View of Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment Analysis dan Stochastik Frontier Analysis
Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment Analysis dan Stochastik Frontier Analysis
Marthen Sengkey*
Fakultas Ekonomi Universitas Klabat
The study employs the three-stage banking models to investigate the performance of 26 state banks in Indonesia from 1994 to 2004. Data envelopment analysis (DEA) results indicate that the average efficiency of state banks was 38.3 percent and deteriorated when the financial crisis struck Indonesia in 1997. Using stochastic frontier analysis (SFA) method, findings suggest that, on average, banks obtained 62.8 percent efficiency. Findings also suggest that banks’ technical inefficiency is affected significantly by government intervention, location, and ownership. Finally, state banking performance was tested by correlating the DEA and SFA models and found no statistically significant correlation. Reported new findings of this paper are additions to banking efficiency literature.
Key words: DEA, state banks, Indonesia, performance, SFA
*corresponding author
INTRODUCTION
Government banks are sometimes appallingly inefficient; in the absense of competitions, private This study used organization theories to
banks may be just as bad. Further, increasing develop such a framework and used that framework to
competition can lead to financial instability, crisis, and examining the efficiency performance of regional
public bailout. In contrast, banking regulations in development banks in Indonesia during 1994 through
some countries are rigorously enforced; financial 2004. This theoretical framework was based on
nurture internationally competitive theories of state banking, bank management, financial
policy
can
industries; and some governments own banks that are performance (bank balance sheet; financial ratio
profitable and prudent.
analysis; capital adequacy), and productive-efficiency State banks will need to undergo sweepong theory and inefficiency.
reforms in this new competitive environment, and so State Banking Theory. Banks are among the
will lose significant market share. In Korea, Taiwan, most important financial institutions in the economy. China Malaysia, Singapore, Indonesia, and India, They are the principal source of credit (loanable funds) state-owned banks played a major role in the banking for millions of households (individuals and families)
sector in the 1980s and 1990s. For instance, in 1997, and for most local units of government (school
China’s Big Four state banks controlled 85 percent of districts, cities, counties, etc) (Rose, 1996). Futher,
total deposits, and Ind onesia’s five lending state banks Rose (1996) states that banks are financial-service
had 41 percent of total deposits. In some cases, the firms, producing and selling professional management of the public’s funds as well as performing many other state was involved in banking as a critical element of a
supplay driven economics strategy, where funneling roles in the economy.
During the 1970, Indonesia’s state banks funds to priority industrial sectors was part of centrally
controlled economic policy.
benefited from supportive government policies, such Given the degree of change, state banks must as the requirement that the growing state enterprise
undergo to become real profit oriented, fully fledged sector banks solely with state banks. State banks were commercial entities, rather than arms of state funding, viewed as agents of development rather than profitable many might be best advised not to attempt the full enterprises, and most state bank lending was in
transformation. Instead, bank could be broken up into fulfillment of government mandated and subsidized
areas specializing in particular activities, and ally programs designed to promote various economic themselves with other entities to extract the value of activities, including state enterprises, and small-scale their customers relationships, and networks without pribumi businesses. State bank lending was subsidized
trying to overcome the enormous cultural challenges through Bank Indonesia, which extended “liquidity credits” at very low interest rates to finance various involved in full change program.
According to, the world’s best-performing programs. Total state bank lending in turn financial institutions typically demonstrate a number repressented about 75 percent of all commercial bank of common characteristics in each area. These lending (U.S. Library of Congress). characteristics are following: leadership, human resources, risk management, marketing, distribution,
and processing. These characteristics are relevant for both state-owned and privately owned banks.
2 Marthen Sengkey Bank Management. Strong competition among
firms, government and foreigner can evaluate the banks encourages the bank’s management to be more
performance of the management of the bank, and for prudent on how to improve their productivity. Stated
the forecast of the future financial position. These that managing a commercial bank promises to be a
would be helpful for investors or credit rating challenging task. He said that some banks and other
professionals in making relevant decisions. depository institutions will fail to face this challenge.
Productive-Efficiency Theory. At the basic level Futhermore, there will be numerous acquisitions and
productivity of the firms measures the ratio of output mergers in the banking and depository indutries. After
to input. In the manufacturing’s skilled labor is often the financial ciris in 1997, many banks, securities
used to measure the productivity of the company . firms, and finance companies closed, merged, or
However, in most industries or manufacturing there effectively withdrew from the market that resulted in
are several factors or variables of production that are loss of jobs for those some people employed in the
of almost equal impact to the output. stated that the financial sector in Asian countries.
process of productivity growth already occurred in the Ba nk’s manager has four primary concerns on
more developed economies in the region. Measures of how to manage bank’s assets and liabilities in order to
multi-factors (total factors) productivity or of capital earn the highest possible profit. The first is to make
productivity rely on the availability of statistical series sure that bank has enough ready cash to pay its
on the prices and quantities of capital services that depositors when there are deposits out flows. Second,
enter the production process. St ates that “productivity the bank manager must pursue an acceptably low level
isn’t everything, but in the long run it is almost of risk by acquiring assets that have a low rate of
everything.” observed that productivity as a concept default and by diversifying assets holdings (assets
can assume two dimensions: total factor productivity management).The third concern is to acquire funds at
(TFP) and partial productivity. The former relates to low cost (liability management). Finally, the manager
productivity that is defined as the relationship between must decide the amount of capital the bank should
output produced and an index of composite inputs; maintain and then acquire the needed capital (capital
meaning the sum of all the inputs of basic resources adequacy management) (Mishkin, 2003).
notably labor, capital goods and natural resources. Risky assets may provide bank with higher
Captioned total factor productivity as “multi-factor earnings when they pay off; but if they do not pay off
productivity ”. For the latter, output is related to any and the bank fails, depositors are left holding the bag.
factor input implying that there will be as many If the bank was taking on too much risk and depositors
definitions of productivity as inputs involved in the were able to monitor the bank easily by acquiring
production process whereby each definition fits a information on its risk – taking activities, they would
given input. According to, efficiency and effectiveness immediately withdraw their deposits.
are actually measures of performance just as Bank regulations that restrict banks from holding
productivity is equally a measure of performance. risky assets such as common stock are a direct means
Furthermore, sums up productivity as comprehensive of making bank avoid too much risk. Furthermore,
measures of how efficient and effective an bank regulations promote diversification, which
organization or economy satisfies five aims: reduce risk by limiting the amount of loan in particular
objectives, efficiency, effectiveness, comparability and categories or to individual borrowers. Requirements
progressive trends.
that banks should have sufficient bank capital are Most literature used Cobb-Douglas production another way to change the bank’s incentives to take on
function to measure the efficiency and productivity of less risk. Bank supervision is also an important
the firms. It can be written as follows: method to protect the consumers or depositors from
(1.1) Financial Statement. Balance Sheet is a list of bank’s assets and liabilities. As the name implies, this
moral hazard (Mishkin, 2003). ß
Y=K ά L
where, Y is related to product or service (output), list has the characteristic: total assets =total liabilities
K is related to capital, L is related to labor, and + capital. Furthermore, a bank’s balance sheet lists exponent ά and ß represent production parameters The
sources of bank funds (liabilities) and the uses which value of the exponent ά and ß each should be greater they are put (assets).
than null but less than one (0 < ά < 1; 0 < ß < 1). The Banks obtain funds by borrowing and by issuing
value of (ά + ß) in this function is particularly other liabilities such as deposits. They then use these
important to determine the return to scale. If (ά + β) is assets such as securities and loans. Banks make
greater than one there are increasing return to scale; if profits by changing an interest rate on their holdings of
(ά + ß) is equal to zero the return to scale is constant; securities and loans that is higher than the expenses on
and if (ά + ß) is less than one, there are decreasing in their liabilities. For example of asset items of
the return to scale.
commercial banks are cash, placement with central The Douglas A. Ruby’s return to scale is shown in the bank and other banks, securities, loans, and other
original illustrations below:
assets such as physical assets. On liabilities side, items such as checkable deposits, nontransaction deposits, borrowings, and bank capital (Mishkin, 2003).
People use the financial statement analysis with the belief that the result of business activities of then firm would be reflected in its financial statement. From bank’s financial statement, households, business
Vol. 8, 2009 Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment 3 Figure 1.2
model and should be useful for researchers working on
stimulation and sensitivity analysis. used a Cobb- Douglas specification that includes the capital stock
Constant Return to scale
and the labor force, as well as the average age of
physical capital and the mean years of education to
account for the quality of capital and labor,
Inefficiency. There are three main parametric
x=300
frontier approaches. The stochastic frontier approach
x=400
(SFA) – sometimes also referred to as the econometric frontier approach – specifies a functional form for the
cost, profit, or production relationship among inputs, outputs, and environmental factors, and allows for
random error. SFA posits a composed error model where inefficiencies are assumed to follow an
Figure 1.3 asymmetric distribution, usually the half-normal, while random errors follow a symmetric distribution,
Decreasing return to scale
usually the standard normal. The logic is that the inefficiencies must have a truncated distribution
because inefficiencies cannot be negative. Both the inefficiencies and the errors are assumed to be
orthogonal to the input, output, or environmental
variables specified in the estimating equation. The
x=200
estimated inefficiency for any firm is taken as the
x=300
conditional mean or mode of the distribution of the
inefficiency term, given the observation of the
x=400
composed error term. The half-normal assumption for the distribution of inefficiencies is relatively inflexible
and presumes that most firms are clustered near full
0 efficiency. In practice, however, other distributions
may be more appropriate.
Some financial institution studies have found that
specifying the more general truncated normal distribution for inefficiency yields minor, but
Figure 1.4 statistically significant, different results from the special case of the half-normal (Berger and DeYoung,
Increasing Return to scale
1996). A similar result using life insurance data occurred when a gamma distribution, which is also more flexible than the half-normal, was used.
700 However, this method of allowing for flexibility in the 600
assumed distribution of inefficiency may make it 500
difficult to separate inefficiency from a random error
in a composed-error framework, since the truncated 400
x=200
normal and gamma distribution may be close to the
300 symmetric normal distribution assumed for the random
200 The distribution-free approach (DFA) also 100
specifies a functional form for the frontier, but separates the inefficiencies from random error in a
0 different way. Unlike SFA, DFA makes no strong 0 100 200 300 400 500 600 700
assumptions regarding the specific distributions of the inefficiencies or random errors. Instead, DFA assumes
Figures 1.2, 1.3, and 1.4 The illustration of Cobb- that the efficiency of each firm is stable over time, Douglas production function where labor and capital
whereas random error tends to average out to zero are input variables by Ruby (2003).
over time. The estimate of inefficiency for each firm in The facts show that the production function of
a panel data set is then determined as the difference Cobb-Douglas form has been widely used in the
between its average residual and the average residual economics literature and has empirically supported
of the firm on the frontier, with some truncation long run property. For example used Cobb-Douglas
performed to account for the failure of the random production function to measure the China’s capital and
error to average out to zero fully. With DFA, productivity using financial resources; used this form
inefficiencies can follow almost any distribution, even to estimate the US industry-level capital labor
one that is fairly close to symmetric, as long as the substitution elasticity, and their estimates provide
inefficiencies are nonnegative. However, if efficiency support for using the Cobb-Douglas specification as a
is shifting over time due to technical change, regularly transparent starting point in parameterizing applied
reform, the interest rate cycle, or other influences, then
2 Marthen Sengkey DFA describes the average deviation of each firm
one point in form the best average-practice frontier, rather than true time.Lastly, the thick frontier approach (TFA)
Deposits are listed as input because banks buy deposits specifies a functional form and assumes that
and other funds to make loans and investments. deviations from predicted performance value within
Deposits are basically considered as the raw materials the highest and lowest performance quartiles of
of a financial institution and are measured by their observations (stratified by size class) represent random
total funds acquisition cost only. The asset approach error, while deviations in predicted performance
stated that the primary role of financial institutions as between the highest and lowest quartiles represent
creators of loans. In essence, this stream of thought is inefficiencies. This approach imposes no distributional
a variant of the intermediation approach, but instead assumptions on either inefficiency or random error,
defines outputs as the stock of loan and investment except to assume that inefficiencies differ between the
assets. Athanassopoulus (1998) categorized the output highest and lowest quartiles, and that random error
variables into four (4) categories as follows: type of exists within these quartiles. TFA itself does not
new accounts (liability sales), loans and mortgages, provide exact point estimates of efficiency for
financial products, and the number of credit cards sold. individual firms but is intended instead to provide an
The conceptual framework of this study has taken estimate of the general level of overall efficiency. The
banks as intermediaries, where the primary function of TFA reduces the effect of extreme points in the data,
the bank is to borrow funds from depositors and lend as can DFA when the extreme average residuals are
these funds to others for profit (Colwell and Davis, truncated (Berger and Humphrey 1997; Bauer et al
1992). From this perspective, deposits are "inputs" and 1993).
loans are "outputs."
McDonell and Rubin (1991) identify sales of Stated that environment variables are ownership deposit and lending products as one of their critical
(public/private, corporate, non-corporate), location success dimensions. There are two well-recognized
(population, density, and average customers size), approaches to modeling bank behavior known as
labor (union power), and government intervention intermediation and production. The intermediation
(regulation).
approach posits deposits as being converted into loans.
Conceptual Framework
The conceptual framework of the study is shown below: Figure 4. Research Paradigm
Regional Development Banks (DMUs)
Group1 Level A Group 2 Level BC classification of CAR prescribed by Central Bank of Indonesia .
SFA Model: DEA- Multistage (VRS Output:
Input Oriented Model): Loans
Technical Efficiency Inputs: 1.Deposit
Output: Loans
2.Operational expenses 3.Capital
Inputs:
4.Fixed assets
1.Deposits
Dummy Variables: 2.Operational expenses 1. Government Intervention
3.Capital 2. Ownership 4.Fixed Assets
3. Location 4.ABC classification
Spearman correlation
The efficiency of Regional Development Banks
Vol. 8, 2009 Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment 5
The DEA and SFA approaches are used to assess ABC classification of CAR prescribed by Central the productive efficiency of the banks’ management to
Bank of Indonesia. Furthermore, the methods used maximize their loans as related to deposits, total
were DEA multistage (input- oriented VRS model) expenses, capital, and fixed assets. Furthermore, both
SFA, and statistical tool such Spearman Rank approaches are used to compute a comparative ratio of
Correlation Coefficient.
outputs to inputs for each unit, which is reported as the Null Hypotheses. Seven major null hypotheses relative efficiency score. The efficiency score is
were tested:
The efficiency performances of Indonesia’s one or 0 and 100 percent. A decision-making unit with
usually expressed as either a number between zero and
H 0 1:
regional development banks are consistent over the
a score less than one is deemed inefficient relative to
period.
other units. In order to avoid a potential problem with
There are no input savings and DEA, operational performance through DEA can be
H 0 2:
output deterioration of bank’s deposit, operational complemented by ratio analysis that measures
expenses, capital, fixed assets, and loan. financial performance of a bank.
H 0 3: There is no significant relationship between Efficiency performance was measured by DEA-
loans with the following variables: Multistage (input oriented VRS model) and SFA. The
Deposit, Operating expenses, Capital, Fixed assets. dependent variable here is total loan, and the
There is no relationship between independent variables are deposits, total operating
H 0 4:
technical inefficiency effects in the production process expenses, fixed assets and capital, which are the
with the following environmental variables: controllable variables by the management. The SFA
Government intervention
model also investigates whether the technical inefficiency of regional development bank’s Ownership
Location
operational performance is affected by government ABC classification of CAR prescribed by Central intervention,
Bank of Indonesia
classification prescribed by Central Bank of Indonesia.
There is no correlation between Further analysis is developed to determine
H 0 6:
DEA and SFA efficiency results. whether there is a correlation between DEA model and
The rejection of these null hypotheses and SFA model. Spearman rank correlation is a tool to
evidence are found in Chapter 4. evaluate correlation of DEA efficiency rank and SFA
efficiency rank. These combined models are employed
RESEARCH METHODOLOGY
generally to examine the performance management of
regional development banks in Indonesia during the This study used the descriptive quantitative period 1994-2004.
research design, using mathematical models of Scope and Limitation of the Study. This study is
performance analysis in a panel data set of 26 regional limited to regional development banks in Indonesia
banks in Indonesia. Two well-known frontier over the time period 1994 to 2004. In this study, 26
approaches were used. Firstly, the non-parametric but regional development banks were categorized into the
deterministic approach, DEA (multi-stage) was used to ABC classification of CAR prescribed by Central
examine the efficiency performance of regional banks. Bank of Indonesia. The main data sets gathered from
the Institutions’ audited annual financial statement Secondly, the parametric estimation known as SFA was used to evaluate the relationship of loans to
reports and statistical reports which were available deposit, total operational expenses, capital, and fixed from the Balitbang (Development Research Agency)
assets and to test whether there is a presence of located in Jakarta, Indonesia. Variables of off-balance
technical inefficiency effects in the model. sheet were not included in this study because of
The third model used was the combination of limited information. Storbeck, (1999) stated that some
Stochastic and DEA models as a new un-researched of the difficulties in obtaining overall efficiency
area in performance analysis, especially in banking. measures in banking applications stem from data
Using this model, the possible linkage between DEA availability. First, banks' databases are often organized
and SFA efficiency scores were tested. to accommodate traditional accounting procedures and
The general performance of Indonesia’s regional do not lend themselves easily to the combined analysis
development banks was evaluated over the time period of marketing, financial, and operational data. Second,
1994-2004, using time series-analysis and panel data. competitor banks are not eager to share comparative
The total sample was comprised of 26 state banks for data. Benchmarking among branches of different
11 years or 286 total observations. This total banks is virtually impossible in this environment.
observation reflected a long-run analysis that could Finally, although one can obtain some data from
yield more credible and unbiased investigation of a central bank or from independent market-research
banking performance.
agencies, these data allow, at best, comparisons of the
bank's overall position vis-à-vis national or regional
DATA AND VARIABLES
averages.
The variables used in this study were deposits, This study used cross-sectional, panel, and time total operating expenses, capital, fixed assets, loan,
series data analysis of 26 regional development banks government intervention, ownership, location and
in Indonesia from period 1994 to 2004. The sample
6 Marthen Sengkey included all countrywide regional development banks,
depositors and lend these funds to others for profit owned by 26 provinces in Indonesia. The time period
(Colwell and Davis, 1992). Thus, this study used the covered from 1994 to 2004 was selected based on the
intermediary approach in the banking performance. availability and completeness of the data of audited
From this perspective, deposits are "inputs" and loans financial reports. As stated in Chapter 1 under the
are "outputs." However, Berger and Humprey (1997) consolidation period (1991 –1997), Bank Indonesia
from a production approach perspective, banks are adopted an open bank resolution strategy during this
modeled as providing service to accounts holders so period only and therefore, data became publicly
labor and physical capital as inputs and transaction and accessible and available.
documents processing are treated as outputs. This There were four (4) independent variables or input
study, on the other hand, considered banks as an data and one (1) dependent variable or output data to
intermediary of funds between savers and borrowers evaluate the efficiency of the regional development
so inputs are sources of funds and loan as an output. banks. As providers of financial services, banks use
The number of Indonesia’s regional development mainly capital and labor to produce loans, deposits,
banks is shown in Table 3.1 below: referrals to auxiliary services, and so forth. In this study, banks act as intermediaries where the primary
function of the bank is to borrow funds from
Table 1. Regional Development Banks
Name of Bank Name
Classification ABC
Code
BPD, Aceh (NAD)
C BPDNAD BPD, North Sumatera
A BPDNS BPD, Bengkulu
C BPDBE BPD Lampung
B BPDL BPD, DKI Jakarta
A BPDDKI BPD, Central Java
B BPDCJ BPD, East Java
C BPDEJ BPD, West Kalimatan
A BPDWK BPD, North Sulawesi
A BPDNSU BPD, Maluku
A BPDM BPD, West Nusa Tenggara
B BPDWNT BPD, East Nusa Tengga
B BPDENT BPD, West Sumatera
C BPDWS BPD, South Sumatera
A BPDSS BPD, Jambi
A BPDJ BPD, Pekanbaru-Riau
A BPDR BPD, West Java
B BPDWJ BPD, DIY
A BPDDIY BPD. Bali
B BPDBa BPD, South Kalimantan
A BPDSK BPD, Central Kalimantan
B BPDCK BPD, East Kalimantan
A BPDEK BPD, South Sulawesi
A BPDSSU BPD, Central Sulawesi
A BPDCSU BPD, South East Sulawesi
A BPDSESU BPD, Papua
A BPDP
A has a CAR more than 4% at the time of disclosure;
B has a CAR less than 4% but greater than – 25% at the time of disclosure;
C has a CAR less than – 25% at the time of disclosure.
Variables . This study used one (1) output Where, the total operating expenses composed of var iable and four (4) input variables to evaluate bank’s
interest expenses, fees and commissions, general and efficiency through the DEA multistage model (input
administrative expenses, salary and employees’ oriented VRS technology). The output variable is total
benefits, loss on fair value on trading account loans and input variables are (1) total deposits, (2)
securities and foreign exchange, while, the capital total operational expenses, (3) capital, and (4) total
composed of capital stock, donated capital, increment fixed assets.
on financial report, unrealized gain (loss) from trading Total loan composed of loan of rupiah currency
account securities, and other comprehensive income, (related parties and third parties) and loan of foreign
and difference on affiliated retained earning. And currency (related parties and third parties). Then, total
fixed assets composed of premises and equipment, deposits composed of demand deposits, saving
assets in direct financing lease and real and chattel deposits, time deposits, and certificate deposits.
properties.
Vol. 8, 2009 Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment 7 All those variables were stated in Indonesian
Environment is the factor which could influence currency (rupiah) in millions. These variables are
the efficiency of a firm, where such factors are not chosen based on studies taking intermediation
traditional inputs and are assumed not under the approach to banking performance.
control of manager. Some examples of environmental According to commercial banks are financial
variables include ownership, location, labor, and intermediaries that supply financial service to surplus
government regulation. If the values of the and deficit units. Most bank assets are financial in
environmental variable can be ordered from the least nature, consisting primarily of money owed by such
to the most detrimental effect upon efficiency, then the non-financial economic units as households, business,
approach of can be followed. On the other hand, if and government. Furthermore, commercial banks issue
there is no natural ordering of the environmental contractual obligations, primarily in deposit or
variable then one can use a method proposed borrowing form, to obtain the funds to purchase these
by.Charnes et al., (1978) stated that the DEA financial assets. He also stated that the role of
technique as an efficiency measure of production unit commercial banking is to fill the diverse desires of
by its position relative to the frontier of the best both the ultimate borrowing and lenders in the
performance, established mathematically by the ratio economy .
of weighted sum of outputs to weighted of sum of McDonell and Rubin (1991) identified sales of
inputs; different decision making units (DMU) can be deposit and lending products as one of their critical
compared based on productivity and efficiency. A success dimensions. There are two well-recognized
common practice in this case is to run DEA where all approaches to modeling bank behavior known as
the inputs are treated as controllable and then regress intermediation and production. The intermediation
the emerging efficiency scores on non-discretionary approach posits deposits as being converted into loans.
inputs.
Deposits are listed as input because banks buy deposits In this study, the multistage DEA model was and other funds to make loans and investments. Other
utilized to compute the total efficiency scores. key inputs are operating and interest costs
According to Coelli et al., (1998, p. 150), the constant (Athanassopoulos, 1998). Under the intermediation
returns to scale (CRS), DEA model is only appropriate approach, performance is assessed using as inputs such
when the firm is operating at an optimal scale. Some as
factors such as imperfect competition, constraints on intermediation approach uses outputs measured in
total operating
finance, banking, corruption, political crisis etc. may dollars. However, there is no consensus on the
cause the bank to be not operating at an optimal level variables that should be used to measure bank branch
in practice.
performance so far (Ibid.). The fall of Soeharto and five (5) years after the Furthermore, in addition to inputs and outputs, the
financial crisis, Indonesia is still struggling to deal study also used the exogenous variables, that are,
with economic restructuring and recovery, political dummy variables in the SFA model. Dummy
transition, decentralization and redefining national variables (z) are government intervention, ownership,
identity. Moreover, the Asian financial and economic location of banks, and ABC classification prescribed
crisis of 1997-1998 hit the country hardest, which by the Central Bank of Indonesia.
caused its real GDP declined by 13 percent in 1998 as
its banking and modern corporate sectors collapsed in technology). DEA was originally introduced by
DEA – Multistage Model (Input-oriented VRS
the wake of short-term capital outflows. Corporate Charnes et al., (1978) and is a non-parametric linear
debts remain largely unreconstructed, bank lending is programming approach, capable of handling multiple
limited, the government owns or controls most of the inputs as well as multiple outputs. DEA assumes that
banking system and substantial business assets, fiscal the inputs and outputs have been correctly identified.
sustainability is questionable, inflationary pressures Usually, as the number of inputs and outputs increase,
are strong and investment climate is unattractive. more DMUs tend to get an efficiency rating of 1 as
To considerall these environmental factors that they become too specialized to be evaluated with
may affect the banking performance in Indonesia, this respect to other units. On the other hand, if there are
study adopted DEA model of variable returns to scale too few inputs and outputs, more DMUs tend to be
(VRS). Due to the consequence of the heavy comparable. In any study, it is important to focus on
intervention by the government in banking system in correctly specifying inputs and outputs. According to
Indonesia as mentioned earlier, bankers may well have Kruger (2003), DEA is a local method in that
been prevented from operating at the optimal level in calculates the distance to the frontier function through
their operation. Therefore, technical efficiency in this
a direct comparison with only those observations in study is calculated using the input-oriented VRS the samples that are most similar to the observation for
model. The envelopment form of the input-oriented of which the inefficiency is to be determined.
CRS and VRS DEA model is specified as stated by The piece-wise linear form of non-parametric
Coelli et al. (1998, pp. 150, 151). frontier in DEA can cause a few difficulty in efficiency measure. The problem arises because of the
min , ,: st y i y 0 , x i x 0
sections of the piece-wise linear frontier, which run parallel to the axes which do not occur in most
N 1 ' 1 (3.1)
parametric function (Coelli et al., 1998).
8 Marthen Sengkey
TE CRS i SE i
TE VRS 0
min , ,: st y i y
x i x 0
possible to those of inefficient points, and that it also
N invariant to units of measurement. For a detailed 1 ' 1
explanation, see Coelli et al., (1998).
Stochastic Frontier Analysis. The SFA method (3.3) provides the means to estimate cost efficiencies. Cost where θ is a scalar and λ is a N*1 vector of constants,
efficiency consists of two components: technical N*1 is an vector of one.
efficiency, which reflects the ability of the firm to In this study, θ i is the technical efficiency score
for each bank, N is number of bank which is 26, λ is obtain maximum output from a given set of inputs, and an allocative efficiency, which reflects the ability of
the lambda weight of each bank to the target or peer, y the firm to use the inputs in optimal proportions, given is the output variable (loan) and x is the input variables
by their respective prices. The SFA model involves the (deposit, total expenses, fixed assets, and capital). The
estimation of a cost frontier, as a function of outputs effic iency score will satisfy if the value of θ is less and and input prices, where deviation from the frontier are
equal than one. If there is a difference in the CRS and assumed to be related to cost inefficiency and VRS TE scores for a particular firm, then this indicates
statistical noise (Greene and Segal, 2004). that the firm has scale inefficiency, and that the scale
The SFA method can statistically test hypotheses inefficiency can be calculated from the difference
and construct confidence intervals, allowing for between CRS and VRS TE (Coelli et al., 1998,
random error. Stochastic frontier analysis is an pp.134, 140, and 141). Furthermore, the nature of the
econometric frontier approach that specifies a scale inefficiencies for particular firm can be
functional form for the cost, profit, or production determined by seeing whether the non- increasing
relationship among inputs, outputs, and environmental return to scale (NIRS) technical efficiency (TE) of
factors, and allows for random error. SFA posits a NIRS TE score is equal to the VRS TE score. If they
composed error model where inefficiencies are are unequal, then increasing return to scale exists for
assumed to follow an asymmetric distribution, usually the firm. If they are equal, then decreasing return to
the half-normal, while random errors follow a scale applies. And if TE CRS = TE VRS the firm is
symmetric distribution, usually the standard normal operating under constant return to scale CRS (Coelli et
(Berger et al.,1997).
al. 1998, pp.150- 151). The efficiency scores in this
study were estimated, using the computer program The following stochastic frontier model can be run: known as Efficiency Measurement System -EMS.
t=1,…,T parametric frontier in DEA can cause a few difficulties
Ly n ( )
it x it v it u it , i=1,…,N;
Slacks. The piece-wise linear form of the non-
in efficiency measurement. The problem arises
u it exp nt T u i (3.5)
because of the sections of the piece-wise linear frontier
which run parallel to the axes which do not occur in where y it denotes the output for the i th bank at t th most parametric functions Coelli et al., (1998). Some
time period; x it denotes a (1*K) vector of value of authors argue that both the Farrell measure of
technical efficiency (θ) and any non-zero input or inputs and other appropriate variables associated with
a suitable functional form (e.g., the Cobb-Douglas output slacks should be reported to provide an accurate model); β is a (K*1) vector of unknown scalar indication of technical efficiency of a firm in DEA
parameters to be estimated; the v it s are random errors; analysis Coelli et al., (1998). They sated that the
the u it s are the technical inefficiency effect in the output slacks will be equ al to zero if and only if Yλ-
model (Coelli, et al., 1998).
y 1 =0 and the input slacks will be equal to zero if and In this study, y is total loan, x i only if θx are deposit,
1 - Xλ=0 (for the given optimal values of θ and λ). operational expenses, capital and fixed assets. While
u it is other environmental variable that is not included Coelli et al., (1998) stated that there are two major
in the input or output variables, which influence the problems associated with the second stage LP. The
result of technical efficiency score. first and most obvious problem is that the sum of the
effects of government slacks is maximized rather than minimized. Hence, it
location and ABC identifies not the nearest efficient point but the furthest
intervention,
ownership,
classification described by the Central Bank of efficient point. The second major problem associated Indonesia, of the Indonesia’s regional development with the second – stage approach is that is not
banks on technical inefficiency, the u s it are non- invariant to unit of measurement. To avoid the two
negative random variables, which are assumed to be problems mentioned, the multi-stage DEA method was
independently distributed, which represent the used. Coelli (1998) stated that the multi-stage method
technical inefficiency term. This random error involves a sequence of radial DEA models and hence
variables capture the effect of external factors of is more computationally demanding that the first-stage
production tha t are beyond the bank’s control, i.e. and second-stage methods. However, the benefits of
government intervention, ownership, location and the approach are that it identifies efficient projected
ABC classification of CAR prescribed by Central points which have input and output mixes as similar as
Vol. 8, 2009 Efisiensi Bank Pembangunan Daerah Menggunakan Data Envelopment 7 Bank of Indonesia represents the technical inefficiency
Z 1it = represents the government intervention i – th in term. Where u it is defined mathematically as:
the t –th year of observation; Z 2 it = represents the bank’s ownership i – th in the t –
u it =δ 0 + δ 1 z 1 it +δ 2 z +δ 2 it 3 Z3 it + δ 4 z 4 it D it (3.6)
th year of observation; Z3 it = represents the bank’s location i – th in the t-th
where : year of observation; input or output cannot result in a reduction in the TE Z4 it = represents the ABC classification of CAR
scores.
prescribed by central bank of Indonesia i-th in the t-th The principal disadvantage of DEA is that it year of observation;
assumes data to be free of measurement error. When
D it is dummy variable having value one and zero if the the integrity of data has been violated, DEA results
i – th bank in the t - th year of observation include the cannot be interpreted with confidence. While the need government intervention.
for reliable data is the same for all statistical analysis, The computer program software known as
DEA is particularly sensitive to unreliable data Frontier 4.1 (Coelli, 1996) was used to find maximum because the units deemed efficient determine the
likelihood estimates of a subset of the stochastic efficient frontier and thus, the efficiency scores of frontier production functions.
those units under this frontier. For example, an Strength of SFA. The SFA method can
unintended reclassification of the efficient units could statistically test hypotheses and construct confidence
lead to recalculation of efficiency scores of the intervals allowing for random errors.
inefficient units. This potential problem with DEA is Weaknesses of SFA. Some weaknesses of SFA
addressed through stochastic DEA designed to account are follows: the selection of a distributional form for
for random disturbances. Two recent examples in this the inefficiency effects may be arbitrary and the
area are.
production technology must be specified by a Another caveat of DEA is that those DMUs particular functional form (Coelli et al., 1998);
indicated as efficient are only efficient in relation to Eventhough SFA can statistically test hypotheses and
others in the sample. It may be possible for a unit construct confidence intervals allowing for random
outside the sample to achieve a higher efficiency than errors , it may lose some flexibility in model
the best practice DMU in the sample. Another way of specification.
expressing this is to say that an efficient unit does not Strengths of DEA. DEA modeling allows the
necessarily produce the maximum output feasible for a analyst to select inputs and outputs in accordance with
given level of input.
a managerial focus. Furthermore, the technique works Spearman Rank Correlation Coefficient. To with variables of different units without the need for
assess the correlation between DEA- the non- standardization (e.g. dollars, number of transactions,
parametric approach and SFA- the parametric analysis or number of staff). That is, DEA does not assume a
in this study, Spearman ranks correlation coefficient particular production technology or correspondence.
was used to address objective (6). The Spearman rank The importance of this feature of DEA is that a bank's
correlation when coefficient
efficiency can be assessed based on other observed ( R rank ) is used to determine whether there is a performance. As an efficient frontier technique, DEA
significant difference between DEA efficiency rank identifies the inefficiency in a particular DMU by
and SFA efficiency rank (Berger and Humphrey, comparing it to similar DMUs regarded as efficient,
1997). They stated that some studies found significant rather than trying to associate a DMU's performance
different relationship between the findings of different with statistical averages that may not be applicable to
techniques, while others find strong relationships. The that DMU.
test of independent sample, paired sample, and Assessment of operational performance through
spearman rank correlation are computed through DEA can be complemented by ratio analysis that
Statistical Program for Social Sciences (SPSS) version measures financial performance of a branch. DEA is
that it allows management to nominate the inputs and Webster, (1992) stated that Spearmen’s rank outputs entering the analysis. DEA allows inputs to be
correlation coefficient is used to assesses how well an classified as either controllable or uncontrollable by
arbitrary monotonic function could describe the management. This facilitates an analysis where
relationship between two variables, without making performance can be interpreted in the context of
any assumptions like in Pearson product-moment uncontrollable environmental conditions. DEA models
correlation coefficient (Pearson r). It measures the can offer much potential for a significant advance in
relationship between two variables that have been the comparative analysis of financial institutions by
ordinally ranked from lowest to highest (or highest to enabling the concurrent study of the multiple variables
lowest). The value of correlation coefficient falls that affect bank efficiency over time (Bauer et al.,
between -1 and 1, where the negative sign indicates 1997)
that there is a negative correlation between the The limitation of DEA as stated by Coelli et al.,
variables and positive sign indicates that there is a (1998) are the following: measurement error and other
positive correlation between the variables. The noise may influence the shape and position of the
difference between the ranks of corresponding value frontier; the exclusion of an important input or output
of each observation on the two variables is calculated can result in biased results; and the addition of extra
following the equation below:
10 Marthen Sengkey
6 2 d +1. And if r
value is exactly +1 indicates a perfect
nn 1
r s 1 2 (3.10)
positive correlation. On the other hand, a negative
correlation occurs: If x and y have a strong negative where: d i is the difference between the rankings for
linear correlation, r s is close to -1. And if r s value of each observation and n is the sample size of the
exactly -1 indicates a perfect negative correlation. No observation (Webster, 1992). The quantity r s called the