The used as input and output variables. Apart

The research methodology of the
selected topic follows in these ways:


3.1Sample of the Study;

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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.


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


X1. Operating Expense / Total Funds

X2. Operating Expense / Interest Income

X3. Operating Expenses / Interest Expense



Y1. Operating Expense/ Profit Before


Ratios for Earnings


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



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

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.


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:

the efficiency of unit j 0,

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.