Research on explanatory factors to determine
efficiency of water suppliers in Japan using
panel data: focusing on the merger effect on
DEA efficiency
JAPPM FUTURE LEADERs CONFERENCE 2019Feb 29, 2020
（Presenter*） *Akira TOYAMA（Tokyo Institute of Technology）
Tatsuro SAKANO（Tokyo Institute of Technology）

Contents• Introduction• Background• Previous research• Purpose of research• Method• “productivity” and “efficiency”• DEA• Data and variables• Result• Trend of efficiency change from 2007 to 2016
• Effect of merger• Conclusion
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Introduction• Challenges faced by Japanese water industry
Deterioration of facilities
Decrease in income due to population decline
ØIt is necessary to improve efficiency in order to maintain thewater industry• Aims and Assumptions of Concession Law of 2018
Aiming to increase efficiency by①Changing ownership②Inducing mergers to take advantage of scale economy
ØIt is necessary to check these assumptions
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Previous research• Ownership Effect (Abbot and Cohen, 2009)
Ownership structure does not affect the efficiency of watersupplier• Scale Economy (Nakayama,2002, Abbot & Cohen, ibid)
Scale economy works up to the suppliers operating less than
100 thousand subscribersØMerger under the optimal level is desirable, but the ones
beyond that should be avoidedØThis analysis used only cross section data and did notcompare directly the efficiency change after mergers for eachsupplier4

Purpose of research
1. Calculating the efficiency of all the retail water supplier inJapan for 10 years from 2007 to 2016 using DEA, andexamine the general trends of efficiency change for these
10 years
2. Identifying the suppliers which experienced merger during
this period and detect the changes in efficiency aftermerger for each supplier using longitudinal data5

Methodological Problem:
Productivity vs. Efficiency
1. Productivity• defined by output⁄input• measured by estimating production functions or cost functions• It is possible to know whether scale economy works or not fromthe shape of the functions in the industry• However, this approach does not assume inefficiency of suppliers

2. Efficiency• measured by distance from the frontier production function• Stochastic frontier analysis (SFA) and Data envelopment analysis(DEA) are the commonly used techniques• SFA does not separate scale efficiency and agency efficiency
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Two Concepts of Efficiency in DEA
Fig. 1 DEA The case of 1 input and 1 output• Determine efficiency
values with reference tofrontiers composed of themost productive DMUs
(decision making units)

OutputFrontier(CRS)

Frontier(VRS)DMU4• The constant returns toscale model (CRS) and thevaluable returns to scalemodel(VRS)

DMU2apqb

DMU6

DMU3

• CRS: efficiency = ap/ab
VRS: efficiency = aq/ab

DMU1ODMU5Input

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Scale Efficiency and Agency Efficiency• In CRS, efficiency is expressed as the product of VRS efficiency
and Scale Efficiency.
• VRS is a model that eliminates the effect of scale on efficiency,
so VRS efficiency can be interpreted as Agency Efficiency• The ratio of the efficiencies of VRS to CRS can be interpreted
as scale efficiency
CRS efficiency = Scale efficiency X Agency efficiency
CRS efficiency = ap/ab
VRS efficiency (Agency efficiency) = aq/ab
Scale efficiency = ap/aq8Three Domain of Mergers
Output• By using VRS, it is possible todivide the production space
into three domains:DRSCRSD

IRS (increasing return to scale)CRS (constant return to scale)DRS (decreasing return to scale)

BIRS• Economy of scale is expected
to work only for the agencies
positioned in IRS domain

FCA

O

E
Input

Fig. 2 Three Domains of Mergers

9Data and variables
Table 1 The number of retail water suppliers examined
Year

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

Number of 1325
suppliers

1316

1289

1284

1281

1281

1279

1276

1273

1263

(Data Source: Local Government Enterprise Yearbook for the fiscal year 2007-2016)

Table 2 Variables to measure efficiencyOutput Y : annual total volume of water sold (yen)Input X1 (labor): the number of workers (person)
X2 (capital): tangible fixed assets (yen)X3 (other input): sum of variable cost (yen)10Table 3 Annual average of efficiency (2007-2016)
CRS
Year

VRS
Ave.

Std.

Max

Min

Year

Ave.

Std.

Max

Min

2007

0.393

0.143

10.059

2007

0.484

0.185

10.102

2008

0.405

0.144

10.077

2008

0.491

0.186

10.108

2009

0.418

0.146

10.02

2009

0.493

0.184

10.107

2010

0.423

0.147

10.067

2010

0.506

0.188

10.1172011

0.438

0.156

10.044

2011

0.517

0.193

10.087

2012

0.416

0.147

10.001

2012

0.501

0.190

10.07

2013

0.410

0.148

102013

0.497

0.192

10.076

2014

0.432

0.149

10.001

2014

0.508

0.188

10.064

2015

0.443

0.157

10.002

2015

0.517

0.193

10.092

2016

0.434

0.153

10.005

2016

0.523

0.195

10.08411

Fig 3 Annual average of efficiency (2007-2016)
0.600

Efficiency average (CRS)

0.550

Efficiency average (VRS)

0.500
0.450
0.400
0.350
0.300
20072008

2009

2010

2011

2012

2013

2014

2015

2016

Efficiency seems to be increasing year by year12

Table 4 Efficiency of Merger Experienced Suppliers
CRSAll suppliers
After merger
experienced

VRS
1.018

1.014

1.153

1.333

There were 48 cases of merger involving 105 suppliers• the average annual rate of change in the efficiency of all
suppliers for 10 years is 1.018(CRS) and 1.104(VRS)• the efficiency change one year after merger is
1.153(CRS) and 1.333(VRS)Ø positive effects detected on efficiency both for CRS and VRS.
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Findings and Discussions (1)• Both of scale efficiency and agency efficiency worked bymerger.
• However, the latter was larger than the former
Ø Managerial formalization can be a source of thelatter efficiency.
Ø the effect of the formalization is larger than technicalefficiency improvement.
Small scale enterprise
M

L

L
L
L

Large scale enterprise
M

L

L

L

L
L
L
L
L
L

formalize

M

L
L

L
L

L
L
L
L

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Table 5 Domain Change Patterns by Merger
and Corresponding Efficiency Chane Rate
Domain Change
Patterns
IRS-IRSIRS-CRSIRS-DRSDRS-IRSDRS-CRSDRS-DRSCRS-IRSCRS-CRS
CRS-DRS

Number of Suppliers
118450138
002

Efficiency Change Rate after Merger
CRSVRS

1.179
1.094
1.256

0.923
0.875
1.561

0.944
1.069

0.921
1.302

0.640

1.142

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Findings and Discussions(2)• 70 % of merger experience suppliers are positioned in IRSdomain• Actually, CRS efficiencies are larger than 1 for all themergers in this domainØConsidering scale efficiency is to be worked in thisdomain, this result shows most of merger wereconducted as rational decisions• However, not all of VRS efficiencies in this domain are larger
than 1• The largest change of VRS efficiency were observed in thesuppliers whose after- merger position were in DRS domainØImplying that scale of IRS domains is not large enoughfor managerial improvement

16Conclusion• A slight positive yearly trend effect was confirmed• The improvement of the efficiency by merger was
higher than the trend effect of the whole waterindustry-> there is economy scale in Japanese water industry,
and it is possible to increase efficiency by merger• The scale efficiency works only for the suppliers in IRS
domains. Even so, managerial efficiency is considered
to work in DRS domains->the merger in DRS domain is not always decreasing
efficiency
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Thank you for listening.

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