Global COE Hi-Stat Discussion Paper Series 218

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Energy-Saving Technological Change in Japan

Hi-Stat Discussion Paper

Takeshi Niizeki

January 2012

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Energy-Saving Technological Change in Japan ∗Takeshi Niizeki†
Graduate School of Economics, Hitotsubashi University
January 10, 2012

Abstract
The energy-dependence of Japan’s economy declined considerably following the ﬁrst oilcrisis in 1973. This paper examines what caused the sharp drop in the use of energy perunit of gross national product (GNP) observed in the 1970s and 1980s, using a simple neoclassical growth model with energy as a third production input. Two possible candidates areinvestigated: (i) the substitution eﬀect due to changes in the relative price of energy, and (ii)energy-saving technological progress. The ﬁndings are as follows. First, the substitution eﬀect
alone is weak and alone cannot account for the decline in the energy-GNP ratio. Second,the estimated level of energy-saving technology more than tripled between 1970 and the late1980s, and the model with energy-saving technological progress is able to explain the drop in
the energy-GNP ratio well.

Keywords: relative energy price, energy-saving technological progress∗ I would like to thank my dissertation supervisor, Naohito Abe for his support and discussions on this paper.
I also thank Etsuro Shioji, Makoto Saito, Prakash Loungani, Shiba Suzuki, Jun-Hyung Ko, and participants of
the Macroeconomic Lunch Seminar at Hitotsubashi University, the DSGE Workshop at Senshu University, and theTokyo Environmental Economics Workshop at Sophia University for their helpful comments. This work is supportedby the Global Center of Excellence Project at Hitotsubashi University.
† Email: ed091003@g.hit-u.ac.jp1

1

Introduction

In the 1970s and 1980s, Japan experienced a dramatic change in the relationship between realenergy use and real gross national product (GNP). One way to gauge this is to look at real energy
use relative to real GNP, or what will be referred to as the energy-GNP ratio hereafter, where realenergy use is calculated as the total quantity of fossil fuels1 (petroleum, coal, and liquid naturalgas) consumed measured in constant prices.2 Figure 1 depicts the trend in Japan s energy-GNP
ratio over the past four decades. As can be seen, the energy-GNP ratio stood at close to 2.4% in1973 but subsequently declined sharply. By 1988, it had fallen to about 1.3%, i.e., almost half ofthe 1973 value and since then has remained at this level.

Figure 1: Real energy use-real GNP ratio. Real energy use is the total quantity of fossil fuelsconsumed measured in constant prices.
Discussion to explain the drop in the energy-GNP ratio has generally focused on two possible
candidates: (i) the substitution eﬀect, and (ii) energy-saving technological progress. The substitution eﬀect works as follows. When the relative price of energy rises, energy is substituted withother inputs such as labor and capital. Thus, as output increases, we would expect the input ofenergy per unit of output, or the energy-GNP ratio, to decrease. The trends in the actual relative
price of energy and in real energy use are depicted in Figure 2, where the relative price of energy is
calculated by dividing the energy price deﬂator by the GNP deﬂator.3 As can be seen, the relative
price of energy shot up in 1973, the year of the ﬁrst oil shock, and again in 1979, the year of
the second oil shock, so that by the mid-1980s it had more than tripled when compared with the
1 Energy use here excludes nuclear power due to the lack of price data.
2 Real energy use here is measured in yen terms rather than in terms of quantity such as joule or British thermal
units (Btus) to make it easier to compare energy use with GNP. See the Appendix for details of the data construction.
3 The calculation of the energy price deﬂator is described in the Appendix.

2

Figure 2: Real energy use and relative energy pricebeginning of the 1970s. On the other hand, real energy use measured in yen, dipped following theﬁrst oil shock and declined substantially following the second. Therefore, the substitution eﬀect isa good potential candidate for explaining the drop in the energy-GNP ratio.
Against this background, the purpose of this paper is to examine the reasons for the drop in
the energy-GNP ratio during the 1970s and 1980s by quantitatively examining the two possible
explanations. To do so, a simple neoclassical growth model with energy as a third input for
production is constructed and two simulations are conducted. In the ﬁrst simulation, the actual
path of the relative price of energy is fed into the model as an exogenous variable to examine thequantitative impact of the substitution eﬀect on the energy-GNP ratio. In the second simulation,an estimated path of energy-saving technology is additionally fed into the model to examine therole of energy-saving technological change.
From an economic perspective, there are at least two reasons why it is important to understand
why the energy-GNP ratio has fallen. The ﬁrst is related to the carbon dioxide emissions associatedwith fossil fuel consumption, which represent a negative externality. Since the energy consideredin this paper consists of fossil fuel, a reduction in the energy-GNP ratio implies a reduction in thisnegative externality per unit of GNP. The second reason why it is important to understand why theenergy-GNP ratio has fallen is in the context of business cycles. Taking their cue from the Great
Moderation debate going back to Stock and Watson (2002), which suggests that the United Statesand other major economies, including Japan, Germany and France, have experienced a decline in
the volatility of business cycle ﬂuctuations in recent decades, Ko and Murase (2010) examined thecase of Japan. They ﬁnd that the volatility of output in Japan declined in the mid-1970s, although
it did increase again in the late 1980/early 1990s and again in the late 2000s.4 The decline in the
4 The increase in volatility of output in the late 1980s/early 1990s coincides with the collapse of the bubble
economy that Japan experienced in the second half of the 1980s, while that in the late 2000s coincides with the3energy-GNP ratio may be one possible explanation for the decrease in the volatility of output inthe mid-1970s, since it may have made the economy less sensitive to energy price shocks.
The ﬁndings of this paper are as follows. The substitution eﬀect due to changes in the relative
price of energy is weak and, taken alone, cannot account for the drop in the energy-GNP ratio.
On the other hand, once the estimated path of energy-saving technology is incorporated into themodel, the energy-GNP ratio generated by the model ﬁts well with the actual data.
This remainder of the paper is organized as follows. Section 2 describes the model, while Section
3 discusses the calibration. Next, Section 4 presents the simulation results and conducts sensitivity
analyses. Section 5 concludes the paper.

2

The Model

The model employed here is based on that developed by Kim and Loungani (1992), who incorporate
energy as a third input into an otherwise standard real business cycle model.5 The model assumes
that there is a representative household with Nt members at time t. In addition, for simplicity it
is assumed that the size of household does not grow over time.6 The household chooses the pathof consumption, leisure, and investment so as to maximize the life-time utility functionmax ∞{ct ,ht ,kt+1 }t=0∞∑

β t Nt [ln ct + A ln(1 − ht )]

(1)

t=0

subject to
Ct + Xt = wt Ht + rt Kt(2)

Xt = Kt+1 − (1 − δ)Kt ,(3)

where Ct is aggregate consumption, Xt is aggregate investment, wt is the wage rate, Ht isaggregate hours worked, rt is the rental rate of capital, δ is the depreciation rate, and β is thediscount factor. The time endowment is normalized to unity and is divided into labor and leisure.
The representative ﬁrm faces the following proﬁt maximization problem:max{Kt ,Ht ,Et }Yt − rt Kt − wt Ht − pt Et(4)subject to
Yt = τt Htθ [(1 − α)Kt−ι + αEt−ι ]−

(1−θ)
ι

,

(5)

where Yt is aggregate output, τt is total factor productivity (TFP), pt is the energy price interms of ﬁnal goods, and Et is aggregate energy use. As will be discussed below, several studies,such as Hassler, Krusell, and Olovsson (2011), suggest that the elasticity of substitution between
energy and other inputs is considerably less than unity. Therefore, a nested constant elasticity ofrecent ﬁnancial crisis. The general trend of the volatility of output, however, is downward-sloping.
5 Kim and Loungani (1992) assume that ﬂuctuations in the relative price of energy are stochastic, while the model
employed here incorporates the actual path of the relative energy price into the model. In other words, there is no
uncertainty in the model here.
6 The simulation results remain largely unaﬀected when this assumption is changed and the population is allowed
to grow.

4substitution production function with constant returns to scale is used.7 The ﬁrm imports energy
from abroad at exogenously given price pt per unit.8 TFP is also exogenous to the ﬁrm and isassumed to grow over time at the average TFP growth rate for the period 1970-2009. A numberof studies have highlighted the important role of the time-varying growth rate of TFP (e.g., Coleand Ohanian 1999, Hayashi and Prescott 2002, Otsu 2008) in macroeconomic analyses. However,since improvements in TFP simply result in a simultaneous increase in GNP and energy use, they
do not play a crucial role in changes in the energy-GNP ratio.9 Therefore, a constant rate of TFP
growth is assumed in this paper.
The resource constraint is as follows:
Ct + Xt = Yt − pt Et ≡ V At ,(6)

where V At denotes value-added at time t. That is, output produced domestically is either
consumed, invested, or exported as payment for imported energy. Note that exports are equal
to imports in each period, so that the trade balance is always zero. Finally, as in the studies by
Hayashi and Prescott (2002), Chen, İmrohoroğlu, and İmrohoroğlu (2006), and Hassler, Krusell,and Olovsson (2011), it is assumed that agents have perfect foresight about the sequence of exogenous variables. This assumption is relaxed in Section 4.3. The model is then solved numericallyby applying a shooting algorithm given the initial capital stock level and the path of exogenous
variables. The initial capital stock is taken from the actual data.10

3

Calibration

There are six parameters {β, δ, θ, A, α, s} to calibrate. s is the elasticity of substitution between
capital stock and energy, and s ≡ 1/(1 + ι).
The value for β is borrowed from Otsu (2008) and set at 0.98. δ is obtained from Hayashi
and Prescott (2002) and set at 0.089. The capital stock series are constructed using the perpetualinventory method. For θ, the average labor income share in GNP for the period 1970-2009 is used.
The leisure weight in preferences, A, is obtained by solving the intra-temporal optimal condition
for A,
A=θ

Yt 1 − ht
,
Ct ht

(7)

and averaging equation (7) over the 1970-2009 period.11 To calibrate α, the production function
and the ﬁrst-order condition for energy use are combined as follows:
7 Hassler, Krusell, and Olovsson (2011) employ an alternative speciﬁcation of the utility function, namely:

] ε
[
ε−1
ε−1 ε−1
Yt = (1 − γ)[At Ktα L1−α] ε + γ[AEt Et ] εt
The simulation results are robust to this alternative utility function.
8 In the case that fossil fuels are extracted domestically, an alternative interpretation of the energy price would
be that pt represents the unit cost of fossil energy extraction. However, since Japan imports almost all its fossil
energy from abroad, this interpretation is not employed here.
9 Note that to replicate the trend shown in Figure 1 a shock that diminishes energy use for a given level of GNP
is needed.
10 It is assumed that the capital stock reaches its balanced growth level in 1989. Thus, the initial capital stock is
obtained as (k1970 /k1989 ) ∗ kss ≃ 0.36 ∗ kss, where kss denotes the steady state level of capital stock.
11 Weekly hours worked per working-age person is deﬁned as

5

1−α
=
α

(

(1 − θ)Yt − pt Et
pt Et

)(

Et
Kt

)−ι
(8)

Equation (8) is then solved for α and α is then averaged over 1970-2009.
Previous studies provide numerous estimates of s, the elasticity of substitution between capitalstock and energy. For instance, Kim and Loungani (1992) use two values, s = 0.588 taken from
Morrison and Berndt (1981) and s = 1.000 taken from Griﬃn and Gregory (1976), and conduct
separate simulations to compare the results. Backus and Crucini (2000) report a value of s = 0.09,
while Miyazawa (2010) conducts a generalized method of moments estimation and reports valuesof s = 0.100 and s = 0.086. Finally, Hassler, Krusell, and Olovsson (2011)12 use maximum
likehood estimation and arrive at an elasticity of substitution between energy and the capital/laborcomposite of 0.053. In this paper, s = 0.15 is employed. Note that as long as s is around 0.1, themain results shown in Section4 are not substantially aﬀected.
The path of exogenous variables after the observation period also needs to be speciﬁed in order
to conduct the simulation below. Here, it is simply assumed that the relative price of energy, pt ,and the TFP growth rate after 2009 are the same as the averages over the period 1970-2009. The
calibration results are shown in Table 1.
Parameters
s
θ
δ
β
A
α

Description
Elasticity of subst. btw. capital and energy
Labor share
Depreciation rate of capital
Discount factor
Leisure weight in preferences
Share of energy in capital-energy composite

Value
0.15000.61570.08900.98002.30470.0358

Table 1: Parameter values

4

Results

4.1

The role of the relative price of energy

As can be seen in Figure 2, there were two major spikes in the relative price of energy in the
1970s ― one in 1973 and one in 1979. Using the simple growth model introduced here, let us
now examine whether the substitution eﬀect alone, triggered by the surge in the relative energy
price, can explain the observed decline in the energy-GNP ratio. The simulation result is shownin Figure 3.
As can be seen in Figure 3, energy price ﬂuctuations inﬂuence the energy-GNP ratio, but
not substantially. The energy-GNP ratio does decrease after 1973 and 1979, but the extent isℓt ∗ M t,
Nt ∗ 16 ∗ 7
where ℓt is average weekly hours worked per worker and Mt is employment. Following Otsu (2008), it is also
assumed that the maximum number of hours worked per day is 16.
12 Note that their production function, shown in footnote 7, is slightly diﬀerent from the one employed here.
ht ≡6

Figure 3: Energy-GNP ratio taking only the change in the relative energy price into consideration

very limited. In addition, in the model, the energy-GNP ratio continues to rise in the mid-1980s
reﬂecting the downturn in the relative price of energy, while in the actual data the ratio declines.
To examine the large discrepancy between the data and the model after the 1970s, the actual
data and the simulation results for GNP and energy use are shown separately in Figure 4. Bothvariables are detrended at 2% per year and normalized to 100 for 1970.13 As can be seen, thediscrepancy in the energy-GNP ratio between the data and the model is mainly due to the use ofenergy, not GNP.
The next task therefore is to examine what leads the model to overpredict energy use. The
answer lies in the ﬁrst order condition for energy use:
pt = (1 − θ)τt Htθ [(1 − α)Kt−ι + αEt−ι ]−

(1−θ)
−1
ι

αEt−ι−1 ,(9)where the left hand side is the marginal cost, while the right hand side is the marginal product,
and hence the marginal beneﬁt, of energy use. Although these are equal in equilibrium, it is notguaranteed that they are equal in practice. Figure 5 shows the marginal beneﬁt relative to themarginal cost of energy use calculated from the actual data. As can be seen, from the 1980s
onward, the marginal beneﬁt considerably outweighs the marginal cost of energy use. This implies
that it would be optimal for ﬁrms to increase energy input so that the marginal beneﬁt equals
the marginal cost of energy use. Since this was not the case, the question arises why ﬁrms did
not purchase more energy after the 1970s. A possible answer to this question is energy-saving
technological progress.
13 Following Hayashi and Prescott (2002), a trend growth rate of 2% is used here because it is the average growthrate of the U.S. economy in the 20th century. In other words, the model here assumes that all variables except labor
input grow at 2% once the model economy reaches its balanced growth path.

7

Figure 4: GNP and energy use: Data vs. model

Figure 5: Marginal beneﬁt relative to marginal cost of energy use calculated from the actual data

8

4.2

The role of energy-saving technological progress

The previous subsection suggested that, from the 1980s, ﬁrms did not increase their energy input
even though, according to the model, this should have aﬀorded them with greater proﬁts. Thissuggests the possible presence of energy-saving technological progress.
There are a number of empirical studies that have sought to examine the role of energysaving technological change. For instance, Popp (2002), using U.S. patent data from 1970 to
1994, looks at the impact of increases in energy prices on energy-eﬃciency innovations. He ﬁnds
that the rise in energy prices has a statistically signiﬁcant positive impact on energy-eﬃciency
innovations. On the other hand, Newell, Jaﬀe, and Stavins (1999) investigate whether energy
prices aﬀect the energy eﬃciency of new models of energy-using consumer durables, such as room
air conditioners and gas water heaters, and conclude that for some products the direction of
innovation is inﬂuenced by changes in energy prices. For Japan, Fukunaga and Osada (2009)
measure energy-saving technological change by estimating time-varying biases of technical change.
They report that the bias of technical change for energy input in the 1980s was energy-saving.
Another strand of studies deals with energy-saving technological change from a theoreticalperspective. Alpanda and Peralta-Alva (2010) introduce technology-speciﬁc capital and irreversible
investment in a two-sector model and succeed in generating the drop in the energy-output ratio
observed in the United States after the ﬁrst oil crisis. Meanwhile, Hassler, Krusell, and Olovsson(2011) developed a neoclassical growth model with non-renewable resources and measured thelevel of energy-saving technology in the United States, assuming perfect competition in input
markets. They ﬁnd that energy-saving technological progress started in 1973 and, using theirmodel, moreover show that it is essential for generating the actual time path of real energy.
In this paper, the level of energy-saving technology is measured as follows. First, zt is added
into the production function:
Yt = τt Htθ [(1 − α)Kt−ι + α(zt Et )−ι ]−

(1−θ)
ι

,

(10)

where zt is the level of energy-saving technology. In macroeconomic analyses, the level oftechnology, such as zt here, is generally estimated as a residual. However, that strategy does notwork in this case in this case, since there are two unknowns {τt , zt } but only one equation (equation(10)). To estimate zt , the ﬁrst-order condition for energy use shown below is used, and equations(10) and (11) are solved simultaneously for τt and zt :pt = (1 − θ)τt Htθ [(1 − α)Kt−ι + α(zt Et )−ι ]−

(1−θ)
−1
ι

α(zt Et )−ι−1 zt(11)Since the eﬀect of energy-saving technological progress is removed from TFP growth, τt is now
renamed “modiﬁed TFP.” The measured level of energy-saving technology, TFP and modiﬁed TFP
are displayed in Figure 6. TFP is measured as a residual using equation (5), so that it includes
the eﬀect of energy-saving technological progress.
The ﬁgure shows that the energy-saving technology level starts to rise in the early 1970s andexceeds a value of 3 by the mid-1980s. After that, it continues to ﬂuctuate around a value of 3.5.14
Table 2 shows the average annual growth rates of TFP, modiﬁed TFP, and the energy-saving
technology level in each period. As can be seen, the rate of growth in the energy-saving technology
level in the 1970s and 1980s was substantial and remained non-negligible thereafter. In addition,
the average annual growth rate of TFP over the 1970-2009 period was 2.18%, whereas the modiﬁed
14 Note that in Section 4.1 it was assumed that z

t is always equal to 1.

9

Figure 6: Measured level of energy-saving technology, TFP and modiﬁed TFP. The initial levels
are normalized to unity.

Variables
TFP
Modiﬁed TFPEnergy-saving technology

1970-79
0.46%
0.40%
5.21%

1980-89
4.11%
2.46%
8.61%

1990-99
0.49%
0.29%
0.82%

2000-09
2.94%
2.04%
0.40%

1970-2009
2.18%
1.53%
3.34%

Table 2: Average annual growth rates of exogenous variables

TFP growth rate was only 1.53%. This suggests that about 30% ≃ 100 ∗ (1 − (1.53/2.18)) of the
TFP improvements in this period is attributable to energy-saving technological progress. This
number may be too large. There are at least two possible reasons to think why this might be
the case. First, the deﬁnition of energy here excludes nuclear energy, resulting in overestimationof energy-saving technological progress. Nuclear power plants started to be built in Japan in
the late 1960s, and in ﬁscal 2009, nuclear energy accounted for approximately 12% of Japan’s
total energy supply. Second, during the period, Japan’s industrial structure changed from one
dominated by heavy industries (such as steel and shipbuilding) to one dominated by knowledgeintensive industries (such as electronics), which decreased energy use. This change is not directly
related to energy-saving technological progress but is included in the measured z.
Another problem with the series of zt is that it suggests that the level of energy-saving technology occasionally declines ― something that runs counter to our perceptions of technology. The
likely reason is that zt is estimated as a residual so that it contains other elements which are notrelated to energy-saving technological progress. Similarly, the jump seen for 2009 unlikely reﬂects
a sharp rise in the level of energy-saving technology and instead simply is due to the fact that10

in this year energy use decreased despite the drop in the relative energy price shown in Figure 2.
Thus, short-term ﬂuctuations in zt need to be regarded with a degree of caution; however, from alonger-term perspective, Figure 6 is likely to present a relatively accurate picture of improvementsin the level of energy-saving technology.
Next, the impact of energy-saving technological progress on the dynamics of the energy-GNP
ratio is examined. In addition to the relative energy price, the time path of the level of energy-saving
technology obtained in Section 4.2 is fed into the model. Figure 7 presents the simulation result.
This time, the model with energy-saving technological progress closely ﬁts the data. The reason
is as follows. After 1973, the level of energy-saving technology starts to increase considerably, andby the end of the 1980s, it has more than tripled. Due to energy-saving technological progress, theenergy required to produce the same amount of output for a given level of capital stock and hours
worked declined. As a result, the energy-GNP ratio decreased over this period.

Figure 7: Energy-GNP ratio with energy-saving technological progress

4.3

Sensitivity analysis

So far it has been assumed that economic agents have perfect foresight about the future path of
the relative price of energy. In other words, deterministic simulations were conducted. However,
it would be more plausible to treat energy price shocks as surprising events. Therefore, in thissubsection a stochastic simulation is conducted à la Chen, İmrohoroğlu, and İmrohoroğlu (2006) toexamine how much the results obtained in Section 4 depend on the perfect foresight assumption.
In the stochastic simulation, it is assumed that economic agents believe that the relative price ofenergy indeﬁnitely remains constant at its average price. However, at the beginning of each period,
they learn the actual energy price level. Thus, the energy price can be seen as the forecast error
and represents a “surprise” or “energy price shock.” Note that even though they face a “surprise”
or “energy price shock” every period, they still assume that the energy price will remain constant11

at its average in the future.
Figure 8 compares the simulation results of the deterministic and the stochastic model. The
two simulated paths are quite similar, yielding the conclusion that surprise shocks to the relative
energy price play a limited role in explaining the changing dynamics in the energy-GNP ratio.

Figure 8: The role of expectations

5

Conclusion

In this paper, a simple neoclassical growth model with energy as a third factor of production isconstructed, and it is examined to what extent the model can account for the observed decline
in the energy-GNP ratio. The ﬁndings can be summarized as follows. First, the substitution
eﬀect resulting from a rise in the relative price of energy alone cannot explain the movementin the energy-GNP ratio when an elasticity of substitution between capital and energy use in areasonable range is assumed. Second, the estimated level of energy-saving technology more thantripled during the 20 year period from 1970 to the late 1980s. And third, when energy-saving
progress is incorporated, the model can account for the decrease in the energy-GNP ratio.
There are some possible extensions to improve the analysis presented here. First, as discussed
in Section 4.2, because the energy-saving technology level is estimated as a residual, it probably
contains other factors which are not related to energy-saving technological change. This meansthat it is necessary to estimate “pure” energy-saving technological change. Second, since energysaving technological change is treated as exogenous, endogenizing technological progress represents
another potentially interesting extension. These issues are left for future research.

12

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[17] Newell, R. G., Jaﬀe, A. B., and Stavins, R. N. (1999) “The Induced Innovation Hypothesis
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14

6

Appendix

This Appendix brieﬂy describes the construction of the data series for the current study. The data
are obtained from two distinct sources: the “Trade Statistics of Japan” published by the Ministryof Finance, which are used for the energy data, and the study by Kobayashi and Inaba (2006),
from which data for other aggregate variables are obtained.

6.1

EnergyIn the analysis here, the energy-related variables are aggregate energy use, Et , and the relative priceof energy, pt . These variables are constructed based on the methodology developed by Atkeson
and Kehoe (1999). Aggregate energy use Et at time t is calculated as follows:∑
Et ≡Pi,0 Qi,t ,(12)
iwhere i denotes the type of energy. In the analysis here, there are three types of energy:
petroleum, coal, and liquid natural gas. Pi,0 is the price of type i energy in the base year, which is2000. Note that Pi,0 is the CIF price converted into Japanese yen, so that exchange rate changes
are already taken into account. Qi,t is the amount of imported type i energy in year t. Note that
Qi,t is the amount of imports, not the amount of consumption of type i energy. However, sincemost of the energy imported in any given year is consumed within the year, Qi,t is treated as theamount of consumption of type i energy in year t.
To construct the relative price of energy, the energy price deﬂator at time t, denoted as DEFtP ,is derived as follows:∑P
i Pi,t Qi,t∑
DEFt ≡(13)
i Pi,0 Qi,tThen the relative price of energy, pt , is constructed by dividing the energy price deﬂator by the
GNP deﬂator, whose base year is also 2000:
pt ≡

DEFtP
,
DEFtY

(14)

where DEFtY is the GNP deﬂator at time t.

6.2

Other aggregate variables

Other aggregate variables are constructed based on the study by Kobayashi and Inaba (2006),
which extended Hayashi and Prescott’s (2002) data set with some adjustments. There are four
diﬀerences between Kobayashi and Inaba’s (2006) data and my data set. First, my data set is
updated to the latest year, 2009. Second, since the government sector is not included in the analysis
here, government consumption is incorporated in aggregate consumption Ct , while government
ﬁxed capital formation is included in aggregate investment Xt . Third, the capital stock series
are constructed using the perpetual inventory method. Fourth, because energy is an input, it issubtracted from gross output to obtain value added.

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