r&d shocks and news shocks - canon-igs.org · r&d shocks and news shocks ∗ ryo jinnai†...
TRANSCRIPT
R&D Shocks and News Shocks∗
Ryo Jinnai†
September 5, 2012
Abstract
Most of the theoretical work in the news shock literature abstracts away from structural
explanations, assuming instead that news is a pure signal giving agents advance notice that
aggregate technology will undergo exogenous change at some future point. This paper proposes
that a surprise improvement in sector-specific productivity in the research and development
sector can be seen as news about aggregate productivity. I not only offer a deeper explanation
for news but also show that the model performs better in matching a broad set of empirical
facts than a standard, one-sector neoclassical growth model augmented with exogenous news
shocks does.
1 Introduction
The expectation-driven business cycle hypothesis postulates that news about the future can be
an important source of business cycle fluctuations. This theory was originally advanced by Pigou
∗I thank Nobu Kiyotaki for his advice and encouragement. I am also grateful to Roland Benabou, Saroj Bhat-
tarai, Francesco Bianchi, Toni Braun, Kenichi Fukushima, Jean-Francois Kagy, Amy Glass, Tatsuro Iwaisako, Den-
nis Jansen, Dirk Kruger, Per Krusell, Alisdair McKay, Marc Melitz, Tamas Papp, Woong Yong Park, Bruce Pre-
ston, Ricardo Reis, Esteban Rossi-Hansberg, Felipe Schwartzman, Chris Sims, Satoru Shimizu, Takuo Sugaya, Jade
Vichyanond, Yuichiro Waki, and Anastasia Zervou for their comments.†Texas A&M University, 4228 TAMU, College Station, TX 77843; Email: [email protected]; Phone:
1-979-845-7380; Fax: 1-979-847-8757
1
(1927) and was resurrected by Beaudry and Portier (2006) in a modern, empirical form that at-
tracted renewed interest from contemporary economists. However, it is difficult to apply this hy-
pothesis to the standard dynamic stochastic general equilibrium (DSGE) model because the model
predicts that the wealth effect of good news causes households to seek additional consumption of
both goods and leisure; hence, contrary to the hypothesis, the model predicts that production will
slow on the arrival of good news. A large body of literature has subsequently been developed that
seeks mechanisms through which the model can generate the appropriate co-movement, i.e., an
economic boom defined as simultaneous expansion in output, consumption, investment, and hours
worked. A short list of the relevant studies includes Beaudry and Portier (2004), who propose
a multi-sector model with complementarity between services and infrastructure; Den Haan and
Kaltenbrunner (2009), who present a matching framework with equilibrium underinvestment; and
Jaimovich and Rebelo (2009), who introduce a class of preferences that weaken the wealth effect
on labor supply. These articles propose many novel solutions that provide important contributions
to our understanding of the sources of business cycles and macroeconomic modeling.1
Conversely, a recent empirical study suggests that the literature’s focus on impact effects may
have been somewhat misplaced. This point was made by Barsky and Sims (2011), who develop a
novel method for identifying news shocks through the application of principal components. Their
method is arguably an improvement over other approaches because it relies solely upon a weak
assumption that a limited number of shocks leads to movements in aggregate technology, whereas
other approaches rely upon auxiliary assumptions about other shocks or on the persistence of
variables. Applying the technique to vector autoregression (VAR) models estimated with U.S. data
leads to surprising results, namely that favorable news about future total factor productivity (TFP)
1Schmitt-Grohe and Uribe (2008) and Fujiwara, Hirose, and Shintani (2011) perform structural Bayesian estima-
tions of the importance of anticipated shocks.
2
is, on impact, associated with an increase in consumption and decreases in output, investment,
and hours. These results are consistent with the predictions of a wide class of existing DSGE
models, including the most basic neoclassical models.2 Because Barsky and Sims also find that the
identified news shocks explain an important share of output variance at medium frequencies, the
authors argue that the literature should move away from fixing impact co-movements and towards
deeper structural explanations for news.
The current paper proposes such an explanation. Specifically, I propose that a surprise improve-
ment in sector-specific productivity in the research and development (R&D) sector can be seen as
news about aggregate productivity. This idea is laid out in an otherwise standard two-sector neo-
classical growth model with sector-specific productivity shocks that is then evaluated in light of the
data, including the data reported by Barsky and Sims (2011). I show that this two-sector model
performs better in matching a broad set of empirical facts than a standard, one-sector neoclassical
growth model augmented with news shocks does. In other words, the two-sector model offers not
only a deeper explanation for news but also better explanations for the data than the one-sector
model, in which news shocks are introduced in a standard way as in the news shock literature.
In my model economy, R&D is pursued for product development. Specifically, I introduce
product entry subject to sunk product development costs as in Bilbiie, Ghironi, and Melitz (2012).
These authors stress the consumer love for variety; however, based on an alternative interpretation
that entry and exit take place in the intermediate goods sector as in variety-based endogenous
growth models (see, for example, Romer (1990); Grossman and Helpman (1991); Aghion and
Howitt (1997)), product development can be interpreted as a productivity-enhancing activity.
However, I make two modifications to Bilbiie, Ghironi, and Melitz (2012), each of which I
2See also Nam and Wang (2010), who apply Barsky and Sims’s identification technique to analyze exchange rate
dynamics.
3
demonstrate is important in accounting for the empirical findings of Barsky and Sims (2011).
First, I introduce a simple product cycle; that is, a product is initially monopolistically produced
and later, competitively produced. Futagami and Iwaisako (2007) introduce such a structure to
analyze the effects of patent length on social welfare; however, because I take a broad view that the
source of monopoly incorporates not only the formal patent system but also informal protections
surrounding trade secrets and brand image, I call products in the first stage of the product cycle
“innovative products” and products in the second stage of the product cycle “maturing products.”
I also assume that the transition from an innovative product to a maturing product takes place
stochastically.
Second, I introduce knowledge spillover. Specifically, I assume that a larger stock of innova-
tive products improves product innovation efficiency and, more importantly, that this knowledge
spillover is not an externality but is internalized by agents performing R&D. In the endogenous
growth literature, this type of knowledge spillover is introduced to analyze the role of private knowl-
edge accumulation for in-house R&D (see, for example, Smulders and van de Klundert (1995);
Peretto (1996); Peretto (1998)). However, my specification is closer to McGrattan and Prescott
(2010), in which intangible capital is simultaneously useful in both goods-producing sectors and
intangible capital-producing sectors. In particular, the product innovation function in my model
economy is constant returns to scale, as is the production function of intangible capital in McGrat-
tan and Prescott’s model. This assumption greatly simplifies the analysis because it allows the
introduction of an aggregate product innovation function to the model economy.3
I begin my analysis by examining impulse response functions. Along these lines, Barsky and
3This is an important difference from the aforementioned prominent contributions in the endogenous growth
literature; that is, adopting a particular knowledge creation function, Smulders and van de Klundert (1995), Peretto
(1996), and Peretto (1998) analyze how detailed market structure, such as the number and size distribution of firms,
affects the aggregate economy.
4
Sims (2011) demonstrate that the one-sector model fares relatively well in matching the data; i.e.,
impulse responses of TFP, consumption, output, investment, and hours to a news shock in the
one-sector model are very similar to estimated impulse responses to an identified news shock in
their VAR models. I calibrate the two-sector model so that both a sector-specific productivity
shock in the two-sector model and a news shock in the one-sector model generate nearly identical
dynamic responses of TFP. I find that responses of consumption, output, investment, and hours
are also very similar across models and hence, also to the data, although they are not targeted in
the calibration.
There is, however, one variable over which predictions from the one-sector model and the two-
sector model strongly disagree: the aggregate stock market value. In the one-sector model, it falls
on the impact of a positive news shock, whereas in the two-sector model, it rises on the impact of
a positive sector-specific productivity shock. Such a difference is possible despite similar responses
of consumption, output, investment, and hours because the items composing the aggregate stock
market value are different. Specifically, in the one-sector model, it is measured as capital stock,
whereas in the two-sector model, it is measured as the sum of capital stock and the value of
innovative products, the latter of which responds positively to sector-specific productivity shocks.
The two-sector model’s prediction is empirically supported by Barsky and Sims (2011), who find
that an aggregate stock market index rises on the impact of their identified news shock.4
Next, I investigate the forecast error variance decompositions. Once again, along this dimension,
the one-sector model fares relatively well in replicating the estimates of Barsky and Sims (2011).
In particular, the model’s prediction that news shocks become more important in accounting for
variations of TFP, consumption, and output at longer forecast horizons is in line with the data.
4Other identification approaches also find that a stock market boom is associated with news shock (e.g., Beaudry
and Portier (2006)).
5
However, there are three important discrepancies between the model’s predictions and the data.
First, the one-sector model overemphasizes news shocks’ contributions to the forecast error variance
of consumption at high frequencies. Second, the one-sector model overemphasizes news shocks’
contributions to the forecast error variance of hours at medium frequencies. Third, the one-sector
model underestimates news shocks’ contributions to the forecast error variance of the aggregate
stock market value at high frequencies.
Interestingly, these problems largely disappear in the two-sector model. First, because product
development is an investment, the resource constraint does not allow consumption to increase
after a sector-specific productivity shock to the degree that it does after a news shock in the one-
sector model. Second, because TFP improvement is achieved by high product entry rates but new
products are monopolistically produced, producers of new products do not hire as many hours after
a sector-specific productivity shock as competitive firms do after a news shock in the one-sector
model. Third, sector-specific productivity shock accounts for a large share of the forecast error
variance of the value of the aggregate stock market at high frequencies because it is associated with
a stock market boom.
I also calculate unconditional second moments of important aggregate variables at various fre-
quencies. Along this dimension, both the one-sector model and the two-sector model are equally
well matched to the data. As Barsky and Sims (2011) emphasize, the one-sector model improves
the simplest real business cycle model that is driven solely by surprise technology shocks in the
sense that correlations between variables are all nearly one in the one-shock model; conversely, if
the model is augmented with news shocks, the correlations are all positive but not too close to one,
which are more in line with the data. The same advantage is shared by the two-sector model. In
addition, both the one-sector model and the two-sector model are broadly consistent with general
6
patterns of what Comin and Gertler (2006) call medium-term business cycles, cyclical components
of up to 200 quarters. This is because both news shocks in the one-sector model and sector-specific
productivity shocks in the two-sector model add persistence to their respective models.
The remainder of this paper is organized as follows. Section 2 presents the model economies,
with the one-sector model presented first. The same model is adopted by Barsky and Sims (2011) for
demonstrating that this simple model performs relatively well in matching their empirical findings.
The model is extended to the two-sector model by enriching the supply side. I also substitute news
shock with sector-specific productivity shock. Section 3 reports the main results. Section 4 presents
a sensitivity analysis. I demonstrate that both product cycles and knowledge spillover are important
amplification mechanisms. Specifically, I show that if either of them is excluded, a sector-specific
productivity shock no longer generates an immediate stock market boom but, instead, generates a
crash in the stock market. Section 5 concludes the paper.
2 Model economies
2.1 One-sector model
The one-sector model consists of the representative household, the representative firm, and the
government. The household maximizes the expected lifetime utility value, defined as:
0
" ∞X=0
Ãlog ( − −1)−
1+1
1 + 1
!#
subject to the flow budget constraint and the capital accumulation rule,
+ = (1− ) ( +)
7
+1 =¡1−
¢ +
Variable definitions are standard. The income tax is set by the government. Preference shock
follows a stationary process,
log = log−1 +
The representative firm is competitive, maximizing profits,
− ( +)
by operating production technology,
= ()
1−
The level of TFP is exogenous, and I follow Section 4 of Barsky and Sims (2011) in specifying its
dynamic property; that is, TFP is decomposed into two parts:
log = log + log
where and follow stochastic processes given by
log = log−1 +
∆ log = ∆ log−1 + −1
Note the timing of the shocks. On the one hand, the variable is a transitory surprise technology
8
shock whose innovation has an immediate impact on the level of TFP. On the other hand, the
variable is a permanent news shock whose innovation has no contemporaneous effects on the
level of TFP but diffuses slowly into TFP with a time lag.
The government consumes a share of private output,
=
where is an exogenous, random variable following a stationary process,
log =¡1−
¢log + log −1 +
The government maintains a balanced budget, implying that
=
holds in every period.
I omit derivation of the first order conditions because they are entirely standard. The com-
petitive equilibrium is defined in the standard way, and the market clearing condition is given
by
+ + =
Because capital is the only asset in this economy, the value of the aggregate stock market is
defined as
≡ +1
9
Table 1. One-sector model summary
Production = ()
1−
TFP =
Consumption 1−−1 − +
h³
−+1−
´i= 0
Hours (1− )(1−)
=
1
Eular equation =
h+1
³(1− +1)
+1+1
+ 1− ´i
Capital accumulation +1 =¡1−
¢ +
Resource constraint (1− ) = + Stock market value = +1
The model is summarized in Table 1. The eight equations in the table jointly determine the
equilibrium dynamics of the eight variables , , , , , , , and .
2.2 Two-sector model
The one-sector model is extended to the two-sector model by enriching the supply side. Final good
is produced by a representative competitive final good aggregator with a CES technology:
=
∙Z∈Ω
()−1
¸ −1
(1)
where Ω denotes the set of differentiated products available for production in period . The cost
minimization problem leads to a downward sloping demand curve
() =
µ ()
¶−
for each available product, where () denotes the nominal price of () and denotes the
aggregate price index given by
=
∙Z∈Ω
()1−
¸ 11−
10
Each intermediate good is produced by an atomistic producer or producers depending on the
good’s location in life cycle. Specifically, I assume that a product is monopolistically produced
initially but is later competitively produced. Futagami and Iwaisako (2007) introduce such a
product cycle to analyze optimal patent duration, but because I take a broad view that the source of
monopoly incorporates not only the formal patent system but also informal protections surrounding
trade secrets and brand image, I call products in the first stage of the product cycle “innovative
products” and products in the second stage of the product cycle “maturing products.”
The production function of an intermediate product is given by
() = () ()
1−
Cobb-Douglas technology implies that the real marginal cost of producing an intermediate product
is given by
=1
µ
¶µ
1−
¶1−
The producer of an innovative product chooses nominal price to maximize the profits defined as
≡ max
µ−
¶µ
¶−
She obtains the optimal markup pricing,
=
− 1 (2)
A producer of a maturing product sets the nominal price at the nominal marginal cost because
11
competition drives profits to zero:
=
Let denote the mass of innovative products and
denote the mass of maturing products
in period . Their transition rules are given by
+1 =
¡1−
¢(1− )
¡ +
¢(3)
+1 =
¡1−
¢ ¡ +
¡ +
¢¢where
denotes the mass of newly invented products in period . The underlying assumptions
are the following: (i) products are innovative when they are invented, (ii) a fraction of randomly
chosen innovative products evolve into maturing products in every period, and (iii) as in Bilbiie,
Ghironi, and Melitz (2012), there is both a time-to-build lag and a death shock; i.e., products
invented in period start producing in period + 1, and a fraction of both randomly chosen
innovative and randomly chosen maturing products become permanently unavailable to the econ-
omy. Let denote the mass of total products, i.e., the measure of Ω. Because = +
,
its transition rule is given by
+1 =¡1−
¢ ¡ +
¢Note that = 0 corresponds to an important special case in which products are uniformly innova-
tive, i.e., = . This case is revisited in Section 4.
The household maximizes the expected lifetime utility value, defined as
0
" ∞X=0
Ãlog ( − −1)−
1+1
1 + 1
!#
12
The flow budget constraint is given by
+ + = (1− )¡ + +
¢(4)
The variable denotes investment in physical capital, whose accumulation rule is given by
+1 =¡1−
¢ +
The variable denotes R&D spending for product developments. New products are created with
the technology given by
=
¡
¢1−
where is the sector-specific productivity shock, following a stationary process,
log = log−1 +
This product innovation function is simple and flexible, accommodating two interesting cases. When
= 1, product entries increase in a linear fashion with R&D spending as in Bilbiie, Ghironi, and
Melitz (2012).5 This special case is revisited in Section 4. When 0 1, the product innovation
function exhibits diminishing returns to scale in R&D spending, but at the same time, marginal
product innovation efficiency of R&D spending improves with the stock of innovative products.
I interpret the latter effect as knowledge spillover because a larger stock of innovative products
facilitates product developments.
5 In fact, the working paper version of their work (Bilbiie, Ghironi, and Melitz (2007)) is closer because both labor
and capital involve the product development costs. In the published version (Bilbiie, Ghironi, and Melitz (2012)),
only labor is involved.
13
The first-order conditions are given by
1
− −1− +
∙
µ −+1 −
¶¸= 0
(1− ) = 1
=
£+1
¡(1− +1)+1 + 1−
¢¤− +
¡1−
¢(1− )
= 0
− +
"
Ã+1 (1− +1) +1 + +1
¡1−
¢(1− )
Ã1 + (1− )
+1
+1
!!#= 0 (5)
where and are Lagrangian multipliers for (3) and (4), respectively.
The government behaves in the same way as in the one-sector model; that is, it consumes a
fraction of private output = and maintains a balanced budget, implying that = holds
every period.
2.3 Equilibrium
Competitive equilibrium is defined as a sequence of quantities and prices such that (i) they are
optimally chosen by the household, the aggregator, and intermediate goods producers and (ii) the
goods, labor, and capital market clear in every period:
= + + + (6)
=
+
14
=
+
where and denote labor input and capital input to an innovative product, respectively, and
and denote labor input and capital input to a maturing product, respectively.
We can simplify the aggregate production function (1) using equilibrium conditions. Because
products are symmetric in each group, the aggregate production is written as
=
∙
¡¢ −1
+
¡¢ −1
¸ −1
(7)
where denotes the production of an innovative product and denotes the production of a
maturing product. Because the demand for an innovative product is lower than the demand for a
maturing product to the extent of the price differential, we find
=
µ
¶−=
µ
− 1¶−
(8)
Combining (7) and (8), we find
=
" +
µ
− 1¶−1#
−1
(9)
Applying the same argument to the factor market clearing conditions, we find
=
+
=
" +
µ
− 1¶# (10)
=
+
=
" +
µ
− 1¶# (11)
15
Substituting (10) and (11) into (9), we find
= ()
1−
where TFP is given by
= 1
−1
"
+
µ
− 1¶−1#
−1"
+
µ
− 1¶#−1
These are key equations. Note that exogenous news shock in the one-sector model, , is replaced
by an endogenous mechanism. Specifically, the level of TFP is affected by the number of products,
, and the composition of products, . This is the main idea behind the proposition that
sector-specific productivity shock in the two-sector model can be thought of as news shock. Because
there is a time-to-build lag in product development, a sector-specific productivity shock does not
have a contemporaneous effect on the level of TFP; rather, as it sluggishly affects the number
and composition of products with a time lag, a sector-specific productivity shock slowly diffuses
into TFP similarly to how a news shock does in the one-sector model. I will show that dynamic
responses of TFP to these shocks are not only qualitatively but also quantitatively similar under
reasonable calibration.6
The equilibrium conditions lead to the accounting identity. The goods market clearing condition
(6) summarizes the usage of the aggregate production in the economy,
= + +
6Long-run implications are different because a news shock in the one-sector model has a permanent effect on TFP,
while a sector-specific productivity shock in the two-sector model does not. However, they generate similar dynamic
responses of TFP at high, medium, and low frequencies, at least up to 200 quarters. Therefore, the difference in the
permanent future is not an especially serious concern for the current study as long as the focus is on fluctuations.
16
Aggregate production is the sum of consumption, investment, and government spending, where
investment is defined as the sum of investment in physical capital and product developments:7
= +
Combining the household budget constraint and the goods market clearing condition yields the
income account,
= + + (12)
Aggregate production is equal to the sum of the income generated by production. It is interesting to
observe that, unlike in standard neoclassical growth models, in the current model economy, income
shares are not constant but fluctuate with an endogenous mechanism. A few steps of derivations
verify this claim. First, by substituting factor market clearing conditions (10) and (11) into the
total costs of production, we find
+ =¡
+
¢ " +
µ
− 1¶#
Because the markup pricing (2) implies that equilibrium costs and profits of producing an innovative
product have a stable relation as +
= ( − 1) , we find
+ = ( − 1) " +
µ
− 1¶#
7 I include product development costs to investment, following Bilbiie, Ghironi, and Melitz (2012). McGrattan and
Prescott (2010) do not include intangible investment in the measured investment but treat it as business spending
instead.
17
Substituting this equation into the income account (12), we find
=
"
+
µ
− 1¶−1#−1
The remainder of the income is divided by capital and labor with constant shares:
= (1− )£ −
¤
= £ −
¤Therefore, factor shares are affected by the composition of products. Specifically, the dividend
share increases with the share of innovative products in total products, and both capital and labor
shares decrease with the share of innovative products in total products. Changes in this intensive
margin turn out to be a very powerful amplification mechanism, which is most clearly observed in
Section 4, in which the special case of homogenous products is revisited. However, the number of
products is neutral to factor shares given that the composition of products is equal. This is because
a change in this extensive margin has proportional effects on both the aggregate production and
the individual components of income.
The value of the aggregate stock market is defined as the sum of capital stock and the
value of innovative products,
≡ +1 + ¡ +
¢where is defined as ≡
¡1−
¢(1− ) . Its economic interpretation becomes clearer
18
once we rewrite the household’s first order condition (5) as
=
"+1
¡1−
¢(1− )
Ã(1− +1) +1 + +1 (1− )
+1
+1
+ +1
!#(13)
This is the pricing equation for the end-of-the-period value of an innovative product, reflecting the
product’s dual role. On the one hand, an innovative product is a monopolistic product generating
a sequence of profits. Let denote the asset value of an innovative product focusing on this aspect,
which is given by
=
∙+1
¡1−
¢(1− ) ((1− +1) +1 + +1)
¸(14)
On the other hand, an innovative product is a useful input in the R&D sector. Let denote the
asset value of an innovative product focusing on this aspect, which is given by
=
"+1
¡1−
¢(1− )
Ã(+1 + +1) (1− )
+1
+1
+ +1
!#(15)
It is clear that = + because adding (14) and (15) leads to (13).
The model is summarized in Table 2. The sixteen equations in the table jointly determine the
equilibrium dynamics of sixteen endogenous variables, , , , , , , , , ,
,
,
, , , , and .
2.4 Calibration
Calibration is summarized in Table 3. The parameters are divided into three groups. The first group
lists parameters that are common to both the one- and two-sector models. For those parameters,
19
Table 2. Two-sector model summary
Production = ()
1−
TFP = 1
−1
∙
+³1−
´³
−1´−1¸
−1∙
+³1−
´³
−1´¸−1
Consumption 1−−1 − +
h³
−+1−
´i= 0
Hours (1− )(1−)(−
)
= 1
Eular equation =
∙+1
µ(1− +1)
(+1−+1+1)
+1+ 1−
¶¸Capital accumulation +1 =
¡1−
¢ +
R&D spending = ( + )
Monopoly value =
£+1
¡1−
¢(1− ) ((1− +1) +1 + +1)
¤R&D value =
h+1
¡1−
¢(1− )
³(+1 + +1) (1− )
+1
+1
+ +1
´iDividend
=
∙
+³1−
´³
−1´−1¸−1
Product innovation =
¡
¢1−()
Innovative products +1 =
¡1−
¢(1− )
¡ +
¢Total products +1 =
¡1−
¢ ¡ +
¢Resource constraint (1− ) = + +
Investment = +
Stock market value = +1 + ( + )¡ +
¢I follow Barsky and Sims (2011) and set them at = 099, = 08, = 1, = 0025, = 033,
= 02, = 095, = 08, and the standard deviations of and at 0.15 percent.
The parameters in the second group are unique to the two-sector model. There are four such
parameters. I set the size of the death shock at = 0025 and the elasticity of substitution
between products at = 38, following Bilbiie, Ghironi, and Melitz (2012). I set the transition
probability of an innovative product becoming a maturing product at = 180 so that the average
duration of a product being innovative matches the actual patent length. The research elasticity
is calibrated to match a salient feature of the data; that is, the ratio of R&D spending to corporate
profits is roughly constant, as shown in Figure 3.8 The model counterpart is derived as follows:
8Total domestic R&D and corporate profits with inventory valuation adjustment and capital consumption adjust-
ment are taken from the BEA.
20
from the optimality condition equating marginal costs and benefits of R&D spending, we find that
=
+
³ +
´(16)
holds in the steady state, where and are the steady state values of ¡ +
¢and
¡ +
¢, respectively. This equation shows that steady state R&D spending is a fraction
of the steady state value of new products. At a given level of new products’ steady state value, an
increase in leads to a larger steady state R&D spending because it slows the diminishing returns
to scale. The steady state value of new products is replaced with steady state R&D spending
and steady state dividend income in the following way. I first rewrite the pricing equation of ,
obtaining
=
µ(1− ) +
+
¶(17)
This equation shows that the steady state value of innovative products as monopolistic products
is the discounted sum of steady state after-tax future dividend income. I also rewrite the pricing
equation of , obtaining
=
µ
+
³ +
´− +
+
¶(18)
This equation shows that the steady state value of innovative products in the R&D sector is the
discounted sum of steady state future R&D profits, defined as the steady state value of new products
minus steady state R&D spending. I use (18) to replace in (16) with and and then use (17)
21
Figure 1: The ratio of R&D spending to corporate profits from 1959 to 2007. Dotted line shows
the hostorical average.
to replace with , obtaining
=
∙1− 1−
1− (1− ( +))
¸(1− )
This is an increasing function of . It takes the minimum value of zero when = 0, and takes
the maximum value of = 0629 when = 1, given our calibration of , , , and . Our
target value is 0313 (the historical average, plotted by the dotted line in Figure 3). Hence, I set
at = 0175.
The parameters in the third group are those governing technology shocks. For the one-sector
model, they are parameters determining stochastic processes of surprise technology shock and
news shock . These are calibrated to match the dynamic properties of TFP reported by Barsky
and Sims (2011). Specifically, I set = 098 and the standard deviation of at 0.75 percent
so that the model-implied impulse response of TFP to a surprise technology shock matches the
empirically observed impulse response of TFP to its own innovation.9 I set = 0822 and the
standard deviation of at 0.098 so that the model-implied share of the forecast error variance of
TFP attributable to news shock at various forecast horizons matches its empirical counterpart.
9See page 287 of Barsky and Sims (2011).
22
For the two-sector model, the parameters determine the stochastic processes of neutral produc-
tivity shock and sector-specific productivity shock . These are calibrated so that the impulse
responses of TFP are similar across models. Specifically, I set = 0978 and the standard de-
viation of at 075 percent so that a neutral productivity shock in the two-sector model and
a surprise technology shock in the one-sector model generate similar dynamic responses of TFP.
The standard deviations are set at the same value so that the initial responses to a one standard-
deviation innovation to each shock are identical. The persistence is slightly lower in the two-sector
model because product entries add extra persistence in the two-sector model. Similarly, I set the
persistence of the sector-specific productivity shock at = 0806 and the standard deviation of
at 910 percent so that a sector-specific productivity shock in the two-sector model and a news
shock in the one-sector model generate similar dynamic responses of TFP. A small value of
indicates that the model contains a strong, endogenous amplification mechanism.
3 Results
In Figure 2, I plot impulse responses to a neutral productivity shock in the two-sector model
(solid line) and impulse responses to a surprise technology shock in the one-sector model (dotted
line). The top-left panel shows that the TFP responses are nearly identical in both models, which
confirms the calibration strategy. Responses of consumption, output, hours, and investment are
also very similar across models. However, a large difference is observed in responses of the value of
the aggregate stock market: while both models predict a positive response, the size of the initial
jump is several times larger in the two-sector model than in the one-sector model.
To understand the difference, in Figure 3, I plot impulse response functions of an expanded
23
Table 3. Calibration
Common parameters one-sector two-sector
Time discount factor 0.99 0.99
Degree of habit 0.8 0.8
Elasticity of leisure 1 1
Capital depreciation rate 0.025 0.025
Capital elasticity 0.33 0.33
Average government spending share 0.2 0.2
Standard deviation of 0.0015 0.0015
Persistence of log 0.95 0.95
Standard deviation of 0.0015 0.0015
Persistence of log 0.8 0.8
Parameters unique to the two-sector model two-sector
Death shock 0.025
Elasticity of substitution between products 3.8
Maturation rate 1/80
Research elasticity 0.175
Parameters calibrated to match TFP response one-sector two-sector
Standard deviation of 0.0075 0.0075
Persistence of log 0.980 0.978
Standard deviation of 0.0098
Persistence of ∆ log 0.822
Standard deviation of 0.0910
Persistence of log 0.806
24
Figure 2: Impulse responses to a neutral productivity shock () in the two-sector model (solid
line) and a surprise technology shock () in the one-sector model (dotted line). Log deviations
from the steady state are plotted.
25
list of variables in the two-sector model. We observe that investment in physical capital responds
very similarly across models, as does capital stock. This observation leads us to conclude that a
large impact response of the aggregate stock market value in the two-sector model is caused by
the other component of the total asset value, i.e., the asset value of innovative products; responses
are plotted in the second row. The value of innovative products as monopolistic products, ≡
¡ +
¢, increases because improved productivity leads to larger dividend income,
, as
observed in the right panel of the same row. The value of innovative products in the R&D sector,
≡ ¡ +
¢, also increases because the expectation of large future profits stimulates R&D,
which in turn makes innovative products in the R&D sector more valuable given that they are a
complementary input with R&D spending. The third row plots product dynamics. A period of
high product entry rates follows a neutral productivity shock, which increases both the number of
products and the share of innovative products in the total products.
Figure 4 shows the results of our main interests: it compares impulse responses to a news
shock in the one-sector model (dotted line) with impulse responses to a sector-specific productivity
shock in the two-sector model (solid line). The TFP responses are nearly identical in both models.
A sector-specific productivity shock looks similar to a news shock in this sense. Consumption,
output, hours, and investment also respond similarly across models. Specifically, consumption
increases whereas output, hours, and investment decrease on impact; these findings are consistent
with Barsky and Sims (2011). However, responses of the aggregate stock market value are very
different. In the one-sector model, it falls on the impact of a news shock, whereas in the two-sector
model, it rises on the impact of a sector-specific productivity shock. The prediction from the two-
sector model is empirically supported; that is, Barsky and Sims (2011) find that an aggregate stock
market index rises on impact of their identified news shock.
26
Figure 3: Impulse responses to a neutral productivity shock () in the two-sector model. Log
deviations from the steady state are plotted.
27
Figure 4: Impulse responses to a sector-specific productivity shock () in the two-sector model
(solid line), and impulse responses to a news shock () in the one-sector model (dotted line).
Log deviations from the steady state are plotted.
28
To understand the difference, Figure 5 presents impulse response functions of an expanded list
of variables in the two-sector model. We observe that investment in physical capital decreases but
R&D spending increases significantly after a sector-specific productivity shock. A large volume
of R&D spending raises the value of innovative products in the R&D sector. The other half of
innovative products’ value, i.e., innovative products’ value as monopolistic products, decreases on
the impact of a sector-specific productivity shock because product entries will dilute per product
monopoly profits. Because capital stock also decreases, we conclude that the value of the aggre-
gate stock market rises on the impact of a sector-specific productivity shock because the value of
innovative products in the R&D sector rises.
Figure 6 shows forecast error variance decomposition. Five panels report the forecast error
variance decomposition of five important variables, i.e., TFP, consumption, output, hours, and
aggregate stock market value. There are three lines and a confidence band in each panel. One line
is data, taken from Barsky and Sims (2011), depicting the fraction of the forecast error variance
attributable to an identified news shock in their VAR model. One standard error confidence band is
also taken from Barsky and Sims (2011). The two remaining lines show theoretical predictions from
each of the two models, i.e., the fraction of the forecast error variance attributable to news shock in
the one-sector model and the fraction of the forecast error variance attributable to sector-specific
productivity shock in the two-sector model. The three lines are almost perfectly overlapped in the
top-left panel, which reports the forecast error variance decomposition of TFP. This overlap in the
three lines is due to the calibration.
Barsky and Sims’s estimates of the contribution of identified news shock vary not only across
variables but also across forecast horizons. At short horizons, identified news shocks account for
a very small share of the forecast error variances of consumption and output, a large share of the
29
Figure 5: Impulse responses to a sector-specific productivity shock () in the two-sector model.
Log deviations from the steady state are plotted.
30
forecast error variances of hours, and a modest share of the forecast error variances of aggregate
stock market value. At longer horizons, the identified news shock contributes more significantly
to the variance decomposition of aggregate variables with the exception of hours, in which the
contributions of news shocks are quickly weakened, resulting in an L-shaped plot.
The one-sector model successfully replicates the general pattern of the data. In particular,
the model’s prediction that news shocks become more important in accounting for variations of
TFP, consumption, and output at longer forecast horizons is in line with the data. However, a
closer examination reveals three important discrepancies between the model’s predictions and the
data. First, the one-sector model overemphasizes news shocks’ contributions to the forecast error
variance of consumption at a very short horizon. Second, the one-sector model predicts that news
shocks make a significant contribution to the variance decomposition of hours at both short and
long horizons, resulting in a V-shaped plot. Third, the one-sector model predicts that news shocks
account for a negligible share of the forecast error variances of the aggregate stock market value at
short horizons, with nearly zero contribution two years after a shock.
Interestingly, all three problems largely disappear in the two-sector model. First, sector-specific
productivity shocks account for a smaller share of the forecast error variance of consumption at
short horizons. This is because, as product development is investment, the resource constraint
does not allow consumption to increase after a sector-specific productivity shock as much as it
does after a news shock in the one-sector model. Second, sector-specific productivity shocks make
weaker contributions to the forecast error variance of hours at medium frequencies. The product
cycle plays an important role, meaning that because TFP improvement is achieved by high product
entry rates but new products are monopolistically produced, producers of new products do not hire
as many hours as competitive firms in the one-sector model do after a news shock. Third, sector-
31
specific productivity shocks account for a large share of the forecast error variance of the aggregate
stock market value. This is because a sector-specific productivity shock generates a large, positive
impact response of the aggregate stock market value consistent with the data.
Finally, I report unconditional second moments of selected macroeconomic variables at various
frequencies.10 The sample period of the data is from the first quarter of 1948 to the second quarter
of 2008. One thousand artificial data sets of the same sample size are generated from each of the two
models, and the median, 5th, and 95th percentiles of the moments across simulations are calculated.
Table 4 shows that both the one- and two-sector models are able to replicate general patterns of
the U.S. business cycle, i.e., cyclical components from 2 quarters to 32 quarters, extracted using the
Band-Pass filter of Christiano and Fitzgerald (2003). Empirical moments of the key macroeconomic
variables, i.e., output, consumption, investment, and hours, are particularly closely matched. As
Barsky and Sims (2011) emphasize, the one-sector model improves the simplest real business cycle
model that is driven solely by surprise technology shocks in the sense that correlations between
variables are all close to one in the one-shock model; however, if they are augmented with news
shocks, the correlations are all positive but not too close to one, which are the findings that are
more in line with the data. The same advantage is shared by the two-sector model. Empirical
moments of TFP and labor productivity are also well replicated by both the one-sector model
and the two-sector model. Volatility of the aggregate stock market value in the two-sector model
10Nominal variables are divided using the nonfarm business sector implicit price deflator, taken from the BEA.
Output is measured as production in the nonfarm business sector, taken from the BEA. Consumption is measured as
personal consumption expenditures on service and nondurable goods, taken from the BEA. Investment is measured as
personal consumption expenditures on durable goods and fixed private investment, taken from the BEA. Equity value
is measured as S&P 500 stock price index. These series are divided by the civilian, non-institutional population that
is over 16 years old, taken from the BLS. Labor productivity is measured as real nonfarm business output divided
by the hours worked by all persons in the sector. TFP is calculated by the author using real nonfarm business
output, the capacity utilization rate, the hours worked by all persons in the sector, and capital service. The capacity
utilization rate is that of the manufacturing sector, taken from the Board of Governors. Capital service is taken from
the BLS, annual observations of which I interpolate assuming constant growth over a year. Labor elasticity is set at
the average labor share over the sample period.
32
Figure 6: Forecast error variance decompositions. The horizontal axis measures the forecast
horizon. Estimates of Barsky and Sims (2011) are referred to as Data, which are the fraction of the
forecast error variance of each variable at various forecast horizons (1, 4, 8, 16, 24, and 40 quarters)
attributable to identified news shock in their VAR model. One standard error confidence band is
taken from Barsky and Sims (2011). The other two lines show the fraction of the forecast error
variance attributable to news shock in the one-sector model and the fraction of the forecast error
variance attributable to sector-specific productivity shock in the two-sector model, respectively.
33
Table 4. Second moments, Business-cycle frequency (2-32)
Standard deviation Correlation with output Autocorrelation
one- two- one- two- one- two-
Variable Data sector sector Data sector sector Data sector sector
2.22 120(100 145)
114(096 138)
1.00 100(100 100)
100(100 100)
0.84 072(062 080)
071(061 079)
1.09 039(029 051)
038(029 050)
0.81 060(046 072)
061(051 069)
0.84 092(089 095)
093(089 095)
4.89 449(384 526)
393(337 463)
0.86 097(096 098)
097(096 098)
0.85 067(057 075)
067(056 075)
1.82 042(036 049)
032(028 037)
0.89 083(076 089)
085(077 090)
0.89 066(056 074)
066(056 075)
1.24 098(082 118)
098(082 118)
0.84 098(098 099)
099(098 099)
0.74 071(061 079)
071(061 079)
1.05 089(074 107)
089(074 108)
0.57 097(095 098)
098(097 099)
0.68 073(063 080)
072(062 080)
10.21 032(023 042)
046(038 056)
0.52 040(032 046)
084(078 089)
0.82 093(091 095)
077(068 084)
is higher than that in the one-sector model, although both are much lower than their empirical
counterpart. In the one-sector model, the aggregate stock market value is not strongly correlated
with output because it is insensitive to a surprise technology shock.
Table 5 shows that both the one- and two-sector models are also able to replicate U.S. economic
fluctuations at a low frequency, from which I extract cyclical components from 33 to 200 quarters
by the Band-Pass filter before calculating the same set of second moments. Given the good fit
with the data at both the business-cycle and medium frequencies, it is not surprising that both the
one- and two-sector models are able to replicate what Comin and Gertler (2006) call medium-term
business cycles, cyclical components from 2 to 200 quarters, as reported in Table 6. Both news
shock in the one-sector model and sector-specific productivity shock in the two-sector model add
persistence to their respective models. I conclude that in terms of accounting for unconditional
second moments, both the one-sector model and the two-sector model perform equally well.
34
Table 5. Second moments, Medium frequency (33-200)
Standard deviation Correlation with output Autocorrelation
one- two- one- two- one- two-
Variable Data sector sector Data sector sector Data sector sector
4.05 293(184 446)
274(171 420)
1.00 100(100 100)
100(100 100)
0.99 099(099 099)
099(099 099)
2.87 217(126 343)
208(122 333)
0.91 090(083 094)
090(083 094)
0.99 099(099 099)
099(099 099)
7.76 686(450 987)
588(388 856)
0.83 090(083 094)
089(084 093)
0.99 099(099 099)
099(099 099)
3.76 055(035 075)
043(028 060)
0.78 077(057 090)
069(040 088)
0.99 099(099 099)
099(099 099)
2.42 214(138 321)
211(132 318)
0.65 098(097 099)
096(092 099)
0.99 099(099 099)
099(099 099)
2.72 252(156 395)
248(149 381)
0.67 099(098 099)
099(098 099)
0.99 099(099 099)
099(099 099)
29.28 240(137 390)
220(129 355)
0.75 074(059 084)
090(083 094)
0.99 099(099 099)
099(099 099)
Table 6. Second moments, Medium-term cycle (2-200)
Standard deviation Correlation with output Autocorrelation
one- two- one- two- one- two-
Variable Data sector sector Data sector sector Data sector sector
4.64 319(221 463)
299(207 437)
1.00 100(100 100)
100(100 100)
0.96 096(091 098)
095(091 098)
3.10 221(133 345)
213(130 335)
0.88 086(076 091)
085(077 091)
0.98 099(099 099)
099(099 099)
9.25 834(636 1098)
717(554 945)
0.83 090(085 093)
090(085 093)
0.95 090(083 094)
090(082 094)
4.21 069(055 089)
054(042 069)
0.80 076(061 086)
071(051 085)
0.98 088(080 092)
088(080 092)
2.71 239(171 338)
236(166 335)
0.68 098(097 099)
097(093 098)
0.94 095(090 097)
095(090 097)
2.91 269(181 405)
264(176 391)
0.64 099(098 099)
099(098 099)
0.96 097(093 098)
097(092 098)
31.25 243(141 391)
226(139 358)
0.71 069(054 080)
088(081 092)
0.98 099(099 099)
099(097 099)
35
4 Sensitivity
4.1 Role of heterogeneous products
This section closely examines the role of heterogeneous products. Heterogeneity is the result of
the product cycle, and hence, one way to determine its significance is by experimenting with a
parameter configuration that shuts the product cycle down, i.e., setting at = 0. Products
are uniformly innovative under this calibration. I keep the other parameters set at the same
values except for those governing technology shocks, which are re-calibrated so that the impulse
response functions of TFP under the alternative calibration resemble those under the benchmark
calibration. Figure 7 presents impulse response functions to a sector-specific productivity shock.
With the exception of TFP, many variables respond differently relative to their responses under
the benchmark calibration, when the parameter is set at zero. This result shows that, in spite of
its simplicity, the product cycle serves as a powerful amplification mechanism.
The difference in the response of the aggregate stock market value is striking. While it rises on
the impact of a sector-specific productivity shock under the benchmark calibration, it falls under
the alternative calibration. The key to understanding the difference is to understand the changes
in the composition of products. Remember that the dividend income share is given by
=1
"
+
µ
− 1¶−1#−1
which increases with the share of innovative products in total products. Under the benchmark
calibration, a sector-specific productivity shock has a strong effect on dividend income because
new products are innovative, and therefore, both the share of innovative products and the share
36
of dividend income increase after the shock. Although high product entry rates dilute per product
monopoly profits, the above-mentioned mechanism prevents a catastrophic crash in the value of
innovative products as monopolistic products. Under the alternative calibration, however, this
amplification mechanism is inactive because products are uniformly innovative, and hence, =
1 always holds. The dividend income share is therefore
=1
for every period. Factor shares are completely rigid. Fluctuations in dividend income are greatly
limited, and hence, a sector-specific productivity shock leads to a larger decrease in the value of
innovative products as monopolistic products.
The value of innovative products in the R&D sector rises under the alternative calibration,
but the size of the response is approximately half the size of the response under the benchmark
calibration. Because both R&D spending and product entry rates respond similarly under the two
calibrations, this difference between responses of the value of innovative products in the R&D sector
can be puzzling at first. In fact, it is simply a reflection of a difference in the steady states: the
steady state value of innovative products is much larger under the alternative calibration than under
the benchmark calibration because all products are innovative under the alternative calibration,
whereas only approximately two thirds of products are innovative under the benchmark calibration.
With this difference, similar product entry rates lead to different percentage deviations from the
steady state values.
37
Figure 7: Impulse responses to a sector-specific productivity shock () under the alternative
calibration with = 0 (solid line) and under the benchmark calibration (dotted line). Log
deviations from the steady state are plotted.
38
4.2 Role of knowledge spillover
This section closely examines the role of knowledge spillover. For this purpose, I experiment on an
alternative parameter configuration with = 1. Under this calibration, product entries increase in
a linear fashion with R&D spending. No diminishing returns to scale set in and the efficiency of
product innovation is unaffected by the stock of innovative products. The other parameters are set
at the same values with the exception of those governing technology shocks, which are re-calibrated
so that the impulse response functions of TFP resemble those under the benchmark calibration.
Figure 8 presents impulse response functions to a sector-specific productivity shock. Responses
of TFP are unable to be perfectly matched because the alternative calibration removes persis-
tence. The lack of persistence indicates the importance of knowledge spillover as an amplification
mechanism.
Once again, the responses of the aggregate stock market value are strikingly different. Although
aggregate stock market value rises on the impact of a sector-specific productivity shock under the
benchmark calibration, under the alternative calibration, it falls. The cause is easily understood.
Under the benchmark calibration, the aggregate stock market value is decomposed into three parts:
capital stock, the value of innovative products as monopolistic products, and the value of innovative
products in the R&D sector. Among those three parts, only the last, the value of innovative products
in the R&D sector, responds positively to sector-specific productivity shocks, hence contributing to
capital gain in aggregate stock market value. Under the alternative calibration, however, innovative
products have no use in the R&D sector. Therefore, aggregate stock market value consists of only
two parts: capital stock and the value of innovative products as monopolistic products. Without
capital gain in the value of innovative products in the R&D sector, a sector-specific productivity
39
shock leads to a crash in aggregate stock market value.
5 Conclusion
Most of the theoretical work in the news shock literature abstracts away from structural explana-
tions, assuming instead that good news is a pure signal giving agents advance notice that aggregate
technology will undergo exogenous change at some future point. This assumption is convenient for
the purposes of introducing optimism and pessimism into the rational expectation model. However,
such an assumption is arguably unrealistic, and without a structure detailing the cause of future
technological progress, analysis based on this assumption may lead to misguided policy recommen-
dations.
Searching for a structural explanation for news is therefore important, and the current paper
contributes to that search. Specifically, it proposes that a surprise improvement in sector-specific
productivity in the R&D sector can be seen as news about aggregate productivity. Given a large
body of literature that identifies R&D as an important contributor to aggregate productivity im-
provement (Romer (1990); Grossman and Helpman (1991); Aghion and Howitt (1997)), I believe
it is a natural place to look for the structural origin of news about aggregate productivity.
The model economy proposed in this paper performs very well in matching the data. Specifically,
a sector-specific productivity shock generates dynamic responses of TFP that are close to dynamic
responses of TFP to identified news shocks estimated by a prominent empirical study (Barsky and
Sims (2011)). Moreover, the model is able to match important aspects of the data better than a
textbook neoclassical growth model augmented with news shocks. In other words, the model offers
not only a deeper explanation for news but also better explanations for the data than a simple
40
Figure 8: Impulse responses to a sector-specific productivity shock () under the alternative cal-
ibration with = 1 (solid line) and under the benchmark calibration (dotted line). Log deviations
from the steady state are plotted.
41
model in which news shocks are introduced in a standard way as they are in the literature.
I believe that the proposed mechanism is reasonable and that the model’s ability to match data
is largely satisfactory, but I also recognize that there are other possibilities that can explain news
equally well. For example, Comin, Gertler, and Santacreu (2009) explore an alternative explanation,
proposing an unexpected advancement of the technology frontier as news that slowly diffuses to
the economy through the costly implementation of new ideas. Such competing explanations should
be further explored as the effort will ultimately lead to a better understanding of news, the source
of technological progress, and the source of economic fluctuations.
References
Aghion, P., and P. Howitt (1997): Endogenous Growth Theory, vol. 1 of MIT Press Books. The
MIT Press.
Barsky, R. B., and E. R. Sims (2011): “News shocks and business cycles,” Journal of Monetary
Economics, 58(3), 273 — 289.
Beaudry, P., and F. Portier (2004): “An Exploration Into Pigou’s Theory of Cycles,” Journal
of Moneray Economics, 51, 1183—1216.
(2006): “Stock Prices, News, and Economic Fluctuations,” American Economic Review,
96, 1293—1307.
Bilbiie, F., F. Ghironi, and M. J. Melitz (2007): “Endogenous Entry, Product Variety, and
Business Cycles,” NBER Working Papers 13646, National Bureau of Economic Research, Inc.
42
Bilbiie, F. O., F. Ghironi, and M. J. Melitz (2012): “Endogenous Entry, Product Variety,
and Business Cycles,” Journal of Political Economy, 120(2), pp. 304—345.
Christiano, L. J., and T. J. Fitzgerald (2003): “The Band Pass Filter,” International Eco-
nomic Review, 44, 435—465.
Comin, D., and M. Gertler (2006): “Medium-Term Business Cycles,” The American Economic
Review, 96, 523—551.
Comin, D. A., M. Gertler, and A. M. Santacreu (2009): “Technology Innovation and Dif-
fusion as Sources of Output and Asset Price Fluctuations,” Discussion Paper 15029, NBER
Working Paper Series.
Den Haan, W., and G. Kaltenbrunner (2009): “Anticipated growth and business cycles in
matching models,” Journal of Monetary Economics, 56(3), 309 — 327.
Fujiwara, I., Y. Hirose, and M. Shintani (2011): “Can News Be a Major Source of Aggregate
Fluctuations? A Bayesian DSGE Approach,” Journal of Money, Credit and Banking, 43(1),
1—29.
Futagami, K., and T. Iwaisako (2007): “Dynamic Analysis of Patent Policy in an Endogenous
Growth Model,” Journal of Economic Theory, 132, 306—334.
Grossman, G. M., and E. Helpman (1991): Innovation and Growth. The MIT Press, Cambridge.
Jaimovich, N., and S. Rebelo (2009): “Can News about the Future Drive the Business Cycle?,”
American Economic Review, 99, 1097—1118.
43
McGrattan, E. R., and E. C. Prescott (2010): “Unmeasured Investment and the Puzzling
U.S. Boom in the 1990s,” American Economic Journal: Macroeconomics, 2, 88—123.
Nam, D., and J. Wang (2010): “The Effects of News About Future Productivity on International
Relative Prices: An Empirical Investigation,” Unpublished.
Peretto, P. F. (1996): “Sunk Costs, Market Structure, and Growth,” International Economic
Review, 37(4), pp. 895—923.
(1998): “Technological Change and Population Growth,” Journal of Economic Growth,
3, 283—311, 10.1023/A:1009799405456.
Pigou, A. (1927): Industrial Fluctuations. MacMillan, London.
Romer, P. M. (1990): “Endogenous Technological Change,” The Journal of Political Economy,
98, S71—S102.
Schmitt-Grohe, S., and M. Uribe (2008): “What’s News in Business Cycles,” Working Paper
14215, National Bureau of Economic Research.
Smulders, S., and T. van de Klundert (1995): “Imperfect competition, concentration and
growth with firm-specific R & D,” European Economic Review, 39(1), 139 — 160.
44