The research methodology of the

selected topic follows in these ways:

3.1Sample of the Study;

There are 57 scheduled banks in

Bangladesh, within this 6 state owned commercial banks, 40 private commercial

banks that is a mix of 32 conventional private commercial banks and 8 Islami

Shariah based commercial banks and the rest 9 are Foreign commercial banks. My

study is on 40 private commercial banks. When choosing sample Islami Shariah

based banks are excluded from the sample because of the significant difference

in operation. 21 banks are taken from among the rest 32 private commercial

banks as the sample. All the sample banks are listed in the DSE.

3.2 Data Collection and Variables

The study is basically based on

secondary data. For this purpose, data are collected from the annual reports of

Bangladesh Bank and the sample banks for the period of last SIX

years from 2011 to 2016. Some other related websites are used to collect data.

Moreover the journals, articles, reports and surveys have been referred.

To

make the study elaborate, in depth and informative, related financial

ratios have been used as input and output variables. Apart from the interest

expense, operating expenses are the major expenditure of a bank and here four financial ratios have been used to measure the efficiency

in cost control, thus three are input and one is output. As a financial institution bank’s earning is the

key function of it and for this eight financial ratios have been used to measure the earnings

efficiency. Hence seven

ratios are used as the input and the rest one is used as the output. The financial ratios are presented

below and their explanations are to be given in the annexes.

Ratios for Cost Efficiency

Input

X1. Operating Expense / Total Funds

X2. Operating Expense / Interest Income

X3. Operating Expenses / Interest Expense

Output

Y1. Operating Expense/ Profit Before

Provisions

Ratios for Earnings

Efficiency

Input

X1. Interest Income / Total Loan

X2. Operating Profit /

(Total Interest + Investment Income)

X3. Profit before

Provision / (Total Interest + Investment income)

X4. Return from

Investment/ Total Investment

X5. Interest Expense /

Interest Income

X6. Other Income /

Total Interest Income

X7. Operating Expense

/ Interest Income

Output

Y1. Net Income after Tax / Total Earnings

3.3 Time frame:

The study has focused on the conventional private commercial

banks from 2011 to 2016.

3.4 Measures

Used

For conducting the study following measures have been used

·

Data Envelopment Analysis

·

Regression Analysis

3.5 Study

Procedure and Model

To achieve the goal of

the study that is measuring the cost and earnings efficiency firstly cost efficiency and the earnings

efficiency are estimated using Data Envelopment Analysis. And later it is tried

to interpret the result for the population.

To measure both the

cost and earnings efficiency the respective ratios of each sample banks were

calculated first then the results were arranged according to the DEA guideline

and test the efficiency using open solver.

3.6 Data Envelopment Analysis (DEA)

DEA has been selected as a tool to

measure the efficiency because there is a possibility that

restrictive atmosphere

and market imperfections distort the prices of inputs and outputs to a great

extent in developing

countries. This makes the application of parametric techniques for computing

cost and revenue efficiency more complicated

(Bhattacharyya et al. 1997). Furthermore, parametric techniques require prior estimation of

the functional form and availability of large data for determining income and cost efficiency, which is not

always possible in the context of a developing country like Bangladesh (Uddin and Suzuki 2011). DEA

is a nonparametric method of measuring the efficiency of a decision-making unit (DMU) such as a

firm or a public sector agency, first introduced into the operations research (OR) literature by

Charnes, Cooper and Rhodes (CCR) in EJOR in 1978.

Charnels,

Cooper and Rhodes(3) recognized the difficulty in seeking a common set of

weights to determine relative efficiency. They recognized the legitimacy of the

proposal that units might value inputs and outputs differently and therefore

adopt different weights, and proposed that each unit should be allowed to adopt

a set of weights which shows it in the most favorable light in comparison to the

other units. Under these circumstances, efficiency of a target unit j0 can be

obtained as a solution to the following problem:

Maximize

the efficiency of unit j 0,

Subject

to the efficiency of all units being < =1.
The
variables of the above problem are the weights and the solution produces the
weights most favorable to unit j0 and also produces a measure of efficiency.
The
algebraic model is as follows:
Model 1:
Subject to
For the depot data, the
efficiency of depot 1 is obtained by solving the following model:
Model
2:
Subject to
…………for remaining depots
And
The u's and v's are
variables of the problem and are constrained to be greater than or equal to
some small positive quantity in order to avoid any
input or output being totally ignored in determining the efficiency. The
solution to the above model gives a value h0, the efficiency of depot 1, and
the weights leading to that efficiency. If h0 = 1 then depot I is efficient
relative to the others but if ho turns out to be less than l then some other
depot(s) is more efficient than depot l, even when the weights are chosen to
maximize depot l 's efficiency.
This flexibility in the
choice of weights is both a weakness and strength of this approach. It is a
weakness because the judicious choice of weights by a unit possibly unrelated
to the value of any input or output may allow a unit to appear efficient but
there may be concern that this is more to do with the choice of weights than any
inherent efficiency. This flexibility is also a strength, however, for if a
unit turns out to be inefficient even when the most favorable weights have been
incorporated in its efficiency measure then this is a strong statement and in
particular the argument that the weights are incorrect is not tenable.
DEA thus may be
appropriate where units can properly value inputs or outputs differently, or
where there is a high uncertainty or disagreement over the value of some input
or outputs.
The DEA model M1 is a
fractional linear program. To solve the model it is first necessary to
convert-it into linear form so that the methods of linear programming can be
applied. The linearisation process is relatively straightforward. The linear
version of the constraints of Ml is shown in model M3. For the objective
function it is necessary to observe that in maximizing a fraction or ratio it
is the relative magnitude of the numerator and denominator that are of interest
and not their individual values. It is thus possible to achieve the same effect
by setting the denominator equal to a constant and maximizing the numerator.
The resultant linear program is as follows:
Model
3:
Subject to
There
are two assumptions regarding the scale of efficiency in using inputs for
output. They are
explained below:
3.6.1 Constant Return to Scale (CRS):
The
purpose of DEA is to construct a non-parametric envelopment frontier over the
data points such that
all observed points lie on or below the production frontier. If there are data
on K inputs and M
outputs on each of N firms or DMUs, then we need to solve the following
equation:
Where, u is an M×1 vector of output
weights and v is a K×1 vector of input weights. y and x are the matrix of inputs and outputs for
each DMU.
To solve this problem using linear
programming, we need to convert the equations into linear ones.
Then the
equations are as follows:
Subject to
3.6.2 Various Returns to Scale (VRS):
The CRS assumption is only appropriate
when all DMUs are operating at an optimal scale.
Imperfect competition, constraints
on finance, etc. may cause a DMU to be not operating at
optimal scale. So, the
analysts suggested an extension of the CRS DEA model to account for
variable returns to
scale (VRS) situations. The use of the CRS specification, when not all DMUs
are operating at the
optimal scale, will result in measures of TE which are confounded to be scale
efficiencies.
Many studies have
decomposed the TE scores obtained from a CRS DEA into two components,
one due to scale
inefficiency and due to "pure" technical inefficiency. This may be done by
conducting both a CRS
and a VRS DEA upon the same data. If there is a difference in the two
TE scores for a
particular company, then this indicate that the company has scale inefficiency,
and that the scale
inefficiency can be calculated from the difference between the VRS TE score
and the CRS TE score.