Economies of scale and input costs efficiency of commercial banks in vietnam, 2006 2014

The three key inputs of commercial banks during their operations are labor, financial capital and fixed assets are all inelastic and as such, they may be substitute for one another.. Emp

Ho Chi Minh City, Vietnam Erasmus University of Rotterdam

The Netherland

VIETNAM- THE NETHERLANDS PROGRAMME FOR M.A IN

DEVELOPMENT ECONOMICS

ECONOMIES OF SCALE AND INPUT COSTS EFFICIENCY OF

COMMERCIAL BANKS IN VIETNAM, 2006-2014

By Dang Tri Dung Supervisor

Dr Vo Hong Duc

Thesis submitted for the Degree of Master of Art in Development Economics

Vietnam - Netherlands Programme, November 2013

University of Economics

Ho Chi Minh City, Vietnam

VIETNAM- THE NETHERLANDS PROGRAMME FOR M.A IN

DEVELOPMENT ECONOMICS

ECONOMIES OF SCALE AND INPUT COSTS EFFICIENCY

OF COMMERCIAL BANKS IN VIETNAM, 2006-2014

By Dang Tri Dung

A thesis submitted in Partial fulfillment of the Requirements for the

Degree of Master of Art in Development Economics

Under the supervision of Dr Vo Hong Duc

Vietnam - Netherlands Programme, November 2015

DECLARATION

I hereby declare that the thesis "Economies Of Scale And Input Costs Efficiency Of Commercial Banks In Vietnam, 2006-2014" was made by myself under the supervision of Dr Võ Hồng Đức

I also hereby declare that all the data and the results of this thesis are collected and calculated by me In addition, the conclusions and recommendations are not copied by any research

Đặng Trí Dũng

The above declaration is affirmed

Dr Võ Hồng Đức

ABSTRACT

This study is conducted to determine and quantify the performance of the commercial banks in Vietnam in relation to their economies of scale and the possibility of substitute of inputs in their operations Data used in this study were collected from 32 commercial banks in Vietnam for the period from 2006 to 2014 The Iterate Semmingly Unrelated Regression (ITSUR) with the support of STATA software is used in this study The findings from this study provide empirical evidence to confirm that the operation scale of the commercial banks in Vietnam is increasing return to scale This means that increasing the scale of operations from the commercial banks in Vietnam may result in an increase of their profitability This finding appears to be consistent with a merger and acquisition taking place in the Vietnam’s banking system at the moment with the lead of the State Bank of Vietnam

In addition, the commercial banks in Vietnam have demonstrated that cost inefficiencies during operations are problematic The three key inputs of

commercial banks during their operations are labor, financial capital and fixed assets are all inelastic and as such, they may be substitute for one another As such,

controlling labour costs appears to be essential for the efficient operations of the commercial banks in Vietnam

Empirical findings from this empirical study are drawn to provide some implications for both the commercial banks and the State Bank Vietnam in relation

to the scale efficiency of operations for the commercial banks and the leading roles

of the central banks in providing guidance and assistance for the entire banking

system to grow further

Keywords: Ecnomies of scale; Financial capital; Labor; Fixed assets;

Elasticity; Commercial banks; Vietnam

ACKNOWLEDGMENT

I sincere thanks to my supervisor Dr Vo Hong Duc He was enthusiastically helped and gave me advice during the research process Dr Vo Hong Duc suggested useful ideas for my research

In addition, I am also wish to thank to all the lecturer of the Netherlands program The lecturers helped me to get the knowledge of development economics Furthermore, the teachers helped me to know the research methods in the economic field

Vietnam-CONTENTS

DECLARATION i

ABSTRACT ii

ACKNOWLEDGMENT iii

CONTENTS iv

LIST OF TABLES vii

LIST OF FIGURES viii

ABBREVIATIONS ix

CHAPTER 1 INTRODUCTION 1

1.1 Problem Statements 1

1.2 Research Objectives 2

1.3 Research Questions 3

1.4 The Scope of this Research 3

1.5 Methodology 3

1.6 The Structure of the Study 4

CHAPTER 2 LITERATURE REVIEW 5

2.1 Overview of the Commercial Banking System in Vietnam 5

2.2 Studies On The Scale Economies Of Commercial Banks 6

2.3 Studies On The Price Elasticity Of Inputs In Banking 7

2.4 Translog Cost Function Theory 8

2.5 The Estimation Method Of The Scale Economies and The Elasticity 10

2.5.1 Estimation Method Of The Scale Economies 10

2.5.2 The Own-Price Elasticity And Cross-Price Elasticities 11

CHAPTER 3 RESEARCH METHODOLOGY 14

3.1 The Hypothesis Testing 14

3.2 Identification Of Variable 14

3.1.1 The Dependent Variable 17

3.3 Data Collection And Expected Results 20

3.4 The Research Methodology 23

3.1.1 The Model 23

3.1.2 The Estimation Method 25

CHAPTER 4 EMPIRICAL RESULTS 32

4.1 Descriptive Statistical Analysis 32

4.1.1 The Data Description 32

4.1.2 The Summary Statistic 32

4.1.3 Correlation Matrix 33

4.2 Regression Results 35

4.2.1 The Results From Translog Cost Function 35

4.2.2 Empirical Finding 39

4.2.3 The Result Of The Scale Economies 41

4.2.4 The Own-Price Elasticity and Cross-Price Elasticity 44

CHAPTER 5 CONCLUSIONS AND POLICY IMPLICATIONS 51

5.1 Conclusions 51

5.2 Policy Implications 52

5.3 Limitations And Future Research 53

REFERENCES 54

APPENDIX A 59

APPENDIX B 66

APPENDIX C 72

APPENDIX D 73

APPENDIX E 74

APPENDIX F 75

APPENDIX G 76

APPENDIX H 77

APPENDIX I 78

APPENDIX J 79 APPENDIX K 80

LIST OF TABLES Table 1 The Variables Of Equation System That Analyzes The Relationship

Between Financial Capital And Labor 15

Table 2 The Variables Of Equation System That Analyzes The Relationship Between Financial Capital And Fixed Assets 16

Table 3 The Variables Of Equation System That Analyzes The Relationship Between Labor And Fixed Assets 16

Table 4 The Dependent Variables 21

Table 5 The Independent Variables 22

Table 6 Statistics Of Variables In The Equation System (9) 32

Table 7 Statistics Of Variables In The Equation System (10) 33

Table 8 Statistics Of Variables In The Equation System (11) 33

Table 9 The Correlation Matrix Of Variables In The Equation System (9) 34

Table 10 The Correlation Matrix Of Variables In The Equation System (10) 34

Table 11 The Correlation Matrix Of Variables In The Equation System (11) 35

Table 12 The Results Of The Equation System (09) 36

Table 13 The Results Of The Equation System (10) 37

Table 14 The Results Of The Equation System (11) 38

Table 15 The scale economies of Vietnam Commercial banks in 2006-2014 41

Table 16 The scale economies of Joint stock commercial banks and State commercial banks in 2006-2014 41

Table 17 The Own-Price Elasticity And Cross-Price Elasticities From Two Outputs Model 44

Table 18 The Own-Price Elasticity And Cross-Price Elasticities From Models Including Loan 45

Table 19 The Own-Price Elasticity And Cross-Price Elasticities From Models Including Deposits 46

Table 20 The Relationship Between The Inputs 47

LIST OF FIGURES Figure 1 Total Assets And Return On Total Assets Of Commercial Banks In

Vietnam 2013-2015 6

ABBREVIATIONS IPO: Initial Public Offering

NPLs: Nonperforming loans

ROA: Return On Total Assets

Agribank: Bank For Agriculture And Rural Development

Vietinbank: Bank For Industry And Trade

BIDV: Bank For Investment And Development

VCB: Bank For Foreign Trade of Vietnam

OLS: Ordinary Least Squares

FGLS: Feasible Generalized Least Squares

CHAPTER 1 INTRODUCTION

This chapter presents problems statements that the author will solve in this thesis The problem statements of study will be interpreted through detailed research objectives and research questions Next, the scope of research and research methods will be presented in order to clarify the research objectives of the thesis

1.1 Problem Statements

In recent years, the total assets of the commercial banks in Vietnam have increased continuously Monthly Report 5-2015 from the State Bank of Vietnam (SBV) showed that the total assets of the State Commercial Bank System was 2,896,430 billion VND and total assets of the Joint Stock Commercial Bank System

is 2,715,910 billion VND.1 In addition, the average growth rate of the total assets of the State Commercial Bank System from 1/2013 to 5/2015 is 1.14%/month and the Joint Stock Commercial Bank System is 0.89%/month These data showed that the commercial banks Vietnam were always trying to increase their scale The increase

of scale creates conditions for using more inputs such as labor, capital and fixed assets However, the increase of scale does not always bring the expected profits that the commercial banks desire The increase of the scale have to be in accordance with capability of the management of the commercial banks Therefore, the commercial banks can find a best way that combines the inputs to maximize the outputs If the scale of the banks is less than the one, the increase of scale will facilitate to increase profitability as expected However, if their scale is currently larger than one, the increase of scale would increase costs and as such, reduce profits

The research of Akhigbe and McNulty (2003) with data of the commercial banks in the US concluded that small banks will be more profitable than large

banks Pasiouras and Kosmidou (2007) study for European banks also provided evidence that the increase of scale would increase their cost and it has a negative impact on bank profitability In contrast, research by Williams (1998) in the case of foreign branches in Australia concluded that the profitability of branches will have a positive impact from the increase of scale of their parent bank In the study conducted for Indian banks, Das and Ghosh (2009) also reached a similar view when they concluded that the increase of scale will have positive impact on bank profitability

In the case the commercial banks of in Vietnam, banks always put effort to increase their scale However, the return on assets (ROA) appears to decrease Therefore, it is argued that the authentic approach to determine the scale efficiency

of Vietnam’s the commercial banks is an essential issue The economies of scale condition of the Vietnam the commercial banks should be determined Therefore, it

is expected that findings from this empirical study will provide further evidence for the commercial banks to make their decisions

In short, this study aims to achieve two key objectives: (i) determining the

economies of scale of the commercial banks; and (ii) considering the possibility of

varying inputs in order to achieve the operate efficiently

1.3 Research Questions

In accordance with research objectives, the two relevant research question

should be answered are:

 The first question: Are the economies of scale of Vietnam commercial banks increasing return to scale, decreasing return to scale or constant return to scale?

 The second question: Are the inputs substitutable?

1.4 The Scope of this Research

The purpose of the study is to establish the quantitative evidence about the scale economies of the commercial banks in Vietnam Therefore, data from 32 the commercial banks in Vietnam in the period from 2006 to 2014 were collected The research covers the period of 2006-2014 mainly because the commercial banks in Vietnam disclose their information relatively sufficient during this period Some commercial banks are removed in the process of collecting data because they do not provide enough information or their operations were terminated during the research period

1.5 Methodology

The quantitative approach is used in this study to estimate the scale economies

of the commercial banks in Vietnam Using the translog cost functions adopted in various relevant previous empirical studies, this study uses quantitative approach to determine the impact of factors such as the input prices and control variables to the cost of the commercial banks in Vietnam The Iterate Semmingly Unrelated Regression (ITSUR) method is used in this research with the support of STATA software

1.6 The Structure of the Study

This study includes five chapters with the key contents included in each chapter can be summarized below

 The first chapter presents an overview of this study including the Problem Statement, Research Method and Data

 Chapter two presents the literature reviews This chapter firstly describes the overview of the commercial banking system and the process that the commercial banks in Vietnam increase their scale Then, this chapter presents relevant previous studies in relation to estimating the scale and elasticity of the inputs This chapter ends with theoretical model of translog cost function and estimation method about the scale economies and the elasticity of the inputs These theory will be used to model in detail in the next chapter

 Chapter three present the research method The theoretical model will be detailed into the three systems of equations that they are appropriate with the research objectives Chapter three will also show how this research estimates variables in the model using the collected data Finally, this chapter ends with appropriate regression methods to estimate for system of equations

 Chapter four presents the results estimated using the model adopted in chapter three In addition, this chapter also presents results from the scale economies and the elasticity of the input of the commercial banks in Vietnam during the research period from 2006-2014 Finally, the results from the model will be explained in detail

 The final chapter presents the conclusions which are drawn from this study

On the ground of these empirical findings, policy recommendations for the State Bank are formed Finally, this chapter will present the limits of this research and ways for future research

CHAPTER 2 LITERATURE REVIEW 2.1 Overview of the Commercial Banking System in Vietnam

By the end of July 2015, Vietnam commercial banking system consists of 40 banks Banking system is classified as Joint stock commercial banks and state commercial banks

The State commercial banks are Bank For Agriculture And Rural Development (Agribank), Bank For Industry And Trade (Vietinbank), Bank For Investment And Development (BIDV) and Bank For Foreign Trade (VCB) Vietinbank has the largest charter capital in State commercial banks with 37,234 billion VND charter capital Whereas, Saigon Thuong Tin Commercial Joint Stock Bank has the largest charter capital among Joint stock commercial banks with 12,425 billions VND charter capital In 2006, the State Bank has requested commercial banks to increase their chartered capital2

In 2015, many bank mergers happened, they increased the scale of banks Some large mergers such as Petrolimex Bank merged into Vietinbank; Housing Bank of Mekong Delta merged into Bank For Investment And Development Saigon Thuong Tin Commercial Joint Stock Bank merged into Southern Bank The purpose of this merger is to modernize commercial banking system in Vietnam and improve the effectiveness of the system in the integration context Total Assets and ROA of commercial banking system is represented by Figure 1

Figure 1 Total Assets And Return On Total Assets Of Commercial Banks In

Vietnam 2013-2015

Note:

- Data were collected from the State Bank of Vietnam

- Total assets is shown in the left column chart with units million billion VND

- ROA is shown in the right column chart with units percent

2.2 Studies On The Scale Economies Of Commercial Banks

Jagtiani and Khanthavit (1996) studied with the US Commercial banks in the period 1984-1991 Results achieved from this research showed that the major US banks have achieved efficiency on scale, but these banks have continued to increase

0,00% 0,10% 0,20% 0,30% 0,40% 0,50% 0,60% 0,70% 0,80% 0,90%

their scale The studies of Isik and Hassan (2003) for Turkish banks have shown that there is no consistency in the performance of commercial banks The banks do not have the scale efficiency and they are inefficiency due to the greater impact of technological inefficiencies than the impact of the allocation of resources And then, these banks have become ineffective on the scale due to the impact of minimum regulation about risk based capital level However, the research by Bos and Kolari (2005) is based on the data of US and European banks in the period from 1995 to

1999 showed that banks had not yet reached the optimum scale and they may increase their profit by increasing their products

Several studies have been conducted to compare the scale efficiency of domestic banks and branches of foreign banks Havrylchyk (2006) studied on domestic banks and branches of foreign banks in Poland Author suggested that the domestic banks and branches of foreign banks did not improve the scale efficiency for the period 1998-2001 However, this research also concludes that the branches

of the banks that joined later have better scale efficiency of domestic banks In addition, the efficiency of foreign bank branches is not improved when competing with domestic banks

Research by Valverde, Humphrey, and del Paso (2007) was performed in the context of banking consolidation in Europe The results showed the banks in 10 European countries have a similar efficiency, the business environment of each country does not affect the operation efficiency of the bank Therefore, banks have improved their efficiency by merging and expanding markets

2.3 Studies On The Price Elasticity Of Inputs In Banking

Research by Noulas, Ray, and Miller (1990) for the large US the banks has shown that the elasticity of input factors has changed monotonically with changes in scale The fund will increasingly substitute for labor and deposits with the increase

become weaker and weaker The importance of capital will be increasing, when banks want to increase their scale, because financial capital can easily be reserved and converted into other inputs

Hughes and Mester (1998) also showed that banks may easily substitute labor, fixed assets by financial capital, but objective of minimizing costs and increase profits are not made in a simple way, it also depends on the ability of risk management and portfolio management of banks Banks can set a target to reduce costs or increase profits by changing outputs Research by Humphrey and Vale (2004) used data of the US banks in 1988-1997,the results showed that banks want

to expand output products such as business loans will cost less than the consumer loans The cause of this difference is the price elasticity of businesses loans is smaller than consumer loans However, banks have increased their scale by merging, this will not affect the cost of businesses loans and consumer loans This suggests that the scale economies of banks depends on not only the ability to combine inputs but also the choice of the appropriate output with ability to manage risk

However, other studies for microfinance institutions have different results Hartarska, Shen, and Mersland (2013) researched on the microfinance institutions from 69 countries in 1998-2000 The research results shown that the inputs such as labor, fixed assets and financial capital is inelastic The large of the change in the labor price will be substituted by other inputs such as financial capital or fixed assets Similarly, significant changes of the financial capital will make using more fixed assets In addition, this research also showed that when the microfinance institutions could increase their scale, their costs will decrease and increase profits

2.4 Translog Cost Function Theory

Methods efficiency scale analysis for financial intermediation are usually Cost function and Profit function However, Bos and Kolari (2005) suggested that there

is a homogeneous result while using Cost function and Profit function The cost function analyzes the cost effectiveness that now is achieved through the production

process, the cost effectiveness is understood as the minimum cost of the business

when they combine different inputs (Camanho & Dyson, 2005) Ferrier and Lovell

(1990) shown that when the banks increased the scale, this will affect the cost efficiency of banks

Cost effectiveness is evaluated by a Translog Cost Function Binswanger

(1974), Ferrier and Lovell (1990), Kumbhakar (1997), Hartarska et al (2013) shown that translog cost function may be presented:

With C is total cost; 𝑞𝑖 and 𝑞𝑗 are the outputs; 𝑝𝑘 and 𝑝𝑙 are the input prices;

zm are the control variables; α, β, δ, and γ are the coefficients ; lnv are the residual

sk = ∂lnc

∂lnpk

sk = βk+ ∑ βlklnpl+ ∑ δjklnqj+ ∑ γkmzm+ lnvk (5)

2.5 The Estimation Method Of The Scale Economies and The Elasticity

2.5.1 Estimation Method Of The Scale Economies

The scale economies is determined by taking the derivative of the model with respect to the logarithm of output

Begg, Fischer, and Dornbusch (2005) shown that there are three reasons for

the scale efficiencies First, the businesses can not divide the production process

When the business begins manufacturing, they need a minimum quantity of inputs, whether the businesses have produced or not These factors are usually fixed and do

not change over output Second, the businesses can specialize in the manufacturing

process When the scale of the businesses is expanded, employers will have to hire more employee, each employee will be able to focus on different jobs, so they will

work better Finally, when the scale of the businesses is increased, the input will be

arranged closer together At that time, manufacturing time and transport costs of inputs will decrease A business is increasing return to scale when scale economies

of bussiness is less than one On the other hand, a business is decreasing return to scale when scale economies of bussiness is larger than one Finally, a business is constant return to scale when scale economies of bussiness is equal to one

2.5.2 The Own-Price Elasticity And Cross-Price Elasticities

The combination of inputs also affects the operational efficiency of the bank Because inputs have different costs, different combinations of inputs will produce different outputs and profits

This study estimates the price elasticity of inputs such as The own-price elasticity and cross-price elasticities The own-price elasticity should be understood

as a percentage change of the input demand if its price changes one percentage Meanwhile, The cross-price elasticity should be understood as percentage change of

the input demand if its price of other one changes one percentage (Ollinger, Ralston,

& Guthrie, 2011)

According to Uzawa (1962), Berndt and Wood (1975) The Allen partial

elasticities between k input and l input:

Cross-The Own-price elasticity:

According to (Begg et al., 2005):

For The Own-price elasticity:

o The Own-price elasticity is greater than 1: input is elastic

o The Own-price elasticity is less than 1: input is inelastic

o The Own-price elasticity is equal to 1: input is unit elasticity

For The Cross-price elasticity:

o The Cross-price elasticity is greater than 0: two inputs are substitute

o The Cross-price elasticity is less than 0: two inputs are complementary

CHAPTER 3 RESEARCH METHODOLOGY 3.1 The Hypothesis Testing:

In chapter 2, the author has analyzed overview of Vietnam commercial banks The data of Figure 1 showed that the total assest of Vietnam commercial banks increase continuously However, the ROA of Vietnam commercial bank decrease continuously In the other hand, the literature review of scale efficiency showed the case of the bussiness have inefficient scale If the bussiness increase their scale, the inefficient cost will be increase and their profit will be decrease Therefore, this study expects the scale economies of Vietnam commercial bank is inefficiency In addition, the inputs of Vietnam commercial bank can not subtitute for each other to minimize their total cost Therefore, this study expects the input of Vietnam comercial bank is inelasticity

Hypothesis 1: The scale economies of Vietnam commercial bank is

decreasing return to scale

Hypothesis 2: The inputs of Vietnam commercial Bank is complementary

3.2 Identification Of Variable

Base On the foundation of empirical research that has been done by Ferrier and Lovell (1990), Hughes and Mester (1998), Lensink, Meesters, and Naaborg (2008) and Hartarska et al (2013) The study estimated the cost efficiency of

Vietnam Commercial banks The outputs include Loans and Deposits, the inputs include Labor, Financial capital and Fixed assets The control variables include

Risk and Time Trend This research has established three equations systems which are based on translog cost function and cost share of inputs The conditons (2), conditons (3) and conditons (4) should be restricted The adjusted price of input and adjusted total costs used in these systems equations

The first system of equations analyzed the relationship between finance capital

and labor The dependent variables of the first equation system are Total cost, Cost share of financial capital and Cost share of labor The independent variables are the Loans, Deposits, Price of financial capital, Price of labor, Risk and Time trend The

variables of the first system of equation showed in Table 1

Table 1 The Variables Of Equation System That Analyzes The Relationship

Between Financial Capital And Labor

Kind of variable Variables Meaning of variable

The dependent variable lnCC The adjusted total cost

CSL Cost share of labor CSF Cost share of financial capital The independent variables lnL Loans

showed in Table 2

Table 2 The Variables Of Equation System That Analyzes The Relationship

Between Financial Capital And Fixed Assets

Kind of variable Variables Meaning of variable

The dependent variable lnCL The adjusted total cost

CSF Cost share of financial capital CSC Cost share of fixed assets The independent variables lnL Loans

The third system of equations analyzed the relationship between fixed assets

and labor The dependent variables of the first equation system are Total cost, Cost share of labor and Cost share of fixed assets The independent variable are the Loans, Deposits, Price of labor, Price of fixed assets, Risk and Time trend The

variables of the third system of equation showed in Table 3

Table 3 The Variables Of Equation System That Analyzes The Relationship Between Labor And Fixed Assets

Kind of variable Variables Meaning of variable

The dependent variable lnCF The adjusted total cost

CSL Cost share of labor CSC Cost share of fixed assets The independent variables lnL Loans

3.1.1 The Dependent Variable

As per the previous chapter, this research choose translog cost function to estimate the operational efficiency of Vietnam Commercial banks Therefore, total cost of Commercial banks is the dependent variable According to research by Koutsomanoli-Filippaki, Mamatzakis, and Staikouras (2009) and Han, Orea, and Schmidt (2005), total cost variable used in the function translog cost includes the interest expense and operating costs Therefore, total cost of this study includes costs such as the cost of services, cost of management, risk provision expenses, interest expense and other operating cost Data of these costs are collected from the annual income statement and the annual report of Vietnam Commercial banks

This research estimates the coefficients through equation system which including three equations Therefore, the remaining dependent variables are the rate

of other capital costs, labor cost ratio and expense ratio of fixed assets

3.1.2 The Independent Variable

Deposits (D):

Deposits are considered to primarily inflow for Commercial banks According

to Humphrey (1985), two approaches estimating the operational efficiency of

commercial banks are The production and Intermediation approache This research uses The production approach Therefore, the deposits are considered a product that

commercial banks provide Results findings of Kaparakis et al (1994) for US banks over the period 1986-1994 have shown that if banks increase the mobilizing deposits, total cost will be a positive affect Meanwhile, the findings of Hughes and Mester (1993) Meanwhile, the findings of Hughes and Mester (1993) for all US banks in 1988-1990 have shown that the increase of deposits does not affect total cost In this study, the author suggests that the deposit is expected to increase total cost of Commercial banks

Expectation: Deposits have a positive impact on total cost

4.2.2.2 The Inputs

The price of labor (PLC, PLF):

The price of Labor is considered the cost that banks pay to employees The increasing of labor price would make Commercial banks have to pay more If banks lay off current employees and hire new employees, the bank will have to pay higher wages and more retraining costs Therefore, the increase of labor prices is expected

to increase total cost Kaparakis et al (1994) and Hughes and Mester (1993) showed that the labor price had a positive effect on total cost banks

Expectation: Price of labor have a positive effect on total cost

The price of financial capital(PFC, PFL):

Similar labor price, the price of financial capitalare considered the price of financial capital cost If the price of financial capitalincrease, banks will have to pay more to mobilize capital Therefore, the increasing of the price of financial

capitalwould increase total cost Das and Das (2007) studied for Indian banks in the period from 1992 to 2003, the result showed that the price of financial capitalhas a positive impact on total cost Therefore, the increase of the price of financial capitalis expected to increase total cost

Expectation: Price of financial capital have a positive effect on total cost

The price of fixed assets (PCL, PCF):

Similar labor price and financial capital price, price of fixed assets is considered the price of fixed assets cost If the price of fixed assets increases, the banks will have to pay more to construct fixed assets Hughes and Mester (1993) suggested that the price of fixed assets have a positive effect on total cost Therefore, the increase of the price of fixed assetss is expected to increase total cost

Expectation: Price of fixed assets have a positive effect on total cost

4.2.2.3 The Control Variables

Risk (R):

Risks are non performing loans (NPLs) that borrowers do not repay on time or irrevocable3 If the risk increases, this increases total cost of the bank Because the bank will have to increase the cost of redundancy Banks can lost the capital and other operating costs when they lend NPLs Therefore, the increase of risk is expected to increase total cost The research results of Hughes and Mester (1993) provided evidence that NPLs will increase total cost Because the banks have to require more provision costs Therefore, the risk is expected to increase total cost

Expectation: Risk has a positive effect on total cost

Time trend (T):

Technology serving the banking industry always develops The development

of technology is expected to reduce the cost of banks J Allen and Liu (2007) studied on Canada large banks in the period 1983 to 2003 has confirmed that the development of technology will support reducing cost of banks Therefore, time trend is expected to reduce total cost of banks

Expectation: Time trend has a negative effect on total cost

3.3 Data Collection And Expected Results

Data were collected from the financial statements and annual reports of 32 Vietnam Commercial banks in the period 2006-2014 Some financial statements haven't provided any sufficient data, so author has also based on data from the annual reports The data were collected from the balance sheet and income statement of Commercial banks In addition, the data also were collected through an explanatory section of financial statements such as number of employees, employee salaries However, some banks did not publish sufficient data For the year that bank do not publish insufficient data will be ignored Finally,this study collected

160 observers from 32 Vietnam Commercial banks in the period 2006-2014

Table 4 The Dependent Variables

Variable label Meaning of variable Variable measurement

lnCC The adjusted total cost

Ln ( Total cost Cost of Fixed assets ) lnCL The adjusted total cost

Ln ( Total costCost of labor) lnCF The adjusted total cost

Ln ( Total cost Cost of financial capital) CSF Cost share of financial capital

Ln (1 −Operation cost − Employee salaries

CSC Cost share of fixed assets

Ln (Operation cost − Employee salaries

Ln (Employee salaries

Total cost )

Table 5 The Independent Variables

Variable

label Meaning of variable Variable measurement

Expected sign

lnPFC The adjust price of financial

capital

Ln (Price of financial capital

lnPLC The adjust price of labor

Ln ( Price of labor

lnPFL The adjust price of financial

capital

Ln (Price of financial capital

lnPCL The adjust price of fixed asset

Ln (Price of fixed asset

lnPLF The adjust price of labor

Ln ( Price of labor

lnPCF The adjust price of fixed asset

Ln ( Price of fixed asset

3.4 The Research Methodology

3.1.1 The Model

The study is based on empirical research that has been conducted by Ferrier and Lovell (1990), Hughes and Mester (1998), Hartarska et al (2013) The study estimates the efficiency cost of banks The study estimated the cost efficiency of

Vietnam Commercial banks The outputs include Loans and Deposits, the inputs include Labor, Financial capital and Fixed assets The control variables include

Risk and Time Trend

The equation systems must satisfy the Condition 2, Condition 3 and Conditions 4 These conditions are required to ensure that the equation systems are

homogeneity However, Hartarska et al (2013) suggested that these conditions could be eliminated by dividing total cost and input prices by the price of fixed assets Similar studies of Lensink et al (2008) analyzed the relationship between financial capital and fixed assets, the author has divided total cost and the input prices by the price of labor

Therefore, this study developed a system of equations that analyzes the relationship between the price of financial capital and labor price by dividing total cost and input prices by the price of fixed assets Similarly, the equation system analyzes the relationship between the price of financial capital and the price of fixed assets by dividing total cost and input prices by the price of labor Finally, the equation system analyzes the relationship between the price

of labor and the price of fixed assets by dividing total cost and input prices by the price of financial capital

The equation systems are described in formula forms:

The equation system contains the relationship between the price of finance capital and the price of labor:

The equation system contains the relationship between the price of fixed assets and the price of labor:

3.1.2 The Estimation Method

The equations of The equation system 9, The equation system 10 and The equation system 11 must be simultaneously evaluated The recent studies have

proven that the simultaneous estimation of the production function and the first derivative of the production function will have better results than the estimating from single equation (León-Ledesma, McAdam, & Willman, 2009)

Therefore, this study used ITSUR method for estimating the linear equation systems

System of linear equations must estimates:

𝑦𝑖 is column vector Tx1 of the dependent variables of ith observation; 𝑋𝑖

is the matrix TxK of observations; 𝛽𝑖 is column vector Kx1 of the coefficient

in ith equation; 𝜀𝑖 is column vecto Tx1 of residual in ith equation; T is the

number of observations, K is the number of independent variables and M is the number of equation

M equations can be rewritten in matrix form:

ε1

ε2

…

εM] (12)

Define the MT x 1 vector of disturbances:

𝜀 = [𝜀1,, 𝜀2,, … 𝜀𝑀, ]′

According to Green (2012) model assumptions are:

a Functional forms of The equation system (12) is linear in parameters

b The mean of error term in The equation system (12) is value equal 0

E(μ) = 0

c Distribution of errors in the equation system (12) is nonspherical

distribution and must satisfy the assumptions:

o The variance of error in each individual equation is a constant

o The variance of error in each individual equation may be different

o The error term of each individual equation is not autocorrelation

o The error term between the different equations may be correlation

e The error term of the equation system (12) is not correlated with the

independent variable in equation

Covariance matrix of error:

𝜎𝑗𝑗 is the variance of the error in the jth equation, 𝜎𝑖𝑗 is the covariance of error

in ith equation and jth equation

⊗ is Kronecker product In this case, Ω matrix is estimated by are estimated by multiplying each element in the matrix Σ by 𝐼𝑇 matrix

The equation system (12) can be estimated by:

o Ordinary least squares (OLS)

o Generalized least squares (GLS)

o Feasible Generalized Least Squares (FGLS)

o Iterative Generalized Least Squares (ITGLS)

According to Green (2012) OLS method is unbiased but ineffective

Estimation of GLS method is unbiased, efficiency, and maximum likelihood estimator (MLE)

Step 1: Use the OLS for each individual equation

Step 2: Use the residuals of OLS to estimate the variance and covariance

of the error term for M equations:

σii =μiTμi

T and σij=μi

T

μ j T

With μ̂i is the residual vecto of ith equation; μ̂j is the residual vecto of jth

equation

Step 3: Estimate the covariance matrix and covariance of The equation

system (12)

Ω̂ = Σ̂ ⊗ ITEstimation of FGLS method is asymptotic with estimation of GLS and also a MLE According to Green (2012) if the range the parameters to be great, for

heteroscedasticity and autocorrelation, FGLS will be more effective than OLS However, if the violation of assumptions is not too serious, OLS may be more effective in small samples Therefore, The estimation results of FGLS are also asymptotically unbiased, efficient and consistent However, Green (2012) suggested that the Wald statistic often performs poorly in the small sample sizes typical in this area