0
Dt (xt , yt ) and
Dt 1 (xt 1 , yt 1 )
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respectively is the distance function according to which the
0
The production point is compared with the frontier technology at time t and t +1.
Dt (xt 1 , yt 1 ) and Dt 1 (xt , yt ) are the output distance functions according to which the production point
0 0
output is compared with the frontier technology at different points in time.
According to Caves, Christensen and Diewert (1982) [29], the Malmquist productivity index by output is defined as follows:
Dt (xt 1, yt 1 )
M t 0
(38)
0
0 Dt (xt , yt )
Where M 0t measures the change in productivity resulting from the change in technical efficiency from period t to t +1 with the technology from period t +1 given as:
Dt 1 (xt 1 , yt 1 )
M t 1 0
(39)
0
0 Dt 1 (xt , yt )
To avoid choosing an arbitrary threshold, we will specify the Malmquist productivity change index by output as the geometric mean of the two Malmquist productivity indices mentioned above:
Dt (xt 1, yt 1 ) Dt 1 (xt 1, yt 1 )
0 0
Dt (xt , yt )
0
0
Dt 1 (xt , yt )
0
M ( x t 1, y t 1, x t , y t ) (40)
The Malmquist index of productivity change by output can be decomposed
wall:
Dt (xt 1, yt 1 ) Dt (xt , yt )
0 0
D (x , y ) D (x , y )
t 1 t 1 t 1
0
0
t 1 tt
Dt 1 (xt 1, yt 1 )
0
M ( x t 1, y t 1, x t , y t ) 0
(41)
0
Dt (xt , yt )
In which, the first term on the right side
Dt 1( xt 1, yt 1 )
0
measure change
0
Dt ( xt , yt )
relative efficiency between year t and t +1 under constant efficiency conditions
Dt (xt 1, yt 1 ) Dt (xt , yt )
0 0
D (x , y ) D (x , y )
t 1 t 1 t 1
0
0
t 1 tt
scale. The second term on the right side represents
index of technical change, that is, the marginal technological change between two periods t
and t +1, evaluated at x t and x t+1, so we have:
0
TE Dt 1 (xt 1 , yt 1 )
0
Dt (xt , yt )
(42)
Dt (xt 1, yt 1 ) Dt (xt , yt )
0 0
D (x , y ) D (x , y )
t 1 t 1 t 1
0
0
t 1 tt
TC (43)
Increasing productivity will be represented by a Malmquist index greater than 1. Decreasing productivity will be associated with a Malmquist index less than 1. Furthermore, an increase in each component of the Malmquist index will result in the value of that component being greater than 1. By definition, the product of efficiency change and technical change will equal the Malmquist index, and these components can change in opposite directions.
d) Select input variables and inputs to estimate efficiency measures for commercial banks in the DEA model.
The outstanding feature in the operation of the banking industry is that the service industry has many inputs and many outputs, so the concern is how to reasonably specify the outputs and inputs of banks. In fact, there is currently no complete and clear theory or definition on determining the inputs and outputs of banks. This gives rise to two major problems in many studies, which are related to the role of deposits, when they are inputs and when they are outputs, and whether inputs and outputs should be measured in quantity or monetary units. As a result, in studies on the operational efficiency of banks in the world today, people have proposed five approaches in determining the input and output variables of a bank, specifically:
Production approach: pays much attention to the technical efficiency of financial institutions, considering the activities of banks as providers of services. Therefore, deposits are considered as outputs and interest payments on deposits are not included in the total costs of banks (Ferrier and Lovell, 1990 [46]). According to this approach, inputs and outputs are taken as quantitative units (number of accounts, transaction processes...).
Intermediation approach: based on the view that banks are financial institutions that mobilize and allocate lending funds and other assets; therefore, deposits are considered as inputs and interest payments are part of the total operating costs of the bank.
Asset approach: differs from the intermediate approach in that it considers liabilities as inputs and assets as outputs.
Value added approach: consider any item in the balance sheet as an output if it attracts the respective contributions of labor and capital, otherwise it is considered an input. According to this approach, deposits are considered as output because it implies that it creates value added
The user cost approach considers the net contribution to bank revenue defined as outputs and inputs; thus in this case deposits are considered as outputs.
In short, based on the collected data and the actual operations of the bank, choose the appropriate approach to select the best input and output variables, most suitable for measuring the performance metrics of commercial banks.
1.1.3.3. Model for analyzing factors affecting the performance of commercial banks
After estimating the efficiency measures, Tobit regression model is used to analyze the factors affecting these efficiency measures (because using OLS regression - least squares estimation - can make the parameter estimates biased).
The Tobit regression model was first introduced by Tobin in 1958, and it is also known as the Tobin probit model or the truncated normal regression model. It is a linear regression model with a dependent variable being a dichotomous latent variable in which some observations of the latent variable are missing when the latent variable is above or below a certain threshold, such a variable is called a truncated variable and the regression with such variables is called a truncated regression. Theoretically, the standard Tobin model can be defined for a sample of i banks as follows:
y* ' x
(44)
iii
y y* if y* ' x
0 , and (45)
iiiiii
y 0 if y* ' x 0
(46)
iiii
Where x i and are vectors of explanatory variables and unknown parameters.
need to find,
y* is an implicit or truncated variable,
yi is a measure of bank efficiency
i
ith (restricted to the interval greater than 0 and less than and equal to 1) .
Based on the values y i and x i of observations comprising i banks, the likelihood function
( L ) is maximized to find the values of and as follows:
L (1 - F ) 1 e -[1/(2 2 )](yi - xi )2
(47)
yi 0
i
y 0
(2 2 )1/ 2
In which F
∫ i 1 e 2 dt
(48)
x / -t / 2
i -
(2)1/ 2
i
The first term of the function L is the number of observations reflecting banks as fully efficient and the second term is the number of observations reflecting banks as inefficient and F i is the distribution function of the standardized value
standardize at
' x
/ .
However, empirically the Tobit model can be simply rewritten as the equation below:
it
nm
0 ∑ j D jit ∑ j Z jit
(49)
j1 j1
In which, it is the technical efficiency of bank i in year t estimated by DEA or SFA method; D jit is a dummy variable (such as bank type...) and Z jit are variables reflecting: scale, ownership type, number of years of observation, market power, market share, stability of deposits... The selection of these variables is often based on evaluation indicators according to CAMEL standards including capital adequacy (C), asset quality (A), management ability (M), income (E) and liquidity (L). In addition, the selection of these variables is also based on actual surveys as well as the review requirements and demands of management agencies as well as bank administrators in financial analysis in general and analysis of bank operations in particular. Furthermore, after summarizing studies such as Xiaoqing Fu and Shelagh Hefferman (2005) [90], Ji-Li Hu, Chiang-Ping Chen and Yi-Yuan Su (2006) [65], Donsyah Yudistira (2003) [40], Tser-yieth Chen (2005)
[89], Berger and Master (1997) [17], Berger and colleagues (1993) [21], Master (1993) [83] ...and the requirements of the management, supervision and administration of commercial banks, the variables that can be selected in the Tobit regression model to assess the level of its impact on efficiency measures are:
Currently, banks in Vietnam are classified as small and medium sized compared to banks in other countries in the region and the world. Thus, we expect that the performance of banks will improve if the size of the bank increases. Therefore, the variable BANKSIZE equal to the natural logarithm of total assets is taken as a proxy for the size of a commercial bank.
OWNERNN and OWNERCP are two dummy variables introduced to test for possible efficiency differences between bank types. Thus, OWNERNN takes the value of 1 if the bank is a SOCB and takes the value of 0 if it is another type of bank and OWNERCP takes the value of 1 if the bank is a JSCB and takes the value of 0 if it is another type of bank.
TCTR: total cost/total revenue to reflect the ability to adjust each relationship between the input output ratio to achieve efficiency. Therefore, the smaller this ratio will give a higher efficiency index.
DLR is the deposit-loan ratio - to consider the impact of this ratio on the inefficiency of the input-to-output ratio. On the other hand, we also know that the main profit of commercial banks is the difference between interest income and interest expenditure. Therefore, one of the ways to increase the efficiency of the bank is to make good use of mobilized capital, by lending out to generate interest income. Thus, if the DLR ratio is high, it means that the bank has not made good use of its mobilized capital and vice versa, the bank has made good use of its mobilized capital. A bank that makes good use of its capital will have greater interest income and better operating efficiency, so the relationship between this variable and the efficiency measure has a negative expected sign. This variable was recently included by Chin S. Ou, Chia Ling Lee and Chaur-Shiuh Young to evaluate its impact on the operating efficiency of Taiwanese banks [35].
ETA: equity/total assets if this ratio is large, it will increase the return on equity and at the same time it shows that the financing of assets with equity increases, reducing the risk for shareholders and bondholders of the bank. Theoretically, this ratio can have a positive as well as negative impact on the efficiency level and it is used to reflect the regulatory conditions for banks. According to Berger and DeYoung (1997), the higher the liquidity and capital adequacy ratio of the bank, the lower the bad debts and therefore there is no need to increase the cost to compensate for these loans. On the contrary, if the capital adequacy ratio is low, it can create moral hazard behaviors, because, knowing that their bank has liquidity problems, but for profit, they can still carry out business activities and make risky investments and of course in the short term, these activities can bring efficiency to the bank, although in the long term they may have to pay the price for the consequences of their fraudulent behaviors.
MARKSHARE is included in the Tobit regression model to test market share and is calculated as total assets of each bank/total assets of all banks. This variable has been considered by Isik and Hassan 2003a [63] in their study of factors affecting the performance of banks in Türkiye.
LOANTA is the ratio of loans to total assets, which is an indicator reflecting the liquidity risk in the bank's operations, it shows the portion of assets allocated to the least liquid assets. Therefore, this variable partly shows the management capacity of the bank, according to Isik and Hassan 2003a [63] explained that if a bank makes many reasonable loans, it will make operating costs lower and allow this bank to gradually increase its share of the lending market.
NPL = overdue debt/total outstanding loans, is an indicator reflecting credit risk in bank operations. If this ratio is high, it can push the bank to bankruptcy. Thus, the impact of NPL on bank performance is expected to be negative.
FATA is the ratio of physical capital to total assets used to analyze the relationship between efficiency and risk, the higher the ratio, the greater the risk.
KL is the ratio of K to L, this variable is included in the model to examine the impact of capital equipment level per labor on the overall operating efficiency of the bank.
Nowadays, due to the pressure of the integration process, commercial banks are not only competing with domestic and foreign banks but also with other financial institutions, so the interest rate margin tends to decrease and makes the income from traditional banking services decrease. At that time, it is clearly predictable that only banks that develop modern banking activities based on the foundation of technological progress can increase the overall efficiency of the bank. Therefore, the variable TRAD = the ratio of interest income/operating income is included in the model to capture these changing trends in the development strategy of banks.
In addition, to capture changes in the macro environment, as well as changes in the bank's production technology during the study period, time variables were included in the model, which are defined as follows: Y02 = 1 if the year under consideration is 2002 and other years are 0, Y03 = 1 if the year under consideration is 2003 and other years are 0, Y04 = 1 if the year under consideration is 2004 and other years are 0, and Y05 = 1 if the year under consideration is 2005 and other years are 0.
1.2. Domestic research situation and experience in evaluating the performance of commercial banks in other countries: quantitative analysis approach
Studies on the performance of banks have used many different methods in terms of assessment techniques and data sets. But most of these studies are focused on developed countries. This section will review the research results in Vietnam and the research results in some countries according to the marginal efficiency analysis approach.
1.2.1. Research situation in Vietnam
Domestic studies on the operational efficiency of the commercial banking system have recently received attention from a number of authors, however, most of these studies only rely on qualitative studies such as: the study of PhD student Le Thi Huong in 2002 on " improving the efficiency of investment activities of Vietnamese commercial banks " , or the study of PhD student Le Dan ( 2004 ) " applying statistical methods to analyze the operational efficiency of Vietnamese commercial banks " , although it has somewhat approached quantitative analysis but still mainly stops at statistical indicators , or the study of Dr. Pham Thanh Binh ( 2005 ) with the topic " improving the competitiveness of the commercial banking system " . " Vietnam 's trade in the context of regional and international economic integration " also mainly stops at qualitative analysis .
Quantitative studies on measuring the performance of commercial banks are generally few. Recently, there was a study by Bui Duy Phu (2002) that evaluated the performance of commercial banks through the production function and the cost function. However, the limitation of that study was that it simply stopped at determining the cost function and directly estimating this cost function to find the parameters of the model, so it was impossible to separate the non-productive part.
efficiency in banking operations. Nguyen Thi Viet Anh (2004) estimated inefficiency factors for the Vietnam Bank for Agriculture and Rural Development using the stochastic frontier function method and estimated in the form of the Cobb-Douglas cost function. However, the basic limitation of the study is the specification of the function form.
Thus, it can be said that the application of quantitative analysis methods in the study of the performance of the banking industry in Vietnam is still very limited. In fact, it is also shown that currently in the analysis of the performance of the banking industry from the bank level to the industry level, analysts are still used to using traditional approaches, because, at present, this is still an easy-to-understand and easy-to-calculate approach.
1.2.2. Research situation in countries
Studies on the evaluation of the performance of banks, using quantitative analysis methods, have been used in studies such as Nathan and Neave (1992) [85] applying the stochastic frontier method to analyze the performance of Canadian banks during the period 1983-1987. The authors used the value-added approach and the intermediate approach to estimate the cost function. In which, to estimate the cost function, the authors used 3 inputs (labor, capital and funds) and 4 outputs (commercial and industrial loans, other types of loans, time deposits and demand deposits) according to the value-added approach, while for the intermediate approach, the authors used 3 inputs similar to the above approach and 3 outputs (commercial and industrial loans, other types of loans, securities and investments). The research results show that large banks do not have a clear cost advantage over small banks, which is similar to the US study where economies of scale are observed in both small and large banks.
Berger, Hanweck, and Humphrey (1987) [18] also applied a parametric approach to examine the economies of scale of 413 State Bank branches and 241 state commercial banks with total assets of less than $1 billion in 1983. Using two inputs: capital and labor and five outputs: demand deposits, savings and time deposits, real estate loans, commercial loans, and installment loans, the authors calculated an average economic efficiency of 0.96 for state commercial banks and 0.98 for State Bank branches. Diseconomies of scale were observed in state commercial banks with assets of more than $100 million, but this was not observed in State Bank branches.
Miller and Noulas (1996) [84] applied the data envelopment analysis (DEA) method to estimate the efficiency of 201 large US banks (banks with assets of over 1 billion USD in the period 1984-90. By using 4 inputs: Total payment deposits, total time deposits, total interest expenses and total non-interest expenses and 6 outputs: industrial and commercial loans, consumer loans, real estate loans, securities investments, interest income, non-interest income. According to the two authors, the average inefficiency (including pure inefficiency and scale inefficiency) of 201 banks is about 5%. At the same time, the research results show that most banks are too large and are falling into the area of decreasing efficiency with scale.
Fukuyama (1993) [50] also applied the data envelopment analysis (DEA) method to estimate the efficiency of 143 commercial banks in Japan in 1991. Fukuyama used 3 inputs: Labor, capital (including headquarters and bank real estate, intangible assets...), capital mobilized from customers (including deposits, certificates of deposit, discount certificates, loans, foreign currency and other amounts) and two outputs: interest income from loans, and revenues from other banks.
other banking operations. Fukuyama concluded that the main cause of overall technical inefficiency was pure inefficiency rather than scale inefficiency. The results of the study also showed that most banks were operating under conditions of increasing returns to scale. Finally, the group of large banks with assets of over 8 billion yen operated most efficiently.
Zaim (1995) [91] applied data envelopment analysis (DEA) to estimate the performance of 42 Turkish commercial banks before liberalization and 56 banks after liberalization based on data from 1981 and 1990. Four inputs (Labor, interest payments, depreciation and raw material costs) and four outputs (demand deposits, time deposits, short-term loans and long-term loans) were used to estimate the performance of these banks. The results showed that, on average, resources were wasted by about 75% above the minimum cost in the pre-liberalization period and by 38% above the minimum cost in the post-liberalization period. While most of the economic inefficiency in state-owned banks is caused by allocative inefficiency, the main factor causing economic inefficiency in private banks is technical inefficiency. Finally, when comparing efficiency indices, the author finds that state-owned banks are more efficient than private banks.
Ferrier & Lovel (1990) [46] used both stochastic frontier analysis (SFA) and data envelopment analysis (DEA) to evaluate the efficiency of 575 banks operating in 1984. The authors used 3 inputs (total number of employees; employee expenses, machinery and equipment expenses, and raw material and material expenses) and 5 outputs (number of demand deposit accounts, number of real estate loans, number of installment loans, and number of industrial loans). According to the DEA method