Measuring energy economic efficiency: A mathematical programming approach

Measuring energy economic efficiency: A mathematical programming approach

Applied Energy 179 (2016) 479–487 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Measu...

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Applied Energy 179 (2016) 479–487

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Measuring energy economic efficiency: A mathematical programming approach Hua Liao a,b,c, Yun-Fei Du a,b,c, Zhimin Huang a,b,c,d, Yi-Ming Wei a,b,c,⇑ a

School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China Center for Energy and Environmental Policy Research, Beijing Institute of Technology, Beijing 100081, China c Collaborative Innovation Center of Electric Vehicles in Beijing, China d Robert B. Willumstad School of Business, Adelphi University, Garden City, NY 11530, USA b

h i g h l i g h t s  Energy efficiency in cost concept is measured based on mathematical programming.  The properties of the measurement method are discussed.  The energy efficiency in electricity sector of 23 IEA countries is compared.

a r t i c l e

i n f o

Article history: Received 23 March 2016 Received in revised form 25 May 2016 Accepted 22 June 2016

Keywords: Energy economic efficiency Electricity generation sector Mathematical programming

a b s t r a c t The widely used measurement for energy efficiency are in form of physical quantity, thus neglecting the economic cost and the imperfect substitution among energy and other production factors such as capital and labor. In the real world, least energy input does not always leads to optimal factor combinations in production processes. The goal of producers is to minimize the total factor cost or maximize the profit instead of minimizing the physical input. The optimum factor combination is constrained not only by the available technology but also by the relative prices of factors. Based on the production theory and mathematical programming, the ‘‘energy economic efficiency (ee )” is constructed to calculate energy efficiency which connects energy productivity and economic efficiency (Ee ). In this paper, we have a further discussion on the properties of the energy economic efficiency diagrammatically and mathematically and measure the efficiency in electricity generation sector of 23 International Energy Agency (IEA) countries. Compared with traditional energy efficiency indicators (in physical form), we develop a more proper way of evaluating energy efficiency with better performance. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction There are many indicators to measure energy efficiency, such as the energy intensity which is measured by the usage of energy per unit of GDP, and the energy conversion efficiency which is measured by the laws of thermodynamics. According to World Energy Council, energy efficiency is defined as ‘‘the ratio between outputs and inputs” [1]. After examining some energy efficiency indicators based on previous studies, Ang [2] gave out an energy efficiency index which is economy-wide and composite by using

⇑ Corresponding author at: School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China E-mail address: [email protected] (Y.-M. Wei). http://dx.doi.org/10.1016/j.apenergy.2016.06.115 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

bottom-up approach. And energy efficiency is widely used in various fields. Mukherjee [3] analyzed the energy use efficiency in US manufacturing industry based on the 1970–2001 data. Wang and Feng [4], analyzed China’s E3 (energy, environmental and economic) efficiency and the sources of E3 productivity growth. Karmellos et al. [5] proposed a multi-objective model for prioritization of energy efficiency measures in buildings. Some studies, such as Sheng et al. [6], considered the imperfect substitution among different energy. When measuring energy efficiency the imperfect substitution among energy and other production factors should be considered, such as capital and labor. And the substitution should be reflected in the physical quantity of the production factors. A lot of attempts have been taken to measure efficiency. The distance function, which was introduced respectively by

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Malmquist [7] and Shephard [8], is an important method in evaluating efficiency. Farrell [9] developed the measurement of productive efficiency based on Debreu [10] and Koopmans [11] work. Färe et al. [12] decomposed the productivity growth into technical change and efficiency change using the Malmquist index which was introduced by Caves et al. [13]. And Johnson and Ruggiero [14] further that decomposition into efficiency, technological and environmental changes. The economic efficiency is the ratio of the optimal (minimal) cost to the real cost. It’s an integrated index in production. The final goal held by producers is to achieve the maximum economic efficiency. Kuosmanen and Post [15], Kuosmanen and Post [16] extended the theory of efficiency measurement, and applied it to the large European Union commercial banks. Rogge and Jaeger [17] analyzed the cost efficiency of municipalities in the collection and processing of the household waste fractions by applying the data which includes 293 municipalities in Flanders, Belgium to a DEA model. Silva and Thanassoulis [18] proposed a new method to compute the cost efficiency based on the DEA framework. According to his model we can decompose the cost efficiency when the producers are not input price takers. The economic efficiency can be decomposed into the allocative efficiency and the technical efficiency. The technical change save inputs for producers on certain level of output; and the producers cost less by reallocating the input factors. That decomposition has been widely used in many fields: Hartman et al. [19] analyzed the bank branches in Sweden, [20] analyzed Spain’s cargo handling firms, and Haelermans and Ruggiero [21] analyzed the Dutch secondary schools. The energy intensity is a most commonly-used indicator in measuring energy efficiency of different countries, regions and sectors. Peter and Henri [22] analyzed the structural change and convergence of energy intensity by calculating the energy efficiency across 18 OECD countries and 50 sectors during 1970–2005. The method itself is quite straightforward but we can get more information by analyzing its details: Kepplinger et al. [23] and Timma et al. [24]. González [25] explored the influence that the changes in sectoral composition in most EU economies have had relying on the decomposition of aggregate energy intensity. Proskuryakova and Kovalev [26] discussed the advantages and disadvantages of the energy intensity in the aspects of physics and economy. And Mi et al. [27] suggested that the intensity target and the amount target should be balanced. The traditional methods in measuring efficiency are well-suited for evaluating energy efficiency, such as the DEA model and the distance function according to Lin and Du [28] and Wang and Wei [29]. But the commonly used energy efficiency indicators may sometimes conflict with the economic efficiency. Few attentions have been paid to energy price, cost constraints, and the imperfect substitution among energy and other production factors apart from physical quantity. And each indicator can no longer hold beyond specific scope of application. Increasing energy productivity does not always lead to improving the economic efficiency. Energy efficiency is not only energy-related but has strong correlations with other production factors. Recently Liao [30] classified energy efficiency indicators into seven groups and pointed out that few of them take economic factors into consideration. To serve this purpose, Liao proposed the energy economic efficiency (ee ), which is a component of the economic efficiency (Ee ). In this paper, we have a further discussion on this theory and the properties of the energy economic efficiency diagrammatically and mathematically, especially the seven properties. We then illuminate the detailed form of this theory by empirically applying it to the electricity generation sectors in 23 IEA countries. And it’s the first application of this theory.

2. Theoretical analysis 2.1. The derivation of energy economic efficiency Suppose there are only two input factors X and Y as shown in Fig. 1, CC 0 is the isoquant, point T represents a possible situation for factor combination, point Q 0 is the optimal point and slope of line AA equals to price ratio of two factors. Based on these assumptions, the technical efficiency Eu , the allocative efficiency (or the price efficiency) Ea , and the economic efficiency Ee are defined as follows:

jORj jOTj jOSj Ea ¼ jORj jOSj Ee ¼ jOTj

Eu ¼

ð1Þ ð2Þ ð3Þ

After some simple deductions, the relationship among them is shown as follow:

Ee ¼ Eu  Ea

ð4Þ

For simplicity, we consider the two factors as factor E (Energy) and factor X (Other factors). We get some new meaningful definitions on the component of factor E (see Fig. 2). Similar to the definitions of the energy allocative efficiency ea , the energy utilize efficiency eu and the energy economic efficiency ee are defined as follows:

jOE2 j jOE1 j jOE1 j eu ¼ jOE0 j jOE2 j ee ¼ jOE0 j

ea ¼

ð5Þ ð6Þ ð7Þ

And the relationship among them is similar:

ee ¼

jOE2 j jOE1 j  ¼ ea  eu jOE1 j jOE0 j

ð8Þ

To evaluate the efficiency consistent with its definition, we use the ratio of the total cost which is the summation of all input factors’ cost (product of price and quantity). So the original mathematic form in calculating of the energy efficiency is as follow:

Ee ¼

P X 2 X 2 þ P E2 E 2 P X 0 X 0 þ P E0 E 0

Fig. 1. Technical efficiency, allocative efficiency and economic efficiency.

ð9Þ

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Each xie ði ¼ 1; 2; . . . ; nÞ is the component of Ee . Ee ¼ 1 means that the allocation and the utilization of each input factor reach the optimal state. That is to say, point P, R, and Q 0 coincide. So that, for each input factor, xie ¼ 1ði ¼ 1; 2; . . . ; nÞ. Property 1.2. Consider the n input factors ðx1 ; x2 ; . . . ; xn Þ. If for all xie ¼ 1ði ¼ 1; 2; . . . ; nÞ , then Ee ¼ 1. Proof:

Fig. 2. Derivation of energy allocative efficiency and energy economic efficiency.

where P is the price of each input factors (see Fig. 2). With the assumption of same price, the total cost at point Q 0 is equal to that of point S . Finally, the definition (9) is equal to the definition (3) based on some mathematic deductions. When considering energy economic efficiency, the energy cost should be used (see Eq. (10)). Given same price for energy, the energy economic efficiency is

jOE2 j , jOE0 j

not

jOE3 j jOE0 j

(like the definition of

the economic efficiency). The reason of the difference in the definition between the allocative efficiency and the energy allocative efficiency is the same.

ee ¼

PE2 E2 jOE2 j ¼ PE0 E0 jOE0 j

ð10Þ

2.2. Some properties related to energy economic efficiency Similarly, we can define the labor economic efficiency, the capital economic efficiency, the intermediate inputs economic efficiency, the service economic efficiency, and so on. The energy economic efficiency put forward in this paper has some obvious advantages. We will further some in-depth discussions on the properties of the energy economic efficiency based on diagrammatical and mathematical methods. Following previous analysis, most properties discussed in the coming part are based on Fig. 3 and the assumptions that two input factors ðX; EÞ. T n ðn ¼ 1; 2; . . . ; 10Þ represent some possible production point, xe represents the other factor economic efficiency and ee represents the energy economic efficiency. Property 1.1. Consider the n input factors ðx1 ; x2 ; . . . ; xn Þ. If Ee ¼ 1, then xie ¼ 1ði ¼ 1; 2; . . . ; nÞ.

Assume that: Oix : the optimal cost of each input factors ði ¼ 1; 2; . . . ; nÞ Rix : the real cost of each input factors ði ¼ 1; 2; . . . ; nÞ Oc : the optimal cost Rc : the real cost We have that:

Oc ¼

n X Oix i¼1

Rc ¼

n X Rix i¼1

Oix xie ¼ ¼ 1 ) Oix ¼ Rix ði ¼ 1; 2; . . . ; nÞ Rix

Pn Oix So, Ee ¼ ORcc ¼ Pi¼1 ¼1 h n R i¼1 ix

Property 2.1. At point Q 0 , ee ¼ 1 and xe ¼ 1. On the radial QT 04 , ee ¼ 1 and xe < 1. Such as T 4 . On the radial Q 0 T 7 , ee < 1 and xe ¼ 1. Such as T 5 and T 7 . In the area of C 0 Q 0 T 4 , ee > 1 and xe < 1. Such as T 1 , T 8 and T 10 . In the area of T 4 Q 0 T 7 , ee < 1 and xe < 1. Such as T 6 and T 9 . In the area of T 7 Q 0 C, ee < 1 and xe > 1. Such as T 3 . Property 2.2. The point T on the line which is parallel to the E axis has the same xe . The point T on the line which is parallel to the X axis has the same ee . Property 3. The line T 7 T 8 is parallel to the line AA0 , so all the points on the line T 7 T 8 has the same total cost, such as T 4 , T 6 , T 7 , T 8 and T 9 . When a point shifts from T 4 to T 7 , the ee and xe shift from ee ¼ 1, xe < 1 to ee < 1, xe ¼ 1 with the same cost. Property 4. For the point whose ee > 1 (the same xe ), the bigger ee is, the closer to the production frontier CC 0 the point is. Such as T 1 , T 8 and T 10 . But bigger ee means bad energy allocation. As for the point whose ee < 1 (the same xe ), the smaller ee is the further away from the frontier. Property 5. In terms of energy, the closer to 1 ee is, the better. Because if ee equals to 1, the optimal production situation Q 0 can be reached by improving the technology of other input factors respectively.

Fig. 3. Discussion of the properties of energy economic efficiency.

Property 6. There is non-existent point whose ee and xe are bigger than 1 at the same time. And except for point Q 0 , there is no point whose ee and xe are equal to 1 at the same time. In other word, if ee > 1, then xe < 1; or if xe > 1, then ee < 1.

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That property can be easily extended to the n kinds of input factors’ situation. And one corollary of that property is that all the input factors’ economic efficiency (xe and ee ) can’t be bigger (or smaller) than the economic efficiency at the same time. Property 7. The ee and xe are influenced by the position of Q 0 significantly, and the position of Q 0 is determined by the price. So the ee and xe are influenced by the price significantly. 2.3. The computational energy economic efficiency model based on mathematical programming

ee ¼

E Pe e Pe E

ð14Þ

We can better simulate real conditions under specific settings through adjustments in objective function and constraint conditions. In reality, one producer faces not only constraints from factors like K, L, E, M and S, but also from technology availability (T). In this sense, an extra constraint (Eq. (15)) should be added to the model (13) which is

 Te 0 þ

n X ki T i 6 0;

TP0

ð15Þ

i¼1

The newly constructed measurement of energy efficiency can depict energy efficiency from the economic perspective, and may contribute to more comprehensive understanding on energy efficiencies. To achieve this object, more input data is needed. It’s necessary to know detailed solving process of economic efficiencies, because that the energy economic efficiency is the energy component of the economic efficiency. Based on some classical economic theories, economic efficiency is measured by the following model:

e0 min P 0 X st: f ðXÞ 6 Y

ð11Þ

In the objective function, tax and subsidies, as well as other policies relevant to factors’ costs are not taken into consideration. The improved objective function Eq. (16) is as follows

e 0 ¼ PK K e 0 þ PL e e 0 þ PS e min P0 X E 0 Þ þ PM M L 0 þ f ðPE ; e S0

ð16Þ

If all variables increase proportionally to kðk > 0Þ times, the results will remain unchanged. That means changing unit of variables will not alter the final results. One thing needs to be pointed out is that E can be decomposed into ðe1; e2; e3; . . .Þ to measure the energy economic efficiency of each component.

where f ðXÞ is the production function. This constraint condition describes the technology limitation. With the idea of DEA model, the general constraint condition can be described as follows:

3. A case study: Application to the efficiency assessment on the electricity generation sectors of IEA countries

e0 min P 0 X 8 n X > > e0 > ki X i 6 X > > > > < i¼1 n st: X > ki Y i P Y > > > > i¼1 > > :e X 0 P 0; ki P 0;

3.1. The data sources

in this model. Y is the output. And the vector P represents the input factors’ price. The constraint condition simulates the isoquant properly; the production frontier is determined by all producers. And the aim is to get the minimal cost of certain producer under the technical and price constraints.

We will comprehend the energy efficiency at the economic level from the model (12). Different from traditional measurements of energy efficiency, we develop the efficiency index with the price data and the intermediate input data. In this paper, we apply this model to the electricity generation sectors. Data are obtained from BP Statistical Review of World Energy [31] and the World Input–Output Database (WIOD) [32]. Due to data availability, we select data for 23 IEA countries during the period 1995–2007. List of 23 countries includes Australia (AUS), Austria (AUT), Belgium (BEL), Canada (CAN), Czech Republic (CZE), Germany (DEU), Denmark (DNK), Spain (ESP), Finland (FIN), France (FRA), United Kingdom (GBR), Greece (GRC), Hungary (HUN), Ireland (IRL), Italy (ITA), Japan (JPN), Korea (KOR), Poland (POL),Netherlands (NLD), Portugal (PRT), Slovak Republic (SVK), Sweden (SWE), Turkey (TUR), United States (USA).

e 0 ¼ PK K e 0 þ PL e e 0 þ PS e S0 L 0 þ PE e E 0 þ PM M min P 0 X

3.2. Data processing

ð12Þ i ¼ 1; 2; . . . ; n

Vector X are input factors. Usually X includes Labor (L), Capital (K), Energy (E), Intermediate Inputs (M) and Service (S). After expanding e 0 is the variable needed to solve the vector X, we can get Eq. (13). X

8 n X > > >  ki Y i 6 Y 0 > > > i¼1 > > > n > X > > e0 þ > ki K i 6 0 > K > > > i¼1 > > > n > X > e > > ki Li 6 0 L0 þ > > > > i¼1 > > < n X st:  e ki Ei 6 0 E0 þ > > i¼1 > > > n > X > > e0þ > M ki M i 6 0 > > > > i¼1 > > > n X > > > > e ki Si 6 0 S0 þ > > > i¼1 > > > > e ;e e 0; e > K L ;e E ;M S 0 ; ki P 0 > > : 0 0 0 i ¼ 1; 2; . . . ; n

According to Eq. (13), our input factors cover K, L, E, M and S. Data of quantity and shadow price are required for further analysis. We drop factors M and S for its small quantity in electricity generation sector. As a result, our inputs include K, L and E. And our model can be described as Eq. (17).

e 0 ¼ PK K e 0 þ PL e min P0 X L 0 þ PE e E0 ð13Þ

e 0 and P 0 X 0 . So the ee is the result on the The Ee is the ratio of P 0 X component E (see Eq. (14)).

8 X n > >  ki Y i 6 Y 0 > > > > i¼1 > > > n > X > > e0 þ > ki K i 6 0 > K > > > i¼1 > > < n X st: e L0 þ ki Li 6 0 > > i¼1 > > > n > X > > > ki Ei 6 0 E0 þ > e > > > i¼1 > > > > e ;e > L ;e E ;k P 0 K > : 0 0 0 i i ¼ 1; 2; . . . ; n

ð17Þ

H. Liao et al. / Applied Energy 179 (2016) 479–487

We use the electricity generation sector’s GFCF1995 (real fixed capital stock, 1995 price) and the electricity generation sector’s GFCF_P (price levels of gross fixed capital formation, 1995 = 100) to compute the real fixed capital stock for each year as the K’s quantity of the electricity generation sector. Similarly we obtain the total sectors’ real fixed capital stock. We then compute K’s shadow price as the total sectors’ CAP (capital compensation) divided by the total sectors’ real fixed capital stock. We use the electricity generation sector’s H_EMP (total hours worked by persons engaged) as L’s quantity of the electricity generation sector. We compute L’s shadow price as the total sectors’ LAB (labor compensation) divided by the total sectors’ H_EMP. As for the Energy, we use the electricity generation sector’s energy use as E’s quantity. And we compute the E’s shadow price as electricity generation sector’s II (intermediate inputs) divided by the E’s quantity. All values in WIOD are expressed in local national currency. We use the exchange rate to conform them to US dollars. Table 1 The data of the electricity generation and the input factors (2007). COUN.

AUS AUT BEL CAN CZE DEU DNK ESP FIN FRA GBR GRC HUN IRL ITA JPN KOR NLD PRT SVK SWE TUR USA

Electricity generation (TWH)

Capital Q (HM)

P

Q (M)

Labor P

Q (PJ)

Energy P

251 64 89 620 88 637 39 312 81 570 397 63 40 28 314 1180 425 105 47 28 156 192 4365

887 459 404 1856 336 3165 402 1494 310 2092 1264 372 214 400 2676 6642 2134 662 280 216 126 849 718

92 60 43 53 69 72 63 45 53 50 50 51 39 70 50 87 30 55 51 98 2609 26 53

185 51 42 182 106 420 23 138 25 239 192 49 125 26 213 809 215 48 42 59 21 58 187

28 32 42 26 9 33 41 23 32 38 36 16 9 33 27 21 13 38 14 7 1408 6 162

2663 355 881 3982 1054 6401 400 2372 727 5864 3418 601 490 223 2652 9432 4094 847 310 333 1251 1466 41,385

7 70 10 3 9 15 14 22 6 12 32 7 17 22 29 14 9 40 46 23 6 14 4

Notes: Q represents quantity, and P represents price. The quantity of capital and labor is measured by the US dollar; M represents million, and HM represents hundred million. 1 PJ = 1015 J. The price is calculated as the value divided by the quantity.

483

At last, output Y in electricity generation is obtained from the [31] Workbook in terawatt-hours. After processing the data, we obtain a series of panel data which include 23 IEA countries’ electricity generation sectors data over the period 1995–2007. Table 1 shows the processed data for 2007. And all the processed data can be found and downloaded online. 3.3. The results We build the world’s production frontier in electricity generation sector for each year under all constraints in the models. We calculate each country’s Ee and ee of the electricity generation sectors for each year. It requires to solve the Eq. (13) for 23 ⁄ 13 times. And the source code can be found and downloaded online. All the results can be found in the two Tables A1 and A2. Appendix Table A1 is the computed energy economic efficiency, while appendix Table A2 is the computed economic efficiency. The capital economic efficiency (appendix Table A3) and the labor economic efficiency (appendix Table A4) are listed as the byproducts. Based on the previous theoretical analysis, the energy economic efficiency is an economic index to measure energy efficiency. The approximate position of one specific producer can be speculated based on its energy economic efficiency (ee ) and other input factors economic efficiency (xe ) according to the property 2. That provides some information to estimate the utilize efficiency and allocative efficiency. 3.4. Discussions The process of building that model above implies that the energy economic efficiency, which does not have the transitive property, has been influenced significantly by the relative situation of technology and the market. We find that only America’s efficiency (both Ee and ee ) is always 1 over the period 1995–2007. On the one hand, America’s technology of electricity generation is in the lead of the world, on the other hand the price of K, L and E is more market-oriented under the America’s open economy. All these contribute to America’s leading stance on the world’s production frontier in electricity generation sectors. The energy economic efficiency is an indicator calculated with each country’s given price which reflects the market situation to some degree. The interesting thing is that ee is bigger than 1 for some data which means producer can cost less while using more energy even though energy cost is increasing. For example, Canada’s energy economic efficiency is always at a high level (ee > 1). It suggests Canada needs to use more energy instead of labor or capital to

Fig. 4. Economic efficiency (Ee ), energy economic efficiency (ee ) and output per energy use in 2007. Notes: We set the USA’s output per energy use as 1.

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achieve the optimal economic. Conversely, if ee is smaller than 1, producer should use less energy to minimize the total cost. In this situation, there are two possibilities. One is that the energy was not used at its maximum potential, and the other one is that the price of energy is too high. The only efficient production point appears when ee is equal to value 1. Though containing some DEA’s ideas when building this model, the results are quite different. The calculated efficiencies can be well interpreted not only when being compared with the effective unit, but also the different values of the efficiency. Just as in Fig. 5, the closer to the unit circle, the better. Fig. 4 shows all the countries’ Ee , ee and output per energy use in 2007. The economic efficiency and the energy economic efficiency are not always consistent with the output per energy use indicator. It supports that the traditional energy efficiency indicator is in conflict with the efficiency in economics. In usual sense, it’s impossible to change a lot for each input factor and the technology in a short term which means efficiency will

Fig. 5. Energy economic efficiency (ee ) in 1995–2007.

not fluctuate drastically. Exceptional circumstances can be caused by huge variation in labor, capital and energy in unstable market. Fig. 5 shows some countries’ ee changes from 1995 to 2007. Fig. 6 shows the points whose ee is smaller than 1. All the points are above the 45-degree line. That indicates the energy is overused compared with the other input factors. And there is not enough evidence to prove that there is a positive correlation between Ee and ee . The energy economic efficiency is just the ratio of the energy cost under the highest economic efficiency’s situation. It reflects how market mechanism works when allocating all factors of inputs among economic agents and managing or planning energy utilization in internal enterprises or regions. 4. Conclusions The prevalent work on energy efficiency is just from the unidirectional view of energy. In this way, we can easily get the local optimum solution which achieves lower energy intensity. However local optimum solution is quite different from global optimum solution, sometimes they are contradictory solutions. The producers’ aim is to maximize the profit or minimize the cost which requires us to improve the production according to the global optimum solution (economic effective). That aim requires the producers to properly allocate production factors at given price. Fig. 4 is a good example; sometimes high output per energy use does not mean high economic efficiency. In order to get the minimum cost, increasing the cost of energy instead of labor and capital is needed in some situation. Because we cannot achieve least total cost only through increasing output per energy use. The energy economic efficiency is a method to solve this problem. We use the production frontier to simulate the technology constraints. But the objective function is an economic objective, which minimize the total cost considering the price and the physical quantity of each production factor. It gives out a specific ways to improve the production by adjusting each input factor based on its relative price. In this paper, we explain the energy economic efficiency theory, and take some derivations in detail. After that we find some basic properties. After carefully processing the parameters, functions and data, we apply it to the electricity generation sectors of some IEA countries. And it’s the first application of this theory. According to the results, we discuss some features of the energy economic efficiency which is more reasonable compared with traditional energy efficiency indicators. It reflects how market mechanism works when allocating all factors of inputs among economic agents and managing or planning energy utilization in internal enterprises or regions. It also provides us with an operable way to improve our energy efficiency from the economic perspective. We have shown some basic properties of the energy economic efficiency while other features remains further exploration, such as the relationship among each input factor’s economic efficiency, and the comparison of ee in different side of value 1. Acknowledgements

Fig. 6. Relationship between economic efficiency (Ee ) and energy economic efficiency (ee ).

We sincerely thank the financial supports from the National Key R&D Program (2016YFA0602603, 2016YFA0602801), ‘‘Strategic Priority Research Program” of the Chinese Academy of Sciences (No. XDA05150600), National Natural Science Foundation of China (No. 71521002, 71322306 and 71273027), Fok Ying Tung Education Foundation. We appreciate the constructive comments from the reviewers and editor. The views expressed in this paper are solely authors’ own and do not necessarily reflect the views of the supporting agencies and author affiliations. The authors alone are responsible for any remaining deficiencies. And we express our gratitude to Dr. Wang Ke (CEEP-BIT), Mr. Li Musen (SHU),

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Ms. Chen Tianqi (BJFU) and Ms. Cai Jiawei (CEEP-BIT) for their specific advice of this paper. We also would like to thank the anonymous referees for their helpful suggestions and corrections on the earlier draft of our paper according to which we improved the content.

Appendix A See Tables A1–A4.

Table A1 Energy economic efficiency (ee ). COUN.

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

AUS AUT BEL CAN CZE DEU DNK ESP FIN FRA GBR GRC HUN IRL ITA JPN KOR NLD PRT SVK SWE TUR USA

0.98 1.94 0.93 1.49 0.68 0.87 0.85 1.11 1.12 0.96 0.96 0.88 0.72 0.99 1.23 1.09 1.07 1.06 1.20 0.70 1.12 0.66 1.00

0.97 1.77 0.92 1.51 0.69 0.87 0.91 1.20 1.09 0.94 0.95 0.96 0.73 0.99 1.26 1.09 1.05 1.07 1.38 0.69 1.01 0.82 1.00

1.00 1.82 0.91 1.52 0.70 0.89 0.90 1.18 1.09 0.94 0.95 0.98 0.69 0.98 1.31 1.10 1.03 1.10 1.36 0.67 1.12 0.82 1.00

0.94 1.83 0.93 1.49 0.70 0.89 0.89 1.17 1.16 0.93 0.96 1.00 0.69 0.97 1.32 1.09 1.03 1.08 1.31 0.68 1.07 0.84 1.00

0.92 1.58 0.93 1.51 0.72 0.89 0.91 1.15 1.13 0.95 0.99 1.00 0.69 0.97 1.36 1.10 1.02 0.93 1.24 0.72 1.16 0.81 1.00

1.00 1.51 0.98 1.58 0.82 0.96 0.97 1.19 1.20 0.99 0.81 1.01 0.74 1.10 0.86 1.17 0.98 0.88 1.05 0.79 1.32 0.99 1.00

0.96 1.51 0.99 1.55 0.81 0.94 0.96 1.26 1.16 1.00 0.84 1.00 0.75 1.09 0.94 1.18 1.00 0.90 1.13 0.81 1.26 1.02 1.00

0.88 1.59 0.96 1.54 0.78 0.92 0.96 1.15 1.11 0.95 1.06 0.99 0.75 1.05 1.12 1.16 1.02 0.93 1.29 0.81 1.18 0.88 1.00

0.90 1.55 0.95 1.51 0.76 0.94 0.98 1.23 1.03 0.93 1.05 1.00 0.71 1.10 1.14 1.23 1.01 1.09 1.43 0.75 1.13 0.95 1.00

0.90 1.52 0.94 1.48 0.76 0.95 0.97 1.22 1.08 0.93 1.07 0.99 0.71 1.13 1.11 1.20 0.96 0.97 1.34 0.78 1.14 1.28 1.00

0.90 1.33 0.95 1.52 0.80 0.94 0.94 1.04 1.07 0.92 0.89 0.99 0.60 1.13 0.94 1.20 0.96 0.93 1.06 0.79 1.21 1.14 1.00

0.86 1.44 0.94 1.47 0.80 0.94 0.97 1.24 1.01 0.92 0.92 1.02 0.74 1.13 0.94 1.21 0.94 0.99 1.20 0.80 1.16 1.14 1.00

0.89 1.44 0.96 1.48 0.79 0.94 0.93 1.06 1.06 0.92 0.93 1.00 0.77 1.20 0.95 1.19 0.99 1.00 1.23 0.79 1.18 1.05 1.00

Table A2 Economic efficiency (Ee ). COUN.

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

AUS AUT BEL CAN CZE DEU DNK ESP FIN FRA GBR GRC HUN IRL ITA JPN KOR NLD PRT SVK SWE TUR USA

0.24 0.56 0.26 0.11 0.14 0.21 0.11 0.34 0.23 0.40 0.45 0.08 0.17 0.10 0.28 0.24 0.33 0.38 0.56 0.22 0.15 0.74 1.00

0.24 0.51 0.27 0.11 0.21 0.20 0.14 0.37 0.26 0.40 0.43 0.09 0.19 0.10 0.29 0.22 0.38 0.39 0.62 0.21 0.15 0.72 1.00

0.26 0.51 0.26 0.12 0.21 0.20 0.13 0.38 0.25 0.39 0.44 0.10 0.20 0.10 0.33 0.22 0.36 0.41 0.59 0.20 0.18 0.70 1.00

0.27 0.49 0.27 0.14 0.21 0.21 0.13 0.37 0.25 0.40 0.45 0.11 0.22 0.10 0.30 0.20 0.35 0.40 0.60 0.18 0.20 0.68 1.00

0.26 0.46 0.27 0.15 0.21 0.21 0.12 0.37 0.24 0.25 0.48 0.12 0.21 0.08 0.32 0.19 0.30 0.39 0.57 0.18 0.20 0.69 1.00

0.29 0.46 0.27 0.19 0.25 0.23 0.13 0.42 0.26 0.29 0.50 0.13 0.25 0.10 0.31 0.20 0.31 0.40 0.61 0.22 0.22 0.70 1.00

0.27 0.50 0.31 0.19 0.24 0.24 0.15 0.46 0.25 0.30 0.51 0.13 0.25 0.12 0.33 0.20 0.34 0.43 0.66 0.24 0.23 0.69 1.00

0.26 0.55 0.31 0.19 0.25 0.24 0.15 0.42 0.25 0.29 0.54 0.15 0.27 0.11 0.33 0.18 0.32 0.45 0.61 0.27 0.20 0.72 1.00

0.24 0.64 0.26 0.19 0.25 0.25 0.17 0.45 0.26 0.30 0.55 0.16 0.28 0.11 0.35 0.19 0.33 0.49 0.64 0.26 0.19 0.75 1.00

0.23 0.62 0.27 0.19 0.26 0.26 0.17 0.45 0.25 0.31 0.61 0.15 0.31 0.10 0.34 0.19 0.32 0.48 0.60 0.25 0.21 0.71 1.00

0.23 0.59 0.31 0.20 0.23 0.26 0.15 0.52 0.25 0.35 0.66 0.18 0.32 0.16 0.37 0.19 0.35 0.48 0.61 0.25 0.23 0.65 1.00

0.21 0.71 0.32 0.19 0.25 0.28 0.19 0.55 0.26 0.39 0.70 0.19 0.34 0.23 0.40 0.21 0.36 0.52 0.67 0.25 0.23 0.63 1.00

0.20 0.73 0.32 0.20 0.26 0.29 0.18 0.55 0.25 0.38 0.67 0.21 0.38 0.19 0.40 0.24 0.37 0.54 0.67 0.23 0.23 0.61 1.00

Table A3 Capital economic efficiency (ke ). COUN.

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

AUS AUT BEL CAN CZE DEU

0.04 0.01 0.02 0.04 0.03 0.02

0.04 0.01 0.03 0.04 0.03 0.02

0.04 0.02 0.03 0.05 0.03 0.02

0.05 0.02 0.03 0.05 0.03 0.02

0.05 0.09 0.03 0.05 0.03 0.02

0.05 0.10 0.03 0.05 0.04 0.03

0.05 0.09 0.03 0.05 0.03 0.03

0.05 0.10 0.03 0.05 0.03 0.02

0.05 0.10 0.03 0.05 0.03 0.02

0.05 0.10 0.03 0.05 0.04 0.03

0.05 0.09 0.04 0.05 0.04 0.03

0.05 0.11 0.04 0.05 0.04 0.03

0.05 0.11 0.04 0.05 0.04 0.03

(continued on next page)

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H. Liao et al. / Applied Energy 179 (2016) 479–487

Table A3 (continued) COUN.

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

DNK ESP FIN FRA GBR GRC HUN IRL ITA JPN KOR NLD PRT SVK SWE TUR USA

0.01 0.03 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.02 0.01 0.04 0.06 0.14 1.14 1.00

0.02 0.03 0.03 0.03 0.03 0.02 0.02 0.01 0.01 0.02 0.02 0.01 0.04 0.05 0.14 0.36 1.00

0.02 0.03 0.04 0.03 0.03 0.02 0.03 0.01 0.01 0.02 0.03 0.02 0.04 0.04 0.17 0.42 1.00

0.01 0.03 0.04 0.03 0.03 0.02 0.03 0.01 0.02 0.02 0.03 0.02 0.05 0.04 0.18 0.43 1.00

0.01 0.03 0.04 0.03 0.03 0.02 0.03 0.01 0.02 0.02 0.03 0.09 0.05 0.04 0.19 0.45 1.00

0.01 0.04 0.04 0.04 0.19 0.03 0.03 0.02 0.09 0.02 0.03 0.10 0.24 0.04 0.20 0.13 1.00

0.01 0.04 0.04 0.04 0.18 0.02 0.03 0.01 0.08 0.01 0.03 0.09 0.23 0.04 0.20 0.12 1.00

0.01 0.03 0.04 0.04 0.04 0.02 0.02 0.01 0.02 0.02 0.03 0.11 0.04 0.04 0.18 0.48 1.00

0.02 0.03 0.04 0.03 0.04 0.02 0.02 0.01 0.02 0.02 0.03 0.02 0.04 0.03 0.16 0.51 1.00

0.02 0.03 0.04 0.04 0.05 0.02 0.02 0.01 0.02 0.02 0.03 0.12 0.03 0.03 0.19 0.15 1.00

0.01 0.17 0.04 0.04 0.27 0.03 0.12 0.01 0.09 0.02 0.03 0.11 0.17 0.03 0.21 0.15 1.00

0.02 0.17 0.04 0.04 0.25 0.03 0.03 0.01 0.10 0.03 0.03 0.13 0.14 0.02 0.20 0.18 1.00

0.02 0.04 0.04 0.05 0.29 0.03 0.03 0.01 0.10 0.03 0.03 0.12 0.18 0.03 0.20 0.18 1.00

Table A4 Labor economic efficiency (le ). COUN.

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

AUS AUT BEL CAN CZE DEU DNK ESP FIN FRA GBR GRC HUN IRL ITA JPN KOR NLD PRT SVK SWE TUR USA

0.08 0.06 0.11 0.21 0.03 0.06 0.09 0.09 0.13 0.12 0.09 0.04 0.01 0.05 0.06 0.08 0.08 0.08 0.04 0.02 0.42 1.70 1.00

0.07 0.04 0.08 0.16 0.02 0.05 0.10 0.07 0.11 0.09 0.07 0.03 0.01 0.04 0.05 0.06 0.06 0.07 0.03 0.02 0.30 0.55 1.00

0.10 0.06 0.11 0.21 0.03 0.07 0.10 0.10 0.14 0.12 0.09 0.04 0.01 0.05 0.06 0.08 0.08 0.09 0.04 0.02 0.43 0.56 1.00

0.09 0.06 0.11 0.19 0.02 0.06 0.09 0.09 0.14 0.11 0.09 0.04 0.01 0.05 0.06 0.07 0.09 0.09 0.04 0.02 0.42 0.63 1.00

0.08 0.14 0.09 0.17 0.02 0.05 0.07 0.08 0.11 0.10 0.08 0.03 0.01 0.04 0.05 0.06 0.08 0.21 0.04 0.02 0.36 0.62 1.00

0.07 0.15 0.08 0.16 0.02 0.06 0.06 0.08 0.11 0.10 0.25 0.04 0.01 0.04 0.16 0.06 0.08 0.23 0.12 0.02 0.32 0.33 1.00

0.08 0.14 0.09 0.16 0.03 0.06 0.08 0.09 0.13 0.10 0.22 0.04 0.01 0.04 0.16 0.06 0.10 0.22 0.13 0.02 0.38 0.31 1.00

0.08 0.16 0.10 0.18 0.03 0.07 0.09 0.10 0.14 0.11 0.09 0.05 0.01 0.05 0.06 0.06 0.13 0.25 0.05 0.02 0.36 0.74 1.00

0.07 0.17 0.10 0.15 0.03 0.07 0.10 0.10 0.16 0.11 0.10 0.05 0.01 0.04 0.07 0.06 0.09 0.09 0.05 0.02 0.32 0.83 1.00

0.06 0.16 0.08 0.11 0.03 0.05 0.07 0.08 0.13 0.09 0.08 0.04 0.01 0.03 0.05 0.05 0.08 0.27 0.04 0.02 0.29 0.35 1.00

0.05 0.15 0.08 0.11 0.03 0.05 0.06 0.28 0.10 0.09 0.30 0.04 0.03 0.04 0.18 0.05 0.09 0.26 0.15 0.02 0.29 0.37 1.00

0.06 0.17 0.09 0.15 0.04 0.07 0.07 0.31 0.14 0.10 0.28 0.06 0.01 0.05 0.20 0.06 0.08 0.29 0.15 0.02 0.32 0.45 1.00

0.06 0.18 0.08 0.12 0.03 0.06 0.08 0.09 0.13 0.10 0.31 0.04 0.01 0.04 0.20 0.06 0.09 0.29 0.16 0.02 0.29 0.43 1.00

Appendix B. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apenergy.2016. 06.115.

References [1] WEC. Energy efficiencies policies and indicators. London: World Energy Council; 2006. [2] Ang BW. Monitoring changes in economy-wide energy efficiency: from energy–GDP ratio to composite efficiency index. Energy Policy 2006;34 (5):574–82. [3] Mukherjee K. Energy use efficiency in US manufacturing: a nonparametric analysis. Energy Econ 2008;30(1):76–96. [4] Wang ZH, Feng C. A performance evaluation of the energy, environmental, and economic efficiency and productivity in China: an application of global data envelopment analysis. Appl Energy 2015;147:617–26. [5] Karmellos M, Kiprakis A, Mavrotas G. A multi-objective approach for optimal prioritization of energy efficiency measures in buildings: model, software and case studies. Appl Energy 2015;139:131–50. [6] Sheng Y, Wu YR, Shi XP, Zhang DD. Energy trade efficiency and its determinants: a Malmquist index approach. Energy Econ 2015;50:306–14. [7] Malmquist S. Index numbers and indifference surfaces. Trabajos de Estatistica 1953;4(2):209–42.

[8] Shephard RW. Cost and production functions. Princeton, New Jersey: Princeton University Press; 1953. [9] Farrell MJ. The measurement of productive efficiency. J R Statist Soc Ser A CXX 1957:253–90. Part3. [10] Debreu G. The coefficient of resource utilisation. Econometrics 1951;19 (3):273–92. [11] Koopmans TC. An analysis of production as an efficient combination of activities. In: Koopmans TC, editor. Activity analysis of production and allocation, cowles commission for research in economics, monograph, vol. 13. New York: Wiley; 1951. [12] Färe R, Grosskopf S, Norris M, Zhang ZY. Productivity growth, technical progress and efficiency changes in industrialised countries. Am Econ Rev 1994;84(1):66–83. [13] Caves DW, Christensen LR, Diewert WE. Multilateral comparisons of output, input, and productivity using superlative index numbers. Econ J 1982;92 (365):73–86. [14] Johnson AL, Ruggiero J. Nonparametric measurement of productivity and efficiency in education. Ann Oper Res 2014;221(1):197–210. [15] Kuosmanen T, Post T. Measuring economic efficiency with incomplete price information: with an application to European commercial banks. Eur J Oper Res 2001;134(1):43–58. [16] Kuosmanen T, Post T. Measuring economic efficiency with incomplete price information. Eur J Oper Res 2003;144(2):454–7. [17] Rogge N, Jaeger DS. Measuring and explaining the cost efficiency of municipal solid waste collection and processing services. Omega-Int J Manage Sci 2013;41(4):653–64. [18] Silva Portela MCA, Thanassoulis E. Economic efficiency when prices are not fixed: disentangling quantity and price efficiency. Omega-Int J Manage Sci 2014;47:36–44.

H. Liao et al. / Applied Energy 179 (2016) 479–487 [19] Hartman TE, Storbeck JE, Byrnes P. Allocative efficiency in branch banking. Eur J Oper Res 2001;134(2):232–42. [20] Rodriguez-Alvarez A, Tovar B, Trujillo L. Firm and time varying technical and allocative efficiency: an application to port cargo handling firms. Int J Prod Econ 2007;109(1–2):149–61. [21] Haelermans C, Ruggiero J. Estimating technical and allocative efficiency in the public sector: a nonparametric analysis of Dutch schools. Eur J Oper Res 2013;227(1):174–81. [22] Peter M, Henri LFdeG. Structural change and convergence of energy intensity across OECD countries, 1970–2005. Energy Econ 2012;34(6): 1910–21. [23] Kepplinger D, Templ M, Upadhyaya S. Analysis of energy intensity in manufacturing industry using mixed-effects models. Energy 2013;59 (15):754–63. [24] Timma L, Zoss T, Blumberga D. Life after the financial crisis. Energy intensity and energy use decomposition on sectorial level in Latvia. Appl Energy 2016;162:1586–92.

487

[25] González PF. Exploring energy efficiency in several European countries. An attribution analysis of the Divisia structural change index. Appl Energy 2015;137:364–74. [26] Proskuryakova L, Kovalev A. Measuring energy efficiency: is energy intensity a good evidence base? Appl Energy 2015;138:450–9. [27] Mi ZF, Pan SY, Yu H, Wei YM. Potential impacts of industrial structure on energy consumption and CO2 emission: a case study of Beijing. J Cleaner Prod 2015;103:455–62. [28] Lin BQ, Du KR. Technology gap and China’s regional energy efficiency: a parametric metafrontier approach. Energy Econ 2013;40:529–36. [29] Wang K, Wei YM. China’s regional industrial energy efficiency and carbon emissions abatement costs. Appl Energy 2014;130:617–31. [30] Liao H. Econometric modeling on energy efficiency and its applications Ph.D dissertation. Beijing: Chinese Academy of Sciences; 2008. [31] BP. Statistical Review of World Energy 2013. London: BP; 2013. [32] Timmer MP. The World Input-Output Database (WIOD): Contents, sources and methods. WIOD Working Paper Number 10; 2012.