Economica Series No. 1 (2) – 2013 ISSN: 2285 – 8067 Page 35 Copyright  2013 Academica Science Journal. All rights reserve d. ECONOMETRIC MODEL FOR… [625189]

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 35 Copyright  2013 Academica Science Journal. All rights reserve d.

ECONOMETRIC MODEL FOR DEFAULT RISK IN BANKS

Ioan B ĂTRÂNCEA
Babes-Bolyai University, Teodor Mihali 58-60, Cluj- Napoca, Romania
Ioan STOIA
Babes-Bolyai University, Teodor Mihali 58-60, Cluj- Napoca, Romania
Sandor CSEGEDI
Babes-Bolyai University, Teodor Mihali 58-60, Cluj- Napoca, Romania
Andrei MOSCVICIOV
Babes-Bolyai University, Horea 7, Cluj-Napoca, Roma nia
Anca NICHITA
Babes-Bolyai University, Teodor Mihali 58-60, Cluj- Napoca, Romania
Diana ANDONE
Babes-Bolyai University, Teodor Mihali 58-60, Cluj- Napoca, Romania

Abstract: Supervisors around the world recognize the advantag es of rating systems,
including a better allocation of resources. Owing t o the development of national economy,
the banking market and related regulations, Uniform Bank Rating System in Romania is
continuously perfecting. Asset quality is one of th e quantitative component of this model is
particularly important because through indicators u sed in its determination reflects credit
risk, the latter being the main cause of bank failu res .
JEL: G21

INTRODUCTION
Supervisory authority has the major role in prevent ing systemic risk and promoting effective banking
supervision, to ensure stability and viability of t he banking system. With this aim in Romania was nec essary
implementation Uniform Bank Rating System (CAMEL). This model is a tool for assessing the credit
institutions and aims to identify those economic en tities are financially and operationally effective or show
unfavorable trends, the latter requiring attention from the supervisor.
Term rating is often associated and even confused w ith the scoring (the latter being related to loan a n
economic or financial stability analysis of economi c entities). Unlike scoring, rating can be defined as: an
evaluation of risk attached to a debt instrument th at allows a ranking.
Bank rating system used by the National Bank of Rom ania is influenced by many factors among which
include the following: development of national econ omy, the banking and banking regulations, which is why
this system is subject to a process of continuous i mprovement. The six components of the CAMEL model
are: capital adequacy, quality of ownership, asset quality, management, profitability and liquidity.

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 36 Copyright  2013 Academica Science Journal. All rights reserve d.

Rating of the component that is called asset qualit y reflects the potential risk of loans, investments , other
assets and off-balance sheet transactions. Credit r isk is called the risk of insolvency of the debtor and the
bank occurs when the client does not carry out all or part of the loan agreement.
A correct sizing credit risk of major importance, g iven that the primary function of a bank is to gran t loans and
also because credit risk is the main cause of bank failures.
System implemented by the National Bank of inspirat ion is American, in connection with CAMEL model, so in
what follows I will refer to a brief review of the literature regarding the American approach.
In 2002 he appeared in the journal entitled Review of Quantitative Finance and Accounting 7:01 p.m. ar ticle
number belonging to Dominic Gasbarro referring to c hanging relations between CAMEL ratings and
soundness of the banking system during the Indonesi an banking crisis. Through constructing a panel
demonstrated empirically that while the economy was stable four of the five components of the model
(except profitability) analysis suggested that bank s are solid, showing the opposite during the period of crisis.
Keshari J. Baral in his article, which appeared in 2005 in The Journal of Nepalese Business Studies Vo lume
II number one, entitled "Checking soundness of comm ercial banks with CAMEL model. Case Study: Banking
groups in Nepal "demonstrates empirically that soun dness banking groups, examined the CAMEL model is
superior to that seen in other commercial banks, bu t as demonstrated three years earlier Dominic Gasba rro
these findings can be misleading in a banking crisi s.
Fotios Pasiouras In 2006, together with his collabo rators, writes an article investigates the impact o f
regulation and supervision of banking, market struc ture and bank characteristics on banks' internal ra tings of
seventy-one countries. It has been shown that large banks have higher profitability achieved higher ra tings.
In The Journal of Risk Finance is, in 2007, an arti cle that refers to predicting bank failures in emer ging
financial markets (with special reference to the ba nking crisis in Turkey) by using the CAMEL rating s ystem.
The results showed that the CAMEL model should be c orrelated with other models (such as the
econometric) for better predictability of bank fail ures.
On January 23, 2011, Simon published an article Var otto attempting a correlation between credit risk,
liquidity risk, market risk and bank capital. Based on Basel III regulations and conduct a stress test (which is
based on economic and financial crisis of 2007-2009 ) demonstrates that bank capital requirements shoul d
increase.
METHOD AND RESULTS
In quantitative research, outlined by the attached bibliography, as well as qualitative research, the data
collected, we used the method of observation and co mparison. We also conducted a quantitative research
programs using Microsoft Office Excel 2003 and EVie ws 5.1. In order to filter out selected information was
used, in addition to the aforementioned methods, th e method of synthesis.
Corresponding theoretical basis of this paper consi sts of all specialized books and articles that have
connection issues studied, occurring in different y ears and corresponding author: B ătrâncea John Trenca
John, Monica Roman, Georgescu Golosoiu Ligia, Fotio s Pasiouras, Simone Varotto, Dominic Gasbarro and
J. Baral Keshari.
Informational basis used is the data presented in t he financial statements of Commercial Bank of quart erly
Carpathian website and the related bank BSE, but al so statistical conferred through monthly bulletins issued
by the National Bank of Romania during 2005-2010.
In this study we performed a multiple linear regres sion in which we tested correlations between: the v olume
of loans (exogenous variable), liquidity effective, immediate liquidity and quarterly unemployment rat e
(endogenous variables). Given that in any model whe re the initial data are absolute and are non-statio nary
and require differentiation (ie working with variat ions from one period to another) indicating their l ogarithms in
advance and I'll logarithmic model variables with b ased on the following formula: ln (yt / YTS) = ln ( yt)-ln
(YTS). The motivation for choosing this form of log arithms of the model consists of the following vari ables:
endogenous variable data consists of exogenous vari ables in absolute and relative data in this way lin ear

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 37 Copyright  2013 Academica Science Journal. All rights reserve d.

model coefficients can be interpreted as elasticity , transformation agrees differences in terms of met hodology
because after logarithm stabilize variance and expo nential trends are linear.
We use the following abbreviations of variables CRA (lending to), LE (actual liquidity), LN (liquidity needed)
and Ratios (unemployment rate). The data we use are presented for the first three variables in the Ann ex to
the number five and the last component in the table below:
Table 1: Quarterly Unemployment
RATAS RATAS RATAS RATAS
2005-T1 6,17 2006-T3 5,52 2008-T1 4,20 2009-T3 6,90
2005-T2 5,87 2006-T4 5,43 2008-T2 3,80 2009-T4 7,80
2005-T3 5,76 2007-T1 4,90 2008-T3 3,90 2010-T1 8,40
2005-T4 6,30 2007-T2 4,00 2008-T4 4,40 2010-T2 7,44
2006-T1 6,23 2007-T3 3,90 2009-T1 5,60 2010-T3 7,35
2006-T2 5,90 2007-T4 4,10 2009-T2 6,00 2010-T4 6,87
Source : NBR's Monthly Bulletins in 2005-2010 – own processing

First we play the same logarithmic chart the evolution of the four variables as follows:

-.3 -.2 -.1 .0 .1 .2 .3 .4
2005 2006 2007 2008 2009 2010
CRA LE LN RATAS

Source: own in EViews 5.1

Figure 1 : Evolution of model variables
According to the graph above it is found that varia bles appear to move "together", ie "have common
stochastic trend" and therefore may be a cointegrat ion relationship (ie a stable linear regression) be tween
them. The next step in building the model refers to the nature of causality testing, so first tested w hether the
variables are stationary using the ADF test.
Usefulness of classical tests proposed by Dickey -Fuller (1978 , 1981) is represented by a series stationarity check and
determine the order of integration and corresponding null hypothesis of these tests is non -stationary.
The basic models proposed in the DF tests have the following form:

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 38 Copyright  2013 Academica Science Journal. All rights reserve d.




β+α=α==
ε+−ρ+ =
ttdtd0td
,t 1tytdty
with yt variable at moment t și ), 0.( d . i . it εσ →ε (Todea, 2010, 16)
In this sense initial test Dickey-Fuller was devolo ped for testing the following hypothesis: 1 :H0 =ρ follows
walk process, the alternative hypothesis 1 :H0 <ρ : process is asymptotically stationary.
Based on this test three different models were buil t the following form:

β+α=α==
ε+ φ+ =∆−
t dd0d
, y dy
ttt
t 1t t t by: 1−=ρφ.
In this case the unit root hypothesis is in testing , 0=φ resulting in a random walk process and is integrate d
series of at least first order. Using Monte Carlo s imulations Dickey and Fuller studied asymptotic dis tribution
of the estimator φ under the hypothesis H0, so that φt if higher critical value, the null hypothesis is
accepted and variables will follow a random walk, i e there is a unit root and therefore returns are di fferences
of order 1, will be stationary.
Given the fact that when the values of autocorrelat ion statistics suffer Student movements was propose d by
the same authors, an enhanced version of the test: Augmented Dickey-Fuller (ADF). With the introductio n as
exogenous variables, lagged values of the variable explained autocorrelation is performed eliminating waste.
Constructed models have the following form:

β+α=α==
ε+ ∆α + φ+ =∆∑−
=− −
t dd0d
, y y dy
ttt
t1p
1i1ti 1t t t

always be possible to choose a large enough order t o preserve the assumption of white noise tε.
In the present model we chose to test the ADF test version intercept as model components tend to fluct uate
around a constant (as can be seen from the chart ab ove):

Table 2: ADF test applied to logarithmic variables
CRA LE LN RATAS
Test value -2.617230 -3.959601 -4.103618 -2.306657
Critical values -3.769597 (1%)
-3.004861 (5%)
-2.642242 (10%) -3.769597 (1%)
-3.004861 (5%)
-2.642242 (10%) -3.769597 (1%)
-3.004861 (5%)
-2.642242 (10%) -3.957386 (1%)
-3.040391 (5%)
-2660551 (10%)
Probability 0.1047** 0.0066 0.0048 0.1804**
** significantly different at 5%
Source: own in EViews 5.1

From the above table it can be seen that the CRA an d Ratas variables have unit root (stochastic trend) so
that they differentiate, while using the ADF test a nd to determine the order of integration and obtain the order
of integration one CRA and for Ratas integration or der two, and the results we present in the followin g table:

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 39 Copyright  2013 Academica Science Journal. All rights reserve d.

Table 3: ADF test used in determining the order of integration
CRA (D1) RATAS (D1) RATAS (D2)
Test value -8.126354 -1.097790 -8.952497
Critical values -3.788030 (1%)
-3.012363 (5%)
-2.646119 (10%) -3.857386 (1%)
-3.040391 (5%)
-2.660551 (10%) 3.857386 (1%)
-3.040391 (5%)
-2.660551 (10%)
Probability 0.0000 0.6928** 0.0000
** significantly different at 5%
Source: own in EViews 5.1

Achieve this distinction because the model is valid only stationary data and also because this distinc tion
resolves a series of regressions false, but only st atistically.
Before testing a model is important to test the nat ure of relationships between its variables and to d o this you
use in this case the methodology proposed by Grange r in 1969. With special reference to two variables Y
and X procedure involves quantifying the proportion related to the current level of variable Y that ca n be
explained by its historical value and then checking that if such variables are added x t -i explained variance
increases. Through Granger test identifies whether the variable X brings additional information, excep t those
relating to the past of Y, which can be used in pre diction of Y.
If considering causality between two variables invo lves the following steps:
1. tests whether X is relevant to Y by estimating t he following equation for the regression:
∑ ∑
= =− − ε+ α + β +µ=k
1ik
1jt jtj iti t X Y Y
where k is fixed so that type errors are white nois e (which is a sequence of independent and identical ly
distributed random variables with zero mean). This equation is fixed relative to the following assumpt ions:
0 … :Hl 2 1 0 =α==α=α
(ie X is not relevant for Y) and 0 :Hi 1 ≠α∃
2. Tested whether Y is relevant to X, from the regr ession:
∑ ∑
= =− − ε+ δ + ϕ +µ=k
1ik
1jt jtj iti t Y X X Null hypothesis and alternative hypothesis are:
0 … :Hl 2 1 0 =δ==δ=δ (Y is relevant to X) or 0 :Hi 1 ≠δ∃
3. Applying the two tests may leads to one of the f ollowing four conclusions: (Laz ăr, 2009, p.57)
• unidirectional causality: X is relevant to Y when the null hypothesis is rejected at the first test and
accepted the second test;
• unidirectional causality: Y is relevant to X if t he null hypothesis is rejected test number two and accepted
the test one;
• bidirectional causality: X ↔Y if the null hypothesis is rejected both the test and the test one second;
• two variables are independent if the null hypothe sis is accepted if the first and the second.

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 40 Copyright  2013 Academica Science Journal. All rights reserve d.

By applying Granger causality test, the number of l ags equal to two, gain acceptance null hypothesis ( valid
also for a number of lags equal to three or four), with explicit reference to the pattern you want to test
namely:
1. there is causality from unemployment towards len ding to (P = 0.96598> 0.05);
2. History of effective liquidity significantly con tribute to explaining the current value of loans (P = 0.18582>
0.05);
3. Granger causality type is present from the neces sary liquidity into credit volume (P = 0.28907> 0.0 5);
4. No Granger causality type from the CRA into LE ( for lag = 4 obtained P = 0.02067 <0.05) respectivel y into
LN (for lag = 4 obtained P = 0.02968 <0.05).
By estimating multiple linear regression equation o btained the following result (where R2 = 0.520015) = –
2.518312 * DCRA LE + 2.253681 * 0.299346 * DRATAS + LN + RESIDUES where we denoted by DCRA
once distinguished series of loans to and different iated twice DRATAS series of quarterly unemployment rate
and the statistically coefficients we obtained for the following results:
Table 3: Multiple linear regression
Coefficient Std. Error t-Statistic Prob.
C(1) -2.518312 1.009780 -2.493921 0.0226
C(2) 2.253681 0.891956 2.526673 0.0211
C(3) 0.299346 0.088494 3.382669 0.0033
Source: own in EViews 5.1

Next you perform regression tests on waste to verify that there is a cointegration relationship between variables .
Table 4 : ADF test applied to waste
RESIDUES
Test values -6.147489
Critics values -3.808546 (1%)
-3.020686 (5%)
-2.650413 (10%)
Probability 0.0001
(Source: own in EViews 5.1)
From the series ADF test chart and waste residues i s shown that the regression are stationary (station ary
fluctuating around 0 with Prob = 0.0001 <5%). There fore the four variables there is a cointegration
relationship, which is as follows:
DCRA = -2.518312 * 2.253681 * LN + LE + 0.299346 * DRATAS.

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

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-.15 -.10 -.05 .00 .05 .10 .15
2005 2006 2007 2008 2009 2010
REZIDURI
( Source: own in EViews 5.1)

Figure 2: Evolution of model residues
This regression indicates that: an increase of 1% e ffective liquidity will cause a decrease in loans t o 2.52%,
the same percentage increase liquidity necessary to CRA will increase by 2.25% and not eventually incr ease
the unemployment rate by 1% will lead to an increas e in loans to 0.3%. Coefficients so determined shal l be
construed as elasticity coefficients and because re sidues are stationary, regression is valid (estimat es for the
coefficients are "trusted").

CONCLUSIONS
Constitute a permanent risk of banking. Among the t en categories of risks listed in the regulations is sued by
the National Bank falls and credit risk. The latter includes the following risks: default risk, risk e xposure,
recovery risk, migration risk, increase the risk of spread and country risk. Rating systems used in cr edit risk
analysis quantifies risk due to loss if a borrower falls into default, and the recovery of these losse s. Risk
rating agencies measure quality, not financial situ ation of the debtor, and now the world market is do minated
by three major rating agencies namely Standard & Po or's Ratings Group, Moody's Investors Service and
Fitch-IBCA.
Credit institution operating in specific market con ditions and as a result is subject to accumulation of risks,
which is why they were built bank rating systems, o f which the most popular are: the United States (CA MEL)
and uniform system bank rating of Romania (CAMEL). Supervisory authorities worldwide use bank rating
systems to prevent the occurrence of the phenomenon of indirect contamination. Uniform Bank Rating
System in Romania – CAMEL is a useful tool in ident ifying credit institutions financially and operatio nally
inefficient and those who experience adverse trends and thus require more attention from the superviso r.
Credit institution incorporated as a bank, a primar y aim in attracting surplus cash resources, existin g on the
market at a time, with the purpose of providing loa ns as applicants. Carpathian Commercial Bank was
founded in 1999 and is part of private domestic ban ks.
CAMEL model simulation was performed based on the b ank's quarterly financial statements analyzed in th is
paper includes only four quantitative components SL G. Compared to the base period (first quarter of 20 05)
rated the value of capital adequacy two at the end of the analysis (fourth quarter 2010), which indica tes that
the capital is satisfactory in comparison with the risk profile of the bank. Asset quality rating equa led four in
the last quarter under review, which means an asset quality and satisfactory credit administration pra ctices.
Component maintains its profitability during the pe riod under review a rating alarming amount of five,
suggesting that there is a deficient amount of inco me and also that the financial institution has obta ined loss,
which induces a serious threat to its viability thr ough the erosion of capital . Three liquidity ratin g given at the
end indicates that management practices need improv ement funds because this institution has quick acce ss
to funds on reasonable terms or significant deficie ncies recorded during the administration of funds.

Academica Science Journal
Economica Series No. 1 (2) – 2013
ISSN: 2285 – 8067

Page 42 Copyright  2013 Academica Science Journal. All rights reserve d.

Proposed econometric model consists of a multiple l inear regression, which are linked through four var iables:
the volume of credits, effective liquidity, the liq uidity necessary and unemployment. Because this mod el are
stationary residues (which was confirmed by ADF tes t and graphical residues) shows that this model is valid.
Regarding a possible way to improve the model devel oped (since R2 is an average) approach is to perfor m
monthly and the sub division: first subperiod cover ing the period before the financial crisis, and the second
reflecting sub-period during the financial crisis.
BIODATA
– Ioan B ĂTRÂNCEA is professor PhD at Babe ș-Bolyai University, Teodor Mihali 58-60, Cluj-Napoc a, România,
email: i_batrancea@yahoo.com.
– Ioan STOIA is PhD Student at Babe ș-Bolyai University, Teodor Mihali 58-60, Cluj-Napoc a, România,
email: saicont2004@yahoo.com .
– Sandor CSEGEDI is PhD Student at Babe ș-Bolyai University, Teodor Mihali 58-60, Cluj-Napoc a, România,
email: exkontalex@yahoo.com.
– Andrei MOSCVICIOV is assistant professor Ph.D, Babes-Bolyai Universi ty, Horea 7, Cluj-Napoca, Romania,
email:andreim@anvico.ro
– Anca NICHITA is teaching assistant PhD at Babe ș-Bolyai University, Teodor Mihali 58-60, Cluj-Napoc a,
România, email:coudyro@yahoo.com.
– Diana ANDONE is PhD Student at Babe ș-Bolyai University, Teodor Mihali 58-60, Cluj-Napoc a, România,
email:andradiana@hotmail.com.

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Economica Series No. 1 (2) – 2013
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