Data Analysis








A project submitted in partial fulfilment of the requirements for the Degree of

Bachelor of BA (Hons) in Actuarial Studies



















1.0        INTRODUCTION.. 5






























Chapter 4: Data Analysis

  • Stochastic Frontier Analysis to get the cost efficiency measures
  • Tobit Analysis to compare the effect of non performing loan on the cost efficiency measures obtained from tobit analysis
  • Other required topics

Chapter 5: Findings and Discussions

Chapter 6: Conslusions and Recommendations

  • Policy Implications
  • Contribution of the study
  • Limitation of the study
  • Directions of future research









The background of the study, the research problem and objectives, research questions, limitations of the study and the scope and the significance of the study, in addition to the hypothesis and the research framework will be discussed further in this chapter.




The financial sectors according to the business dictionary is primarily the section of the economy that provide services related to finance to their commercial and retail customers. The financial sectors include a wide range of firms and industries namely, banking institutions, brokers, investment companies, insurance companies, real estate firms, etc. Among the financial sectors, we are going to focus on the banking institutions in Bhutan. In the Asian  and Pacific region, the banking sector stays as the primary form of financial intermediation, and as such is the largest conduit for the domestic savings mobilization and the main source of foreign capital for firm and the key player in the payment system. (ZainiAbd Karim, Chan and Hassan, 2010). According to him, it is necessary to develop an efficient banking system for the economic growth of the countries in the region.


Banks can be defined as intermediaries between depositors and borrowers in an economy (Heffernan,1996). Banks facilitate the flow of funds from surplus units to deficit units in an economy through its traditional role that include accepting deposits (mainly from household sector) and extending credit to all sectors (mainly business sectors) (Rajha, 2017). Well-functioning banking sector accelerate economic growth, while poorly functioning banking sector is an impediment to economic progress and aggravate poverty (Richard,2011). According to Rajaraman and Visishtha, growth of economy is impossible without a sound banking sector.


Loans, among others make up the bulk of banks’ assets (Njanike,2009). Providing loans requires banks to firstly assess the customers ability to repay the amount(principal) and interest on time and their creditworthiness but one can never be sure of what can happen in the future. Lending or providing loans can lead to a big problem for the banking sector which is called non-performing loans (Chhimpa J, 2002). According to the Reserve Bank of India Occasional Papers’ Vol. 24, No. 3, Winter 2003, the then director of the Reserve Bank of India, Rajiv Ranjan and the then Assistant Adviser in Department of Economic Analysis and Policy, Reserve Bank of India, Sarat Chandra Dhal stated that the banking sectors’ non-performing loan assumes critical importance and attention among various indicators of the financial stability because it not only reflects about the quality of the asset but also on the credit risk and the efficiency in the allocation of resources to the productive sectors. Non-performing loan according to Wikipedia (NPL) is a sum of money which has been borrowed or basically a loan, upon which the debtor has not made the pre-scheduled payment for a specified period and is also known as bad debt. Non-performing loans (NPLs) has attracted a great deal of interest among researchers and policy makers during the last four decades as these increasing non-performing loans are causing banking crisis which are turning into banking failures (Barr and Siems,1994). Studies in recent years have taken into account asset quality like NPL in estimating bank efficiency(Zaini Abd Karim, Chan and Hassan, 2010).


It has been concluded by Altunbas et al. (2000),Giradone (2004)and Fan and Shaffer (2004) that non-performing loans resultinto the banking sector being inefficient. This has happened because banks which are efficient, manage their credit risk better (Berger and DeYoung, 1997). Limited study and researches have been done on small, developing countries like Bhutan.This research is aimed at investigating the relationship between cost efficiency of the banks and NPL (non-performing loans). A stochastic cost frontier approach assuming normal-gamma efficiency distribution model proposed by Greene would be used to estimate the cost efficiency. The cost efficiency scores will be obtained. These scores will then be used in the second stage. The second stage isto use Tobit model to find out the relationship between NPLs and bank efficiency.



Bhutan is a landlocked country located in Asia with a population of of over 700,000 and the area of 38,392 sq. km. Royal Monetary Authority(RMA) of Bhutan was established in 1982. It took over theexternal reserves management,the issue of the national currency,  andoperations involving foreign exchange. After Bhutan became a Democratic Constitutional Monarchy in 2008, the RMA Act 2019 passed by the Parliament in June 2010 replaced the RMA Act elevating to that of an autonomous Central Bank with great powers while functioning and undertaking decision-making process. Now, RMA has five banking institutions under it namely, Bank of Bhutan (BOB), Bhutan National Bank (BNB), Druk PNB Bank (PNB), Bhutan Development Bank Ltd(BDBl) and T Bank. According to a RMA, Bhutan’s non-performing loans has increased from Ngultrum 5.73 billion in 2016 to Ngultrum 8.25 billion in 2017. This is a rising concern in the Bhutanese community as non-performing loan as it has been a challenge in economic growth.




A few studies have found a negative relationship between problem loans and efficiencies among banks which have not failed (Kwan and Eisenbeis, 1995). Tsai and Huang (1999) found out that the non-valuable activities of bad assets which are added, lead to a negative impact on the performance operation. The recent studies on the efficiencies of banks have started considering non-performing loan as an important variable. In bank efficiency, this variable may result as an enormous measure. The global financial crisis (2007-2009) which has harmed the economies of the US and many other countries (Adebola, Wan Yusoff and Dahalan, 2011). Banks having lower cost efficiency approach failure (Wheelock and Wilson,1994).


Bhutan’s non-performing loans has increased to Ngultrum 8.25 billion in 2017from Ngultrum 5.73 billion in 2016. According to the World Bank, the average value for Bhutan’s non-performing loans to total gross loans data between 2009 to 2017 was 6.37% with a minimum of 3.92 % in 2011 and maximum of 8.42% in 2017. This reflects the slow rate in the growth of economy of the country. Banks add extra costs for operation like handling the collection while collecting the loans. These added costs include activities like cross checking the collateral made assessible by the customer, paying the cost incurred while negotiating the contract, and the costs to hold and dispose the collateral when the loan becomes non-payable. It also includes the expenses for monitoring the loan quality and the costs incurred for winning the trust from the management, shareholders and public. Moreover, a lot of minor problems which lead to extra expenses, are ignored when the management’s attention is drawn by the increasing amount of non-performing loans. This increase in the operating costs and escalation in the expenses deteriorates the cost efficiency of the bank.


Banks in Bhutan have worse asset quality than Sri Lanka and India but are better in shape than Maldives, which has high ratio of non-performing loan to the gross loans. Howsoever, no specific research on the relationship between non -performing loan and the efficiency of the banks have been done in Bhutan. There are five banking institutions in Bhutan namely, Bank of Bhutan (BOB), Bhutan National Bank (BNB), Druk PNB Bank (PNB), Bhutan Development Bank Ltd (BDBl) and T Bank.


Table1: Nonperforming Loans by Industry

(Percent of Total NPLs)








Source: Royal Monetary Authority, Annual report 2013 to 2014, Thimphu

This table shows the amount of non-performing loans by industry. As of 2014, trade and commerce has accounted to the highest ration of non-performing loan which is 29% followed by housing which is 17.4%, personal which is 15%, manufacturing and industry which is 13.3% and service and tourism which is 11.1%. Trade and Commerce had just 10.8% non-performing loan ratio two years ago and housing accounted only 12.5% in 2012. A lot of factors contribute to the banking sectors being inefficient in managing loan portfolios which may in turn result in a poor credit rating of a loan which is already approved, leading tomore non-performing loans. Therefore, non-performing loans may resultin bank inefficiency.






The research is aimed to study the relationship between non-performing loan and cost efficiency of the banking sectors in Bhutan.




  • To study the effect of non-performing loan on the cost efficiency of the financial sectors in Bhutan
  • To study the effect of cost inefficiency of the financial sectors on non-performing loans in Bhutan.




  • Does non-performing loan have a positive or negative impact on the cost efficiency of the financial sectors in Bhutan.
  • Does cost efficiency of the financial sectors have a positive or negative impact on the non-performing loans in Bhutan.















For estimating the cost efficiency measure, the inputs would be the expenses on land, buildings and equipment per deposit (Capital), wage and salary expenses  per employee (Labor), and interest expenses per deposit (Deposits). A specification of the prices of the inputs is required to estimate the measure of cost efficiency. The price of labor would be labor costs over total assets, the price of the capital is obtained by dividing other operating expenses, by total fixed assets, and the price of the deposits would be the interest expense divided by total deposits. The cost efficiency measure obtained will then be used to test its relationship with non-performing loans.




The objective of this study is to examine the relationship between the non-performing loan and the efficiency of the financial sectors in Bhutan. This research will help magnify awareness about the efficiency of the different banking sectors in Bhutan and their impact on the efficiency of the Banks.



In a theoretical perspective, this research is aimed to provide knowledge and information on the efficiencies of banking sectors in Bhutan and the impact of the non-performing loan on their efficiencies. It is hoped that the future researchers would be helped and supported by this research in their studies to prove their findings and theories with relevant references. It will contribute in creating a paved path for such researches in future and hence provide a deeper insight on the topic.



This study will help the administration and management in comparing the efficiencies of the institutions. Banking sectors can understand the impact of non-performing loans on the cost efficiency and hence will provide the employee with the true notion of the non-performing loans. Since this study would point out the impact of non-performing loans on the efficiency of the banking sectors, the banking sectors would be aware of the impact and would work accordingly.



This research will act as a guide to those students who would want to study the efficiencies of the financial sectors or non-performing loans.This research will serve as an additional reference source forpeople trying to work on similar projects as there are very limited resources available. This study will serve as an added reference or a vital source of information to the students and academicians irrespective of the field of the study as it finds out the efficiency of the financial sectors in Bhutan and thethe impact of non-performing loans.




In this research, the relationship between the efficiency of the banking sectors in Bhutan and non-performing loans will be studied.A quantitative study will be performed using secondary data. The cost efficiency measure will be estimated using a Stochastic Frontier Analysis(SFA) method and its relationship with non-performing loans will be tested using Tobit analysis. Since, very limited researches has been in Bhutan regarding non-performing loan and its relationship with the cost efficiency of the financial sectors, I thought it would be knowledgeable and informative  to perform the studies on the banking sectors in the country.

Due to the time constraints and very limited budget available to the student researcher, there was a restriction to view many literatures which were done on similar topics. Moreover, least researches has been done on a small, developing country like Bhutan due to which it led to a limited activity to be carried out for this research.




Throughout this research, the effect of non-performing loan on the cost efficiency of the banking sectors in Bhutan will be analyzed and tested. This chapter was just a brief overview of the entire research. In the following chapter, past literatures will be reviewed for a deeper understanding and knowledge on the research.











Related concepts and literatures on the research topic that is, non-performing loan and efficiency of the banking sectors will be reviewed and analyzed so that the relationship between non-performing loans and the cost efficiency of the financial sectors can be determined.





Banking sectors which are well-functioning increase the rate of economic growth where as banking sectors which poorly function, are a hindrance to economic growth, hence promoting poverty (Richard,2011). The non-performing loans are not significantly affected by the lending rates and  these assets have a negative and significant influence(Swamy, 2012) and he found out that even though non-performing loans are a permanent phenomenon in financial institutions’ balance sheets, which if not taken care of properly can lead to yet bigger risks that can negatively impact the financial health of the sector.


According to Skimping hypothesis, non-performing loans are apparent in the long run when a greater number of borrowers start borrowing money from the banks. The risk-averse managers, as confirmed by the risk-averse management hypothesis by Koutsomanoli, Filippaki and Mamatzakis (2009), incur huge costs in monitoring and screening the loan, which then leads to the decrease in the bank efficiency (Abel, 2018).It has been found by Fan and Shaffer (2004), Giradone (2004) and Altunbas (2000),  that in-efficient banks fail to manage their credit risks efficiently which resultin non-performing loans increasing bank inefficiency as Altunbas et al.(2000) undertook the study of estimation of banks’ cost efficiency regarding non-performing loans in commercial banks in Japan from a period of 1993 to 1996. He found a significant negative correlation between NPLs and the cost efficiency of  theJapanesescommercial banks.

In a study of 6 Nationalized banks’ sample in India, Jain, Dr. Kamlesh M. and Raval and Manish (2013) found out a negative correlation between non-performing assets and profitability, moreover concluded that non-performing loan was not the only variable which affects the profitability of banks. Peterson K Ozili had studied the influence of financial development on non-performing loans using a global sample and found out that bank efficiency and ratio of loan loss coverage , competition and stability of the banking system  are inversely associated with non-performing loans(Ozili, 2017).It has been found by MohdZainiAbd Karim, Sok-Gee Chan and Sallahudin Hassan (2010) that the the cost efficiency is reduced by higher non-performing loans and an inefficient bank leads to a higher ratio of non-performing loan after considering the evidences from Malaysia and Singapore.




Author/Date Research Topic Methodology Analysis and Results
MohdZaini, Abd Karim, Sok-Gee Chan, Sallahudin Hassan (2010) Bank Efficiency and Non-Performing Loans: Evidence from Malaysia and Singapore Stochastic Cost Frontier Analysis, Tobit Analysis Highernon-performing loan reduces the cost efficiency of banks
YenerAltunbas, Ming-Hau Liu, Philip Molyneux and Rama Seth (2000) Efficiency and Risk in Japanese Banking Data Envelopment Analysis There is a negative relationship between non-performing loan ratio and performance of the Japanese commercial banks.
Sanderson Abel (2018) Cost Efficiency and Non-Performing Loans in Zimbabwean Banking sector Non-parametric (mathematicalprogramming) method, Granger Causality Test Cost inefficiency negatively Granger-causes non-performing loans in Zimbabwean banking sector.
Peterson K Ozili (2019) Non-performing loans and Financial Development Modified version of the models of Ozili (2015) Efficiency of Banks, ratio loan loss coverage, competitionthe stability of the banking system are inversely associated with non-performing loans.
ZhannaMingaleva, MyrzabikeZhumabayeva and GulzhanKarimbayeva (2014) Non-performing loans and perspectives of economic growth Econometric modeling, Factor and structure analysis Non-performing loans are  a big obstacle and hinders the recovering of economy.
AkinolaMorakinyo, Colette Muller and MabuthoSibandha (2018) Non-performing loans, Banking system and Macroeconomy Structural vector Autoregressive model Non-performing loan has a negative impact on the banking system and macroeconomy in the long run.
Peter YeltulmeMwinlaaru, Isaac KwesiOfori, KwadwoAgyemanAdiyiah and Anthony Adu-AsareIdun (2016) Non-performing loans and Universal Bank’s Profitability Auto Regressive Distributed Lag (ARDL) In both short run and long run, NPL had a significant negative impact on the profitabilities of the Universal Banks
OzgeSezgin Alp, SenolBabuscu, OnurSunal, Adalet Hazar (2016) The Effect of sales of non-performing loans to Asset Management Companies on Bank Efficiency Directional Distance function Efficient banks are not affected from the sales of non-performing loans while the efficiency of the non-efficient banks are positively affected by non-performing loans
Huseyin Cetin (2019) The Relationship between Non-performing loans and selected EU Member Banks Profitabilities Bayesian Impulse Response Analysis Non-performing loans and return on assets is negatively correlated for many EU members banks
Md. Sazzad Hossain Patwary and Nishat Tasneem


Impact of Non-performing loan on the Profitability of Banks in Bangladesh Ordinary Least Square method, Vector Auto regression (VAR) model Non-performing loan ratio negatively impacts the return on assets, hence reducing profitability
Benazir Rahman and Nusrat Jahan (2018) Non-performing Loans in Islamic Banks of Bangladesh Regression, Principal Component Analysis There is a negative correlation between the non-performing loans and the profitability of Islamic banks in Bangladesh
FirasNa’elRawhiHashem, Khalid Ali Ahmad Alduneibat and Mohammad AbdallahFayadAltawalbeh (2017) The Impacts of Non-performing loans upon the stock prices of Stocks in Jordanian Comnmercial Banks Descriptive Analytical Approach There is a statistically significant impact for the non-performing loans upon the prices of stocks in Jordanian commercial banks.
Suryanto (2015) Non-performing Loans on Regional development Bank in Indonesia and Factors that influence Random Effects Model, Multiple Regression Non-performing loan is significantly affected by the level of efficiency of banks, mortgage interest rate and liquidity of banks
AtillaCifter (2015) Non-performing loans and Bank Concentration Fully Modified Ordinary Least Square approach, Generalised Method of Moments The relationship between the bank concentration and the non-performing loans in regard to the Central and Eastern European countries, is ambiguous.
AlmirAlihodzic (2014) Analysis of Non-performing loans Movement and Profitability of the Banking Market in B and H. Regression Analysis There is a strong statistical relationship of non-linear direction between non-performing loans and return on average shareholders’ equity.
HellenAraka, VitalisMogwambo and SimiyoOtieno (2018) Effect of Non-performing loans on the Financial Performance of Commercial Banks in Kenya Multiple Linear Regression Analysis Interest rate regulations contribute to non-performing loans which in turn affects the financial performance of commercial banks in Kenya.
K. Prasanth Kiran and T. Mary Jones (2016) Effect of non-performing Assets on the profitability of Banks in India Descriptive Study Except for SBI, all other banks exhibit a negative correlation between their gross non-performing loans and net profits.
Nitin Bajirao (2016) The Study of the Effect of Nonperforming Assets on Return on Assets(ROA) of Major Indian Commercial Banks Multiple Regression As non-performing assets increase, it negatively affects the return on assets of banks.
Himanshu Mathur (2016) Impact of Non-performing Assets on the Profitability of Banks inBaroda Coefficient of Correlation and t-test There is a negative correlation between the net profits and non-performing loans in Baroda.





In this literature review chapter, the researches done in the past has been reviewed and studied to get a better and deeper understanding on the topics of non-performing loans and efficiency of the banking sectors. Various researchers had their own different findings and views on similar research topics, I will choose the best models for this study based on these past researches and hence discuss it further in the next chapter.












This chapter will briefly explain about the research methodology used to conduct the specific and overall research and thus to obtain the results and findings. There are a lot of researches done using Stochastic Cost Frontier Analysis to compare the efficiency of the banking sectors. Stochastic Cost Frontier Analysis would be used to estimate the cost efficiency of the banking sectors in Bhutan. The cost efficiency scores obtained would then be used in the second stage Tobit Simultaneous Equation Regression to determine the effect of non-performing loans on bank efficiency. A yet deeper insight and a better discussion on the methodology would be done further in this chapter.




There has been a growing interest in the study of methodology and their relative applications to real-life situations since Farrell’s (1957) seminar paper on efficiency measurement (Ogundari, 2010). Farrell tested the productive efficiency under physical efficiency of input output Transformation and price efficiency indicating optimum use of resources (Koopmans, 1951). He had introduced a method by which the overall efficiency of a production unit can be decomposed into its allocative and technical components. The technical component referred to the production of maximum output with the lowest possible input and the allocative component meant finding out the output value according to the given price of input, and properly interpreting the overall micro-economic and macro-economic situation. The product of these two components, technical and allocative efficiencies provide a score of overall cost efficiency. Empirically, there were two approaches developed for measuring efficiency namely, parametric and non-parametric. Parametric uses an econometric approach where as non-parametric had been traditionally regarded into Data Envelopment Analysis (DEA) which was a mathematical programming model. Econometricians criticize Data Envelopment Analysis (DEA) because it cannot differentiate among random variations in variations and productivity in efficiency (Ogundari, 2010). This problem was avoided by Stochastic Frontier Analysis (SFA) model. This model assumed that the variations or departures from the best practices’ frontier can be deterministic or stochastic. The two main approaches developed for estimating efficiency are discussed further below.




Data Envelopment Analysis (Charnes et al. (1978) and (1981)) is a non-parametric approach based on linear programming that takes the observed output and input values and forms a production possibility set making certain assumptions (Banker, Charnes and Cooper, 1984).

DMU denotes Decision Making Units.


  • n DMUs indexed by j in {1,2,…,n}
  • q inputs
  • p outputs

DMUj has inputs b1j,b2j,…,bpj and outputs d1j,d2j,…,dqj.

In primal model, the variables are xj which denotes the amount of DMUj used and w which denotes the proportion of the input bundle of DMUk which is needed to produce its own output bundle.

In order to evaluate DMUk we have the model as follows:

Minimise      w

subject to:     -d11x1-b12x2-…- b1nxn+ b1kw  ≥ 0

-b21x1 – b22x2 -…- b2nxn + b2kw   ≥ 0


-bp1x1 – bp2x2 -…- bpnxn + bpkw    ≥ 0

d11x1 + d12x2 +…+ d1nxn              ≥ d1k

d21x1 + d22x2 +…+d2nxn                 ≥ d2k


dq1x1 + d12x2 +…+ dqnxn                 ≥ dqk

xj ≥ 0,   j = 1,2,…,n

Here, aij is the quantity of input I used by DMUj for i = 1,…,p and cij denotes the quantity of output t produced by DMUj for t = 1,…,q.

We first select a special mixture of decision-making units (DMU) to at least give the outputs of DMUk considering the smallest possible multiple of inputs of DMUk. The best outputs of DMUk will be produced by a mixture other decision-making units (DMUs) than its inputs using a fraction w (0 < w < 1 of all its inputs, denoting DMUk as inefficient. In this inefficiency, w is its efficiency number. The best output of DMUk is possible to be attained using all its inputs, referring DMUk as efficient. Here in this efficiency, xj = 0, xk = 1 for all j ≠ k and w = 1.

Using Fourier – Motzkin elimination (Williams, 1986), we project out the variables x1, x2,…,xn and the model takes the form of

The optimal value of w is w*, which gives DMUk’s efficiency number and can be obtained as follows:

λim and µtm are the weightings which w* should use for its outputs and inputs with the aim to maximise the ratio of weighted outputs to inputs.

The best extreme ray gives the maximum ratio of outputs to inputs and w* = 1 for certain efficient DMUs which means the efficiency number is one. We need to obtain the multiples of the DMUs to show that the current DMU is inefficient. To obtain the multiples, we solve binding constraints as equations for the variables (Variables represent the comparator DMUs). IF a model has p inputs and q outputs, this frontier will have dimension p + q – 2(Read, 1998).




Stochastic Frontier Analysis (SFA) model is widely applied to the banking sectors and other industries from the time of its introduction by Aigner et al. (1977), Meeusem and van de Broeck (1977), and Battese and Corra (1977). It was developed to introduce random factors by plugging in a production or cost function and allowing the frontier to shift around the fitted function for individual components(Read, 1998). This is done by using an error term. The error term is split into one-sided and two-sided. One-sided error term measures the firm-specific inefficiency whereas the two-sided error term presents the random fluctuations which is distributed across the firm independently and identically.


Stochastic Frontier Analysis would be used in this research to estimate the cost efficiency score. Cost function would be used to measure the efficiency of the financial sectors instead of the production function as we want to study how cost efficient the banking sector is and its relationship with non-performing loans. The method doesn’t require the specification of the functional form a priori, hence removing the possibility of measurement errors.The stochastic frontier Analysis gives us a cost function score and the cost function consist of variable costs like prices of the input variables, amount of the output variables and fixed outputs or inputs required for the production of goods and services in the financial sectors as well as the factors that influence the costs and the random error.

The cost function general equation is as follows:

Yit = α + X′itβ + Z′itγ + εit , εit = vit + µit

  • Yit – Cost Function of the bank i at time t
  • X′it-Matrix of prices of inputs and outputs
  • Z′it – Bank Specific Variables for bank i at time t
  • εit – Random Error
  • µit – Unconditional mean of the random variable

Based on Stochastic Frontier Analysis (SFA) approach, we assume that the inputs of the banks in the sample is the translog cost function. The translog cost function is the most frequently used function in measuring efficiency (Greene,1980).

  • lnCit – Natural logarithm of the total cost
  • lnyit– Natural logarithm of the jth output where j = 1,2,…,n
  • lnwkit – Natural logarithm of the kth input price where k = 1,2,…,m
  • t – Year of observation
  • β – Coefficients to be estimated
  • vits – Random variable associated with measurement errors in the input variable
  • uits – Non-negative random variables associated with inefficiency of inputs used.

Given the input and output values, the cost efficiency of inputs utilized for the the i-th bank in t-th year of observation, is the ratio of the stochastic frontier input use to the observed input use(Zaini Abd Karim, Chan and Hassan, 2010).

The cost efficiency for firm I at time t is given by the following equation if a trans log frontier cost function is considered

, CEit ≤ 1. The reciprocal exp(uit) can be interpreted as a cost efficiency measure of input usage.

The estimation of cost efficiency employs the normal-gamma model proposed by Greene (1990), which will be used in our research, because the model corrects the problem in stochastic frontier analysis as a result of the one-sided disturbances in the half-normal distribution model (Zaini Abd Karim, Chan and Hassan, 2010). The half-normal distribution model uses a single parametric distribution, assuming that the disturbances’ density concentrates mostly near zero which will lead the deviation in the output variable damaging the analysis. Normal-gamma model doesn’t require us to assume that the firm-specific inefficiency measures be predominantly near zero (Greene,1990). Moreover, the inefficiency distribution can assume different shapes as the range of random variables is not restricted.





Efficiency can be described as the relation between ends and means (Afriate, 1972) and has an application in production analysis as well as in consumption theory and demand analysis. We use a cost function instead of the production function to measure the efficiency of the financial sectors we want to study how cost efficient the banking sector is and its relationship with non-performing loans (Zaini Abd Karim, Chan and Hassan, 2010). A stochastic Frontier Analysis would be used to obtain the banks’ cost efficiency score.


For estimating the cost efficiency measure, the inputs would be the expenses on land, buildings and equipment per deposit (Capital), wage and salary expenses  per employee (Labor), and interest expenses per deposit (Deposits). The outputs are total income and total loans. A specification of the prices of the inputs is required to estimate the measure of cost efficiency. The price of labor would be labor costs over total assets, the price of the capital is obtained by dividing the other operating expenses, by total fixed assets, and the price of the deposits would be the interest expense divided by total deposits. The cost efficiency measure obtained will then be used to test its relationship with non-performing loans.




Tobit Model would be used in this research to determine the relationship between cost efficiency and non-performing loansas the scores of efficiency are bounded between zero and one. This Model was developed by Tobin (1958) and is also known as truncated or censored regression model, where expected errors are not zero (McDonald and Moffitt, 1980). Ordinary Least Squares (OLS) assumes that the error term is normally distributed and hence, would lead to bias in the analysis.


The standard Tobit model can be presented as follows:

EFFi* = β’X + εii~ N(0,σ2) if 0 <EFFi* < 1

EFFi= 0 if EFFi* = 0 and EFFi= 1 otherwise.

  • EFFi* – the cost efficiency scores obtained from Stochastic Cost Frontier Analysis
  • β – Estimator parameters vector
  • X – Explanatory variables vector
  • εi– Error term

The explanatory variables used for applying Tobit Analysis in this study would be Non-performing loan (NPL), asset and age. It has been found out that the relationship between cost efficiency and non-performing loan is bi-directional and not unidirectional (Zaini Abd Karim, Chan and Hassan, 2010). By using these variables, we can come up with a Tobit simultaneous equation regression model which can be presented as follows:

EFFit = α0 + δ1NPLit + α1STATEit2FOREIGNit + α3ASSETit + α4AGEit + ε

NPLit = β0 + δ1EFFit + β1STATEit2FOREIGNit + β3ASSETit + β4AGEit + ε

  • NPL – Ratio of non-performing loan to total loans
  • STATE – Dummy variable which takes the value ‘0’ if the bank is owned privately or ‘1’ if a bank is owned by the state
  • FOREIGN – Dummy variable which takes value ‘1’ for foreign bank or ‘0’ for a local bank.
  • ASSET – Natural Logarithm of the total asset
  • AGE – Firm’s age to control for experience of the bank

A Tobit simultaneous equation regression model has been used in this research to determine the relationship between the non-performing loans and the cost efficiency of the banking sectors for simultaneity affect.




In this chapter, the different kinds of approaches to estimate the cost function have been discussed based on past researches, hence giving us a deeper insight on how and when to use those models. Tobit Method has also been discussed in this chapter since its simultaneous equation helps us determine simultaneity affect in the relationship between NPLs and the cost efficiency of banks. Based on the findings, the most suitable models will be chosen for testingon the data set of banks in Bhutan.
























In this chapter, the research methodology explained in the previous chapter will be used to conduct the specific and overall research and thus to obtain the results and findings. Of the different types of approaches reviewed in the previous chapter, the best suitable model will be chosen and tested for its suitability for testing the cost efficiency of the financial sectors. The cost efficiency function obtained using the most suitable approach, would then be tested for its relation with the non-performing loan.


4.1 DATA

In this research, the effect of non-performing loans on the cost efficiency of the financial sectors in Bhutan will be studied. The financial sectors included in the study would be the five banks listed under the Royal Monetary Authority of Bhutan. The effect of non-performing loans on the cost efficiency of the five financial sectors mentioned below in the table; over the span of nine years(2011-2019) will be studied. The outputs and the inputs to be used as explained in the earlier chapters is collected from the annual reports of the Banks for the time span available and the few missing reports was collected by requesting the main office.

Table 4.1 List of Financial sectors involved

Sl. No Financial Sector
1 Bank of Bhutan (BOB)
2 Bhutan National Bank (BNB)
3 Druk PNB Bank (PNB)
4 Bhutan Development Bank Ltd (BDBl)
5 T Bank.





Zaini Abd Karim, M., Chan, S. and Hassan, S. (2010). Bank Efficiency and Non-Performing Loans: Evidence from Malaysia and Singapore. Prague Economic Papers, 19(2), pp.118-132.

Abel, S. (2018). Cost efficiency and non-performing loans: An application of the Granger causality test. Journal of Economic and Financial Sciences, 11(1).

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