Evaluating advance efficiency of Bangladeshi online banks using stochastic frontier analysis

Online bank advance efficiency and various factors causing the efficiency level of banks are investigated using stochastic frontier technique for the period 2001-2007. A sample of 20 banks are used following four different groups like NBs (National Banks), ISBs (Islamic Banks), FBs (Foreign Banks), and PBs (Private Banks). A group wise, year wise, and individual banks with their efficiency scores are compared in this study. The significant variations of advance efficiency of banks during this reference period were observed. The year wise average efficiency of banks was estimated (0.516) from the advance frontier model while group wise average technical efficiency was 0.592. Nationalized Commercial Bank had the highest advances producing group compared to others; Private Banks are at the lowest level in producing advances. ISBs, FBs, and PBs are observed inefficient in producing advances. The most efficient banks are found to be government owned Sonali and Janata Bank with efficiency score (0.94) while lowest efficient bank was experienced by Shahajalal Islamic Bank with efficiency score of 0.34.


INTRODUCTION
There has been a widespread discussion on lack of sufficient technical efficiency of banks in developing countries compared to their counterparts in the developing world (Das, 1997;Shanmugan and Lakshmanasamy, 2001;Kumar and Verma, 2003;Kumbhakara and Sarkar, 2003;De, 2004;Mohan and Ray, 2004;Das et al., 2005).Even some works have been done for Bangladesh banking sector (Raihan, 1998;Choudhury et al., 1999;Choudhury 2002).No attempt has been made to check the performance and efficiency measure of the commercial banks with advance output.Again, question arises how successfully the nationalized private commercial banks are serving the country, how far they have achieved their desired goals.Studies on online Bangladeshi banks will give answer to such questions.This study intends to reveal the overall performance of commercial banks with loan default and measuring technical advance efficiency of banks in Bangladesh.
Stochastic production frontier model proposed by Battese and Coelli (1995) is used in this paper to measure advance efficiency of banks individually and in accordance with four groups namely NBs, IBs, FBs, and PBs in Bangladesh.To determine the important factors causing advance efficiency differential on banking industry in Bangladesh is also of interest in this study.The remainder of the paper is organized as follows.Section two begins with a formulation of stochastic Translog production frontier model with its functional form.Likelihood ratio (L-R) test statistic is explained here for the purpose of testing null hypotheses.A detailed description of variables, sources and different types of *Corresponding author.E-mail: baten_math@yahoo.com,anton@usm.my.data used are discussed in this paper.In section three, we have analyzed advance frontier model in measuring efficiency for different banks of Bangladesh.The last section contains concluding remarks.

Bank efficiency based on stochastic frontier analysis
The stochastic frontier model proposed by Battese and Coelli (1995) where it Y is the output of the i th bank in t th period; it X is a vector of input quantities; i  's are unknown parameters to be estimated; it V 's random variables which are assumed to be i.(1 ) p  vector of variables which may influence the inefficiency of bank industry and  is a ( 1) p  vector of parameters to be estimated.The impact of the inefficiency term, as measured by the contribution of its variance to overall variance, is denoted by  it K denotes capital (fixed assets of a online bank in a year which also adds premises, furniture and fixture) of i-th online bank industry in the t-th period; it M represents materials (the sum of expenditure on printing and stationeries and postage, telegrams and telephones etc) of i-th online bank industry in the tth period; it L represents labor (the total number of employees which include officers, sub-ordinates and clerks) of i-th online bank industry in the t-th period; T represents year of observation; "ln" refers to the natural logarithm.Further the technical inefficiency effects are the function of some explanatory variables defined as follows:

Likelihood ratio tests and hypothesis
The likelihood ratio test is used to determine whether Translog production function is better.The hypotheses require testing with the generalized likelihood ratio test statistic defined by is assumed to be asymptotically distributed as mixture of chi-square distribution with degree of freedom equal to the number of restrictions involved.The restrictions imposed by the null hypothesis are rejected when  exceeds the critical value (Taymaz and Saatci, 1997).
The following null hypotheses will be tested:

Data set
We have used data for the period of 2001-2007 from 20 commercial banks of Bangladesh.Banks are grouped into four categories: (i) National Banks (NBs), (ii) Islamic Banks (ISBs), (iii) Foreign Banks (FBs), (iv) Private Banks (PBs).Most of the data are collected from the annual reports of the specific banks of Bangladesh and the rest of them are collected from annual accounts of Scheduled Commercial Banks published by Bangladesh Bank, the Central Bank of Bangladesh.All nominal values are converted on real by deflating with GDP deflator and all values are in their natural logarithms.

Dependent variables
Advance (Y): Advances are used as output and equal to total loans and advances.These values are also deflated by relevant consumer price index (CPI).

Independent variables
Capital (X1): Capital is the input variable used to represent the fixed assets of a bank in a year which also adds premises, furniture and fixture.Capital figures are deflated by capital price index.Labor (X2): Labor is the inputs to measure the productivity of a firm.
Here labor means number of employee and is measured as the total number of employees which include officers, sub-ordinates and clerks.Material (X3): Material is used as the sum of expenditure on printing and stationeries and postage, telegrams and telephones etc. Material prices are deflated by non-food price index.

Time (X4):
To find the productive efficiency of a bank over time is used as the input variable.Data used in this study for seven years from 2001 to 2007 and considered 1 for year 2001, 2 for 2002 and so on.

Explanatory variables
Total Asset (Z1): Total asset is used as the influencing variable and it is the sum of all assets and courses of their book value.Herfindahl Index (Z2): Herfindahl index is known as measure of competition which is measured as the sum of squared of the output share of each of bank in the output of considered total banks in Bangladesh.
NB, ISB, FB, and PB are bank group specific dummies for National Bank, Islamic Bank, Foreign Bank, and Private Bank respectfully.The dummy variables can take either 1 or 0 depending on data availability or not respectively.

Estimation of advances efficiency model
Ordinary Least Square Estimates (OLS) and Maximum Likelihood Estimates (MLE) estimates of the parameters of Translog frontier production function are reported in Tables 1 -3.First, by grid search the ordinary least square estimates of parameters are obtained and then OLS estimates are used to estimate the maximum likelihood estimates of the parameters in the context of Translog production function.

Hypothesis tests of advances frontier model
The results of various hypothesis tests of the advances frontier model are presented in Table 4. Since the hypothesis 0 :  5).

DISCUSSION
All the coefficients of the first order parameters are found statistically significant at 1 percent level of significance but the second order coefficients of material and time are insignificant.The significant result indicated that these input variables importantly affect the level of producing bank advances.
The maximum likelihood estimates of the parameters of advances frontier model using Translog production function are mentioned in Table 3.We observe that all the first-order coefficients except labor and second-order coefficients are found significant excluding interaction variables material and labor, material and time, labor and time.In case of producing advances we can infer that the number of labor is not an affecting variable.Hence, to uphill the advances productivity the bank authority needs to improve the skill of employees.The most significant variable is capital which includes all physical value of fixed assets to increase efficiency of a bank.In both OLS and MLE we have observed that the coefficient of labor holds negative sign which is not surprising but indicating that some banks may be still overstaffed even after many years of reforms.Here the important thing is that the competition among the bank decreases the advances inefficiency.From the coefficients of the dummy variables it is observed that ISB, FB, and PB dummies are significant at 5 percent level and all of them are positive sign indicating that they are highly inefficient.The year wise average advances efficiency of 20 banks are delineated in Figure 1.From the analysis it is observed that in the year 2001 the technical efficiency is     period.
The average advances efficiency of 20 banks was estimated for advances model which is displayed in Figure 3.The most efficient bank (Janata Bank) with an average technical efficiency of 94.3 percent, followed by Sonali Bank (94.1 percent) and Islami Bank Bangladesh ltd.(75.9 percent) showed advances services.Among the private banks, one bank and Premier bank are most inefficient banks with efficiency scores of 0.370 and 0.371, respectively.All other banks are identical.The temporal behavior of advance efficiency shows that it has declined marginally for the maximum banking industry in the year 2003; it may be because banks have taken time to adjust to the new regulation and competitive framework.However this differs at the bank group level.The advance efficiency of selected banks, which decreased in the year 2003 and increased for the remaining study period but the advance efficiency of Sonali Bank and Janata Bank are found almost stable.

Conclusion
This paper studied the development of online bank advance efficiency in Bangladesh and it applied the Stochastic Frontier Approach in evaluating the efficiency, to a sample of 20 banks during the period of 2001-2007.The findings showed that the average efficiency of the overall considered banks has increased after the year 2003 while the average efficiency trend has been decreased during the period, 2001 to 2003.The results suggested that the mean technical efficiency improved during the reference period.The technical efficiency of nationalized commercial banks was 94.2%, higher than the Islamic banks, foreign banks and private banks where the technical efficiency was 49.5, 47.1 and 46.2%, respectively.The most efficient banks were observed for both Janata bank (94.3%) and Sonali bank (94.1%) while most inefficient banks were found to be One bank and Premier bank with efficiency scores of 0.370 and 0.371 respectively.
are the value of the likelihood function for the advance frontier model under the null and alternative hypotheses.Under the null hypothesis , this test statistic that identifies an appropriate functional form either the restrictive Cobb-Douglas or Translog production function.specifies that the technical inefficiency effects in online banks are zero.If the null hypothesis is accepted this would indicate that 2 u is zero and hence that the it U term should be removed from the model, leaving a specification with parameters that can be consistently estimated using ordinary least square (OLS).that the technical inefficiency effects are time invariant i.e., there is no change in the technical inefficiency effects over time.If the null hypothesis is true, the generalized likelihood ratio statistic  is asymptotically distributed as a chi-square (or mixed chi-square) random variable.
is a technical inefficiency effect in the model.From the outcome it is observed that the null hypothesis

Figure 1 .
Figure 1.Year wise average advances efficiency of Banks in Bangladesh.

Figure 3 .
Figure 3. Advance efficiency of Banks in Bangladesh.
can be expressed as:

Table 2 .
Maximum-likelihood estimates of translog advances frontier production function and inefficiency effects model.
Total assets and Herphindahl index gives negative sign in advances inefficiency model indicating that both total assets and Herphindahl index reduce inefficiency.

Table 3 .
Inefficiency effects of model estimates.

Table 4 .
Likelihood-ratio test of hypothesis of the stochastic advances frontier production function.

Table 5 .
Advance efficiency of banks in Bangladesh.