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Is There News in Inventories?
WP 20-03
Christoph Görtz
University of Birmingham
Christopher Gunn
Carleton University
Thomas A. Lubik
Federal Reserve Bank of Richmond
Is There News in Inventories?
Christoph Görtz
University of Birminghamy
Christopher Gunn
Carleton Universityz
Thomas A. Lubik
Federal Reserve Bank of Richmondx
May 2020
Abstract
We identify total factor productivity (TFP) news shocks using standard VAR methodology and document a new stylized fact: in response to news about future increases in
TFP, inventories rise and comove positively with other major macroeconomic aggregates. We show that the standard theoretical model used to capture the e¤ects of news
shocks cannot replicate this fact when extended to include inventories. To explain the
empirical inventory behavior, we therefore develop a framework that relies on the presence of knowledge capital accumulated through a learning-by-doing process. The desire
to take advantage of higher future TFP through knowledge capital drives output and
hours choices on the arrival of news and leads to inventory accumulation alongside the
other macroeconomic variables. The broad-based comovement we document supports
the view that news shocks are an important driver of aggregate ‡uctuations.
Keywords: News shocks, business cycles, inventories, knowledge capital, VAR.
JEL Classi…cation: E2, E3.
We are grateful to Paul Beaudry, Jean-Paul l’Hullier, Alok Johri, Hashmat Khan, Andre Kurmann,
Mathias Paustian, Franck Portier, Cedric Tille, and Mark Weder for useful comments and suggestions.
We thank seminar and conference participants at the 2018 Canadian Economics Association Conference,
the 2019 conference on Computing in Economics and Finance, the 7th Ghent University Workshop on
Empirical Macroeconomics, the 2019 UVA-Richmond Fed Research Workshop, the 2019 Money, Macro and
Finance Research Group Annual Conference, the 2019 AEA meeting, the 3rd University of Oxford NuCamp
Conference, the College of William & Mary, the Deutsche Bundesbank, the University of She¢ eld, the
University of Windsor, and Drexel University. 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
1
Introduction
There is substantial evidence that expectations about future total factor productivity (TFP)
are an important source of aggregate ‡uctuations (see Beaudry and Portier, 2014, and references therein). Such TFP news shocks give rise to the observed comovement of aggregate
quantities as identi…ed in a large body of empirical work on the incidence and e¤ects on news
(e.g., Beaudry and Portier, 2004). Theoretical business cycle models can explain these …ndings under reasonably general assumptions and modeling components (see Jaimovich and
Rebelo, 2009) and imply substantial explanatory power of news shocks when taken to the
data directly (e.g., Schmitt-Grohé and Uribe, 2012; Görtz and Tsoukalas, 2017). At the
same time, the news-shock literature has largely ignored inventory investment – a component of aggregate output and an adjustment margin to shocks that has long been recognized
to play a large role in explaining aggregate ‡uctuations (see Ramey and West, 1999; Wen,
2005).
In this paper, we argue that inventories should take central stage for understanding
the implications of news shocks. In the same vein, we argue that news shocks are an
important component in understanding the behavior of inventory investment in addition
to the standard mechanisms. Our paper thereby provides further evidence that news is an
important component of aggregate ‡uctuations and that it provides a litmus test by looking
at inventories. In particular, we develop a new stylized fact and explain this fact in a general
equilibrium model of inventory investment, where we introduce knowledge capital as a key
new modeling element.
Our …rst contribution is the identi…cation of a new fact for the inventory and news-shock
literature. Using standard news-shock identi…cation methodology1 for a structural vector
autoregression (VAR) that includes inventories besides other quantity variables, we …nd
that in response to anticipated news about higher future TFP, inventories rise on impact
along with output, consumption, investment, and hours worked. This is a robust …nding
not only for the aggregate data, but also across the retail, wholesale and manufacturing
sector as well as for …nished goods, work-in-process, and input inventories. Our …ndings
support the insight from the existing literature that news shocks are important drivers
of business cycles. Furthermore, the consensus in the literature is that, unconditionally,
inventory investment is procyclical (e.g., Ramey and West, 1999), whereby we identify a
1
Our baseline identi…cation scheme is an extension of the approach in Francis et al. (2014). We discuss
robustness to alternative identi…cation assumptions in the online appendix.
2
factor that induces conditional procyclicality.2
The observation that inventories rise in response to news about higher future TFP is
not a priori self-evident. In a conventional neoclassical framework with inventories, positive
news about future TFP implies a wealth e¤ect. The associated rise in sales of consumption
and investment goods creates a demand e¤ect, which drives up inventories in order to
avoid stockouts and enhance demand. However, the associated joint increase in sales and
inventories can only be met through higher production. This implies rising marginal costs,
which provides incentives for …rms to partly satisfy higher demand by drawing down the
inventory stock. This is reinforced by an intertemporal substitution e¤ect, whereby positive
news provides incentives to reduce current inventory stock, but build it up again in the
future when high productivity is realized and marginal cost is lower. To the extent that
both e¤ects are present, our empirical results suggest the negative substitution e¤ect is
dominated by the positive demand e¤ect.
Our second contribution is to identify a theoretical mechanism by which positive news
about future TFP generates an expansion of all macroeconomic aggregates, including inventories. Speci…cally, we reconcile the empirical …ndings with the standard news-shock model
with inventories by providing a role for intangible capital, which we refer to as knowledge
capital3 , based on earlier work by Chang et al. (2002), Cooper and Johri (2002) and Gunn
and Johri (2011). The accumulation of intangible knowledge through a learning-by-doing
process involving labor addresses the shortcomings of the standard model in a straightforward manner. Periods of accelerated technological change involve a reorganization of
production as the economy prepares for the new technological environment, including the
acquisition of new skills, machines, production processes, and materials. In a one-good
neoclassical model where all these underlying changes are hidden, we argue that a simple mechanism whereby agents make investments in intangible knowledge to prepare for the
future increase in TFP serves as a supply-side proxy for complex production reorganization.
Households acquire skill-enhancing knowledge through a learning-by-doing process from
experience in production. The arrival of news about a future increase in TFP raises the
value of knowledge in the present, inducing households to increase their labor supply in order
2
We …nd that the TFP news shock explains between 47-71% and 47-65% of the forecast error variance
in GDP and inventories, respectively, over a horizon from 6-32 quarters.
3
Knowledge capital can be interpreted as an intensive margin of hours worked, for instance, as the
knowledge of a worker how to best put to use an hour of work. This includes knowledge about operational
processes, handling of machines and materials, and such. See Chang et al. (2002) for an early application
in a neoclassical business cycle model and d’Alessandro et al. (2019) for a recent application and further
discussion.
3
to accumulate knowledge through experience. This has the e¤ect of both contributing to
the rise in hours worked, and thus production, and of suppressing the rise in the real wage
during the initial boom. Consequently, the presence of knowledge capital limits the rise in
marginal costs and increases the incentive to accumulate inventories. More succinctly, the
accumulation of knowledge capital allows the news-shock-driven demand e¤ect to dominate
the substitution e¤ect in production.
The core of our model is the framework of Jaimovich and Rebelo (2009) which nests
the model of Schmitt-Grohé and Uribe (2012). It includes the trio of particular speci…cations of preferences, investment adjustment costs and variable capital utilization, which are
features generally recognized in the news literature as needed for generating comovement
of macroeconomic aggregates in response to a TFP news shock. We extend this model
to include …nished goods inventories based on the stock-elastic demand model of Bils and
Kahn (2000).4 The standard news-shock business cycle model supplemented with inventories cannot replicate the facts from our identi…ed news-shock VAR, as inventories respond
countercyclically to TFP news in the model. This behavior results from a too-strong procyclical rise in marginal costs during the expansion. In turn, this countercyclical response of
inventories suppresses the positive response of hours and as a result dampens the response
of utilization and output. Since …rms can satisfy any news-induced increase in sales by
drawing down inventories, the demand for labor falls, suppressing the response of hours,
utilization, and output relative to sales.
Our …ndings contribute to the large literature on the role of news shocks as drivers
of aggregate ‡uctuations. Considerable work has been done on studying mechanisms that
generate procyclical movements in consumption, investment, and hours in response to TFP
news shocks, e.g., Jaimovich and Rebelo (2009) and on studying their e¤ects empirically in
identi…ed VARs and estimated DSGE models, for instance, Barsky and Sims (2011, 2012)
and Schmitt-Grohé and Uribe (2012). The new aspect our paper adds to this literature
is the focus on inventories, both in terms of their behavior in a VAR with news shocks
and in developing a theoretical framework to study the empirical results. A large longstanding literature investigates the empirical relation of inventories with macroeconomic
‡uctuations and the implications of introducing inventories in theoretical frameworks (see
Ramey and West, 1999, for a comprehensive survey and critical assessment). In our theoretical modeling of inventories, we are guided by Bils and Kahn (2000), who highlight the
unconditionally limited role of intertemporal substitution for variations in inventories that
4
This mechanism enjoys substantial empirical and theoretical support and is hence a widely used motive
to give rise to inventory holdings, see e.g. Lubik and Teo (2012) and Jung and Yun (2013).
4
is also documented in our work in the context of expectations about productivity.
Our paper is most closely related to Crouzet and Oh (2016), who introduce inventories
into a variant of the standard news-shock model of Jaimovich and Rebelo (2009), utilizing
a reduced-form stockout-avoidance speci…cation. They show that, while this setup can
generate positive comovement of investment, consumption, and hours in response to TFP
news shocks, it fails to do so in the case of inventories. The countercyclical inventory
movement is then used to inform sign restrictions in a structural VAR to identify TFP news
shocks. Given the unconditional procyclicality of inventory investment and the imposed
negative sign restriction on this variable, Crouzet and Oh (2016) come to the conclusion
that TFP news shocks are of limited importance for aggregate ‡uctuations. In contrast,
we use a standard and widely used VAR methodology to identify the response of inventory
movements to TFP news …rst. We thereby establish positive comovement of inventories as a
robust stylized fact that we then rationalize in an inventory model with a learning-by-doing
propagation mechanism.
The remainder of the paper is structured as follows. Section 2 contains the main empirical results. We …rst discuss the identi…cation strategy for news shocks and the data
used in the VAR analysis, followed by a discussion of the baseline results. We corroborate
these in an extensive robustness analysis. Section 3 introduces the theoretical model that
we use to rationalize the empirical …ndings with a focus on inventory modeling and the role
of knowledge capital. In section 4 we present the main quantitative results of the paper
based on a calibration analysis, while section 5 contains a simulation study that reconciles
the theoretical and empirical …ndings of the paper. Section 6 concludes.
2
Inventories and News: Evidence From an Identi…ed VAR
This section presents our key empirical …ndings: the positive response of inventories to news
shocks and the strong comovement with other macroeconomic aggregates. The results are
based on an estimated structural VAR where we identify news shocks based on the so-called
Max Share approach. We discuss the empirical model, the identi…cation scheme and the
data used in the estimation …rst, followed by the main empirical results and a wide-ranging
robustness analysis.
5
2.1
VAR-Based Identi…cation of News Shocks
We consider the following vector autoregression (VAR), which describes the joint evolution
of an n
1 vector of variables yt :
yt = A(L)ut :
(1)
A(L) = I + A1 L + ::: + Ap Lp is a lag polynomial of order p over conformable coe¢ cient
matrices fAp gpi=1 . ut is an error term with n
n covariance matrix
. We assume a linear
mapping between the reduced form errors ut and the structural errors "t :
ut = B0 "t ;
(2)
where B0 is an identi…cation matrix. We can then write the structural moving average
representation of the VAR:
yt = C(L)ut ;
(3)
where C(L) = A(L)B0 , "t = B0 1 ut , and the matrix B0 satis…es B0 B00 = . B0 can also
e0 D, where B
e0 is any arbitrary orthogonalization of
be written as B0 = B
and D is an
orthonormal matrix such that DD0 = I.
Identi…cation of news shocks in a structural VAR is based on the idea that information
about future movements of a variable such as TFP, namely news, generally a¤ects outcomes even before the shock is realized. At longer time horizons, however, it is likely that
the dominant sources of movements in TFP are its own anticipated and unanticipated components. This idea can be utilized explicitly as an identifying assumption for news shocks.
At the same time, a second assumption is needed to separate unanticipated shocks from
news shocks to TFP. Consistent with Barsky and Sims (2011) and Forni et al. (2014), we
impose a zero-impact restriction on TFP to recover the anticipated component based on
the assumption that news does not a¤ect TFP contemporaneously.
Mechanically, we identify the news shock by …nding a rotation of the identi…cation
e0 , which maximizes the forecast error variance of the TFP series at some …nite
matrix B
horizon. In this, we follow the Max Share approach of Francis et al. (2014). Speci…cally,
the h-step ahead forecast error is given by:
yt+h
Et
1 yt+h
=
h
X
=0
e0 D"t+h
A B
:
(4)
The share of the forecast error variance of variable i attributable to shock j at horizon h is
then:
Vi;j (h) =
e0i
Ph
=0 A
e0i
e0 Dej e0 D0 B
e 0 A0
B
0
j
Ph
=0 A
A0
ei
6
ei
=
Ph
e
=0 Ai; B0
Ph
=0 Ai;
0B
e 0 A0
0 i;
0
Ai;
;
(5)
where ei denotes a selection vector with one in the i-th position and zeros everywhere else.
e0 is therefore an n 1 vector
The ej vector picks out the j-th column of D, denoted by . B
corresponding to the j-th column of a possible orthogonalization and can be interpreted as
an impulse response vector.
At a long enough horizon h, variations in TFP are plausibly accounted for by anticipated
or unanticipated shocks to this variable. We thus write as an identifying assumption that:
V1;1 (h) + V1;2 (h) = 1;
(6)
where we assume that TFP is ordered …rst in the VAR system and that the unanticipated
and the anticipated (news) shocks are indexed by 1 and 2, respectively. We recover the
unanticipated shock as the innovation to observed TFP. It is therefore independent of the
identi…cation of the other n
1 structural shocks. The share of total TFP variance that
can be attributed to this shock at horizon h is thus V1;1 (h), while the remainder is due to
news shocks.
e0 to make this restriction on forecast
The Max Share approach chooses the elements of B
error variance share hold as closely as possible. This is equivalent to choosing the impact
matrix so that contributions to V1;2 (h) are maximized. Consequently, we choose the second
column of the impact matrix to solve the following optimization problem:5
Ph
0B
e
e 0 A0
0 i;
=0 Ai; B0
;
arg maxV1;2 (h) =
Ph
0
Ai;
=0 Ai;
s.t.
We restrict
0
= 1,
(7)
e0 (1; j) = 0, 8j > 1:
(1; 1) = 0, B
to have unit length to be a column vector of an orthonormal matrix. The
second and third constraints impose that a TFP news shock cannot a¤ect TFP contemporaneously.6 We therefore identify a TFP news shock from the estimated VAR as the shock
that: (i) does not move TFP on impact; and (ii) maximizes the share of variance explained
in TFP at a long but …nite horizon h.
2.2
Data and Estimation
We use quarterly U.S. data for the period 1983Q1 –2018Q2, which is guided by the observed
di¤erences in cross-correlation patterns of several macro-aggregates in samples before and
5
The optimization problem is written in terms of choosing conditional on any arbitrary orthogonalizae0 to guarantee that the resulting identi…cation belongs to the space of possible orthogonalizations of
tion B
the reduced form.
6
Kurmann and Sims (2019) do not impose this exclusion restriction since they argue that TFP is mismeasured and that therefore anticipated and unanticipated movements are indistinguishable at short horizons.
We show in the appendix that our results are robust to applying this and other identi…cation methods used
in the literature.
7
after the mid-1980s (e.g., Galí and Gambetti, 2009; Sarte et al., 2015). In particular,
McCarthy and Zakrajsek (2007) document that signi…cant changes in inventory dynamics
occur in the mid-1980s due to improvements in inventory management. Moreover, several
of the time series that we use in the analysis, such as total business inventories and its
sectoral components, are only available over part of the post-Great Moderation sample. In
our robustness analysis, we document that our results hold also for a longer sample, data
availability permitting.
We consider two di¤erent measures of total inventories in the VAR. First, non-farm
private inventories, which are de…ned as the physical volume of inventories owned by private
non-farm businesses. These are valued at average prices of the period, which captures the
replacement costs of inventories. Our second measure, business inventories, di¤ers from the
…rst in how the inventory stock is valued, namely by the cost at acquisition, which can
be di¤erent from the replacement cost. In NIPA data, inventory pro…ts and losses that
derive from di¤erences between acquisition and sales price are shown as adjustments to
business income. Unfortunately, business inventories are available only from 1992Q1 on.
We therefore reduce the sample horizon accordingly if they are included in the VAR.7
Output is measured by GDP, and total hours as hours worked of all persons in the nonfarm business sector. Investment is the sum of …xed investment and personal consumption
expenditures for durable goods. Fixed investment is the component of gross private domestic
investment that excludes changes in private inventories. Finally, consumption is de…ned as
the sum of personal consumption expenditures for non-durable goods and services. The time
series are seasonally adjusted and expressed in real per-capita terms using total population,
except for hours, which we do not de‡ate. In addition to the quantity aggregates, we also use
a measure of in‡ation that we construct from the GDP de‡ator and a consumer con…dence
indicator that is based on the University of Michigan Consumer Sentiment Index.8 This set
of variables is standard in the literature, apart from inventories. The consumer con…dence
measure provides forward-looking information that potentially captures expectations or
sentiment.9
7
Apart from robustness considerations, the use of business inventories is appealing since this measure is
available at a disaggregated level for di¤erent sectors and inventory types, which we subsequently also use
in the VAR.
8
This indicator, labeled E5Y, summarizes responses to the following question: “Turning to economic
conditions in the country as a whole, do you expect that over the next …ve years we will have mostly good
times, or periods of widespread unemployment and depression, or what?” The indicator is constructed as a
di¤usion index, namely as the percentage of respondents giving a favorable answer less the percentage giving
an unfavorable answer plus 100.
9
See, for instance, Barsky and Sims (2012). An alternative measure to capture forward-looking information is the S&P 500 stock price index. Our results are robust to including the S&P 500 instead of the
8
Key to identifying the news shock is a measure of observed technology. We follow
the convention in the empirical literature and use the measure of utilization-adjusted TFP
provided and regularly updated by Fernald (2012).10 We identify TFP news shocks from
the estimated VAR using the Max Share method outlined in the previous section. Following
Francis et al. (2014) we set the horizon h to 40 quarters. All variables enter in levels in line
with the news shock VAR literature (e.g., Beaudry and Portier, 2004; Barsky and Sims,
2011). We use Bayesian methods to estimate the VAR with three lags for a Minnesota
prior. Con…dence bands are computed by drawing from the posterior.
2.3
Results
Figure 1 shows impulse response functions to an identi…ed TFP news shock in the speci…cation with private non-farm inventories. What is striking is that all activity variables
increase prior to a signi…cant rise in TFP. In response to news about higher future productivity, TFP does not move signi…cantly for the …rst 12 quarters. This pattern extends
considerably beyond what is imposed by the zero impact assumption of no movements of
TFP in the …rst period. The TFP response peaks toward the end of the horizon.
In contrast, all quantity variables signi…cantly rise on impact and follow a hump-shaped
pattern. Moreover, the peak response occurs considerably before TFP hits its highest
point. Positive comovement between output, consumption, investment, and hours over this
post-Great Moderation sample has been documented before, for instance by Görtz et al.
(2017). We add to these previously established stylized facts the behavior of private nonfarm inventories, which respond in a similar manner to a news shock: they rise somewhat
on impact and continue to do so in a hump-shaped pattern until reaching a peak at about
10 quarters. The change in the stock of inventories, inventory investment, is negative
afterwards, while its level never falls below the zero line, its starting point.11
As a robustness exercise, we also consider longer sample periods for the speci…cation
with non-farm private inventories, namely samples starting in 1948Q1 and 1960Q1. These
results are reported in the online appendix. We …nd that the impulse response patterns
identi…ed in our baseline speci…cation carry over to the two longer samples qualitatively
and to a large extent also quantitatively. Overall, across these di¤erent samples, the TFP
Michigan consumer con…dence index which we document in the online appendix.
10
We use the 2018 vintage, which contains updated corrections on utilization from industry data.
11
We also report a short-lived decline in in‡ation and an anticipation of the future increase in TFP in the
consumer con…dence indicator, both of which are consistent with previous …ndings. The signi…cant increase
in consumer con…dence validates our news shock identi…cation and con…rms existing literature (e.g., Barsky
and Sims, 2011).
9
news shock is important for ‡uctuations in inventories and GDP as it explains between
47-65% and 47-71% of the forecast error variance in inventories and GDP, respectively, over
a horizon between 6-32 quarters.12
Figure 2 reports the impulse response functions of the speci…cation with business inventories. By necessity, this sample is shorter as the inventory series and its subcomponents
are only available since 1992Q1. We consider this alternative speci…cation important as it
is not a priori obvious at which prices inventories should be measured. The …gure shows
that the rise in inventories prior to TFP is robust when we use the business inventory series.
All variables exhibit qualitative responses that are very similar to the baseline, although
the shorter sample results in somewhat wider con…dence bands. Overall, this speci…cation
con…rms the comovement of macroeconomic aggregates, including inventories, in response
to an anticipated TFP shock and prior to the rise in TFP itself.
In the next step, we study the e¤ects of news shocks on inventories in the manufacturing, wholesale, and retail sectors, which comprise the overwhelming majority of inventory
stocks. Figure 3 shows the responses of business inventories in each of these sectors to the
aggregate TFP news shock. The VAR is estimated by including the sectoral inventories one
by one instead of the aggregate inventory measure. The sectoral impulse responses exhibit
almost identical hump-shaped patterns: a rise on impact towards a peak response around
10 quarters before declining gradually over the forecast horizon. These results support the
…nding from the aggregate baseline speci…cation in that the expansion of the inventory stock
and other variables is broad-based across sectors.
We also dig deeper into the composition of inventory holdings. The two trade sectors,
wholesale and retail, hold almost entirely …nished goods inventories, while the inventory
stock in the manufacturing sector is split across …nished goods inventories (36%), work in
process (30%) and input inventories in the form of materials and supplies (34%) over the
restricted 1992Q2–2018Q2 sample period for business inventories and their components.
Figure 4 shows the responses of inventory types in the manufacturing sector when included
one by one in the VAR.13 Finished goods and input inventories in the manufacturing sector
rise strongly before the realization of anticipated higher productivity as in the baseline
speci…cation and all other variations considered above.
We can summarize our …ndings at this point as follows. Evidence from an identi…ed
VAR shows that a news shock about higher future productivity leads to an increase and
12
The full set of results from the variance decomposition is reported in the online appendix.
The responses of the other variables in the VAR are very similar to the ones reported in Figure 2 and
are available upon request.
13
10
subsequent positive comovement of all aggregate variables considered. The new fact that
we document is that this pattern extends to the response of inventories and is broad-based
across di¤erent aggregate measures, sectors, and types of inventories. Why the behavior
of inventories follows this pattern is a priori not obvious. Conceivably, they could decline
initially to satisfy higher demand instead of higher production. Moreover, higher TFP in
the future reduces the cost of replenishing a drawn down inventory stock. At the same time,
…rms may increase inventories to maintain a desired inventory-sales ratio, which counters
this e¤ect. It is along these margins that the success of a theoretical model to replicate the
empirical …ndings rests.14
Jaimovich and Rebelo (2009) document the necessary model elements to facilitate comovement of consumption and investment in response to news about future higher TFP.
Speci…cally, they show that a strong increase in utilization and hours worked are key components. Positive news stimulates consumption through a wealth and income e¤ect. The
latter is driven by increased hours worked to raise production in order to satisfy that demand. Similarly, investment increases to support the higher capital stock to take advantage
of higher future TFP. This reasoning is corroborated in our structural VAR, where we add
additional variables one at a time. Selective impulse responses to a TFP news shock are
reported in Figure 5.15
We …nd a strong increase in capital utilization which turns negative after about four
years once a su¢ ciently larger capital stock is in place. The positive hump-shaped response
of the real wage is consistent with the increase in hours documented in Figure 1. The pattern
of the real wage is also indicative of a hump-shaped increase in knowledge capital. Figure
5 further shows that the inventory-to-sales ratio moves countercyclically in response to a
news shock. This is a key observation that informs our thinking about a theoretical model.
Countercyclicality of the inventory-to-sales ratio is a necessary condition for comovement
14
Görtz et al. (2019) construct aggregate measures of debt and equity cost of capital and implied cost-ofcapital measures from …rm-level data. In response to a TFP news shock, all measures decline signi…cantly
prior to the realization of higher TFP. We also study the response of various measures of marginal cost to
a TFP news shock. However, none of these measures shows a decline in marginal costs that would point to
a strong incentive to run down current inventories and build up stocks again once the higher productivity
is realized. Overall, we …nd evidence against a strong negative substitution e¤ect, but support for a strong
positive demand e¤ect. This …nding serves further to motivate a demand-enhancing motive for holding more
inventories in line with Bils and Kahn (2000).
15
The inventory-to-sales ratio is the ratio of private non-farm inventories and …nal sales of domestic
business as in Lubik and Teo (2012). Utilization is provided by Fernald (2012) and consistent with our
utilization-adjusted measure for TFP. The real wage is compensation of employees, non-…nancial corporate
business, in real per-capita terms. The change in inventories is the change in private non-farm inventories.
The series for intellectual property products is real per-capita nonresidential intellectual property products
available from the Bureau of Economic Analysis.
11
of inventories with the other macroeconomic aggregates. The literature on inventories often
does not only consider their level but also their change, which provides an indication about
inventory investment. The fourth subplot in Figure 5 shows a positive response of inventory
investment in light of a TFP news shock. It peaks at about four quarters before it declines
towards zero. This pattern is broadly consistent with the response of the level of inventories
documented in Figure 1.
Finally, we include intellectual property products in the VAR to provide suggestive
evidence for a possible channel of how news propagates and a¤ects the production process.16
The third subplot in the …gure shows that intellectual property products rise in response to
a news shock, commensurate with the behavior of other variables considered so far. This
suggests that a key component of a news-driven business cycle model that is consistent
with the empirical evidence is the accumulation of knowledge, residing with households as
human capital or embodied in physical capital. In the next section we build a theoretical
model along these lines.
3
A News Shock Driven Business Cycle Model with Inventories
We now develop a business cycle model that rationalizes the …ndings of the empirical analysis. The core of the model is the framework of Jaimovich and Rebelo (2009), which includes
a particular speci…cation of preferences, investment adjustment costs and costly capacity
utilization. This model has become the workhorse model in the news shock literature designed to capture comovement of consumption, investment and hours-worked in response to
news about TFP. We augment this model with two additional elements. First, we introduce
inventories as in Lubik and Teo (2012), based on the stock-elastic demand model of Bils
and Kahn (2000), where …nished goods inventories are sales-enhancing.17 Second, we add
intangible capital as an additional input into production. We think of this input as capturing knowledge that evolves over time as a learning-by-doing process. Following Chang et al.
(2002) and Cooper and Johri (2002), we assume that households acquire new technological
knowledge through their experiences in supplying labor to the production process. This
aspect of the model is key to capturing the behavior of inventories to news shocks that we
16
We are not aware of any direct and readily available empirical measure of knowledge capital as interpreted
in this paper. We thus provide an indication by capturing some of the e¤ects with this proxy.
17
Our framework thereby abstracts from materials or input inventories that are unquestionably important
but constitute the smaller part of total inventories in the data.
12
see in the data.18
3.1
Model Environment
The model economy consists of a representative in…nitely lived household, a competitive
intermediate goods-producing …rm, a continuum of monopolistically competitive distributors, and a competitive …nal goods producer. The intermediate goods …rm owns its capital
stock and produces a homogeneous good that it sells to distributors. This good is then
di¤erentiated by the distributors into distributor-speci…c varieties that are sold to the …nalgoods …rm. The varieties are aggregated into …nal output, which then becomes available for
consumption or investment. We adopt this particular decentralization since it is convenient
for modeling …nished goods inventories by separating the production side of the economy
into distinct production, distribution, and …nal goods aggregation phases. Following Chang
et al. (2002), we assume that the household accumulates knowledge capital and supplies
e¤ective labor to …rms as the product of knowledge capital and hours worked. The model
economy contains several stochastic shock processes. We include a suite of other shocks in
addition to the TFP shocks to facilitate estimation and simulation later in the paper.
3.1.1
Household and Government
The household’s lifetime utility is de…ned over sequences of consumption Ct and hours
worked Nt :
E0
1
X
t
Ct
Nt Ft
t
1
t=0
where:
1
F t = Ct f F t
f
1
1
1
;
(8)
(9)
is a preference component that makes consumption and labor non-time-separable and is
consistent with the balanced-growth path in a growing economy. This preference structure is based on Jaimovich and Rebelo (2009) and nests the no-income e¤ect structure of
18
The idea of learning-by-doing, and in particular skill-accumulation through work experience, has a long
history in labor economics, where empirical researchers have found a signi…cant e¤ect of past work e¤ort
on current wage earnings. Both Chang et al. (2002) and Cooper and Johri (2002) study the propagation
properties of learning-by-doing in the context of business cycle models. Since then various researchers have
exploited these properties to help business cycle models better …t various features of the data. This includes
Gunn and Johri (2011), who show how learning-by-doing can yield comovement of consumption, investment,
hours worked, and stock prices in response to TFP news. More recently, d’Allesandro et al. (2019) extend a
standard New Keynesian model with learning-by-doing to account for the response of various macroeconomic
aggregates to a government spending shock.
13
Greenwood et al. (1988) in the limit as
preference shock process, and 0 <
< 1,
f
tends toward zero.
> 0,
> 1,
t
is a stationary stochastic
> 0, and 0 <
f
1.
The household owns the stock of physical capital Kt . Each period, it rents capital
e t = ut Kt to the intermediate goods producers at a rental rate rt , whereby ut is
services K
the utilization rate of the capital. The capital stock evolves according to:
Kt+1 = [1
(ut )] Kt + mt It [1
where ( ) is a depreciation function that satis…es
0 <
k
0
S (It =It
( ) > 0,
00
1 )] ;
( ) > 0 and (1) =
(10)
k,
with
< 1. mt is a stationary exogenous stochastic process and captures the marginal
e¢ ciency of investment. S ( ) is an investment adjustment cost function as in Christiano et
al. (2005) with S g I = S 0 g I = 0 and S 00 g I = s00 > 0, where g I is the steady state
growth rate of investment.
We assume that the household accumulates knowledge capital Ht according to:
Ht+1 = Ht h Nt h ;
where 0
h
< 1, and
h
(11)
> 0.19 It represents the household’s state of technological
knowledge (or skill level) based on past labor supplies in the vein of the learning-by-doing
framework of Chang et al. (2002). The household gains knowledge as it engages with the
production process through supplying labor.20 The household’s skill level directly a¤ects
et = Ht Nt , for which it earns the wage
the e¤ective units of labor supplied to the …rms, N
wt . This element is the key mechanism that explains the inventory response to a news
shock in our framework. It helps suppress the rise in marginal costs during the demanddriven expansion phase of the news boom. This e¤ect of learning-by-doing on inventories
is novel within the literature.21 Moreover, this particular extension also has a distinct
advantage in terms of its parsimony: it adds only an additional input into production and
an accumulation equation, while leaving the other elements of the model una¤ected. In
addition, it nests the more standard model without intangible capital.
19
The log-linear speci…cation used by Chang et al. (2002) and d’Alessandro et al. (2019) is common in
the literature.
20
In this speci…cation, knowledge capital is stationary due to the stationarity of hours-worked even in
a growing economy. This implies that the long-run growth path of output is determined by exogenous
technological factors only. This form of knowledge capital can be thought of as an index, which conditions
on the e¤ect of hours in production over the business cycle, as the household responds to ‡uctuations in the
exogenous stochastic drivers of growth.
21
The general aspect of learning-by-doing as a supply-side mechanism that enhances the dynamics of
business cycle models is, of course, not new. While learning-by-doing has a long history in studying long-run
issues such as growth, e.g. in Arrow (1962), more recent work such as Chang et al. (2002), Cooper and Johri
(2002), and Gunn and Johri (2011) examines the mechanism in terms of its propagation characteristics in
response to various business cycle shocks (including TFP news shocks).
14
The household’s budget constraint is given by:
Ct +
where
t
t It
et + rt ut Kt +
+ Tt = wt N
t;
(12)
is a non-stationary exogenous stochastic investment-speci…c productivity process,
Tt denotes lump-sum taxes, and
that the growth rate of
t,
t
captures collective pro…ts ‡owing from …rms. We assume
namely gt =
t=
t 1,
is stationary. Revenues from taxation go
directly to government spending Gt , where we assume that the budget is always balanced
such that Gt = Tt . Furthermore, government spending follows the process Gt = 1
1
"t
Yt ,
where "t is a stationary stochastic government spending shock.
The household chooses sequences of Ct , It , Nt , ut , Kt+1 and Ht+1 to maximize intertemporal utility subject to the constraints above. In the following, we only highlight those
optimality conditions with a direct impact of knowledge capital, namely optimal choices for
Nt and Ht+1 , since the remainder are standard.22 Respectively, we have:
t Ft Vt
Nt
h Ht+1
;
h t
Nt
1
=
t wt Ht
+
h
t
=
Et
t+1 wt+1 Nt+1
+
where Ft is the utility component de…ned above and Vt = Ct
function to ease notation;
t
and
h
t
(13)
h Ht+2
h t+1
Ht+1
;
(14)
Nt Ft is the periodic utility
are the multipliers on the household’s budget constraint
and the law of motion for knowledge capital.
The presence of knowledge capital adds an additional term into the household’s optimality condition for supplying labor, equation (13). This drives a wedge between the marginal
utility of leisure and the marginal contribution of hours to earnings, which serves as a shift
to the labor supply. All else equal, a rise in the value of knowledge capital
h
t
increases labor
supply as the household desires to increase its knowledge by engaging in production. The
optimality condition for Ht , equation (14), then describes the marginal value of knowledge
as a function of the expected discounted value of its marginal contribution to wage earnings
next period and the continuation value of that knowledge capital. The intertemporal accumulation of knowledge capital makes it worthwhile to increase labor on the arrival of news
despite the potential presence of a wealth e¤ect that dominates standard models. Once
knowledge capital is in place, the returns are higher than they otherwise would be in the
face of higher future productivity. We now turn to the production side of the model to
develop this link.
22
We list the full set of optimality conditions in the online appendix.
15
3.1.2
Intermediate Goods Firm
The competitive intermediate goods …rm produces the homogeneous good Yt using the
technology:
e
where
t
e1
K
t
t Nt
Yt =
;
(15)
is a non-stationary exogenous stochastic productivity process. We assume that the
growth rate of
t,
namely gt =
t= t 1,
is stationary. In each period, the …rm acquires
et at wage wt from the labor market, and capital services K
e t at rental
e¤ective labor N
rate rt from the capital services market. It then sells its output Yt at real price
t
to the
distributors.
et and K
e t to maximize Y =
The …rm’s pro…t maximization problem involves choosing N
t
e
e
wt Nt rt Kt subject to the production function. This results in standard demand
t Yt
functions for labor and capital services, respectively: wt =
Yt
t e
Nt
and rt = (1
)
Yt
t e .
Kt
Additionally, we …nd it convenient to de…ne the marginal cost of production for intermediate
et is the marginal product of e¤ective labor. It then
goods as mct = wt , where M P N
et
MP N
follows from the intermediate goods …rm’s …rst-order condition that the output price
t
is
equal to the the marginal cost of production mct .
3.1.3
Final Goods Firm
The competitive …nal goods …rm produces goods for sale St by combining varieties Sit ,
i 2 [0; 1] according to the technology:
St =
Z
1
0
where
it
1
1
1
it Sit di
;
> 1;
(16)
is a taste shifter that depends on the stock of goods available for sale Ait . The
latter is composed of current production and the stock of goods held in inventory.23 We
assume that
it
is taken as given by the …nal goods producer:
it
=
Ait
At
;
> 0:
At is the economy-wide average stock of goods for sale, given by At =
(17)
R1
0
Ait di. The
parameters and capture, respectively, the elasticity of substitution between di¤erentiated
goods and the elasticity of demand with respect to the relative stock of goods.
23
This structure follows Bils and Kahn (2000) and is standard in modeling demand for goods drawn from
inventories. It also supports a convenient decentralization of production.
16
The …rm acquires each variety i from the distributors at relative price pit = Pit =Pt , where
R1
Pt = 0 Pit 1 di is the aggregate price index. It sells the …nal good for use in consumption
or as an input into the production of investment goods. The …rm maximizes the pro…t
R1
function st = pit St
0 pit Sit di by choosing Sit , 8i. This results in a demand function for
Sit for the ith variety:
Sit =
An increase in
it
it pit
St :
(18)
shifts the demand for variety i outwards. This preference shift is in‡uenced
by the availability of goods for sale of variety i, relative to aggregate sales, which thereby
provides an incentive for …rms to maintain inventory to drive customer demand and avoid
stockouts.
3.1.4
Distributors
We now close the production side of the model by introducing inventories at the level of the
distributors. In the nomenclature of the literature, these are …nished goods or output inventories that are ready for sale. Intuitively, they can be thought of as warehouses attached to
retail establishments. We follow Bils and Kahn (2000) in modeling inventories as a mechanism that helps generate sales, while at the same time implying a target inventory-sales
ratio that captures the idea of stockout avoidance. In addition, this modeling framework
creates a wedge between the marginal cost of producing …nished goods and the marginal
cost of generating a sale, which can come either from inventory stock or new production. It
is this margin along which the substitution e¤ect of inventories in response to news shocks
operates.
Distributors acquire the homogenous good Yt from the intermediate goods …rms at real
price
t.
They di¤erentiate Yt into goods variety Yit at zero cost, with a transformation
rate of one-to-one. Goods available for sale are the sum of the di¤erentiated output and
the previous period’s inventories subject to depreciation:
Ait = (1
x ) Xit 1
+ Yit ,
(19)
where the stock of inventories Xit are the goods remaining at the end of the period:
Xit = Ait
and 0 <
x
Sit ,
(20)
< 1 is the rate of depreciation of the inventory stock.
The distributors have market power over the sales of their di¤erentiated varieties. The
ith distributor sets price pit for sales Sit of its variety subject to its demand curve (18).
17
Each period, a distributor faces the problem of choosing pit , Sit , Yit , and Ait to maximize
pro…ts:
Et
1
X
k
t+k
[pit+k Sit+k
t Yit+k ] ;
(21)
t
t=0
subject to the demand curve (18), the law of motion for goods available for sale (19), and
the de…nition of the inventory stock (20). Pro…t streams are evaluated at the household’s
marginal utility of wealth
t.
Substituting the demand curve for Sit , and letting
a
t
and
x
t
be
the multipliers on the two other constraints, we can then …nd a representative distributor’s
…rst-order conditions:
t
=
a
t;
x
t
= (1
a
t
=
(22)
x)
Et
t+1
t
pit
Sit
+
Ait
x
t
a
t+1 ;
(23)
Sit
Ait
1
;
(24)
x
;
1 t
which are, respectively, the optimal choices of Yit , Xit , Ait , and Pit .
pit =
(25)
The distributor’s optimality conditions allow us to connect the varying marginal costs
of production, sales, and inventory holdings in an intuitive manner. The law of motion for
Ait , equation (19), implies that inventories at the beginning of a period are predetermined.
A distributor can only further increase its stock of available goods for sale by acquiring
additional output Yit , which has to be purchased at price
t.
Therefore, the cost of gener-
ating an additional unit of Ait is equal to the price of output, that is, its marginal cost of
production mct , as derived from the intermediate …rm’s pro…t maximization problem. At
the optimum, equation (22) implies that the cost of an additional unit of goods for sale
is equal to the value of those goods for sale, namely
t
a.
t
The inventory de…nition (20) implies that for a given level of goods available for sale,
any increase in sales results in a reduction in stock holdings. The opportunity cost of sales
for the distributor is equal to the value of foregone inventory
x,
t
which can be thought of
as the marginal cost of a sale. The optimality condition (23) relates the current value of
an additional unit of inventory to the expected discounted value of the extra level of goods
available for sale next period generated by holding inventory. This, in turn, equals the price
of future output. We can therefore conclude that in this model of inventory holdings the
marginal cost of sales is equal to the expected discounted value of next period’s marginal
cost of output. Increasing sales by drawing down stock in order to forgo production today
means that the distributor will need to increase production eventually in the future.
18
The optimality condition (24) connects the marginal value
a
t
of a unit of goods available
for sale to the value of the extra sales generated by the additional goods available plus the
value of the additional inventory yield from the unsold portion of the additional goods. We
can combine the marginal cost expressions to derive:
t
= pit
Sit
+ (1
Ait
x)
Et
t+1
t+1
1
t
Sit
Ait
:
(26)
This equation implies that the distributor chooses Ait , such that the bene…t of accumulating
goods for sale, either via purchasing new production or stocking inventory, is equal to the
marginal cost of output
t.
We will refer to this equation as the distributor’s optimal
stocking condition.
Finally, the optimal pricing choice (25) sets the distributor’s relative price as a constant
markup over the marginal cost of sales. In standard ‡exible price models with imperfect
competition, but without inventories, the marginal cost of sales is equal to the marginal
cost of output. It follows that the pricing condition is the same as in the standard model.
However, the presence of inventories drives a wedge between the marginal costs of output
and of sales to the e¤ect that there is no longer a constant markup but one that varies with
the value of foregone inventory
x.
t
Essentially, the optimality condition combines two types
of markups: those between marginal costs of output and of sales, and the markup between
the marginal cost of sales and price.
The optimal stocking condition (26) describes the adjustment of the …rst markup through
inventories; the optimal pricing condition (25) describes the adjustment of the second
markup through price-setting. With ‡exible prices the latter markup is constant, but the
former is not. The total markup between marginal cost of output and price varies as the
distributors use inventories to adjust the markup between marginal cost of production and
the marginal cost of sales. We can thus combine the distributor’s optimality conditions into
equations at the aggregate level that re‡ect the trade-o¤s faced by inventory accumulation
in terms of the various marginal cost concepts:
1
= (1
x)
t+1
Et
t+1 ;
(27)
t
t
=
St
+
At
1
;
(28)
where we have imposed symmetry on the monopolistic agents’actions. We now turn to a
discussion of the stochastic driving processes and calibration of the model before presenting
the results from a …rst quantitative evaluation of the theoretical model.
19
3.2
Model Solution and Calibration
The model economy contains …ve stochastic processes: a preference shock
t,
a shock to the
marginal e¢ ciency of investment mt , a shock to the growth rate of permanent investmentspeci…c productivity gt , a government spending shock "t , and a shock to the growth rate
of non-stationary productivity gt . We assume that these stochastic processes follow individually stationary …rst-order processes and are mutually uncorrelated. We allow for news
shocks to all stochastic processes with the exception of the preference shock. We thus
assume that the innovation ujt , j 2 mt ; gt ; "t ; gt , in a shock process contains both antic-
ipated and unanticipated components. Moreover, news signals arrive with horizons of 4, 8
and 12 quarters as is standard in the literature. The innovations are thus given by:
ujt =
where
0
jt
0 + 4
jt
jt 4
0 ;
jt
+
8
jt 8
+
12
jt 12 ;
j = mt ; gt ; "t ; gt
j= t
is an unanticipated shock, whereas for h = 4; 8; 12,
agents receive in period t
p
jt h
;
(29)
is a news shock that
h about the innovation in time t. All innovations are mean zero
and uncorrelated over time and with each other.
The model economy contains two non-stationary stochastic processes, for productivity
t
and for investment-speci…c productivity
t.
In order to …nd a stationary solution for the
model, we express the variables in terms of deviations from their respective stochastic trends.
Speci…cally, we divide non-stationary variables by their permanent component to yield a
stationary version of the model. The resulting equation system is then linearized around the
steady state of the stationary system and solved using standard methods for linear rational
expectations models. The original levels of the trending variables can be recovered by
adding the respective stochastic trends back in. The stochastic trend components of output
and capital are given by Xty =
1
t
t
and Xtk =
1
t
t,
respectively. The stochastic
trends of all another non-stationary variables can then be expressed as some function of Xty
and Xtk . We provide the details of this transformation and show the resulting stationary
equilibrium system in the online appendix.
We report the baseline calibration in Table 1. Our choice of parameter values is guided by
the existing literature where we strive to maintain comparability with Jaimovich and Rebelo
(2009) and Schmitt-Grohé and Uribe (2012) for the aspects of the news shock mechanism,
Lubik and Teo (2012) for the inventory component, and Chang et al. (2002) and Gunn and
Johri (2011) in terms of knowledge capital. We conduct a robustness analysis for the key
parameters underlying our mechanism in section 4.3.
We set the household’s discount factor
to 0.9957, which is implied by the real interest
20
rate computed from average in‡ation and the federal funds rate over our sample period.
The elasticity of intertemporal substitution is as in Jaimovich and Rebelo (2009),
The disutility of working parameter
= 1.
is set to 2, which implies a unit Frisch elasticity of
labor supply. This choice places us between the ranges found in Christiano et al. (2005),
Jaimovich and Rebelo (2009), and Schmitt-Grohé and Uribe (2012). Finally, we set
f,
the
preference parameter that determines the strength of the income e¤ect, to 0.01 based on
Schmitt-Grohé and Uribe (2012).
On the …rm side, we set the elasticity parameter in the production function to
= 0:64
as in Jaimovich and Rebelo (2009). For the parameters related to physical capital, we
…x steady-state physical capital depreciation at
utilization
00
0
k (1)= k (1)
= 0:025 and the elasticity of marginal
= 0:15. There is a wide range of values for this elasticity to be
found in the literature. For example, Christiano et al. (2005) …nd estimates of 0:01, while
Schmitt-Grohé and Uribe (2012) have 0:34, and Smets and Wouters (2007) report 0:54. We
choose a value of 0:15 within this range, close to the value of 0:25 used in Jaimovich and
Rebelo (2009). In our robustness analysis we …nd that our results are essentially invariant
to a wide range of these values. Similarly, the literature also …nds a wide range of values
for the investment adjustment cost parameter s00 . Smets and Wouters (2007) estimate it
to be 5:7, Christiano et al. (2005) …nd 2:48, and Schmitt-Grohé and Uribe (2012) 9:1. We
choose the middle ground in this range and set s00 = 5.
The parameters related to inventories are based on the empirical estimates in Lubik and
Teo (2012). The inventory depreciation rate
x
is set to 0:05. The taste shifter curvature
is chosen as 0:67 to yield a steady-state sales-to-stock ratio of 0:55, as in Lubik and
Teo (2012). The goods aggregator curvature parameter
is set to 6:8, which results in a
steady-state goods markup of 10%. We assume constant returns to scale in the knowledge
accumulation equation, setting
h
= 0:75, the contribution of prior knowledge capital in its
own production, which implies
h
= 0:25.
Finally, a number of steady-state parameter values are implied by average values in
the data, such as the (quarterly) steady-state growth rates of GDP g y and the relative
price of investment (RPI) g RP I , which we …nd to be 0:43 and
0:58, respectively (for
further discussion and derivation see the online appendix). We also set the steady-state
government-spending ratio to output to g=y = 0:18 following Smets and Wouters (2007)
and target a level of hours in steady state of 0:2, while steady-state capacity utilization is
targeted at one. We choose the persistence parameters of the TFP shock process
= 0:95
for the calibration analysis alone. The variances and persistence parameters of all shocks
21
are later estimated using likelihood-based methods.
4
Model Results
Our analysis focuses on the model’s behavior when subjected to TFP news shocks. We aim
to identify the modeling elements needed to understand the empirical facts we uncovered in
section 2. We …rst study the dynamic responses of the key variables to TFP news shocks.
In the next step, we disentangle the contribution of the modeling components in generating
these outcomes. Finally, we assess the robustness of our baseline calibration to alternative
parameter choices. We leave it to section 5 to contrast the simulation …ndings from the
theoretical model with the empirical VAR more formally.
4.1
Response to News Shocks
We …rst investigate the response of our model economy to a non-stationary TFP news shock,
which corresponds conceptually to the identi…ed shock in the empirical VAR analysis. In
Figure 6 we report the impulse responses of key model variables to current news about a
future increase in TFP that will be realized in 12 quarters as anticipated (solid blue lines).
The actual behavior of TFP is depicted in the bottom right hand corner of the panel. When
the shock materializes, TFP rises quickly to its new long-run level since the level of TFP is
a random walk with drift. All other variables either rise on arrival of the news or increase
steadily. Notably, output increases on impact on account of a strong hours and capacity
utilization response.
In addition, inventories increase on impact and continue rising through the boom before
the actual increase in TFP. Over the adjustment period, until the actual TFP rise occurs,
the expansion is supported by a rise in investment and thus capital. With higher TFP in
place in period 12, activity continues to expand and eventually overshoots after around 5-6
years when the wealth and income e¤ects take hold. Figure 6 shows that in response to
news about a future increase in TFP, inventories rise over time, which is the central …nding
from the VAR results and substantiated by our theoretical model. Before we demonstrate
how the knowledge capital mechanism produces procyclical inventory movements we …nd it
helpful to …rst discuss how this channel drives an expansion in hours and output.
The value of an additional unit of knowledge capital today,
h,
t
depends on the additional
future wage earnings that knowledge capital yields (see the household’s …rst-order condition
for labor, equation (13)). When news about higher future TFP arrives, the household anticipates that wages will be high in the future relative to today as TFP eventually increases.
22
This raises the marginal value of having additional knowledge in terms of higher wage earnings in the future and drives up the current value of knowledge capital
h
t
in a manner that
is complementary to the e¤ect of higher TFP and physical capital. The rise in
h
t
shifts the
household’s labor supply curve outwards as it seeks to increase its knowledge by supplying
additional labor. This, in turn, suppresses the real wage rise, which contributes to an increase in hours and thereby output. In that sense, the mechanism behind the knowledge
capital channel is akin to the physical capital channel, whereby the household builds up its
knowledge base to take advantage of higher productivity in the future.24
4.2
Understanding Inventory Dynamics
We now turn to a discussion of the behavior of inventories in our model and show how the
introduction of knowledge capital into a standard news shock framework is the key element
for understanding the comovement we uncovered in the empirical section. The exposition
centers on the optimal stocking condition from the distributor’s …rst-order conditions:
t
=
St
+
At
1
=
1
+
1 + Xt =St
1
;
(30)
which governs inventory dynamics in the model. It implies that the distributor targets
a speci…c sales-to-stock ratio
St
At
=
St
St Xt
=
1
1+Xt =St ,
St
At ,
or equivalently, a speci…c inventory-sales ratio
for a given level of marginal costs
t.
Xt
St ,
since
All else equal, the distributor
increases inventory holdings along with a rise in sales, what may be labeled the demand
channel, and reduces it along with a rise in current marginal costs, the cost channel.25
We now consider the e¤ects of a TFP news shock on the joint dynamics of inventories
and their determinants. We …nd it convenient to frame the discussion in terms of demand
and supply schedules in the market for produced output Yt with market-clearing price
t,
24
We note that the mechanism and crucial modeling elements identi…ed by Jaimovich and Rebelo (2009)
are in operation here in addition to the new knowledge capital mechanism. In the former, given the particular
form of investment adjustment costs, the shadow value of capital declines today on account of the value of
increasing investment today so as to lower future adjustment costs. This, in turn, leads to a reduction in
the cost of capacity utilization and as a result an outward shift in labor demand by the intermediate goods
…rm, whose cost depends inversely on the value of capital, as it increases capacity utilization.
Gunn and Johri (2011) show that the knowledge capital mechanism on its own is su¢ cient to induce comovement of consumption, investment, and hours in the absence of the Jaimovich and Rebelo (2009) mechanism. In our framework, the low-income e¤ect preferences and variable capacity utilization of Jaimovich
and Rebelo (2009) help to enhance the boom, while variable capacity utilization helps suppress the rise in
marginal costs.
25
1
1
The constant term
represents the expected value of future marginal costs since
=
t+1
(1
x ) Et
t+1 . When adjusting inventory holdings, the distributor considers the level of marginal
t
costs today relative to expected future marginal costs, which can be described as an intertemporal substitution channel. Since the former is constant, only variation in the latter impacts inventory. The constancy
of expected future marginal costs is an artifact of ‡exible prices in the current model.
23
which is also the marginal cost of production. The optimal stocking condition above can
thus be thought of as a demand curve for Yt . We can rewrite it as:
t
=
St
x ) Xt
(1
which is downward-sloping in (Yt ,
t )-space.
1
+ Yt
+
1
;
All else equal, higher
(31)
t
implies a lower
inventory-sales ratio, and thus lower demand for Yt , as distributors seek to run down inventory stock. Similarly, an increase in sales shifts the curve outward and raises the demand
for Yt as the distributors seek to maintain their sales-inventory ratio by increasing their
holdings.
We can combine the household’s labor supply conditions, the intermediate …rm’s labor
demand, and the production technology to derive a supply curve for output as a function
of
t.
Abstracting from the (small) income e¤ect (
normalization of the preference shock
t
@ t
@Yt
=
1
Yt
t
f
= 0) for ease of exposition and
to unity, this results in:
Qt
Yt
h
h
t
Ht+1 ;
(32)
t
> , so that the curve is upward-sloping for reasonably elastic labor suph
h
e 1 , and t Ht+1 = Et t+1
ply, all else equal. We note that Qt = t K
t+1 Yt+1 + h t+1 .
t
t
t
where
> 0 for
A rise in the value of knowledge capital
h
t
shifts the output supply curve outward as the
household increases its labor supply in order to acquire more knowledge. This lowers the
real wage for a given level of hours and implies a reduction in marginal cost for a given level
of output. We depict the supply and demand curves for output Yt at marginal cost
t
in
Figure 7.
We can now study the response of inventories to TFP news using their impact on supply
and demand in the market for produced output. Arrival of positive news about future TFP
movements implies a wealth e¤ect that drives up current demand for consumption. In our
inventory framework, this also raises the demand for sales of distributors, which shifts their
output demand curve (31) outward from D to D0 in Figure 7 as they increase their demand
for newly produced goods. That is, at given marginal costs, output needs to be higher to
be consistent with the TFP news-driven increase in demand as captured by the shifter St
in this representation.
Alternatively, given supply, the shift in demand puts upward pressure on
t,
which
would imply a lower inventory-sales ratio via the optimal stocking condition. We can see
from equation (31) that for a given rise in sales, the extent of the rise in marginal cost
determines whether inventories rise or fall. If the rise in marginal costs is large, inventories
24
must fall in order to reduce the inventory-to-sales ratio enough for equation (31) to still
hold, as it becomes more attractive for distributors to draw down stock in the present in
order to avoid the high current production costs. On the other hand, if the rise in marginal
costs is small, inventories can still rise along with increasing sales, as long as the rise is
proportionally less than sales such that the inventory-to-sales ratio still falls and (31) holds.
Therefore, whether inventories rise or fall for a given increase in sales depends on the
magnitude of the increase in marginal costs relative to sales. This is determined by the
slope of the supply curve and the labor supply elasticity parameter speci…cally. The
e t , such that contemporaneous increases in capacity
slope is decreasing in Qt , and thereby K
utilization ‡atten it, which helps suppress the rise in marginal costs. In the presence of
knowledge capital, the rise in its value
h
t
on arrival of the news mitigates the rise in
t
as it
shifts the output supply curve outward, from S to S 0 in Figure 7. This allows for a smaller
drop in the inventory-sales ratio and thereby supports an increase in inventories along with
sales. However, as long as marginal costs increase, a countercyclical inventory-sales ratio,
which is consistent with our empirical evidence in section 2.4, is a necessary condition for
positive comovement of inventories with other aggregate quantities.
We assess the role of knowledge capital in determining the strength of this mechanism
by imposing
h
= 0 and
h
= 0; that is, we shut down the knowledge capital mechanism
in the model. This leaves the demand curve una¤ected, while the output supply curve
reduces to
t
=
Qt
Yt
1
. The red lines in Figure 6 are the responses of the model
economy without knowledge capital to a TFP news shock as discussed above. In response
to this shock, inventories now fall over time in advance of the anticipated rise in TFP.
Without the shift in the supply curve due to the presence of knowledge capital, marginal
costs rise too much, which leads to a larger fall in the inventory-sales ratio and thus a fall in
inventories. In Figure 8, we show the responses of sales, inventories, and marginal cost for
the speci…cations with (blue lines) and without (red lines) knowledge capital. The response
of inventories depends on the relative response of sales and marginal cost via equation (31).
In order to assess the strength of this mechanism, we scale the responses in the model
without knowledge capital to have the same peak sales response as in the full model.26
It is notable that sales and inventories rise more in the model with knowledge capital,
while marginal costs are at …rst below those for the version without knowledge capital.
Moreover, they reach a lower peak later when the TFP shock is realized. TFP news raises
26
Scaling to the same impact response for marginal costs delivers the same result. Since the presence of
knowledge capital engenders considerably more propagation (see Figure 6), we scale the responses to focus
on and isolate the respective demand and substitution patterns.
25
sales demand and thereby demand for new production to increase the inventory stock. This
e¤ectively shifts output demand along an upward-sloping output supply curve, while the
supply curve also shifts right on account of the presence of knowledge capital, but not
enough to make marginal cost fall (see Figure 7). This e¤ect is not unlike diminishing
returns to labor in the absence of any shift in productivity, which as a result drives up
marginal cost in a standard neoclassical production model.
In the model without knowledge capital, we see the reverse of this pattern. Without any
rightward shift in the output supply curve, it becomes too costly to satisfy sales demand
with new production. The …rm therefore runs down its inventory. Consequently, there is
less of an increase in demand for new output, that is, less of a rightward shift in new output
demand, and as a result, less of a rise in marginal cost. When the TFP shock arrives in
period 12, the knowledge capital model has accumulated a stock of this component, which
ultimately drives down marginal cost. Moreover, agents still have an incentive to keep
increasing their labor supply because the shock is persistent and the value of knowledge
remains high on account of its continued bene…t in the future. The key to explaining the
inventory response to news is therefore the behavior of labor supply engendered by the
incentive e¤ects of knowledge capital.
Additionally, the presence of inventories in the Jaimovich-Rebelo model (without knowledge capital) impacts the comovement of other macroeconomic variables such as hours,
output, and investment negatively. Despite the increase in labor demand via the standard
Jaimovich-Rebelo channels, distributors can reduce their demand for produced goods when
compared to the model without inventories. This is possible since they can meet sales demand by drawing down inventories, which in turn reduces the demand for labor and capacity
utilization as inputs into production. The fall in inventories is thus intimately linked to the
muted response of hours, which then leads to a muted response in output and utilization
and other quantities. In addition, investment falls initially until higher TFP is realized,
which suggests that, at least in our baseline calibration, the Jaimovich-Rebelo result breaks
down in the presence of inventories. However, comovement of investment is restored in our
model with knowledge capital.27
Finally, this discussion highlights similarities and di¤erences between our approach and
Crouzet and Oh (2016). Consistent with our discussion above, they derive a fairly general
condition to show that under realistic calibrations inventories fall in an otherwise standard
27
This …nding of a fall in physical capital investment in the Jaimovich-Rebelo model without knowledge
capital is not general over the entire plausible parameter space. At best, however, the investment response
to TFP news is very much muted in the presence of inventories.
26
Jaimovich-Rebelo model. They demonstrate that this general condition nests the stockelastic demand model as well as a speci…cation with an explicit stockout avoidance motive.
However, they focus on stationary TFP shocks, while we consider the empirically more
relevant non-stationary case. Therefore, Crouzet and Oh (2016) derive their identifying
restrictions from a di¤erent speci…cation so that their empirical results capture responses
to a shock that is not directly comparable to the non-stationary TFP shock considered in
our analysis above.
4.3
Robustness
We now assess the sensitivity of our central …nding to variations in some key parameters.
The results are reported in Figures 9-13 which consider robustness to the labor supply
parameter , the elasticity of marginal utilization
knowledge capital
h
00
0
k (1)= k (1),
and the share of labor in
in the speci…cation with and without knowledge capital, whereby we
maintain the assumption of constant returns to scale in the accumulation of knowledge
capital. All three parameters a¤ect the output supply curve directly and thus drive the
response of marginal costs, which we argue above is the key component of the inventory
mechanism. As before, we consider a news shock about an anticipated rise in TFP 12
quarters ahead. We report the impulse responses for a wide range of parameter variations
in the same graph.
Figures 9-11 show the responses for our benchmark speci…cation. The model appears
sensitive to the labor supply elasticity. Changes appear large for somewhat lower values
than in the benchmark calibration case of
= 2, but the positive comovement pattern
remains robust. A less elastic labor supply makes the responses less volatile, as can be
expected, but is not su¢ cient for overturning the positive investment response. In contrast,
in the corresponding Figure 12 without knowledge capital, inventory declines over the time
horizon until the TFP shock materializes for all variations of the labor supply elasticity,
while the other aggregate variables increase. This pattern therefore lends strong support to
the centrality of the knowledge capital channel in driving positive inventory comovement.
Figures 10 and 13 contain the dynamic responses for variations of the utilization parameter, which has no signi…cant impact on comovement patterns. Finally, Figure 11 reports
variations to the labor elasticity in intangible capital, where the baseline calibrated value
is
h
= 0:25. While there is some variation in the extent of the response, the identi…ed
comovement patterns remain robust. With a larger value of
h,
the pattern strengthens,
while for lower values it weakens but is largely unchanged. It is only for
27
h
= 0:1 that the
inventory response can turn negative over the anticipation horizon.
We conclude that our key …nding from the benchmark calibration is invariant to these
parameter robustness checks. What explains the across-the-board positive comovement to
anticipated TFP shocks is the presence of a knowledge capital channel, which stimulates
production on arrival of the news and tends to negate the strong intertemporal substitution
e¤ect via marginal costs. Elastic labor supply supports our mechanism, as it does for
Jaimovich and Rebelo (2009), but it is not su¢ cient.
5
Confronting the DSGE Model with the Empirical VAR
Evidence
We establish in a structural VAR framework that a positive news shock induces strong
positive comovement of aggregate quantities, especially of inventories. This new fact proves
to be di¢ cult to explain in standard theoretical models of news shocks, such as Jaimovich
and Rebelo (2009) and Crouzet and Oh (2016). We have demonstrated in the section above
that a standard model with knowledge capital can generate a positive inventory response
alongside an expansion in all other macroeconomic aggregates. We now go a step beyond
this analysis and assess the model’s performance somewhat more formally. Speci…cally, we
now allow news to arrive at multiple horizons and let the TFP news shocks compete with
other disturbances that have been found relevant in the literature.
We estimate the model using Bayesian techniques, where we retain the structural parameter values of the baseline calibration and only estimate parameters related to the model’s
shock processes. We allow for four-, eight- and twelve-quarter-ahead news shocks to the
growth rate of TFP. These TFP news shocks compete with a number of other anticipated
and unanticipated shocks in explaining model dynamics as detailed in section 3.2. Our
setup of shock processes, treatment of observables, and prior speci…cations is standard and
close to related studies such as Schmitt-Grohé and Uribe (2012) or Khan and Tsoukalas
(2012). We estimate the model over the horizon 1983:Q1 - 2018:Q2, which is the same as
in the VAR analysis, using GDP, consumption, investment, hours worked, and inventories
as observables. Details on the estimation are provided in the online appendix.
Once the model is estimated, we perform a Monte Carlo experiment. We generate 500
samples of arti…cial data from the DSGE model by drawing parameter values from the
posterior distribution. For each sample, we construct the level of the model-generated time
series for 142 periods, consistent with the sample length in the empirical VAR analysis. We
then compare the empirical responses from the VAR model with the responses estimated
28
on the arti…cial data samples under identical VAR speci…cations.
In order to facilitate comparison between empirical and model-implied TFP news shocks
in the VAR, we construct the productivity series based on model variables as:
T F Pt =
Yt
Nt (ut Kt )1
=(
t Ht )
:
(33)
This speci…cation corresponds to the empirical measure for productivity as in Fernald
(2012). The latter is adjusted for capital utilization, but given the lack of a precise measure
for knowledge capital, it cannot fully account fot the fact that variations in this variable
impinge on TFP movements and thereby on the identi…cation of news shocks. In the online appendix, we provide additional evidence that our empirical …ndings on the positive,
news-driven comovement of all macroeconomic aggregates, including inventories, in section
2 are robust to a potential contamination of productivity by knowledge capital.28
Figure 14 shows impulse response functions at the posterior median (thick blue line) and
16% and 84% posterior bands (dashed blue lines) from the empirical VAR model, as well as
the median (thin black line) and posterior bands (gray shaded areas) from the Monte Carlo
experiment. The dynamic responses from the VAR on simulated data are qualitatively
in line with the responses from the empirical VAR. Crucially, inventories rise on impact
in response to the TFP news shock as do output, investment, consumption, and hours
worked. Quantitatively, the empirical and model-implied responses are close as posterior
bands overlap for the large majority of periods. Given that the DSGE estimation includes
a much larger number of anticipated and unanticipated innovations than the six-variable
VAR, any comparison between the two methodologies to identify TFP news shocks has its
limitations.29
Overall, we …nd that the responses are qualitatively consistent between the actual and
simulated samples. We regard this as strongly suggestive evidence that our framework with
28
Fernald’s productivity measure is widely used in the literature and is, despite potential measurement
error, arguably the most comprehensive aggregate measure for US productivity. The robustness …ndings
in the appendix address the following concerns as to the use of this measure. First, knowledge capital is a
state variable, so that the zero-impact restriction in the VAR is not a¤ected by including this variable in
the productivity measure. We show that a Max Share identi…cation without zero-impact restriction delivers
almost identical results to our baseline responses. Second, we consider a news shock identi…cation based
on patents, suggested by Cascaldi-Garcia and Vucotic (2019) that is independent of Fernald’s productivity
measure. Consistent with the results in section 2, we show in the appendix that a news shock under this
alternative identi…cation delivers broad comovement of all macroeconomic aggregates and a delayed response
of TFP.
29
Conceptually, the news shock identi…cation in the VAR and DSGE methodologies is very di¤erent, which
arguably underlies the observation that the respective responses are quantitatively di¤erent. Speci…cally,
the VAR identi…es the shock based on the TFP series. In the DSGE model the whole spectrum of auto- and
cross-correlations of all observables are used to identify the shock.
29
knowledge capital can reproduce our new empirical fact, namely that inventories comove
alongside the other macroeconomic variables in response to TFP news shocks. This is
notwithstanding that our parsimonious framework, which eases the discussion of propagation mechanisms, limits the quantitative consistency between empirical and model-implied
VAR responses due to the omission of transmission mechanisms that have been found important in the literature on estimated DSGE models.30
6
Conclusion
Our paper makes two contributions to the literatures on news shocks and inventory dynamics. First, we establish empirically that a news shock in terms of an anticipated rise in
TFP in the future raises inventory holdings in the present and induces positive comovement
with other macroeconomic aggregates. Based on standard VAR identi…cation, this fact is
robust across many dimensions, such as sectors, types of inventories, and alternative identi…cation schemes for news shocks. Our empirical …nding corroborates the view that TFP
news shocks are important drivers of macroeconomic ‡uctuations. We also consider this an
important result as it provides a dimension along which standard inventory frameworks can
be evaluated as to their empirical viability. This is where our second contribution lies.
We show that the standard theoretical framework used in the news shock literature
cannot explain procyclical inventory movements in response to TFP news shocks. We argue
that an additional mechanism, namely the accumulation of knowledge capital, is needed to
capture the behavior of inventories. This mechanism addresses two shortcomings of previous
frameworks. First, they fail to reproduce the procyclical inventory movements in response
to TFP news shocks due to a strong substitution e¤ect that moves production into the
future. Second, introducing inventories in standard frameworks implies an intertemporal
labor choice that makes even comovement of consumption, investment, and hours much
harder to achieve. Knowledge capital provides an incentive for …rms and workers to engage
in production today to accumulate the know-how needed for taking full advantage of higher
TFP in the future. This leads to inventory accumulation in the present.
Even though inventories are strongly procyclical unconditionally, conditional on TFP
news shocks, our empirical …nding is not a priori self-evident. Conventional views would
suggest two potential counteracting e¤ects on inventories in response to news. A negative
substitution e¤ect provides incentives to reduce the current inventory stock and increase
30
For a discussion on the importance of nominal rigidities and …nancial frictions in estimated models with
anticipated technology shocks see, for example, Görtz and Tsoukalas (2017).
30
stockholding in the future when the higher productivity is actually realized. We provide
evidence in Görtz et al. (2019) that this substitution e¤ect is dominated by a demand e¤ect
due to which …rms increase inventories in response to sales in light of rising consumption
and investment. This …nding is based on …rm-level data and supports the insights from the
aggregate data in the current paper. In addition, our theoretical insights provide a new
transmission channel for news shocks to the literature. A rigorous investigation of the datagenerating mechanism, including multiple sectors and the use of input as well as …nished
goods inventories, goes beyond the scope of this paper and is left for future research.
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33
Table 1: Summary of calibrated parameters
Description
Parameter
Value
Subjective discount factor
Household elasticity of intertemporal substitution
Determinant of Frisch elasticity of labor supply
Wealth elasticity parameter
Labor elasticity in production
Depreciation elasticity of capacity utilization
Capital depreciation
Investment adjustment cost
Inventory depreciation
Goods aggregator curvature
Taste shifter curvature
Contribution of prior intangible capital in its production
Labor elasticity in intangible capital
TFP growth process persistence
Steady state government spending over output
Steady state hours
Steady state capacity utilization
Steady state GDP growth rate (in %)
Steady state RPI growth rate (in %)
β
σ
ξ
γf
α
δk00 (1)/δk0 (1)
δk
s00
δx
θ
ζ
γh
νh
ρΩ
g/y
n
u
gy
g RP I
0.9957
1
2
0.01
0.64
0.15
0.025
5
0.05
6.8
0.67
0.75
0.25
0.50
0.18
0.2
1
0.42545
-.58203
34
Figure 1: IRF to TFP news shock including Private Non-Farm Inventories. 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. The units of the vertical axes
are percentage deviations.
35
Figure 2: IRF to TFP news shock including Business Inventories. Sample 1992Q12018Q2. 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 3: IRF of business inventories by sector to TFP news shock. Sample 1992Q1-2018Q2.
Subplots result from eight variable VARs comprising TFP, GDP, consumption, investment, hours,
inventory measure, in ation, E5Y. The inventory measures were included one-by-one in the VAR
system. 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.
36
Figure 4: IRF of business inventories in the manufacturing sector by inventory type to
TFP news shock. Sample 1992Q1-2018Q2. Subplots result from eight variable VARs comprising
TFP, GDP, consumption, investment, hours, inventory measure, in ation, E5Y. The inventory
measures were included one-by-one in the VAR system. 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 5: IRF to TFP news shock. Subplots result from VARs comprising TFP, GDP, investment, hours, in ation and one of the plotted variables above at a time. 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.
37
Output
Inventory
6
Investment
10
6
4
4
5
2
2
0
0
0
0
20
40
Consumption
0
0
40
Hours
3
4
20
4
1
2
40
Capacity utilization
6
2
20
3
2
1
0
0
20
40
Knowledge Capital
3
0
0
20
40
Value of Knowledge Capital
4
0
20
40
TFP
2
2
3
1
1
2
0
0
20
40
0
0
20
40
0
20
40
Figure 6: IRF to 12 period ahead unit TFP news shock. Baseline model (solid-blue) and
model without knowledge capital (dashed-red).
Figure 7: Supply and Demand curves for output, Yt , and marginal cost τt .
38
Sales
7
Inventory
8
6
Marginal cost
0.15
6
5
4
0.1
4
2
3
0
2
-2
1
0
0
0.05
10
20
30
-4
0
40
10
20
30
0
0
40
10
20
30
40
Figure 8: IRF to 12 period ahead TFP news shock. Baseline model (solid blue) and model
without knowledge capital (dashed red). The responses of the model without knowledge capital are
scaled so that the maximum impact of sales corresponds to the one in the baseline model.
TFP
2
1
0
0
Output
20
10
10
10
20
30
40
0
0
Investment
30
Inventory
20
10
20
30
40
Consumption
0
0
10
20
30
40
30
40
Hours
10
10
20
0
0
5
5
10
10
20
30
40
0
0
10
20
30
40
0
0
Figure 9: IRF sensitivity for 12 period ahead TFP shock.
{1.4, 1.5, 2, 2.5, 3} (thin to thick lines).
39
10
20
Baseline model.
ξ =
TFP
2
Output
8
6
1
4
2
0
0
10
20
30
40
Investment
0
0
6
10
10
20
30
40
30
40
0
0
0
10
20
10
20
30
40
Output
30
40
0
Investment
10
10
5
5
0
0
8
15
10
10
20
30
40
Consumption
0
0
20
30
40
model.δk00 (1)/δk0 (1)
=
Inventory
10
20
30
40
30
40
Hours
4
6
10
4
5
0
0
40
1
TFP
1
30
2
Figure 10: IRF sensitivity for 12 period ahead TFP shock. Baseline
{0.05, 0.1, 0.15, 0.25, 0.4} (thin to thick lines).
2
20
Hours
2
20
10
3
4
10
Inventory
Consumption
5
0
0
8
6
4
2
0
-2
0
2
2
10
20
30
40
0
0
10
20
30
40
0
0
Figure 11: IRF sensitivity for 12 period ahead TFP shock.
{0.1, 0.2, 0.25, 0.3, 0.35} (thin to thick lines).
40
10
20
Baseline model.
ν =
TFP
2
Output
Inventory
4
4
2
1
0
0
2
10
20
30
40
0
0
Investment
6
0
10
20
30
40
Consumption
10
20
30
40
30
40
Hours
3
3
4
2
2
2
1
0
-2
0
-2
0
10
20
30
40
1
0
10
20
30
40
0
0
10
20
Figure 12: IRF sensitivity for 12 period ahead TFP shock. Model without knowledge capital.
ξ = {1.4, 1.5, 2, 2.5, 3} (thin to thick lines).
TFP
2
Output
4
Inventory
4
2
1
2
0
0
0
10
20
30
40
Investment
6
0
0
2.5
4
2
2
1.5
0
1
-2
0
10
20
30
40
0.5
0
10
20
30
40
-2
0
10
Consumption
20
30
40
30
40
Hours
1.5
1
0.5
10
20
30
40
0
0
10
20
Figure 13: IRF sensitivity for 12 period ahead TFP shock. Model without knowledge capital.
δk00 (1)/δk0 (1) = {0.05, 0.1, 0.15, 0.25, 0.4} (thin to thick lines).
41
Figure 14: TFP news shock. The blue solid (blue dashed) line is the median (16% and 84%
posterior band) response to a TFP news shock from a six-variable VAR. The solid black line (gray
shaded areas) is the median (16% and 84% posterior band) response to a TFP news shock estimated
from a VAR on 500 samples generated from the DSGE model. Units of the vertical axes are
percentage deviations.
42
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