Applied Energy 88 (2011) 1441–1446
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Cost efficiency of Japanese steam power generation companies: A Bayesian comparison of random and fixed frontier models A. George Assaf a,⇑, Carlos Pestana Barros b, Shunsuke Managi c,1 a
Isenberg School of Management, University of Massachusetts-Amherst, 90 Campus Center Way, Amherst 01002, United States Instituto Superior de Economia e Gestão, Technical University of Lisbon, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal c Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aramaki-Aza Aoba, Aoba-Ku, Sendai 980-8579, Japan b
a r t i c l e
i n f o
Article history: Received 9 September 2009 Received in revised form 23 July 2010 Accepted 24 September 2010 Available online 12 November 2010 Keywords: Japan Steam power generating companies Random frontier model Fixed frontier model Bayesian
a b s t r a c t This study analyses and compares the cost efficiency of Japanese steam power generation companies using the fixed and random Bayesian frontier models. We show that it is essential to account for heterogeneity in modelling the performance of energy companies. Results from the model estimation also indicate that restricting CO2 emissions can lead to a decrease in total cost. The study finally discusses the efficiency variations between the energy companies under analysis, and elaborates on the managerial and policy implications of the results. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The efficiency analysis of energy firms is an important topic for policy debate on resource scarcity and climate change [36,39]. In spite of several decades of extensive academic research on efficiency and its related implications, the empirical findings discussing its causes and effects remain inconsistent and debatable. The understanding of the general relationship between managerial practices and efficiency has proven to be an elusive goal [27], so that efficiency can now be viewed as ‘‘one of the most intriguing problems in the management of organizations’’ [7]. In the energy sector, the efficiency of energy companies has also been the focus of most recent research [21,22,16,10,26,45,28]. Motivated by the above, the present study aims to extend the efficiency literature in the energy sector by analysing on the cost efficiency of Japanese steam power generation companies. The increased competition among Japanese energy companies resulting from deregulation and liberalization has placed energy companies in a much more competitive environment, and under more pressure to upgrade their efficiency. Benchmarking analysis is one of the ways to drive energy companies towards the frontier of best practices [29]. ⇑ Corresponding author. Tel.: +1 413 545 1492; fax: +1 413 545 1235. E-mail addresses:
[email protected] (A.G. Assaf),
[email protected] (C.P. Barros),
[email protected] (S. Managi). 1 Tel.: +81 22 795 3216; fax: +81 22 795 4309. 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.09.022
The methodology used in this paper presents a new contribution to the literature. Most recent studies adopt the data envelopment analysis (DEA) or stochastic frontier analysis (SFA) methods to analyse the efficiency of energy companies. While both DEA and SFA are advanced and well established, they are based on the limited assumption that energy companies share exactly the same production possibilities and differ only with regards to their level of inefficiency. It is true that this assumption might be appropriate if the sample under analysis contain energy companies that share homogenous characteristics. However in most cases energy companies operate under different environmental conditions and thus ignoring the issue of heterogeneity might ‘‘seriously distort’’ the efficiency results [43,14]. There is the additional concern that policy design may be faulty if policy recommendations are drawn from a miss-specified technology. This is particularly crucial in the context of Japanese firms where average unit emission is widely heterogeneous between plants ranging from 0.350 to 0.660 kg–CO2/kWh. There are differences because some firms use more liquefied natural gas, which is cleaner energy than coal and oil. Furthermore, differences in company or plant size are large, ranging from about 4 to 32%. Some key studies on Japanese energy included Hattori et al. [15] and Nakano and Managi [29]. These studies use the traditional DEA or the stochastic frontier approach, which as mentioned before ignore the heterogeneity between energy firms in the estimation of efficiency. The need to account for technological differences is therefore crucial in efficiency modelling. In this paper, we adopt for that purpose the Bayesian random stochastic frontier model. In contrast
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to traditional stochastic frontier models, the main benefit of this model is that it separates the cost efficiency estimates from the technological difference (i.e. heterogeneity) among energy companies. We compare the model with the fixed Bayesian frontier model which assumes no heterogeneity between firms. The Bayesian approach is considered an innovation in the energy sector, where most previous studies in the area have adopted the Maximum likelihood approach. One of the main advantages of the Bayesian method is that it allows the inclusion of ‘‘prior’’ information about the parameters in inferences. The rest of the paper is organized as follows: Section 2 presents a background of the energy companies analysed in this study. Section 3 provides a review of the literature. Section 4 describes the methodology, and Section 5 presents the data and results. Discussions and summary of the main findings then follow in Sections 6 and 7, respectively. 2. Institutional setting
mental Protection signed in Washington, DC, on August 5, 1975. Later, Japan also signed the Rio agreement in 1992, aiming to bring together two contending issues: environmental protection and economic growth. In 2005, Japan signed the Kyoto Protocol in Rio de Janeiro in 1992 [6,25]. All these international accords signal the aim towards environmental protection. Research on Japanese energy companies include Sueyoshi [41], Sueyoshi and Goto [42], Hattori et al. [15], Nemoto and Goto [30], Nemoto and Goto [31], Nakano and Managi [29]. As mentioned before, most of these studies use the simple DEA or stochastic frontier approaches, while the present research innovates in terms of adopting the Bayesian random frontier model and taking into account the CO2 produced. Table 1 shows the large difference in size between the energy companies analysed. Therefore, it is crucial to account for the heterogeneity of companies in our analysis. 3. Literature survey
The Japanese electricity industry has undergone regulatory reforms since the mid-1990s, but most significant reforms started with the amendment of the Electricity Utility Industry Law in 1995. Since then, the law was also amended several times and the electricity industry has undergone structural change to encourage efficiency improvement. The amendment, however, made it possible for other companies to enter into the generating market by introducing the competitive bidding system in the wholesale market. New entrants are called ‘‘Independent Power Producers’’. The government also introduced the yardstick regulation, which refers to the whole vertically integrated utility, and aims to promote the cost cutting competition. Under the yardstick regulation, the electricity price of each electricity company is determined partly by comparing its performance with that of other companies. Companies with larger cost than others suffer losses, while those with smaller cost generate profits. Partial liberalisation in energy retail markets was introduced in 2000. The market was liberalized only for electricity through transmission lines over 20,000 V and when maximum power demand is over 2000 kW. This market accounts for almost 30% of the total electricity supply by electricity companies. This amendment also made it possible for the power producer and supplier to enter the market. To realize this new market structure, a system was developed in which the transmission lines of electricity companies could be used by new entrants. Furthermore, the 2003 amendment stipulated the extension of the boundary of liberalization. The markets for maximum power demand over 500 kW and over 50 kW were liberalised from April 2004 and April 2005, respectively. Table 1 presents some characteristics of the companies analysed. Relative to CO2, the first environment agreement that Japan has adopted was a US–Japan Agreement on Cooperation in Environ-
Efficiency analysis in the energy sector mainly concentrates on distribution networks [19,20,10,9]. Papers analysing the efficiency of electricity generating plants include Kleit and Terrell [21], Raczka [35], Hiebert [16], Arocena and Waddams Price [3], Knittel [22]. Jamasb and Pollitt [18] review the frequency with which different input and output variables are used to model electricity distribution. The most frequently used outputs are units of energy delivered, number of customers and size of the service area. The most widely used inputs are number of employees, transformer capacity and network length. A recent and comprehensive survey of research on energy efficiency can be found in Jamasb et al. Jamasb et al. [20]. Restricting the literature review to a sample of recent energy production papers, it is observed that these papers adopt one of two complementary efficiency methodologies: DEA and the homogenous stochastic frontier model. Exception to this traditional tendency are Barros and Peypoch [5] who adopted a random frontier model to account for the heterogeneity of energy companies. Table 2 displays a detailed review of the available studies. As it is clear, none of the existing studies use the Bayesian random frontier model adopted in this study, despite the fact that most energy companies operate under heterogeneous characteristics. Thus, the present study innovates in this context. 4. Stochastic frontier model with random coefficients As mentioned before, the unique feature of the random frontier model is that it can account for both technological differences (i.e. heterogeneity) and cost efficiency. In this paper, we compare the model with the Bayesian fixed frontier model of Koop et al. [23]. However, we do not provide the technical details of the fixed
Table 1 Characteristics of the Japanese energy companies. Nobs.
Steam power generation companies
Vintage (years)
CO2 (kg)
Electricity (Mwh)
1 2 3 4 5 6 7 8 9
Chubu electric power Chugoku electric power Hokkaido electric power Hokuriku electric power Kansai electric power Kyushu electric power Shikoku electric power Tohoku electric power Tokyo electric power Mean Median St. dev.
22.092 18.573 23.131 22.020 27.087 18.875 13.833 24.464 17.203 20.809 22.020 4.057
14,877,652.14 3,230,985.83 3,476,816.74 5,680,131.45 2,782,217.5 4,531,272.03 3,964,921.9 9,432,305.14 23,883,348.37 7,984,406 4,531,272 7,121,761
13,840 27,161 17,913 55,996 180,963 90,430 17,661 21,835 31,847 50,849 27,161 54,592.47
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frontier model given that it is well established in the literature. For technical details of the model refer to Coelli et al. [8]. To explain the Bayesian random frontier we start with the following model:
yit ¼ a þ x0it ci þ v it þ uit
I ¼ 1; . . . ; N;
t ¼ 1; . . . ; T
ð1Þ
where yit represents the total cost for the ith observation of year t, xit is a (K 1) vector of observations for the explanatory variables, vit is a random error distributed as i.i.d N(0, r2), uit is a non-negative random error accounting for cost inefficiency, and ci is a vector of random coefficients, and a is an intercept. To complete the model assumption, we consider uit to be exponentially distributed2 with parameter k:
f ðuit Þ ¼ k expðkuit Þ
ð2Þ
The parameters ci are assumed to be distributed according to a (K 1)-variate normal distribution as follows:
ci Nðc; XÞ
ð3Þ
is a vector of parameter means, and X is a positive definite where c covariance matrix. If X is restricted to zero (i.e. X = 0), then the model in (1) will converge to the traditional or fixed stochastic frontier model which is commonly used in the literature. Thus, it is this additional assumption that makes the main difference between the random model and the fixed stochastic frontier model of Koop [24]. ; X are Some additional assumptions of the model are that ci j c independently distributed, and vit as well as uit are independent of x0it . Thus, with the current model assumption, each firm has its own cost function with parameters ci which accounts for the heterogeneity between firm, and a non-negative disturbance uit which accounts for the level of cost inefficiency. For more detail about the likelihood, priors, and the conditional posteriors of the model refer to Tsionas [43]. 5. Data and results A balanced panel is used, comprising 9 Japanese energy companies during 28 years from 1976 to 2003 (9 28 = 252 observations). The variables follow the existing literature and are presented in Table 3, where monetary magnitudes are expressed in thousand yens, deflated by the GDP deflator and denoted at prices of 2002. Total cost, price of labour, and price of energy are obtained from Nikkei Needs Cooperation. Electricity produced, volume of CO2, and all other variables used are obtained from Review of supply and demand of electricity published by the Ministry of Economy, Trade and Industry, Japan. The stochastic cost frontier model used in this study is of the restricted translog form and can be expressed as follows:
ln
C it PLit ¼ ait þ cElec ln Elecit þ cCO2 ln CO2it þ cPL ln þ cK ln K PEit PEit þ cElec;Elec ln Elecit ln Elecit þ cCO2 ;CO2 ln CO2it ln CO2it þ cElec;CO2 ln Elecit ln CO2it þ kElec;PL ln Elecit ln þ cCO2 ;PL ln CO2it ln ln
PLit PEit
PLit PLit þ cPL;K ln ln K þ cPL;PL PEit PEit
where Cit is the total cost for each energy company, Elecit is eelectricity produced in MWH, CO2it is the volume of CO2 emissions produced in kilogram, K is the capital-premises, measured by the value of the total assets, PLit is the price of labour, measured by dividing total wages between the number of workers, PEit price of energy, measured by the oil rate, Reg is a dummy variable which takes the value of one post the 1990s, when the companies started to be deregulated, Size is a dummy variable that takes the value of 1 for large energy companies and zero otherwise, t is a time trend, vit is a random error identically and independently distributed as Nð0; r2v Þ, and uit is a non-negative random error which captures the level of cost inefficiency. Note that we divided the total cost and price of labour by the price of energy to ensure homogeneity in price for the cost function. Gibbs Sampling with data augmentation has been applied to the above data using 50,000 iterations (first 10,000 iterations are dropped to avoid sensitivity of starting values). The value r i was set at 0.875 following other studies in the literature [43,44]. The posterior estimates and posterior standard deviations are reported in Table 4. It is clear that the model is well fitted with most parameters significant, correctly signed and in line with the theoretical requirements. As mentioned before, for comparison purpose, we also estimate the traditional Bayesian frontier model of Koop et al. [23]. The estimates of this model are also reported in Table 4. As it is clear from the results the posterior mean of cost function parameters are reasonably close for both models. The largest difference pertains to the posterior mean of r2, standard error of the cost function parameters and the efficiency scores. Tsionas [43] converged to the same conclusion and explained that the difference in r2 might be attributed to the heteroscedastic nature of the stochastic frontier model. The average efficiency scores across the period of study are reported in the last row of Table 5, and as shown, the average efficiency score of the random frontier (85.39%) is higher than that of the fixed frontier (79.30%). Differences in efficiency scores could also be attributed to the fact that the Bayesian fixed frontier model does not take intro account the heterogeneity between firms and thus can sometimes provide misleading efficiency results. It is clear from Table 5 that the ranking of firms in terms of their efficiency is also different between the random and fixed frontier model. In general, most companies operate at a high efficiency rate but there is a clear variation between the highest efficient (0.951) and lowest efficient company (0.816) which signifies that significant improvement can still be made at certain companies. In order to provide further confirmation on the suitability of the Bayesian random stochastic frontier model in modelling the efficiency of Japanese energy companies, we also used the DIC test to compare it against the fixed frontier model. Models with lower DIC are considered to be a better fit [40]. The test results indicate that the random model outperform the fixed frontier model with a DIC value of 49.45, in comparison to DIC value of 80.11 for the fixed frontier model. Note that one can also use the Bayes factor as an alternative method to compare the adequacy of the two models. More details about the mathematical formulation of the Bayes factor are provided in Tsionas [43].
6. Discussions
PLit PLit ln þ cK;K ln K ln K þ creg Reg þ csize Size PEit PEit
þ ct t þ ct2 t2 þ v it þ uit
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ð4Þ
2 Other distributions are also possible, but the exponential distribution is generally the most common in the Bayesian framework. For more specific details refer to Koop [24].
The results from both frontier models are similar indicating that the results are robust, with the variables depicting the same sign on both models. It is clear that total cost increases significantly with the input prices and outputs, with the exception of the price of labour. Such results were initially expected. The insignificant impact of the price of labour, for instance, might have resulted from its low use in energy plants, which are capital intensive. On
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Table 2 Recent papers on energy production. Papers
Method
Stochastic frontier models Kleit and Bayesian Cobb-Douglas cost Terrell [21] stochastic frontier model
Units
Endogenous variable
Exogenous variables
USA, 78 steam plants, observed in 1996
Total cost
USA, unbalanced data from 1981 to 1996 on investor-owned electricity coal, gas and oil utilities (5040 observations) 412 US municipal utilities observed from 1988–1997
Output (mwh)
(i) Annual output (mwh); (ii) peak output (mwh); (iii) wage(dólars); (iv) price of fuel; (v) price of capital; (vi) log of relative wage; and (vii) log of relative fuel price (i) Capital; (ii) labour; (iii) coal; (iv) oil; (v) vintage; and (vi) vintage squared
Knittel [22]
Cobb-Douglas stochastic production frontier model
Hiebert [16]
Translog cost frontier model USA
Farsi and Filippini [10]
Cobb-Douglas cost frontier
Switzerland, 59 utilities observed from 1988 to 1996
Total annual costs per-kwh
Farsi and Filippini [11]
Cobb-Douglas cost frontier
Switzerland, 26 gas utilities, 1996–2000
Total cost
Goto and Tutsui [13]
Translog production function
22 USA electricity power utilities, 1992–2000
(i) Generation electricity; (ii) transmission/distribution of electricity; and (iii) general administration
Farsi and Filippini [12]
Translog cost frontier (several stochastic frontiers)
Switzerland, 34 multi utilities observed from 1997–2005
Total costs
Arcos and Toledo [2]
Cost function with several specifications
Spain, 11 electricity companies 1878–1997
Total cost
Data envelopment analysis Papers Method
Total operating and maintenance costs are regressed in several explanatory variables
(i) Net electricity generation (in megawatt hours); (ii) price of fuel (in dollars per-million British thermal units); (iii) time trend; (iv) the vintage of the plant in years (calculated as the sum of the vintages of the units); (v) the age of the plant (in months); and (vi) the number of units comprising the plant. For coal, a dummy variable is included (i) Annual output in gwh; (ii) number of customers; (iii) load factor; (iv) service area; (v) average annual labour price per employee; (vi) average capital price per kva installed; (vii) average price of input power, (viii) high voltage network dummy; (ix) auxiliary revenues more than 25%; and (x) share of forest area more than 40% (i) Annual output in MWh; (ii) labour price; (iii) capital price; (iv) energy price; (v) number of customers; (vi) number of terminal blocks; (vii) service area; (viii) number of customers per km network length; (ix) network length in km Generating model inputs: (i) capital; (ii) labour; (iii) fuel; and (iv) net generated electricity. Transmission/ distribution model inputs: (i) capital; (ii) transmission line in km; (iii) distribution transformers; (iv) labour; (v) total sales; and (vi) total customers. General administration model inputs: (i) capital; (ii) labour; (iii) employees; (iv) sales; Environmental variables: (i) nuclear generation ratio; (ii) demand density index; and (iii) large consumer ratio (i) Electricity distribution; (ii) gaz distribution; (iii) water distribution; (iv) customer density; (iv) capital price; (v) labour price; (vi) electricity price; and (vi) gaz price. (i) Labour cost; (ii) taxes; (iii) depreciations; and (iv) cost opportunity of assets
Units
Inputs
Outputs
Pollitt [32]
Two-stage model DEA model. First stage a CCR DEA model. Second stage a battery of statistical tests (ANOVA, Tobit regression, etc.)
78 Nuclear power stations in the USA, UK, Canada, Japan and South Africa,
Energy produced in KWh
Arocena and Waddams Price [3] Raczka [35]
Two DEA models: (i) graphyperbolic malmquist; (ii) malmquist Index
28 Spanish generating plants observed from 1984 to 1997 41 Heat plants from Wielkopolska, Poland observed in 1997
(i) Labour; (ii) capital;, (iii) fuel; (iv) price of labour; (v) price of capital; (vi) price of fuel, separated into historic and current; and (vii) other input descriptors (age and reactor type). (i) Capital proxied by average capacity (mw); (ii) labour average number of workers); (iii) fuel (million of therms) (i) Labour; (ii) fuel; and (iii) pollution
DEA two-stage procedure: in the first stage, DEA allocative model is used; in the second stage, a Tobit model regresses the efficiency scores in
(i) Annual power produced (mwh)
(i) Heating production
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Method explanatory variables DEA CCR models, input oriented. One base model and two strategic behaviour models: a gaming operating costs model and a model with restricted outputs DEA distance function
Jamasb et al. [20]
Estache et al. [9]
Abbott [1]
DEA Malmquist
Pombo and Taborda [33]
Several DEA models including a malmquist index
Barros [4]
DEA Malmquist
Zhou and Ang [46]
DEA Shepard input distance
Barros and Peypoch [5]
DEA two-stage model, Simar and Wilson [38] model
Ramos-Real et al. [34]
DEA Malmquist index
Units
Endogenous variable
Exogenous variables
28 USA utilities observed in 2000
(i) Distribution operating costs
(i) Units of electricity delivered; (ii) number of customers; and (iii) length of network.
84 South American companies, observed from 1994 to 2001
(i) Distribution lines and (ii) transformation capacity in MVA. Environmental variables: Residential sales/sales and GNP per-capita PPP units (i) Capital stock; (ii) energy used; and (iii) labour employed (i) Employees; (ii) number of transformers and substations, (iii) power line in km; and (iv) regional GDP; and (v) national installed capacity in electricity generation (i) Number of workers; (ii) capital; (iii) operational cost; and (iv) Investment
(i) Sales in gwh; (ii) number of customers; and (iii) service area in 2 km
(i) Total primary energy
(i) Desirable output: gross domestic product and (ii) undesirable output: CO2 emissions from fuel combustion (i) Production in MWh and (ii) maximum capacity (MW).
6 Australian states, 1969– 1999 12 Colombian distribution companies, 1985–2001
Portugal electricity company hydroelectric plants, 2001–2004 OECD countries, 2001– 2002 Portugal electricity company, thermoelectric plants, 1996–2004 Brazil, 18 electricity distribution companies, 1998–2005
the other hand, CO2 can indirectly increase cost through the investment in equipment that restrict emissions. This might be explained
Table 3 Descriptive statistics of the data. Variable
Mean
St. dev.
Median
Minimum
Maximum
ln C ln Elec ln CO2 ln PL ln PE ln K
13.503 10.216 15.393 5.888 0.039 13.440
0.952 0.847 0.743 0.844 0.291 0.912
13.548 10.150 15.308 5.781 0.004 13.354
11.217 8.305 13.511 4.128 0.635 11.333
15.723 12.106 16.989 8.218 0.901 15.411
Table 4 Posterior parameter estimates. Bayesian random frontier model
Bayesian fixed frontier model
Parameters
Mean
St. dev.
Parameters
Mean
St. Dev.
a cElec cCO2 cPL cK cElec,Elec cCO2 ;CO2 cElec;CO2 cElec,PL cCO2 ;PL cPL,K cPL,PL cK,K creg csize ct ct 2
0.235 1.122 0.967 0.286 2.255 0.521 0.189
0.988 0.605 0.368 0.671 0.775 0.136 0.090
0.157 1.126 1.101 0.284 2.570 0.501 0.191
0.995 0.611 0.583 0.654 0.781 0.136 0.081
0.650 0.181 0.190 0.063 0.128 0.029 0.466 0.068 9.940E4 1.601E6 0.020
0.235 0.046 0.111 0.101 0.039 0.026 0.037 0.028 7.564E4 3.762E6 0.004
a cElec cCO2 cPL cK cElec,Elec cCO2 ;CO2 cElec;CO2 cElec,PL cCO2 ;PL cPL,K cPL,PL cK,K creg csize ct ct2
0.646 0.185 0.191 0.062 0.132 0.027 0.462 0.062 9.941E4 1.640E6 0.045
0.205 0.047 0.106 0.102 0.041 0.025 0.040 0.031 7.564E4 3.762E6 0.004
r2
r2
(i) Number of workers; (ii) book value of physical assets; and (iii) operational costs (i) Sales; (ii) number of customers
(i) Electricity consumed (i) Total sales; (ii) total customers; and (iii) urban area served
(i) Production in MWh and (ii) capacity utilization in% of total
(i) Length of electricity grid; (ii) number of employees; (iii) power losses in GWh; and (iv) service area
Table 5 Cost efficiency scores. Bayesian random frontier model
Bayesian fixed frontier model
Energy company
Average
Energy company
Average
Hokkaido Tohoku Tokyo Chubu Hokuriku Kansai Chugoku Shikoku Kyusyu Overall average = 0.853
0.879 0.951 0.868 0.848 0.900 0.877 0.891 0.884 0.816
Hokkaido Tohoku Tokyo Chubu Hokuriku Kansai Chugoku Shikoku Kyusyu Overall average = 0.793
0.845 0.835 0.823 0.750 0.743 0.826 0.746 0.752 0.841
by the background threat of future regulation born of the social pressure to avoid global warming. The results from the dummy variables included in the model are also important. The negative sign of regulation signifies that regulation did not impose restrictions on energy companies, but rather led to a decrease in cost. Similarly, firm size seems to have a significant impact on total cost, reflecting the economies of scale inherent in large companies. What are the implications of the public policy in this context? From a managerial perspective Japanese energy companies should be aware that cost efficiency is of paramount importance to decreasing costs without decreasing inputs use. The decrease in input usage could lead to underinvestment [17] and therefore should be abandoned. The regular use of benchmark analysis by Japanese energy companies is also encouraged to identify the sources of cost inefficiency, or other possible successful strategies. As the data set is relatively short, Bayesian or alternative bootstrap analysis should be adopted to eliminate bias in the estimates. The use of the random frontier is encouraged as it takes into account heterogeneity and thus provides a more accurate benchmarking process. In this line of reasoning, the public policy should give incentives for
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energy companies to increase their cost efficiency towards the frontier of best practices. The energy company with the upper cost efficiency score should be used as reference for the least efficient to increase their efficiency. As size is an important cost determinant, it should also be taken into account in any future benchmarking of Japanese energy companies. From an environmental policy perspective, the positive sign of CO2 implies that emission increases costs (i.e., decrease in CO2 emission decrease costs) and therefore should be diminished by adopting non-emission increasing technologies (e.g., less carbon intensive technologies or renewable energy use). Whether CO2 adopted abatement in Japanese energy companies is used efficiently, it is crucial to investigate its role of cost structure of the energy companies. Considering the importance of CO2 reduction for the environment, detecting the relationship between CO2 and costs is important. 7. Conclusions This paper adopted a Bayesian frontier model to estimate the cost efficiency of Japanese steam power generation companies from 1976 to 2003. In comparison to the previous literature in the area, our research overcame the bias towards DEA models by accounting for heterogeneity in modelling the efficiency of energy companies. The use of Bayesian modelling added to the accuracy of the model estimation. Two frontier models were estimated, a random and a fixed (homogenous) frontier model. The results indicated that the random frontier was a better fit to the data, providing therefore further evidence that Japanese energy companies operate in different environmental and technological characteristics. This was initially expected since steam power generation companies are not homogeneous. These are small and large and medium sized companies, and operate under different demand and supply conditions. The results further indicated that higher emissions can increase costs. Thus, restricting CO2 emissions is an environmental as well as a cost policy that should be adopted by the Japanese steam power companies (see [37], for other country’ example). Future studies are encouraged to build on the results of this study to gain more insight into the between the companies analysed in this study. In order to draw more generalised conclusions, a larger data set might be also needed, with the inclusion of additional countries. References [1] Abbott M. The productivity and efficiency of the Australian electricity supply industry. Energy Econ 2006;28:444–54. [2] Arcos A, Toledo PA. An analysis of the Spanish electrical utility industry: economies of scale, technological progress and efficiency. Energy Econ 2009;31:473–81. [3] Arocena P, Waddams Price CW. Generating efficiency: economic and environmental regulation of public and private electricity generators in Spain. Int J Ind Organ 2002;20:41–69. [4] Barros CP. Efficiency analysis of hydroelectric generating plants: a case study for Portugal. Energy Econ 2008;30:59–75. [5] Barros CP, Peypoch N. Technical efficiency of thermoelectric generating plants. Energy Econ 2008;30:3118–27. [6] Bosseti V, Buchner B. Data envelopment analysis of different climate scenarios. Ecol Econ 2009;68:1340–54. [7] Caverly N. Civil Service resiliency and coping. Int J Pub Sec Manage 2005;18:401–13. [8] Coelli TJ, Prasada Rao DS, O’Donnell CJ, Battese GE. An introduction to efficiency and productivity analysis. 2nd ed. New York: Springer; 2005. [9] Estache A, Rossi M, Ruzzier CA. The case for international coordination of electricity regulation: evidence from the measurement of efficiency in South America. J Regul Econ 2004;25:271–95. [10] Farsi M, Filippini M. Regulation and measuring cost-efficiency with panel data models: application to electricity distribution utilities. Rev Ind Organ 2004;25:1–19.
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