ARTICLE IN PRESS
Socio-Economic Planning Sciences 41 (2007) 91–106 www.elsevier.com/locate/seps
Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons$ Kaoru Tonea,, Miki Tsutsuia,b a
National Graduate Institute for Policy Studies, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8677, Japan Central Research Institute of Electric Power Industry, 1-6-1 Ohtemachi, Chiyoda-ku, Tokyo 100-8126, Japan
b
Available online 5 December 2005
Abstract This paper presents a new formula for decomposing cost efficiency into technical, price, and allocative efficiencies in an environment marked by the fact that unit input prices differ among certain enterprises. We employed this formula in comparing cost efficiency between Japanese and US electric power companies, and found a significant difference in the price-based efficiency. However, negligible differences were found in the technical and allocative efficiencies. r 2005 Elsevier Ltd. All rights reserved. Keywords: Cost efficiency; Technical efficiency; Price efficiency; Allocative efficiency; DEA
1. Introduction Technology and cost are the wheels that drive modern enterprise; some enterprises have advantages in terms of technology while others have it in cost. Hence, management is eager to know how and to what extent their resources are being effectively and efficiently utilized, compared to other enterprises in the same, or similar, field. Under multiple input–output correspondences, data envelopment analysis (DEA) has created a new route map for this purpose. Given the quantities of input resources and output products, the representative DEA models, e.g., CCR [1], BCC [2], and SBM [3], can evaluate the relative technical efficiency of a given enterprise, termed DMU (decision-making unit) in DEA terminology. Furthermore, if the unit prices of the input resources are known, the cost efficiency model can be utilized to explore the optimal input-mix that produces the observed outputs at minimum cost. Based on this solution, the cost and allocative efficiencies are obtained. For example, see Farrell [4] and Fa¨re et al. [5]. However, these traditional cost and allocative efficiencies, which assume given uniform input prices, suffer from a critical shortcoming if the unit prices of the inputs are not identical across DMUs in the economy, as pointed out by Tone [6]. To cite a case, if two DMUs have the same inputs and outputs and the unit price for one DMU is twice that of the other, then the traditional cost efficiency model assigns the same cost efficiency $
Research supported by Grant-in-Aid for Scientific Research (C), Japan Society for Promotion of Science.
Corresponding author.
E-mail addresses:
[email protected] (K. Tone),
[email protected] (M. Tsutsui). 0038-0121/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2005.10.007
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to both. This is, however, unacceptable in analyzing an actual economic situation. After identifying this shortcoming, Tone [6] proposed a new scheme that is free from such inconsistencies. The current paper can be positioned as an extension of Tone [6], as seek to decompose observed total cost into the global optimal (minimum) cost and loss due to input inefficiency, as follows: Actual cost ¼ Minimum cost þ Loss due to input inefficiency: Furthermore, we represent this loss due to input inefficiency as dependent on technical inefficiency, input price differences, and inefficient cost mix as follows: Loss due to input inefficiency ¼ Loss due to technical inefficiency þ Loss due to input price difference þ Loss due to inefficient cost mix: Among these components, technical efficiency is measured using the traditional CCR model [1] within the technical production possibility set. Then, using the thus obtained optimal input value, we construct a costbased production possibility set and solve the New Tech and New Cost models [6] on that set. This enables us to obtain two efficiency indices, i.e., the price efficiency index and the global allocative efficiency index. The former reflects the differences in input unit prices, while the latter evaluates the efficiency of the input cost mix, which we rate is not the same as allocative efficiency. The remainder of the paper unfolds as follows. In Section 2, we develop our methodology, while in Section 3 we apply the scheme to electric power industries in Japan and the US and compare the efficiencies of their performance from 1992 to 1999. It is often considered that the price of electricity in Japan is higher than that in other countries; this may be due to productive inefficiency or higher input prices. Indeed, prior studies indicated that the productive efficiency of Japanese electric power companies was higher than that of their US counterparts.1 It has also been mentioned that input prices in Japan are higher than those in the US. However, there exist few studies that have comprehensively examined the influence of productive inefficiency and higher input prices over the total cost. This study will analyze and demonstrate the degree of loss caused by (1) technical inefficiency, (2) input price differences, and (3) suboptimal cost mixes between Japanese and US electric power companies. In Section 4, we develop some extensions of this model, and summarize the results, and conclude the paper, in the final section. 2. Methodology In this section, we develop our scheme and discuss its rationale. 2.1. Data Throughout this paper, we consider n DMUs, each having m inputs for producing s outputs. For each DMUo ðo ¼ 1; . . . ; nÞ; we denote the input and output vectors by xo 2 Rm and yo 2 Rs , respectively. The input and output matrices are defined as X ¼ ðx1 ; . . . ; xn Þ 2 Rmn and Y ¼ ðy1 ; . . . ; yn Þ 2 Rsn , respectively. We assume that X40 and Y40. For each DMUo ðo ¼ 1; . . . ; nÞ; the input factor price vector for input xo is denoted by wo 2 Rm ; and the input factor price matrix is defined as W ¼ ðw1 ; . . . ; wn Þ 2 Rmn . For DMUo, the actual total input cost Co is calculated as follows: Co ¼
m X
wio xio ,
(1)
i¼1
where xio is the amount of the ith input utilized by DMUo, and wio is the input factor price. We assume that the elements w1o x1o ; . . . ; wmo xmo are denominated in homogenous units, viz., dollars, in order that the summation is measurable. 1
See Goto and Tsutsui [7] and Hattori [8].
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2.2. Technical efficiency The production possibility set P is defined as P ¼ fðx; yÞjxXX l; ypY l; lX0g.
(2)
The technical efficiency y of DMUo is measured using the traditional input-oriented CCR model: ½CCR y ¼ min y, y;l;s ;sþ
subject to yxo ¼ X l þ s ; yo ¼ Y l s þ ;
(3) þ
lX0; s X0; s X0: Let ðy ; l ; s ; sþ Þ be an optimal solution for [CCR]. In solving, we employ the usual two-phase approach. * First, Ps y þby solving [CCR], and then, fixing y at y , we maximize the objective function2 Pm we obtain i¼1 si =xio þ r¼1 sr =yro subject to the [CCR] constraint. Projection to the efficient frontier is then given by ½CCR projection xo ¼ y xo s ;
yo ¼ yo þ sþ ,
(4)
where xo indicates the vector of technically efficient inputs for DMUo for producing yo in that (xo,yo) is projected into the point ðxo ; yo Þ on the strongly efficient portion of the production possibility set P. The corresponding technically efficient total input cost for DMUo is calculated as C o ¼
m X
wio xio ¼
i¼1
m X
wio ðy xio s i Þpy
i¼1
m X
wio xio ¼ y C o pC o .
(5)
i¼1
The loss in input cost due to this technical inefficiency is expressed as follows: Lo ¼ C o C o ðX0Þ.
(6)
2.3. Price efficiency ðxo ; yo Þ is the production pair in the production possibility set P, and its input cost wo xo cannot be reduced further by radially reducing the input xo . However, taking into account the differences in input prices under the situation that the unit prices might differ from DMU to DMU, the cost can be reduced by reducing the input factor prices. Traditional cost (price) efficiency models, e.g. Fa¨re et al. [9], are based on the common (or average) unit-price assumption. This assumption causes irrational price-efficiency measure as pointed out by Tone [6]. Hence, in order to avoid such an issue, we view the cost-based production possibility set Pc as follows: Pc ¼ fðx; ¯ yÞjxX ¯ X¯ m; ypY m; mX0g,
(7)
where X¯ ¼ ðx¯ 1 ; . . . ; x¯ n Þ 2 Rmn and x¯ o ¼ ðx¯ 1o ; . . . ; x¯ mo Þ with xio ¼ wio xio ði ¼ 1; . . . ; mÞ: It should be noted that xo represents the vector of technically efficient inputs for producing yo. Hence, we utilize wio xio instead of wio xio in order to eliminate the technical inefficiency to the maximum extent possible. Then, we solve the CCR model on Pc in a similar manner as that of [NTec] in Tone [6] to obtain ½New Tech r ¼ min r, r;m;t ;tþ
2
When we do not employ slacks (s, s+) in the CCR-projection, we cannot evaluate the excess inefficient input for a part of the input factors. In this paper, we thus employ the CCR-projection including slacks in order to accurately identify the factor-oriented inefficiency.
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subject to
rx¯ o ¼ X m þ t ; yo ¼ Y m t þ ;
mX0; t X0;
(8) and
þ
t X0:
Let ðr ; m ; t ; tþ Þ be an optimal solution for [New Tech]. In solving [New Tech], we also employ the usual two-phase approach as in solving [CCR]. Then, r x¯ o ¼ ðr w1o x1o ; . . . ; r wmo xmo Þ indicates the radially reduced input vector on the (weakly) efficient frontier of the cost-based production set Pc . Hence, r wo ¼ ðr w1o ; . . . ; r wmo Þ, assuming wo ¼ r wo is the radially reduced input factor price vector for the technically efficient input xo that can produce yo , however, these prices need not be available to the DMU. In traditional economic theory, it is assumed that, under perfect competition, the input factor price is determined to be a single market price, and this is treated as a given condition. However, the actual market does not necessarily function under perfect competition and differences in input factor prices are not uncommon. In comparison, higher factor prices have an impact on the total costs of DMUs as well as their productive inefficiencies. We therefore focus on the level of input factor prices, and use r to indicate the radial difference in the observed input price vs. the minimum input price in the same cost mix. In this study, the input price difference is labeled as price efficiency.3 The [New Tech] projection is given by ½NewTech projection x¯ o ¼ r x¯ o t ;
yo ¼ yo þ tþ .
C o ,
We define the radial efficient cost which is the technical and price efficient cost, and the loss the difference of the input price as follows: C o ¼
m X
x¯ io ¼
i¼1
m X
ðr x¯ io t i Þpr
i¼1
m X
x¯ io ¼ r C o pC o ,
(9) L o
due to
(10)
i¼1
L o ¼ C o C o ðX0Þ.
(11)
As the ratio of C o vs: C o ; we define price efficiency of DMUo as Price efficiency ¼
C o ðp1Þ. C o
(12)
Here we compare our price (cost) efficiency with the traditional cost efficiency ðg Þ which is defined by g ¼
wo x , wo xo
(13)
where x is a vector obtained as the optimal solution of the following linear program: ½COST min wo x, x;l
subject to
xXX l; yo pY l; lX0:
(14)
This cost efficiency has irrationality demonstrated as follows. Suppose that two DMUs A and B have the same levels of inputs and outputs, i.e., xA ¼ xB and yA ¼ yB . Assume that the factor price of DMU A is twice that of B for each input, i.e., wiA ¼ 2wiB ði ¼ 1; . . . ; mÞ: Then, the optimal solutions xA and xB for both A 3
Farrell [4] termed (local) allocative efficiency as ‘‘price efficiency,’’ which is a notion different from that used in this paper. Fa¨re and Grosskopf [10] and Fa¨re et al. [9,11] focused on ‘‘price space,’’ which is the dual of input space, and indicated price efficiency on price space, similar to technical and cost efficiency on input space, in order to identify shadow prices and calculate losses due to market imperfection. Price efficiency in this paper is similar to ‘‘dual technical efficiency’’ or ‘‘input price measure of technical efficiency’’ in Fa¨re et al. [9,11]. Compared to these studies, we sought to indicate technical and price inefficiency and the new allocative inefficiency on the same axis as input cost, as described in Section 2.5.
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and B are the same, since both have the same cost gradient. Hence, their cost efficiency, as defined by Eq. (13), is the same. This is irrational in that A and B have the same cost efficiency even though the cost of B is half that of A. This irrationality is caused by the definition of the production possibility set P in Eq. (2). P is defined only by using technical factors X and Y, but has no concern with the factor price W ¼ ðw1 ; . . . ; wn Þ. In order to overcome this shortcoming, Tone [6] proposed the cost-based production set Pc in Eq. (7), and new cost-based technical and allocative efficiencies that are free from such difficulties. We demonstrate key shortcomings of the traditional cost efficiency model in the empirical study of Section 3. 2.4. Allocative efficiency We here solve the [New Cost] model on Pc, formulated as follows: ~ ½New Cost C ¼ min ex, ~ x;m
~ X¯ m; subject to exXe yo pY m;
(15)
mX0; where eARm is a row vector in which each element is equal to 1. Let ðx¯ o ; m Þ be an optimal solution. Then, the cost-based pair ðx¯ o ; yo Þ is the cost minimum production in the supposed production possibility set Pc , which can substantially differ from P if the unit prices of the inputs vary from DMU to DMU. The (global) allocative efficiency a of DMUo is defined as follows:
Allocative efficiency ¼
C o ðp1Þ. C o
(16)
The traditional (local) allocative efficiency is the adjustment to the optimal input mixture based on the given input price ratio. In comparison, the allocative index in Eq. (16) represents the adjustment to the optimal cost mix, viz., the combination of the optimal input amount and input price mixture.4 We also define the loss, L o , due to the suboptimal cost mix as L ¼ C o C o ðX0Þ. o
(17)
2.5. Decomposition of the actual cost Given Eqs. (6), (11), and (17), we arrive at the following theorem. Theorem 1. C o XC o XC o XC o .
(18)
Furthermore, we can obtain the relationship between the optimal cost and losses, where the actual cost (Co) can be decomposed into three losses and the minimum cost (C o ): Lo ¼ C o C o ðX0Þ
Loss due to technical inefficiency;
L o ¼ C o C o ðX0Þ Loss due to price inefficiency; L ¼ C o C o ðX0Þ Loss due to allocative inefficiency; o C o ¼ Lo þ C o ¼ Lo þ L o þ C o ¼ Lo þ Lo þ Lo þ C o . 4
ð19Þ
The traditional cost model is solved under the given input price ratio (the slope of the isocost line) because the cost function is homogeneous of degree +1 in input prices. In contrast, the new cost model [6] has no restriction on input prices. In this case, the optimal solution will be determined based on the activity in Pc that employs the most inexpensive total cost. The optimal cost mix expressed by the global allocative efficiency is the cost mix of this activity.
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The ratios of these costs explain the respective efficiencies, while the minimum cost can be decomposed into the following indices: C o ðp1Þ Technical efficiency ðTEÞ; Co C E o ¼ o ðp1Þ Price efficiency ðPEÞ; Co C o ðp1Þ ðGlobalÞ allocative efficiency ðAEÞ; E o ¼ C o Eo ¼
C ¼ C o o Eo ¼ Co Eo Eo ¼ Co Eo Eo Eo , C o ¼ E o E o E o ðDecomposition of total cost efficiency into TE; PE; and AEÞ: Co
ð20Þ
Furthermore, we establish an identity that connects the total cost efficiency with the three loss ratios in the following additive form. 1 ¼ Lo =C o þ L o =C o þ Lo =C o þ C o =C o .
(21)
C o ,
If the DMUo is fully efficient, i.e., C o ¼ then the technical, price, and allocative losses are zero; whereas, if it is inefficient (C o 4C ), we can attribute the inefficiency to the three losses. o If Lo =C o dominates L o =C o and Lo =C o , the inefficiency of the DMU is primarily caused by technical inefficiency. On the other hand, if Lo =C o dominates Lo =C o and L o =C o , it is judged that the inefficiency results from the comparatively higher input factor prices of the DMU. In the case of L o =C o dominating Lo =C o and L o =C o , the inefficiency of the DMU results from the suboptimal input cost mix.
3. An empirical study We applied this combined model to the comparison of electric power companies in Japan and the US. 3.1. Background It has been pointed out that the electric power price in Japan is relatively higher than those of the other developed countries; this might be caused by the inefficiency of Japanese electric power companies. On the other hand, selected prior studies found that the productive efficiency of the Japanese companies was higher than for their US counterparts [7,8]. It was suggested that differences in electricity prices between the two countries must be due to other factors, such as differences in input factor prices.5 Despite the above, traditional DEA models have not taken differences in exogenously determined input factor prices into consideration. As noted above, using [New Tech] model (Eq. (8)), and applying the optimal value of the CCR model, the differences in input factor prices can be clearly considered. We can then decompose the total loss into losses due to technical inefficiency, the differences in input price levels, and the suboptimal cost mix. Using this combined model, the current study attempted to compare the losses of the total supply costs between Japan and the US, and to search for reasons why electric power prices were higher in Japan. 3.2. Japan– US data For DMUs, we considered 19 investor owned vertically integrated electric power companies (9 Japanese and 10 US) from 1992 to 1999. There are 10 integrated electric power companies in Japan; however, this study 5 In Japan and the US, electricity price was based on the supply cost under the rate of return regulation before liberalization. The differences in electricity prices between the two countries were thus directly affected by the differences in supply cost, i.e., differences in input factor prices and/or productive efficiency.
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Table 1 Japanese and US companies considered in the study Japan 1 2 3 4 5 6 7 8 9
US
Hokkaido Electric Power Co. Tohoku Electric Power Co. Tokyo Electric Power Co. Chubu Electric Power Co. Hokuriku Electric Power Co. Kansai Electric Power Co. Chugoku Electric Power Co. Shikoku Electric Power Co. Kyusyu Electric Power Co.
10 11 12 13 14 15 16 17 18 19
AmerenUE Arizona Public Service Co. Baltimore Gas & Electric Co. Carolina Power & Light Co. Duke Energy Corp. Florida Power & Light Co. Niagara Mohawk Power Corp. PPL Electric Utilities Corp. Public Service Electric & Gas Co. Virginia Electric & Power Co.
excluded one of them—Okinawa Electric Power Company—because it is very small and only services customers in the Okinawa islands. We selected US investor owned companies that were equivalent to the Japanese companies with respected to key factors such as scale of electric power sales, possession of nuclear power plant, etc. Table 1 lists the sample companies considered in this study. Vertically integrated companies perform several internal functions, such as generation, transmission, distribution, etc. However, the current study used overall data from the companies since the focus was on their managerial performance. The input and output datasets are thus as follows: Input 1 Input 2 Input 3 Cost 1 Cost 2 Cost 3 Output 1
Capital data (Divisia index) Labor data (Number of employees) Fuel data (British thermal unit) Total capital cost Total labor cost Total fuel cost Net electricity power sales
For capital data (Input 1), we used an integrated index of the representative capital asset of each function. We therefore adopted a Divisia index6 constructed on the basis of four factors: generation capacity (giga watt: GW), transmission line length (kilo meter: km), distribution transformer capacity (volt-ampere: VA), and index of capital stock7 for the general administrative division. The cost data corresponding to Input 1 (Cost 1) was the total cost for capital input, equal to the sum of maintenance and depreciation. The labor data (Input 2) were the total number of employees, where the corresponding cost (Cost 2) was the total amount of salaries and wages. In this case, we did not account for outsourcing costs simply because of the unavailability of data. The fuel data are related only to the generation division; however, they are important as the share of fuel cost is comparatively high (see Fig. 1). Since fuel consumption units differ amongst gas, coal, and petroleum, they were converted to British thermal units (BTU) in order to sum the fossil fuel data. In contrast, the heat quantity from consumed nuclear fuel is difficult to measure. We thus performed backward calculations with the amount of nuclear power generation, assuming the thermal efficiency to be 0.35. The corresponding cost (Cost 3) was then total fuel cost including both fossil and nuclear components. We obtained the input factor prices as the ratio: cost to input, e.g., (Cost 1)/(Input 1). 6
We followed the method in Caves et al. [12] to calculate the Divisia index. Index of capital stock for the general administrative division was based on the book value of this division in 1992, adding the net increase in capital stock each year. These values were converted to US$ using the average exchange rate during the study period. 7
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100% Fuel Cost 80% Salaries and Wages 60%
General Admin
Transmission
Capital Cost
Distribution
40%
20% Generation 0% JP
US Fig. 1. Summary of cost structure.
As part of the above, Japanese yen were converted to dollars using purchasing power parities (PPP)8, with the cost data deflated by the producer price index of the US. On the basis of these inputs, we assumed that electric power companies produced net electric power sales9 (giga watt hour: GWh) excluding that power purchased from other companies. The Japanese dataset for this study was obtained from the ‘‘Handbook of Electric Power Industry’’ [14], published by the Federation of Electric Power Companies (FEPC) in Japan, while the US data came from the ‘‘FORM No.1’’ [15] and ‘‘FORM No.423’’ [16] published by the Federal Energy Regulatory Commission (FERC) and ‘‘Form EIA-860’’ [17] published by Energy Information Administration (EIA). The major statistics of the datasets are described in Table 2. 3.3. Empirical results 3.3.1. Verification of the performance of the price efficiency index First, we verify whether the price efficiency index introduced in this study corresponds well to the level of input factor prices. Fig. 2 shows the price efficiency index for each DMU in 1999. In this figure, the vertical axis indicates the measured price efficiency index while the horizontal axis indicates the average of three input factor prices for each DMU. According to our analytical framework, the price efficiency index should decrease with a rise in input factor prices. In effect, the price efficiency index is plotted in decreasing order. It is clearly seen that the higher the average input price, the smaller the index: we can thus conclude that the price efficiency index expresses the level of input factor prices well. In order to compare our proposed price efficiency with the traditional one, we evaluate g* in Eq. (13) and exhibit ‘‘average input factor price vs. traditional cost efficiency’’ in Fig. 3. Note that no significant relationship appears between the two. Factor prices indicate as independent of cost efficiency. This is additional evidence of the superiority of our proposed scheme vs. the traditional one.
8
We used PPP for GDP from 1992 to 1999 calculated by OECD [13]. The average value for this period was f170.03/US$, while the corresponding average exchange rate was f112.86/US$. 9 We also considered the number of customers as an output, but ultimately viewed it as inappropriate because the scale of customers served between the two countries was very different.
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Table 2 Major statistics of datasets from 1992 to 1999 (average) Japana
US
Av.
S.D.
Max
Min
Av.
S.D.
Max
Min
Capital (Divisia indexb) Generation (GW) Transmission (km) Distribution (VA) General admin (Index) Employees (#) Fuel (109BTU) Net elec. power sales (GWh)c
1.766 19,486 9,833 29,594 181,350 15,831 673,686 71,461
1.262 15,845 5,035 24,211 94,257 10,738 614,639 62,576
4.684 57,846 20,724 86,149 377,628 41,067 2,289,134 231,797
0.417 4,451 3,016 5,177 44,101 5,060 97,458 12,486
1.089 10,550 7,423 20,703 75,180 8,421 394,248 38,515
0.483 4,658 4,381 9,518 45,718 3,034 169,817 17,690
2.065 20,012 15,010 42,656 168,371 17,666 780,175 77,778
0.418 1,869 1,073 10,557 19,948 3,978 115,970 12,859
Total capital costd Generation division Transmission division Distribution division General admin division Salaries and wages Fuel cost
2,995 1,517 655 694 129 824 1,176
2,517 1,210 661 609 70 593 1,041
9,716 4,690 2,667 2,320 285 2,331 4,300
554 281 98 130 36 229 156
469 280 29 139 21 355 513
185 123 15 57 11 137 290
1,153 732 62 326 50 685 1,383
249 135 10 57 9 171 166
The unit of cost data is million US$ (1995 price). a All Japanese cost data are converted to US$ using purchasing power parities (PPP). b Divisia Index is constructed on the basis of generation capacity (giga watt: GW), transmission line length (km), distribution transformer capacity (volt-ampere: VA), and index of capital stock for the general administrative division. c The unit of Net electric power sales is giga watt hour (GWh). d Japanese total capital cost includes other miscellaneous capital costs. Therefore, the total sum of four divisions’ data is not equal to total capital cost data.
Price Efficiency Index
1.2 1 0.8 0.6 0.4 0.2 0
0
200
400
600
800
1000
1200
Average Input Price * The horizontal axis indicates the average of three input factor prices for each DMU. ** The curved line passing through the dots indicates an approximation.
Fig. 2. Comparison of price efficiency index and input factor prices (1999).
3.3.2. Decomposition of efficiency indices Table 3 and Fig. 4 present the results for technical efficiency ðE o Þ, price efficiency ðE o Þ, and allocative efficiency ðE o Þ for Japanese and US DMUs on average. These results indicate that Japanese average technical efficiency (TE) and allocative efficiency (AE) are superior to their US counterparts; however, the differences are negligible. Using the Wilcoxon test, these differences are statistically insignificant except for TE in 1992, and AE in 1992, 1994, and 1999 at the 5% significance level. In contrast, the difference in the price efficiency index between the two countries is large, with the US average significantly greater than that of the Japanese. Figs. 5 and 6 portray the decomposition of total actual supply cost. While Fig. 5 is based on these costs and losses standardized by net electric power sales (cent/kWh), Fig. 6 focuses on the structural ratio of losses.
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Traditional Cost Efficiency Index
100
1.2 1 0.8 0.6 0.4 0.2 0
0
200
400
600
800
1000
1200
Average Input Price * The horizontal axis indicates the average of three input factor prices for each DMU. ** The curved line passing through the dots indicates an approximation.
Fig. 3. Comparison of traditional cost efficiency index and input factor prices (1999).
Table 3 Results of the efficiency indices 1992
1993
1994
1995
1996
1997
1998
1999
Technical efficiencya JP Ave 0.906 US Ave 0.811
0.887 0.847
0.889 0.841
0.882 0.869
0.890 0.861
0.929 0.863
0.923 0.884
0.921 0.883
Price efficiencya JP Ave US Ave
0.309 0.705
0.316 0.729
0.315 0.721
0.306 0.722
0.308 0.773
0.324 0.757
0.330 0.763
0.985 0.934
0.988 0.941
0.949 0.931
0.964 0.945
0.971 0.918
0.987 0.925
0.982 0.925
0.320 0.772
Global allocative efficiencya JP Ave 1.000 US Ave 0.899 a
Technical, Price and Global Allocative Efficiencies are defined in Eq. (20).
Although the Japanese average actual supply cost has been declining over the years, it remains nearly twice that of the US average. Figs. 5 and 6 also indicate that the largest loss of Japanese companies is due to differences in the input price levels, and thus it is much larger than the other losses in Japan as well as the losses in the US. In contrast to the price difference loss, losses due to technical and allocative inefficiencies in Japan are comparatively smaller than those in the US; however, as mentioned previously, the differences are statistically insignificant. Taken together, these results imply that comparatively higher electricity prices in Japan are caused by higher input factor prices and not technical inefficiency. In an economics context, market prices are uncontrollable and treated as a given condition. The loss due to the price difference, as shown in Fig. 5, might be uncontrollable for DMUs. For instance, the price gap could be caused by differences in business conditions between Japan and the US. It is common knowledge, for example, that Japanese utilities have spent considerable amounts to maintain superior reliability of electricity supply and pollution control. They must also protect against natural disasters such as earthquakes, typhoons, snowfall, and salt damage, which occur frequently. Furthermore, Japan is not rich in natural resources and relies on imports for the majority of generation fuel, while the US utilities can procure cheaper fuel domestically. These business conditions apparently contribute to the relatively high cost of electricity supply for Japanese utilities as exhibited in Fig. 5. However, at the same time, inefficiency of the utilities may result in higher input prices, e.g., they might purchase equipment at unnecessarily higher prices. This study does not identify the
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1.0 0.8 0.6 0.4
US Ave
JP Ave
0.2 0.0 1992
1993
(a)
1994
1995
1996
1997
1998
1999
1998
1999
1998
1999
Technical Efficiency
1.0 0.8 0.6 0.4 0.2
JP Ave
US Ave
0.0 1992
1993
1994
(b)
1995
1996
1997
Price Efficiency
1.0 0.8 0.6 0.4
JP Ave
US Ave
0.2 0.0 1992 (c)
1993
1994
1995
1996
1997
Allocative Efficiency
Fig. 4. The results of the efficiency indices of Japanese and the US companies on average.
primary cause of higher input prices; it only shows that a higher input price has a greater effect on the higher supply cost than does productive inefficiency.
4. Extensions of the model We extend our basic model as described in Section 2 to a factor-oriented decomposition and evaluate the losses due to scale efficiency.
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102
Price Loss
10
10
9
9
8
8
7
7
6 5
6 5
4
4
3
3
2
2
1
1
0
0 y92
y93
y94
y95
y96
y97
y98
Minimum Cost
Technical Loss
Cent/kWh
Cent/kWh
Allocative Loss
y99
y92
y93
y94
y95
y96
y97
y98
y99
y97
y98
y99
US average
Japan average Fig. 5. Decomposition of actual supply cost.
Allocative Loss
Price Loss
Technical Loss
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0% y92
y93
y94
y95
y96
y97
y98
y99
Japan average
y92
y93
Minimum Cost
y94
y95
y96
US average
Fig. 6. Decomposition of actual supply cost (ratio oriented).
4.1. Factor-oriented decomposition By focusing on each input factor, the decomposition can be examined in greater detail. The loss formulas in Eq. (19) are redefined as follows: Lio ¼ wio xio wio ðy xio s i Þ ¼ wio ðxio y xio þ si Þ,
(22)
L ¯ io ðr x¯ io t io ¼ x i Þ,
(23)
ARTICLE IN PRESS K. Tone, M. Tsutsui / Socio-Economic Planning Sciences 41 (2007) 91–106
Fuel Loss
Labor Loss
10
10
9
9
8
8
7
7 Cent/kWh
Cent/kWh
Allocative Loss
6 5
5 4
3
3
2
2
1
1 y92
y93
y94
y95
y96
y97
y98
y99
Minimum Cost
6
4
0
Capital Loss
103
0 y92
y93
y94
Japan average
y95
y96
y97
y98
y99
US average Fig. 7. Factor-oriented decomposition.
whereP Lio and L due to the technical and price inefficiencies for input i, respectively, and io represent Pmlosses Lo ¼ m L and L ¼ L represent these losses for all inputs. Considering the losses by factor, we o i¼1 io i¼1 io can further decompose the actual total cost (Co) into losses in greater detail than in Eq. (19) as follows: Co ¼
m X i¼1
Lio þ
m X
L io þ Lo þ C o .
(24)
i¼1
Furthermore, these losses can be classified into factor-oriented losses as Co ¼
m X
Lio þ L o þ Co ,
(25)
i¼1
P Pm where Lio ¼ m i¼1 Lio þ i¼1 Lio represents the sum of the technical inefficiency loss ðLio Þ and the price inefficiency loss ðLio Þ for input i. This decomposition is useful for verifying which input factor cost results in a greater loss. Fig. 7 describes the factor-oriented decomposition for Japanese and US utilities in 1999. It is clearly seen that the capital cost loss in Japan is much larger than that in the US. 4.2. The loss due to scale inefficiency We can measure scale efficiency using the BCC model [2] which assumes variable returns-to-scale (VRS). ½BCC Z ¼ min Z, Z;l;s ;sþ
subject to Zxo ¼ X l þ s ; yo ¼ Y l s þ ; el ¼ 1;
(26)
lX0; s X0; sþ X0: The projection is given by
½BCC projection xVRS ¼ Z xo s ; yVRS ¼ yo þ sþ . o o
(27)
ARTICLE IN PRESS K. Tone, M. Tsutsui / Socio-Economic Planning Sciences 41 (2007) 91–106
104
Price Loss
Scale Loss
Pure Technical Loss
10
10
9
9
8
8
7
7 Cent/kWh
Cent/kWh
Allocative Loss
6 5
6 5
4
4
3
3
2
2
1
1
0
Minimum Cost
0 y92
y93
y94
y96
y95
y97
y98
y92
y99
y93
y94
y95
y96
y97
y98
y99
US average
Japan average
Fig. 8. Further decomposition including scale inefficiency.
The corresponding pure technically efficient total input cost for DMUo is calculated as
¼ C VRS o
m X
wio xVRS ¼ io
i¼1
m X
wio ðZ xio s i ÞpZ
i¼1
m X
wio xio ¼ Z C o pC o .
(28)
i¼1
We defined the loss due to pure technical inefficiency as
VRS Lp ðX0Þ. o ¼ Co Co
(29)
Then, we construct data set (XVRS, YVRS) consisting of ðxVRS ; yVRS Þ, j ¼ 1,y,n, and evaluate the technical j j VRS
VRS
; yj Þ with respect to (XVRS, YVRS) under the constant returns-to-scale (CRS) efficiency of ðxj 10 assumption. Let the optimal solution be (xCRS ; yCRS ), with cost C CRS ¼ wo xCRS ðpC VRS Þ: We thus o o o o o obtain the loss due to scale inefficiency as follows:
C CRS ðX0Þ. Lso ¼ C VRS o o
(30)
In order to measure price efficiency and allocative efficiency using [New Tech] and [New Cost] as explained by Eqs. (8) and (15), the cost-based production possibility set Pc is defined with x¯ o ¼ wo xCRS . Finally, the cost o decomposition proceeds as follows: s C o ¼ Lp o þ Lo þ Lo þ Lo þ C o .
(31)
Fig. 8 shows the further decomposition including the scale inefficiency loss for Japanese and US utilities in 1999. It suggests that the loss due to scale inefficiency is comparatively smaller than the other losses in both countries, and that the loss due to price inefficiency remains the largest impact on total supply cost in Japan. 5. Conclusion In this paper, we decomposed actual total cost into the minimum cost and losses due to technical inefficiency, input price differences, and inefficient cost mix using the traditional CCR, New Tech, and New 10
Generally, scale inefficiency is measured as the radial gap between the CCR and BCC frontiers. In the case that the optimal solution ; yCRS ) considers slacks, the scale inefficiency may not be radial gap. under the CRS assumption (xCRS o o
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Cost models. The combination of these models enabled us to clarify the influence of not only technical inefficiency due to input excess (or output shortfall) but, also, the comparatively higher input factor price on the total supply cost. The latter cannot be identified under the usual assumption of given uniform input factor prices. However, it is common to find price differences among, and even within, nations. As shown in Fig. 2, applying the new combined model to data of the electric utilities, we obtained an important index, suggesting that the model was effective in examining cost performances. As a result of our decomposition, we found that higher electricity prices in Japan are caused by comparatively higher input factor prices, rather than by technical and allocative inefficiencies. Our model has potential use in a broad range of applications, including other industries such as automobile, textile, electric appliance, etc. In terms of future research, we should identify the reason of inefficiency measured by DEA model, which is caused by uncontrollable and/or controllable factors for companies. Inefficiency caused by uncontrollable factors, such as differences in business environment, cannot be improved by companies, while that caused by controllable factors must be the ‘‘real’’ inefficiency of companies. As mentioned in Section 3, the gap in input factor prices between Japan and the US might be caused by several factors. It is thus difficult to determine whether this gap can be reduced by efforts of the DMUs. From the standpoint of model applicability and implication to company management, this would be an important issue to resolve. Throughout this paper, we have employed radial-based models, i.e., CCR and BCC, for measuring the technical efficiencies. We can, however, utilize the non-radial SBM (slacks-based) models [3] for this purpose. Comparisons of results obtained from the two approaches would also be an interesting subject for future research efforts. Acknowledgements The authors wish to acknowledge the many helpful comments and suggestions received from Professor W.W. Cooper and the Editor-in-Chief, Dr. B.R. Parker. References [1] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research 1978;2:429–44. [2] Banker RD, Charnes A, Cooper WW. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 1984;30:1078–92. [3] Tone K. A slack-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 2001;130:498–509. [4] Farrell MJ. The measurement of productive efficiency. Journal of Royal Statistical Society Series A 1957;120:253–381. [5] Fa¨re R, Grosskopf S, Lovell CAK. The measurement of efficiency of production. Boston: Kluwer Academic; 1985. [6] Tone K. A strange case of the cost and allocative efficiencies in DEA. Journal of the Operational Research Society 2002;53: 1225–31. [7] Goto M, Tsutsui M. Comparison of productive and cost efficiencies among Japanese and US electric utilities. Omega 1998;26: 177–94. [8] Hattori T. Relative performance of US and Japanese electricity distribution: an application of stochastic frontier analysis. Journal of Productivity Analysis 2002;18:269–84. [9] Fa¨re R, Grosskopf S, Lovell CAK. Production frontiers. Cambridge: Cambridge University Press; 1994. [10] Fa¨re R, Grosskopf S. Measuring shadow price efficiency. In: Dogramaci A, Fa¨re R, editors. Application of modern production theory: efficiency and productivity. Boston: Kluwer Academic; 1988. p. 223–34. [11] Fa¨re R, Grosskopf S, Nelson J. On price efficiency. International Economic Review 1990;31(3):709–20. [12] Caves DW, Christensen LR, Tretheway MW. US Trunk Air Carriers, 1972–1977: A multilateral comparison of total factor productivity. In: Cowing TG, Stevenson RE, editors. Productivity measurement in regulated industries. New York: Academic Press; 1981. p. 47–76. [13] OECD. Purchasing power parities (PPPs) for OECD countries 1970–2000. Organization for Economic Co-operation and Development. [14] FEPC. Handbook of electric power industry. Federation of electric power companies, 1993–2000 (each year) [in Japanese]. [15] FERC. FORM No.1: Annual report of major electric utility. Federal energy regulatory commission, 1992–1999 (each year). [16] FERC. FORM No.423: Cost and quality of fuels for electric plants. Federal energy regulatory commission, 1992–1999 (each year). [17] EIA. Form EIA-860: Annual electric generator report. Energy information administration, 1992–1999 (each year).
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Kaoru Tone (‘‘Decomposition of Cost Efficiency and its Application to Japanese-US Electric Utility Comparisons’’) is Research Fellow at the National Graduate Institute for Policy Studies. He holds a B.A. in Mathematics from the University of Tokyo and the Ph.D. in Operations Research from Keio University, Japan. Dr. Tone’s research interests include issues of theory and applications of OR/MS, with emphasis on efficiency analysis and multiple criteria decision-making. His work has appeared in such journals as Mathematical Programming, European Journal of Operational Research, Omega, Socio-Economic Planning Sciences, International Journal of Production Economics, Policy and Information, Journal of Productivity Analysis and Journal of Operations Research Society of Japan. He has co-authored Data Envelopment Analysis—A Comprehensive Text with Models, Applications, References and DEA-Solver Software with W.W. Cooper and L.M. Seiford, published by Kluwer. He has also developed the software DEA-Solver which is being utilized worldwide. Dr. Tone serves on the Editorial or Advisory Boards of Omega, Socio-Economic Planning Sciences, Metamorphosis and Journal of Operations Research Society of Japan. He served as President of the Operations Research Society of Japan from 1996 to 1998.
Miki Tsutsui (‘‘Decomposition of Cost Efficiency and its Application to Japanese-US Electric Utility Comparisons’’) is a researcher at the Central Research Institute of Electric Power Industry in Japan and has been engaged in productivity and efficiency analysis for the electric power industry. She holds a B.A. degree in Economics from Keio University, and is currently a doctoral student at the National Graduate Institute for Policy Studies, Tokyo, Japan. Ms. Tsutsui has written several reports on productivity and efficiency change for electric power companies in Japan. Recently, she has been involved in a series of research projects involving energy policy and the management of electric power companies. Her research interests focus on issues of multi-utility strategy development. She has published papers in Omega and Energy Policy. Her professional memberships include the Operations Research Society of Japan.
