SCALE EFFICIENCY OF THE CITIES IN INDONESIA [622860]

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SCALE EFFICIENCY OF THE CITIES IN INDONESIA
USING DATA ENVELOPMENT ANALYSIS (DEA)

Winarno , Sjafrizal , Nasri Bachtiar , Hefrizal Handra
Faculty of Economics, Andalas University, Padang, Indonesia

Abstract : This study aims to analyze the scale efficiency a nd formulate the efficiency policy implication
of the cities in Indonesia. This study use Data Envelopment Analysis (DEA) method. The results of this
study show that the cities with relatively rather small input and output, in this case could be categorize d
as small cities, tend to be more efficient.The cities with the highest average scale efficiency are in
Sumatra (Cluster I). Their scale efficiency tend to be in decreasing return to scale. The cities in Java
and Bali (Cluster II) also tend to have scale efficiency in decreasing return to scale. Meanwhile, the
cities with lower average scale efficiency are in Kalimantan, Sulawesi, Nusa Tenggara, and Papua
(Cluster III). Their scale efficiency tend to be in increasing return to scale.

Keywords : Scale Effi ciency, Data Envelopment Analysis, Cities, Urban Planning

Introduction

This papers seeks to assess urban economic performance in Indonesia by measur ing scale efficiency of
the cities in Indonesia and formulate the efficiency policy implication of the ci ties in Indonesia. This study
use data envelopment analysis (DEA) method .

The regions appointed as the objects in this study are the 98 cities in Indonesia. The data used were from
2010 -2014, which include the data of Regional Gross Domestic Product (RGDP ) with constant price in
2010 base year of the cities in Indonesia, the data of gross fixed capital formation of the cities in Indonesia,
the data of population size of Indonesia aged 15 years and above working during the last week in the cities
of Indones ia. The data were obtained from Statistics Indonesia .

Literature Review

This study reviews some studies regarding the city efficiency. Halkos and Tzeremes (2010) calculate d the
regional economy efficiency in Greece prefectures by using the Data Envelop ment Analysis (DEA)
method. The calculation was conducted for the economic growth policy of the Greece prefectures based
on the neoclassical growth model by using private and public investment. It also use d employees as the
input and per capita RGDP of the time period of 2003 -2007 as the output (George Emmanuel Halkos &
Tzeremes, 2010 ). Another research by Halkos and Tzeremes (2013) investigate d the rela tionship between
the renewable energy consumption and the efficiency economy in European countries. Data Envelopment
Analysis (DEA) was used to that relationship in 25 European countries in 2010 (George E. Halkos &
Tzeremes, 2013 ). The Halkos and Tzeremes’ research (2013) merely investigate d the economy efficiency
and its relation with renewable energy consumption .Nondo (2014) studie d the technic al efficiency
evaluation in African countries by using DEA and bootstrap approach. His research was conducted in 42
African countries in two stages. In the first stage, Nondo (2014) calculate d the efficiency of the African
countries. In the second stage, a fter the efficiency obtained, he identifies the factors influencing the
efficiency by using government effectiveness, renewable energy, phone usage of 1000 citizens, and
government debt and corr fuption as the variables (Nondo, 2014 ). A sound description was contributed by
Charnes et al (1989) by using Data Envelopment Analysis (DEA) to analyze the economy performance of
the cities in China. They also r einvestigate d the most productive scale size introduced by Banker (1984).
The input variables of the research were labor force, labor fund,and investment. On contrary, the output
variables were the value added of an industry, tax income, and retail sale (Abraham Charnes, Cooper, &
Li, 1989 ). Loikkanen and Susiluoto (2006) stud ied the cost efficiency of basi c welfare service provision in
353 cities in Finland during 1994 -2002. Data Envelopment Analysis (DEA) was used to calculate the city
efficiency (Loikkanen & Susiluoto, 2006 ).

Researches in Indonesia concerning the regional efficiency by using Data Envelopment Analysis (DEA)
have been conducted by some researchers including Tirtosuharto (2009), who perform ed a study to

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measure the regional efficiency of Indonesian provinces before and aft er the decentralization policy
proceeded. The results of the research show that the efficiency rate of the provincial government after the
policy being proceeded was lower than before it had been proceeded. In the study, the input variables were
capital exp enditure and regional operational expenditure, while the output variables were the regional
income and private investment (Tirtosuharto, 2009 ). Following Tirtusuharto (2009), Mokoginta and Wijaya
(2014) also conduct ed a study to measure the efficiency of regional economy management after th e
decentralization and regional expansion policies ensued for 10 years. By using DEA technique, their stud y
concludes that not all of the 27 provinces investigated during 2010 -2011 operate in optimal way.
(Mokoginta & L.Wijaya, 2014 ). The M okoginta’s resea rch attempt ed to fulfill the Tirtosuharto’s (2009) by
adding government role in its production model.

Research Method

The city scale efficiency was calculated by using Data Envelopment Analysis (DEA) method. DEA is a
linear programming based on the performance rate calculation of an efficiency in an organization by using
Decision Making Unit (DMU). The term DMU in DEA may refer to various units, such as banks, hospitals,
units of factories, departments, universities, schools, power stati on, the police, the one roof system office,
department of taxation, prison, and anything that has the operational characteristics (Ramanathan, 2003 ).
DEA is able to solve the limitation in partial ratio or multiple regression analysis . It is a procedure designed
specifically to calculate the relative efficiency of a decision m aking unit (DMU) with its many inputs and
outputs. In the relative efficiency of DEA, DMU is defined as the ratio of the ou tput total compared to its
weighted input. The core of DEA is to determine the weights for each output and input of DMU. The weight
does not have negative value and is universal, which means that each of its sample must use a series of
similar weight to evaluate the ratio (total weighted output/total weighted input) and the ratio cannot be
more than one (total weighted output/total wei ghted input ≤ 1).

The output variable used in this study is RGDP based on the constant price in 2010 (Y1); on the other
hand, the input variable is the data of gross fixed capital formation , which include the procurement ,
production , and purchaseof the capita l goods .The capital goods refer to the goods used for production
process, are durable ,or used for more than one year, such as buildings, machines, and transportation . It
also includes the major improvements that extend the age of or alter the form or capa city of the goods
(X1). Other input variables are the data of the employees, which are the population size working and aged
15 years and above (X2).

There are some models in Data Envelopment Analysis method: CRS model, VRS model, and the
comparison betwe en the CRS and VRS (scale efficiency). The basic model of DEA is the CRS model
introduced by Charnes, Cooper, and Rhodes in 1978. This model uses efficiency size for each decision
making unit (DMU), which is the maximum ratio between the weighted output a nd input. Each weight in the
ratio is determined by limiting the same ratio for each DMU must value less than or equals one (A.
Charnes, Cooper, & Rhodes , 1978 ).This model assumes that the ratio between the addition of the input
and output is the same (constant return to scale). It means that for each x time addition of input, the output
would also increase x time. Another assumption utilized by this mo del is that every city (DMU) operates in
optimal scale. The ratio of output and input would be calculated for each DMU, u’qi/v’x iwhere u is M x 1 is
the output weight and v is N x 1 which is the input weight. To select the optimal weight, the mathematic
equation needed is (Coelli, Rao, Donnell, & Battese, 2005 ) :

), (1)
St
)

u,v

The above equation is a solution for u and v limited to constraint, that the efficiency must be fewer than or
equals one. The problem of the equation is the possibility of infinite number. To prevent it happens, v’xi= 1,
so that:

), (2)
St

,v

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Where there is an alteration fro m u and v to µ, which describes transformation. It is called the multiplier
form of the linear programming. By using duality linear program, the equation can be written in the form of
envelopment:

(3)
St

Where θ is a scalar and λ is I x 1 the constant vector. θ is the efficiency value for the i -th DMU. The result
would fit the θ ≤ 1, 1 indicates the point in the frontier and the DMU becomes technically efficient. The
linear program must be solved for I times for each DMU.

The VRS model was developed by Banker, Charnes& Cooper in 1984. It is the development of C RS
model. This mo del presupposes that area/city would not/would have not operated in the optimal scale.
The assumption of the model is that the ratio between the addition input and output is different (variable
return to scale). It means that the addition input for x time would not cause the output to increase x time; it
may be bigger or smaller than x time.

The VRS formula can be written in the mathematical program as (Coelli et al., 2005 ):

(4)
St

I1
λ = 1 states that the inefficient unit would only be compared to the unit with the same value. In CRS, the
inefficient unit can be compared to the unit which is smaller or bigger than it.

The output oriented VRS model is:

(5)
St

Where I <
<OO, dan
-1 is the proportional increase in outputs that could be achieved by i -th region, with
input quantities held constant.

To determine whether a region is efficient or inefficient, one needs to consider the CRS and VRS models.
CRS assumes the set of the production probabilityas the constant return scale and the CRS value is
named as the global efficiency technique. Contrariwise, VRS assumes the combination of convex from an
area and the VRS value is named as the local pure technique. Providing a region has 100% technical
efficiency in both CRS and VRS, the regio n operates in the maximum scale. However, if the region has
efficient CRS value and lower CRS value, the region operates efficiently in local (and not in the global)
based on the scale efficiency. Therefore, the scale efficiency (SE) is the ratio between t he CRS and VRS,
which can be defined as:

(6)

To analyze the city scale efficiency, the cities are clustered in the data analysis. The cluster intends to
equalize the characteristics o f the regions researched, since the cities in Java are different from the cities
in Sumatra, for example. The three clusters are (Sjafrizal, Winarno, Suhairi & Wau, 2016) :
1. The 34 cities in Sumatra island (Cluster I)
2. The 35 cities in the Java and Bali islan ds (Cluster II)
3. The 29 cities in the Kalimantan, Sulawesi, Nusa Tenggara, Maluku, and Papua islands (Clus

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Results

Table 1 describes the scale efficiency in 2010 – 2014 from the cities in Sumatra (Cluster I). The mean
scale efficiency in the year 2010 is 0 .8726, with Dumai, Lhokseumawe, and Sibolga as the cities with the
highest scale efficiency (score 1). Meanwhile, the lowest scale efficiency isSabang with score 0.3567. In
2011, the mean scale efficiency is 0.8844. The city with the highest scale efficien cy is Sibolga with score
0.9999, while the lowest is Sabang with score 0.4161. In 2012, the mean scale efficiency is 0.8869, with
Sibolga as the city with highest scale efficiency (score 1), and the lowest is Sabang with score 0.3962. The
mean scale effici ency in 2013 is 0.8899. The city with the highest scale efficiency is Bukittinggi with score
0.9975, whereas the lowest is Sabang with score 0.4013. The mean scale efficiency in 2014 is 0.8926,
with Bukittinggi as the city with the highest scale efficiency (score 0.9970), and the lowest is Sabang with
score 0.5106.

Table1
The Descriptive Statistics of Cities Scale Efficiency in Sumatra (Cluster I)
for theTime Period 2010 -2014
Year 2010 2011 2012 2013 2014
Mean 0.8726 0.8844 0.8869 0.8899 0.8926
Median 0.9438 0.9384 0.9368 0.9391 0.9340
Max 1.0000 0.9999 1.0000 0.9975 0.9970
Min 0.3567 0.4161 0.3962 0.4013 0.5106
STDEV 0.1524 0.1277 0.1244 0.1243 0.1108
Source: the data output scale efficiency processed by using MaxDEA

Referring to the mean of each city from 2010 – 2014, it is observed that the highest mean scale efficiency
during 2010 -2014 is Sibolga with the mean score 0.9970. It is followed by Bukittinggi with mean score
0.9968, and TanjungBalai with score 0.9905. The l owest scale efficiency is Sabang with the mean score
0.4162.

For Java and Bali (Cluster II) the mean scale efficiency in 2010 is 0.8417, with Kediri and Sukabumi as the
cities with the highest scale efficiency (score 1). Meanwhile the lowest efficiency sc ale isMojokerto with
score 0.4148. In 2011, the mean scale efficiency is 0.8475. The city with the highest scale efficiency is
Kota Batu with 0.9982, while the lowest one is Magelang with score 0.4307.The mean scale efficiency in
2012 is 0.8405, with Pasur uan as the city with the highest scale efficiency with 0.9981, while the lowest
one is Magelang with 0.3727. In 2013, the mean scale efficiency is 0.8464. The city with the highest scale
efficiency is Pasuruan with score 0.9977, while the lowest one is Mag elang with score 0.4359. In 2014, the
mean scale efficiency is 0.8442. The cities with the highest scale efficiency are Central Jakarta and Kediri
with score 1, whereas the lowest one is Magelang with score 0.4350.

Table 2
The Descriptive Statistics of Cities Scale Efficiency in Java and Bali (Cluster II)
for theTime Period 2010 -2014
Year 2010 2011 2012 2013 2014
Mean 0.8417 0.8475 0.8405 0.8464 0.8442
Median 0.8999 0.9073 0.9054 0.9068 0.9138
Max 1.0000 0.9982 0.9981 0.9977 1.0000
Min 0.4148 0.4307 0.3727 0.4359 0.4350
STDEV 0.1524 0.1552 0.1608 0.1557 0.1594
Source: the data output scale efficiency processed by using MaxDEA

Looking at the mean of each city from 2010 – 2014, it is observed that the highest mean scale efficie ncy
during 2010 -2014 is Kediri with the mean score 0.9973. It is followed by Tegal with the mean score 0.9950,
and Kota Batu with score 0.9944. The lowest mean scale efficiency is Magelang with the mean score
0.4186.

For Kalimantan, Sulawesi, Nusa Tenggar a, Maluku, and Papua (Cluster III) the mean scale efficiency in
2010 is 0.7525, with Bontang and Gorontalo as the cities with the highest scale efficiency (score 1).
Meanwhile the lowest efficiency scale isTual with score 0.3351. In 2011, the mean scale ef ficiency is
0.7411. The city with the highest scale efficiency is Pontianak with 0.9984, while the lowest one is
Tomohon with score 0.3079. The mean scale efficiency in 2012 is 0.7463, with Bontang as the city with the
highest scale efficiency with 0.9989, while the lowest one is Makasar with 0.3122. In 2013, the mean scale
efficiency is 0.7570. The city with the highest scale efficiency is Bontang with score 0.9932, while the
lowest one is Makasar with score 0.2530. In 2014, the mean scale efficiency is 0. 7585. The city with the

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highest scale efficiency is Pontianak with score 0.9941, whereas the lowest one is Makasar with score
0.2200.

Table 3
The Descriptive Statistics of Cities Scale Efficiency in Kalimantan, Sulawesi, Nusa Tenggara,
Maluku, Papua (Clu ster III) for the Time Period 2010 -2014
Year 2010 2011 2012 2013 2014
Mean 0,7525 0,7411 0,7463 0,7570 0,7585
Median 0,7782 0,8087 0,8202 0,8461 0,8284
Max 1,0000 0,9984 0,9989 0,9932 0,9941
Min 0,3351 0,3079 0,3122 0,2530 0,2200
STDEV 0,2103 0,210 8 0,2181 0,2222 0,2316
Source: the data output scale efficiency processed by using MaxDEA

Looking at the mean of each city from 2010 – 2014, it is seen that the highest mean scale efficiency during
2010 -2014 is Bontang with the me an score 0.9965. It is followed by Pontianak with the mean score
0.9932, and Samarinda with score 0.9865. The lowest mean scale efficiency is Tual with the mean score
0.3261.

By using the DEA method, how optimal the production capacity of the DMU (how opt imal the input usage
to produce the output) can be measured and determined. In this case, DMU should have one of the three
conditions of Return to Scale (RTS): Increasing Return to Scale (IRS), Constant Return to Scale (CRS),
and Decreasing Return to Scale (DRS). From the data analysis, it is observed which cities are efficient and
inefficient for each year. The factor technically influencing the inefficiency is the lack of input capacity
usage. It is identified from the RTS value in the increasing return t o scale.

The data analysis result in Sumatra (Cluster I) from 2010 – 2014shows that there are only 4 efficient DMUs .
It is shown in the constant return to scale (CRS). 42 DMUs are in the increasing return to scale (IRS ), while
the other 122 DMUs are in the decreasing return to scale (DRS ). The cities in Cluster I tend to be in the
decreasing return to scale, in which the rise of the input cannot increase the output with the same or larger
value.

On the other hand, the result of the data analysis in Java an d Bali (Cluster II) shows that there are only 4
efficient DMUs in the Return to Scale (RTS) as shown in the constant return to scale (CRS). 39 DMUs are
in the increasing return to scale (IRS ), while the other 130 DMUs are in the d ecreasing return to scale
(DRS) . The cities in Java and Bali (Cluster II) tend to be in the decreasing return to scale, in which the rise
of the input cannot increase the output with the same or larger value.

The result of the data analysis in Kalimantan, Sulawesi, Nusa Tenggara, Maluku, and Papua (Cluster III)
shows that there are only 2 efficient DMUs in the Return to Scale (RTS) as shown in the constant return to
scale (CRS). 113 DMUs are in the i ncreasing return to scale (IRS) , while the other 26 DMUs are in the
decreasing re turn to scale (DRS) . The cities in Cluster III tend to be in the increasing return to scale, in
which the rise of the output is larger than the rise of the input. It is tremendously different from the
circumstance in Java and Bali.

Policy Implication

There are some efforts done to improve the efficiency of the cities in Indonesia, which is to improve the
output (RGDP). The number of the output to be improved can be calculated by using both the CCR and
BCC models as shown in the following tables:

Table 4
The Potential of Efficiency Oriented Output Improvement by Using CRS Method
Cluster Actual RGDP
(000 Rp) The Increase
Potential of
RGDP (000 Rp) The RGDP
Target
(000 Rp) %
Potential
Cluster I
(Sumatra) 14,488,565,430 6,477,484,400 20,966,049,820 44.71
Cluster II (Java and Bali) 65,254,932,480 63,478,766,120 128,733,698,600 97.28
Cluster III (Kalimantan, Sulawesi,
Nusa Tenggara, Maluku, and Papua 13,815,349,480 33,010,173,420 46,825,522,890 238.94
Source: the data outputs processed by MaxDEA

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Table 5
The Potential of Efficiency Oriented Output Improvement by Using VRS Method
Cluster Actual RGDP
(000 Rp) The Increase
Potential of
RGDP (000 Rp) The RGDP
Target
(000 Rp) %
Potential
Cluster I
(Sumatra) 14,488,565,430 2,665,648,720 17,154,214,140 18.40
Cluster II (Java and Bali) 65,254,932,480 26,472,431,850 91,727,364,330 40.57
Cluster III (Kalimantan, Sulawesi,
Nusa Tenggara, Maluku, and Papua 13,815,349,480 15,619,319,500 29,434,668,980 113.06
Source: the data outputs processed by MaxDEA

Efforts from t he central, regional and provincial governments are needed to overcome the low efficiency of
some cities. Other than the policy to increase the output as mentioned previously, the cities with low
efficiency are the ones with mean scale efficiency index bel ow 0.75 during the time period 2010 -2014.
Sumatra has 6 cities fit that category, while Java has 6 cities. Kalimantan, Sulawesi, Nusa Tenggara,
Maluku, and Papua, on the other hand, has 11 cities. The cities with low mean efficiency are located in the
eastern parts of Indonesia. The cities needed to be focu sed on by the governments are:

Table 6
Cities with Low Efficiency (below 0.75)
NO DMU SE Score SE Score SE Score SE Score SE Score Mean
2010 2011 2012 2013 2014 2010 -2014
1 Bandar Lampung 0.7095 0.7118 0.7216 0.7158 0.7087 0.7135
2 Medan 0.6785 0.6878 0.7460 0.7216 0.7468 0.7161
3 Padang 0.7369 0.7329 0.7296 0.7276 0.7227 0.7300
4 Padang Panjang 0.6868 0.6812 0.7187 0.7310 0.7110 0.7058
5 Sabang 0.3567 0.4161 0.3962 0.4013 0.5106 0.4162
6 Subulussalam 0.4909 0.7561 0.7429 0.8029 0.8763 0.7338
7 West Jakarta 0.5763 0.5689 0.5465 0.5348 0.5387 0.5531
8 South Jakarta 0.5968 0.6114 0.5910 0.5917 0.5790 0.5940
9 East Jakarta 0.6687 0.6544 0.6088 0.5815 0.5734 0.6174
10 North Jakarta 0.6919 0.7199 0.6382 0.7031 0.6865 0.6879
11 Magelang 0.4307 0.3727 0.4359 0.4350 0.4186
12 Mojokerto 0.4148 0.5524 0.6412 0.6839 0.6641 0.5913
13 Balikpapan 0.6536 0.5252 0.4304 0.3861 0.3425 0.4676
14 BanjarBaru 0.6960 0.7124 0.7229 0.7439 0.7571 0.7265
15 Bau-Bau 0.5762 0.5890 0.5815 0.6494 0.6694 0.6131
16 Bima 0.5708 0.5765 0.5969 0.6109 0.6301 0.5971
17 Kotamobagu 0.4606 0.4775 0.5004 0.5191 0.5347 0.4985
18 Makasar 0.5869 0.4011 0.3122 0.2530 0.2200 0.3546
19 Palopo 0.6487 0.6487 0.6751 0.6936 0.7128 0.6758
20 Pare-Pare 0.6222 0.6363 0.6544 0.6350 0.6758 0.6447
21 TidoreKepulauan 0.4255 0.4572 0.4878 0.5121 0.5266 0.4818
22 Tomohon 0.3360 0.3079 0.3352 0.3603 0.3672 0.3413
23 Tual 0.3351 0.3526 0.3152 0.3249 0.3030 0.3261
Source: the data output processed by MaxDEA

Conclusion

There are some conclusions drawn from the analysis of the scale efficiency of the cities in Indonesia:
1. The efficient cities are the ones with the not -so-big number of input and output. In other words, they
are the small ci ties.
2. The cities with the highest mean scale efficiency are in Sumatra (Cluster I), followed by the cities in
Java and Bali (Cluster II). Meanwhile, the cities with low mea n scale efficiency are Kalimantan,
Sulawesi, Nusa Tenggara, Maluku, and Papua (Clust er III).
3. The cities in Sumatra (Cluster I) tend to have the scale efficiency in the decreasing return to scale and
so do the cities in Java and Bali (Cluster II). On the other hand, the cities in Kalimantan, Sulawesi,
Nusa Tenggara, Maluku, and Papua ten d to be in increasing return to scale.

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