A panel data parametric frontier technique for measuring total-factor
energy ef
ficiency: An application to Japanese regions
Satoshi Honma
a, Jin-Li Hu
b,*aSchool of Political Science and Economics, Tokai University, Hiratsuka, Japan bInstitute of Business and Management, National Chiao Tung University, Taiwan
a r t i c l e i n f o
Article history:Received 23 March 2014 Received in revised form 21 October 2014 Accepted 25 October 2014 Available online 18 November 2014 Keywords:
Stochastic frontier analysis Data envelopment analysis TFEE (total-factor energy efficiency) Panel data
Shephard distance functions
a b s t r a c t
Using the stochastic frontier analysis model, we estimate TFEE (total-factor energy efficiency) scores for 47 regions across Japan during the years 1996e2008. We extend the cross-sectional stochastic frontier model proposed by Zhou et al. (2012) to panel data models and add environmental variables. The results provide not only the TFEE scores, in which statistical noise is taken into account, but also the de-terminants of inefficiency. The three stochastic TFEE scores are compared with a TFEE score derived using data envelopment analysis. The four TFEE scores are highly correlated with one another. For the in-efficiency estimates, higher manufacturing industry shares and wholesale and retail trade shares correspond to lower TFEE scores.
© 2014 Elsevier Ltd. All rights reserved.
1. Introduction
After the Fukushima Daiichi nuclear disaster on March 11, 2011, energy conservation has become an urgent issue in Japan. All 54 nuclear reactors in Japan were shut down following the accident. The resulting shortages in electricity supply made “Setstuden,” which means “saving electricity” in English, into a mantra throughout Japan. In July 2012, the Japanese government decided to reactivate reactors #3 and #4 of the Oi nuclear power plant in response to the electricity shortages experienced in the Kansai Electric Power Company's jurisdiction in summer 2012. Both re-actors, however, were shut down again in September 2012 following a periodic check.
Although a new feed-in tariff to promote renewable energy was introduced in July 2012, it cannot fully compensate for the shortfall in energy that has resulted from the cessation of nuclear power generation. Despite the full-capacity operation of the country's thermal power plants, including some plants that were inactive before the Fukushima disaster because of outdated technology, and efforts byfirms and households to save energy, serious electricity shortages remain. Vivoda[1]asserted that nuclear reactors should be restarted as soon as possible because Japan is facing an energy
security predicament. However, this option is politically difficult because of the growing anti-nuclear public sentiment.
Severe energy constraints in Japan cause the following four serious problems[2]. First, dependence on fossil fuels for electricity generation amounted to 88% in 2012, which is greater than the dependence during the first oil crisis, 76%. Second, Japan loses approximately 3.6 trillion yen (3.5 million US dollars) per year in international trade related to importing additional fossil fuels after the Fukushima disaster; this amounts to approximately 30 thou-sand yen (290 US dollars) per capita. Third, electricity prices are higher now than before the Fukushima disaster, with a standard family facing an average appreciation rate of 20%. Fourth, general electric utilities have increased carbon dioxide emissions by 110 million tons, which corresponds to 9% of the nation's emissions in 2010. We believe that improving energy efficiency is one feasible solution to the problems listed above. Morikawa[3]surveyed more than 3000firms and determined that 45% of Japanese firms have been directly or indirectly affected by rolling blackouts and regu-lation of electricity usage.
Japan has pursued an energy conservation policy since thefirst oil crisis in 1973. The Energy Conservation Law was enacted in 1979 and has since been revised eight times. We should examine whether such revisions have exerted a significant effect on Japan's energy situation. Therefore, we require a more accurate measure-ment of regional energy efficiency.
Energy is a fundamental factor from the viewpoints of both national security and the economy, and many empirical studies
* Corresponding author.
E-mail address:[email protected](J.-L. Hu).
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have examined energy efficiency. In this section, we classify these studies into three approaches.
Thefirst approach is based on energy intensity, which is defined as energy consumption per unit of output, such as GDP (gross do-mestic product), or energy productivity (the reciprocal of energy intensity). This approach is considered the traditional energy ef fi-ciency index because it is easily calculated and has been widely used to compare countries [4e8] and to investigate particular countries or industries [e.g.,[9,10]]. However, this approach com-bines energy with other inputs, such as labor and capital stock. Therefore, because it is a partial-factor framework, energy intensity has limited utility for measuring energy efficiency[11,12].
The second approach DEA (data envelopment analysis), which is a non-parametric linear programming methodology that is used to measure the efficiency of multiple decision-making units. Hu and Wang[12]and Hu and Kao[13]incorporated the TFEE (total-factor energy efficiency) index into the DEA model, thereby resulting in creating an approach method that was subsequently applied to Japan by Honma and Hu[14,15], to China by Zhao et al.[16], to Taiwan by Hu et al.[17], and to OECD (Organisation for Economic Co-operation and Development) countries by Honma and Hu[18]. Moreover, S€ozen and Alp[19]compared Turkey's energy efficiency with that of the EU (European Union) countries by incorporating energy consumption, greenhouse gas emissions, and local pollut-ants into the DEA model. Lozano and Gutierreza[20]proposed DEA models with undesirable outputs to estimate the maximum GDP (minimum greenhouse gas, or GHG, emissions) compatible with given levels of population, energy intensity, and carbonization in-tensity (levels of population, GDP, energy inin-tensity, or carboniza-tion index). Mukherjee[21]evaluated the energy efficiency of six sectors and found that the highest energy consumption occurs in the United States. Recently, Goto et al.[22]proposed a new DEA approach with three efficiency concepts that separates inputs into two categories and applied the approach to the manufacturing and non-manufacturing industries of Japan's 47 regions. Although DEA has been widely applied in energy efficiency studies, its drawback is that its efficiency analysis suffers from statistical noise. The third approach uses SFA (stochastic frontier analysis), which was devel-oped by Aigner et al.[23]and Meeusen and van den Broeck[24]
(For a comparison of DEA and SFA, see Refs.[25,26]). To overcome the statistical noise problem, several authors applied the SFA approach to measure energy efficiency. Filippini and Hunt [27]
measured economy-wide energy efficiency in OECD countries. Stern [28] computed energy efficiency by applying SFA to 85 countries and examining the determinants of inefficiency. Herrala and Goel[29]investigated global carbon dioxide (CO2) efficiency
(which is defined as the ratio of the CO2frontier to actual
emis-sions) for more than 170 countries. Refs.[27]and[29]employed a stochastic cost function in which energy or CO2was the cost, GDP
was a main explanatory output variable, and neither labor nor capital stock data were used. In contrast[28], used labor and capital stock data, but energy intensity was an explained variable. Recently, Menegaki[30]employed SFA models to renewable energy management and economic growth in European countries.
Unlike the aforementioned studies, we measure energy ef fi-ciency on the basis of a standard CobbeDouglas production func-tion within the SFA approach. The study that is most closely related to ours is Zhou et al. [31], who proposed a parametric frontier approach by using the Shephard energy distance function. Their approach essentially uses a single-output production frontier model. One feature of their estimation technique is that it deems the reciprocal of energy consumption to be an output that is pro-duced using labor, capital stock, and GDP as inputs. This method-ology enables us to parametrically estimate energy efficiency, taking into account the statistical noise involved. Hu[32]expanded
the cross-sectional model presented by Ref.[31] to a panel data model to measure the energy efficiency of regions in Taiwan. Recently, Lin and Du [33], using the metafrontier procedure of Battese et al.[34], also expanded the work of[31]to conduct a panel data SFA estimation of the first stage of Chinese regional energy efficiency. However, their model does not include environmental variables.
The purpose of the present study is threefold. Thefirst goal is to expand the cross-sectional SFA model proposed by Zhou et al.[31]
to a panel data model and simultaneously estimate the de-terminants of inefficiency. The second purpose is to estimate the TFEE scores for 47 administrative regions in Japan during the years 1996e2008 and examine the effects of Japan's energy-saving pol-icies over that period. The third goal is to compare the SFA results with those from DEA with respect to not only efficiency but also its determinants.
In our SFA model, efficiency measurements are based on the Shephard energy distance function, which is assumed to take the CobbeDouglas functional form. Following Ref.[31], we also assume that the reciprocal of energy consumption is produced by GDP, la-bor, and capital stock. The ML (maximum likelihood) estimator is used to estimate the parameters, including the inefficiency component.
In a departure from the studies conducted by Refs.[31e33], we simultaneously estimate the determinants of inefficiency by employing the technical inefficiency effects model proposed by Battese and Coelli[35]. Before Ref.[35], a two-stage approach was employed in which efficiency was estimated in the first stage; then, this estimated efficiency was regressed against the determinants in the second stage. This two-stage approach has been criticized because both stages suffer from serious biases [[36],p.[39]].
In contrast, the potential determinants of inefficiency can be estimated using the two-stage DEA model. However, this model exhibits two problems[36]. One problem is the possible correlation between the inputeoutput variables and the ef ficiency-determinant factors. The other problem arises from the fact that the interdependency of the DEA efficiency scores violates the basic assumption of independence within the sample. Instead of a non-parametric DEA approach, our non-parametric approach provides an alternative method to estimate efficiency and its underlying factors. The remainder of this study is organized as follows. Section2
describes our methodology and data. Section3presents the TFEE results and the determinants of inefficiency for both the SFA and DEA models. Section4discusses the results' implications. Section5
concludes with a brief summary of the study. 2. Methodology and data
2.1. SFA model for input efficiency
Zhou et al.[31]applied the single-equation, output-oriented SFA model to estimate the TFEE. Their cross-sectional SFA model was used to analyze 21 OECD countries in 2001. Combining the studies of Zhou et al.[31]and Battese and Coelli[35], this study expands the panel data SFA model further by estimating the TFEE.
Following Ref.[31], we assume that the stochastic frontier dis-tance function is included in the CobbeDouglas function as
ln DE(Kit, Lit, Eit, Yit)¼
b
0þb
Kln Kitþb
Lln Litþb
Eln Eitþb
Yln Yitþ vit, (1)
where DE(,) is the distance function, Kitis the amount of capital
stock, Litis labor employment, Eitis the energy input, Yitis the real
economic output, i indicates the region, t indicates the time, and vit
Because the distance function is homogeneous to one degree in the energy input, the above equation can be rearranged as
ln DE(Kit, Lit, Eit, Yit)¼ ln Eitþ
b
0þb
Kln Kitþb
Lln Litþb
Eln 1þ
b
Yln Yitþ vit, (2)which can be rewritten as
ln Eit¼
b
0þb
Kln Kitþb
Lln Litþb
Eln 1þb
Yln Yitþ vitln DE(Kit, Lit, Eit, Yit). (3)
Thus,
ln(1/Eit)¼
b
0þb
Kln Kitþb
Lln Litþb
Yln Yitþ vit uit, (4)where uitis the inefficiency term, which follows a non-negative
distribution, and vit uitis the error component term of a
sto-chastic production frontier. Eq.(4)is consistent with the panel data stochastic frontier model proposed by Battese and Coelli[35]. The free software Frontier Version 4.1, which was kindly provided by Professor Coelli[37], can be used to estimate Eq.(4). The TFEE of region i at time t is then
TFEEit¼ exp(uit). (5)
Therefore, we can apply the panel data stochastic production frontier approach to estimate the TFEE, but we are limited to use of the input-oriented DEA suggested by Refs.[12,13]. Moreover, if we use disaggregated energy inputs, we can change the logged inverse energy inputs on the left-hand side of Eq.(4)and keep the other logged inputs on the right-hand sidefixed, thereby obtaining the TFEE scores for different energy inputs.
Battese and Coelli[35]added the following inefficiency equation for performing simultaneous estimates with a stochastic frontier in the form of Eq.(4):
uit¼ d0 þ d1z1itþ … þ dHzHitþ εit; (6)
where the z1,…, zHare environmental variables and ε
itis white
noise, which is normally distributed. Consequently, we can simul-taneously estimate Eqs.(4) and (6)by applying the approaches of
[35,36].
2.2. DEA
DEA is a linear programming method that is used to assess the comparative efficiency of DMUs (decision-making units), such as countries, regions,firms, and other organizations. There are K in-puts and M outin-puts for each of the N regions. Because the SFA modelfinds a frontier with curvature, we assume VRS (variable returns to scale) in the DEA model. The VRS envelopment of the i-th region can be derived using the following linear programming problem, which was proposed by Banker et al.[38]:
Minq;lq s:t: yiþ Yl 0 qxi Xl 0 el¼ 1 l 0; (7)
where
q
is a scalar that represents the efficiency score of the i-th DMU, e is a 1 N vector of ones,l
is an N 1 vector of constants, yiis the M 1 output vector of DMU i, Y is the M N output matrix that is composed of all of the output vectors of the N DMUs, xiis the
K 1 input vector of DMU i, and X is the K N input matrix that is composed of all of the input vectors of the N DMUs.
The efficiency score satisfies 0
q
1, which is a radialcontraction coefficient for the inputs. If
q
¼ 1, DMU i operates on the efficiency frontier and is technically efficient. This is an input-oriented model in which the radial adjustment coefficient,q
, mul-tiplies the input vector of DMU i. Following literature studies that have used DEA, such as[12e14], the TFEE score of DMU i at time t can be found by dividing its target energy input (which is deter-mined by the DEA model) by its actual energy input:TFEEit¼ Target Energy Inputit/Actual Energy Inputit. (8)
To control the annual environment, all efficiency scores and input targets for region i in year t are determined by comparing them with the regional efficiency frontier in year t. Note that the VRS-DEA model in this study uses regional observations from the same year.
In the second-stage regression, the determinants of inefficiency are estimated using the following equation:
lnTFEEit
¼ g0þ g1z1itþ … þ gHzHitþ εit; (9)
where ε is normally distributed white noise. Because TFEESFAit ¼ exp(uit) in the SFA model, for consistency, we take the
corresponding inefficiency term in the DEA, uit¼ lnðTFEEDEAit Þ, as
the dependent variable in the second-stage regression. Because the dependent variable lnðTFEEDEA
it Þ is censored at zero when
TFEEit¼ 1, we use Tobit regression left censored at zero.
2.3. Data and variables
In our SFA model, we assume that the reciprocal of energy consumption is based on regional real GDP (million yen), labor (person), and capital stock (million yen). These data are taken from Refs.[39], in which all monetary values are given in million yen based on the year 2000 and labor is represented by the number of employees.
Data on energy regarding are taken from Ref.[40], where in which aggregated energy consumption is the sum of oil, gas, coal, electricity, and industrial heat presented in terms of thermal units (tera joules [TJ]). In contrast with previous studies that take considered regional/national energy consumption as a whole as one input[12e14,17,31], our aggregated energy consumption data do not include residential and transportation sectors or non-energy use. Residential energy consumption, such as cooking, heating, and hot water supply systems, generates no added value and are is hence excluded from the aggregated energy consumption data. For the same reason, energy consumption by private vehicles is also excluded. Data regarding energy consumption in the business transportation sector are unavailable because fuel consumed outside regional borders cannot be accurately allocated by region. Using the selected energy consumption data allows more precise measurement of energy efficiency than was previously possible.
We employ industry shares as the environmental variables in two technical inefficiency effects models. The first model (whose efficiency score is hereafter referred to as TFEESFA,M) includes as
environmental variables the regional GDP shares of the manufacturing industry, service activities, and both wholesale and retail trade. The second model (hereafter TFEESFA,E) replaces the manufacturing share with shares of the following five energy-intensive industries: chemicals; iron and steel; non-ferrous metals; non-metallic mineral products; and pulp, paper, and pa-per products.
Data regarding industry shares are taken from Ref.[41]. The data about each energy-intensive industry's shares exclude Okinawa
Prefecture because such data are unavailable for this prefecture, which comprises several small islands. All data are annual, and as mentioned above, the sample period spans the years 1996e2008.
Table 1summarizes the input, output, and environmental variable statistics.
3. Results 3.1. TFEE scores
The ML estimates of the TFEE scores are given inTable 2together and with the DEA TFEE are presented inTable 2. The estimates of the SFA TFEE scores are calculated using the Frontier 4.1 software package provided by Coelli[37]. (For more details, see Coelli et al.
[42].). Space limitations allow us to show present only the mean TFEE scores and rankings of the four TFEE scores for the years 1996e2008. The TFEE scores of each region are stable during the sample period. Following Refs.[31]and[32], TFEESFA,Orepresents the estimated TFEE scores without the environmental variables, whereas following [12e14], TFEEDEA represents the DEA TFEE scores under VRS assumptions. TFEESFA,Oand TFEEDEAare mainly presented here as comparisons with TFEESFA,Mand TFEESFA,E.
It should be emphasized that the rankings are similar; never-theless, the TFEE scores differ among the four methods. The maximum value of the DEA TFEE scores reaches unity because they do not take into account statistical noise. Tokyo, Nara, and Tottori achieve unity scores for TFEEDEAthroughout the sample period.
In comparing the four TFEEs, we observe that the rankings be-tween TFEESFA, Mand TFEESFA, E are similar, while those among others are not. There may be several explanations for why some regions experience different rankings between TFEESFA, O and TFEESFA, Mand between TFEESFA, Oand TFEESFA, E. Because the ex-pected mean inefficiency terms in TFEESFA,M and TFEESFA,E vary
across regions depending on their individual environmental vari-ables, regions located in a more-advantageous environments are relatively more efficient. Tottori, Shiga, and Tokyo vary widely across the ranks of the TFEEs. Tottori is rankedfirst on in terms of TFEEDEAbut 10th, 21st, and 19th in terms of on TFEESFA,O, TFEESFA,M, and TFEESFA,E, respectively. Shiga is ranked 8th in terms of on TFEEDEAbut 33rd in terms of on TFEESFA,Mand 32nd in terms of on TFEESFA,E. Tokyo is ranked 1st in terms of on TFEEDEAbut 25th in terms of on TFEESFA,O. This result likely reflects whether statistical noise is considered. In addition, we assume that if a regional economy is far from average size, the estimated TFEE score is less accurate.
Next, we examine individual TFEE scores by region. The top threedYamagata, Tokyo, and Nagasakidexhibit similar relation-ships between TFEESFA,M and TFEESFA,E. These regions have very high TFEE scores (exceeding 0.95), except for Tokyo's TFEESFA,E. This
result indicates that these regions have little potential to further reduce energy consumption (less than 5%). Observing Tokyo's re-sults, a significant divergence exists between the TFEESFA,Oand each
of the TFEESFA,Mand TFEESFA,Escores. This result may reflect Tokyo's more-advantageous environment for the variables included in TFEESFA,Mand TFEESFA,E. Chiba, Okayama, and Oita are the bottom three regions for all TFEE scores and also exhibit similar rankings between them. Their TFEE scores for all four models are very low (<0.2), which implies that the potential energy savings are great (>80%) for all three regions. We discuss possible improvements that can be implemented in regions that have very low TFEE scores in Section4.2.
Table 3 shows the correlation coefficients for the four TFEE scores. Pearson correlation coefficients are presented below the diagonal, and Spearman rank correlation coefficients are presented above the diagonal. The four TFEE scores are highly correlated with one another. Whereas the correlation coefficients between the three SFA TFEE scores are greater than 0.9, those between the SFA TFEE scores and DEA TFEE are approximately 0.8. All correlations presented inTable 3are significant at the one percent level.
Fig. 1aed presents histograms of the four TFEEs during the years 1996e2008. In the histogram of TFEESFA,O, two peaks, which are located in the ranges of 0.5e0.6 and 0.9e1.0, are observed, and the frequency decreases in the 0.8e0.9 range (Fig. 1a). Only the histo-grams of TFEESFA,Mand TFEESFA,Eare very similar. In these histo-grams also, two peaks are observed but in the ranges of 0.6e0.7 and 0.8e0.9 (Fig. 1b and c). In the histogram of TFEEDEA, the peak is
located in the range of 0.9e1.0 (Fig. 1d).
3.2. Simultaneous estimates of determinants of inefficiency by SFA
Table 4presents the estimated coefficients and determinants of inefficiency in the SFA TFEE scores. Except for the coefficients of log regional GDP in TFEESFA,Oand TFEESFA,E, the coefficients for the log regional GDP, log labor, and log capital stock are significant. How-ever, the coefficients of GDP are not directly interpretable. For example, the coefficient of log GDP in TFEESFA,M(0.306) means
in-dicates that a 1% increase in GDP reduces energy consumption by 0.306%. Thisfinding is inconsistent with the standard production theory. We note that these implausible results may stem from the underlying assumption that attributing inefficiencies regarding in outputs and inputs can be attributed to energy use.
In the ML estimates, the variances of v and u,
s
v2ands
u2, arere-parameterized as
s
2 ¼s
v2 þs
2u andg
¼s
u2/s
2, respectively. Theparameter
g
must lie between 0 and 1, and it indicates the relative contributions of u to the error components. The large values ofg
(0.999, 0.999, and 0.994) for the three SFA TFEE scores imply that the variance in the error components is almost explained by technical inefficiency.
Table 1
Statistical summary of inputs, outputs, and environmental variables.
Variable Unit Mean SD Min Max Obs
Regional GDP million yen 11,267,620 14,899,507 2,070,534 100,982,870 611
Labor person 1,358,697 1,437,445 300,652 8,746,255 611
Capital stock million yen 36,051,479 34,440,744 7,662,999 230,327,688 611
Energy TJ 203,883 221,225 28,331 1,181,999 611
Manufacturing industry share proportion 0.21239 0.07702 0.04031 0.43107 611
Chemical industry share proportion 0.01798 0.01867 0.00021 0.10745 598
Iron and steel industry share proportion 0.01395 0.01466 0.00044 0.10167 598
Non-ferrous metals industry share proportion 0.01359 0.00945 0.00198 0.09322 598
Non-metallic mineral products industry share proportion 0.00854 0.00588 0.00124 0.03798 598
Pulp, paper, and paper products industry share proportion 0.00575 0.00591 0.00006 0.04200 598
Service activities share proportion 0.19281 0.02771 0.11619 0.29261 611
The trend of the time-varying inefficiency parameter,
h
, (Battese and Coelli,[43]) is also estimated in TFEESFA,Oinstead of the share variables. A positive (negative)h
implies that efficiency decreases (increases) over time. For TFEESFA,O,h
is slightly positive (0.001) but insignificant.The determinants of inefficiency are simultaneously estimated for TFEESFA,Mand TFEESFA,Eusing the technical inefficiency model
[35]. Note that a positive (negative) coefficient for an industry's share implies an inefficiency-reducing (inefficiency-inducing) fac-tor. For TFEESFA,M, the estimated coefficients for the shares of manufacturing and the wholesale and retail trade, 15.531 and 11.332, respectively, are highly significant, but that for the service industry is insignificant. We find that higher shares of manufacturing and wholesale and retail trade correspond to lower efficiency. The estimates of TFEESFA,Ein Column 3 provide a more
comprehensive analysis of the determinants of inefficiency. With the exception of the non-ferrous metals industry, which has a negative coefficient, the other four energy-intensive industri-esdchemicals; iron and steel; non-metallic mineral products; and pulp, paper, and paper productsdare highly significant in reducing efficiency. The wholesale and retail trade industry share continues to affect inefficiency levels, but its coefficient decreases to a lower value in TFEESFA,Ethan in TFEESFA,M.
Generalized likelihood ratio tests of various null hypotheses for the three SFA TFEE models are presented inTable 5. The generalized likelihood-ratio test statistic,
l
¼ 2(log likelihood(H0)loglikeli-hood (H1)), has an approximately chi-square or mixed chi-square
distribution for which the parameter is the number of parameters set to be zero in the null hypothesis, H0. All null hypotheses are
rejected at the 1% level. The hypothesis H0:
g
¼ 0, which specifiesthat the regions are fully technically efficient, is rejected for each case. In particular, for TFEESFA, Mand TFEESFA, E, the null hypothesis that all of the coefficients associated with various industry share variables (and the constant term) are zero is rejected.
3.3. Second-stage estimates of the determinants of inefficiency by DEA
To compare the simultaneous estimates of the determinants of inefficiency of TFEESFA,Mand TFEESFA,Ewith those of TFEEDEA, we
regress the inefficiency of TFEEDEAon industry shares using the
Tobit model. As in the previous subsection, we exclusively use the manufacturing industry share and the five energy-intensive in-dustry shares.
Table 6presents the results for the second-stage regression of the inefficiency of TFEEDEAon the environmental variables. Note
that in the inefficiency equation of the SFA model, the inefficiency term is related to the efficiency score as TFEESFA
it ¼exp(uit) for
re-gion i at time t. For consistency in the second-stage regression, the inefficiency term under DEA is obtained by the transformation as uit¼lnðTFEEDEAit Þ for region i at time t. Column 1 inTable 6presents
the estimation results that involve the manufacturing industry share, which is significantly positive in Column 1. A higher manufacturing industry share corresponds to less-efficient energy use. Note that a coefficient of Tobit regression is generally not comparable with that of another model on account of the distortion to the distribution due to the censored data. However, in our model, the marginal effects computed are similar to the coefficients pre-sented inTable 6. Regarding the manufacturing share, the coef fi-cient of TFEESFA,M, 15.531, in Table 4 are greater than the corresponding coefficient for TFEEDEA, 3.083, inTable 6. We
hy-pothesize that this occurs mainly because the inefficiency terms in TFEESFA,Mdepend upon the industry shares as the environmental
variables in Eq.(6), whereas the efficiency measurement of TFEEDEA
does not use industry shares. The signs for the shares of service activities and the wholesale and retail trade industry are positive, but the sign is significant only for the latter.
Column 2 of Table 6 presents the estimation results for involving the shares of thefive energy-intensive industries. All coefficients of these industry shares are significant at the 1% level. Among them, energy-intensive industries, except for the non-ferrous metals industry, are highly significant in reducing TFEE.
Table 3
Pearson (below diagonal) and Spearman rank (above diagonal) correlation co-efficients between the TFEE scores by model.
TFEESFA,O TFEESFA,M TFEESFA,E TFEEDEA
TFEESFA,O 1 0.912 0.921 0.826
TFEESFA,M 0.931 1 0.998 0.761
TFEESFA,E 0.937 0.999 1 0.770
TFEEDEA 0.843 0.808 0.814 1
Table 2
Mean TFEE scores and rankings by region in Japan (1996e2008).
Region TFEESFA,O TFEESFA,M TFEESFA,E TFEEDEA
Hokkaido 0.406 (33) 0.641 (25) 0.607 (25) 0.488 (33) Aomori 0.528 (29) 0.574 (30) 0.567 (30) 0.526 (31) Iwate 0.770 (14) 0.845 (14) 0.838 (13) 0.727 (22) Miyagi 0.584 (23) 0.674 (22) 0.676 (21) 0.626 (28) Akita 0.877 (9) 0.888 (9) 0.886 (10) 0.867 (12) Yamagata 0.971 (3) 0.966 (1) 0.967 (1) 0.884 (11) Fukushima 0.689 (17) 0.802 (16) 0.793 (15) 0.799 (16) Ibaraki 0.181 (43) 0.225 (43) 0.223 (42) 0.243 (43) Tochigi 0.564 (24) 0.614 (26) 0.623 (24) 0.664 (26) Gunma 0.663 (18) 0.750 (17) 0.754 (16) 0.704 (23) Saitama 0.53 0 (28) 0.727 (19) 0.731 (18) 0.577 (29) Chiba 0.105 (47) 0.146 (45) 0.144 (44) 0.128 (47) Tokyo 0.562 (25) 0.951 (3) 0.949 (3) 1.000 (1) Kanagawa 0.233 (40) 0.345 (39) 0.344 (38) 0.311 (41) Niigata 0.513 (30) 0.656 (24) 0.637 (23) 0.671 (25) Toyama 0.530 (27) 0.533 (32) 0.532 (31) 0.809 (14) Ishikawa 0.920 (8) 0.889 (8) 0.907 (8) 0.943 (9) Fukui 0.785 (11) 0.747 (18) 0.745 (17) 0.959 (7) Yamanashi 0.964 (6) 0.881 (12) 0.900 (9) 0.987 (5) Nagano 0.777 (13) 0.914 (7) 0.914 (7) 0.780 (17) Gifu 0.617 (22) 0.704 (20) 0.701 (20) 0.659 (27) Shizuoka 0.434 (32) 0.585 (29) 0.58 (28) 0.501 (32) Aichi 0.305 (38) 0.479 (34) 0.469 (33) 0.414 (36) Mie 0.207 (42) 0.229 (42) 0.230 (41) 0.312 (40) Shiga 0.543 (26) 0.514 (33) 0.527 (32) 0.953 (8) Kyoto 0.734 (16) 0.814 (15) 0.835 (14) 0.778 (18) Osaka 0.375 (34) 0.599 (28) 0.589 (27) 0.481 (34) Hyogo 0.254 (39) 0.352 (38) 0.347 (37) 0.337 (39) Nara 0.982 (2) 0.887 (10) 0.916 (6) 1.000 (1) Wakayama 0.349 (35) 0.341 (40) 0.338 (39) 0.464 (35) Tottori 0.800 (10) 0.690 (21) 0.704 (19) 1.000 (1) Shimane 0.987 (1) 0.924 (5) 0.920 (4) 0.990 (4) Okayama 0.111 (46) 0.125 (46) 0.125 (45) 0.162 (46) Hiroshima 0.219 (41) 0.269 (41) 0.268 (40) 0.290 (42) Yamaguchi 0.137 (44) 0.148 (44) 0.146 (43) 0.211 (44) Tokushima 0.634 (20) 0.571 (31) 0.578 (29) 0.802 (15) Kagawa 0.477 (31) 0.447 (36) 0.456 (34) 0.536 (30) Ehime 0.337 (36) 0.363 (37) 0.361 (36) 0.389 (37) Kochi 0.632 (21) 0.602 (27) 0.598 (26) 0.748 (19) Fukuoka 0.328 (37) 0.452 (35) 0.448 (35) 0.345 (38) Saga 0.967 (5) 0.919 (6) 0.917 (5) 0.964 (6) Nagasaki 0.935 (7) 0.958 (2) 0.961 (2) 0.830 (13) Kumamoto 0.785 (12) 0.882 (11) 0.881 (11) 0.736 (21) Oita 0.117 (45) 0.115 (47) 0.116 (46) 0.168 (45) Miyazaki 0.660 (19) 0.665 (23) 0.669 (22) 0.682 (24) Kagoshima 0.758 (15) 0.853 (13) 0.844 (12) 0.739 (20) Okinawa 0.970 (4) 0.938 (4) na 0.919 (10) Mean 0.570 0.621 0.614 0.640 SD 0.270 0.257 0.258 0.265 Max 0.987 0.988 0.988 1.000 Min 0.104 0.104 0.105 0.107
Note: Figures indicate the mean TFEE scores, and parentheses indicate rankings in each column.
Only the coefficient of the non-ferrous metals industry share is positive. These results are consistent with those for TFEESFA,E. Each (absolute) value of the coefficients for TFEEDEA is smaller
less than that of the corresponding coefficients for TFEESFA,E in
Table 4. This result can be attributed to the same reason as that given above.
4. Discussion
4.1. Importance of incorporating the environmental variables
In this subsection, we discuss the advantage of energy efficiency estimation using a stochastic model with environmental variables
Fig. 1. Histograms of the TFEEs.
Table 4
ML estimates of the stochastic frontier function parameters for the Japanese regions.
Variable Inefficiency of TFEESFA,O Inefficiency of TFEESFA,M Inefficiency of TFEESFA,E
Constant (b0) 0.530 (0.458) 3.491*** (6.940) 2.912*** (6.804)
Log regional GDP 0.069 (1.271) 0.306* (1.861) 0.181 (1.451)
Log labor 0.576*** (6.410) 0.971*** (7.492) 0.928*** (9.109)
Log capital stock 0.084*** (2.827) 0.354*** (3.735) 0.239*** (2.907)
Constant (d0) 5.369*** (2.389) 1.640*** (3.866)
Manufacturing industry share (d1) 15.531*** (4.187)
Chemical industry share (d2) 18.872*** (11.527)
Iron and steel industry share (d3) 35.694*** (15.276)
Non-ferrous metals industry share (d4) 8.696** (2.517)
Non-metallic mineral products industry share (d5) 41.388*** (7.098)
Pulp, paper, and paper products industry share (d6) 24.243*** (4.925)
Service activities share (d7) 4.120 (0.610) 0.785 (0.453)
Wholesale and retail trade industry share (d8) 11.332** (2.504) 7.359*** (6.392)
s2¼s v 2þs u 2 2.311 (0.986) 1.397*** (3.982) 0.254*** (9.846) g¼su2/s2 0.999*** (1292.201) 0.999*** (1646.483) 0.994*** (353.468) m 1.961 (0.623) h 0.001 (0.956) Log likelihood 901.151 287.998 122.431 Number of observations 611 611 598 Number of regions 47 47 46
instead of one without environmental variables. The coefficients of labor and capital of TFEESFA,Oand TFEESFA,Ediffer considerably from one of TFEESFA,OinTable 4. Incorporating the environmental vari-ables allows us to estimate a more-adequate stochastic frontier. Thus, the estimated frontier may be an imprecise curvature without the environmental variables, and the resulting efficiency values would provide a misleading evaluation. As for our sample, TFEESFA,O underestimates TFEEs for much of the inefficient regions (Fig. 2).1 4.2. Policy implications of the TFEE scores
How should policy makers consider the values of the various TFEE scores? In what follows, we discuss the policy implications of our TFEE results. It is ideal but implausible for all regions to achieve scores that are near unity. As previously stated, inefficiency is successfully explained by industry shares, which cannot be radi-cally changed. In addition, regions that specialize in energy-intensive industries supply energy-energy-intensive goods to regions that barely produce them. In fact, industry composition should be considered asfixed to some extent.
Policy makers in an inefficient region may target a minimum efficiency level that could be achieved given the region's industry composition. This target can be set by comparing with regions that have similar industry compositions.
4.3. Simultaneous estimation versus second-step estimation In Eq.(3)of the stochastic approach, all regions have the same intercept,
b
0. This value can vary by region if unobservedhetero-geneity exists. Greene[45,46]proposes the truefixed-effects and true random-effects models to estimate unit-specific constants. This line of research should be explored in energy efficiency research. However, unobserved heterogeneity in the parameter estimates is beyond the scope of this study, in which our plain panel results serve as the benchmark.
5. Concluding remarks
This study parametrically and non-parametrically estimates the TFEE scores for 47 regions in Japan and the determinants of in-efficiency for the years 1996e2008. We extend the SFA approach employed by Zhou et al. [31] and Hu [32] and incorporate the technical inefficiency effects model proposed by Battese and Coelli
[35]. Our two technical inefficiency effects models exclusively include the manufacturing industry share and the five energy-intensive industry shares as environmental variables that in flu-ence inefficiency, the scores of which are referred to as TFEESFA,M
and TFEESFA,E, respectively. For comparison, a stochastic TFEE without environmental variables, TFEESFA,O, is also computed. In
addition, we use the DEA technique to measure a non-parametric TFEE score under VRS, TFEEDEA.
The four TFEE scores are highly correlated with one another, especially TFEESFA,O, TFEESFA,M, and TFEESFA,E. The trend of the mean TFEE scores suggests that energy efficiency improved during the sample period. However, there is considerable potential for further savings on reductions in energy consumption in the Japanese re-gions. For the bottom three regionsdChiba, Okayama, and Oitadthe TFEE scores in all four models are very low (<0.2). This
Table 5
Generalized likelihood-ratio tests of hypotheses of parameters of the stochastic frontier and technical energy inefficiency.
Null hypothesis Log-likelihood value Test statistic (l) Critical value Decision Given TFEESFA,O
H0:g¼ 0 505.410 2813.121 10.50 Reject H0
H0:h¼ 0 261.466 1279.369 6.63 Reject H0
H0:m¼ 0 654.311 493.679 6.63 Reject H0
Given TFEESFA,M
H0:g¼d0¼d1
¼d7¼d8¼ 0
505.410 434.824 14.33 Reject H0
H0:d0¼d1¼d7¼d8¼ 0 363.874 151.754 13.28 Reject H0
H0:d1¼d7¼d8¼ 0 338.729 101.462 11.34 Reject H0
Given TFEESFA,E
H0:g¼d0¼d2¼d7¼ 0 498.232 751.603 20.97 Reject H0
H0:d0¼d2¼ … ¼d8¼ 0 362.442 480.022 20.09 Reject H0
H0:d2¼ … ¼d8¼ 0 341.182 437.502 18.48 Reject H0
Note: All test statistics are statistically significant at the p < 0.01 level. The correct critical values for the hypotheses that involveg¼ 0 are obtained fromTable 1of Kodde and Palm[44].
Table 6
Second-stage estimates of the determinants of inefficiency.
Variable Inefficiency of TFEEDEA
Constant 0.872*** (2.746) 0.536*** (2.808)
Manufacturing industry share 3.083*** (7.478)
Chemical industry share 10.571*** (10.284)
Iron and steel industry share 22.117*** (8.398)
Non-ferrous metals industry share
10.245*** (8.142) Non-metallic mineral products
industry share
13.114*** (3.432) Pulp, paper, and paper
products industry share
7.453*** (2.831) Service activities share 1.251 (1.105) 0.014 (0.017) Wholesale and retail trade
industry share 4.514*** (6.402) 5.092*** (8.712) Sigma 0.556*** (26.417) 0.4203*** (22.440) Number of observations 611 598 Number of regions 47 46 Log likelihood 520.207 359.426
Note: Robust t-values are in parentheses. Statistical significance at the one-, five-, and ten-percent levels are indicated by ***, **, and *, respectively.
Fig. 2. Scatter plot of TFEESFA,Magainst TFEESFA,O. Note: The vertical and horizontal
axes correspond to TFEESFA,Mand TFEESFA,O, respectively.
1 Because the scatter plot of TFEESFA,Eagainst TFEESFA,Ois almost the same, we
result suggests the possibility of conserving reducing energy con-sumption by more than 80% in all three regions.
We compare not only the TFEE scores but also the determinants of inefficiency between SFA and DEA. In SFA, the determinants are estimated simultaneously with inefficiency. This simultaneous estimation suitably incorporates influences from environmental variables into inefficiency. This is SFA's advantage over the two-step estimation performed in DEA. However, in the SFA estimation, we must introduce additional assumptions regarding the functional form of the frontier and the distributions of the inefficiency and error terms compared to with the DEA. In contrast, the inefficiency of the DEA TFEE scores is regressed on environmental factors via a Tobit approach. The signs of the Tobit model are consistent with those of the SFA estimation. For both SFA and DEA, the results that include the manufacturing industry share indicate that higher manufacturing and wholesale and retail trade shares correspond to lower energy efficiencies. The results that include shares from energy-intensive industries e chemicals; iron and steel; non-metallic mineral products; and pulp, paper, and paper products e indicate that higher shares of energy-intensive industries corre-spond to significantly lower levels of efficiency.
Our study has two limitations. First, in our SFA model, all in-efficiencies are attributed to energy input. This may lead to over-estimating energy inefficiency. On this point, DEA is superior to SFA because the DEA TFEE takes into account both radial and non-radial slack with respect to energy inputs. The second limitation is that the estimates do not consider unobserved heterogeneity.
Our approach can be extended in various directions. First, the environmental variables that affect energy efficiency should be further explored. It is important not only to measure efficiency but also to examine the determinants of inefficiency. Second, the functional form can be easily changed from the CobbeDouglas function to more general functional forms, such as a translog function. Third, replacing energy input with undesirable outputs or natural resources would allow us to estimate environmental ef fi-ciency using the total-factor framework. Fourth, our model can be applied to other regions for a cross-country comparison. If so, environmental variables should be explored.
Acknowledgments
The authors thank the three anonymous referees and partici-pants at the 2013 APEC Conference on Low Carbon Towns and Physical Energy Storage. This work was supported by the Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (#25380346) and Taiwan's National Science Council (NSC 102-2410-H-009-045).
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