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Is There News in Inventories?
ONLINE APPENDIX
Christoph Görtz
University of Birminghamy
Christopher Gunn
Carleton Universityz
Thomas A. Lubik
Federal Reserve Bank of Richmondx
May 2020
The views expressed in this paper are those of the authors and not necessarily those of the Federal
Reserve Bank of Richmond or the Federal Reserve System.
y
Department of Economics. University House, Birmingham B15 2TT. United Kingdom. Tel.: +44 (0)
121 41 43279. Email: c.g.gortz@bham.ac.uk
z
Department of Economics. Loeb Building, 1125 Colonel By Drive. Ottawa, ON, K1S 5B6. Canada.
Tel.: +1 613 520 2600x3748. Email: chris.gunn@carleton.ca.
x
Research Department, P.O. Box 27622, Richmond, VA 23261. Tel.: +1-804-697-8246. Email:
thomas.lubik@rich.frb.org.
1
A
Additional VAR Evidence
A.1
Forecast Error Variance Decomposition
Figure 1 reports the forecast error variance decomposition for our baseline speci…cation in
the main text. It shows the variance shares explained by the TFP news shock over a 40period (10-year) time horizon. In the long run, the news shock explains about 50% of TFP
‡uctuations, the remainder being due to unanticipated movements in productivity. For all
other quantity variables the contribution of TFP news is above 50%, with the contribution
of GDP at around three quarters. This is consistent with the …ndings in the literature which
attribute similar importance to anticipated TFP movements.
A.2
News Shocks and the Response of Inventories over a Longer Sample
Period
It has been widely documented in the literature (for instance, McCarthy and Zakrajsek,
2007) that changes in the behavior of inventories coincide with the onset of the Great
Moderation in the early 1980s. It is this observation, in addition to data availability issues
that we highlight in the main text, that we and most of the literature focus on a post-Great
Moderation sample. Nevertheless, it is interesting to evaluate whether the rise of inventories
in anticipation of higher future TFP is present also over a longer horizon.
Figure 2 shows the impulse responses for the 1960Q1- 2018Q2 sample period, computed
using the same news shock identi…cation procedure as in the baseline. The individual graphs
reveal strong comovement of all macroeconomic aggregates, including inventories, several
quarters before TFP increases signi…cantly. This sample is restricted by the availability of
the E5Y consumer con…dence measure. Using the S&P500 stock index in its place we can
consider a 1948Q1-2018Q2 sample.
Figure 3 shows that responses to a news shock based on this sample are qualitatively
and also largely quantitatively very similar to the results based on our 1983Q1- 2018Q2
baseline sample and the 1960Q1-2018Q2 sample period. Overall, we …nd that the fact that
inventories rise in response to a TFP news shock is robust at longer sample periods.
A.3
Robustness to Alternative VAR News Shock Identi…cation
In our baseline speci…cation, we identify news shocks using the Max Share method proposed
by Francis et al. (2014). This approach is widely used in the literature; it identi…es a news
shock as the shock that (i) does not move TFP on impact, and (ii) maximizes the variance
2
of TFP at a 40-quarter horizon. We assess the robustness of our …ndings using three closely
related alternative approaches.
First, we consider the identi…cation scheme suggested by Barsky and Sims (2011). Their
method recovers a news shock by maximizing the variance of TFP over horizons from zero
to 40 quarters and the restriction that the news shock does not move TFP on impact.
The second alternative identi…cation scheme is Forni et al. (2014), which is similar in
spirit to the Max Share method. They identify the news shock by imposing a zero-impact
restriction on TFP and maximize the impact of the shock on TFP in the long run. Third,
we use identi…cation suggested by Kurmann and Sims (2019), who recover news shocks
by maximizing the forecast error variance of TFP at a long horizon without imposing a
zero-impact restriction on TFP conditional on the news shock.1
Figure 4 provides a comparison between the median responses based on the Max Share
method and the methods proposed by Barsky and Sims (2011) and Forni et al. (2014). The
median responses of the Max Share methodology and the Forni et al. (2014) methodology
are virtually indistinguishable. In turn, both are very similar to the median responses
based on the Barsky and Sims (2011) approach. Figure 5 shows that responses based on
the methodology proposed by Kurmann and Sims (2016) are qualitatively and quantitatively
close to the ones based on the Max-share method. Perhaps most importantly, all methods
suggest inventories increase in anticipation of higher future TFP.
A.4
News Shock Identi…cation Based on Patents
We also consider as a robustness exercise identi…cation of news shocks that relies on valueweighted patents. In this we follow the idea in Cascaldi-Garcia and Vukotic (2019) who
argue that patent …lings include information about future TFP movements since …rms
engage in activities to take advantage of expected technological improvements or are the
originators of such productivity advancements. The patent system is designed to reveal
such news without the full set of improvements necessarily being in place.
Kogan et al. (2017) use observations on patents associated with stockmarket listed …rms
in the CRSP database. They compute the economic value of a patent based on a …rm’s
stock-price reaction to observed news about a patent grant, controlling for factors that could
move stock prices but are unrelated to the economic value of the patent. Kogan et al. (2017)
provide an annual index, while Cascaldi-Garcia and Vukotic (2019) use the associated micro
data to aggregate to a quarterly index. They then use this index to identify responses to
1
Kurmann and Sims (2019) argue that allowing TFP to jump freely on impact, conditional on a news
shock, produces robust inference to cyclical measurement error in the construction of TFP.
3
patent-based news shocks in a Bayesian VAR based on a simple Cholesky identi…cation with
the patent series ordered …rst.
Figure 6 shows impulse response functions to this patent-based news shock. They are
broadly consistent with the responses in the baseline setup. TFP rises signi…cantly only
with a delay, even though there is no zero-impact restriction applied. Inventories rise on
impact together with the other activity variables as well as consumer con…dence. Unfortunately, the availability of the Kogan et al. (2017) value-weighted patents series restricts the
sample to end in 2010Q4, while at the same time the composition of the index is limited
to stockmarket-listed …rms only. Nevertheless, the qualitative consistency of responses to
a patent-based news shock with our baseline results is reassuring since the identi…cation of
the former is independent of the observable for TFP.
B
DSGE Model Equations
The DSGE model introduced in section 3 of the main text is described by a set of optimality
conditions. They de…ne a symmetric competitive equilibrium as a set of stochastic processes
fCt ; It ; Gt ; St ; Yt ; Nt ; ut ; Ft ; Kt ; Ht ; Xt ; At ; wt ; rt ;
t;
f
t;
k;
t
h;
t
1
t gt .
In the following, we list
these equations and detail how to transform the non-stationary system, which is driven by
stochastic trends, into a stationary counterpart amenable to solution and estimation.
B.1
Optimality Conditions
We de…ne Vt = Ct
addition, we denote
nt Ft as the periodic utility function argument to ease notation. In
f
t,
k,
t
h,
t
and
t
as, respectively, the multipliers on the de…nition of
Ft (equation (9) in the main text), physical capital accumulation (equation (10) in the main
text), knowledge capital accumulation (equation (11) in the main text) and the household
budget constraint (equation (12) in the main text). The …rst-order necessary conditions are
then as follows:
Ct +
t It
+ Gt = S t ;
(1)
1
Ft = Ct f Ft
Kt+1 = [1
f
1
;
(ut )] Kt + mt It 1
Ht+1 = Ht h Nt h ;
1
Gt =
1
Yt ;
"t
4
(2)
S
It
It
;
(3)
1
(4)
(5)
t Vt
+
t Vt
f
t f
Nt
Ft
Ct
1
=
Ft =
rt =
t;
(6)
t wt H t
k
t
=
(7)
0(ut );
t
t t
Ht+1
h
;
t h
Nt
+
k
t mt
1
=
k
t
=
Et
h
t
=
Et
t Vt
Yt = zt (
It
S
It
S0
1
n
+
t+1 wt+1 Nt+1
+
(ut Kt )1
t Ht Nt )
It
It
It
1
+
(9)
1
2
;
f Ft+1
;
f )Et t+1
Ft
Nt + (1
t+1 rt+1 ut+1
It
It+1
It
It+1
It
k
t+1 mt+1 S0
+ Et
f
t
(8)
k
t+1 [1
(10)
o
(ut+1 )] ;
Ht+2
h
t+1 h
Ht+1
(11)
;
(12)
;
(13)
Yt
;
t
Ht Nt
wt =
rt = (1
At = (1
(14)
Yt
;
ut Kt
x )Xt 1 + Yt ;
)
(15)
t
Xt = At St ;
1
=
(1
x )Et
(16)
(17)
t+1
t+1 ;
(18)
t
t
=
St
+
At
1
:
In addition, we have laws of motion for the exogenous processes
and gt =
B.2
t= t 1
(19)
t,
mt
t,
gt =
t=
t 1
as described in the main text.
Stationarity and Solution Method
The model economy inherits stochastic trends from the two non-stationary stochastic processes
for
t
and
t.
Our solution method focuses on isolating ‡uctuations around these stochastic
trends. We divide non-stationary variables by their stochastic trend component to derive
a stationary version of the model. We then take a linear approximation of the dynamics
around the steady state of the stationary system.
The stochastic trend components of output and capital are given by Xty =
Xtk
=
1
t,
1
t
t
and
respectively. The stochastic trend components of all another non-stationary
variables can be expressed as some function of Xty and Xtk . In particular, de…ne the following
5
Ct
,
Xty
stationary variables as transformations of the above 19 endogenous variables: ct =
it =
It
,
Xty
gt =
xt =
Xt
,
Xty
at =
and
t
At
,
Xty
= (Xty )
and gtk =
vt =
Gt
,
Xty
Vt
Xty
Xtk
Xtk 1
st =
wt =
t.
St
,
Xty
wt
,
Xty
yt =
Yt
,
Xty
nt = Nt , ut = ut , ft =
Xtk
r,
Xty t
rt =
t
=
t,
f
t
= (Xty )
f
t,
Ft
,
Xty
qtk =
In addition, de…ne the two additional stationary
Kt
, ht = Ht ,
Xtk 1
h=
Xtk ( kt = t )
, qth = tX y t
Xty
t
Xy
variables, gty = X yt
kt =
t 1
as the growth-rates of the stochastic trends in output and capital, and
as the de…nition of the stationary counterpart of the periodic utility function
argument Vt de…ned above.
The stationary system is then given by:
ct + it + gt = st ;
(20)
ft = ct f
kt+1 = [1
1
ft 1
gty
(ut )]
f
;
(21)
kt
+ mt it 1
gtk
ht+1 = ht h nt h ;
1
yt ;
gt =
1
"t
ft
f
= t;
t vt + t f
ct
ht+1
1 ft
= wt ht + qth h
;
t vt nt
nt
t
rt = qtk 0(ut );
it gtk
1 = qtk mt 1 S
it 1
qtk
=
=
qth =
t vt
(25)
(26)
(27)
S0
yt = (ht nt )
wt =
rt = (1
t
yt
;
ht nt
)
t
f )Et
t+1
t
t+1
ut
kt
gkk
it gtk
it gtk
it
ii
1
t+1 k
qt+1 mt+1 S0
t
y
Et gt+1 gt+1
(22)
(24)
nt + (1
y
Et gt+1
;
(23)
y
+ Et gt+1 gt+1
f
t
it gtk
it 1
S
y
gt+1
1
;
(28)
k
it+1 gt+1
it
!
f ft+1
;
t+1
ft
n
k
rt+1 ut+1 + qt+1
[1
h
wt+1 nt+1 + qt+1
t
1
+
1
h
ht+2
ht+1
k
it+1 gt+1
it
!2
;
(29)
o
(ut+1 )] ;
(30)
;
(31)
(32)
(33)
yt
;
ut gkkt
(34)
t
6
at = (1
x)
xt 1
+ yt ;
gty
xt = at st ;
1
y
=
(1
x )Et gt+1
t
=
st
+
zt
(
gyy = gt gt
gtk =
gty =gt
in addition to the exogenous processes
C
1
(35)
(36)
t+1
t+1 ;
;
1)=
(38)
;
;
t,
(37)
t
(39)
(40)
mt
t,
gt and gt .
Shock Processes and Bayesian Estimation
To estimate the model, we include the following exogenous disturbances: a shock to the
growth rate of TFP (gyy ), a shock to the growth rate of IST (gt ), a marginal e¢ ciency of
investment (MEI) shock (mt ), a preference shock ( t ) and a government spending shock
("t ). Each exogenous disturbance is expressed in log-deviations from the steady state as
a …rst-order autoregressive process, whose stochastic innovation is uncorrelated with other
shocks, has a zero mean, and is normally distributed. In addition to the unanticipated
innovations to the above shocks, the model allows for anticipation e¤ects. In particular, all
shock processes (with the exception of the preference shock) include four, eight and twelve
quarter-ahead innovations. Our treatment of anticipated and unanticipated components is
standard and in line with the literature.2
We estimate the model over the period from 1983Q1 to 2018Q2, as in the VAR analysis.
We use GDP, consumption, investment, inventories, and hours worked as observables. The
variables are expressed in real per-capita terms as outlined in Section 2 in the main text,
while GDP, consumption, investment, and inventories enter the vector of observables in …rst
di¤erences. We demean the data prior to estimation.
We only estimate the persistence parameters of the shocks and their standard deviations,
while the remaining parameters shown in Table 1 in the main text are calibrated. The prior
distributions follow the assumptions in Schmitt-Grohé and Uribe (2012). The prior means
assumed for the news components are in line with these studies and imply that the sum
2
For example Schmitt-Grohé and Uribe (2012) also include news components in the processes for government spending shocks and stationary as well as non-stationary neutral and investment-speci…c technology
shocks. News shocks also arrive at the four, eight and twelve quarter-horizons as in Görtz et al. (2017), for
example.
7
of the variance of news components is, evaluated at prior means, at most one half of the
variance of the corresponding unanticipated component. Table A.1 provides an overview
about prior and posterior distributions. Overall, the data are informative and indicate
strong persistence in the MEI shock, but also in government spending. At the same time,
TFP and IST growth exhibit a reasonably high degree in serial correlation, in line with the
behavior of U.S. quantity variables such as GDP.
References
[1] Barsky, Robert B., and Eric R. Sims (2011): “News shocks and business cycles”. Journal
of Monetary Economics, 58(3), pp. 273-289.
[2] Cascaldi-Garcia, Danilo, and Marija Vukotić (2019): “Patent-based news shocks”.
Forthcoming, Review of Economics and Statistics.
[3] Forni, Mario, Luca Gambetti, and Luca Sala (2014): “No news in business cycles”.
Economic Journal, 124, pp. 1168-1191.
[4] Francis, Neville, Michael Owyang, Jennifer Roush, and Riccardo DiCeccio (2014): “A
‡exible …nite-horizon alternative to long-run restrictions with an application to technology shocks”. Review of Economics and Statistics, 96, pp. 638-647.
[5] Görtz, Christoph, John Tsoukalas, and Francesco Zanetti (2017): “News shocks under
…nancial frictions”. Technical Report.
[6] Kogan, Leonid, Dimitris Papanikolaou, Amit Seru, and Noah Stockman (2017): “Technological innovation, resource allocation, and growth”. Quarterly Journal of Economics,
132(2), pp. 665-712.
[7] Kurmann, Andre, and Eric Sims (2019): “Revisions in utilization-adjusted TFP and
robust identi…cation of news shocks”. Forthcoming, Review of Economics and Statistics.
[8] McCarthy, Jonathan, and Egon Zakrajsek (2007): “Inventory dynamics and business
cycles: What has changed?” Journal of Money, Credit and Banking, 39(2-3), pp. 591613.
[9] Schmitt-Grohé, Stephanie and Martín Uribe (2012): “What’s news in business cycles?”
Econometrica, 80(6), pp. 2733-2764.
8
Figure 1: Forecast error variance decomposition (FEVD) of variables to the TFP news shock.
Sample 1983Q1-2018Q2. The solid line is the median and the dashed lines are the 16% and 84%
posterior bands generated from the posterior distribution of VAR parameters.
Figure 2: IRF to TFP news shock. Sample 1960Q1-2018Q2. The solid line is the median
and the dashed lines are the 16% and 84% posterior bands generated from the posterior distribution
of VAR parameters. The units of the vertical axes are percentage deviations.
9
Figure 3: IRF to TFP news shock. Sample 1948Q1-2018Q2. The solid line is the median
and the dashed lines are the 16% and 84% posterior bands generated from the posterior distribution
of VAR parameters. The units of the vertical axes are percentage deviations.
Figure 4: IRF to TFP news shock. Sample 1983Q1-2018Q2. The black solid line is the median
response identi ed using the Max-share method. The shaded gray areas are the corresponding 16%
and 84% posterior bands generated from the posterior distribution of VAR parameters. The blue
line with crosses (red line with circles) is the median response identi ed using the Barsky and Sims
(2011) (Forni et al. (2014)) methodology. The units of the vertical axes are percentage deviations.
10
Figure 5: IRF to TFP news shock. Sample 1983Q1-2018Q2. The black solid (red dash-dotted)
line is the median response identi ed using the Max-share (Kurmann and Sims (2016)) method. The
shaded gray areas (dashed red lines) are the corresponding 16% and 84% posterior bands generated
from the posterior distribution of VAR parameters. The units of the vertical axes are percentage
deviations.
Figure 6: IRF to patent based TFP news shock. Sample 1983Q1-2010Q4. The black solid
(dash-dotted) line is the median (16% and 84% posterior bands) response identi ed using the value
weighted patent based identi cation as in Cascaldi-Garcia and Vucotic (2019). Posterior bands are
generated from the posterior distribution of VAR parameters. The units of the vertical axes are
percentage deviations.
11
Table 1: Prior and Posterior Distributions
Parameter Description
Shocks: Persistence
ρb
ρµ
ρg
ρa
ρv
Preference
Marginal e ciency of investment
Government spending
TFP growth
IST growth
Shocks: Volatilities
σb
σµ
σµ4
σµ8
σµ12
σg
σg4
σg8
σg12
σg
σa4
σa8
σa12
σv
σv4
σv8
σv12
Preference
Marginal e ciency of investment
MEI. 4Q ahead news
MEI. 8Q ahead news
MEI. 12Q ahead news
Government spending
Gov. spending. 4Q ahead news
Gov. spending. 8Q ahead news
Gov. spending. 12Q ahead news
TFP growth
TFP growth. 4Q ahead news
TFP growth. 8Q ahead news
TFP growth. 12Q ahead news
IST growth
IST growth. 4Q ahead news
IST growth. 8Q ahead news
IST growth. 12Q ahead news
Prior Distribution
Posterior Distribution
Distribution Mean Std. dev.
Mean
10%
90%
Beta
Beta
Beta
Beta
Beta
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
Inv Gamma
0.5
0.5
0.5
0.5
0.5
0.2
0.2
0.2
0.2
0.2
0.5281
0.9997
0.9552
0.4395
0.6343
0.5216
0.9995
0.9194
0.3798
0.5555
0.5364
0.9999
0.9287
0.5025
0.7173
0.5
0.5
0.289
0.289
0.289
0.5
0.289
0.289
0.289
0.5
0.289
0.289
0.289
0.5
0.289
0.289
0.289
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
2*
0.3177
0.8943
1.3817
0.2860
0.3644
0.2615
0.4545
0.2581
3.0040
0.6382
0.1458
0.1360
0.6294
0.3357
0.6004
0.1664
0.3769
0.1298
0.1856
0.9850
0.0681
0.0966
0.1450
0.1026
0.0681
2.7129
0.5778
0.0861
0.0723
0.5419
0.1652
0.4435
0.0797
0.2352
0.5160
1.3684
1.8498
0.5308
0.6623
0.3772
0.8695
0.5098
3.3181
0.7072
0.2177
0.1959
0.7248
0.4781
0.7898
0.2557
0.5091
Notes. The posterior distribution of parameters is evaluated numerically using the random walk Metropolis-Hastings
algorithm. We simulate the posterior using a sample of 500,000 draws and discard the rst 100,000 of the draws.
12
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