Economies of Scale and Scope and Yardstick Cost Comparison in Japan s Electric Power Industry

Transcription

1 Economies of Scale and Scope and Yardstick Cost Comparison in Japan s Electric Power Industry Takanori Ida Kyoto University, Faculty of Economics, Japan Tetsuya Kuwahara Kyoto University, Faculty of Economics, Japan Address: Takanori Ida ida@econ.kyoto-u.ac.jp Hattyo-nawate, Takatsuki, Osaka , Japan 0

2 Economies of Scale and Scope and Yardstick Cost Comparison in Japan s Electric Power Industry Abstract: This paper utilizes a fixed-effects model of panel data analysis and estimates the translog cost function of the Japanese electric power industry from 1978 to First, we investigate whether the Japanese electric power industry is naturally monopolistic. We find that all electric power companies still benefit from both scale and scope economies and therefore this industry remains a naturally monopolistic industry. Second, in order to apply the idea of yardstick-type competition to a naturally monopolistic industry where costs are quite different between companies, we introduce two kinds of cost-comparison coefficients, one for the individually specific effects and the other for scale and scope economies. Keywords: electric power industry, regulatory reform, yardstick competition, economies of scale, economies of scope 1

3 I. Introduction A wave of liberalization is sweeping through the Japanese electric power industry, a previously monopolistic industry. In 1995, the entry regulation in power generation was abolished leading to the introduction of a bidding system for the wholesale acquisition of electric power that allowed six power companies to accept supply bids from power wholesalers. Furthermore, in 2000, partial liberalization began in the retail section for largevolume consumers of 2,000 kilowatts or more of 20,000 volts or higher voltage supply. Tokyo, Kansai and Hokuriku Electric Power companies submitted new rate schedules for unregulated areas in anticipation of broader liberalization in the future, while Mitsubishi Corporation s subsidiary Diamond Power applied for approval as a power producer and supplier (PPS) in the power retail market 1. A study of partial liberalization in the power retail market and a review of existing systems to expand liberalization was done in At this point, it would be useful to examine the meaning of "monopoly" before arguing whether liberalization brings about an improvement in industrial efficiency. There are two types of monopoly: legal and natural monopoly. Even if legal monopoly is abolished, in the case where the industrial structure still remains naturally monopolistic, the economic significance of liberalization will be limited. In this sense, a mechanism such as yardstick competition, which was introduced to some extent to the Japanese electric industry in 1995, is required so that companies are encouraged to achieve greater efficiency. 2

4 This paper investigates the cost structure of Japan s nine incumbent power companies (except Okinawa Electric Power) over the past 20 years by using the translog cost function which is the most widely used flexible function in the cost estimation of public utilities. At the same time, we adopt the fixed-effects model of panel data analysis, utilize the information about the individually specific effects of electric power companies, and measure the cost-comparison coefficients 2. The contribution this paper seeks to make is not only to verify whether the natural monopoly of the Japanese electric power industry still remains, but also to measure the cost-comparison coefficients to introduce yardstick-type competition to improve efficiency 3. There are two main conclusions in this paper. First, evidence of widespread economies of scale and scope in the Japanese electric power industry is found implying that the industry is still naturally monopolistic in character. (For all that, this does not necessarily mean that the classic public utilities regulation is valid.) Second, we measure the costcomparison coefficients from two different viewpoints: the economies of scale and scope and the individually specific effects. Based on the cost-comparison coefficients, we can introduce a yardstick cost comparison into the industry where the assumption of equality of average costs among companies is seldom satisfied. The paper consists of the following five sections. Section II introduces definitions of variables and a method of estimating the cost function. Section III provides a definition of the economies of scale and scope in the context of the power industry and some estimation results. 3

5 The paper then further develops its theme by presenting in Section IV definitions of costcomparison coefficients and the result of a measurement of those coefficients. Section V concludes the paper. II. The Definitions of Variables and the Estimation of Translog Cost Function This section provides definitions and sets out the method to be used. We introduce the cost function to be estimated, explain the data used in the empirical model, and finally discuss the estimated results. We assume in this paper that there are two kinds of output in the electric power industry, power generation (Y 1 ) and power transmission-and-distribution (Y 2 ), and that there are three kinds of production inputs, labor (L), fuel (F), and capital (K) 4. In addition, other explanatory variables are defined as follows: labor cost =P L, fuel cost =P F, capital cost =P K, year index=t, and capacity utilization rate of power plants=cu. The long-term translog cost function, all of whose inputs we assume here to be variable, can be defined as follows, taking the symmetry of coefficients into consideration 5 : lnc(p L, P F, P K, Y 1, Y 2, t, CU) = a i +b L lnp L +b F lnp F +b K lnp K +(1/2)b LL (lnp L ) 2 +(1/2)b FF (lnp F ) 2 +(1/2)b KK (lnp K ) 2 +b LF lnp L lnp F +b LK lnp L lnp K +b FK lnp F lnp K +c 1 lny 1 +c 2 lny 2 +(1/2)c 11 (lny 1 ) 2 4

6 +(1/2)c 22 (lny 2 ) 2 +c 12 lny 1 lny 2 +d L1 lnp L lny 1 +d L2 lnp L lny 2 +d F1 lnp F lny 1 +d F2 lnp F lny 2 +d K1 lnp K lny 1 +d K2 lnp K lny 2 + t=1 21 e Lt D t lnp L + t=1 21e Ft D t lnp F + t=1 21 e Kt D t lnp K +f 1 t+f 2 t 2 +f cu lncu. (1) The terms, a, b, c, d, e, and f, are coefficients to be estimated. The term D t is a zero-one dummy equal to 1 at time t and 0 otherwise. The reason why we include the terms, D t lnp L, D t lnp F and D t lnp K, in the model is that since we do not assume the neutrality of the cost share of each input with regard to technical change, we use year dummies of the input prices to remove the influence of technical change on the cost function, as originally proposed by Watanabe and Kitamura (1998). The term a i for i=1 9, represents the constant term of each power company. Since the fixed effects model is used here with panel data from nine power companies for the period 1978 to 1998, the estimated coefficient a i represents what is called the individually specific effect of each power company. Although it is standard practice in the literature to estimate a translog cost function with several dummy variables, the model may sometimes be overparametized. In the case the number of samples is strictly limited, it is preferable to adopt simpler models, such as a translog cost function without dummy variables or Cobb-Douglas function. It is possible even in such cases to calculate the cost-comparison coefficients discussed in the following sections. In addition, the following constraints of linear homogeneity are imposed on the cost function given above: 5

7 b L +b F +b K =1, b LL +b LF +b LK =0, b FF +b FL +b FK =0, b KK +b LK +b FK =0, d L1 + d F1 + d K1 =0, d L2 + d F2 + d K2 =0, e Lt +e Ft +e Kt =0. (2) The reason why we assume e Lt +e Ft +e Kt =0 for each period (t=1,,21) is to avoid the problem of perfect multicollinearity between the terms, D t lnp L, D t lnp F and D t lnp K. Thus, together with b L +b F +b K =1, the linear homogeneity of input prices, b L +b F +b K +e Lt +e Ft +e Kt =1, always hold for each period. From Shephard s lemma, the share equations of inputs are obtained as follows : S L =b L +b LL lnp L + b LF lnp F +b LK lnp K + d L1 lny 1 + d L2 lny 2 + t=1 21 e Lt D t, S F =b F +b FF lnp F + b LF lnp L +b FK lnp K + d F1 lny 1 + d F2 lny 2 + t=1 21 e Ft D t, S K =b K +b KK lnp K + b LK lnp F +b FK lnp F + d K1 lny 1 + d K2 lny 2 + t=1 21 e Kt D t. (3) (Note: since the sum of three share equations must be 1, one of them can be dropped.) Data used here are extracted from the Statement of Income and Financial Report of Japan s nine incumbent electric power companies published for each fiscal year. As a deflator for capital, gross investment, and depreciation expenses, we use the capital-goods price index reported in the Price Index Statistics of the Bank of Japan. The definitions of variables are given below. (Note: Each variable is normalized by its mean.) Output-related Generation: Y 1 generated output station-use electricity. Transmission-and-distribution: Y 2 ([ ( middle value of voltage spectrum route length of transmission lines)] number of contracts/customers) 1/2. Inputs/expenditure-related 6

8 Labor cost: P L ( total personnel expenses expenses of consignment meter-reading and consignment payment collection) / number of regular employees at the end of the fiscal year. Fuel cost: P F (total fuel expenses for steam, internal combustion engine, and nuclear power generation) / heat consumption of conversion into heavy oil. Capital stock; K t (1- t )(K t-1 - LAND t-1 ) + I t + LAND t. Note: t depreciation expenses at t / equipment expenses at the end of t-1; LAND t land values at t = LAND t-1 + LAND t ; I t K t - K t-1 - LAND t + depreciation expenses at t. Capital cost: P K [WPI(r t + )(1-u t z t )] / (1-u t ). Note: WPI price index of investment goods; r t interest payments at t / (corporate bond + long-term loan at the beginning of t-1); u t corporation-tax rate; z t ratio of the present value of the deduction of depreciation expenses to that of capital good (See Hayashi and Inoue,1991 for further details). The other definition Capacity utilization rate of power plants: CU the generated output / the installed generating capacity. We can now estimate the simultaneous equations of the long-term translog cost function and the share equations except the capital one, by using Zellner s Seemingly Unrelated Regressions model (SUR). 7

9 Table 1 illustrates the main results of the estimation. For serial correlation, we carry out the Durbin-Watson test. A Durbin-Watson statistic of 0.30 indicates the presence of serial correlation, as previous studies on the estimation of the cost function attribute to omitted relevant variables. We consider this to be a weak point of our research as the estimators may not be statistically efficient and hypothesis testing ignoring serial correlation is likely to be problematic. We try to solve this problem by using the White heteroscedasticity consistent covariance estimator. However, we think a future approach would be to use the Newey-West autocorrelation consistent covariance estimator. <Table 1> We test for heteroscedasticity by performing separate Goldfeld-Quandt tests on two period ( vs ) and two firm-size (large vs. small) subsamples. The test statistic of the cost function using period subsamples is 0.96; and the F-statistic obtained shows that we cannot reject the null hypothesis of homoscedasticity. With respect to firmsize subsamples obtained by dividing the power companies into the larger five companies and the smaller four companies, we again apply the Goldfeld-Quandt test that yields a test statistic equal to The F-statistic allows us to reject the null hypothesis of homoscedasticity using firm-size subsamples. For this reason, we adopt the White heteroscedasticity consistent estimator. 8

10 III. Definition of and Testing for Economies of Scale and Scope Due to characteristics known as bottleneck or essential facility arising from the presence of huge plants and equipment for power generation, transmission, and distribution, the electric power industry has conventionally been considered to be naturally monopolistic. Natural monopoly is defined by the subadditivities of cost. As is well known, the necessary and sufficient condition that the subadditivities of cost equal the economies of scale and scope does not exist in the case of multi-goods 6. However, it is the sufficient condition of being a natural monopoly that economies of scale exist for each good and economies of scope hold. Although there are various kinds of indexes for the economies of scale and scope, the following are used in this paper 7. The index of overall economies of scale is defined as: O 1-[ lnc(y 1,Y 2 )/ lny 1 + lnc(y 1,Y 2 )/ lny 2 ] (4) If O is positive (negative), overall economies of scale (diseconomies of scale) exist. Moreover, the degree of scale economies becomes progressively smaller (larger) as O moves closer to 0 (1). The economies of scale of each good i is defined as: S 1- lnc(y 1,Y 2 )/ lny i. (5) If S is positive (negative), the economies of scale (diseconomies of scale) of each good i exist. Likewise, there is a seemingly positive relationship between S and the degree of scale economies such that as S moves closer to 0 (1), the degree of scale economies progressively decreases (increases). 9

11 The economies of scope is defined as: C 2 C(Y 1,Y 2 )/( Y 1 Y 2 ) (6) If C is negative (positive), the economies of scope (the diseconomies of scope) between two goods exist 8. Testing for economies of scale and scope, we obtain results expressed in mean values as shown in Table 2. The following can be observed: since the economies of scale, overall or product-specific, are all positive, this proves that the economies of scale exist on average; and since the economies of scope are negative, this shows that the economies of scope exist on average. <Table 2> To discuss in more detail, we analyze four subsample periods: , , , and Table 3 illustrates the results of the analysis of the economies of scale and scope for each electric power company during each period. <Table 3> Several points can be made concerning economies of scale. It is common practice to divide the Japanese power companies into three groups. Based on the estimated economies of scale, we similarly classify power companies into three groups. The first group consists of 10

12 large-scale companies such as Tokyo, Chubu, and Kansai Electric Power operating in the three largest metropolitan areasof Tokyo, Nagoya, and Osaka respectively. The overall-scaleeconomies figures over the period of 1978 to 1998 range from 0.3~0.4 for this group. The intermediate group is made up of companies such as Hokkaido, Chugoku, and Kyushu Electric Power operating in the urban areas of Sapporo, Hiroshima, and Fukuoka. The average figures for the intermediate group over the sample period approximate 0.5. The last group consists of small-scale companies, such as Tohoku, Hokuriku, and Shikoku Electric Power operating in rural areas (the values are larger than 0.6) 9. Although Tokyo Electric Power is by far the largest company in Japan, it still benefits from the presence of economies of scale. Furthermore, the extent of economies of scale in the power industry appears to be fairly steady in the long run (the national average of the value from 1978 to 1998 is approximately 0.5). However, that of power generation rose once in the 1980s and has taken a downward trend thereafter, while that of transmission-and-distribution fell only once in the 1980s and has been rising since. In addition, the scale economies of transmission-anddistribution are clearly larger than those of power generation (the national average ( ) of the value for product-specific-scale-economies are about 0.6 for Y 1 and 0.9 for Y 2 ). This indicates that the bottleneck or essential facility characteristics are stronger in the transmission-and-distribution section than in the power-generation section. Based on the index of scope economies, the electric power companies are classified into three groups. The first group consists of companies that have small economies of scope 11

13 (average values for ( ) exceed -0.1), such as Tokyo and Kansai Electric Power. The next group is made up of companies with intermediate scope economies (average values range from -0.1 to -0.3), such as Hokkaido, Tohoku, Chubu, Chugoku, and Kyushu Electric Power. The last group is comprised of companies exhibiting large scope economies (average values over the sample period are less than -0.5) such as Hokuriku and Shikoku Electric Power. Interestingly, the largest firm, Tokyo Electric Power, still reaps benefits from the economies of scope. It is observed, however, that the economies of scope tend to fall in the long run (the national average have been fluctuating within the range of -0.4 to -0.2). We conclude from the above that since both the economies of scale for each good and the economies of scope exist, the Japanese electric power industry is still naturally monopolistic. In order to verify the hypothesis that the economic bottleneck exists to a high degree in the distribution sector compared to the power generation sector, an analysis of each sector is needed. However, the accounting separation between the two sectors in the Japanese power industry is not easy, and finding effective ways how to do this is a potential subject for future research. It is interesting to note at this point that even if an industry is naturally monopolistic, it may not put up barriers to entry and exit in a contestable market. However, we cannot assume contestability in the Japanese electric power industry since this requires strict conditions, such as the non-existence of sunk costs and the symmetry of demand and cost environments between an incumbent and an entrant. Therefore, it cannot be expected that 12

14 efficiency of resource allocation will be realized automatically just by abolishing the legal monopoly of Japan s electric power companies. IV. Measuring Cost-comparison Coefficients In this section yardstick cost comparison is discussed. It is sometimes pointed out that the yardstick cost comparison of business performance provides strong incentives for executive officers to improve management efficiency 10. We show how to derive costcomparison coefficients with the fixed effects model of panel data analysis in the following section. For cost comparison between firms, there are two methods: (1) marginal cost comparison and (2) average cost comparison. In this paper, we adopt the latter for two reasons. First, the Japanese electric power industry is vertically integrated and we are interested in cost comparison of the joint production process as a whole. In this case, we use an aggregate measure of output to calculate average cost. Second, we obtain the individually specific effects from the panel data analysis, which represent firm-specific fixed costs. To utilize the individually specific effects for the cost comparison, we compare average costs instead of marginal costs. The cost function estimated in Section 3 is broken down into the individually specific effects and a component which we call the standard cost function. If the cost 13

15 function of firm j is defined as C j, the individually specific effect as K j, and the standard cost function as c 0, then we obtain the following formula: C j (Y 1, Y 2 ) =K j +c 0 (Y 1, Y 2 ). Let us assume that j=a,b and K A =0. Since the case of two goods is considered in this paper, the Euclid distance, [(Y 1 ) 2 +(Y 2 ) 2 ] 1/2, between the numerical value of outputs, Y=(Y 1,Y 2 ), is defined as the total output, Y, and the total cost of firm j divided by its total output, C j (Y 1,Y 2 ) / Y j, is considered as the average cost of j, that is, AC j. We understand that such an artificial method of aggregation of units may be problematic. Instead of aggregation, we can adopt a method of calculating the cost-comparison coefficient depending on each output. Otherwise, we can adopt monetary units such as sales for ease of aggregation. The cost-comparison coefficients of firm B in comparison with those of A can be defined as follows: The cost-comparison coefficient with respect to individually specific effects is: = AC A(Y B ) AC B (Y B ) = c 0 (Y B )/ Y B (K B + c 0 (Y B )) / Y B ). (7) The cost-comparison coefficient with respect to economies of scale and scope is: = AC A(Y A ) AC A (Y B ) = c 0(Y A )/ Y A c 0 (Y B )/ Y B. (8) The overall cost-comparison coefficient is: = AC A(Y A ) AC B (Y B ) = c 0 (Y A )/ Y A (K B + c 0 (Y B )) / Y B ) = AC A(Y B ) AC A (Y A ) =. (9) AC B (Y B ) AC A (Y B ) Eq. (7) represents the coefficient of the cost comparison with respect to individually specific effects 11, Eq. (8) represents the coefficient of the cost comparison with respect to the economies of scale and scope 12, and Eq. (9) represents the coefficient of the cost comparison 14

16 integrating both the individually specific effects and the economies of scale and scope 13. See Figure 1, to sum up. <Figure 1> Having defined the cost-comparison coefficients, we analyze the results in more detail by again dividing the whole period into four sub-periods: , , , and Table 4 shows the results for the cost-comparison coefficients of the Japanese electric power companies. It is noted here that the higher the cost-comparison coefficient, the cheaper the electricity production cost. <Table 4> We also observe that the individual effect coefficients,, and the scale-and-scope economy coefficients,, tend to move in opposite directions, and the overall coefficients,, remain relatively steady around 1. If we classify electric power companies into three groups according to and, for the group of large companies including Tokyo, Chubu, and Kansai, is lower than 1, representing a disadvantageous individual effect, while is higher than 1, representing advantageous scale-and-scope economies. For the medium-sized companies such as Tohoku, Chugoku, and Kyushu both and approximate 1. For small companies such as Hokkaido, Hokuriku, and Shikoku, is higher than 1, representing an advantageous individual effect, while is lower than 1, representing disadvantageous scale and scope economies. 15

17 Moreover, by comparing the overall cost-comparison coefficients,, we can carry out a yardstick-type assessment of the Japanese electric power industries. In the case of >1, the average cost is assumed to be low; on the other hand, the case of <1 is associated with high average costs. If we were to base the calculation of cost-comparison coefficients for the period assuming firm A is Kyushu Electric Power, the average cost of Hokkaido is thought to be lower by 40.2%; for Tohoku, lower by 14.4%; for Tokyo, higher by 0.3%; for Chubu, lower by 5.1%; for Hokuriku, lower by 0.2%; for Kansai, lower by 8.8%; for Chugoku, lower by 1.7%; and for Shikoku, lower by 10.7% 14. However, as the numerical values of overall coefficients,, fluctuate yearly, a frequent revision of the assessment is desirable. V. Conclusion Using the fixed-effects model of panel data analysis and estimating the translog cost function of the Japanese electric power industry from 1978 to 1998, we find that all electric power companies still benefit from both scale and scope economies. Second, we introduce two kinds of cost-comparison coefficients for the individually specific effect and scale and scope economies. Unlike in previous studies that adopted complicated econometric models, we utilize a simple framework of the fixed effects model of panel data analysis to propose useful policy guidelines. We leave as future research the task of refining the model and techniques used in this paper. In particular, the following refinements are needed: (1) the 16

18 adoption of a three-output model with power generation, transmission and distribution treated as three separate products; (2) the adoption of a generalized translog cost function such as the Box-Cox transformation; (3) the estimation of the short-term cost function given that capital is a quasi-fixed input and testing for the existence of over-capitalization or undercapitalization; and finally, (4) the estimation of a cost function allowing for regulatory bias and various technical inefficiencies. These are some important issues pointed out in this paper that need to be addressed in future research. 17

19 References Baumol, W.J., J.C. Panzar and R.D. Willig, 1982, Contestable Markets and the Theory of Industrial Structure. Harcourt Brace and Jovanovich. Baltagi, B.H., 1996, Econometric Analysis of Panel Data. John Wiley & Sons. Christensen, L.R. and W.H. Greene, 1976, Economies of Scale in U.S. Electric Power Generation, Journal of Political Economy. 84.4, pp Gilsdorf, K., 1994, Vertical Integration Efficiencies and Electric Utilities: Cost Complementary Perspectives, The Quarterly Review of Economics and Finance. 34.3, pp Goto, M., and T. Sueyoshi, 1998, On the Economies of Scale of Japan s Electric Power Industry (written in Japanese), Koeki Jigyou Kenkyu (Journal of Public Utilities Economics). 50.1, pp Hayashi, F. and T. Inoue, 1991, The Relation between Firm and Q with Multiple Capital Goods: Theory and Evidence from Panel Data on Japanese Firms, Econometrica. 59.3, pp Hsiao, C., 1986, Analysis of Panel Data. Cambridge University Press. Kaserman, D.L. and J.W. Mayo, 1991, The Measurement of Vertical Economies and the Efficient Structure of the Electric Utility Industry, Journal of Industrial Economics. 39.5, pp Kerkvliet, J., 1991, Efficiency and Vertical Integration: the Case of Mine-Mouth Electric Generating Plants, Journal of Industrial Economics. 39.5, pp Koike, N., 1999, An Empirical Analysis of the Yardstick Assessment of the Electric Power Industry (written in Japanese), Koeki Jigyou Kenkyu (Journal of Public Utilities Economics). 51.3, pp Krautmann, A.C. and J.L. Solow, 1988, Economies of Scale in Nuclear Power Generation. Southern Economic Journal, 55, pp Nakanishi, Y. and N. Ito, 1998, On the Economies of Scale in the Electric Power Industry (written in Japanese). The Central Research Institute of Electric Power Industry Report, Y Nelson, R.A. and Wohar, M.E., 1983, Regulation, Scale Economies, and Productivity in Steam-Electric Generation. International Economic Review, 24.1, pp Nemoto, J., Y. Nakanishi and S. Madono, 1993, Scale Economies and Over-Capitalization in 18

20 Japanese Electric Utilities. International Economic Review, 34.2, pp Shinjo, K. 1994, Natural Monopoly and Economies of Scale (written in Japanese). in: M. Uekusa (Ed.) Lectures on the Public Regulation and Industries vol. I, NTT Publication. Torii, A., 1994, Regulation and Company Efficiency (written in Japanese). in: M. Uekusa (Ed.) Lectures on the Public Regulation and Industries vol. I, NTT Publication. Toyama, Y., et al., 2000, Public Utility Industries in Japan. Michigan State University Papers. Wales, T.J., 1977, On the Flexibility of Flexible Functional Forms. Journal of Econometrics, 5, pp Watanabe, H. and M. Kitamura, 1994, The Economies of Vertical Integration in Japan s Electric Power Industry (written in Japanese). The Central Research Institute of Electric Power Industry Report, Y Watanabe, H. and M. Kitamura 1998, Analysis of the Long-term Cost Structure of Japan s Electric Power Industry (written in Japanese). The Central Research Institute of Electric Power Industry Report, Y

21 Notes 1 In August 2000, the Ministry of International Trade and Industry accepted bids from power providers and Diamond Power won a bid, a landmark case for a new entrant to the retail market. 2 There are two models of panel data analysis: the fixed effects and the random effects models (see Hsiao 1986; Baltagi 1996 for details). Briefly, the chief drawbacks of the two models are: the random effects model yields a biased estimator in the case where there is a correlation between the constant term and explanatory variables while in the fixed effects model there are problems in the economic interpretation of individually specific effects and that the degree of freedom in estimation is diminished by dummy variables. If multi-collinearity among variables cannot be avoided and if the economic interpretation of the individually specific effect is relatively easy, such as in the electric power industry, the fixed effects model seems to be more suitable than the random effects model. 3 Previous studies analyzing the natural monopoly properties of the Japanese electric power industry can be briefly summarized as follows: though it is conventionally supposed that Japan s electric power industry exhibits economies of scale and scope, the extent of this has gradually decreased (see Nakanishi and Ito 1987). On the other hand, more recent studies, taking the tendency of overcapitalization into consideration, reveal that the economies of scale would almost disappear in the long-term (see for example Nemoto et al., 1993; Watanabe and Kitamura 1998; Goto and Sueyoshi 1998). For a general and informative discussion about Japanese network utilities, see Toyama The output structure of the electric power industry should initially be divided into three: generation, transmission, and distribution. However, there is a strong correlation between transmission and distribution. As a result, the problem of multi-collinearity occurs and adversely affects the estimates. For this reason, we adopt the two-output model considering transmission and distribution as one output in this paper. In the literature, there seems to be no agreement concerning the combined output of transmission-and-distribution, and various definitions have been discussed. Although Gilsdorf (1994) defines the output of transmission-and-distribution as a product, the difference between companies becomes too large due to the multiplying procedure. In this paper, we define the output of transmission-and-distribution as the geometric mean of transmission and distribution. 5 It is often said that the tendency of over-capitalization exists in the electric power industry and capital is not adjusted to the optimum level. Though not explained in detail here, we estimate the short-term cost function in the case where capital is considered as a quasi-fixed input, besides the long-term cost function, and confirm the tendency of over-capitalization in the Japanese electric power industry. 20

22 6 It may be suitable to use an expression called the economies of vertical integration rather than the economies of scope, since power generation and transmission-and-distribution can be considered as a vertically continuous stage in the production of electric power. See Kaserman and Mayo (1991) for further discussion of vertical economies. 7 See Baumol, Panzar and Willig (1982) for further discussion of the economies of scale-and-scope. 8 Originally, the economies of scope should be judged according to whether or not the sum of each stand-alone cost exceeds the overall cost. However, since we cannot assume output=0 due to the intrinsic nature of the translog cost function, we substitute the weak complementarities of cost for the test of economies of scope. In fact, the weak complementarities are only a sufficient condition for the economies of scope. A device that adopts the generalized translog cost function, such as the Box-Cox transformation, is also a means whereby output = 0 can be set. 9 It should be noted that benefiting from the economies of scale does not necessarily mean producing high output levels, because the economies of scale are influenced by the different input price structures for each firm. And it is because the partial derivatives of outputs on the total cost are negative that the figures for Hokuriku and Shikoku sometimes exceed 1 for several fiscal years. In this respect, our estimation model may not be completely suitable. However, economies of scale still exist in such a case. 10 A yardstick regulation was introduced in January 1996 into the fee schedules of electric power and gas industries by the Agency of Natural Resources and Energy under the umbrella of the then Ministry of International Trade and Industry (now called Ministry of Economy, Trade and Industry). 11 The average cost of firm B for output Y B is AC B (Y B ). When the individually specific effect of firm B is not taken into consideration, namely K B =0, the average cost of B for output Y B is AC A (Y B ). 12 When the individually specific effect of firm B is not taken into consideration, namely K B =0, the average cost of B for output Y B is AC A (Y B ) and the average cost of B for output Y A is AC A (Y A ). 13 The average cost of B for output Y B is AC B (Y B ). When the individually specific effect of firm B is not taken into consideration, namely K B =0, the average cost of B for output Y A is AC A (Y A ). 14 This result is very different from the general belief that the cost per kwh of Hokkaido is much higher than those of others. One reason for this is that the output of transmission-and-distribution becomes very large especially in Hokkaido whose area is very large when we define output to include transmission-and-distribution as well as generation. 21

23 Table 1: The estimation result of translog cost function Variable a1(hokkaido) a2(tohoku) a3(tokyo) a4(chubu) a5(hokuriku) a6(kansai) a7(chugoku) a8(shikoku) a9(kyushu) bl bf blf Coefficient t-ratio -8.53** -6.38** 6.27** 5.65** -5.41** 5.96** -5.47** -5.53** ** 56.96** 25.77** -8.55** Variable blk bfk c1 c2 c11 c22 c12 dl1 dl2 df1 df2 el1 Coefficient t-ratio ** ** 7.56** 2.13** 3.27** 2.80** -2.66** -8.32** 1.91* 4.64** Variable el2 el3 el4 el5 el6 el7 el8 el9 el10 el11 el12 el13 Coefficient t-ratio -5.92** -7.27** -7.18** -7.98** -9.31** ** ** ** ** ** ** ** Variable el14 el15 el16 el17 el18 el19 el20 el21 ef1 ef2 ef3 ef4 Coefficient t-ratio ** ** ** ** ** ** 15.06** ** ** -1.88* -2.97** -4.18** Variable ef5 ef6 ef7 ef8 ef9 ef10 ef11 ef12 ef13 ef14 ef15 ef16 Coefficient t-ratio -4.87** -6.03** -6.38** -7.37** -7.80** -8.11** -7.47** -6.79** -6.06** -6.01** -6.51** -7.19** Variable ef17 ef18 ef19 ef20 ef21 ft1 ft2 fcu Coefficient t-ratio -7.30** -7.79** -7.86** -7.46** -6.67** 9.61** -2.07** -4.53** Note1: Cost-function; adjusted-r 2 =0.99, Durbin-Watson statistic=0.29 Note 2: Labor-share; adjusted-r 2 =0.86, Durbin-Watson statistic=0.34 Note 3 : Fuel-share; adjusted-r 2 =0.91, Durbin-Watson statistic=0.21

24 Table2: The economies of scale and scope (in mean values) Variable Overall economies of scale Economies of scale of Y 1 Economies of scale of Y 2 Economies of scope Coefficient t-ratio 6.09** 15.88** 8.81** -1.76*

25 Table3: The economies of scale and scope Average Overall economies of scale Hokkaido Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Tohoku Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Tokyo Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Chubu Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Hokuriku Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Kansai Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Chugoku Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Shikoku Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Kyushu Economies of scale of Y Economies of scale of Y Economies of scope Overall economies of scale Average Economies of scale of Y Economies of scale of Y Economies of scope

26 Table 4: The cost-comparison coefficients Average (individual effect) Hokkaido (scale-and-scope economies) (comprehensive) (individual effect) Tohoku (scale-and-scope economies) (comprehensive) (individual effect) Tokyo (scale-and-scope economies) (comprehensive) (individual effect) Chubu (scale-and-scope economies) (comprehensive) (individual effect) Hokuriku (scale-and-scope economies) (comprehensive) (individual effect) Kansai (scale-and-scope economies) (comprehensive) (individual effect) Chugoku (scale-and-scope economies) (comprehensive) (individual effect) Shikoku (scale-and-scope economies) (comprehensive) (individual effect) Kyushu (scale-and-scope economies) (comprehensive)

27 Figure 1: The cost-comparison coefficients AC B (Y B ) AC B AC A (Y A ) AC A (Y B ) AC A Y B Y A