An analysis of the economic efficiency of the banking sector in vietnam

GLS Generalized least squares SFA Stochastic Frontier Analysis SFM Stochastic Frontier Model DEA Development Envelopment Analysis PE Profit efficiency CRER Credit risk LIQD Liquid

VIETNAM THE NETHERLANDS

PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS

AN ANALYSIS OF THE ECONOMIC EFFICIENCY OF THE

BANKING SECTOR IN VIETNAM

BY

NGUYEN THI PHUONG THAO

MASTER OF ARTS IN DEVELOPMENT ECONOMICS

HO CHI MINH CITY, NOVEMBER 2015

This study measures economic efficiency of commercial banks in Viet Nam and its determinants The Stochastic Frontier Model is applied for a profit function We include internal factors (including price of fund, price of physical capital, price of labor, price of loan and price

of other earning assets) and macroeconomic factors (economic growth, inflation rate, and other macroeconomic environment variables) in the profit function The empirical results show that the efficiency of Vietnamese commercial banks seems to be fluctuated steeply over the period 2008-

2013 In terms of the efficiency of different groups of commercial banks, the profit efficiency of the State-owned commercial banks and Private commercial banks follow different trend Particularly, the state owned commercial bank’s group seems to have extremely higher profit efficiency score then private commercial bank

GLS Generalized least squares

SFA Stochastic Frontier Analysis

SFM Stochastic Frontier Model

DEA Development Envelopment Analysis

PE Profit efficiency

CRER Credit risk

LIQD Liquidity

CON Concentration

DEV Banking development

INF Inflation rate

PROFIT Total profit

PBT Profit before tax

Obs Number of observations

SOBs State-owned commercial banks

PCBs Private commercial banks

LIST OF TABLES

Table 3.1: Variables of potential correlates of profit efficiency function 32 Table 3.2: Data sample of observations over period 2008-2013 43 Table 4.1: Overview of variable in profit function 35 Table 4.2: A summary statistics of profit before tax, inputs, outputs and prices used in the profit efficiency estimation for the whole period 2008-2013 38 Table 4.3: A summary statistics of inputs, outputs and prices used in the profit efficiency estimations: (million VND units for X1, X2, X3, Y1, Y2) 39 Table 4.4: A summary statistics of potential correlated of profit efficiency 40 Table 4.5: Potential correlates of profit before tax (PBT) with time-invariant fixed-effects model 41 Table 4.6: Banking profit efficiency scores in the period 2008-2013 with time-invariant fixed-effects model 42 Table 4.7: Potential correlates profit efficiency through time-invariant fixed-effect model 43 Table 4.8: Potential correlates of profit before tax (PBT) with Cornwell et al (1990) time varying fixed-effects model 44 Table 4.9: Banking profit efficiency scores in the period 2008-2013 with time-varying Battese and Coelli (1995) model 45 Table 4.10: Potential correlates profit efficiency with Kumbhakar (1990) time-varying

parametric model (half-normal) 46 Table 4.11: Average banking profit efficiency score of 27 commercial bank in Vietnam and its ranking from 2008 to 2013 48

Figure 1.1: Input-oriented efficiency 13 Figure 1.2: Output-oriented efficiency 14 Figure 4.1: Graph of scatter between Profit before tax (Pbt) and total number of staff (X1) from

2008 to 2013 36 Figure 4.2: Graph of scatter between Profit before tax (Pbt) and total fixed - asset (X2) from

2008 to 2013 36 Figure 4.3: Graph of scatter between Profit before tax (Pbt) and total deposit from customer

(X3) from 2008 to 2013 36 Figure 4.4: Graph of scatter between Profit before tax (Pbt) and total loan from customers (Y1) from 2008 to 2013 36 Figure 4.5: Graph of scatter between Profit before tax (Pbt) and total asset (Y2) from 2008 to

2013 36 Figure 4.6: Graph of scatter between Profit before tax (Pbt) and Price of labor (W1) from 2008

to 2013 36 Figure 4.7: Graph of scatter between Profit before tax (Pbt) and Price of capital (W2) from 2008

to 2013 37 Figure 4.8: Graph of scatter between Profit before tax (Pbt) and Price of fund (W3) from 2008

to 2013 37 Figure 4.9: Graph of scatter between Profit before tax (Pbt) and Price of loan (P1) from 2008 to 2013 37 Figure 4.10: Graph of scatter between Profit before tax (Pbt) and Price of other earning asset

(P2) from 2008 to 2013 37 Figure 4.11: Profit efficiency score from 2009 to 2013 with time-invariant fixed-effects model

43 Figure 4.12: Profit efficiency score of SOBs, PCBs and all banks from 2009 to 2013 with time-varying Battese and Coelli (1995) model 46

Appendix 1: List of Vietnamese commercial banks in Vietnam Data was collected from

www.taichinhvietnam.com and sorted based on their charter capital 57 Appendix 2: The result of estimation about the determinants of banking profit before tax and its potential correlate through different type of model 59 Appendix 3: Descriptive statistics of profit efficiency estimation through different type of model 67

LIST OF ABBREVIATION iii

LIST OF TABLES iv

LIST OF FIGURES v

LIST OF APPENDIXES: vi

CHAPTER I: INTRODUCTION 0

1 Introduction: 0

2 Research objective 1

CHAPTER II: LITERATURE REVIEW 2

1 Theory of the efficiency 2

2 Reviews of empirical study on bank efficiency 5

2.1 Overview on bank efficiency 5

2.2 Determinants of banking efficiency 7

2.3 Bank efficiency measurement 9

CHAPTER III: DATA AND METHODOLOGY 21

1 Overview of the banking industry in Vietnam 21

2 Analytical framework 23

3 Research method 23

4 Theoretical Model 23

5 Estimation Methodology 24

6 Model specification 25

7 Functional form 26

8 Profit Efficiency 26

9 Variables description 28

10 Data sources: 33

CHAPTER IV: RESULTS AND DISCUSSION 35

1 Descriptive statistics 35

2 Regression results 38

2.1 Time-invariant fixed-effects model 38

REFERENCES 49 APPENDIX 54

Prior studies in the body of literature indicate that there are a wide range of factors affecting the bank efficiency which can be classified into two main groups namely external factors (e.g macroeconomic factors and industrial factors) and internal factors of commercial banks (e.g size, losses, liquidity, and other factors) Particularly, Hasan and Marton (2003) examines the relationship between the development and efficiency of banking sector while Hou, Wang, and Zhang (2014) measure the linkages among market structure, risk taking and efficiency of commercial banks Due to their importance on the financial sector and their influence on the national economy, this sector requires a high regulation by the government However, in most developing countries like Vietnam, there is lacks of perfect regulation to support this sector to stabilize and develop Like other countries, the banking system in Vietnam provides many products from retail banking such as saving accounts, deposits, credit/debit card, mortgage, loans to commercial banking such as business loan, capital equity, risk management, and credit services

As commercial banks have evolved in Vietnam before the investment banks, this service is one of the most sensitive business which suffers direct and indirect impacts on several intrinsic obstacles of the economy as well as the external effects, thus stabilizing the currency and the banking system play an important factor, primarily in the financial system stabilization Therefore, understanding the efficiency of the banking system as well those factors affecting the banking operations attracts a lot of attention from many economists and scholars all over the world In measuring efficiency, people usually choose between technical efficiency and economic efficiency We choose economic efficiency as this is more comprehensive In this thesis, the profit function is used to measure economic efficiency

2 Research objective

While the capital funds raised for the national economy from those commercial banks are enormous, limited research was carried out about how these banks operate and whether they operate efficiently With a proper measurement about banking efficiency together with a wealth of predictive determinants will help the public to indicate how well a certain commercial bank operate in the competitive market like Vietnam Secondly, by improving the performance of individual banks, the whole national banking system will function much more efficiently and effectively However, at the moment, most of studies focused on qualifying the efficiency of the commercial banks (Nguyen, Roca, & Sharma, 2004) or determining certain large-scale economic factors affecting commercial banks (Athanasoglou, Brissimis, & Delis, 2008) without quantifying these factors to rank these commercial banks

in the global scale Hence, the aim of this thesis is to verify the connection between the current financial growth at the national scale and the efficiency performance of commercial banks in Vietnam

In details, this thesis is to understand the connection between the economic efficiency and the economic growth of the banking system based on two following smaller objectives:

 How efficient are commercial banks in Vietnam?

 Which factors affect the economic efficiency of commercial banks?

This is the research of Vietnamese banks efficiency that will convey the managers to identify the banks’ weakness as well as the causes of those weaknesses so that they can come

up with the right strategies, which will bring the best result given the same level of resource inputted In addition, this will be a useful research to analyze inefficiencies and minimize it in order to improve the performance of Vietnamese banking industry Moreover, this research also demonstrates the reality of Vietnamese banking industry, which will be a useful guide for foreign investors to start financing their equity in this dynamic industry

CHAPTER II: LITERATURE REVIEW

The concept “efficiency” in general and “bank efficiency” in particular are common terms in the body of literature of economic discipline These could be used to refer to the competitive capability of entities in the economy The chapter covers a broad review on foundational theories on efficiency, bank efficiency and characteristics of the terms The measurement approaches as well as factors affecting bank efficiency

1 Theory of the efficiency

In the production economics, the definitions of efficiency and productivity are two concepts proxy for two different things Firstly, the definition of “productivity” and

“efficiency” in terms of firm production has to be differentiated Clearly speaking,

“productivity” considers the entire elements that decide the level of output achieved with the amount of input given Efficiency, however, have a different meaning compared to productivity

Efficiency includes three types (technical efficiency, allocative efficiency and economic efficiency) The function of economic efficiency consists of profit efficiency and cost efficiency In this study, profit efficiency function is used to measure economic efficiency

It relates to the production frontier This frontier presents the level of output that can

be reached a peak with the same level of input amount The firm, which produces on this frontier, will be considered efficiency Also, going beyond this frontier is unrealistic because there is a limitation of its performing ability Similarly, it is inefficient producing below this frontier The further distance, the more inefficiency the firm is

Even though productivity and efficiency are two separate concepts, they are closely related Therefore, if the firm expects to improve its productivities, they will have to produce more efficiently Other elements that makes the level of productivity are changed in the quantities and proportion of inputs (changing its scale efficiency), an innovation of technology (change in technology level), or according (Coelli et al., 2005) we make combinations between all above factors

The definition of efficiency is about the transforming performance between the numbers of inputs into outputs (Forsund & Hjalmarrson, 1979) Hence, the efficiency is

usually considered as an essential competitive force of entities in an economy such as a branch, industry, or an entire system However, as the society gets more advanced, the definition of efficiency changes to be more specific For example, Saha & Ravisankar (2000) focused on the basic stage to measure the value of output at a given amount of input from the engineering perspective In order to attain an efficient point, Koopmans (1951) proposed the necessary of balancing the equivalent unit of different outputs In other word, the most efficiency is the point at which one output is used to maximize a given amount of the input Given that, Debreu (1951) and Sephard (1953) developed a quantitative measurement of efficiency for the outputs and inputs respectively Debreu (1951) measured the distance between the produced output and the predicted output that could have been produced from a given amount of inputs while Sephard (1953) measured the difference the actual input and the minimum possible amount of inputs

Later, Farrel (1957) brought the measurement of efficiency into the next level by establishing the distance functions between efficient point and practical producing point – the theory of Production Possibility Frontier (PPF) Based on the PPF theory, Kablan (2010) measured the efficiency by measuring the optimal set of points of inputs in order to produce one unit of output which is defined as the Production Possibility Frontier Line (PPF 8 Line) and compared with the actual production unit The firm is called to be efficient only when its outcome is on the PPF line and vice versus Moreover, the theory of PPF can also be approached from two sides: Input-Oriented approach (IO) and Output-Oriented approach (OO) (Farrell, 1957) While the firm uses IO to measure the minimum amount of inputs to produce a given set of outputs, OO is used to predict the maximum level of outputs from a given level of inputs

Although there is no consensus on the proper results of IO and OO in banking efficiency measurement, the IO approach is mostly preferred than the OO one because banks are able to focus on controlling the inputs (cost) rather than relying on the outputs (outcome) (Dipasha et al., 2012) although there are some exceptions by employing both approaches (Beccalli, Casu, & Girardone, 2006)

Among the above studies, Farrell (1957) was one of the first pioneer who proposed the efficiency as a technical term that can be measured by two main elements Figure 1.1 demonstrates a firm with two inputs X1 and X2, YY’ is an isoquant which shows every minimum set of inputs that could be used to produce a given output If a firm operates on this

isoquant (the frontier), it will be technically efficient in an input-oriented way for the reason that the inputs amount of this firm is minimized The iso-cost line CC’ (which can be constructed when the input-price ratio is known) determines the optimal proportion of inputs

in order to archive lowest cost

Figure 1.1: Input-oriented efficiency

The first one is technical efficiency (TE) which focus on the ability of bank to achieve the maximal output with a given fixed set of inputs, Technical efficiency (TE) can be calculated by the percentage rate of OR/OP, the second one is allocative efficiency (AE) equals the percentage rate of OS/OR The multiplication of AE and TE expresses the overall efficiency of the firm, called economic efficiency (EE) (i.e.EE = AE × TE) Figure 1.2 illustrates the case where the bank uses one input and produces one output The f(X) curve determines the maximum output can be obtained by using each level of input X (the frontier) The firm will be technical efficient operating on this frontier In this situation, TE equals BD/BE

Figure 1.2: Output-oriented efficiency

Regarding to the concept of efficiency measurement in banking sector, a bank can be said to be efficient only if it has an ability to produce an expected result with a minimum effort or resources

In the body of literature, bank efficiency has been discussed in a variety of studies from Berger & DeYoung (1997), Berger and Humphrey (1997), Timothy J Coelli (1998), and Bonin, Hasan, & Wachte (2005) In order to evaluate the efficiency of commercial banks, several measurement criteria need to be taken into account such as scale efficiency, allocative efficiency, productive efficiency, technical efficiency However, as knowledge of bank efficiency has evolved, many factors have to be considered as suggested by Fu et al (2014), Berger, Hasan, and Zhou (2009), and Tecles and Tabak (2010) These studies suggested the bank efficiency measurement can be determined by both internal and external factors

In summary, the theoretical foundation on efficiency and bank efficiency have been well-established and attracted a lot of academic interests who not only studied about the efficiency measurement but also evaluate different determinant of bank efficiency in the aspect of economic world

Measurements and analyses of TE were conducted by a huge number of studies with two main approaches – Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) The next section briefly discusses these two methods

2 Reviews of empirical study on bank efficiency

2.1 Overview on bank efficiency

Bank efficiency has been applied since 19th century when Sherman and Gold (1985) applied specific DEA (CCR Model) to analyze the efficiencies of 14 branches of a US savings bank Their study was able to indicate six out of 14 branches were operating inefficiently at that time Milin Sathye (2002) also applied a similar methodology to measure the efficiency of 94 India banks during the period of 1997-1998 He developed two independent models to rank the efficiency based on the variation of inputs and outputs In the first model, inputs are expenses, both interest and non-interest while outputs are nominated as net income accordingly Hence, compared to the private sector and foreign commercial banks, the public sector banks have showed a higher score in the average efficiency in India

In the second model, he designated inputs as deposits and staff numbers, while outputs as net

loans and non-interest income As a result, the second model showed the opposite result, meaning the private sector commercial banks scored a higher mean efficiency than the public sector ones

Among the prior studies, the banking efficiency received an greatest academic interest among many industries (Liadaki & Gaganis, 2010; Saha & Ravisankar, 2000; Yin, Yang, & Mehran, 2013) As given by Saha and Ravisankar (2000), the bank efficiency is of the most reliable indicator to drive the competitveness in the banking industry The authors argued that the commercial banks require an efficient operation system to gain more chances to sustain their business Tecles and Tabak (2010) indicated that the efficiency of the banking sector plays a vital role in both the finance development sector as well as the economic growth A comprehensive review on the efficiency of financial institutions can be seen in the study by Berger and Humphrey (1997)

Taking into account the banking industry of a specific country, a study by Tecles and Tabak (2010) measured the level of efficiency of156 commercial banks in Brazil from 2007

to 2010 and determine different bank’s characteristics that are associated with, e.g size, ownership, market share, non – performing loans and equity value As a result, it showed that the larger size the banks were, the more efficient the banks got Bank efficiency measurement has also been applied for the Vietnamese banking system as Vietnam is in the transition economy with the high economic growth in recent years Concise evidences can be found from reports by Nguyen (2011) and Lieu and Vo (2012) Chao and Nguyen (2006), for example, researched the methodology to evaluate the efficiency of commercial banks in Vietnam Labor and various kinds of expense were used to measure the total loans as outputs and total deposits as inputs for efficiency measurement similarly to model by Milin Sathye (2002) The results were consistent to other research in the region, meaning, the larger asset size of banks have exhibited 11 times higher efficiency than the small ones Ngo (2010) also conducted a research to estimate the performance of 22 Vietnamese commercial banks in

2008 The study also used labor, capital and funds as well as income for testing variables The conclusion is that these banks achieved the average efficiency scores close to the optimal score, as an evidence for the bank improvement in Vietnam

Another conduct by Nguyen (2011) focused on measuring the efficiency 20 commercial banks in Vietnam in the 3-year period (2007-2010) with more efficiency determinants to be evaluated In details, labor, fixed assets and deposits as inputs, and interest

and non-interest income as outputs are all taken into account The finding indicated that the state-owned banks had lower efficiency scores as compared to their join-stock commercial banks competitors Later, a study of Lieu and Vo (2012) showed that since 2006, the competition between banks was extremely high due to the financial crisis, especially with the wide fluctuation in in the input value of deposits and changes in the operating efficiencies of joint stock banks However, the research scope of the study was still limited as a traditional methodology was applied in evaluating key financial ratios of commercial banks

In the recent years, the stock market of Vietnam has been considered as one of the fastest growing markets among emerging countries, hence more commercial banks has listed their stocks on on the stock exchange However, very few studies have focused on the efficiency of the banking sector in Vietnam due to data limitation Hence, it is important to set a standard measurement of banking efficiency of Vietnamese commercial banks which will provides valuable information for managers, customers and investors

2.2 Determinants of banking efficiency

2.2.1 Macroeconomic factors

There have been many researches regarding the relationship between macroeconomic indicators and banking efficiency As a result, several economic factors are proven to have the impacts on bank efficiency such as economic growth and stock performance

For example, Avadi and Arbak (2013) researched the relationship between bank’s efficiency and economic growth especially in the southern Mediterranean region After analyzing insight information and data, they found out that the profits from banking industry had a huge impact on the economic growth Also, Ferreira (2012) also conduct a study of the same topic but in the European The outcome of this study was the evidence of how the bank’s cost efficiency affect the economic growth, especially GDP

Regarding the stock market performance, Beccalli et al., (2006) in his research suggested that bank’s efficiency also has impacts on the stock market performance The study was focused on measuring various European bank’s efficiency and used those results to prove that changes in cost efficiencies of target banks may cause changes in the prices of bank shares, that means bank’s efficiency and the stock market are having a relationship, through which it could create changes to the economy Similar results could be found in the study by

Liadaki and Gaganis (2010) who indicate the changes in both cost and profit efficiency have affected stock prices of commercial banks operating in EU markets over the period from

2002 to 2006

2.2.2 Banking industry factors

It could be seen that there are a wide range of banking industry factors taken into consideration with regard to the bank performance in the body of literature Some common factors can be indicated such as industry development, industry competition, industry concentration or industry growth, and other factors These factors are discussed in several studies by Athanasoglou, Brissimis, and Delis (2008), Owoputi (2013), and Pulungan and Yustika ((2014)

A study by Athanasoglou, Brissimis, and Delis (2008) examines the impacts of industry specific factors and bank profitability of Greek commercial banks over the period

1985 – 2001 Particularly, the authors use two determinants including ownership and concentration to measure the industry specific indicators; however, they find industry structure does not significantly affect bank profitability

Naceur and Omran (2011) investigate the effect of two indicators of the banking system, namely regulation and competition, on bank margin and cost efficiency across 11 countries over the 1988 – 2005 period Additionally, taken into account the industry development indicator, the authors use the size of the credit to private sector as a percentage

of the GDP to measure the impacts of bank financing in the entire economy The proxies of the banking sector development seem to have no impacts on the bank market but have negative signs with the cost efficiency They conclude that the well – developed banking sector may lower its operating costs

2.2.3 Bank Specified factors

There are several factors that can be utilized to measure specific characteristics of the bank, such as financial leverage, and the bank’s size, equity and risk, etc However, an evidence mentioned in an observational studies shows the keen interest between the bank specific indicators and the performance of the bank (how liquid and profitable it is)

A study conducted by Fu et al., investigates the relationships between the return on equity and both cost and profit efficiency Several bank specific factors mentioned above

were used in the study The findings indicate that there is a significant influence of the bank size, market risk and credit risk (bank specific factors) Other bank specific factors, equity to total assets and return on assets ratios, were also used by Lensink, Meesters, and Naaborg in a study to examine the impact of both factors on cost efficiency The researchers examined the efficiency of the bank and the foreign ownership of a large commercial bank in more than

100 countries (from 1998 to 2003)

In conclusion, many prior studies were taken into consideration when determining the relationship between macroeconomic factors, and bank specific factors and performance (ratios) However, it is worth to mention that the researchers have also taken into consideration that bank efficiency has emerged recently, and that the findings in the observational studies on bank efficiency and factors are not consistently supported This leads

to the need of further investigating the relationships between the bank efficiency and indicators of commercial banks including industry specific and bank specific factors

2.3 Bank efficiency measurement

In this literature, different methods will be discussed that can be used to measure bank efficiency These methods are based on different aspects of bank efficiency As given by Yin, Yang, and Mehran (2013), two specific aspects are taken into account for bank efficiency measurement in terms of achieving the maximization of output or requiring the minimal inputs As such two approaches namely the production approach and the intermediation approach can be applied to determine the bank inputs and outputs (Sufian, 2009; Yin et al., 2013) Particularly, the production approach considers loan, deposit and other financial services as inputs and the intermediation approach considers deposits, labors, and capitals as its input In the production approach, output variables are bank deposit and loan transactions while in the intermediation approach, bank loans and investments are known as outputs However, as indicated by Yin, Yang, and Mehran (2013) and Thoraneenitiyan and Avkiran (2009), commercial banks focus on intermediation services rather than physical goods, hence the intermediation approach will be more appropriately used to measure their bank efficiency

Regarding to the methodology to measure bank efficiency, many studies have proposed several methods such as Berger and Humphrey (1997) and Beccalli et al (2006) The most traditional and simple method is to use key financial ratios to analyze bank’s performance However, due to the increasing input/output determinants in bank efficiency

measurement, a large number of authors support two more advanced group classes, namely parametric and nonparametric approaches Particularly, the nonparametric methods cover two main approaches which are Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH) The methods draw a linear connection to rank the best practicing DMUs by comparing the operation of two different banks in one sample set These methods do not require any specific production function and are suitable for a small size of data set On the other hand, the parametric method includes Stochastic Frontier Analysis (SFA) or more advanced techniques such as Thick Frontier Approach (TFA) and Distribution Free Approach (DFA) The later method requires more variable and specifies a functional form for efficiency functions such as production function, profit function or cost function For specific commercial bank industry in particular to determine its profit efficiency, as commercial banks do not produce physical goods but provide intermediation services, both the inputs and outputs of banks must be determined by different groups of inputs and outputs Among these above methods, the DEA and SFA are commonly used by many researchers in recent studies (Kohers, Huang, & Kohers, 2000; Thoraneenitiyan & Avkiran, 2009), hence, the details of these two methods are given as follow

2.3.1 Data Envelopment Analysis model and Stochastic frontier model

a Data Envelopment Analysis model:

The Data Envelopment Analysis (DEA), categorized as a non–parametric method, is a linear programming model As given by Farrel (1957), the model was developed from the piecewise -linear convex hull approach and further developed by Charnes, Cooper, and Rhodes (1978) who employed a mathematical planning model with “constant returns to scale” (CCR model) to measure the technical efficiency frontier Then, Banker et al (1984) extended the model by providing variable returns to scale and output orientation In the DEA method, no functional form for the data is required It allows a production frontier reflected in the weights for the inputs and outputs can be calculated

In the DEA method, how a particular decision making unit (DMU or bank in this study) operated is examined relative to the other units in the sample Based on the DMUs or banks, the production frontier set, is then set to rank from the most efficient banks to the most inefficient ones using efficiency scores

Profit efficiency model

While cost efficiency focuses only on cost, profit efficiency considers both cost and revenue aspects Accordingly, the profit efficiency model developed by Färe, Grosskopf, and Lovell (1988) is employed to measure profit efficiency for bank j as follows

𝑀𝑎𝑥 ∑ 𝑟𝑠 𝑗𝑠𝑦𝑗𝑠 − ∑ 𝑐𝑚 𝑗𝑚𝑥𝑗𝑚

Subject to: 𝑥𝑗𝑚 ≥ ∑ 𝑥𝑖 𝑖𝑚ƛ𝑖 ∀m, 𝑦𝑗𝑠 ≤ ∑ 𝑦𝑖 𝑖𝑠ƛ𝑖 ∀s,

∑𝑛 ƛ𝑖 𝑖=1 ƛ ≥ 0 The assumptions to this model is a combination of the optimal output supply vector

y∗j = (y∗j1 …y∗js) and the optimal input demand vector x∗j = (x∗j1 …x∗jm) in a possible production curve set that the same condition of given input prices c and output prices r, the profit will be maximized, and the bank j will be the best one when it uses least level of input

to produce optimal output with a bank’s linear combination is obtained, it leads this hypothetical bank to have an optimal profit P∗j = ∑ rjsy∗

js

s − ∑ cjmx∗

jm

m which, by definition, this optimal profit will be equal to or higher than the actual banking profit j (Pj=

∑ ri jsyjs i − ∑ cm jmxjm ) As a result, the banking profit efficiency for j could be calculated

as follows

𝑃𝐸𝑗 = 𝑃𝑗

𝑃∗𝑗 =

∑ 𝑟𝑖 𝑗𝑠y𝑗𝑠 𝑖 − ∑ 𝑐𝑚 𝑗𝑚𝑥𝑗𝑚 ∑ 𝑟𝑗𝑠𝑦∗

𝑗𝑠

𝑠 − ∑ 𝑐𝑚 𝑗𝑚𝑥∗𝑗𝑚

b Stochastic frontier model

The first SFA model was developed by Aigner, Lovell and Schmidt (1977) and Broek, Førsund, Hjalmarsson, and Meeusen (1980) based on the production function estimation namely the Cobb-Douglas production function Later, several other functions are listed in the SFA model including Quadratic, Translog, Generalized Leontief, Normalized Quadratic, and Constant Elasticity of Substitution (CES) forms (Griffin, Montgomery, and Rister, 1987) Among those function, Cobb-Douglas and Translog function are most commonly used (Jiang et al., 2009; Liadaki & Gaganis, 2010; Yin et al., 2013) Frequently, the Cobb-Douglas model is used for its parsimony while the Translog model is used for its

flexibility More particularly, the Cobb-Douglas functional form assumes there is no change

in the value of production elasticity and other factor substitution; while the Translog functional form does not As such, The production function can be tested in the Translog form to provide more realistic and less restrictive results

However the Translog model poses some weakness when the number of parameters increases, it appears cross and squared terms On the other hand, if the number of observations is not limited, this increase in parameters leads to the decrease in freedom Given that, it is necessary to combine both models provide consistent results of bank efficiency Examples can be seen in the study by Kohers et al.(2000), and Thoraneenitiyan and Avkiran (2009)

Profit efficiency model:

On the other hand, using the SFA methodology, according to Berger and Mester (1997), the measurement of the profit efficiency model can be quantified similarly to the cost efficiency model with the exception that the inefficiency values are with a negative sign in the regression as follow

Ln𝑍𝑖,𝑡 = f (𝑌𝑖,𝑡 𝑃𝑖,𝑡 ) - 𝑢𝑖,𝑡 + 𝑣𝑖,𝑡Where 𝑙𝑛𝑍𝑖,𝑡 presents the logarithm of profit efficiency, 𝑢𝑖,𝑡 is the measure of inefficiency, it is a negative error term since with a higher inefficiency leads to decrease profit and 𝑢𝑖,𝑡 is always positive The 𝑣𝑖,𝑡 is the noise component, which is outside the control of management, assumed to follow a normal distribution

c Trade-offs between DEA and SFA

Based on many difference from approaching method, there are many advantages and disadvantages when we make a choice using DEA or SFA in our research It means that researchers have to face the trade-offs when researchers use DEA or SFA to estimate the study According to Ray & Mukherjee, 1995 DEA is a non-parametric method, a deterministic approach, it does not mention about the specification of the production function meanwhile SFA is a parametric method, a stochastic technique using econometric tools and must have a model specification of production function From that key difference, DEA is considered to be non-statistical, which assumes that the data have no noise Data noise can come from measurement errors or random factors which can be controlled by banks This

restrict seems to be stubborn in realistic situation SFA is statistical, so it allows and takes into account statistical noise In other words, it is more flexible with real world data, in which random factors and error in collecting is unavoidable

Wagstaff, 1989 found that using SFA must satisfy assumptions about the functional forms, specifications of the model, distribution of parameters and error terms In DEA approach, every bank counts as inefficiency operating when every factor that leads the bank away from its frontier While in SFA, the residual will be decomposed into two components One part, which is not under the control of the firm itself, is accounted to be the noise and has the zero mean The other part, which is known as the inefficiency, is the weakness of the bank which makes it produce below the frontier So, generally, the efficiency measured from SFA will be higher relatively (Ferrier & Lovell, 1990) DEA has the advantages with the ability to be applied in various complicated condition of production Without the requirement

of a definite production function, it helps simplifying the linkage from inputs to outputs of a production process Without statistical properties, no test can be used to test DEA’s goodness

of fit or specification In spite of having troubles with model specification, SFA still has econometric tools to test whether the model is suitable or not The most beneficial advantage

of SFA is the capability of dealing with statistical noise

Generally, for industries that the production processes are controlled strictly, DEA seems to be the better choice of measuring efficiency This is because the random fluctuation

in these industries is minimized and the production process is very stable (from a given amount of inputs, the number and quality of outputs is likely to be determined precisely) For those natures of the industries the thesis analyzed, SFA is the better model to be applied The next part discusses in detail SFA method with panel data models

Overall, both the DEA and SFA approach have both advantages as well as disadvantanges While the DEA methodology is sufficient to estimate the efficiency of a given banking system by avoiding misspecification issue Yin et al (2013) illustrated that the DEA approach might lead to some random errors in the ill-defined economic environments

In fact, Jiang et al (2009) had suggested that SFA method is reliable in a context of transition economies However, given that the SFA approach requires an intensive parametric factors, profit efficiency calculation might become exhaustive especially with the multi-hierarchy banking system in developing countries like Vietnam

2.3.2 Stochastic frontier model with panel data

In this section, an overview of stochastic frontier model (SFM) with panel data (repeated observations on each firm) will be present to explain the motivation for the models

in banking efficiency estimation By using panel data rather than cross-sectional data setting, estimation techniques can be carried out without strong distribution assumptions on each variable and repeated observations with panel data can be considered as a substitute of independence between technical efficiency error and other parameters This allows the efficiency measurement to be more robust and consistent (Kumbhabar & Lovell, 2000)

A typical stochastic frontier model firstly developed by Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977) can be written as below:

(1) 𝑦𝑖 = 𝛼 + 𝛽x𝑖 + 𝑣𝑖− 𝑢 𝑖 , i = 1 , …, N

Where i is a production unit (firm), 𝑦 is the log of output, x is the log of input, vis

normal noise, and u is a measure of technical inefficiency Three variables x, v, and u are assumed to be independent, and v and u are assumed in different types of distributions The

formula (1) can be computed as follows

(2) y i = f(x i ;β) exp(v i ) exp(−u i ), i = 1, 2, , N.

Later, several authors have generalized this model for the panel data format setting (N firms

in period time T) by applying time parameters in the assumptions on y, x, 𝑣, and u Here two

main SFA models are considered in which technical efficiency is constant through time (time-invariant model) or allowed to vary for each firm (time-varying model) Especially,

technical inefficiency error (u) explains differences across different firm performances as

well as the same firm performance in different time periods While technical efficiency measurement allows to determine which firms operate efficiency, technical inefficiency error component permits firms to be able to identify causes of inefficiency and learn how to become efficient in practice As a result, several models have been developed in order to make the most appropriate estimation for the technical inefficiency component

a Time-invariant Technical Efficiency

First, it begins by assuming technical inefficiency u i to be constant over time and

restrictedly non-negative (u i ≥ 0) Based on model (1), the time-invariant SFM model is as

i Fixed-effect model by Schmidt and Sickles (1984)

The fixed-effected model is the simplest one which has been developed by Schmidt

and Sickles (1984) In the FE model, the technical inefficiency u i is constant over time but varying among different firms, hence there is no distribution assumption about technical

inefficiency error u i and all the variables are uncorrelated to each other Since there is no

distribution assumptions on u i , technical efficiency (TE i) of individual firm can be estimated

by introducing least squares with dummy variables (LSDV) followed by equation (4):

𝛽0 is estimated from 𝛽0 = maxi{ 𝛽0i }

u i is estimated from u i = 𝛽0 - 𝛽0i

TE i is estimated from TE i = exp {-u i }

In the FE model, at least one firm is assumed to be 100% technically efficient and other firms’ efficiencies are relatively compared to the top firm The LSDV estimation method of technical inefficiency component can be consistent as both the number of firms and time period assessment are large enough (e.g T  ∞ and N  ∞)

ii Random-effect model by Schmidt and Sickles (1984)

While in the FE model, the u i is fixed, in the RE model, the u i value is randomly distributed but with constant mean and variance This allows the technical inefficiency ui to vary across different firms but still constant for each firm Again, all the variables (e.g

between inefficiency error u i and the input x it , or between inefficiency u i and noise errors v it) are uncorrelated to each other Now the model (4) can be written as follows

(5) ln 𝑦𝑖t = 𝛽0 * + ∑ n𝛽n lnx n 𝑖t + 𝑣𝑖t − 𝑢𝑖*

It is available to use standard two-step GLS method to evaluate this model in which:

û i * = 1

𝑇∑ (𝑙𝑛 𝑦𝑡 𝑖𝑡− 𝛽̂0∗− ∑ 𝛽̂𝑛 𝑛𝑙𝑛 𝑥𝑛𝑖𝑡)𝑛

û i = max{u i *}-u i *

Estimation consistency using GLS can be reached when the sample with number of firms N is large enough, e.g the measured random effects are uncorrelated from the regressors Further test from Hausman and Taylor (1981) can be adopted to verify the uncorrelatedness between the fixed-effect estimator by LSDV and the random-effect estimator by GLS

iii Maximum likelihood model by Pitt and Lee (1981)

For time-invariant technical efficiency, a conventional maximum likelihood method can be adapted to estimate the effect β and the technical inefficiency error u i by making independent distribution assumptions for botherror components, the idiosyncratic noise vitand technical inefficiency term ui. There are several distributional assumption models that can be used in the maximum likelihood method including normal-half normal, normal-exponential, normal-gamma, and normal-truncated normal models Pitt and Lee (1981) was the first one to formulate and estimate time-invariant panel data model using the normal-half normal distributional assumption

b Time-varying technical efficiency

In a competitive operating environment like financial services, the assumption of time-invariant efficiency sometimes is unrealistic, e.g it is unlikely that technical inefficiency term remains unchanged especially through a long time panel data setting (Cornwell et al

1990) Hence with a long panel, it is more desirable to relax this assumption, leading to the development of time-varying technical efficiency

Similar to time-invariant technical efficiency, we can use a maximum likelihood or fixed effects or random effects approaches to estimate this model

We can illust the stochastic frontier model using panel data with time-varying technical efficiency as follows

(6) ln𝑦𝑖𝑡=𝛼𝑖𝑡+ 𝛽ln𝑋𝑖𝑡+𝑣𝑖𝑡 (based on model 3)

With 𝛼𝑖𝑡 is time varying firm effects which follows a function of time

The model 6 is also written as a Cobb-Douglas function based on model 4

(7) ln 𝑦𝑖t = 𝛽0t + ∑ n𝛽n ln x n 𝑖t + 𝑣𝑖t − 𝑢 𝑖t = 𝛽it + ∑ n𝛽n ln x n 𝑖t + 𝑣𝑖t where 𝛽it = 𝛽0t - u it

i Fixed effects and random-effects model by Cornwell et al (1990)

In term of the fixed-effect model, the technical efficiency of each bank in the given period t is estimated as:

TE it = exp{-u it } where 𝑢𝑖t= β ^

0𝑡− β ^𝑖𝑡

Hence, in each period t, at least one firm’ technical efficiency is estimated to be 100%, however, the most efficient bank level can change over the time (Zhu, W and Zhao, D., 2007)

As the same reason to the random-effect model for time-invariant technical efficiency, uit can vary over the time but also can be random distributed across different firms Hence, Cornwell et al (1990) also use GLS random-effect estimator like Schmidt and Sickles (1984)

to evaluate the technical efficiency in condition of time-varying The estimator model can be written as:

TE it = exp{-u it } where 𝑢𝑖𝑡=𝛼it −𝛼^𝑖𝑡Where 𝛼it=(𝛼^i 𝑡) by comparing the specific effect of each firm to the most efficient firm in that year

However, since the degree of freedom of these parameters is heavily affected in small

N (firms) and T (time), GLS estimation remains inconsistent Hence, an alternative formulation is proposed by Lee and Schmidt (1993) as follows

𝑢𝑖𝑡=B(𝑡)𝑢𝑖 , where B(t) is set as time dummy variables B(t), 𝑢𝑖 is fixed through time but varied across firms and 𝑢𝑖 follows a half normal distribution

Similarly, if temporal error components vit and uit are independent and available for distributional assumption, we can use the likelihood function to evaluate time-varying technical efficiency (Sangho Kim and al., 2002) Three estimators have been developed by Kumbhakar (1990), Lee and Schmidt (1993), and Battese and Coelli (1992)

Kumbhakar (1990) estimated the temporal technical inefficiency error as follows

𝑢^𝑖𝑡= 𝛾^(𝑡)×𝑢^𝑖 where u i is followed half-normal distribution

The suggested time function is:

Lastly, Lee and Schmidt (1993) replace the time function by a set of dummy variables

𝜃𝑡 which relax the time function as compared to previous estimators The model 6 can be described as

Hence, Green (2005) suggested that uit should be uncorrelated to the rest of model parameters, that means, the most efficient firm identity should be consistent over time while the technical inefficiency vary freely through time (Green, 2008) This kind of so-called heterogeneity has been discussed by Farsi, Filippini, and Kuenzle (2003) as factors beyond the control of firms but belongs to business environment As a result, Greene (2005) suggests

“true” fixed and random effects model as follows

“True” fixed model is described as:

(9) 𝑦𝑖𝑡=𝛼𝑖+𝛽′𝑥𝑖𝑡+𝑣𝑖𝑡−𝑢𝑖𝑡With 𝛼𝑖 is the firm specific constant The similar maximum likelihood as discussed in section 2.2 can also be used to estimate with this model (Green, 2005)

Meanwhile the “true” random effects model can be written as:

(10) 𝑦𝑖𝑡=(𝛼+𝑤𝑖)+𝛽′𝑥𝑖𝑡+𝑣𝑖𝑡−𝑢𝑖𝑡With 𝑤𝑖 is a random constant term that varies across firms

*Note: Green (2005) used the Cobb-Douglas form

In conclusion, with the power of better analysis using panel data, stochastic frontier models with panel data have been used widely to estimate the firm efficiency in both time-invariant and time-varying manners Within these formulations, both fixed-effect, random-effect, and maximum likelihood models can be adapted to estimate the efficiency performance in both measure and empirical works Firstly, with the fixed effect estimator, an introduction of dummy variables as LSDV allows us to estimate the models unbiasedly However, by using dummy variables, all explanatory variables might be lost through calculations, leaving the produced technical efficiency performance inconsistently Secondly, with the random effect estimator, the technical inefficiency error can be randomly distributed under a GLS model, however, leading to the fact that the explanatory variables can be biasedly correlated with the technical inefficiency error Hence, whenever the explanatory variables are tested to unbiased with the technical inefficiency suggested by Hausman and Taylor (1981), random-effect models can be demonstrated to be powerful and consistent estimation methodology Lastly, Green (2005) has also challenged our assumption about time-varying function with the heterogeneity of firms by relaxing the technical inefficiency errors across time and firms

Lastly, xt-frontier calculation from the program STATA is shown to be powerful in estimating the parameters of stochastic cost or production frontier models The program allows to calculate both time-invariant and time-varying technical efficiency based on maximum likelihood estimator by Battese and Coelli (1992) with truncated-normal random variables

CHAPTER III: DATA AND METHODOLOGY

This chapter gives descriptions about current status of banking industry of Vietnam as well as the research model, variables and data used in the research Particularly, details on specific models and measurement of variables are given based on reviews of prior studies The data collection is introduced and discussed

1 Overview of the banking industry in Vietnam

The first independent bank in Vietnam was opened after the August Revolution in

1945, namely Vietnam National Bank (later named the State Bank of Vietnam) and served as the first commercial bank in Ho Chi Minh City which handles personal savings and business loans Since 1992, the Vietnamese banking system pioneers in attracting foreign investment and integrating into the global economy From the beginning, the banking sector was based

on the single/double-level banking system with four govern bent-controlled commercial banks with a limited scale in management or services Nowadays, Vietnam banking system is improving rapidly in different aspects such as credit unions, credit cards, insurance, stock brokerage, or investment funds Current Vietnam banking system consists of a variety of banking ownerships such as national or state-owned, joint-stock, joint-venture, co-operative, private-limited, or foreign banks These banks serves different economic functions such as local banking for local financial business, foreigner banking with 100% foreign investment, retail banking for individual and small businesses, business banking for mid-level financial services, cooperate banking for large business entities, private banking for fund equity, and investment banking for those large-scale financial markets

With effective and customer-oriented reorganization and development strategies, the Vietnamese banking system especially in the joint-stock commercial banking has improved significantly in both quality and scale diversity as compared to those from the 80s At first, the commercial bank licenses were divided into two categories based on their minimal capital The urban joint-stock commercial banks require at a minimum of 50billion Vietnam dong while the suburban ones require 2billion Vietnam dong The momentary policy has changed three times with the highlights: (i) to increase the suburban commercial banks’ minimal capital from 2 to 5 billion Vietnam dong, (ii) to set a threshold of 100 billion Vietnam dong for all urban banks, (iii) to set a new threshold of all joint-stock commercial banks of 3000 billion Vietnam dong until the end of 2010

As a result, until 31/12/2009, there are in total 37 joint-stock commercial banks which contribute 42% of the whole Vietnam banking system The total capital raised approximately 100.000 billion dong, which is twice as much as all the state-owned commercial banks and constituted 60% of total national capital The whole commercial bank network has developed dramatically all over the country – from Lang Son to South East provinces, even the most remote areas The whole collected capital from these banks contributes approximately 42% of the banking capital system

In summary, over the last two decades following the restructuring plan, the Vietnam’s banking sector has experienced significant developments On the one hand, the supervision function of the State Bank of Vietnam is clearly separating into the commercial function of commercial banks The structure of commercial banks, on the other hand, is gradually strengthening with a participation of new strong financial institutions in accordance with the liberalization and international globalization with the global economy

The current Vietnam commercial banking is still considered to be immature as compared with other countries in SEA and internationally, which lead to the instability in both economic and financial industry of the country The banking sector has undergone re-organization since 1990 in order to limit the government dominancy and stimulated the banking development permanently in terms of ownerships and increase in the number of bank names In details, the number of for-profit commercial joint stock banks has increased dramatically However due to low public confidence, regulatory and managerial limitations, the commercial banking system still struggles to find their positions in the Asian financial markets as well as the global sector From 1991 to 1993, the number of commercial banks jumped from 4 to 41 and reached 51 on 1997 After the global financial crisis in 1997, several commercial banks filed bankruptcy or license withdrawal due to inefficient operation, as a result a decrease in the number of operating banks In the period of 2002-2007, most of commercial banks speed up the reorganization process to stabilize and developed the management structure in terms of constructive financial management, mergers and acquisitions, take-over of those small inefficient commercial banks in the end of 1990s Moreover, the number of branches and representative offices of international banks were likely increased in this period according to the US-Vietnam Bilaterial Trade Agreement and ASEAN Framework Agreement on Services As a result, the proportion of local commercial banks decreased visibly from the top of 73% in 1993 down to 40% in 2007

Currently, there are about 40 commercial banks operating in Vietnam which are from state-owned and urban joint-stock commercial (it is described more details in Table 1) excluding government banks, equity funds, wholly foreign-owned banks, and foreign banks representatives

2 Analytical framework

Furthermore, in order to have a deeper analysis, one of the most important aspect of Vietnamese banking industry, which is profitability, was estimated by the stochastic frontier analysis (SFA), first proposed by Aigner, Lovell, and Schmidt (1977) and Meeusen and van der Broeck (1977) We particularly apply the SFA model developed by Green (2005) to examine potential correlates of bank efficiency over the period 2008-2013 to investigating the determinants of bank efficiency

3 Research method

There are different indicators implied on the purpose of researching banking industry development However, since the “banking industry development” and “bank concentration index” have the most recent data and it is always available, it is the most important among all the indicators Regarding the research methods, the Stochastic Frontier Approach is used to measure profit efficiency This method is also applied to examine the relationship between the bank efficiency and banking industry development in Vietnam

For reasons discussed earlier, we employ the stochastic frontier analysis (SFA), first proposed by Aigner, Lovell, and Schmidt (1977) and Meeusen and van der Broeck (1977) to estimate the most important aspects of bank efficiency in Vietnam: profitability We particularly apply the SFA model developed by Green (2005) to examine potential correlates

of bank efficiency over the period 2008-2013

4 Theoretical Model

As discussion, in the banking industry, there are many difficulties in the endogenous variable of input quantities, according to the original approach of production function to make a study about the supply equations might be ambiguous Therefore, it is a common way

to directly analyze the profit functions by taking the dual approach and evaluate the conditions of the economic When we use this approach, we must follow the assumption of profit maximization

In particular, a profit function is determined as the given input prices (W) and output prices (P), the profit is got the maximization:

π= π (W, P) (1)

This function must have characteristics as follow: convex in the output prices (P) and concave in the input prices (W) Moreover, the function of profit must be in conditions of non-increasing in the prices of input (W) and non-decreasing in the prices of output (P)

5 Estimation Methodology

In this study, the Stochastic Frontier Approach (SFA) is used to analyze the banking efficiency, and then it provides the efficiency scores of each bank and ranks them This approach considers about the inefficiency of the banking system based on the results of banking production, it means that if the bank operates with the lower profit and higher cost than another bank in the system with the same environment and conditions, so we can conclude this bank is inefficient In particular, because of the existence of possible firm inefficiency and the random noise, the observations of total banking profit will be deviated from maximum profit efficiency frontier

As a result, when we use the Stochastic Frontier Approach (SFA) to estimate methodology, we must require a specific functional form which is constructed by suitable variables of input and output under random noises in data exists over time Moreover, Stochastic Frontier Approach (SFA) also includes many differences between each bank and for this reason, it is clear to allow for both random errors and environmental factors

For Stochastic Frontier Approach (SFA) with panel data, accordingly to Berger and Mester (1997) we can write the profit function in logs as follow

ln(πit) = π (𝑃𝑖𝑡 𝑊𝑖𝑡 ) + 𝑣𝑖𝑡 - 𝑢𝑖𝑡 (2) Where the profit function is defined as negative sign with inefficiency term (𝑢𝑖,𝑡) in the regression, 𝜋𝑖𝑡 is proxy of total profit of each bank with ith bank (i= 1, 2, 3, N) at the tthyear (t= 1, 2,…) , Pit is the vector of the prices of output prices, Wit is the vector of the prices

of input in the banking industry

6 Model specification

Regarding the inefficiency terms we must mention about distributional assumption

There are three popular distributions for u consist of truncated normal, half normal and

exponential normal Exponential normal distribution and half normal distribution have the advantages and disadvantages when we apply for measuring the efficiency of bank The truncated normal distribution 𝑁+(𝑚𝑖𝑡 , 𝜎2) is assumed distribution of inefficiency term in this study, this is the most flexible one

There are some determinants of the parameter 𝑚𝑖𝑡 for inefficiency can be modeled as follow

𝑚𝑖𝑡 = 𝛿0+ 𝑍𝑖𝑡𝛿 + 𝜔𝑖𝑡Where 𝑍𝑖 is the vector of determinants of 𝑚𝑖 and 𝛿 is the vector of corresponding parameters This is description of the inefficiency model and this model will be simultaneously evaluated with the Stochastic Frontier Approach (SFA) In this study, determinants of inefficiency terms which are proxy by Z is described in Table 3.1 Therefore, this study assumed that the function of Z must be followed a linear function form

There are many various models develop to indicate that how the inefficiency term change overtime when we apply SFA with panel data As discussion in chapter II, we can divide those models into two types: time varying models and time invariant model Based on the estimation techniques, SFA with panel data models can also be classified into two groups: random effects and fixed effects Greene (2005), Cornwell et al (1990), Schmidt and Sickles (1984),and Lee and Schmidt (1993) mentioned about fixed effects models which do not require the assumption that inefficiency term is not correlated with the rest of the model Similarly, Kumbhakar (1990), Pitt and Lee (1981), Schmidt and Sickles (1984), Battese and Coelli (1988, 1992, 1995), and “true” random effects model in Greene (2005) indicated that random effects models which require the assumption of uncorrelated between the inefficiency term and other variables in the model In this study, we chose the model of Cornwell et al (1990) time varying effects which follows a function of time, with αit is time varying firm effects which follows a function of time The author mentions a quadratic function of time with parameters vary across firms described as:

𝑙𝑛 𝑦𝑖𝑡 = 𝛼𝑖𝑡 + 𝛽 𝑙𝑛 𝑋𝑖𝑡+ 𝑣𝑖𝑡

𝛼 = 𝜃 + 𝜃 𝑡 + 𝜃 𝑡2, 𝑢 = 𝑚𝑎𝑥 (𝛼̂ ) − 𝛼̂

7 Functional form

In this study, based on the characteristics of Translog functional form is popular for its flexibility with the drawbacks on tractability and parsimony, it is used to descript the profit function as follow

The level of banking inefficiency can be calculated as the ratio of observed cost/profit

to the optimal cost/profit (i.e the output when the bank is fully efficient or the value of 𝑢𝑖𝑡 is zero)

Profit efficiency: 𝑃𝐸𝑖𝑡 = 𝜋𝑖

𝜋 ∗= 𝑒(𝛽 𝑙𝑛 𝑋𝑖𝑡+𝑣𝑖𝑡−𝑢𝑖𝑡)𝑒(𝛽 𝑙𝑛 𝑋𝑖𝑡+𝑣𝑖𝑡) = 𝑒(−𝑢𝑖𝑡)

In the progress of finding banking efficiency result, this research found that there are endogenous phenomena between profit efficiency and input variables such as price of labor (W1), price of capital (W2) and price of fund (W3) We can define endogenous phenomena

as an appearance of correlate between one of variable in the model with error terms The endogeneity can raise ability error in the result of measurement, auto-regression with auto-correlated errors, omitted variables and simultaneity Basing on these endogenous phenomena, this study generated the lag-variable to treat the endogeneity like lagW1, lagW2, lagW3 for endogenous variables consist of price of labor, price of capital and price of fund, respectively

After that, this research run regression for endogenous variables and then make a predict functions to generate a new variable such as Prlabor, Prcapital, Prfund and three new variables will replace to W1, W2, W3 in the regression

Furthermore, we run Stochastic frontier model with panel data regression to evaluate the effects of inputs and outputs on profit before tax basing on fixed effect model (Schmidt

and Sickles, 1984) and then calculating the efficiency of every bank with time-invariant technical efficiency and with time varying technical efficiency:

 Cornwell et al (1990) time varying effects which follows a function of time, with αit

is time varying firm effects which follows a function of time The authors mentions a quadratic function of time with parameters vary across firms described as:

𝑙𝑛 𝑦𝑖𝑡 = 𝛼𝑖𝑡 + 𝛽 𝑙𝑛 𝑋𝑖𝑡+ 𝑣𝑖𝑡

𝛼𝑖𝑡 = 𝜃𝑖1+ 𝜃𝑖2𝑡 + 𝜃𝑖3𝑡2, 𝑢𝑖𝑡 = 𝑚𝑎𝑥𝑗(𝛼̂𝑗𝑡) − 𝛼̂𝑖𝑡

 Kumbhakar (1990) with the time varying, e described as:

𝑙𝑛 𝑦𝑖𝑡 = 𝛼 + 𝛽 𝑙𝑛 𝑋𝑖𝑡+ 𝑣𝑖𝑡− 𝑢𝑖𝑡With 𝑢𝑖𝑡 = 𝛾(𝑡)𝑢𝑖 where 𝑢𝑖 is fixed through time but varied across firms and 𝑢𝑖follows a half normal distribution The suggested time function is:

𝛾(𝑡) = (1 + 𝑒𝑥𝑝(𝑏𝑡 + 𝑐𝑡2))−1The fact that 𝛾(𝑡) ≥ 0 makes 𝑢𝑖𝑡 always positive in the production

 Battese and Coelli (1992 and 1995) with a technical efficiency and truncated normal distribution at zero:

𝑢𝑖𝑡 = 𝛾(𝑡)𝑢𝑖 (Battese and Coelli 1992) With the form of 𝛾(𝑡) = exp[−𝜂(𝑡 − 𝑇)] and 𝑢𝑖 𝑖𝑖𝑑 |𝑁(𝜇, 𝜎𝑢2)| (truncated normal distribution at zero)

𝑌𝑖𝑡 = 𝑒𝑥𝑝(𝑥𝑖𝑡𝛽 + 𝑉𝑖𝑡− 𝑈𝑖𝑡) (Battese and Coelli 1995)

 Lee and Schmidt (1993) with a function with the time function is replaced by a set of dummy variables:

𝑦𝑖𝑡 = 𝑋𝑖𝑡𝛽 + 𝜃𝑡𝑢𝑖 + 𝑣𝑖𝑡