Number of Banks with Increasing (Icr), Decreasing (Dcr) and Constant Performance by Size (Cons) in the Period 2008-2013.

2011. In which, scale efficiency still contributed more at 0.946 than pure technical efficiency at 0.695. However, in reality, efficiency increased due to increased scale efficiency while pure technical efficiency decreased. This shows that the use of non-optimal resources led to a decrease in pure technical efficiency compared to 2010. There are many reasons such as: implementing Resolution 11/NQ-CP, the growth rate of assets and credit of banks decreased due to having to comply with the growth limit below 20% and the demand for business and consumer loans decreased. In addition, on March 1, 2011, the Governor of the State Bank issued Directive No. 01/CT-NHNN stipulating that by June 30, 2011, the ratio of outstanding loans to non-production sectors compared to total outstanding loans must be a maximum of 22% and by December 31, 2011 a maximum of 16%. This Directive has strongly impacted the operations of commercial banks, forcing them to freeze consumer credit, resulting in consequences for the real estate market and the stock market. In addition, high lending interest rates (up to 25%/year) have exceeded the capacity of customers. In the context of many fluctuations from different markets leading to a sharp decline in credit quality, bad debts tend to increase, thereby exposing weaknesses in risk management of banks. In the face of the general difficulties of the economy and the banking system, the profitability of the system has decreased. In 2011, there was a merger of a number of banks due to temporary illiquidity due to using short-term capital for medium and long-term loans.

2012: Our country's socio-economy continues to be affected by the world economic instability due to the unresolved financial crisis and public debt crisis in Europe. Production and business activities of enterprises are stagnant, inventories are high. Gross domestic product (GDP) in 2012 at 1994 comparative prices increased by 5.03% compared to 2011. Regarding banking activities, in 2012 most banks did not meet their business plan targets. Total assets of the whole system in general and many members in particular decreased. Bank interest rates were mild, on December 21, 2012, for the 6th time this year, the State Bank reduced operating interest rates, lowered the ceiling interest rates on deposits and loans, and stabilized system liquidity. Exchange rate

After many instabilities from 2008 - 2011 to 2012, it was quite stable. But credit growth was difficult, many banks had negative growth. At the beginning of the year, the State Bank expected credit growth for the whole year to be about 15 - 17% but in reality it only reached about 5%. Many banks had excess capital but many banks also had capital shortages. The problem of increasing bad debt has affected the entire banking system. Along with bad debt, the problem of cross-ownership has reached an alarming level and is a potential risk that creates risks in the entire banking system. It can be seen that the efficiency of banks has not fluctuated much compared to 2011, reaching 0.675, in which scale efficiency still contributes the most to the total efficiency, reaching 0.946 while pure technical efficiency reached 0.675. This proves that banks have not yet made optimal use of inputs to increase operational efficiency. In 2012, there were 10 banks rated A, 11 banks rated B and 6 banks rated C.

2013: In the context of Vietnam's economy still facing many difficulties, unresolved problems have affected production and business: Inventories are high, purchasing power is weak, the bad debt ratio of banks is at an alarming level, many businesses have to reduce production or stop operations. Regarding banking activities, as of December 12, 2013, total means of payment increased by 14.64%; capital mobilization increased by 15.61%; credit growth increased by 8.83% compared to the end of 2012 but was still lower than the plan by 12%; liquidity of the banking system was improved, ensuring the payment and payment capacity of the system; foreign exchange rates were stable, foreign exchange reserves increased. In 2013, although there were positive developments, there were still many difficulties: the bad debt ratio decreased but remained at a high level; credit quality has not improved; Bad debts have not been fully and accurately assessed and classified. The income-expense gap of the whole system increased by only 3.2%. The main reason is the adverse impact of economic difficulties. The gap between output interest rates and input interest rates decreased, while the cost of risk provisioning increased sharply due to the decline in asset quality. In addition, 2013 showed significant results achieved from the implementation of Project 254: basically controlling the operations of weak commercial banks, leading to the solvency of banks.

These banks have been improved, positively affecting the operation of the entire system. Weak commercial banks have been closely monitored by the State Bank and have been directed to restructure. After merging, consolidating or self-restructuring, commercial banks have actively implemented comprehensive restructuring solutions in finance, operations, administration and overcoming violations. Basically, they have been operating stably, the safety ratios of operations and payment capacity have been basically guaranteed according to the State Bank's regulations; capital mobilization from the population has increased, bad debts have been actively handled; the management system and organization of the apparatus and network have been consolidated. However, difficulties still remain, leading to low technical efficiency, but the bright spot here is the balance between pure technical efficiency and scale efficiency, demonstrating the rationality in using input factors of banking operations. Of which, the number of banks ranked A is 10, 4 banks are ranked B and 13 banks are ranked C.

Table 3.6 summarizes the estimated results of the DEA model, specifically showing the number of Vietnamese commercial banks operating under increasing, decreasing and constant efficiency conditions according to size (Appendix 3).

Table 3.6: Number of banks with increasing (ICR), decreasing (DCR) and constant performance by size (CONS) during 2008-2013.

2008	2009	2010	2011	2012	2013
DRS	18	17	12	16	13	14
IRS	5	3	16	10	8	4
CONS	8	11	3	5	6	9
Total	31	31	31	31	27	27

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Source: Author's calculation based on estimated results

Table 3.6 shows that the number of banks facing decreasing returns to scale is higher than that of banks with increasing or constant returns to scale. Therefore, these banks should reduce the scale of operations to increase operational efficiency.

dynamic. Based on the calculation results (see Appendix 3), these banks are usually large-scale banks, so to increase operational efficiency, these banks should not focus on expanding their operational scale but should focus on developing new products and product quality to improve the productivity of input factors. As for small banks whose efficiency increases with scale, they should expand the scale of the products they are providing to increase operational efficiency.

3.4.1.2. Estimating technical efficiency with stochastic frontier analysis (SFA)

Stochastic Frontier Method (SFA)

DEA is a linear programming technique to evaluate how a decision-making unit performs relative to other banks in the sample. DEA does not require the determination of a functional form for the efficient frontier and allows for the combination of multiple inputs and multiple outputs in calculating efficiency measures. However, the disadvantage of DEA is that it is sensitive to dominant observations and does not have statistical inference. Therefore, in this section, the author will apply the stochastic frontier analysis (SFA) method_Parametric approach; to evaluate the performance of Vietnamese commercial banks, with the aim of providing more accurate estimates of technical efficiency, as well as trends in the performance of commercial banks in the period 2008 - 2013.

The SFA method is often used in production, cost or profit analysis models. It can also be used in evaluating the performance of financial institutions such as commercial banks or investment funds. However, here we should not understand "input" as production factors, resources used directly to create "output" products. In the optimization problem of commercial banks, "input" can be understood as variables that with a certain "output" output, the enterprise will want to minimize; and "output" is the variables that with a certain set of "inputs", the enterprise will want to maximize.

The model for assessing the performance of banks used in this paper is built on the basis of the research of Battese and Coelli (1992), in which the technical inefficiency of each firm is assumed to follow a truncated normal random variable and change systematically over time. In addition, the technology factor is also assumed to change over time, so the model includes a time variable to characterize this factor.

The production function can be represented as a Cobb-Douglas function or a translog function, and the LR test will be performed to determine the appropriate functional form for the model.

Here, in addition to the usual inputs, we introduce the time variable t into the model as an input. This is to represent the change in technical progress over time.

Suppose there are i firms (decision-making units) to be evaluated, all using k

different inputs to produce output Y in T periods. The model can be represented as:

With In Which

is the output of firm i in period t;

is the input vector of size (k x 1) of firm i in period t;

is a parameter vector characterizing the role of input factors in the production function;

is a random variable assumed to be normally distributed and independent of

where is a non-negative random variable representing technical inefficiency in production, assumed to follow a normal distribution truncated at 0 . is a parameter representing the change in technical inefficiency with respect to

time (to be distinguished from the coefficient of the variable t in the deterministic component of the model)

In addition, the study also estimates the value of the variance of both error components.

: the component of technical inefficiency in error, which can be used to

test whether the use of SFA is really appropriate. If so, the component should be removed from the model and the product function estimated.

output by traditional OLS method.

The estimates in the article are calculated using FRONTIER software.

4.1 of Coelli (1996). The coefficients are estimated using the maximum likelihood method through three steps:

- First OLS regression estimates are performed, the coefficients except the intercept are unbiased estimates.

- Use grid search technique to estimate

- The result obtained from step 2 is used as the initial value of the Davidon – Fletcher – Powell Quasi – Newton iterative algorithm to obtain maximum likelihood estimates.

Then the technical inefficiency of each firm in each period will be calculated according to the expression of Battese and Coelli (1991). The estimate of the average inefficiency of each period is just the algebraic average of the individual values for each firm.

Data description:

The data used in the model are collected from the consolidated financial statements of Vietnamese commercial banks in the period from 2008 to 2013. The input variables used include: equity (EQ), interest expense (IN), operating expenses (OE) and bank risk provision expenses (RiE). The output variable used is pre-tax income (EB).

The selection of input and output variables in the SFA model is relatively complicated and controversial. There are many different views on how to choose, but in the author's opinion, there is no perfect approach that can reflect all the activities of the bank. This article chooses the input variables that are selected as the main costs of the bank, which are closely related to the performance of the bank. At the same time, the model only includes four relatively independent inputs to avoid multicollinearity between variables that distort the results.

The novelty of the model is that in order to represent the progress and innovation that make the technical level change over time, the model introduces the time variable t as a production input. It is necessary to distinguish the meaning of the coefficient corresponding to this input and the coefficient

corresponds to the time component in the variable . corresponds to the deterministic component of the model, representing the technological progress that causes the production capacity of firms to change over time; and corresponds to the random component of the model, representing the non-deterministic nature of the variable.

Production efficiency also changes over time.



The production function chosen is the Cobb Douglas function, specifically the function used for estimation is:

lnEQ

 0  1

ln(EQ)

 ln(IN)

 ln(OE)

 ln(RiE)

 5 t  vit uit

The model uses panel data so the study can both draw conclusions about the performance of banks at the same time and assess the development trends of the commercial banking sector between different years. Another feature of the model is that the data set used does not have complete variables for all banks in each year, which demonstrates the ability of the SFA model to produce results even in cases where the panel data is unbalanced.

Table 3.7: Summary statistics of variables used in the SFA model

Unit: million VND

Variable name	PRINT	EQ	EB	RiE	OE
2008	Medium	2761047	3870392	568858.2	261833.6	585134.6
	Standard deviation	661478.6	729585.7	137665.9	109537.6	174356.5
	Median	1671043	2199046	198723	35338	246401
	Minimum value	80094	577616	6235	1330	29452
	Maximum value	15895605	13790042	2560580	2553515	4957685
	Number of observations	31	31	31	31	31
2009	Medium	2409202	4738562	905538.7	207774.5	784206.6
	Standard deviation	542885.2	865181.2	211664.5	68552.47	195505.6
	Median	1300431	2547985	382632	82122	339896
	Minimum value	138921	1038949	28117	455	46668
	Maximum value	14235364	17639330	5004374	2012282	4536214
	Number of observations	31	31	31	31	31
2010	Medium	4393015	6630237	1272038	312699.3	1141440
	Standard deviation	931681.8	1045967	267858.2	107671.2	300236.6
	Median	2520683	4087344	661413	126283	446990
	Minimum value	334320	2022339	67373	3114	73997
	Maximum value	20590477	24219730	5568850	3024227	7197137
	Number of observations	31	31	31	31	31
2011	Medium	8002242	8004022	1552998	605897.1	1585694
	Standard deviation	1561242	1321671	360545	227049.8	372950.7
	Median	4939280	4644051	565976	148729	657284
	Minimum value	525917	2590976	114012	10519	208355
	Maximum value	35727190	28638696	8392021	4904251	9077909
	Number of observations	31	31	31	31	31
2012	Medium	7864398	9982600	1332970	818180.9	2031277
	Standard deviation	1509979	1932510	379027.5	235059.4	425202.5
	Median	5342662	5748969	479850.5	349325	1234836
	Minimum value	454888	3184140	3474	-564710	284577
	Maximum value	32240738	41553063	8167900	4357954	9435673
	Number of observations	26	26	26	26	26
2013	Medium	3089171.64	4335192.4	654090.8	315452.9	676964.1
	Standard deviation	4008143.88	4368287.63	829094.1	670185.9	1061713.1
	Median	1671043	2266655	221254	35338	264281
	Minimum value	118993	577616	6235	1330	29452
	Maximum value	15895605	13790042	2560580	2553515	4957685
	Number of observations	25	25	25	25	25

Source: Author's own calculation from annual reports of Vietnamese commercial banks

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