Comperative Efficiency using Data Envelopment Analysis (DEA) and

Stochastic Frontier Analysis (SFA) in the Banking Industry

ZAENAL ABIDIN1, R. MAHELAN PRABANTARIKSO2*, EDIAN FAHMY3, AMABEL NABILA4

Perbanas Institute

Jakarta, 12940

INDONESIA

INDONESIA

*Correspondent Author

function, interest expenditure and labor expense have a positive and considerable influence on interest income. This

occurs when deposit interest rates rise, banks gain interest revenue by raising lending rates, and banks increase

non-interest income. According to the SFA of the Cobb-Douglas function, many banks are inefficient, particularly

the first to 49th banks that arise from small banks. The Gamma value is near one (0.999), while the LR test yields a

significant result of 36.14. The Cobb-Douglas SFA model is therefore applicable. The efficiency performance

findings from the two models above reveal the same thing: large banks are more efficient than small banks.

Key-Words: - Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), Banking Performance,

Efficiency, Indonesia.

statements, balance sheets, and profit and loss

statements. However, there are various approaches

for assessing efficiency performance. SFA

(Stochastic Frontier Analysis) and DEA (Data

Envelopment Analysis) are two extensively utilized

efficiency measuring methodologies. SFA is a

created by high-efficiency technology, allowing

technical efficiency to be evaluated.

Since DEA uses linear programming techniques

to estimate a firm's technical efficiency while taking

a range of inputs and outputs into account, [2]. The

DEA, on the other hand, is unable to differentiate

between technological inefficiencies and random

mistakes. Furthermore, the DEA does not generate

standard mistakes. As a result, when analyzing

banking efficiency performance, SFA and DEA

cost-efficiency ratio (CIR). Using the financial ratio

approach, this ratio calculates the percentage of a

bank's operating expenditures to operational income

or efficiency performance. The Covid-19 epidemic

was responsible for the decreasing financial

performance, [3].

Up to this point, there hasn't been much

discussion of how well two methods—Data

Envelopment Analysis (DEA) and Stochastics

Frontier Analysis (SFA)—perform in terms of

challenges from more developed nations.

This paper's objective is to assess and compare

the performance of banking efficiency for the years

2018 and 2019 using DEA and SFA.

2 Literature Review

There are two empirical methods for measuring

efficiency: parametric and non-parametric. The most

common parametric is stochastic frontier analysis

Empirical studies have utilized these two distinct

refers to this combination as inefficiency.

Parametric and nonparametric methodologies

have been utilized in bank efficiency research,

however, there is no consensus on the consistency of

efficiency performance, [5]. Due to the

inconsistency, various efficient bank ratings were

produced.

To conduct a banking study in India, parametric

and nonparametric analyses were used. Researchers

discovered that SFA and DEA models with different

the high cost of human resources.

Organizations that effectively implement digital

business transformation are more efficient in their

use of resources than companies that do not, [8].

Furthermore, government assistance and proper

digital infrastructure have a significant influence on

firm efficiency.

Conclusions on the relevance of digital business

transformation in enhancing firm efficiency and how

DEA analytical methodologies may be utilized to

long time will be more productive and efficient than

organizations that have not been in operation for a

long time, [11], [12].

State-owned and foreign-owned enterprises

outperform private domestic companies in terms of

efficiency, [12], [13].

than small banks since large banks earn money other

than interest, [14].

A study on pandemic situations revealed that

3 Research Method

With 88 banks, the research population included all

conventional commercial banks but excluded Islamic

banks. The secondary data utilized originates from

the Financial Services Authority's publishing report

period for 2018 and 2019, [16]. Banks with

large because their capital is greater than Rp. 5

trillion. Because of the COVID pandemic in 2020,

the author utilizes data from 2018 and 2019. The

company's financial performance dropped throughout

the epidemic, [15]. The bank sample is as follows

(Table 1, Appendix):

DEA and SFA models reflect the financial

intermediation role of a bank and use variables used

technique for DEA, which is based on the input-

output relationship between bank functions. Use

exogenous variables for SFA, such as size (total

asset).

The initial phase in this research is to apply the

DEA approach with the Banxia Frontier Analysis

(BFA) software to estimate the level of efficiency of

small and large banks in the 2018-2019 period. The

DEA approach employs a linear model in a non-

parametric frontier model.

often chosen as outputs since they reflect a bank's

second approach model is the Banker, Charnes,

Cooper (BCC) model, which assumes that the unit

operates at an optimal scale or not.

Since it considers the likelihood that banks might

not operate at their ideal scale due to numerous

challenges and competition, the BCC model is

frequently chosen for studying banks. The VRS

model is used along with DEA to account for the

possibility that banks could operate at various scales

of production. This model makes it possible to

optimally, and the BCC model is more appropriate

for analyzing the efficiency of service companies,

[7].

The DEA degree of efficiency is suppressed data

with a restricted value ranging from 0-100. The

statistical definition of the model is as follows:

Y*0= ßxi + e0,

y0 = y*0 if y*0 > 0

y0 = 0, otherwise

Where:

analysis (SFA) formula, [18].

X3 = represents the natural logarithm of size (total

represents the technical inefficiency term. These

random error variables describe the influence of

external production elements that are outside the

establishment's control. The magnitude denotes the

technical inefficiency term.

SFA models calculate the relation between inputs

(interest costs, labor costs, and size) and outputs

(interest and non-interest income) while taking

random variables (Vit) and technical inefficiency (Uit)

into account. With this strategy, it is recognized that

that explains the link between inputs and outputs by

calculating the likelihood of various subsets of the

model.

companies (55 of 71 banks) never made it to the

border throughout the test period. It demonstrates

that the bulk of the banks' operating efficiency may

Bank Jogja, Bank Victoria, Bank Woori Saudara,

than the mean indicate the presence of outliers -

Table 4. Technical Efficiency (TE)

According to Table 4, the average TE is solely 0.242,

and the distribution of TE is as follows:

Fig. 1: TE Cobb-Douglas function

Figure 1 is the TE of the Cobb-Douglas function,

many banks tend to be inefficient, especially the 1st

to 49th banks that come from small banks, the results

of the CD function are consistent with the DEA

function results are consistent with the DEA results

above; and only a few unique banks demonstrate

efficiency. The range of TE values is wide, ranging

from 0.026 to 0.999, and underlines the large

variability in efficiency levels between the banks

under examination. This disparity in TE ratings

implies that some banks have significantly

streamlined their resource utilization, while others

By using DEA large banks outperform small banks

on average, which is consistent with previous

research, [14], [15]. Large banks, on the other hand,

are simpler to obtain non-interest revenue, [14]. This

could be related to their larger scale and resources,

5 Conclusion

To examine efficiency performance from 2018 to

2019, this study used a non-parametric Data

small banks declined somewhat, with small banks

falling from 0.78 to 0.77 and large banks falling from

0.82 to 0.81. According to the DEA findings, major

banks outperform small banks on average.

Cobb-Douglas (CD) Production Function based

and labor costs, rather than random mistakes. In other

words, the Cobb-Douglas frontier model may be

applied.

As an outcome of the Cobb-Douglas TE

function, many banks are inefficient, notably the first

to 49th banks, which are small, and only a few

specific banks are efficient. The range of TE is wide,

ranging from 0.026 to 0.999.

According to the Cobb-Douglas SFA, interest

and labor expenses have a positive and considerable

banks are government-owned, and others are foreign-

owned.

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