Global COE Hi-Stat Discussion Paper Series 240

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Consolidation and Scale Economies in
the Japanese Sewerage Industry

Hi-Stat Discussion Paper

Eiji SatohSeptember 2012

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Consolidation and Scale Economies
in the Japanese Sewerage Industry∗
Eiji SATOH†
August 2012

Abstract
This study empirically examines cost reductions in the Japanese sewerage industry through mergers by modeling the costs of sewage disposal.
The cost model is specified in a translog form, and treats capital as aquasi-fixed input. Employing the parameters estimated by the model,
the long-run cost function is derived, which indicates that most sewerage operators should be merged to attain scale advantages. Furthermore,while the cost reductions through actual sewerage mergers are estimatedto be 37.9 billion yen, a counterfactual simulation shows that a more farreaching consolidation could achieve cost savings through scale advantages
amounting to 190 billion yen.

Keywords: consolidation, cost function, cost reduction, scale economies,
sewerage
JEL Classification: L11, L95∗ I have benefited from comments by Noriyuki Doi, Takero Doi, Daiji Kawaguchi, Yukinobu
Kitamura, Sadao Nagaoka, Akira Ogawa, Yosuke Okada, Hiroyuki Okamuro, Satoru Tanaka,
Iichiro Uesugi, and seminar participants at Hitotsubashi University, Nanzan University, andthe 2012 Japanese Economic Association Spring Meeting. Financial support from the Global
Centers of Excellence (G-COE) program “Research Unit for Statistical and Empirical Analysis
in Social Sciences (G-COE Hi-Stat)” at the Institute of Economic Research, Hitotsubashi
University, is gratefully acknowledged.
† Graduate School of Economics, Hitotsubashi University. Address: 2-1 Naka, Kunitachi,
Tokyo 186-8601, Japan. E-mail: ed072002@g.hit-u.ac.jp. Phone: ++81-(0)42-580-7767.

1

Introduction

Although for public utilities such as electricity, gas, water, and sewage disposal,
regional monopolies are frequently justiﬁed, the scale of such monopolistic public
utilities is not always optimal. The optimal scale of public utilities depends on
various geographical and demographic factors, and therefore varies signiﬁcantly
within and between areas and over time. Yet, adjusting the scale of public
utilities to changes in demographic characteristics and the size of the market
takes time and may be impeded by institutional constraints, which may giverise to an inexplicit gap between the actual and the optimal scale of a utility.
This gap, in turn, may result in higher costs than would otherwise be the case.
In the Japanese sewerage industry, the scale of sewerage utilities in urban
regions may not be optimal. In 2004 and 2005, in what is often referred to as“the great Heisei mergers,” Japan experienced a large wave of municipal mergers
that also resulted in the merger of numerous municipal sewerage companies.
The aim of the Municipality Merger Promotion Law, which was the trigger
for the large wave of mergers, was to create public utilities that operate at
an eﬃcient scale. However, there were few mergers involving municipalities indensely populated urban regions, which are the regions that have seen the largest
demographic changes since sewerage systems were ﬁrst developed, so that theactual scale of sewerage operations may not be optimal in these regions. Thismeans that sewerage utilities in densely populated urban regions may fail to
exploit potential cost advantages.
Whether or not the scale of public utilities is optimal depends on the existence of scale economies. However, when it comes to the sewerage industry, theliterature is ambiguous with regard to the existence of scale economies. For example, while Knapp (1978) and Bottasso et al. (2011), examining the sewerageindustry in England and Wales, ﬁnd evidence that scale economies exist in the1industry, Saal and Parker (2000) and Stone and Webster Consultants (2004)
ﬁnd no such evidence. Focusing on developing countries, Nauges and van den
Berg (2007, 2008) and Iimi (2008) ﬁnd that signiﬁcant scale economies exist in
some, but not all developing countries.1 Finally, for Japan, Nakayama (2002),
using a small sample of ﬁrms in the sewerage industry, also ﬁnds no signiﬁcantevidence of scale economies.
The purpose of this study is to examine whether scale economies exist in
the Japanese sewerage industry and to estimate the cost reductions achieved
through mergers of sewerage utilities.2 To this end, a cost model speciﬁed intranslog form is developed that treats capital as a quasi-ﬁxed input. Using
data on Japanese sewerage operators from 1999 to 2008, the translog variable
cost function is then estimated employing Zellner’s (1962) seemingly unrelated
regression method. Furthermore, the long-run cost function based on the estimated short-run variable cost function is computed. Calculated short-run andlong-run scale economies indicate that scale economies exist both in the shortand in the long run.
The next part of the analysis consists of an assessment of the cost reductions
achieved through mergers of sewerage utilities. The results show that the cumulative actual cost reductions achieved through sewerage utility mergers during
the period from 1999 to 2008 amount to 37.9 billion yen, or 2.4% of the expenditure on sewage disposal during the period. The consolidation is generally the
result of municipal mergers involving small towns and villages, which may have
led to an increase in the scale of sewerage utilities.
In a further step, in order to examine the cost advantages through economies
1 Nauges and van den Berg (2008), for instance, find evidence of economies of scale in
Moldova, Romania, and Vietnam, but suggest that there are no significant scale economies in
Brazil.
2 The few studies on the sewerage industry that do exist tend to test only the existence ofscale economies, but none of these estimate the cost reduction achieved through mergers ofsewerage operators.

2

of scale that could potentially be attained, a counterfactual scenario in which
it is assumed that sewerage operators merge within their respective prefectures
is considered. The cost reductions that could have been achieved through thesecounterfactual mergers amount to 190 billion yen, or 12% of expenditure on
sewage disposal in 2008. This result suggests that sewerage utilities in neighboring municipalities should cooperate in order to reduce their costs.
The remainder of this paper is organized as follows. Section 2 provides a brief
overview of the Japanese sewerage industry. Section 3 presents the theoreticalframework employed, while Section 4 describes the dataset. Section 5 thenprovides the speciﬁcation of the short-run variable cost function and derives thelong-run cost function from the estimated variable cost function. Next, Section
6 examines the cost reductions resulting from actual mergers in the sewerageindustry and provides the results of the simulation exercise. Finally, Section 7
concludes.

2

Industry Background

2.1

Types of sewerage systems

Sewerage operators in Japan provide their services for certain areas and purposes. Figure 1 depicts the range of services provided by sewerage operators.
Sewerage systems can be broadly distinguished according to whether or notthey are governed by the Sewerage Law. The Sewerage Law divides seweragesystems into ﬁve categories: urban storm drainage systems, regional seweragesystems, sewerage systems for industrial wastewater control, sewerage systems
for environmental protection, and municipal sewerage systems.3 Urban storm
drainage systems mainly perform rainwater drainage outside the coverage area
3 Sewerage utilities not governed by the Sewerage Law include individual sewage disposal
utilities such as septic tanks.

3

Figure 1: The structure of the Japanese sewerage industryof municipal sewerage systems. Regional sewerage systems focus only on ﬁnal
sewage treatment. The other sewerage systems can be distinguished in terms of
their main service areas. When sewage from industrial plants makes up morethan two thirds of the total sewage in a service area, the sewerage system isclassiﬁed as a sewerage system for industrial wastewater control, although suchsewerage systems also remove and treat sewage from households living in theservice area. Sewerage systems for environmental protection aim at protecting
the environment within nature parks and remove and treat sewage from households within nature parks. The coverage area of municipal sewerage systems is
restricted to urban areas and is separate from the coverage areas of sewerage systems for industrial wastewater control and sewerage systems for environmental
protection. Municipal sewerage systems can consign ﬁnal sewage treatment toregional sewerage systems. This study focuses on municipal sewerage systems.

4

2.2

Sewerage and urban planning

Sewerage forms part of urban infrastructures and has been developed based on
the following two laws. The ﬁrst is the Act on Emergency Measures Concerning
the Construction of Sewerage Systems, which was in eﬀect from 1967 to 2003.
The act promoted the speedy development of sewerage, because the developmentof sewerage lagged behind that of other urban infrastructure during the periodof rapid economic growth. Then, in 2004, with the sewerage infrastructure
fully developed, the Act on Priority Plan for Social Infrastructure Development
was put in place, replacing the Act on Emergency Measures Concerning theConstruction of Sewerage Systems. This second act aims at promoting thedevelopment of sustainable urban infrastructures. ince urban plans under these
two acts are ﬁve-year plans, sewerage projects have been based on these ﬁve-yearplans.4

2.3

Municipal mergers and the consolidation of sewerage
operators

Figure 2 depicts he number of municipal mergers as well as mergers of sewerage
operators from 1999 to 2008. The number of both municipal and sewerage
operator mergers increased sharply after 2003 and peaked in 2005. After 2005,
the number of municipal mergers fell back to levels somewhat below those seen
in 2003, resulting also in a drop in mergers of sewerage operators.

4 The construction of new sewerage infrastructure typically takes at least a few years. Basedon quinquennial sewerage projects, sewerage operators need to conduct land surveys, makedetailed plans for building sewer pipes, work out a budget, and then lay the pipes. Finally,
individual households need to be connected to the sewer pipes.

5Figure 2: Number of municipal mergers and sewerage operator mergers, 19992008
1000

Municipal
mergers

100

Sewerage
operator
mergers
10

1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Data source: Local Public Enterprise Yearbook.

3

Model

3.1

Short-run and long-run cost functions

In order to examine the cost structure of sewerage utilities in Japan, a short-run
equilibrium model is employed. Sewerage utilities form part of the urban infrastructure and the capital used in the sewerage industry is of a ﬁxed nature andis subject to urban planning, meaning that capital input is not instantaneously
adjustable to the desired level.
The short-run equilibrium model is used to analyze the cost structure ofsewerage operators by estimating the associated cost function. Each operator
is assumed to choose the amount of labor and capital that minimizes the costof disposing of a given amount of sewage, y, where capital is assumed to bea quasi-ﬁxed input restricted to a certain level, K̄. An operator’s short-run

6variable costs therefore are represented by

V C = V C(y, w; K̄, Z),

where w is the wage rate and Z is a vector of control variables. The short-run
cost function is the sum of short-run variable costs and ﬁxed costs,

ST C(y, w, r; K̄, Z) = V C(y, w; K̄, Z) + rK̄,

where r is the user cost of capital.
The long-run cost function is the lower envelope of the short-run cost function (Varian, 1992). Let K ∗ be the optimal choice of the capital level at output
level y, so that the ﬁrst order condition is as follows:
∂ST C
∂V C
=
+ r = 0.
∂K
∂K

(1)

Since V C(y, w; K ∗ , Z) is the long-run optimal choice of the variable factors, thelong-run cost function is given by
LT C = V C(y, w; K ∗ , Z) + rK ∗ .

(2)Hence, the relationship between the short-run and long-run cost function is
LT C = ST C(y, w, r; K ∗ , Z).

3.2

Economies of scale

Scale economies are frequently measured by the elasticity of costs with respect to
output, which in the case here is the proportional change in costs resulting fromthe proportional change in the sewage disposal amount. Following Christensen
7and Greene (1976), the extent of scale economies is deﬁned as unity minus thecost elasticity. According to this deﬁnition, short-run scale economies are givenby

SSE := 1 −∂ log(ST C)∂ log(V C)=1−.
∂ log(y)∂ log(y)(3)

Similarly, long-run scale economies are given by

LSE := 1 −∂ log(LT C).
∂ log(y)(4)

If SSE (LSE) is positive, the sewerage operator exhibits positive scale economies
in the short run (long run). If SSE (LSE) is negative, scale diseconomies inthe short run (long run) are present. Furthermore, both SSE and LSE are inpercentage terms.

3.3

Minimum eﬃcient scale

The minimum eﬃcient scale (MES) is deﬁned as the level of output at which
the average cost is minimized. When y ∗ is MES, the following is satisﬁed:
d
dy

(

LT C
y

)
= 0.

(5)

If y < y ∗ , average costs are declining to the left of y ∗ , so that
d
dy

4

(

LT C
y

)
≤ 0.

Data

The yearly data used for the analysis are mainly taken from the 1999 to 2008
editions of the Local Public Enterprise Yearbook (Chiho Koei Kigyo Nenkan)
8

published by the Ministry of Internal Aﬀairs and Communications. The Yearbook contains data on the ﬁnancial and managerial accounts of sewerage operators. However, for most sewerage operators, data on capital stock are notavailable.5 Following Garcia and Thomas (2001) and Nauges and van den Berg(2008), the length of sewer pipes under the control of a particular operator istherefore used as a proxy for its capital stock.
Next, information on the rental price of capital is obtained from the Japan
Industrial Productivity (JIP) Database 2011. The JIP Database contains nominal rental price data not only for sewage disposal services but also for otherpublic services, such as public waste disposal services, port and water traﬃccontrol, airport and air traﬃc control, and public administration.
In order to adjust these data for inﬂation, three additional sets of data wereused. The ﬁrst is gross domestic expenditure from the National Accounts ofJapan (Cabinet Oﬃce, Government of Japan) to adjust annual operation andmaintenance costs for sewage treatment. The second set of data consists of real
wage indices from the Monthly Labour Survey (Ministry of Health, Labour andWelfare) to adjust labor expenses, while the third set consists of investment
goods indices from the Price Indexes Quarterly (Bank of Japan) to adjust thenominal rental price of capital.
After deleting observations with missing or implausible values, the resulting
panel dataset contains 11,199 observations. A summary of the deﬁnitions ofvariables and their basic statistics is provided in Table 1.

5 Most sewerage operators are not governed by the Local Public Enterprise Act and employ
an accounting system that does not clearly state capital account balances.

9

Table 1: Basic statistics and deﬁnition of variables
Variablelog(V C)

Mean
12.22

S.D.
1.24

log(y)

7.53

1.69

log(w)
log(K̄)log(Dens)log(P ump)

8.20
4.79
3.45
0.004

0.67
1.19
0.67
0.045

r

68.31

15.85

Definition
Logarithm of annual operation andmaintenance costs for sewage
treatment (¥1,000)
Logarithm of sewage disposal amountper year (1,000m3 )Logarithm of wage rate (¥1,000/person)
Logarithm of sewer pipe length (km)Logarithm of population density (person/ha)
Logarithm of the density of pumping
stations (no./ha)Rental price of capital (¥1,000)

Data sources: JIP Database 2011, Local Public Enterprise Yearbook, National Accounts ofJapan (SNA), Monthly Labour Survey, and Price Indexes Quarterly.
Notes: The wage rate is defined as labor expenses divided by the total number of employees.
Since many sewerage operators have no pumping stations, one is added to the number ofpumping stations per hectare before calculating the logarithm.

5

Cost Estimation

5.1

Speciﬁcation

Following Christensen et al. (1973), a translog variable cost function, which is a
ﬂexible function in the sense that it provides a second-order linear approximation
to any cost function, is speciﬁed:log(V Cit ) = α0 +∑j
αj log(Xit
)+

j

1∑
h
k
αhk log(Xit) log(Xit) + ϵit ,
2

(6)

h,k

where X is a vector consisting of sewage disposal amount y, wage rate w, quasiﬁxed capital stock K̄, population density Dens, and the density of pumping
stations in the coverage area, P ump. In addition, linear homogeneity in input
factor prices is assumed, i.e., αhk = αkh .
Furthermore, a convenient feature of the cost function is that the derived
input demand functions can be easily computed by partially diﬀerentiating thecost function with respect to the input prices, known as Shephard’s lemma

10(Shephard, 1953). In the translog cost function, Shephard’s lemma is represented as follows:∑
wit Lit∂ log(V Cit )hαhw log(Xit),== αw +
V Cit∂ log(wit )(7)hwhere Lit is the labor input of sewerage operator i in year t.

5.2

Estimation results: short-run variable cost function

The next step is to estimate the translog variable cost function (6) along withthe cost share equation (7).6 Following the traditional industrial organization
literature (e.g., Nerlove, 1963, and Christensen and Greene, 1976), the set ofthese equations is estimated using seemingly unrelated regression employing
Zellner’s (1962) technique.
Table 2 presents the estimation results for two diﬀerent speciﬁcations. Speciﬁcation (6.1) employs the explanatory variables introduced above, while speciﬁcation (6.2) drops log(P ump) and cross-terms containing log(P ump) from theexplanatory variables.7 The two diﬀerent speciﬁcations yield virtually identical results. The discussion below therefore focuses mainly on the results for
speciﬁcation (6.1).
Looking at the estimation results, the ﬁrst-order and second-order coeﬃcients on the sewage disposal amount are positive and signiﬁcant. This result
indicates that the short-run variable cost function is monotonically increasingin the sewage disposal amount, which is consistent with economic theory, whichsuggests that cost functions are usually monotonically increasing in output.
6 An often used specification test is the Breusch-Pagan test for independent equations(Breusch and Pagan, 1980). The Breusch-Pagan test statistic is significant at the 1% level,
indicating that the correlation of the residuals in equations (6) and equation (7) is not zero.
7 The reason is twofold. First, because many sewerage operators have no pumping stations,
it was necessary to add one to the number of pumping stations per hectare to take thelogarithm and obtain log(P ump). And second, the cross terms with log(P ump) are notsignificant.

11

Table 2: Estimation results of the short-run variable cost function
Variableconst.
log(y)
log(w)
log(Dens)log(P ump)
log(K̄)(log(y))2(log(w))2(log(Dens))2(log(P ump))2(log(K̄))2log(y) log(w)log(y) log(Dens)
log(y) log(P ump)
log(y) log(K̄)
log(w) log(Dens)log(w) log(P ump)
log(w) log(K̄)
log(Dens) log(P ump)
log(Dens) log(K̄)
log(P ump) log(K̄)

(6.1)
Coef.
(S.E.)
6.696∗∗∗ (0.197)
0.164∗∗(0.065)0.085∗∗(0.035)0.199∗∗(0.088)−6.508∗(3.549)0.431∗∗∗ (0.083)
0.081∗∗∗ (0.007)
0.057∗∗∗ (0.004)
0.018∗(0.011)−1.691∗∗∗ (0.392)−0.063∗∗∗ (0.013)−0.051∗∗∗ (0.008)
0.010(0.009)0.746(0.551)0.024∗∗∗ (0.008)−0.023∗∗(0.011)0.108(0.361)0.008(0.011)0.823(0.547)−0.029∗∗(0.012)−0.161(0.748)

(6.2)
Coef.
(S.E.)
6.660∗∗∗ (0.197)
0.172∗∗∗ (0.065)
0.079∗∗(0.035)0.207∗∗(0.087)0.437∗∗∗
0.081∗∗∗
0.058∗∗∗
0.021∗(0.083)(0.007)(0.004)(0.011)−0.061∗∗∗−0.050∗∗∗0.006(0.013)(0.008)(0.009)0.025∗∗∗−0.022∗∗(0.008)(0.011)

0.005(0.011)−0.027∗∗(0.012)

Notes: Specification (6.1) employs the explanatory variables introduced in the text. Specification (6.2) drops log(P ump) and cross-terms containing log(P ump) from the explanatory
variables. ∗∗∗ , ∗∗ , and ∗ denote significance at the 0.01, 0.05, and 0.10 level respectively. The
number of observations is 11,199.

5.3

Estimation results: long-run cost function

Next, the long-run cost function is derived from the estimated short-run variable
cost function. Once the parameters of the short-run variable cost function are
estimated, equation (1) can be solved with respect to K to obtain the long-run
cost function. However, in the translog functional form, it is impossible to derivea closed-form solution of equation (1) for K. Therefore, equation (1) is solved
numerically using the Newton-Raphson method. Using the numerical solutionof equation (1), the long-run cost function is then obtained from equation (2).
Table 3 presents the results for the estimated ﬁrst-order coeﬃcients of the12Table 3: Estimated ﬁrst-order coeﬃcients of the long-run variable cost function
Variableconst.
log(y)
log(w)
log(Dens)log(P ump)

Coef.
8.003
0.387
0.155
−0.065−7.991(6.1)(Std. Err.)(0.073)(0.012)(0.003)(0.014)(0.079)

Coef.
8.065
0.400
0.123
−0.042(6.2)(Std. Err.)(0.069)(0.012)(0.002)(0.013)

Notes: Specification (6.1) employs the explanatory variables introduced in the text. Specification (6.2) drops log(P ump) and cross-terms containing log(P ump) from the explanatory
variables.

long-run variable cost function. The absolute value of the ﬁrst-order coeﬃcientson the sewage disposal amount in the long-run variable cost function is greaterthan that in the short-run variable cost function. This result indicates that theincrease in costs resulting from a small increase in the sewage disposal amountis greater in the long run than in the short run. The coeﬃcient on log(Dens) in
the long-run cost function is negative, although that in the short-run variable
cost function is positive. The reason for this is that although capital stock is
ﬁxed in the short run, it is variable in the long run.

5.4

Measuring scale economies

The estimated cost parameters can be used to measure the extent of scaleeconomies. Using the estimated cost parameters obtained in speciﬁcation (6.1)
in Tables 2 and Table 3, short-run and long-run scale economies are calculated.
The results indicate that while the average of short-run scale economies is 0.49,
the average of long-run scale economies is 0.39. Testing the null hypothesis thatthe calculated scale economies are zero, the hypothesis can be rejected at the
1% signiﬁcant level. This means that scale economies exist both in the shortand in the long run. The absolute value of the extent of scale economies isgreater in the short run than in the long run. This is consistent with the view13

that sewerage utilities should be subject to increasing returns to scale, given thelarge ﬁxed costs involved.
This result is in contrast with the one obtained by Nakayama (2002), whofound no evidence of signiﬁcant scale economies. A possible reason for the diﬀerent results is that Nakayama used panel data consisting of only 270 observations
covering the period from 1991 to 1999 and limited to relatively large-scale sewerage operators, and directly estimated the long-run cost function. However,sewerage operators cannot instantaneously adjust their capital inputs to thedesired level. Direct estimation of the long-run cost function using yearly data
ignores that sewerage operators are subject to urban planning regulations.

5.5

Measuring minimum eﬃcient scale

Next, the MES for the sewage disposal amount is estimated. Having estimatedthe parameters of the long-run cost function, equation (5) can be solved to obtainthe MES. However, as above, in the translog functional form, it is impossible
to derive a closed-form solution of equation (5), so that equation (5) again issolved numerically employing the Newton-Raphson method. Then, using thenumerical solution of equation (5), the MES is obtained.8
The average estimated MES for sewage disposal amounts is 237.6 million m3 .
While Osaka, Nagoya, Yokohama, and the 23 special wards of Tokyo exceeded
this ﬁgure in 2008, the amount of sewage disposal in all other municipalities
fell well below it and the average for all municipalities was only 9.5 million m3 .
This means that the scale of most sewerage operators is only a fraction of theestimated MES.
This result indicates that most operators outside the major metropolises
8 The long-run average cost function is not always U-shaped. If it is not U-shaped, the
MES for the sewage disposal amount does not take a positive value. However, as indicatedabove, scale economies are positive and significant, meaning that the long-run average costfunction is U-shaped.

14

should merge with neighboring operators to attain scale advantages. In thesewerage industry, capital costs, especially the costs of laying sewer pipes, arequite high, while marginal costs associated with sewage disposal are comparatively small. The merged entities could achieve economies of scale and reduce
ﬁxed costs by closing duplicate departments or operations.

6

Consolidation among Sewerage Operators

This section assesses actual and potential cost reductions through the consolidation of sewerage operators. The ﬁrst part of the analysis focuses on the actual
consolidation of sewerage operators as a result of municipal mergers. The second part then examines the implications of a more far-reaching counterfactual
consolidation to attain scale advantages.

6.1

Cost reductions through actual mergers

This subsection examines cost reductions achieved through the actual consolidation of sewerage operators. A complicating factor in this context is thatthe amount of sewage produced and disposed in any given service area ﬂuctuates from year to year. This means that the amount of sewage disposed of by
post-merger entities is not necessarily simply the sum of the amount of sewage
disposed of by individual pre-merger entities. Because data on the amountof sewage disposal in a particular pre-merger service area after the merger hastaken place are not available, it is therefore necessary to assume that any changes
in sewage disposal amounts aﬀect all pre-merger service areas of a merged entity in equal proportion. Based on this assumption, the reduction in long-run
average costs through actual sewerage mergers can be computed as follows:y′yhdyh + yk

(

LT Ch
yh

)

y′
+ yk
d
yh + yk
15

(

LT Ck
yk

)
.

(8)

where y ′ is the amount of sewage disposed of by the newly merged operator
following the merger between sewerage operators h and k.
Using the estimated cost parameters, equation (8) is calculated for the 192
mergers that took place between 1999 and 2008. The average decrease in longrun average costs as a result of the mergers is 15,000 yen/1,0003 or 8.6% to173,900 yen/1,000m3 . The total cost reduction resulting from the 192 mergers
thus is estimated to be 37.9 billion yen, which is 2.4% of the total current
expenditure on sewage disposal in Japan.9 This result indicates that the 192
mergers achieved a slight cost reduction.
The likely reason that the cost reduction was relatively minor is that theentities created by many municipal mergers were still comparatively small-scale.
The municipal mergers that took place between 1999 and 2008 mainly involved
small towns or villages that merged or were absorbed into larger cities and there
were few mergers involving municipalities in densely populated urban regions.
As a consequence, the consolidation of sewerage operators observed during thisperiod resulted only in relatively minor changes in operational scale.

6.2

Counterfactual simulation

To examine the potential scale advantages that could be attained, this subsection considers the counterfactual case in which sewerage operators merge within
their respective prefectures. Computing wage rates at the post-merger entities
as the weighted average of the wage rates of each pre-merger operator, where thesewage disposal amount of each operator is used as the weight,10 the advantagesof scale can be calculated employing the following procedure. The procedure
starts by focusing on the largest sewerage operator in a prefecture and merges
this with neighboring sewerage operators as long as its long-run average cost
9 In 2008, the total current expenditure on sewage disposal in Japan was 1.58 trillion yen.
10 Calculating post-merger wage rates by simply using the wage rate of the largest pre-merger

operator in the post-merger entity yields virtually identical results.

16

decreases as a result of such mergers. The order in which sewerage operatorswith which the largest operator is to be merged is determined by which operator
provides the most cost reductions. Once such mergers no longer provide any
cost reductions, the focus shifts to the largest remaining (non-merged) operator
in the prefecture, for which the procedure is repeated. The overall procedure isrepeated until no sewerage operators remain whose long-run average costs canbe reduced through mergers.

6.3

Cost reductions in the counterfactual simulation

Using the estimated cost parameters and data for the year 2008, the implications of the counterfactual merger of sewerage operators are examined. For
illustration, Figure 3 presents the geographical pattern of sewerage services inTokyo Prefecture after the counterfactual merger. The two municipalities on
the far left indicated in white, Hinohara and Okutama, have never operated amunicipal sewerage system. Next, the operators in the areas shaded in green
and in red were merged into two large-scale operators covering the geographic
areas indicated. Finally, the sewerage operators in the municipalities of Hinode,
Inagi, and Mizuho, and the 23 special wards of Tokyo, were not merged in the
counterfactual simulation.11
Table 4 presents the results of the simulation, showing by how much thenumber of sewerage operators would decrease and the change in costs this would
bring about. Speciﬁcally, there were 1,058 sewerage operators in Japan in 2008,of which 136 remained ”independent” even after the counterfactual consolidation, while 922 were merged. The consolidation among these 922 operators leads
to a drastic fall in their number to 141 operators.
11 If the two merged large-scale operators were merged with Hinode, Inagi, or Mizuho, theirlong-run average cost would increase. Moreover, the scale of the 23 special wards of Tokyo
exceeds their estimated MES, so that their long-run average cost would also increase as aresult of a merger with neighboring sewerage operators.

17

Figure 3: Geographical pattern of sewerage services in Tokyo Prefecture after
the counterfactual consolidation

Notes: The municipalites of Hinohara and Okutama on the far left (in white) have neveroperated municipal sewerage utilities. The operators in the remaining municipalities weremerged into two large-scale operators, indicated in green and red. The severage operators ofthe municipalities of Hinode, Inagi, and Mizuho, and the 23 special wards of Tokyo were notmerged in the counterfactual scenario.

The resulting long-run cost reduction is quite dramatic. The average decrease in long-run average costs as a result of the counterfactual mergers is
93,900 yen/1,000 m3 or 42.9% to 218,700 yen/1,000m3 . The sum of long-run
total costs after the counterfactual mergers is 722.7 billion yen, meaning thatthe total cost reduction through the counterfactual mergers is 190 billion yen,
12% of the total current expenditure on sewage disposal in Japan.

7

Concluding Remarks

This study examined cost reductions as a result of mergers among sewerage
operators in Japan. Using data on Japanese sewerage operators from 1999
to 2008, translog variable cost functions which regard capital as a quasi-ﬁxed

18

Table 4: Estimated costs before and after the counterfactual consolidation

No. of sewerage operators
Avg. of long-run average costs (1,000 yen/1,000m3 )Sum of long-run total costs (billion yen)

Before
922
218.7
722.7

After
141
124.8
532.7

Notes: The result does not include sewerage operators which were not merged in the counterfactual scenario. The long-run costs are calculated using the estimated parameters from
specification (6.1) in Tables 2 and 3.

input are estimated. Employing the parameters estimated using the model, thederived long-run cost function indicates that most sewerage operators shouldbe merged to attain scale advantages. Furthermore, while the cost reductions
achieved through the actual consolidation of sewerage operators that took place
between 1999 and 2008 amount to 37.9 billion yen, the counterfactual simulation
showed that a more far-reaching merger to attain scale advantages would yieldcost reductions of a further 190 billion yen. This result suggests that sewerageutilities in neighboring municipalities should cooperate in order to reduce theircosts.
Finally, some shortcomings of this study should be mentioned. First, thecapital stock measured here consists only of sewer pipes and does not include
ﬁnal sewage treatment plants. Sewerage utilities can consign ﬁnal sewage treatment to regional sewerage utilities. This means that sewerage utilities stand ina vertical relationship to each other. f, as a result of consolidation, ﬁnal sewage
treatment plants are combined and closed, there may be changes in such vertical
relationships, which may have cost implications not considered in this study.
Second, the analysis may have underestimated cost reductions through theactual mergers of sewerage operators. The long-run cost curve is likely to haveshifted following the mergers. However, sewerage operators would have been
unable to instantly adjust their labor and capital, because sewerage projects

19are typically based on ﬁve-year plans. This means that during the observation
period sewerage operators still would have been in transition to the new long-run
equilibrium and had not fully minimized their costs.
Finally, cost reductions through mergers depend on changes in wage rates.
This study focuses on scale advantages and assumes that wage rates after mergers are the weighted average wage rates of pre-merger operators, where theamount of sewage disposal prior to the mergers is used as weights. However,mergers might result in a considerable drop in wage rates, leading to more drastic cost reductions.

20

References
Bottasso, A., M. Conti, M. Piacenz, and D. Vannoni (2011), “The Appropriateness of the Poolability Assumption for Multiproduct Technologies:
Evidence from the English Water and Sewerage Utilities,” International
Journal of Production Economics, Vol. 130, No.1, pp.112-117.
Breusch, T. S. and A. R. Pagan (1980), “The Lagrange Multiplier Test and
Its Applications to Model Speciﬁcation in Econometrics,” Review of Economic Studies, Vol. 47, No. 1, pp. 239-253.
Christensen, L. R. and W. H. Greene (1976), “Economies of Scale in U.S. Electric Power Generation,” Journal of Political Economy, Vol. 84, No.4 , pp.
655-676.
Christensen, L. R., D. W. Jorgenson, and L. J. Lau (1973), “Transcendental
Logarithmic Production Frontiers,” Review of Economics and Statistics,
Vol. 55, No.1, pp. 28-45.
Garcia, S. and A. Thomas (2001), “The Structure of Municipal Water Supply
Costs: Application to a Panel of French Local Communities,” Journal of
Productivity Analysis, Vol. 16, No. 1, pp. 5-29.
Iimi, A. (2008), “(UN)Bundling Public-Private Partnership Contracts in The
Water Sector: Competition in Auctions and Economies of Scale in Operation,” World Bank Policy Research Working Paper ♯ 4459.
Knapp, M. (1978), “Economies of Scale in Sewage Puriﬁcation and Disposal,”
The Journal of Industrial Economics, Vol. 27, No. 2, pp.163-183.
Nakayama, N. (2002), “The Cost Structure of the Japanese Sewage System”(Gesuido-jigyo no Hiyou-Kozou), Journal of Public Utility Economics (Koeki
Gigyo Kenkyu), Vol. 53, pp. 23-31 (in Japanese).
21

Nerlove, M. (1963), “Returns to Scale in Electricity Supply,” in C. Christ(ed.), Measurement in Economics: Studies in Mathematical Economics
and Econometrics in Memory of Yehuda Grunfeld, Stanford: Stanford
University Press.
Nauges, C. and C. van den Berg (2007), “How ‘Natural’ are Natural Monopolies
in the Water Supply and Sewerage Sector? Case Studies from Developing
and Transition Economies,” World Bank Policy Research Working Paper♯ 4137.
Nauges, C. and C. van den Berg (2008), “Economies of Density, Scale and Scopein the Water Supply and Sewerage Sector: A Study of Four Developing
and Transition Economies,” Journal of Regulatory Economics, Vol. 34,
No. 2, pp. 144-163.
Saal, D. and D. Parker (2000), “The Impact of Privatization and Regulation on
the Water and Sewerage Industry in England and Wales: A Translog Cost
Function Model,” Managerial and Decisions Economics, Vol. 21, No. 6,
pp.253-268.
Shephard, R. W. (1953), Cost and Production Functions, Princeton: Princeton
University Press.
Stone and Webster Consultants (2004), “Investigation into Evidence for Economies
of Scale in the Water and Sewerage Industry in England and Wales, ” Report Commissioned and Published by the Oﬃce of Water Services.
Varian, H. (1992), Microeconomics Analysis (third edition), New York: W. W.
Norton.
Zellner, A. (1962), “An Eﬃcient Method of Estimating Seemingly Unrelated
Regressions and Tests for Aggregation Bias”, Journal of the American

22Statistical Association, Vol. 57, No. 298, pp. 348-368.

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