Investment-Speci…c Technology Shocks: The Source of
Anticipated TFP Fluctuations
Kaiji Cheny
Edouard Wemyz
February 22, 2014
Abstract
This paper explores the importance of investment-speci…c technology changes in
anticipated TFP ‡uctuations. To this end, we identify two types of news shocks with
the maximum forecast error variance approach: news shocks to TFP and news shocks
to the relative price of investment. We show in a model with IST di¤usion and spillover
that the correlation of these two empirically identi…ed shocks can be used to quantify
the importance of the IST shocks in aggregate TFP ‡uctuations. Using postwar U.S.
data, we …nd that these two news shocks are almost perfectly colinear, if both are
identi…ed to capture the long-run movement of the corresponding variable. Moreover
these two news shocks can explain a signi…cant, and surprisingly similar fraction of
the ‡uctuations in other important macro variables over business cycles.. Our …ndings
suggest that embodied technological changes are the main driver of the anticipated
TFP ‡uctuations via spillover to the productivity of the rest of the economy.
Keywords: Investment-speci…c Technical Change, News Shocks, TFP, Generalpurpose Technology, Spillover.
JEL Codes: E22, E32, O47.
We thank André Kurmann, Christopher Otrok, Michael Owyang, Gian Luca Violante, Jian Wang for
helpful discussion and comments.
y
Emory University, Department of Economics, Atlanta, GA 30322. Email: kaiji.chen@emory.edu.
z
Emory University, Department of Economics, Atlanta, GA 30322. Email: ewemy@emory.edu.
1
1
Introduction
Following Beaudry and Portier (2006), recent empirical studies have emphasized news shocks
to TFP as important driving forces of business cycles. Intuitively, a permanent di¤usion
process of technology that is anticipated by economic actors would lead to anticipated future, but not contemporaneous, TFP increase. Nonetheless, factors other than shocks to
expected future technological changes may also underlie the anticipated future TFP ‡uctuations.1 This raises a critical question: how important are future technological changes for
anticipated TFP ‡uctuations over the U.S. business cycles? Moreover, given the quantitative
importance of future technological innovations, are anticipated TFP ‡uctuations driven by
technological changes embodied or disembodied in equipment?2 An answer to both questions would sharpen our understanding of the role of technological changes in business cycle
‡uctuations.
This paper thus explores the importance of investment-speci…c technology changes (“IST”
henceforth) in anticipated TFP ‡uctuations. To this end, we identify two types of news
shocks with the maximum forecast error variance approach (“MFEV” henceforth): news
shocks to TFP and news shocks on the relative price of investment (“PC” henceforth). We
show in a model with IST di¤usion and spillover that the correlation of these two news
shocks, if identi…ed to best explain the long-run movements of the corresponding variable,
can be fruitfully used to distinguish the quantitative importance of IST shocks in anticipated
TFP ‡uctuations.
Using post-war U.S. data, we …nd that these two identi…ed news shocks are almost
perfectly collinear, if both of them are identi…ed by maximizing the FEV of the corresponding
variable over a …nite, but su¢ ciently long horizon. Moreover, both shocks incur almost
identical impulse responses on various macro variables, and can explain a signi…cant fraction
of the ‡uctuations of consumption, hours worked, and output over business cycles. Our
…ndings suggest that embodied technological changes are the main drivers of the anticipated
TFP ‡uctuations via spillover to the productivity of the rest of the economy.
To explore the source of anticipated TFP ‡uctuations, we …rst map the identi…ed news
1
For example, Chen and Song (2013) show both theoretically and empirically that variations in …nancial
frictions on capital allocation translate into anticipated TFP ‡uctuations. Other shocks that may impact
future, but not immediate, TFP include research and development shocks, investment shocks and reallocative
shocks.
2
Technical changes embodied in equipment have been argued to be the source of the fast U.S. productivity
growth in the late 1990s.
2
shocks under MFEV into the primitive shocks in a model featured by IST di¤usion and
spillover. A novel feature of our model is that the improvement in IST not only increases
the TFP of the capital producing sector, but also the TFP of the consumption sector via
spillover, which captures the idea that investment speci…c technology is general-purposed.3
Moreover, in our model, both aggregate TFP and the relative price of investment can be
a¤ected by temporary disturbances, as well as permanent di¤usion processes in both neutral
and investment-speci…c technologies. Accordingly, these two news shocks would map into a
weighted sum of the permanent shocks to neutral technology and IST, and permanent shocks
to IST, respectively, when they are identi…ed to best explain the long-run movements of TFP
and PC. This renders the correlation of the two empirically identi…ed news shocks a useful
measure of the extent to which IST innovations contribute to aggregate TFP ‡uctuations.
The perfect collinearity of our identi…ed news shocks suggests IST as the main source
of anticipated TFP ‡uctuations. In particular, the impact response of TFP to IST news
shocks is essentially zero. In the long run, by contrast, IST news shocks can explain about
50 percent of TFP ‡uctuations. Similarly, the relative price of investment responds little on
impact to news shocks on TFP, which, nevertheless, account for more than 70 percent of its
‡uctuations in the long run. Also importantly, both news shocks can explain a signi…cant,
and surprisingly similar fraction of the ‡uctuations in other important macro variables over
business cycles. The responses of hours worked, output and investment are all positive
on impact and hump-shaped. Our observed high correlation between the two identi…ed
news shocks are very robust to adding more variables, di¤erent lags, alternative measures of
investment de‡ators and alternative TFP series.
We then go a step further to examine the impact of di¤erent forecast horizons chosen
under MFEV on the correlation between the two identi…ed news shocks. We …nd that given
the zero lower bound for the forecast horizon, the correlation drops monotonically as the
upper bound becomes smaller.4 Behind such a drop in correlation is that the identi…ed news
shock to TFP is sensitive to the forecast horizon chosen under MFEV. On the other hand, if
the lower bound for the forecast horizon is su¢ ciently large, say close to 40 quarters, then the
perfect collinearity between the two identi…ed news shocks is very robust to the upper bound
of the forecast horizon. All these …ndings suggest that the news shock to TFP under MFEV
would truly capture the technical di¤usion process only if it is identi…ed by maximizing FEV
at or around a su¢ ciently long forecast horizon.
3
The spillover e¤ect in our model may correspond to technological spillover or unmeasured complementary
investment in intangible capital to accomodate the use of information-intensive equipment and software.
4
For example, the correlation between the two news shocks becomes 0.45 if the upper bound is chosen to
be 40 quarters.
3
Our paper contributes to the VAR-based literature on news shocks in several dimensions.
First, we are the …rst to uncover the source of anticipated TFP ‡uctuations. Despite the
di¤erence in identi…cation strategies, most studies in this literature implicitly identify the
news shocks on TFP to the news shocks on future neutral technology.5 Recent studies on
news shocks to TFP have incorporated shocks to the relative price of investment into SVAR,
but assuming that the shocks to the relative price of investment and the shocks to TFP
are orthogonal to each other.6 We construct a model of IST di¤usion and spillover to show
that IST changes may underlie the long-run ‡uctuations of both TFP and the relative price
of investment. And our empirical …ndings of the perfect collinearity of two identi…ed news
shocks suggest that IST shocks are the main drivers of anticipated TFP ‡uctuations in the
long run and the main driver of business cycle ‡uctuations.
Second, our …ndings shed light on the caveat in choosing the lower and upper bound
of forecast horizon under MFEV to identify the TFP news shocks. Our …ndings suggest
that given the zero lower bound, a su¢ ciently large upper bound is needed to identify
news shocks on TFP that truly capture the di¤usion process of technology. By contrast,
the identi…ed TFP news shocks may well capture the di¤usion process of technology when
maximizing MFEV at a …nite but long horizon. Our …ndings therefore echoes those in
Beaudry, Nam and Wang (2011), which …nd that the TFP news shocks identi…ed under
MFEV are highly correlated with the optimism shocks identi…ed under sign restriction, and
such high correlation is robust if the forecast error variances of TFP is maximized at some
…nite long horizon or if the upper bound is large enough.
The …ndings of our paper contribute to the understanding of the role of IST shocks in
business cycles. Fisher (2006) argues that permanent IST shocks are the main sources of
business cycles. More recently, Jaimovich and Rebelo (2009) and Schmitt-Grohé and Uribe
(2012) argues for the importance of IST news shocks in business cycles. Our …ndings not only
provide additional support for the quantitative importance of IST shocks, but also suggest
that such permanent changes in IST is largely anticipated by economic actors and enhance
aggregate productivity with a delay. The mechanism for IST shocks to impact the economy, as our empirical …ndings suggest, may well be di¤erent from the conventional channel
5
See for example, Beaudry and Portier (2006) and Barsky and Sims (2011).
In their identi…cation scheme 2 (ID2), Beaudry and Lucke (2010) assume that shocks to the relative
price of investment have no permanent impact on TFP. Under this assumption, shocks to the relative price
of investment is better interpreted as other shocks to the price of investment (such as relative markup or
input cost shocks to investment) than IST. Fisher (2010) adopts a similar identi…cation strategy and …nds
that news shocks and IST shocks are equally important in explaining the business cycles.
6
4
however.7 The …nding that future IST innovations are the main drivers of anticipated TFP
‡uctuations suggests that one potentially important channel for IST news shocks to drive
business cycles may be through in‡uencing economic agents’expectation of future productivity ‡uctuations. Thus our …ndings call for additional theoretical work to understand the
role of IST news shocks in business cycles.
In addition, our empirical …ndings provide additional support for the role of investmentspeci…c technical changes in aggregate productivity growth. It has been long argued that
investment-speci…c technical changes are important sources of productivity growth in the
U.S. Using industry-level data, Cummins and Violante (2002) and Basu, Fernald and Oulton
(2004) have found that improvements in IST, such as information communication technology,
contributed to productivity growth in the 1990s in essentially every industry. Accordingly,
they argue that investment-speci…c technical changes represent a general-purpose technology.
Moreover, Jorgenson, Ho, Samuels, and Stiroh (2007) show that much of the total factor
productivity gain in the 2000s originated in the industries that are the most intensive users
of information technology. Our …ndings support the quantitative importance of permanent
IST innovations for the aggregate productive e¢ ciency via in‡uencing the TFP of the rest
of economy, and, thus, strengthen the view of IST technology as general purpose technology.
The remaining sections are structured as follows. In section II, we present our empirical
strategy. In section III, we provide a model with IST di¤usion and spillover and show how the
news shocks identi…ed in our VAR map into the primitive shocks. In section IV, we present
the data and discuss the speci…cation of VAR. In Section V, we provide our empirical results
estimated with postwar U.S. data. Section VI concludes.
2
Empirical Approach
In this section, we identify two types of news shocks: a news shock about future innovations
to TFP (TFP news shock) and a news shock about future innovations to the relative price of
investment. Our identi…cation scheme is fairly standard: we adopt a variant of Uhlig (2003)
approach to extract the shock that explains the maximum amount of the FEV, over a given
horizon, for a given target variable i, where i is either TFP or the relative price of investment
(“PC” henceforth): This approach is applied by Barsky and Sims (2011) to identify news
shocks to TFP. In a similar spirit, we identify a news shock that (in a statistical sense) best
7
In conventional RBC models (e.g. Greenwood, Hercowitz and Krusell,1997 and Fisher, 2006), IST shocks
directly impact the e¢ ciency of investment good production, and the shocks are ampli…ed by hours worked
and capital utilization.
5
explains future movements in the relative price of investment goods and is orthogonal to
contemporaneous movements in the price of investment only. TFP news shock is identi…ed
in a similar fashion but with TFP being the target variable. Di¤erent from Ben Zeev and
Khan (2013), which identify IST news shocks by imposing zero restriction on both TFP and
PC, we only impose one zero restriction, that is, the restriction on either TFP or PC.8
A possible economic interpretation of this shock is the news shock on investment-speci…c
technology (“IST news shocks” henceforth). At this stage, however, we are agnostic about
the structural interpretation of our identi…ed news shocks. In the next section, we provide
a model of IST spillover to o¤er a structural interpretation of the news shocks identi…ed in
this section. We show that the impact response of TFP (PC) to our identi…ed news shocks
on PC (TFP), as well as the correlation of these two news shocks identi…ed in this section,
can uncover the source of anticipated TFP ‡uctuations, which is the focus of the paper.
We start by assuming that we already have the reduced form moving average (Wold)
representation for the VAR system in level:
Yt = C (L) ut ;
where Yt is a m 1 vector of variables at time t, C (L) = I +
lag operator L; and u is a m
matrix given by
P1
i=1
Ci Li is a polynomial in the
1 vector of reduced form innovations with variance-covariance
:
Assume that there exists a linear mapping between reduced-form and structural shocks
ut = A"t
= E [A"t "0t A0 ] = AA0 : This restriction is not
The key restriction on A is that it satis…es
su¢ cient to identify A, because for any matrix A, there exists an alternative matrix A~ such
~ where Q is an orthonormal matrix. This alternative matrix A
e maps ut into
that A = AQ;
~"t : Hence for some arbitrary matrix
another mutually orthogonal structural shock e
"t , ut = Ae
A~ satisfying A~A~0 = , identi…cation amounts to choosing an orthonormal matrix Q.
Assuming that there exists a shock that does not have an immediate impact on variable
yi , but becomes an important factor in yi over the horizon k; k ; then we can identify such
shocks by …nding column q1 of Q that explains most of the FEV of variable yi in Yt over
forecast horizon k = k to k: Speci…cally, we solve the following maximizing problem, given
8
Our results below are robust to the ideniti…cation of news shocks using two zero restrictions.
6
the Cholesky decomposition of
~
; A:
q1 = argmax
k X
k
X
q10 Sq1
q10 [
~ 1
A~0 Cl0 (ei e0i )Cl A]q
(1)
k=k l=0
subject to
q10 q1 = 1
(1)
q1
= 0
(2)
(3)
where S is the sum, over forecast horizon k = k to k; of the contribution of the k-step ahead
forecast error of the ith variable to the variance of Yt . The …rst constraint guarantees that
q1 is a unit-length column vector that belongs to an orthonormal matrix while the second
restriction imposes that the news shock has no contemporaneous e¤ect on the level of TFP
or PC. Uhlig (2003) shows that this problem can be written as a quadratic form in which
the non-zero portion of q1 is the eigenvector associated with the largest eigenvalue of the
(m
1) submatrix of S.
(m
1)
3
Theories with IST Shocks and TFP
We would like to map the identi…ed news shocks to the primitive shocks. To this end, we
now present a business-cycle model which incorporates investment-speci…c technology (“IST”
hereafter) shocks. This model nests di¤erent assumptions concerning the stationarity of the
IST process, and more importantly, the e¤ect of IST on the productivity of the rest of the
economy. We would like to explore the quantitative importance of IST shocks to aggregate
TFP ‡uctuations under these di¤erent assumptions.
The model is a standard two-sector neoclassical model with perfect competition and
common factor shares among the two sectors. One sector produces consumption goods, C,
the other sector investment goods, I: Both sectors produce output by combining capital K
and labor L with the same function F; but separate Hicks-neutral TFP parameters, T F P C
and T F P I . In particular, consider the following social planner’s problem, where utility is
7
logarithm.
max E0
1
X
t
[log Ct
v (Lt )]
t=0
Ct = T F PtC F KtC ; LC
t
It = T F PtI F KtI ; LIt
Kt+1 = (1
) Kt + It
Kt = KtC + KtI
I
Lt = LC
t + Lt
Following Greenwood, Hercowitz and Krusell (1997) (“GHK” henceforth), we de…ne
T F P I =T F P C ; where
is investment-speci…c technology, or so-called embodied technology.
Implicitly, T F P C represents productivity applied to both sectors, while
only applies to
the investment-goods producing sector.
As discussed by Guerrieri, Henderson, and Kim (2010), several assumptions underlying
the above standard two-sector model allow the TFP shock speci…c to capital production
sector,
; to generate equivalent responses of aggregate variables as an IST shock to capital
investment in a one-sector model. These conditions include, …rst, there are no cost adapting
capital used in one sector for use in the other; second, the two sectorial production functions are identical up to a productive factor; …nally, both depreciation rates and investment
adjustment cost functions are the same between the two sectors for capital.9
Thanks to the assumption of perfect competition and common factor shares, this twosector growth model can be decentralized into a two-sector market economy.10 Using consumption goods as the numeraire, the aggregate value-added is de…ned as the sum of consumption and the e¢ cient units of investment.
Yt = Ct + It PtI =PtC
T F Pt F (Kt ; Lt )
It is easy to show that, under the assumption of competitive markets and common factor
9
Moreover, the two-sector model features complete specialization. This allows the MFP shocks to the
capital producing sector to be equivalent to IST shocks to equipment capital.
10
To derive stock prices, consider an isomorphic Lucas-tree economy. In this economy, the representative
household holds shares of a representative …rm, which produces …nal output with productivity T F P C ; and
decides dividend and investment. Investment becomes installed capital under investment-speci…c technical
innovations. The value of …rms (the stock market value) in this economy is the discounted sum of future
pro…ts.
8
shares in production, changes in relative TFP equals changes in relative prices
log T F P I
log T F P C =
log P C
log P I
Also, in this economy changes in investment-speci…c technology equals changes in the relative
TFP of the investment sector. Thus, there is a one-to-one mapping between changes in IST
and changes in the relative price of consumption.
log
=
log T F P I =T F P C =
log P C =P I
(4)
More generally, however, various wedges exist in the above equality. Speci…cally, wedges
between the relative TFP and the relative price include, for example, changes in the relative
markup of the two sectors, changes in the relative capital intensity of the two sectors (say, due
to variations in sector-speci…c factor prices or adjustment cost) and di¤erent factor shares.11
Also, factors driving a wedge between TFP growth and technical changes include returns to
scale, markup, capital utilization and reallocation e¤ect.12
Therefore, we also consider an alternative speci…cation for the changes in the relative
price in a generalized version of the decentralized economy.
log P C =P I =
We assume that ! t is stationary, ! t =
!
!t
1
log
+
t;
(5)
+ !t
t
N (0;
2
). Our argument is that
these factors mentioned above hardly a¤ect the relationship between the relative TFP and
the relative price of investment in the long run. As found by Basu, Fernald, Fisher, and
Kimball (2010) (“BFFK” henceforth), relative prices and relative TFP track each other
fairly well over long periods of time, though these two series can diverge in the short and
medium run.
Consistent with (5), we follow the strategy of Fisher (2006) to identify the investmentspeci…c technology shock as the shock that has a long-run impact on the relative price of
investment in our VAR exercise below. We fully realize that the relative price of investment
in the short and medium run can be a¤ected by other factors. Hence, we would like our
identi…ed IST news shocks to explain the ‡uctuations of the relative price of investment over
the long run.
11
See Justiano, Primiceri and Tambalotti (2011) and Basu, Fernald, Fisher, and Kimball (2010) for a
discussion.
12
See Basu, Fernald and Kimball (2006) for a discussion.
9
We now decompose the dynamics of aggregate TFP. With common factor shares, the
capital-labor ratios in the two sectors are the same. Accordingly, the changes in aggregate
TFP can be decomposed into the sum of changes in sector-speci…c TFP
log T F P = wI
where wI
I
C
P I= P Y
the de…nition of
log T F P I + 1
wI
log T F P C
is the share of investment goods in aggregate value added: Given
; ‡uctuations in aggregate TFP can be rewritten as
log T F P =
According to (6) ; shocks to
log T F P C + wI
log
(6)
may in‡uence the ‡uctuations of aggregate TFP via two
channels: First, the direct e¤ect, which is captured by the second argument; second, indirect
e¤ects: improvement in
may lead to improvement in productivity that is applied to all
sectors, T F P C : Such an indirect e¤ect was emphasized by the literature on IST as general
purpose technology, and was found to be empirically important using either industry or …rmlevel data.13 One focus of this paper is to quantify the contribution of IST improvements
on anticipated aggregate TFP ‡uctuations and the relative importance of each of the two
channels.
The above general setup of the model nests several speci…c cases argued in the literature
about the process of the IST shocks and its role in aggregate TFP ‡uctuations. As will be
shown below, these various cases di¤er in the assumptions regarding the speci…cations of
t
and T F PtC : We now provide a speci…cation general enough to nest all these di¤erent cases.
3.1
IST Di¤usion and Spillover
Let us now consider a speci…cation where innovations to IST include a di¤usion process,
which does not immediately increase productivity. To compare, we also allow the neutral
technology to follow a di¤usion process. In addition to IST news shocks, we allow the
stationary disturbance to in‡uence the relative prices as well.
13
For example, Cummins and Violante (2002) argue that technological improvement in equipment and
software initiated in the 1970s and 1980s brought about acceleration in productivity growth in every industry
in the 1990s, consistent with the idea that information technology represents a general-purpose technology.
Basu, Fernald, Oulton (2004) constructs a model where improvement in ICT technology in‡uences aggregate
TFP through both spillovers and complementary investment in organizational capital.
10
Speci…cally, the data-generating process for the two types of technology is as follows
log
t
=
1
X
dI;I
i
I
1;t i
I
t
+
(7)
i=0
log T F PtC
=
1
X
N
dN
i 1;t i
N
t
+
1
X
+
J
t
I
1
where
N (0;
2
I) ;
N
1
=
N (0;
I
1;t i
(8)
i=0
i=0
dJi = 1
dIi
(
i
J;K )
J J
t 1
I
t
2
N) :
;0
J
2;t ;
+
and
N
t
J;K
0
J
< 1; J = I or N
< 1; J = I or N
capture unanticipated shocks to investment-
speci…c and neutral technology. By construction, all structural shocks are orthogonal to each
other.14
Following Beaudry and Portier (2006), the process Dt =
1
X
dIi
I
1;t i
is called a di¤usion
i=1
process since an innovation,
I
1;
is restricted to have no immediate impact on T F P C ; dI0 = 0:
The e¤ect of the technological innovation on productivity is assumed to grow over time
dIi+1 , and the long-run e¤ect is normalized to 1. The investment-speci…c technology
dIi
also includes a stationary process
I
t:
Moreover, shocks to IST,
I
2;t ;
are unanticipated and
in‡uence the IST on impact.
T F PtC includes three components. The …rst is a non-stationary process to neutral technology. The second, a stationary component,
N
t
can be thought of as a temporary shock to
T F PtC (e.g. technological, policy, or …nancial shocks). The third component is novel, and it
captures the spillover e¤ects of IST shocks, which magnitude is governed by the parameter
: In standard RBC models (e.g. Greenwood, Hercowitz, Krusell, 1997),
if IST is a general-purpose technology,
= 0: By, contrast,
can be sizable. The spillover e¤ect,
; in reality
captures not only the technological spillover, but also managerial innovations (intangible
capital) accompanied by an introduction of information-communication technology (ICT)
capital, which has been found to be important for the U.S. productivity growth during the
late 1990s.15 In general, the di¤usion speed for the two types of technology can be di¤erent,
i.e.,
14
I
6=
N:
The assumption that I1 is orthogonal to N
1 is consistent with the empirical …ndings of BFFK that
the correlation between the consumption sector technology shocks and the relative equipement-investmentconsumption technology shock is close to zero, using BFK approach to measure technology series for each
sector.
15
See Bau, Fernald, and Oulton (2004).
11
Plugging (7) and (8) into (6) ; we can rewrite aggregate TFP as
1
X
log T F Pt =
N
dN
i 1;t i
+
i=1
where
1
X
dIi
I
1;t i
+
(9)
t;
i=1
+wI captures the overall e¤ects of IST shocks on TFP:
wI
t
I
N
t+ t
captures
the transitory component to aggregate TFP. Note that this speci…cation nests the process
of log T F P as Beaudry and Portier (2006) if we assume that there is a single new shock on
TFP, driven by innovations in neutral technology, and a single transitory shock.16
log T F P =
1
X
di
1;t i
+
t
i=1
Now, we would like to explore the contribution of the IST shocks to TFP and the relative
price of investment in our model at di¤erent horizons. Equation (9) implies that the contribution of IST shocks,
I
1;
to the ‡uctuations of aggregate TFP hinges on the magnitude
of ; which further depends on the spillover e¤ects of IST. The larger is the spillover e¤ect,
I
1
the larger is the contribution of
to TFP ‡uctuations, governed by . However, under the
standard RBC models ( = 0), the contribution is arguably small, due to the small share of
investment in GDP in the data. Formally, the contribution of IST news shocks to TFP can
be measured by the share of forecast error variance (“FEV” hereafter) of TFP attributable
to IST shocks,
I
1;
k quarter ahead.
F EV (
=
2 2
I
1
8
>
>
>
<
>
>
>
:
I
1;t ; T F P )
2
I)
(1
2 2
I
1
+
2
N
1
(1
(1
+
(10)
2 h 1
I
1
2
I)
1
2
N)
1
N 2(h 1)
2
N
2
= 1
2 h 1
I
2 h 1
N
+
2
I
= 1
2
I
= 1
2
N
I 2(h 1)
2
I
2
=
9
>
>
>
=
>
>
>
;
where the numerator on the right-hand side of (10) is the contribution of
I
1;t
to the FEV of
TFP k periods ahead. The denominator is the corresponding overall FEV of TFP, which is
16
In Beaudry and Portier (2006), there is no explicit distinction between neutral and investment-speci…c
technology. Aggregate TFP is driven by only one type of technology, which is composed of two components:
one is the di¤usion process, the other is the AR(1) process.
12
I
1;
the sum of the contribution of the three shocks,
N
1
N
2 .
and
Obviously, the magnitude of
the contribution of IST to the FEV of TFP depends on the di¤usion speed of the IST shocks
2 2
and the forecast horizon. Nonetheless, the larger is,
I
1
variance of TFP attributable to
I
1t
=
2
N
1t
; the larger is the forecast error
in all horizons except for the impact period. Intuitively,
the quantitative importance of the IST shocks to overall TFP ‡uctuations depends on both
the internal propagation of the shock, captured by
shock, captured by
2
2
I= N:
, and the relative magnitude of the
If we further assume the di¤usion speeds for the two types of
technological innovations to be the same, and allow k ! 1; the above expression becomes
F EV (
I
1;t ; T F P )
1
=
2
1+
N
1
(11)
2 2
=
I
1
Similarly, we can derive the FEV of the price of investment attributable to IST news
shocks k steps ahead. Combining equation (5) with (7), we can obtain the price of investment
as follows
log P C =
1
X
dIi
I
1;t i
I
t
+
+ !t
i=0
I
1;
The share of forecast error variance of PC attributable to IST shocks,
F EV (
2
=
I
1
8
<
As k ! 1; F EV (
:
I
1;t ; P C)
I
1;t ; P C)
2
I)
(1
2
I
1
(1
+
(12)
2 h 1
I
1
2
I)
1
I 2(h 1)
2
h quarter ahead is
I
2
= 1
2 h 1
I
+
2
(
2
I
= 1
! 2(h 1)
)
=
2
I
9
=
;
:
! 1. Hence, according to equation (11) and (12) the same shock
would maximize the FEV of both TFP and PC in the long run, if the spillover of IST is
su¢ ciently large. This suggests a method to test the magnitude of the spillover e¤ects of
IST, by comparing the correlation of the news shocks to TFP and PC identi…ed under the
MFEV approach with a su¢ ciently long forecast horizon.
We now derive analytically the correlation of the two identi…ed news shocks to shed light
on the link between such a correlation and the relative magnitude of IST news shocks. We
…rst establish the mapping in our model between the structural shocks ( ) and the identi…ed
13
news shocks (") under the MFEV approach. According to our model, the shocks maximizing
the FEV of PC at k = k ! 1 (with zero impact e¤ect) simply maps into the IST shocks.
~"Pt C =
I
1t
(13)
Note that (13) implies that investment-speci…c technological change is the unique source of
the secular trend in the real price of investment, which is consistent with Fisher (2006). On
the other hand, by maximizing the FEV of TFP at k = k ! 1, the identi…ed news shocks
is
~"Tt F P =
I
1t
N
1t
+
That is, the shock that explains the long run ‡uctuations of T F P maps into a linear combination of the two anticipated technological innovations. The correlation coe¢ cient between
the two identi…ed news shocks can therefore be expressed as follows
~"P1tC ; ~"T1tF P
=
cov ~"P1tC ; ~"Tt F P
FP
~
"T
1t
C
~
"P
1t
2
= q
I
1t
2
N
1t
= r
1+
Intuitively, the higher is
2 2
I
1t
=
2
N
1t
, the closer is
2 2
+
I
1t
1
2
N
1t
=
q
2
I
1t
(14)
2 2
I
1t
to 1. More generally, if IST news shocks
are important sources of TFP ‡uctuations in the long run, we should also observe that the
correlation of the identi…ed news shocks to TFP and PC tend to increase with the forecast
horizon chosen under MFEV approach. Equation (14) is the ‡ip side of (11), because as time
goes to in…nity, the contribution of the transitory shocks to FEV of TFP becomes essentially
zero and the contribution of IST to PC is essentially 1.
In summary, we provide a model of IST di¤usion and spillover to o¤er a structural interpretation of the news shocks to PC and TFP identi…ed under the MFEV approach. Based on
the model, we show that the correlation of these two news shocks identi…ed by maximizing
the FEV over a su¢ ciently long horizon sheds light on the quantitative importance of IST
shocks to (anticipated) TFP ‡uctuations.
14
4
Data and Speci…cation Issues
Our empirical exercise uses U.S. data over the period 1961-Q3 to 2008-Q4. The two key series
in our VAR exercise are the price of consumption relative to investment goods, and a measure
of total factor productivity (TFP). To measure the importance of news shocks to macro
variables, we also include consumption, hours worked, output and investment in our baseline
VAR model. Later, we will consider alternative VAR systems for robustness check that
includes a measure of total factor productivity for consumption sector, and larger systems
that also include an index of stock market value (SP), an index on consumer con…dence,
federal funds rate and in‡ation in CPI index. Therefore, we also present the source of these
data.
The inverse of the relative price of investment corresponds to the ratio of the chain
weighted de‡ators for consumption and investment, which is taken from Justiniano, Primiceri and Tambalotti (2011). The denominator is National Income and Product Accounts
(NIPA) de‡ators for durable consumption and private investment. However, Gordon (1990)
and Cummins and Violante (2002) have argued that NIPA’s quality adjustments may underestimate the rate of technological progress in areas such as equipment and software, an
issue that can distort the measured contribution of IST changes to both growth and business
cycles. Consequently, Gordon constructed the alternative price series for producer durable
equipment, which is later updated by Cummins and Violante (GCV de‡ator hereafter).
For our baseline model, we work with the NIPA de‡ators; nonetheless, we also check the
robustness of our results to the use of the GCV de‡ator.17
Both the aggregate and consumption-sector TFP series are taken from Fernald (2009),
measured as business sector TFP and TFP in non-equipment business output, respectively,
updated on John Fernald’s webpage. We would like our TFP series to proxy for technological
changes. Therefore, the TFP series we adopt are those corrected for capital utilization. Our
results below are robust to the choice of TFP series unadjusted for capital utilization.
The consumption measure (C) is the per capita value of real personal consumption of
nondurable goods and services. Investment measure (I) is the per capita value of the sum
of real personal consumption of durable goods and real …xed private domestic investment.
Hours (H) is per capita hours worked in nonfarm business sector, taken from Francis Ramey’s
webpage. Output (Y ) is GDP per capita. We use the corresponding chain-weighted de‡ators
to obtain the real series. All per capita series are obtained by dividing the corresponding ag17
We thank Patrik Higgins from Federal Bank of Atlanta for sharing us the updated series of GCV de‡ators.
15
gregate variables by the civilian non-institutional population age 16 above, which is obtained
from the Bureau of Labor Statistics.
The measure of stock prices is the per capita real S&P 500 index. The S&P 500 composite
index is taken from Robert Shiller’s website. The price de‡ator is the price index for gross
value added in the non-farm business sector, taken from the Bureau of Economic Analysis
(Table 1.3.4). The stock index is converted to a quarterly frequency by taking the average
of monthly stock index over each quarter. The data for consumer con…dence index, federal
funds rate, and CPI index are from Beaudry, Nam and Wang (2011).
4.1
Speci…cation
We estimate Vector Auto-regressions (VARs) in levels of all variables. In addition, according
to standard likelihood methods, four or …ve appears to be the optimal lag order when testing
in an ascendant way for the optimal number of lags from 2 quarters up to three years. We
choose to work with four lags in our baseline model; however, all the results are robust to
adopting a …ve-lag speci…cation. We compute the error band with residual-based bootstrap
as in Kilian (1998). To compare with the results in the literature, in our baseline speci…cation,
we let the lower bound, k; of forecast horizon in (1) to be zero and vary the upper bound of
forecast horizon, k. We also consider alternative MFEV approach under which we equalize
the lower and upper bound of forecast horizon, i.e. k = k = k:
5
Results
In this section, we …rst report the results under the baseline speci…cation. Then, we explore
the correlation of identi…ed news shocks to TFP and PC under the alternative MFEVs.
Finally, we extend our results to larger systems with additional forward-looking and nominal
variables.
5.1
Baseline Speci…cation
We extract the shock that maximizes the FEV of the price of investment over some forecast
horizon. In our baseline estimation, we set the forecast horizon to 0
k
120 quarters.
Our choice is motivated by the fact that, in our model, the price of investment is mostly
driven by IST in the long run. Later, we will vary the forecast horizon to be equal to 40, 60
and 80 to explore how the correlation of the two identi…ed news shocks and their impact on
macro variables change.
16
Figure 1 displays the impulse responses of the variables in our benchmark model to news
shocks to PC (solid line), with 16 to 84 percent posterior coverage intervals shaded in gray.
To compare, we also plot their counterparts to news shocks to TFP (dash line). What is
striking is that the responses of all variables to the two news shocks are surprisingly close to
each other. Speci…cally, under both news shocks, the response of the inverse of the relative
price of investment (the relative price of consumption) is essentially zero on impact. After
that, the relative price of consumption rises gradually, peaks at 25 quarters at 0.7% higher
than its pre-shock value. Turning to TFP, we see that the initial response of TFP to both
shocks is negative until about ten quarters. But since then, news shocks on PC seems to have
a permanent e¤ect on TFP. This is puzzling from the standard real business cycle theory,
but is consistent with the model of IST spillover as described above. In particular, under
news shock to PC, the insigni…cant reaction of TFP on impact and its gradual increase to a
permanently higher level suggests that the news shocks to PC captures a slow, permanent
di¤usion process of general-purposed technology that is anticipated by economic actors.
In terms of the macro variables, we see that the response of all macro variables to these two
news shock are hump-shaped and peaks before TFP starts to rise above zero. In particular,
consumption increases signi…cantly on impact, while hours worked, GDP and investment
barely changes on impact. Note that, however, all variables respond positively on impact
to both types of news shocks. This is di¤erent from the …nding of Barsky and Sims (2011),
who argue that news shock has a negative impact on hours worked, GDP and investment.
Finally, apart from hours worked which converges to the initial level after the peak, all other
variables converge to a new long-run level. This is consistent with our model’s prediction
that the news shocks to embodied technology has permanent e¤ects.
The similarity between the e¤ects of the two types of news shocks and their quantitative
importance is further con…rmed by the inspection of the forecast error variance decomposition
shown in Figure 2. We see that the share of the FEV of both the relative price of investment
and TFP attributable to these two shocks are quantitatively similar. Speci…cally, on impact,
both identi…ed news shocks explain little of the variations in the relative price of investment:
Over time, however, the FEV of PC attributable to news shocks to either PC or TFP
increases monotonically. In particular, news shocks to TFP alone explains more than 70
percent of the ‡uctuations in the price of investment 80 quarters ahead. Meanwhile, both
shocks can explain only a small fraction of the FEV of TFP at horizons of 16 quarters or
less, but more than 50 percent of TFP ‡uctuations in the long run.
Turning to the macro variables, news shocks can account for about sixty percent of the
17
FEV of consumption at business cycle frequencies. More importantly, both news shocks are
important for hours and output ‡uctuations over business cycle frequencies, explaining about
40 percent of their FEVs eight quarters ahead. On the other hand, the contribution of news
shock to TFP and PC to investment increases steadily in forecast horizons. This suggests
that, over business cycles, other shocks, such as …nancial shocks, might play an important
role in investment ‡uctuations. Over the long run, however, technology improvements start
to play an important role in investment movements. Table 1 summarizes the FEV coe¢ cients
attributable to news shocks on PC at di¤erent time horizons.
Figure 3 plots the time series of the identi…ed news shock to TFP and PC, with the
shaded areas representing NBER-dated recession periods. As we can see, both shocks are
counter-cyclical and track each other fairly closely. Moreover, the magnitude of both shocks
are very similar. This further supports the quasi-identity of the two identi…ed news shocks.
To summarize, our …nding suggests that anticipated embodied technology progress is the
main driver of business cycles. Moreover, it is quantitatively important for aggregate TFP
‡uctuations in the medium and long run.
5.2
Alternative Forecast Horizons under MFEV
Our benchmark speci…cation identi…es the news shock to PC or TFP by maximizing the
FEV over the forecast horizon 0
k
120. According to our theoretical model, the longer
is the forecast horizon k; the larger is the contribution of IST shocks to both PC and TFP,
given that either TFP or PC is a¤ected by temporary disturbances as well. Therefore, in
this section we would like to examine how sensitive the high correlation of the two identi…ed
news shocks is to the forecast horizon. We …rst examine the results when news shocks are
identi…ed as shocks that maximize the FEV of a particular variable under 0 k 40. This
range of forecast horizon is commonly adopted by the literature (See Barsky and Sims, 2011
and Otrok and Kurmann, 2013).
It is interesting to see that the impulse response of various variables to the two identi…ed
news shock are drastically di¤erent under this alternative forecast horizon (Figure 4). The
impulse response of TFP to news shock on TFP is positive throughout business cycles.
Speci…cally, TFP rises rapidly in response to TFP news shocks, reaching a peak of slightly
more than 0.2 percent …ve years subsequent to the shocks. By contrast, the initial response
of TFP to news shocks to PC is negative, and only becomes positive after about 10 quarters.
Accordingly, the peak of TFP under news shocks to PC is much later, around 10 years.
Also, consistent with the …ndings of Barsky and Sims (2011), the initial responses of hours
18
worked and output to news shocks on TFP is negative, and only start to increase after
TFP increases. By contrast, the responses of hours worked, output and investment to the
identi…ed news shock to PC are similar to the baseline case when k = 120.
Turning to the FEV of various variables to the two news shocks, we see, in Figure 5,
that news shock to TFP explains less than 25 percent of the ‡uctuations of the price of
investment throughout the forecast horizons. Similarly, news shock to TFP explains about
25 percent of TFP ‡uctuations 16 quarters ahead and about 40 percent of TFP ‡uctuations
10 years ahead, a result reminiscent of the …ndings of Barsky and Sims (2011). Interestingly,
the FEV of TFP attributable to these two news shocks are very close to each other beyond
10 years. Also, the FEV of consumption, output, and in particular, hours worked explained
by news shocks to TFP is much lower than the news shocks to PC.
Table 2 summarizes the correlation of the two identi…ed news shocks under di¤erent
upper bounds of forecast horizon, given the zero lower bound. It is interesting to see that
the correlation increases with the upper bound, k. This suggests that our identi…ed news
shocks might capture shocks other than technological innovations, for example, …nancial
shocks, if the upper bound of the forecast horizon over which the FEV of TFP is maximized
is too small.
Which of our two identi…ed news shocks is more sensitive to the choice of the upper
bound of the forecast horizon? Figure 6 compares the IRFs to news shock to PC under
k = 40 and 120. We see that the IRFs for each variable are fairly close. If any, the identi…ed
news shock under k = 120 is quantitatively more important for all variables in the long run.
The correlation coe¢ cient of the identi…ed news shocks to PC under these two scenarios is
0.9479. By contrast, the correlation coe¢ cient of the news shock to TFP is sensitive to the
choice of the upper bound: the correlation coe¢ cient for TFP news shocks identi…ed under
k = 40 and 120 is only 0.6597. This is intuitive, since over a short horizon, shocks other
than technological changes may underlie the identi…ed news shock to TFP.
Alternatively, we can identify the news shocks to TFP and PC by maximizing the FEV
of the corresponding variables at a …nite, but long horizon. The results are reported in
Table 3. Interestingly, under this alternative MFEV approach, the correlation coe¢ cient
of the two identi…ed news shocks is robust to the choice of forecast horizon. For example,
at k = k = 40; the correlation coe¢ cient of the two identi…ed news shocks is 0.96. The
potential reason behind this robustness, in contrast to the case with 0
k
40; is that
by increasing the lower bound of the forecast horizon, those short-run disturbances to TFP
are more likely to be insulated from the identi…ed TFP news shocks. This makes TFP news
19
shocks capture more precisely shocks that drive the long-run movement of TFP.18 Therefore,
if IST shocks are the main source of anticipated TFP ‡uctuations, it will show up as a high
correlation of the two identi…ed news shocks.
Finally, we ask the follow question: given k = 40; what’s the smallest value for the lower
bound, k; needed to obtain a correlation coe¢ cient of the two news shocks close to 0.8.
We …nd that with k = 35, the correlation is 0.7965.19 According to our model, this would
imply that it takes at least nine to ten years for IST to di¤use to the aggregate economy,
a period in line with the empirical evidence regarding the spillover of IST. For example,
using industry level data, Basu and Fernald (2006) …nd that ICT capital investments in the
late 1980s are positively correlated with the ICT using industries’TFP acceleration in the
late 1990s. Similarly, ICT using industries’ TFP accelerations in the 2000s are positively
correlated with industry ICT capital growth in the 1990s. Cummins and Violante (2002)
…nd that in most asset categories outside of information processing equipment and software
(IPES) productivity growth accelerated only in the 1990s, despite the productivity growth
acceleration of IPES capital since 1970s.
Our …ndings regarding the robustness of the correlation coe¢ cient of two news shocks
to various forecast horizon echo the recent …ndings by Beaudry, Nam and Wang (2011).
They …nd that under the method of Barsky and Sims (2011), the correlation between the
identify TFP news shock and the optimism shock deteriorates as the forecast horizon becomes
shorter. By contrast, if the MFEV method proposed by Francis et. al (2012) is used, then
the identi…ed TFP news shock and the optimism shock are highly correlated, regardless of
the forecast horizon used.
5.3
Large VAR Systems
We next identify the two news shocks in larger VAR systems. We …rst add a measure of
stock prices, and consumer con…dence sequentially into the baseline VAR speci…cation. It has
been argued that both stock prices and consumer con…dence are forward looking. Therefore,
including these additional variables in the system will help to identify the news shocks.
Figure 7 reports the impulse responses to the two news shock in the system with stock
price, which, again, are found to be very close to each other. The correlation coe¢ cient are
reports in Table 4, is 0.94. Also, stock price responds positively to news shocks, consistent
18
We …nd that when k = 40 the correlation coe¢ cient is very robust to the choice of upper bound and
remains to be above 0.95. For example, at k = 120; the correlation coe¢ cient is 0.9887.
19
When k = 30; the correlation coe¢ cient of the two identi…ed news shock drops to 0.7654.
20
with the …nding of Beaudry and Portier (2006). In addition, the dynamics of PC, TFP,
consumption, hours worked, output are very similar to those shown in our baseline VAR
system. The addition of consumer con…dence to our VAR renders very similar outcome.
The correlation coe¢ cient of the two news shocks is 0.93. And consumer con…dence rises
on impact. This suggests that consumer sentiment may at least in part be grounded in
anticipated changes in fundamentals.
We then add into our baseline VAR system two nominal variables, federal funds rate
and the in‡ation measured by the percentage change of the CPI index. Figure 8 reports the
impulse responses to the two news shocks. We see that again our main …ndings hold with
addition of nominal variables. Moreover, the in‡ation rate drops on impact, suggesting that
our identi…ed news shocks capture a supply shock. We conclude that our …ndings are robust
to the addition of other forward look and nominal variables.
5.4
Robustness Check
In this section, we conduct several robustness check of our results. We …rst use the GCV
quality-adjusted investment de‡ator. We also replace the TFP series with the TFP series in
the non-equipment sector. We then check the robustness of our results under di¤erent lags,
VAR speci…cations, and zero restrictions.
5.4.1
Alternative Measures of Price of Investment
We check the robustness of our results with the real price of investment measured by the
GCV de‡ator instead of NIPA de‡ator.20 As is clear in Figure 9, the impulse response of all
variables are very close to our benchmark system under the two news shocks. Hours worked,
GDP and investment all increases on impact. The correlation of the two identi…ed news
shocks are 0.95.21
5.4.2
TFP of Consumption Sector
According to our theory, the high correlation between the two identi…ed news shocks is
due to the spillover of embodied technological progress from the investment (in particular,
equipment and software) sector to the consumption sector and thus the whole economy. To
test this theory, we would like to explore the IRFs of TFP in the consumption sector to the
20
We thank Pat Higgins for sending us the updated GCV investment de‡ator.
We also adopt the GCV de‡ator for equipment and software in our robustness check. The correlation
between identi…ed news shocks to PC and TFP is again very high, 0.885.
21
21
identi…ed news shocks to PC and explore the correlation between news shocks to TFP in the
consumption sector and the news shocks to PC.
We construct the growth rate of TFP in the consumption sector according to
log T F P C =
log T F P
wI
log
=
log T F P
wI
log P C =P I
We then back out the level of TFP in the consumption sector and substitute it for TFP
in the baseline VAR system. Figure 10 reports the IRFs of the variables to these two news
shocks. Again, we see that the IRFs under these two news shocks are very similar. In
particular, TFP of the consumption sector increases steadily in response to the news shocks
to until about 10 years. The correlation between these two shocks are 0.98.
5.4.3
With Di¤erent Lags and Speci…cations
Our results are robust to di¤erent lags (e.g. …ve lags) and alternative VAR speci…cation.
Similarly, our results are robust to the inclusion of the federal fund rate, the term spread,
and other nominal variables in a VAR speci…cation similar to that adopted by Otrok and
Kurmann (2013). The correlation between the two identi…ed news shocks are 0.93.
5.4.4
Without Zero Restriction
In our benchmark speci…cation, we identify the shocks to TFP and PC by imposing the zero
restriction to the particular variable. The natural question is to what extent the long-run
shocks to TFP and PC are anticipated. To this end, we drop the zero restrictions when
identifying the shocks that maximizing the FEV of TFP and PC over a su¢ ciently long
horizon. These shocks are close in spirit to the permanent shocks to TFP and PC and may
contain both the anticipated and unanticipated innovations.
Figure 11 shows that even without the zero restriction, the impact response of PC and
TFP to the long-run shocks to PC and TFP are close to zero. The correlation coe¢ cient
between the two shocks are 0.9878. Moreover, the correlation between shocks to PC without
zero restriction and news shocks to PC is 0.9795. This suggests that permanent changes in
investment speci…c technology are largely anticipated and are one main source of anticipated
TFP ‡uctuations in the long run.22
22
When k = 40; the correlation between shocks to PC and TFP is only 0.3602. This suggests that only
for the long-run, ‡uctuations in TFP and PC are driven by a common primitive shock, which according to
our model, is the IST shock.
22
6
Conclusion
This paper explores the importance of investment-speci…c technological changes in anticipated TFP ‡uctuations. To this end, we identify two types of news shocks with the maximum
forecast error variance approach: news shocks to TFP and news shocks to the relative price
of investment. We establish the link between the identi…ed news shocks and the primitive
shocks in a model of IST di¤usion and spillover. A novel feature of the model is that the
improvement of IST not only increases the TFP of the capital producing sector, but also
the TFP of the consumption sector via spillover. Accordingly, the correlation of the two
identi…ed news shocks can be fruitfully used to distinguish the quantitative importance of
IST shocks in anticipated TFP ‡uctuations.
Our main empirical …nding using postwar U.S. data is that these two news shocks are
almost perfectly collinear if both are identi…ed to capture the long-run movement of the
corresponding variable. The observed dynamics of TFP with respect to the news shocks
to PC closely resembles the responses to a TFP news shock. This quasi-identity also holds
true for the dynamics of the price of investment, consumption, output, hours worked and
investment in response to the two news shocks. Our …nding suggests that embodied technological changes are the main drivers of anticipated TFP ‡uctuations via spillover to the
productivity of the rest of the economy.
Our …nding highlights the potential fruitfulness of exploring why technological breakthrough often originates in the capital-producing sector. Moreover, from both theoretical
and empirical perspectives, more work is called for to uncover the channels through which
IST innovations enhance the productive e¢ ciency of the rest of the economy and the channels
through which such a spillover is anticipated by economic agents.
23
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Cycles.”
25
7
Tables and Figures
Table 1: The Share of the Forecast Error Variance attributable to the IST news Shocks in
the Baseline Speci…cation.
k=0
Inv. rel. price 0.000
TFP
0.036
Consumption 0.5768
Hours
0.0675
GDP
0.1992
Investment
0.0248
k=4
0.0865
0.0455
0.5962
0.2912
0.3166
0.1835
k=8
0.2005
0.0562
0.5792
0.386
0.4344
0.2073
k = 16
0.4219
0.0858
0.6144
0.3509
0.4481
0.2152
k = 40
0.7088
0.2846
0.7195
0.3387
0.5855
0.3478
k = 80
0.7859
0.5314
0.7808
0.3477
0.6708
0.4721
Note: The coe¢ cients are obtained from computing the FEVs in the six variable system with
forecast horizon 0
k
120. The letter k denotes the forecast horizon. The number denotes the
fraction of the total forecast error variance of each variable attributable to the identi…ed IST news
shock.
26
Table 2. The Correlation Coe¢ cients of the Two News Shocks in the Baseline Speci…cation.
Forecast Horizon Correlation Coe¢ cient
0-40
0.4537
0-60
0.6079
0-80
0.8474
0-120
0.9773
Note: The correlation coe¢ cients are obtained from extracting both the IST news shock and the
TFP news shock in the six variable system with 0
27
k
120:
Table 3: Correlation Coe¢ cients in Six-Variable System under Alternative Forecast
Horizons
Forecast Horizon Correlation Coe¢ cient
k = 40
0.9639
k = 60
0.9916
k = 80
0.9916
k = 120
0.9956
Note: The correlation coe¢ cients are obtained from extracting both the IST news shock and the
TFP news shock in the six variable system
28
Table 4. Correlation Coe¢ cients of New Shocks to TFP and PC in Larger VAR Systems
Additional Variable
Stock Price
Consumer Con…dence
CPI In‡ation & FFR
Correlation Coe¢ cient
0.9376
0.9498
0.9808
Note: The coe¢ cient represents the correlation between the identi…ed IST news shock and the
TFP news shock in the seven-variable system. The coe¢ cient is obtained by adding an additional
variable one a time to the six-variable system, identifying both news shocks, and computing their
correlation.
29
Inv . Rel. inv es tment pric e
Corr. Total Fac tor Prod.
0.8
Percent Change
Percent Change
0.4
0.6
0.4
0.2
0
40
Quarters
Cons umption
60
0
-0.2
80
0.6
20
40
60
Quarters
Hours w orked,non-f arm
Percent Change
Percent Change
20
0.2
0.4
0.2
0
20
40
60
Quarters
Gros s domes tic produc t
80
1
0.5
0
80
20
40
Quarters
Inv es tment
60
80
20
60
80
Percent Change
Percent Change
1
0.5
0
20
40
Quarters
60
2
1
0
80
40
Quarters
Figure 1: Impulse Responses to The Two News Shocks in the Baseline Speci…cation
Notes: Impulse responses to IST news shock (black solid line) and TFP news shock (red dashed
line) in the six variable system with forecast horizon 0
k
120. The shaded gray area repre-
sents the 16-percent and 84-percent quantiles of the empirical distribution of the impulse response
functions in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse
responses obtained through the residual-based resampling with 1,000 replications.
30
Inv . Rel. inv es tment pric e
Corr. Total Fac tor Prod.
1
Share of FEV
Share of FEV
1
0.5
0
0
0
20
40
Quarters
Cons umption
60
80
0
20
40
60
Quarters
Hours w orked,non-f arm
80
1
Share of FEV
Share of FEV
1
0.5
0
0.5
0
0
20
40
60
Quarters
Gros s domes tic produc t
80
0
20
40
Quarters
Inv es tment
60
80
20
60
80
1
Share of FEV
1
Share of FEV
0.5
0.5
0
0.5
0
0
20
40
Quarters
60
80
0
40
Quarters
Figure 2: Share of the FEV decomposition attributable to the two News Shocks in the
Baseline Speci…cation.
Note: Forecast error variances (FEVs) to IST news shock (black solid line) and TFP news shock
(red dashed line) in the six variable system with forecast horizon 0
k
120. The shaded gray
area represents the 16-percent and 84-percent quantiles of the empirical distribution of the FEVs
in the identi…cation of the IST news shock. The distribution is the bootstrapped FEVs obtained
through the residual-based resampling with 1,000 replications.
31
2
1
1
0
0
-1
-1
-2
-2
TFP News Shocks
IST News Shocks
2
IS T N e w s S h o c k s
TFP N e w s S h o cks
-3
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
-3
2010
Figure 3: Time Series of Identi…ed News Shocks and U.S. Recession.
Note: The time series of the IST news shock and TFP news shock are obtained from the
six variable system with forecast horizon 0
k
recessions as dated by NBER.
32
120. The shaded areas represent periods of
0 .8
0 .6
0 .4
0 .2
0
60
0 .2
0
-0 .2
-0 .4
80
20
40
60
Q u a rte rs
H o u rs w o rke d ,n o n -fa rm
Percent Change
40
Q u a rte rs
C o n s u m p tio n
Percent Change
20
0 .6
0 .4
0 .2
0
20
40
60
Q u a rte rs
Gro s s d o m e s tic p ro d u ct
0 .5
20
0 .5
0
20
40
Q u a rte rs
60
0
80
1
80
1
Percent Change
Percent Change
C o rr. To ta l Fa cto r P ro d .
Percent Change
Percent Change
In v. R e l. in ve s tm e n t p rice
40
Q u a rte rs
In ve s tm e n t
60
80
20
60
80
2
1
0
80
40
Q u a rte rs
Figure 4: Impulse Responses to The Two News Shocks identi…ed with k = 40.
Notes: Impulse responses to IST news shock (black solid line) and TFP news shock (red dashed
line) in the six variable system with forecast horizon 0
k
40. The shaded gray area represents
the 16-percent and 84-percent quantiles of the empirical distribution of the impulse response functions in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse
responses obtained through the residual-based resampling with 1,000 replications.
33
In v. R e l. in ve s tm e n t p ric e
C o rr. To ta l Fa c to r P ro d .
1
Share of FEV
Share of FEV
1
0 .5
0 .5
0
0
0
20
40
Q u a rte rs
60
80
0
C o n s u m p tio n
60
80
1
Share of FEV
Share of FEV
40
Q u a rte rs
H o u rs w o rk e d ,n o n -fa rm
1
0 .5
0 .5
0
0
0
20
40
Q u a rte rs
60
80
0
G ro s s d o m e s tic p ro d u c t
20
40
Q u a rte rs
60
80
60
80
In ve s tm e n t
1
Share of FEV
1
Share of FEV
20
0 .5
0 .5
0
0
0
20
40
Q u a rte rs
60
80
0
20
40
Q u a rte rs
Figure 5: Shares of Forecast Error Variances attributable to the Two News Shocks under
k = 40:
Note: Forecast error variances (FEVs) to IST news shock (black solid line) and TFP news shock
(red dashed line) in the six variable system with forecast horizon 0
k
40. The shaded gray
area represents the 16-percent and 84-percent quantiles of the empirical distribution of the FEVs
in the identi…cation of the IST news shock. The distribution is the bootstrapped FEVs obtained
through the residual-based resampling with 1,000 replications.
34
In v. R e l. in ve s tm e n t p ric e
C o rr. T o ta l F a c to r P ro d .
0 .8
Percent Change
Percent Change
0 .4
0 .6
0 .4
0 .2
0
20
40
60
0 .2
0
-0 .2
80
20
0 .6
0 .4
0 .2
0
20
40
60
0
80
20
40
60
80
60
80
Q u a rte rs
In ve s tm e n t
Percent Change
1
Percent Change
80
0 .5
G ro s s d o m e s tic p ro d u c t
0 .5
0
40
60
1
Q u a rte rs
20
40
Q u a rte rs
H o u rs w o rk e d ,n o n -fa rm
Percent Change
Percent Change
Q u a rte rs
C o n s u m p tio n
60
2
1
0
80
20
Q u a rte rs
40
Q u a rte rs
Figure 6: Robustness of Impulse Responses to News Shock to PC identi…ed under Di¤erent
Forecast Horizons.
Note: Impulse responses to IST news shock in the case of 0
IST news shock in the case of 0
k
k
120 (black solid line) and
40 (red dashed line) in the six variable system. The
shaded gray area represents the 16-percent and 84-percent quantiles of the empirical distribution
of the impulse response functions in the identi…cation of the IST news shock over the forecast
horizon 0
k
120. The distribution is the bootstrapped impulse responses obtained through
the residual-based resampling with 1,000 replications.
35
C o rr. To ta l F a c to r P ro d .
0 .5
0
20
40
60
80
Percent Change
Percent Change
In v. R e l. in ve s t m e n t p ric e
1
0 .4
0 .2
0
-0 . 2
20
Q u a rt e rs
0 .5
0
40
60
80
0 .5
0
20
Percent Change
Percent Change
0 .5
0
60
40
60
80
60
80
Q u a rt e rs
In ve s t m e n t
1
40
80
1
Q u a rt e rs
G ro s s d o m e s t ic p ro d u c t
20
60
H o u rs w o rk e d ,n o n -fa rm
Percent Change
Percent Change
C o n s u m p tio n
20
40
Q u a rt e rs
80
2
1
0
20
Q u a rt e rs
40
Q u a rt e rs
Percent Change
S t o c k p ric e in d e x
4
2
0
20
40
60
80
Q u a rt e rs
Figure 7: Impulse Responses to the News Shocks in the System with Stock Prices
Note: Impulse responses to IST news shock (black solid line) and TFP news shock (red dashed
line) in the seven variable system with forecast horizon 0
k
120. The shaded gray area repre-
sents the 16-percent and 84-percent quantiles of the empirical distribution of the impulse response
functions in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse
responses obtained through the residual-based resampling with 1,000 replications.
36
C o rr. To t a l F a c t o r P ro d .
0.5
0
20
40
60
80
Percent Change
Percent Change
In v. R e l. in ve s t m e n t p ric e
1
0.4
0.2
0
-0 . 2
20
Q u a rt e rs
0.5
0
40
60
80
20
60
80
Percent Change
Percent Change
0
20
40
60
80
Q u a rt e rs
A n n u a liz e d C P I in f. ra t e
0.4
0.2
0
-0 . 2
60
80
Percent Change
N o m in a l in t e re s t ra t e
Percent Change
80
1.5
1
0.5
0
Q u a rt e rs
40
60
In ve s t m e n t
0.5
20
40
Q u a rt e rs
G ro s s d o m e s t ic p ro d u c t
40
80
0.8
0.6
0.4
0.2
0
Q u a rt e rs
20
60
H o u rs w o rk e d , n o n -fa rm
Percent Change
Percent Change
C o n s u m p t io n
20
40
Q u a rt e rs
Q u a rt e rs
0
-0 . 5
-1
20
40
60
80
Q u a rt e rs
Figure 8: Impulse Responses to the News Shocks in Large System with Nominal Variables.
37
In vR e liIn v. p ric e : T o t a l In v
C o rr. T o t a l F a c t o r P ro d .
Percent Change
Percent Change
0 .4
0 .2
0
20
40
60
0 .2
0
-0 . 2
80
20
Q u a rt e rs
C o n s u m p t io n
60
80
H o u rs w o rk e d , n o n -fa rm
1
Percent Change
0 .6
Percent Change
40
Q u a rt e rs
0 .4
0 .2
0
20
40
60
0 .5
0
80
20
Q u a rt e rs
40
60
80
60
80
Q u a rt e rs
G ro s s d o m e s t ic p ro d u c t
In ve s t m e n t
1
Percent Change
Percent Change
2
0 .5
0
20
40
60
1
0
80
20
Q u a rt e rs
40
Q u a rt e rs
Figure 9: Impulse Response to the Two News Shocks with the GCV Investment De‡ator.
Note: Impulse responses to IST news shock (black solid line) and TFP news shock (red dashed
line) in the six variable system with forecast horizon 0
k
120. The shaded gray area repre-
sents the 16-percent and 84-percent quantiles of the empirical distribution of the impulse response
functions in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse
responses obtained through the residual-based resampling with 1,000 replications.
38
In v. R e l. in ve s t m e n t p ric e
C o rr. TF P fo r c o n s . S e c t o r
0.8
Percent Change
Percent Change
0.6
0.6
0.4
0.2
0
20
40
60
0.4
0.2
0
-0 . 2
80
20
Q u a rt e rs
60
80
H o u rs w o rk e d , n o n -fa rm
1
0.6
Percent Change
Percent Change
C o n s u m p t io n
0.4
0.2
0
20
40
60
0.5
0
80
20
Q u a rt e rs
40
60
80
60
80
Q u a rt e rs
G ro s s d o m e s t ic p ro d u c t
In ve s t m e n t
1
2
Percent Change
Percent Change
40
Q u a rt e rs
0.5
0
20
40
60
1
0
80
20
Q u a rt e rs
40
Q u a rt e rs
Figure 10: Impulse Response to the Two News Shocks with Non-equipment Sector TFP.
Note: Impulse responses to IST news shock (black solid line) and TFP news shock (red dashed
line) in the six variable system with forecast horizon 0
k
120. The shaded gray area repre-
sents the 16-percent and 84-percent quantiles of the empirical distribution of the impulse response
functions in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse
responses obtained through the residual-based resampling with 1,000 replications.
39
Inv. R e l. in ves tm e n t pric e
C o rr. To ta l F a c to r P ro d .
0 .4
Percent Change
Percent Change
1
0 .5
0
20
40
60
0 .2
0
-0 .2
80
20
0 .6
0 .4
0 .2
0
20
40
60
0
80
20
40
60
80
60
80
Q u a rte rs
In ve s t m e n t
Percent Change
1
Percent Change
80
0 .5
G ro s s d o m e s t ic p ro d u c t
0 .5
0
40
60
1
Q u a rte rs
20
40
Q u a rte rs
H o u rs w o rk e d ,n o n -fa rm
Percent Change
Percent Change
Q u a rte rs
C o n s u m p tio n
60
80
2
1
0
20
Q u a rte rs
40
Q u a rte rs
Figure 11: Impluse Response to the Two News Shocks Identi…ed Without Zero Restrictions
Note: Impulse responses to IST shock (black solid line) and TFP shock (red dashed line) in
the six variable system with forecast horizon 0
k
120. The shaded gray area represents the
16-percent and 84-percent quantiles of the empirical distribution of the impulse response functions
in the identi…cation of the IST news shock. The distribution is the bootstrapped impulse responses
obtained through the residual-based resampling with 1,000 replications.
40