measuring energy-saving technological change: international … · 2020. 8. 12. · measuring...
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Measuring Energy-saving Technological Change:
International Trends and Differences*
Emiko Inoue† Hiroya Taniguchi‡ Ken Yamada§
December 2020
Abstract
Technological change is essential for balancing economic growth and environmental sustain-
ability. This study measures and documents energy-saving technological change to understand its
trends in advanced countries over recent decades. We estimate aggregate production functions with
factor-augmenting technology using cross-country panel data and shift–share instruments, thereby
measuring and documenting energy-saving technological change. Our results show how energy-
saving technological change varies across countries over time and the extent to which it contributes
to economic growth in 12 OECD countries from the years 1978 to 2005.
KEYWORDS: Non-neutral technological change; capital–labor–energy substitution; growth ac-
counting.
JEL CLASSIFICATION: E23, O33, O44, O50, Q43, Q55.
*We are grateful to Kenji Takeuchi, Makiko Nakano, and participants in the Japanese Economic Association SpringMeeting and the Annual Conference of the Society for Environmental Economics and Policy Studies for helpful commentsand discussions. Inoue and Yamada acknowledge support from the Sumitomo Foundation. Yamada acknowledges supportfrom JSPS KAKENHI grant number 17H04782.
†Kyoto University. [email protected]‡Kyoto University. [email protected]§Kyoto University. [email protected]
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1 Introduction
One of the greatest challenges facing society is to achieve environmental conservation and sustainable
development. Technological change has been in the past, and will be in the future, the most promising
way to balance economic growth and environmental sustainability. Society must urgently adopt and/or
develop new technology to enable the more efficient use of energy and natural resources in the face
of serious environmental problems, including climate change, environmental pollution, and resource
depletion. Given the global nature of environmental problems, efforts to save energy need to expand
worldwide. However, it has so far been hard to confirm how such efforts have evolved across countries
over time because of the difficulty in assessing the rate of change in aggregate energy-related tech-
nology. The goal of this study is to measure and document the international trends in energy-saving
technological change over recent decades.
Measuring energy-saving technological change is challenging. Environmentally friendly techno-
logical change is typically measured in the literature using data on research and development (R&D)
and patents (Popp, 2019). These measures, however, have some drawbacks. R&D spending is a mea-
sure of an input into the innovation process rather than its outcomes. The number of patents is a
measure of product innovation, but not process innovation. In this study, we measure energy-saving
technology in terms of output and factor inputs along the lines of the Solow (1957) residual, also known
as total factor productivity (TFP). Similarly to TFP, but differently from R&D and patents, our mea-
sure can change depending on the actual circumstances of national income and technology adopted in
the economy, including not only patented product technology but also unpatented product and process
technology. At the same time, our measure differs from TFP in that it allows technological change to
be factor-augmenting.
We measure factor-augmenting technological change using the aggregate production function and
its first-order conditions. Our method builds upon the seminal work by Caselli and Coleman (2002,
2006). We quantify the level and rate of change in energy-saving technology without specifying the
functional forms of technological change for a given value of the elasticity of substitution in the pro-
duction function. Our study differs from that of Caselli and Coleman (2002, 2006) in that it uses the
2
value of the elasticity of substitution estimated after taking into account the variation in unobserved
factor-augmenting technology across countries over time.
We estimate the elasticities of substitution in aggregate production functions using shift–share in-
struments and cross-country panel data from 12 OECD countries. The estimated elasticities of sub-
stitution among capital, labor, and energy inputs are significantly less than one. Our results show that
energy-saving technological change varies substantially across countries over time. Progress in energy-
saving technology is associated with a rise in government spending on energy-related R&D but not
with a rise in the number of energy-related patents. We use our measure of capital-, labor-, and energy-
augmenting technology to decompose the rate of growth in output into specific factor-augmenting tech-
nology as well as specific factor inputs. Our results indicate that energy-saving technological change
contributed to economic growth in many countries from the years 1978 to 2005.
The rest of the paper proceeds as follows. The next section reviews the literature. Section 3 in-
troduces aggregate production functions used to measure energy-saving technological change. Sec-
tion 4 considers the identification and estimation of parameters in the production functions. Section
5 describes data used in the analysis. Section 6 presents empirical results. Section 7 discusses the
interpretation of results when extending the model. The final section summarizes and concludes.
2 Related Literature
This study is related to two strands of the literature. First, it contributes to the literature that measures
non-neutral (factor-augmenting) technological change. The direction and magnitude of non-neutral
technological change can be measured by estimating either a production or a cost function. Brown
and Cani (1963) and David and van de Klundert (1965) develop an approach that uses a constant-
elasticity-of-substitution (CES) production function.1 van der Werf (2008) adopts this type of approach
to measure energy-saving technological change in 12 OECD countries from the years 1978 to 1996.
Binswanger (1974) develops an alternative approach that uses the factor-share equations derived from
1See León-Ledesma, McAdam and Willman (2010, Table 1) for a list of related studies, including Klump, McAdam andWillman (2007), who measure capital- and labor-augmenting technology in the United States from the years 1953 to 1998.
3
a translog cost function.2 Sanstad, Roy and Sathaye (2006) adopt this type of approach to measure
energy-saving technological change in India from the years 1973 to 1994, the Republic of Korea from
the years 1980 to 1997, and the United States from the years 1958 to 1996. The advantages of the former
approach are that it does not require estimating many parameters (or dealing with many endogenous
regressors) and can estimate the key parameters in computable general equilibrium models to analyze
climate and energy policies. However, both approaches have a common limitation that non-neutral
technology is treated as parametric and deterministic components in the production or cost function.
Most studies assume that non-neutral technology changes at a constant rate.
Caselli and Coleman (2002, 2006) develop an approach that measures non-neutral technology from
the production function and its first-order conditions without specifying the functional forms of tech-
nological change for the given values of the substitution parameters in the production function. Caselli
and Coleman (2002) measure non-neutral technology that augments capital as well as skilled and un-
skilled labor in the United States from the years 1963 to 1992, while Caselli and Coleman (2006)
measure non-neutral technology that augments skilled and unskilled labor in 52 countries in the year
1988. Hassler, Krusell and Olovsson (2019) employ the same type of approach in the first part of their
analysis to document fossil energy-saving technological change in the United States from the years
1949 to 2009. As noted by Caselli (2005), however, the intrinsic pitfall of this type of approach is that
it uses parameter values that are not estimated after taking into account the variation in unobserved
non-neutral technology across observations.
This study also contributes to the literature that estimates the elasticity of substitution between
energy and non-energy inputs. The substitution parameter in the CES production function is a key
parameter in the analysis of climate and energy policies using computable general equilibrium models
(Jacoby, Reilly, McFarland and Paltsev, 2006). Among others, Prywes (1986), Chang (1994), Kemfert
(1998), van der Werf (2008), and Henningsen, Henningsen and van der Werf (2019) estimate the elas-
ticities of substitution among capital, labor, and energy inputs. Although this literature provides various
estimates of the elasticities of substitution between energy and non-energy inputs, it ignores the endo-
2See Jorgenson (1986) for a survey.
4
geneity problem associated with non-neutral technological change. Consequently, there may be a bias
in previous estimates of the elasticities of substitution between energy and non-energy inputs. Recently,
Raval (2019) and Oberfield and Raval (2020) estimate the elasticity of substitution between capital and
labor in the United States from the years 1987 to 2007. These studies address the endogeneity problem
associated with non-neutral technological change using shift–share instruments.
3 The Model
We assume that gross output (𝑦) is produced from capital (𝑘), labor (ℓ), and energy (𝑒) using a constant-
returns-to-scale technology in competitive markets. We denote by 𝑟 , 𝑤, and 𝑣 the prices of capital,
labor, and energy inputs, respectively, that are normalized by the output price. The representative firm
chooses the quantities of inputs (𝑘, ℓ, 𝑒) so as to maximize its profits:
𝑦− 𝑟𝑘 −𝑤ℓ− 𝑣𝑒 (1)
subject to production technology:
𝑦 = 𝑓 (𝑘, ℓ, 𝑒;𝑎𝑘 , 𝑎ℓ, 𝑎𝑒) , (2)
where 𝑎𝑘 , 𝑎ℓ, and 𝑎𝑒 are capital-, labor-, and energy-augmenting technology, respectively. We allow
for changes in factor-augmenting technology. Throughout the paper, we interchangeably use the terms
“energy-augmenting technology” and “energy-saving technology” since a rise in 𝑎𝑒 results in a fall in
the cost of production as well as a rise in the output in the model presented here.
We start our analysis by considering the standard one-level CES production function. We then
extend it to the two-level nested CES production function.
One-level CES The standard one-level CES production function is of the form:
𝑦 = [(𝑎𝑘 𝑘)𝜎 + (𝑎ℓℓ)𝜎 + (𝑎𝑒𝑒)𝜎]1𝜎 for 𝜎 < 1. (3)
5
The parameter 𝜎 governs the degree of substitution among capital, labor, and energy inputs. The
elasticity of substitution among capital, labor, and energy inputs is 𝜖𝜎 ≡ 1/ (1−𝜎) > 0. If the elasticity
of substitution is one, the CES production function reduces to the Cobb–Douglas production function,
in which case the relative use of inputs is invariant to technological change.
We consider factor-augmenting technology to be unobserved and stochastic components in the pro-
duction function. In this case, it is difficult to estimate the parameter 𝜎 directly using equation (3).
Profit maximization entails equating the ratio of input prices to the marginal rate of technical sub-
stitution:
𝑤
𝑟=
(𝑎ℓ
𝑎𝑘
) 𝜖𝜎−1𝜖𝜎
(ℓ
𝑘
)− 1𝜖𝜎
, (4)
𝑤
𝑣=
(𝑎ℓ
𝑎𝑒
) 𝜖𝜎−1𝜖𝜎
(ℓ
𝑒
)− 1𝜖𝜎
. (5)
These equations imply that the relative use of inputs varies according to the relative factor-augmenting
technology. When the elasticity of substitution is less (greater) than one, the relative quantity of in-
puts decreases (increases) with a rise in the relative factor-augmenting technology. The elasticity of
substitution can be estimated using equations (4) and (5), as described in the next section. The ratio
of factor-augmenting technology can be calculated as residuals after estimating the elasticity of substi-
tution. However, the level of factor-augmenting technology cannot be measured using only these two
equations.
As noted by Caselli and Coleman (2002, 2006), the system of three equations (3)–(5) contains three
unknowns (𝑎𝑘 , 𝑎ℓ, and 𝑎𝑒). Factor-augmenting technology can be derived from those equations as:
𝑎𝑘 =
(𝑟𝑘
𝑦
) 𝜖𝜎𝜖𝜎−1 ( 𝑦
𝑘
), (6)
𝑎ℓ =
(𝑤ℓ
𝑦
) 𝜖𝜎𝜖𝜎−1 ( 𝑦
ℓ
), (7)
𝑎𝑒 =
(𝑣𝑒
𝑦
) 𝜖𝜎𝜖𝜎−1 ( 𝑦
𝑒
). (8)
6
These equations imply that factor-augmenting technology is log proportional to the factor income share
and output per factor. Under the assumption of competitive markets, national income is equal to the
sum of factor incomes (i.e., 𝑦 = 𝑟𝑘 +𝑤ℓ+𝑣𝑒). Energy-saving technological change can be measured as:
Δ ln𝑎𝑒 = Δ ln( 𝑦𝑒
)+ 𝜖𝜎
𝜖𝜎 −1Δ ln
(𝑣𝑒
𝑦
). (9)
As is clear from the derivation, this approach does not require specifying the functional forms of factor-
augmenting technology.
Two-level CES In the one-level CES production function, the elasticity of substitution between en-
ergy and non-energy inputs is assumed to be identical to the elasticity of substitution between non-
energy inputs. This assumption can be relaxed by considering the following two-level nested CES
production function:
𝑦 =
[[(𝑎𝑘 𝑘) 𝜚 + (𝑎ℓℓ) 𝜚]
𝜍𝜚 + (𝑎𝑒𝑒)𝜍
] 1𝜍
for 𝜍, 𝜚 < 1. (10)
The elasticity of substitution between capital and labor is 𝜖𝜚 ≡ 1/ (1− 𝜚) > 0, while the elasticity of
substitution between energy and non-energy is 𝜖𝜍 ≡ 1/ (1− 𝜍) > 0. When the two substitution param-
eters 𝜍 and 𝜚 are identical, the two-level CES production function (10) reduces to the one-level CES
production function (3).
Profit maximization entails equating the ratio of input prices to the marginal rate of technical sub-
stitution:
𝑤
𝑟=
(𝑎ℓ
𝑎𝑘
) 𝜚 (ℓ
𝑘
) 𝜚−1, (11)
𝑤
𝑣= [(𝑎𝑘 𝑘) 𝜚 + (𝑎ℓℓ) 𝜚]
𝜍−𝜚
𝜚𝑎𝜚
ℓℓ𝜚−1
𝑎𝜍𝑒 𝑒
𝜍−1 . (12)
The first equation remains the same form as equation (4), while the second equation becomes more
involved than equation (5).
7
The system of three equations (10)–(12) contains three unknowns (𝑎𝑘 , 𝑎ℓ, and 𝑎𝑒). Factor-augmenting
technology can be derived from those equations as:
𝑎𝑘 =
(𝑟𝑘 +𝑤ℓ
𝑦
) 1𝜍(
𝑟𝑘
𝑟𝑘 +𝑤ℓ
) 1𝜚 ( 𝑦
𝑘
), (13)
𝑎ℓ =
(𝑟𝑘 +𝑤ℓ
𝑦
) 1𝜍(
𝑤ℓ
𝑟𝑘 +𝑤ℓ
) 1𝜚 ( 𝑦
ℓ
), (14)
𝑎𝑒 =
(𝑣𝑒
𝑦
) 1𝜍 ( 𝑦
𝑒
). (15)
These equations imply again that factor-augmenting technology is log proportional to the factor income
share and output per factor. Energy-saving technological change can be measured as:
Δ ln𝑎𝑒 = Δ ln( 𝑦𝑒
)+
𝜖𝜍
𝜖𝜍 −1Δ ln
(𝑣𝑒
𝑦
). (16)
This equation is of the same form as equation (9) with a different parameter.
4 Estimation
We first discuss how we identify and estimate the elasticity of substitution. We then describe how we
measure the quantitative contribution of factor inputs and factor-augmenting technology to economic
growth.
4.1 Elasticity of substitution
The marginal-rate-of-technical-substitution conditions (4) and (5) form the basis for estimating the
substitution parameter 𝜎 in the one-level CES production function (3). Meanwhile, the marginal-
rate-of-technical-substitution conditions (11) and (12) form the basis for estimating the substitution
parameters 𝜍 and 𝜚 in the two-level CES production function (10).
8
One-level CES Let 𝑖 and 𝑡 denote the indices for countries and years. After taking logs in equations
(4) and (5) and taking differences over time, the estimating equations can be derived as follows:
Δ ln(𝑤𝑖𝑡
𝑟𝑖𝑡
)= − (1−𝜎)Δ ln
(ℓ𝑖𝑡
𝑘𝑖𝑡
)+Δ𝑣1𝑖𝑡 , (17)
Δ ln(𝑤𝑖𝑡
𝑣𝑖𝑡
)= − (1−𝜎)Δ ln
(ℓ𝑖𝑡
𝑒𝑖𝑡
)+Δ𝑣2𝑖𝑡 . (18)
where the error terms comprise the relative factor-augmenting technology, i.e., 𝑣1𝑖𝑡 = 𝜎 ln(𝑎ℓ,𝑖𝑡
/𝑎𝑘,𝑖𝑡
)and 𝑣2𝑖𝑡 = 𝜎 ln
(𝑎ℓ,𝑖𝑡
/𝑎𝑒,𝑖𝑡
).
Four facts about the estimating equations are worth noting. First, the observed and unobserved
terms are additively separable in equations (17) and (18), which makes it possible to estimate the
production function parameter 𝜎. Second, any time-invariant country-specific effects are eliminated
from these equations. This means that even though there are persistent and substantial differences in
the unobserved characteristics across countries, such differences are fully controlled for. Third, the
parameter 𝜎 can be over-identified when using the two equations, which makes it possible to test the
validity of the equations. Finally, estimating the production function parameter from equations (17)
and (18) does not require data on output.
Two-level CES One of the estimating equations can be derived from equation (11) in the same way
as above:
Δ ln(𝑤𝑖𝑡
𝑟𝑖𝑡
)= − (1− 𝜚)Δ ln
(ℓ𝑖𝑡
𝑘𝑖𝑡
)+Δ𝑣3𝑖𝑡 , (19)
where the error term comprises the relative factor-augmenting technology, i.e., 𝑣3𝑖𝑡 = 𝜚 ln(𝑎ℓ,𝑖𝑡
/𝑎𝑘,𝑖𝑡
).
Another estimating equation cannot be derived directly from equation (12) since the observed cap-
ital and labor quantities are not separated from the unobserved capital- and labor-augmenting tech-
nology. A useful fact, which can be derived from equation (11), is that the ratio of capital- to labor-
augmenting technology is log proportional to the relative price and relative quantity of capital to labor.
9
After combining equations (11) and (12), the additional estimating equation can be derived as follows:
Δ ln(𝑤𝑖𝑡
𝑣𝑖𝑡
)= −𝜍 − 𝜚
𝜚Δ ln
(𝑤𝑖𝑡ℓ𝑖𝑡
𝑟𝑖𝑡𝑘𝑖𝑡 +𝑤𝑖𝑡ℓ𝑖𝑡
)− (1− 𝜍)Δ ln
(ℓ𝑖𝑡
𝑒𝑖𝑡
)+Δ𝑣4𝑖𝑡 , (20)
where the error term comprises the relative factor-augmenting technology, i.e., 𝑣4𝑖𝑡 = 𝜍 ln(𝑎ℓ,𝑖𝑡
/𝑎𝑒,𝑖𝑡
).
Consequently, the observed and unobserved terms are additively separable, and time-invariant
country-specific effects are differenced out in both equations (19) and (20). By virtue of these equa-
tions, it is possible to estimate the production function parameters 𝜍 and 𝜚 even when factor-augmenting
technology is neither observed nor deterministic. The parameters 𝜍 and 𝜚 can be over-identified from
the two equations since there are three regressors for the two parameters in the system of two equations
(19) and (20).
Identification If there were no correlation between the changes in the relative input quantities and the
relative factor-augmenting technology, it would be easy to identify the production function parameters,
and hence the elasticities of substitution, from the estimating equations described above. However, the
regressors in the estimating equations are presumably correlated with the error term. The elasticities of
substitution will be biased as a result.3
We address this endogeneity problem in two ways. First, we control for the country-specific non-
linear time trends in the relative factor-augmenting technology. We decompose each error term as:
𝑣𝑛𝑖𝑡 =∑︁𝑠
𝜓𝑠𝑖𝑡𝑠 +𝑢𝑛𝑖𝑡 for 𝑛 = 1,2,3,4, (21)
where 𝑢𝑛𝑖𝑡 is an idiosyncratic shock to the relative factor-augmenting technology. If we used time-series
data from a single country, it would be difficult to isolate the effect of the relative input quantities on the
relative input prices from general time trends. However, since we use panel data from many countries,
3The regressor in equation (17) or (18) is likely to be positively correlated with the error term. The reason for this is that,when 0 < 𝜖𝜎 < 1 (𝜖𝜎 > 1), the relative input quantities should theoretically be negatively (positively) correlated with therelative factor-augmenting technology, and the relative factor-augmenting technology has a negative (positive) coefficientin the error term. The coefficient of the regressor is the negative of the inverse of 𝜖𝜎 . The elasticity of substitution 𝜖𝜎 willbe overestimated regardless of whether 0 < 𝜖𝜎 < 1 or 𝜖𝜎 > 1.
10
it is possible to identify the elasticity of substitution among inputs by exploiting the cross-country and
time variation in the relative input quantities.
Second, we use the shift–share instrument, also known as the Bartik (1991) instrument, to allow for
correlations between the changes in the relative input quantities and idiosyncratic shocks to the relative
factor-augmenting technology. We treat all right-hand-side variables except time trends as endogenous
variables. For each endogenous regressor, we construct the following shift–share instrument:
Δ ln
(𝑧𝑏1,𝑖𝑡
𝑧𝑏2,𝑖𝑡
)=
∑︁𝑗∈J
𝑧1,𝑖, 𝑗 ,𝑡0∑𝑗 ′∈J 𝑧1,𝑖, 𝑗 ′,𝑡0
Δ ln
(∑︁𝑖∈I
𝑧1,𝑖 𝑗 𝑡
)−
∑︁𝑗∈J
𝑧2,𝑖, 𝑗 ,𝑡0∑𝑗 ′∈J 𝑧2,𝑖, 𝑗 ′,𝑡0
Δ ln
(∑︁𝑖∈I
𝑧2,𝑖 𝑗 𝑡
)(22)
for (𝑧1, 𝑧2) ∈ {(ℓ, 𝑘) , (ℓ, 𝑒) , (𝑤ℓ,𝑟𝑘 +𝑤ℓ)} ,
where 𝑗 is an index for industries, I and J are sets of countries and industries, respectively, and 𝑡0 is the
first year of observation. The shift–share instrument consists of shift, which measures global shocks to
industries, and share, which measures the initial local exposure to global shocks. The shift–share instru-
ment is valid if either shift or share is exogenous (Borusyak, Hull and Jaravel, 2020). The identification
assumption is that global industry shocks to relative input quantities are uncorrelated with country-
specific idiosyncratic shocks to relative factor-augmenting technology (conditional on country-specific
non-linear time trends).
GMM The elasticity of substitution 𝜖𝜎 in the one-level CES production function can be estimated
from equations (17) and (18), while the elasticities of substitution 𝜖𝜍 and 𝜖𝜚 in the two-level CES
production function can be estimated from equations (19) and (20). In both cases, the same parameter
appears in different equations, and the error terms are correlated across equations. Hence, it is more effi-
cient to estimate the system of two equations jointly using the generalized method of moments (GMM).
In doing so, all the right-hand-side variables except time trends are treated as endogenous variables us-
ing the shift–share instruments, five-year differences are used, and standard errors are clustered at the
country level to allow for heteroscedasticity and serial correlation.
11
4.2 Growth accounting
We evaluate the quantitative contribution of factor-augmenting technology as well as factor inputs to
the rate of growth in output after measuring factor-augmenting technology for each country. Techno-
logical change is typically measured as the Solow residual, which is the portion of growth in output not
attributable to changes in factor inputs. The limitation of this standard approach is that it does not tell
us the type of technological change. We take the approach one step further by leveraging our measure
of factor-augmenting technology.
We decompose the rate of growth in output (𝑦) into the changes due to the three components in
inputs (𝑘 , ℓ, and 𝑒) and three components in technology (𝑎𝑘 , 𝑎ℓ, and 𝑎𝑒). Given the way in which we
estimate the elasticity of substitution and measure factor-augmenting technology, the decomposition
results are invariant to the normalization of input quantities. The issue that arises in the implementation
of the decomposition is that there is no simple transformation to make the CES production functions
(3) and (10) additively separable in those components. In such a case, the decomposition results can
depend on the order of the decomposition. To address this concern, we use the Shapley decomposition
(Shorrocks, 2013). Appendix A.1 details the decomposition procedure.
5 Data
In this section, we describe the data sources, sample, and variables and present the trends in a key
economic indicator for each country.
5.1 Sample and variables
The analysis described so far requires data on the prices and quantities of capital, labor, and energy
inputs. The data used for the analysis are drawn from the EU KLEMS database and the International
Energy Agency (IEA) database. The EU KLEMS database collects information on the quantities of
and incomes from capital, labor, and energy services in major OECD countries from the years 1970 to
2005, while the IEA database collects information on the energy price since the year 1978. The wage
12
rate can be calculated as the ratio of labor income to hours worked. The rental price of capital can
be calculated in the standard way described in O’Mahony and Timmer (2009). Appendix A.2 details
the calculation procedure. All the variables measured in monetary terms are converted into 1995 U.S.
dollars.
The EU KLEMS database is created from information collected by national statistical offices and
is grounded in national accounts statistics. The March 2008 version is used for the analysis because
later versions contain no information on energy. All countries, industries, and years, for which the data
needed for the estimation are available, are included in the sample. Consequently, our sample comprises
305 country-year observations from 12 countries: Austria, the Czech Republic, Denmark, Finland,
Germany, Italy, Japan, the Netherlands, Portugal, Sweden, the United Kingdom, and the United States.4
Each country is composed of 29 industries.
When we calculate the input prices and quantities, we adjust for the variation in input composi-
tion across countries over time to the extent possible. For this purpose, we make full use of detailed
information on capital, labor, and energy input components in the EU KLEMS and IEA databases.
Appendix A.3 details the adjustment procedure, including the description of data used.
We examine the relationship between our and conventional measures of energy-saving technolog-
ical change. In the literature, energy-saving technological change is typically measured using data on
R&D and patents. For this purpose, we use the amount of government spending on energy-related R&D
and the number of energy-related patents (i.e., patents on climate change mitigation), both of which are
readily available from the OECD.Stat database, to construct the alternative measures of energy-saving
technological change.
5.2 Factor income shares
The share of factor income is one of the key elements in our measure of factor-augmenting technology.
Figure 1 shows the trends in the capital share of income, the labor share of income, and the energy share
of income for each country. The labor share of income tended to decline in many countries, while the
4The results remain unchanged if excluding the Czech Republic from the sample.
13
capital share of income tended to increase, as discussed in detail by Karabarbounis and Neiman (2014).
The rate of change in the capital or labor share of income becomes slightly smaller when energy inputs
are taken into account. The energy share of income tended to peak around the year 1980 in many
countries. Appendix A.4 presents the trends in other key economic indicators, including factor prices
and quantities and output per factor.
Figure 1: Factor income shares
(a) Austria
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(b) Czech Republic
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(c) Denmark
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
(d) Finland
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
(e) Germany
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(f) Italy
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
(g) Japan
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
(h) Netherlands
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(i) Portugal
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(j) Sweden
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(k) United Kingdom
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
capital labor
energy
(l) United States
.4
.5
.6
.7
.1
.2
.3
.4
1980 1990 2000
Notes: The solid, dashed, and dotted lines are the capital share of income, 𝑟𝑘/ (𝑟𝑘 +𝑤ℓ + 𝑣𝑒), the labor share of income,𝑤ℓ/ (𝑟𝑘 +𝑤ℓ + 𝑣𝑒), and the energy share of income, 𝑣𝑒/ (𝑟𝑘 +𝑤ℓ + 𝑣𝑒), respectively. The left vertical axis indicates thescale for the capital or energy share of income, whereas the right vertical axis indicates the scale for the labor share ofincome.
14
6 Results
We start this section by presenting the estimates for the elasticities of substitution among capital, labor,
and energy inputs. We then discuss the international trends and differences in energy-saving techno-
logical change and its correlation with the alternative measures of energy-saving technological change.
We end this section by evaluating the quantitative contribution of energy-saving technological change
to economic growth.
6.1 Production function estimates
Table 1 reports the estimates for the elasticities of substitution in the one- and two-level CES production
functions. The estimated elasticities of substitution are significantly less than one, ranging from 0.48
to 0.73, in the one-level CES production function. The estimated elasticities become smaller as more
extensive controls are added for the time trends. The same applies to the two-level CES production
function. The estimated elasticities of substitution between energy and non-energy range from 0.46 to
0.65, while the estimated elasticity of substitution between capital and labor ranges from 0.47 to 0.83.
Since it is desirable to add extensive controls for the time trends to ensure instrument exogeneity, our
preferred specification is the one in which country-specific quadratic trends are added in the last col-
umn. Our preferred estimate for the elasticity of substitution in the one-level CES production function
is 0.48. Meanwhile, our preferred estimates for the elasticities of substitution in the two-level CES
production function are 0.46 between energy and non-energy and 0.47 between capital and labor.
Two types of test statistics indicate that the shift–share instruments used in our analysis are valid in
the preferred specification. First, the first-stage F statistics under the null hypothesis that the shift–share
instruments are irrelevant are 10.8 for ℓ/𝑘 and 16.8 for ℓ/𝑒 in the one-level CES production function,
while they are 10.8 for ℓ/𝑘 , 13.4 for ℓ/𝑒, and 14.6 for 𝑤ℓ/(𝑟𝑘 +𝑤ℓ) in the two-level CES production
function. Second, the J statistics under the null hypothesis that over-identifying restrictions are valid
are 0.120 with a p-value of 0.729 in the one-level CES production function and 0.963 with a p-value of
0.327 in the two-level CES production function.
15
Table 1: Elasticities of substitution
One-level CES
𝜖𝜎0.734 0.694 0.702 0.625 0.479
(0.128) (0.117) (0.166) (0.089) (0.101)Two-level CES
𝜖𝜍0.647 0.618 0.613 0.584 0.463
(0.122) (0.118) (0.153) (0.159) (0.181)
𝜖𝜚0.703 0.834 0.833 0.558 0.473
(0.170) (0.086) (0.115) (0.118) (0.135)
time trends linear quadratic cubiccountry countrylinear quadratic
Notes: Standard errors in parentheses are clustered at the country level. Specifications in the first to last columns includethe linear, quadratic, cubic, country-specific linear, and country-specific quadratic time trends, respectively.
The estimated elasticity of substitution between capital and labor is not significantly different from
that between energy and non-energy in the two-level CES production function. The 𝜒2 statistic under
the null hypothesis that the two substitution parameters are identical is 0.002 with a p-value of 0.960.
This result indicates that the one-level CES production function cannot be rejected against the two-level
CES production function. Appendix A.5 provides additional results. We confirm in Table A1 that the
estimates for the elasticities of substitution are robust to splitting the sample by industry.
6.2 Energy-saving technological change
Figure 2 displays factor-augmenting technological change for each country. Given the results above,
the one-level CES production function is used to measure factor-augmenting technological change.5
The results shown in the figure indicate that technological change is not factor-neutral. The changes in
capital-, labor-, and energy-augmenting technology are noticeably different for each country. Labor-
augmenting technology exhibits an increasing trend in most of the countries, while capital-augmenting
technology does not in any country. This result is consistent with those of Klump, McAdam and Will-
man (2007) and van der Werf (2008), who find that labor-augmenting technological change is more
dominant than capital-augmenting technological change. In addition, energy-saving technology ex-
hibits a different trend from capital- and labor-augmenting technology in all countries. The magnitude
5The results remain unchanged if measured using the two-level CES production function.
16
and direction of factor-augmenting technological change remain unchanged even if material inputs are
taken into account (see Figure A4 in Appendix A.5), while they vary depending on the value of the
elasticity of substitution (see Figure A5 in Appendix A.5).
Figure 2: Factor-augmenting technological change
(a) Austria
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(b) Czech Republic
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(c) Denmark
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(d) Finland
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(e) Germany
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(f) Italy
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(g) Japan
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(h) Netherlands
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(i) Portugal
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(j) Sweden
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
(k) United Kingdom
−.8
0
.8
1.6
1980 1990 2000
(l) United States
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
Notes: The solid, dashed, and dotted lines are capital-, labor-, and energy-augmenting technology (𝑎𝑘 , 𝑎ℓ , and 𝑎𝑒), respec-tively. The shaded area represents the 90 percent confidence interval for 𝑎𝑒. All series are logged and normalized to zero inthe first year of observations.
Energy-saving technological change is neither linear nor monotonic over time. This result high-
lights the importance of not specifying the functional forms of technological change. Moreover, energy-
saving technological change differs substantially across countries over time. Progress in energy-saving
17
technology is greatest in the United States among the 12 OECD countries during the period between
the years 1978 and 2005. In the United States, energy-saving technology exhibits an increasing trend
after the early 1980s, and the log change in energy-saving technology from the years 1978 to 2005
is ln(𝑎𝑒,2005) − ln(𝑎𝑒,1978) = 1.05. This means that new energy-saving technology would require only
35 (= 100× (𝑎𝑒,1978/𝑎𝑒,2005) = 100× exp(−1.05)) percent of energy to produce the same amount of
output when comparing the years 1978 and 2005. The main reason for the difference between the
United States and other countries is the steady increase in output per energy in the United States (see
Figure A3 in Appendix A.4). In Denmark, energy-saving technology also exhibits an increasing trend
after the early 1980s. In Finland, Italy, Japan, and the United Kingdom, energy-saving technology
sometimes progressed in the 1980s but stagnated in the 1990s and 2000s. The results suggest that new
energy-saving technology would require only 79, 96, 73, 86, and 51 percent of energy to produce the
same amount of output in Denmark, Finland, Italy, Japan, and the United Kingdom, respectively, when
comparing the years 1978 and 2005. In Austria and Germany, energy-saving technology progressed in
the 1990s but stagnated in the 2000s. In the Czech Republic, the Netherlands, Portugal, and Sweden,
energy-saving technology progressed little during the period. Energy-saving technology might have
progressed in more countries if the technology developed in such countries as the United States was
adopted.
Table 2: Correlations with alternative measures
One-level CES Two-level CESR&D Patents R&D Patents
log change log change log change log change𝑎𝑒 0.894 0.286 0.895 0.051 0.895 0.282 0.894 0.045
[0.000] [0.002] [0.000] [0.713] [0.000] [0.002] [0.000] [0.744]𝑎𝑒/𝑎ℓ 0.898 0.314 0.880 0.100 0.900 0.311 0.879 0.097
[0.000] [0.001] [0.000] [0.472] [0.000] [0.001] [0.000] [0.487]𝑎𝑒/𝑎𝑘 0.846 0.283 0.885 0.118 0.849 0.281 0.883 0.114
[0.000] [0.002] [0.000] [0.397] [0.000] [0.002] [0.000] [0.412]Notes: Correlation coefficients are reported. All variables are taken in logs. The numbers in square brackets are p-valuesunder the null hypothesis of no correlation.
The first row of Table 2 reports the correlations between our and conventional measures of energy-
saving technological change. Our measure of energy-saving technology is positively and significantly
18
correlated with energy-related R&D spending by the government and the number of energy-related
patents in logs (columns 1 and 3). The correlation coefficients are then close to 0.9 for both R&D spend-
ing and patents. Our measure of energy-saving technology is also positively and significantly correlated
with energy-related R&D spending but not with energy-related patents in growth rates (columns 2 and
4). The correlation coefficients are then 0.28 to 0.29 for R&D spending but less than 0.1 for patents. The
former result indicates that progress in energy-saving technology is associated with a rise in govern-
ment spending in the innovation process. The latter result suggests that our measure of energy-saving
technological change contains complementary information on unpatented innovation and/or no unnec-
essary information on useless patents. These results are robust to controlling for common factors in
factor-augmenting technological change. Any common factors can be removed by taking the ratio of
energy- to capital- or labor-augmenting technology. The second and third rows of Table 2 reports the
correlation coefficients calculated from 𝑎𝑒/𝑎ℓ and 𝑎𝑒/𝑎𝑘 instead of 𝑎𝑒. The results suggest that tech-
nological change tends to be directed towards energy as government spending on energy-related R&D
increases.
6.3 Growth accounting
Table 3 presents the quantitative contribution of factor inputs and factor-augmenting technology to
economic growth for each country. The first column reports the rate of growth in output during the
sample period, and the second to last columns report the portions attributable to specific factor inputs
and factor-augmenting technology for each country. The decomposition results are calculated based on
the one-level CES production function.6
The contribution rates of capital, labor, and energy inputs are different. Similarly, the contribution
rates of capital-, labor-, and energy-augmenting technology are different. Labor-augmenting techno-
logical change has a greater contribution to economic growth than capital- and energy-augmenting
technological change in all countries except the United Kingdom. Energy-saving technological change
also has a positive contribution to economic growth in many countries, including Denmark, Finland,
6The results remain unchanged if calculated based on the two-level CES production function.
19
Table 3: Sources of economic growth
𝑦 𝑘 ℓ 𝑒 𝑎𝑘 𝑎ℓ 𝑎𝑒Austria 2.23 0.67 0.22 0.74 –0.30 1.30 –0.40Czech Republic 1.72 1.54 –0.14 0.97 –0.86 0.64 –0.42Denmark 1.75 0.62 0.13 0.26 –0.38 1.01 0.11Finland 2.49 0.67 0.17 0.57 –0.30 1.34 0.03Germany 1.38 0.88 –0.22 –0.12 –0.69 1.27 0.26Italy 1.65 0.68 0.28 0.20 –0.63 0.96 0.17Japan 2.98 1.73 –0.04 0.17 –0.61 1.70 0.03Netherlands 2.87 0.86 0.89 0.39 –0.17 1.06 –0.16Portugal 2.28 2.42 0.50 1.09 –1.58 0.56 –0.72Sweden 3.31 1.54 0.47 0.15 –0.49 1.66 –0.01United Kingdom 1.63 0.85 0.32 0.32 –0.46 0.13 0.48Unites States 2.63 1.38 0.80 0.06 –0.59 0.58 0.41
Notes: The first column reports the percentage rate of growth in 𝑦 = 𝑟𝑘 +𝑤ℓ + 𝑣𝑒 from the first year of observation, 𝑡0, tothe year 2005 (i.e., 100× (ln 𝑦2005 − ln 𝑦𝑡0 )/(2005− 𝑡0)). The second to seventh columns report the results of the Shapleydecomposition based on the one-level CES production function.
Germany, Italy, Japan, the United Kingdom, and the United States. The contribution rate of energy-
saving technological change is not negligible, especially in Germany, the United Kingdom, and the
United States. This result holds even when material inputs are taken into account (see Table A2 in
Appendix A.5).
7 Discussion
We end our analysis by discussing how to interpret our results when factor-augmenting technology is
endogenous. The elasticity of substitution among capital, labor, and energy inputs becomes greater
when factor-augmenting technology is endogenous than when it is exogenous. For ease of reference,
we refer to the former as the long-run elasticity and the latter as the short-run elasticity. We show
in Appendix A.6 that the marginal-rate-of-technical-substitution conditions remain the same form as
equations (4) and (5) with a different parameter (long-run elasticity), while factor-augmenting technol-
ogy remains the same form as equations (6)–(8) with the same parameter (short-run elasticity).
The issue is that the elasticity of substitution estimated using the marginal-rate-of-technical-substitution
conditions may be different from that needed to measure factor-augmenting technology. To address this
20
issue, we estimate the elasticity of substitution using one-year differences instead of five-year differ-
ences, and examine how energy-saving technological change can vary according to the change in the
elasticity of substitution. Figure A6 in Appendix A.6 demonstrates that energy-saving technological
change varies little since the estimate for the elasticity of substitution declines only slightly.
Equations (4) and (5) imply that technological change is directed towards scarce (abundant) factors
when the elasticity of substitution 𝜖𝜎 is less (greater) than one; in other words, factor inputs are comple-
mentary (substitutable) to some extent (Acemoglu, 2002; Caselli and Coleman, 2006). Consequently,
energy-saving technology tends to progress in countries with scarce (abundant) energy resources when
the elasticity of substitution is less (greater) than one, as can be seen from equation (8). Our estimates
for the elasticity of substitution imply that energy-saving technology should progress in countries or
years in which energy resources are scarce. In this respect, our results are consistent with and com-
plementary to Hassler, Krusell and Olovsson (2019), who find that fossil energy-saving technological
change in the United States grew faster after the first oil shock in 1973.
8 Conclusion
Technological change is the most, or perhaps only, promising way to balance economic growth and en-
vironmental sustainability. This study has aimed to measure and document energy-saving technological
change to understand its trends in advanced countries over recent decades. For this purpose, we have
used a theoretical result that energy-saving technology can be measured using data on the energy share
of income and output per energy for a given value of the elasticity of substitution. The main challenge
that arises in the measurement of energy-saving technology is to estimate the elasticity of substitution
between energy and non-energy inputs after taking into account the variation in unobserved factor-
augmenting technology across countries over time. We address this issue using cross-country panel
data and shift–share instruments.
The main results of this study can be summarized as follows. First, the estimated elasticities of sub-
stitution between energy and non-energy inputs are significantly less than one, which implies that, ce-
21
teris paribus, energy-saving technology should progress in countries or years in which energy resources
are scarce. Second, technological change is not factor-neutral; namely, there was a noticeable differ-
ence in the direction and magnitude of capital-, labor-, and energy-augmenting technological change
for each country. Third, energy-saving technological change varies substantially across countries over
time. The United States went ahead of the other 11 OECD countries between the years 1978 and 2005.
Global energy efficiency would improve by accelerating international transfers of energy-saving tech-
nology. Fourth, progress in energy-saving technology is associated with a rise in government spending
on energy-related R&D. Finally, energy-saving technological change had a positive contribution to eco-
nomic growth in many countries, although not to the extent of labor-augmenting technological change.
One of the most serious environmental problems in recent years is global warming due to green-
house gas emissions. One future avenue of research is to divide energy into clean and dirty energy
according to whether it emits carbon dioxide, estimate the elasticity of substitution between clean and
dirty energy inputs, and measure changes in technology that saves clean and dirty energy separately.
22
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25
A Appendix
A.1 Shapley decomposition
We describe the procedure to decompose the changes in output into specific factor inputs and factor-
augmenting technology. Let Y denote output and 𝑑𝑚 for 𝑚 ∈ {1,2, . . . , 𝑀} =M denote its determinant
factors, including factor inputs (𝑘 , ℓ, and 𝑒) and factor-augmenting technology (𝑎𝑘 , 𝑎ℓ, and 𝑎𝑒). For a
given country and year, the natural log of output is given by
lnY = F (𝑑1, 𝑑2, . . . , 𝑑𝑀) . (23)
To quantify the contribution of each factor, we consider counterfactual situations in which some or all
of the factors are fixed at the initial level. Let Γ (G) denote the value that lnY takes if the factors 𝑑𝑚
for 𝑚 ∉ G ⊆ M are fixed at the initial level, 𝑜 = (𝑜1, 𝑜2, . . . , 𝑜𝑀) ∈ O denote the order in which the
factors are fixed, and G (𝑜𝜏, 𝑜) = {𝑜𝜏′ | 𝜏′ > 𝜏} denote the set of factors that remain unfixed after the
𝜏-th factor is fixed. The marginal contribution of the 𝑚-th factor to the log changes in output, Δ lnY,
can be measured as:
Λ𝑜𝑑𝑚
= Γ (G (𝑑𝑚, 𝑜) ∪ {𝑑𝑚}) −Γ (G (𝑑𝑚, 𝑜)) . (24)
The marginal contribution, Λ𝑜𝑑𝑚
, depends on the order in which the factors are fixed, but the average of
the marginal contributions over all possible sequences, Λ𝑑𝑚 , does not. The Shapley decomposition is
Δ lnY =∑︁𝑚∈M
Λ𝑑𝑚 , (25)
where
Λ𝑑𝑚 =1𝑀!
∑︁𝑜∈O
Λ𝑜𝑑𝑚. (26)
This decomposition is not only path independent but also exact (Shorrocks, 2013). The results of the
decomposition are expressed in terms of growth rates by dividing by the number of years between the
first and last years.
26
A.2 Rental price of capital
We describe the procedure to calculate the rental price of capital. Capital is divided into capital equip-
ment and structure. Capital equipment is composed of computing equipment, communications equip-
ment, software, transport equipment, and other machinery and equipment, while capital structure is
composed of non-residential structures and infrastructures. The rental price of capital (𝑟) is determined
by the price of investment (𝑞), the depreciation rate (𝛿), and the interest rate (]). The price of investment
is calculated by dividing the nominal value by the real value of investment for each component. The
depreciation rate is calculated as the average of the depreciation rates of the capital subcomponents
weighted by the share of the capital subcomponents. Let 𝑗 ∈ {equipment, structure} denote an index
for the capital components. As described in O’Mahony and Timmer (2009), the rental price of capital
in year 𝑡 +1 is calculated as:
𝑟 𝑗 ,𝑡+1 = 𝛿 𝑗𝑞 𝑗 ,𝑡+1 + ]𝑡+1𝑞 𝑗 𝑡 −(𝑞 𝑗 ,𝑡+1 − 𝑞 𝑗 𝑡
), (27)
where the interest rate is calculated as:
]𝑡 =
∑𝑗 𝑟 𝑗 𝑡𝑘 𝑗 𝑡 −
∑𝑗 𝛿 𝑗𝑞 𝑗 𝑡𝑘 𝑗 𝑡 +
∑𝑗
(𝑞 𝑗 𝑡 − 𝑞 𝑗 ,𝑡−1
)𝑘 𝑗 𝑡∑
𝑗 𝑞 𝑗 ,𝑡−1𝑘 𝑗 𝑡
. (28)
A.3 Adjustment for input composition
We describe the procedure used to adjust for the variation in the composition of capital, labor, and
energy inputs across countries over time when calculating the prices and quantities of capital, labor,
and energy inputs. The procedure is similar to that used by Autor, Katz and Kearney (2008), who
adjust for the compositional changes in labor inputs when estimating the aggregate production function
with two types of labor in the United States. In our case, capital is divided into capital equipment and
structure; labor is divided into skilled and unskilled labor; and energy is divided into sulfur fuel oil,
light fuel oil, natural gas, electricity, automotive diesel, steam coal, and coking coal. The procedure
requires the assumption that the input components are perfect substitutes within each type of input.
27
Here, we denote the price of input by 𝑝 ∈ {𝑟,𝑤, 𝑣} and the quantity of input by 𝑥 ∈ {𝑘, ℓ, 𝑒} ∈
{(equipment, structure), (skilled, unskilled), (sulfur fuel oil, light fuel oil, natural gas, electricity, auto-
motive diesel, steam coal, coking coal)}. We use squiggles to represent unadjusted prices and quanti-
ties. If there were no need to make adjustments to input prices and quantities, we could calculate the
price of input in country 𝑖 and year 𝑡 as 𝑝𝑖𝑡 =∑
𝑗 \𝑥𝑗𝑖𝑡𝑝 𝑗𝑖𝑡 , where \𝑥
𝑗𝑖𝑡is the share of component 𝑗 in input
𝑥 (i.e., \𝑥𝑗𝑖𝑡= �̃� 𝑗𝑖𝑡/
∑𝑗 �̃� 𝑗𝑖𝑡), and the quantity of input in country 𝑖 and year 𝑡 as �̃�𝑖𝑡 =
∑𝑗 �̃� 𝑗𝑖𝑡 .
We adjust for the variation in input composition across countries over time by holding the shares of
input components constant when calculating input prices and by using time-invariant efficiency units
as weights when calculating input quantities. Let 𝑇𝑖 denote the number of years observed for country
𝑖 and 𝐽𝑥 denote the number of components in input 𝑥. We can calculate the composition-adjusted
price of input in country 𝑖 and year 𝑡 as 𝑝𝑖𝑡 =∑
𝑗 \𝑥
𝑗𝑖𝑝 𝑗𝑖𝑡 , where \𝑥
𝑗𝑖 is the country-specific mean of
\𝑥𝑗𝑖𝑡
(i.e., \𝑥
𝑗𝑖 =∑𝑇𝑖
𝑡=1 \𝑥𝑗𝑖𝑡/𝑇𝑖), and the composition-adjusted quantity of input in country 𝑖 and year 𝑡
as 𝑥𝑖𝑡 =∑
𝑗 (𝑝 𝑗𝑖/𝑝𝑖)�̃� 𝑗𝑖𝑡 , where the weight is the country-specific mean of 𝑝 𝑗𝑖𝑡 (i.e., 𝑝 𝑗𝑖 =∑𝑇𝑖
𝑡=1 𝑝 𝑗𝑖𝑡/𝑇𝑖)
normalized by its mean across components (i.e., 𝑝𝑖 =∑
𝑗 𝑝 𝑗𝑖/𝐽𝑥).
We construct the data on the prices of input components �̃� 𝑗 and 𝑤 𝑗 , the shares of input components
\𝑘𝑗
and \ℓ𝑗, and the quantities of inputs �̃� , ℓ̃, and �̃� from the EU KLEMS database and obtain the data
on the energy price �̃� 𝑗 and the share of energy components \𝑒𝑗
from the IEA database (World Energy
Prices and World Energy Balances).
A.4 Factor prices and quantities
We present the trends in factor prices and quantities and output per factor. Relative factor prices are
dependent variables in the analysis, while relative factor quantities are explanatory variables. Output
per factor is another key element in our measure of factor-augmenting technology.
Figure A1 shows the trends in factor prices for each country. The rental price of capital tended to
increase in some countries but decrease in others. The wage rate exhibits an increasing trend in all
countries, although the rate of increase differs across countries over time. The energy price exhibits no
clear trend in all countries, but tended to peak around the year 1980 in many countries.
28
Figure A1: Factor prices
(a) Austria
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(b) Czech Republic
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(c) Denmark
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(d) Finland
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(e) Germany
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(f) Italy
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(g) Japan
−.3
0
.3
.6
.9
1970 1980 1990 2000
r
w
v
(h) Netherlands
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(i) Portugal
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(j) Sweden
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(k) United Kingdom
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
(l) United States
−.6
−.3
0
.3
.6
1970 1980 1990 2000
r
w
v
Notes: The solid, dashed, and dotted lines are the rental price of capital (𝑟), the wage rate (𝑤), and the energy price (𝑣),respectively. All series are logged and normalized to zero in the year 1978 or the first year for which information on allvariables is available otherwise.
Figure A2 shows the trends in factor quantities for each country. The quantity of capital exhibits an
increasing trend in all countries, although the rate of increase differs across countries over time. The
quantity of labor tended to increase in some countries but did not change much in many countries. The
quantity of energy tended to increase substantially in the majority of countries but did not change much
in the remainder.
29
Figure A2: Factor quantities
(a) Austria
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(b) Czech Republic
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(c) Denmark
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(d) Finland
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(e) Germany
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(f) Italy
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(g) Japan
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(h) Netherlands
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(i) Portugal
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(j) Sweden
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
(k) United Kingdom
−.8
−.4
0
.4
.8
1970 1980 1990 2000
k
l
e
(l) United States
−.4
0
.4
.8
1.2
1970 1980 1990 2000
k
l
e
Notes: The solid, dashed, and dotted lines are capital (𝑘), labor (ℓ), and energy (𝑒), respectively. All series are logged andnormalized to zero in the year 1978 or the first year for which information on all variables is available otherwise.
Figure A3 shows the trends in output per factor for each country. Output per capital did not change
much in a few countries but tended to decrease in most countries. Output per labor exhibits an increas-
ing trend in all countries, although the rate of increase differs across countries over time. Output per
energy exhibited different trends across countries; it only tended to increase in a few countries. A rise
in output per energy is noticeable in the United States.
30
Figure A3: Output per factor
(a) Austria
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(b) Czech Republic
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(c) Denmark
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(d) Finland
−.6
−.3
0
.3
.6
1980 1990 2000
(e) Germany
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(f) Italy
−.6
−.3
0
.3
.6
1980 1990 2000
(g) Japan
−.3
0
.3
.6
.9
1980 1990 2000
y / k
y / l
y / e
(h) Netherlands
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(i) Portugal
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(j) Sweden
−.6
−.3
0
.3
.6
1980 1990 2000
y / k
y / l
y / e
(k) United Kingdom
−.6
−.3
0
.3
.6
1980 1990 2000
(l) United States
−.6
−.3
0
.3
.6
1980 1990 2000
Notes: The solid, dashed, and dotted lines are output per capital (𝑦/𝑘), output per labor (𝑦/ℓ), and output per energy (𝑦/𝑒),respectively. All series are logged and normalized to zero in the first year of observations.
A.5 Additional results
We present four sets of additional results. First, we show the extent to which the elasticity of substitu-
tion can vary by industry. Table A1 reports the estimates for the elasticities of substitution in the one-
and two-level CES production functions separately for the goods and service industries.7 The estimated
7Goods industries include five broad categories of industries: agriculture, hunting, forestry, and fishing; mining and quar-rying; manufacturing; electricity, gas and water supply; and construction. Service industries include nine broad categoriesof industries: wholesale and retail trade; hotels and restaurants; transport and storage, and communication; financial inter-
31
elasticities of substitution are significantly less than one in all cases and only moderately different be-
tween the goods and service industries. In the two-level CES production function, the two substitution
parameters are not significantly different with a p-value of 0.303 in the goods industries and 0.275 in
the service industries.
Table A1: Elasticities of substitution by industry
One-level CES Two-level CES𝜖𝜎 𝜖𝜍 𝜖𝜚
Goods Service Goods Service Goods Service0.591 0.599 0.531 0.731 0.669 0.912
(0.142) (0.162) (0.162) (0.211) (0.137) (0.128)Notes: Standard errors in parentheses are clustered at the country level. Country-specific quadratic trends are included inall the specifications.
Second, we show the extent to which the magnitude and direction of factor-augmenting technologi-
cal change can vary after taking into account material inputs. To do so, we consider the CES production
function with capital, labor, energy, and material inputs:
𝑦 = [(𝑎𝑘 𝑘)𝜎 + (𝑎ℓℓ)𝜎 + (𝑎𝑒𝑒)𝜎 + (𝑎𝑚𝑚)𝜎]1𝜎 for 𝜎 < 1,
where 𝑚 is material, and 𝑎𝑚 is material-augmenting technology. Factor-augmenting technological
change remains the same form as equations (6)–(8). In this case, national income is calculated as
𝑦 = 𝑟𝑘 +𝑤ℓ + 𝑣𝑒 + 𝜏𝑚, where 𝜏 is the material price. Figure A4 shows that both the magnitude and
the direction of capital-, labor-, and energy-augmenting technological change remain unchanged. In
addition, there was not much change in material-augmenting technology in most of the countries.
Third, we show how energy-saving technological change can vary according to the value of the
elasticity of substitution. We consider four values {0.479, 0.05, 0.95, 1.25}, the first of which is
used to measure energy-saving technological change in Figure 2. The second and third values are
close to the limit cases when the CES production function converges to Leontief and Cobb-Douglas,
respectively. The fourth value is Karabarbounis and Neiman’s (2014) estimate for the elasticity of
mediation; real estate, renting, and business activities; public administration and defense, and compulsory social security;education; health and social work; and other community, and social and personal services.
32
substitution between capital and labor. Figure A5 shows how energy-saving technological change
varies according to these four values. Note the difference in the scales of right and left vertical axes.
Energy-saving technological change grows tenfold when the elasticity of substitution increases from
0.479 to 0.95. Not only the magnitude but also the direction of energy-saving technological change can
vary when the elasticity of substitution changes from 0.479 to 0.05 or 1.25.
Figure A4: Capital-, labor, energy-, and material-augmenting technological change
(a) Austria
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(b) Czech Republic
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(c) Denmark
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(d) Finland
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(e) Germany
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(f) Italy
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(g) Japan
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(h) Netherlands
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(i) Portugal
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(j) Sweden
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
(k) United Kingdom
−.8
0
.8
1.6
1980 1990 2000
(l) United States
−.8
0
.8
1.6
1980 1990 2000
ak
al
ae
am
Notes: The solid, dashed, dotted, and dashed-dotted lines are capital-, labor-, energy-, and material-augmenting technology(𝑎𝑘 , 𝑎ℓ , 𝑎𝑒, 𝑎𝑚), respectively. The shaded area represents the 90 percent confidence interval for 𝑎𝑒. All series are loggedand normalized to zero in the first year of observations.
Finally, we show the extent to which the results of growth accounting can change when material
33
inputs are included. Table A2 reports the quantitative contribution of capital, labor, energy, and material
inputs and capital-, labor-, energy-, and material-augmenting technology to economic growth for each
country. Naturally, the contribution rates of capital, labor, and energy inputs and capital-, labor-, and
energy-augmenting technology to economic growth become smaller after material inputs are included.
However, the contribution rate of energy-saving technological change is not negligible in Germany, the
United Kingdom, and the United States.
Figure A5: Energy-saving technological change for different values of the elasticity of substitution
(a) Austria
−10
−5
0
5
10
−1
−.5
0
.5
1
1980 1990 2000
(b) Czech Republic
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(c) Denmark
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
(d) Finland
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(e) Germany
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(f) Italy
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(g) Japan
−10
−5
0
5
10
−1
−.5
0
.5
1
1980 1990 2000
(h) Netherlands
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(i) Portugal
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(j) Sweden
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
0.479 0.95
0.05 1.25
(k) United Kingdom
−5
0
5
10
15
20
−.5
0
.5
1
1.5
2
1980 1990 2000
(l) United States
−5
0
5
10
15
−.5
0
.5
1
1.5
1980 1990 2000
Notes: Each line represents energy-saving technology (𝑎𝑒) when the elasticity of substitution (𝜖𝜎) is 0.479, 0.05, 0.95,or 1.25. The left and right vertical axes indicate the scale of 𝑎𝑒 when 𝜖𝜎 is 0.479 or 0.05 and when 𝜖𝜎 is 0.95 or 1.25,respectively. All series are logged and normalized to zero in the first year of observations.
34
Table A2: Sources of economic growth when material inputs are included
𝑦 𝑘 ℓ 𝑒 𝑚 𝑎𝑘 𝑎ℓ 𝑎𝑒 𝑎𝑚Austria 2.20 0.43 0.14 0.48 1.05 –0.20 0.80 –0.26 –0.24Czech Republic 2.35 0.79 –0.07 0.50 3.00 –0.22 0.57 –0.07 –2.15Denmark 1.40 0.41 0.09 0.16 0.70 –0.37 0.39 0.02 0.00Finland 2.49 0.42 0.11 0.36 1.09 –0.18 0.84 0.02 –0.16Germany 1.40 0.58 –0.15 –0.08 0.81 –0.45 0.86 0.18 –0.35Italy 1.60 0.42 0.17 0.12 0.92 –0.41 0.55 0.10 –0.27Japan 2.51 1.10 –0.02 0.10 0.68 –0.63 0.75 –0.01 0.54Netherlands 2.34 0.54 0.55 0.25 0.85 –0.30 0.30 –0.17 0.33Portugal 1.28 1.42 0.29 0.64 1.16 –1.33 –0.13 –0.66 –0.11Sweden 3.04 1.03 0.31 0.10 0.94 –0.44 0.89 –0.05 0.25United Kingdom 1.08 0.57 0.20 0.20 0.44 –0.50 –0.28 0.17 0.27Unites States 2.20 1.06 0.59 0.05 0.52 –0.69 0.11 0.23 0.32
Notes: The first column reports the percentage rate of growth in 𝑦 = 𝑟𝑘 +𝑤ℓ + 𝑣𝑒 + 𝜏𝑚 from the first year of observation, 𝑡0,to the year 2005 (i.e., 100× (ln 𝑦2005 − ln 𝑦𝑡0 )/(2005− 𝑡0)). The second to ninth columns report the results of the Shapleydecomposition based on the one-level CES production function.
A.6 Extension
We discuss how to interpret our results when factor-augmenting technology is endogenous. Following
Caselli and Coleman (2006), we consider a model of technology choice, in which the representative
firm chooses factor-augmenting technology (𝑎𝑘 , 𝑎ℓ, 𝑎𝑒) as well as the quantities of inputs (𝑘, ℓ, 𝑒), so
as to maximize its profits subject to production technology and technology frontier. The technology
frontier, from which the firm chooses the optimal mix of technology, is given by
[(𝑎𝑘
𝐴𝑘
)[+
(𝑎ℓ
𝐴ℓ
)[+
(𝑎𝑒
𝐴𝑒
)[] 1[
≤ 𝐵, for [ >𝜎
1−𝜎(29)
where 𝐴𝑘 , 𝐴ℓ, and 𝐴𝑒 are exogenous variables that govern the trade-offs between capital-, labor-, and
energy-augmenting technology, and 𝐵 is an exogenous variable that governs the technology frontier.
We assume [ > 𝜎/ (1−𝜎) as well as 𝜎 < 1 to satisfy the second-order condition of this problem. This
assumption implies [ > 𝜎 and [𝜎/([−𝜎) < 1.
Suppose that the production technology is represented by the one-level CES production function
35
(3). For a given choice of input quantities (𝑘, ℓ, 𝑒), the optimal choice of technology can be written as:
𝑎𝑘 = 𝐵
[(𝐴𝑘 𝑘)
[𝜎
[−𝜎 + (𝐴ℓℓ)[𝜎
[−𝜎 + (𝐴𝑒𝑒)[𝜎
[−𝜎]− 1
[
𝐴[
[−𝜎𝑘
𝑘𝜎
[−𝜎 , (30)
𝑎ℓ = 𝐵
[(𝐴𝑘 𝑘)
[𝜎
[−𝜎 + (𝐴ℓℓ)[𝜎
[−𝜎 + (𝐴𝑒𝑒)[𝜎
[−𝜎]− 1
[
𝐴[
[−𝜎ℓ
ℓ𝜎
[−𝜎 , (31)
𝑎𝑒 = 𝐵
[(𝐴𝑘 𝑘)
[𝜎
[−𝜎 + (𝐴ℓℓ)[𝜎
[−𝜎 + (𝐴𝑒𝑒)[𝜎
[−𝜎]− 1
[
𝐴[
[−𝜎𝑒 𝑒
𝜎[−𝜎 . (32)
The production function (3) can then be rewritten as:
𝑦 =
[(𝐴𝑘𝐵𝑘)
[𝜎
[−𝜎 + (𝐴ℓ𝐵ℓ)[𝜎
[−𝜎 + (𝐴𝑒𝐵𝑒)[𝜎
[−𝜎] [−𝜎
[𝜎
for[𝜎
[−𝜎< 1, (33)
where [𝜎/ ([−𝜎) represents the degree of substitution among capital, labor, and energy inputs when
the firm can adjust the mix of factor-augmenting technology as well as the mix of factor inputs in
response to changes in factor prices. In this case, the elasticity of substitution among capital, labor, and
energy inputs becomes 𝜖[𝜎 ≡ ([−𝜎)/ ([−𝜎−[𝜎) > 0. This implies that the elasticity of substitution
is greater when both factor inputs and factor-augmenting technology are endogenous than when only
inputs are endogenous (i.e., 𝜖[𝜎 > 𝜖𝜎).
The first-order conditions with respect to 𝑘 , ℓ, and 𝑒 imply that
𝑤
𝑟=
(𝐴ℓ
𝐴𝑘
) 𝜖[𝜎−1𝜖[𝜎
(ℓ
𝑘
)− 1𝜖[𝜎
, (34)
𝑤
𝑣=
(𝐴ℓ
𝐴𝑒
) 𝜖[𝜎−1𝜖[𝜎
(ℓ
𝑒
)− 1𝜖[𝜎
. (35)
These equations are of the same form as equations (4) and (5) with a different parameter. Hence, the
elasticity of substitution (𝜖𝜎 or 𝜖[𝜎) can be estimated using the same equations, irrespective of whether
technology is endogenous or exogenous. Whether we can obtain the estimate of the short- or long-run
elasticity (𝜖𝜎 or 𝜖[𝜎) as a result depends on whether we use differences over a long (short) period during
which technology is endogenous (exogenous) in the estimation.
The coefficients of capital, labor, and energy inputs in the production function (33) can be derived
36
from equations (33)–(35) as follows:
𝐴𝑘𝐵 =
(𝑟𝑘
𝑦
) 𝜖[𝜎
𝜖[𝜎−1 ( 𝑦𝑘
), (36)
𝐴ℓ𝐵 =
(𝑤ℓ
𝑦
) 𝜖[𝜎
𝜖[𝜎−1 ( 𝑦ℓ
), (37)
𝐴𝑒𝐵 =
(𝑣𝑒
𝑦
) 𝜖[𝜎
𝜖[𝜎−1 ( 𝑦𝑒
). (38)
These equations are of the same form as equations (6)–(8) with a different parameter. Moreover, it can
be readily shown that factor-augmenting technology (𝑎𝑘 , 𝑎ℓ, 𝑎𝑒) remains the same form as equations
(6)–(8) with the same parameter, irrespective of whether technology is endogenous or exogenous.
Whether we can measure (𝐴𝑘𝐵, 𝐴ℓ𝐵, 𝐴𝑒𝐵) or (𝑎𝑘 , 𝑎ℓ, 𝑎𝑒) as a result of calculating the right-hand
side of equations (36)–(38) depends on whether we use short- or long-run elasticity (𝜖𝜎 or 𝜖[𝜎) in
the calculation. Our estimates for the elasticities of substitution may be closer to those for long-run
elasticity 𝜖[𝜎 than those for short-run elasticity 𝜖𝜎 since we use five-year differences in the estimation.
In that case, we might have measured Δ ln 𝐴𝑒𝐵 rather than Δ ln𝑎𝑒.
Factor-augmenting technology (𝑎𝑘 , 𝑎ℓ, 𝑎𝑒) is log proportional to the coefficients of inputs in the
production function (𝐴𝑘𝐵, 𝐴ℓ𝐵, 𝐴𝑒𝐵), even though they are not the same. More specifically, energy-
saving technological change can be written as:
Δ ln𝑎𝑒 = Δ ln (𝐴𝑒𝐵) +1[Δ ln
(𝑣𝑒
𝑦
). (39)
The magnitude of its difference depends on the magnitude of the second term.
We finally examine how energy-saving technological change can vary according to the change in
the elasticity of substitution. We consider two values {0.479, 0.469}, the former and latter of which are
the estimates for the elasticity of substitution when we use five- and one-year differences, respectively.
Figure A6 shows that energy-saving technological change remains virtually the same when the elastic-
ity of substitution declines from 0.479 to 0.469. This result implies that the second term in equation
(39) is likely to be quantitatively negligible. We can therefore approximately measure energy-saving
37
technological change using our estimated elasticity of substitution.
Figure A6: Energy-saving technological change for short- and long-run elasticities
(a) Austria
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(b) Czech Republic
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(c) Denmark
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(d) Finland
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(e) Germany
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(f) Italy
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(g) Japan
−.6
−.3
0
.3
.6
.9
1980 1990 2000
(h) Netherlands
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(i) Portugal
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(j) Sweden
−.6
−.3
0
.3
.6
.9
1980 1990 2000
0.479
0.469
(k) United Kingdom
−.3
0
.3
.6
.9
1.2
1980 1990 2000
(l) United States
−.3
0
.3
.6
.9
1.2
1980 1990 2000
0.479
0.469
Notes: Each line represents energy-saving technology (𝑎𝑒) when the elasticity of substitution (𝜖𝜎) is 0.479 or 0.469. Allseries are logged and normalized to zero in the first year of observations.
The same results apply to the case in which the production technology is represented by the two-
level nested CES production function (10).
38