7,50.8) (4,59)
3 1.8 46.9 0.2 48.9 14.9 28.6 26.8 70.2 12.4 39.0 51.4
(0,20.9) (2.7,71.8) (0,20.9) (14.3,78.5) (0.3,32.7) (0.6,57.5) (0.8,45.6) (20.8,86.3) (0.1,45.2) (1.6,65) (9.2,79.9)
6 6.2 49.6 28.5 84.3 15.1 33.6 41.3 90 54.3 24.7 79
(0,30.4) (0.8,71.9) (0.3,46.1) (18.7,90.6) (0.4,32.4) (1.5,61.2) (7.9,55.6) (40.5,93.1) (4.4,75.4) (0.6,54) (26.2,89.2)
12 1.2 61.2 4.9 67.2 0.3 61 14.1 75.4 9.5 36.3 45.8
(0.1,36.2) (0.7,72.2) (0.2,47) (26.6,90.2) (0,28.4) (1.5,73.4) (0.2,44.5) (27.1,90) (0.4,74.1) (0.2,58.5) (12.3,87.3)
ï€€ The numbers in parenthesis correspond to bootstrapped 90% conÃ–dence intervals.
Table 7 - Contribution of shocks to Ã¡uctuations (percent): alternative measure of labor
Productivity Labor Output
Shocksï€ŸSectors R&D C-sector R&D C-sector R&D C-sector
Investment 59.5 56.5 27.3 17.4 73.5 44.8
(36.9,74) (29.2,73.7) (11.4,51.8) (5.7,39) (55.8,82.8) (22.2,62.2)
R&D 20.2 24.3 7.2 11.3 19.5 18.2
(10.8,35.8) (12.1,41.5) (2.4,17.5) (4.4,22.5) (11.5,31.9) (8.5,30.1)
C -speciÃ–c 1 6.4 4.8 6.7 1.3 6.1
(0.3,3.1) (3.3,12) (1.2,12.5) (2.2,14.9) (0.5,3.2) (2.5,11.8)
All Technology 85.2 88.4 46.7 35.3 94.3 61
(70.2,92.2) (64.3,95.5) (27.9,65.2) (19.7,53.5) (84.2,97.4) (32,80.1)
Table 8 - Contribution of shocks to Ã¡uctuations (percent)
without an R&D sector and shocks: alternative measure of labor
Productivity Labor Output
Investment 26.9 11.9 25.5
(6.2,52.3) (1.8,41.7) (6.3,50.7)
Neutral 57.9 37.8 36.4
(28.7,82.2) (12.9,58.8) (10.9,58)
All Techology 93.3 66 71.7
(71.7,97.8) (40.9,83.6) (43.1,87.1)
49
Table 9 - Forecast error decompositions of the output growth rate (percent): alternative measure of labor
R&D Output C-sector Output with R&D Output without R&D
Year C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. All Tech.
1 20.7 45.1 12.1 77.9 0.9 9.1 2.9 12.9 1.5 5 6.5
(1.2,41.6) (14.8,57.6) (1,27.5) (42.5,85.4) (0,13.6) (0.1,26.9) (0,18.5) (3.7,38.6) (0,18.4) (0.1,25.4) (0.8,32.6)
2 5.8 64.8 16.8 87.5 0.3 12.4 12.6 25.3 63.5 0.1 63.6
(0.1,24.4) (26.7,74.5) (1.8,32.8) (51.5,92.7) (0,16.6) (0.1,42.6) (0.1,41.4) (6.3,61.6) (11.4,85.6) (0,17.5) (16.1,88.9)
3 0.8 68.7 25 94.5 9.8 28.2 0.1 38.1 29.9 1.3 31.2
(0,10.8) (36.4,77.5) (7.1,41.6) (67,96.6) (0.1,29.5) (0.8,57.7) (0,20.3) (11.2,71.2) (0.6,64.8) (0,28.3) (4.1,71.1)
6 0.2 66 33.4 99.6 24.4 45.2 24.1 93.7 0.1 17 17.1
(0,3.4) (38.9,78.4) (17.6,52.6) (87,99.6) (4,42.2) (9,67.2) (1.7,41.6) (43.8,98) (0.1,56.2) (0.1,55.5) (2.6,75)
12 0 69.1 30.8 100 23.9 42.8 33 99.6 13 14.9 27.9
(0,1.1) (38.1,83) (15.5,57.5) (93.9,100) (5.7,41.4) (5.8,68.7) (7.2,53.5) (62.3,99.9) (0.2,72.8) (0.1,53) (3.9,82.5)
ï€€ The numbers in parenthesis correspond to bootstrapped 90% conÃ–dence intervals.
50
Table 10 - Forecast error decompositions of hours (percent): other measure of hours: alternative measure of labor
R&D Hours C-sector Labor with R&D Labor without R&D
Year C -speciÃ–c Invest. R&D All Tech. C -speciÃ–c Invest. R&D All Tech. Neutral Invest. All Tech.
1 1.8 39.8 0.5 42.1 14.8 10.6 18.9 44.3 43.7 0.1 43.7
(0,9.7) (22.1,52.1) (0,6) (26.9,55.9) (1.6,29.8) (0.8,24.8) (3.9,34.4) (22.9,59.3) (23.3,59.1) (0,7) (25,60.3)
2 19.2 10.5 20.4 50.1 4.3 0.1 24.1 28.5 67.8 0.3 68.1
(0.8,39.6) (0.1,40.6) (0.7,44.5) (17.4,78.4) (0,21.9) (0,18.1) (1.7,47.8) (7.1,65.2) (25.1,85.7) (0,12.8) (30.1,88)
3 10.2 9.1 19.8 39.1 1.4 0 18.2 19.6 43.2 0.4 43.6
(0.2,28.4) (0.1,40.7) (0.6,41.4) (11.3,69.6) (0,17) (0,24.4) (0.3,42.9) (5,58.5) (3.3,72.3) (0,21.9) (9.1,76.3)
6 2.6 18.9 8.1 29.6 3.9 32.2 3.5 39.6 0.7 13.5 14.2
(0,25.1) (0.1,65.9) (0.1,44.2) (7.6,79.6) (0,27.3) (0.2,63.9) (0.1,35.5) (7.4,80.4) (0.1,54.9) (0.1,55.3) (2.7,74.4)
12 14.6 32.1 0.6 47.3 10.2 43 0.8 54 18.1 21.8 39.9
(0.1,33.5) (0.2,69.4) (0.1,46.6) (13,86.6) (0.1,32.6) (0.2,68.5) (0.1,47.5) (11.9,86.5) (0.2,73.4) (0.1,54.6) (4.2,82.7)
ï€€ The numbers in parenthesis correspond to bootstrapped 90% conÃ–dence intervals.