International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 1876
ISSN 2229-5518
Modeling NPA Time Series Data in Selected
Public Sector Banks in India with Semi
Parametric Approach
Gour Bandyopadhyay
Abstract- The research paper, entitled, ‘Modeling NPA Time Series Data in Selected Public Sector Banks in India with Semi Parametric Approach’ is devoted to an analytical study to reveal the movement of the financial parameter, GNPA over time. Diagnostic tool like Residuals vs Predictor Plot, Quantile Comparison Plots of the Residuals and and QQ Plot have been employed to examine appropriateness of Penalized Spline (Semi Parametric Curve Fit) model, to check the presence of outliers, and to detect departures from normality in the residual distribution for our data respectively. It is observed that Penalized Spline (Semi Parametric Curve Fit) model fits well with the given dataset. It is also observed that there exist very few outliers in some of the selected banks and residuals follow approximately normal distribution for the sample dataset. Penalized Spline (Semi Parametric Curve Fit) Model, establishes curve linearity in the given data. Goodness of fit statistics represented by R2, Sig of F statistics establishes high precision of the model and excellent fit for dataset in respect of the parameter GNPA. Finally, the Penalized Spline (Semi Parametric Curve Fit) model is extended to get the forecasted values for the respective data-set. Forecasted Values of GNPA for three years (2013, 2014 and 2015) of all the selected PSBs clearly demonstrates future upward trend in respect of the financial parameter GNPA for all the selected PSBs, which puts question mark on the wisdom and integrity of the top management in PSBs in India in handling credit portfolio. Such a situation undoubtedly deserves immediate and serious attention on the part of the regulators to relook into the practices of credit appraisal and monitoring of credit in PSBs in India.
Index Terms— Analysis of Trend of NPA, Forecasting Model, Gross Non Performing Assets, Non Performing Assets, Penalized Spline
Technique, Public Sector Banks in India, Semi Parametric Approach, Time Series Data
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N a developing country like India, banking is seen as an instrument of development and has to essentially develop dynamism and capacity for adaptation for adjusting itself to the sweeping changes in the economy (Sharma, 1985) [1]. The evolution of Indian financial system, since the mid-eighties in general, and the launching of the economic policy in 1991, in particular, has been characterized by profound transformation as a result of prolonged and effective reform initiatives by Re- serve Bank of India (RBI). The fundamental philosophy of the development process in India has shifted from closed and highly regulated regime to free market economy and the con- sequent liberalization, deregulation and globalization of the economy. One of the major challenges that the banking indus- try in India is facing today is the credit risks. Various dimen- sions of credit risks expose this fast growing industry to
mounting Non Performing Assets (NPAs).
Though macro environmental factors including global re-
cession, economic slowdown, rising inflation and inadequate
legal frame work contributed heavily towards growth of dis-
tress asset in the banking sector, micro banking factors, includ-
ing poor appraisal and follow-up, defect in the mindset of the
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• Gour Bandyopadhyay is currently pursuing PhD degree program in Man- agement in West Bengal University of Technology, India, PH-
919432083462. E-mail:gaur_banerjee@yahoo.co.in
borrower and lender are no less important. Pressure from reg- ulators towards strict adherence to international norms on asset quality has also contributed to rising bad loans figures in absolute terms in the Public Sector Banks (PSBs) in India in the last two decades.
The micro and macro impact of such deadly virus are as under:
Micro or bank specific impact of NPA:
NPA is like a “double – edged knife” as it not only re-
duces net interest margin (as interest cannot be charged
on such accounts), but also erodes current profit gener-
ated by other performing assets due to stringent provi-
sioning norms on impaired loans (Selvarajan and Vadi-
valagan, 2012) [2]. Moreover it puts deterrent effect on the solvency and liquidity of the bank.
Asset quality of a bank is measured inter-alia, in terms of the percentage of NPA to total advances and there- fore a higher level of NPA leads to adverse comments and criticism by all stake holders which in-turn, ad- versely affects bank’s image. It also de-motivates the staff and creates investor apathy and shakes the cus- tomer’s loyalty.
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Additional time and efforts required in management of bad loans involve indirect cost which a bank has to bear for no incremental gain. NPA creates a serious problem of asset liability mismatch as the money lent for a par- ticular period if not recovered in time, meeting the matching liability will be extremely difficult and often becomes costly.
The cost of financial intermediation by banks is high partly because of the cross subsidization of their NPAs. The immediate consequence of large amount of NPAs in the balance sheet of a bank is bank failure, (Hou,
2007) [3]. There are evidences that even among the banks that do not fail, there is a negative relationship between NPA and performance efficiency.
Macroeconomic/ industry impact of NPA:
NPA implies bad loans and is a drag on bank’s re-
sources. Scarce resources of the bank get blocked, re-
stricting the recycling to the productive sectors of the
economy. Once the credit to various sectors of the econ-
omy slows down, the economy is badly hit. There is a
slowdown in growth in GDP and consequent depres-
sion in the economy.
Indirectly the burden of NPA is to be borne by the so-
indicates low quality of credit portfolio in absolute terms. Such a high figure of loan defaults is directly eating away vi- tality of the PSBs and forces us to relook on the credit apprais- al and follow up techniques applied by the banks. (Sharma,
2005) [4]. Therefore, managing asset portfolio has become the top most priority in PSBs in India, which requires focused and planned effort including forecasting future value of NPA and their effective management.
From perusal of balance sheet of any bank, it is observed that lion’s share of aggregate asset are loans and advances and in- vestments. Loan Assets of a bank are broadly classified as:
quarter. These assets have well defined credit weakness that
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ciety as a whole. When government comes to rescue by
way of infusion of capital to a sick bank due to erosion of capital on account of NPAs, the same comes out of government’s budgetary resources which is contributed by the public in general, either in the form of tax reve-
nues or from the hard earned savings of the investing public. In any case, the society is bearing the cost of these NPAs, (Sharma, 2005) [4].
RBI Report on NPA stated that reduction in NPA should be treated as a national priority. Though Indian banks remained well-capitalised, concerns about the growing non-performing assets (NPAs) loomed large. Banks’ exposure to the stressed power and airline sec- tors particularly added to deterioration in their asset quality, (India. RBI, 2012) [5].
Management of NPAs, is as such sacrosanct to ensure effective re-cycling of funds, and improvement of bot- tom lines. Therefore, it is necessary that NPAs in a bank should be kept at the minimum possible level.
Banking is a financial intermediary which mobilizes savings of the surplus units in the form of deposits and channelizes them in deficit units including agriculture, industry and services, as loans and advances. As a lending institution, NPA in banking business is an eventuality and cannot be avoided.
NPAs have dampening effect on banking system since long, though they were not in the public domain till early 90s (Khasnobis, 2006) [6]. Norms on NPA was implemented for the first time by RBI in 1992-93, when Gross Non Performing Asset (GNPA) of all PSBs were Rs 39253 crores, representing
23.18% of Gross Advances (GAs), which rose to Rs 112489 crores, representing 3.17% of the GAs as on March 2012. This
jeopardize the liquidation of debts and may be characterized
by distinct possibilities that bank will sustain some losses. In
other words, an NPA may be defined as a credit facility in
respect of which the interest and/or installment of principal
has remained unpaid for a specified period of time. With a
view to moving towards international best practices and to
ensure greater transparency, it has been decided by RBI to
adopt the “90 days’ overdue” norm for identification of NPAs
in India, from the year ended March 31, 2004.
Classification of NPAs are done, taking into account the
degree of credit weaknesses, risks and extent of dependence on collateral security for realization of dues. NPA accounts are classified into following three categories.
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little value that its continuance as a bankable asset is not war- ranted, although there may be some salvage or recovery value. However, NPA account where there is potential threats to re- covery on account of erosion in the value of security or non availability of security or fraud by the borrower, it should be straight way classified as Doubtful or Loss asset as appropri- ate.
Public Sector Banks Group comprises of:
State Bank of India and its Subsidiaries, popularly known as State Bank Group
Other Nationalized Banks, popularly known as Nation- alised Bank Group
these models are found to have more representative power many times, when compared against different performance criteria, to explain and model the real-life data situations. To capture the data characteristics, emanated from a real life data situation, in this research paper, we have employed Penalized splines technique of semi parametric approach.
Penalized splines have gained much popularity as a flexible tool for smoothing and semi-parametric modeling. Penalized splines are low-rank smoothers, i.e. amount of knots used for estimation is far less than the number of observations, which significantly reduces the numerical effort. According to Yao and Lee (2008) [8] there are two important components in fit- ting penalized splines – a) selection of the smoothing parame- ter and b) choice of the number of knots and their location.
The theoretical framework for developing a Penalized Spline fit as described by Nettleton (n.d.) [9], in his Lecture note ‘Smothing Scatterplots Using Penalized Splines’ in Iowa State University is stated below:
Let us consider the model where i=1,2….n
If f(x) is linear, then
The linear model tries to approximate f(x) as a linear combina- tion of two basis functions: where bo (x) =1 and b1 (x) = x, then
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consists of all the nonstandard assets like as sub-standard, doubtful, and loss assets. In other words, GNPA is the amount outstanding in the borrower’s accounts in the books of the banks other than the interest which has been recorded and not debited to the borrower accounts.
Similarly, for a quadratic model i.e. we
can write,
Let us consider,
where, k1 is a specified real value. Therefore f(x) can be ap- proximated by
Where u1
is an unknown parameter (like β0
and β1 ).
Semi parametric regression is concerned with the flexible in-
corporation of non-linear functional relationships in regres-
sion analyses. Any application area that benefits from regres-
sion analysis can also benefit from semi parametric regression.
Since a semi parametric regression model contains both para-
metric and non parametric parts, it offers a good compromise
between parametric and non parametric regression models
(Wu, 2010) [7].
Researchers devoted serious attention on semi parametric
modeling of either independent or dependent time series data.
Their focus on research interest has been primarily on estima-
tion and testing of both parametric and non parametric com-
ponents in semi parametric models. Interest of researchers also includes use of semi parametric methods in model estimation, specification testing and selection of non linear time series data. The semi parametric modeling technique comprises the
two aims, flexibility and simplicity of statistical procedures by introducing partial parametric components. The flexibility of semi parametric modeling has made it a widely accepted sta- tistical technique.
Semi parametric regression can also be of substantial value in complex real life problem. Such models reduce the com- plexity in the dataset to summarize that we can understand. Appropriate applications of such models ensure retaining es- sential features of the data set while discarding unimportant details and hence they aid sound decision making. Indeed,
It may be noted that,
This function is a continuous function since it is a linear com- bination of continuous function. At the same time it is piece- wise linear. It is simple example of linear spline. In this case k1 is known as knot. In case of polynomial regression, we consid- er a linear spline model as a special case.
The linear spline function can become more flexible by adding
more knots k1 … kk when f(x) is approximated by,
Thus the model becomes,
In many cases f(x) becomes non-smooth. Hence a less flexible (more smooth) estimate of f(x) is usually preferred. This can be obtained using penalized least squares.
For this two things are important
(i) Smoothing parameter and (ii) Penalty for roughness. It is
for the researcher to choose proper smoothing parameter and
the knots (k1 , k2 … kn ). If smoothing parameter is small we get a non smooth fit.
Now, there are few strategies for choosing the smoothing parameter.
A) Cross Validation–It is a general strategy for choosing smoothing parameter.
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B) Generalized Cross Validation– It is an approximation to cross validation. The amount of smoothing can be selected by using the generalized cross validation function (Kageyama et al. 2004) [10].
Next the number of knots and their locations has to be de- cided. Ruppert (2002) [11] states that “there must be enough knots to fit features in the data, but after this minimum neces- sary number of knots has been reached, further increases in K often have little effect on the fit” (p. 740). Here, K means num- ber of knots. Eilers and Marx (2004) [12] stress that “equally- spaced knots are always to be preferred”, while Ruppert (2002) [11] emphasize utilization of quantile-based knots. In general, both approaches do the work equally well for most of the cases. Wu (2010) [7] points out that both the location and number of knots are equally important for splines as they de- termine the degree of smoothing. Knots can either be placed uniformly or all the distinct time point can be used as knots. The percentile based knot placing rule can also be used. Thus it can be said that a good fit can be obtained if there are enough knots. Penalization prevents a fit that is too rough even when there are many knots.
In our case the semi-parametric model is fitted using the SemiPar package from the R statistical system. SemiPar is a simple tool to construct a nonlinear regression. This package
provides a convenient way to fit splines to data using R. In the
ed, they are plotted against either the corresponding fitted values or (more commonly) the values of the original X varia- ble. Then, a semi parametric regression curve is fitted to the points within the residual plot. This new application of the semi parametric regression smoother should produce a flat line located at the zero value on the vertical axis in the residu- al plot. The reasons are as follows. The semi parametric re- gression residuals measure the variability in Y that remains after the dispersion of the fitted values (and hence, the smooth curve) is taken into account. Any systematic functional de- pendencies between X and Y should be picked up by the orig- inal smooth curve fitted to the bivariate data. To the extent that the semi parametric regression fitting process does so successfully, there should be no discernible patterns of any kind among the residuals; this, in turn, would produce a hori- zontal line when a smooth curve is fitted to the residual plot. If the plot does not reveal any kind of systematic relationship (whether linear, cubic, quadratic, etc.) between the residuals and the predicted values, we may say penalized spline model is appropriate for our data.
This plot shows the residual plot from the original penal- ized spline curve that is fitted to the data. The points in this
figure are obtained by plotting the penalized spline residual
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SemiPar package, f is estimated using penalized spline
smoothing.
For univariate smoothing, SemiPar’s default basis function
is radial: | x− κk |p, where κk is the location of the kth knot, and p is the degree. The default degree for the radial basis is 3,
so the default function is:
where, k=1,…… K
Best fit in semi parametric regression is found with proper variable selection as well as the choice of smoothing parame- ter. The residuals from a semi parametric regression fit can be employed as a useful diagnostic tool as described below. Such residuals are used in order to determine whether the smooth curve adequately incorporates all of the interesting structure in the data. The residuals are scrutinized for systematic pat- terns that may remain after a hypothesized structural repre- sentation has been fitted to the empirical data.
The semi parametric regression residuals are defined as the difference between the observed values of the Y variable, and the corresponding fitted values for the respective occurrences of the X variable values: 
The equation above is very similar to the familiar formula
for calculating residual values in regression analysis. Howev-
er, there is one important difference. The K knots used to find
the semi parametric regression curve are imaginary values
which are usually different from the n observed values of the independent variable, X. Therefore, the fitted values for the empirical observations, fˆ(xi ) are typically obtained from the model.
Once the semi parametric regression residuals are calculat-
values (on the vertical axis) against normal norm quantiles
plot (on the horizontal axis) to check the presence of outliers in
the data variables. The plot is also used to detect departures
from normality in the residual distribution.
A Q-Q plot ("Q" stands for quantile) is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other. First, the set of intervals for the quantiles are chosen. A point (x, y) on the plot corresponds to one of the quantiles of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). Thus the plot obtained in this way represents a Q-Q Plot.
If the quantiles of the two distributions being compared are similar, the points in the Q-Q plot will approximately lie on the line y = x. If the quantiles of the two distributions differ only in their location or scale, the points in the Q-Q plot will fall on or near line, y = ax + b. The slope a and intercept b are visual estimates of the scale and location parameters of the theoretical distribution. The Q-Q plot can provide an graphical assessment (rather than reducing to a numerical summary) of "goodness of fit" and hence can be used to compare two theo- retical distributions. A normal Q-Q plot compares a randomly generated, independent data-set plotted on the vertical axis to a standard normal deviate population plotted on the horizon- tal axis. The linearity of the points on the plot suggests that the randomly generated data are normally distributed.
When a semi parametric regression curve is fitted to data, attention is usually focused on the shape of the resultant curve
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because that feature is most revealing of the structure within the data. However, it is also useful to consider how well the smooth curve characterizes the empirical data values. This latter phenomenon is usually called ‘goodness of fit’, although that term is only partially appropriate in the case of semi par- ametric regression. A summary fit statistic similar to an R2 value can be obtained by taking the ratio of the sum of squares in the semi parametric regression fitted values to the total sum of squares in the dependent variable.
A relatively high R2 value would lead to the conclusion that the smooth curve summarizes nearly all of the total dispersion in the dependent variable.
The concept of degrees of freedom for semi parametric re- gression models is not as intuitive as for linear models since there are no parameters estimated. Nonetheless, the degrees of freedom for a semi parametric regression model are a general- ization of the number of parameters in a parametric model. The analogy to the linear model is not perfect, but approxi- mate. Using the approximate degrees of freedom, we can carry out F-tests to compare different estimates applied to the same dataset; Compare different levels of polynomial fits; Compare
the smoothed model to a linear model etc. Determining the
in six selected PSBs;
ii) to develop a forecasting model with the help of univariate
dataset of GNPA (dependent variable) and Time (inde-
pendent variable)
The study undertakes an empirical approach to analyse the movement of NPAs in six selected PSBs India over the last two decades, based on secondary data related to the strategic banking variable, ie, NPAs. The secondary data have been collected from RBI publications, Prowess Database of Centre for Monitoring Indian Economy and the Annual Reports of the selected PSBs.
The study includes examination of movement of NPA over time, developing forecasting model for medium term with NPA as dependent variable. For the purpose of our analysis, a time series data-set on parameter GNPA for 17 years i,e March
1996 to March 2012 for six selected PSBs have been captured and analysed by using SemiPar package of R software in order to draw relevant inference.
To examine dynamicity of NPA over time as stated in the first objective, semi parametric, nonlinear regression models have been invoked by employing Penalised Spline technique and the best fitted model to represent the trend has been ob-
tained in case of each data-set. The forecasted values have
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degrees of freedom is also necessary for constructing confi-
dence envelopes around the fitted curve. Unlike in linear
model, the degrees of freedom for semi parametric regression
model are not necessarily whole numbers.
F-tests comparing the residual sums of squares for alterna-
tive nested models can be carried out in exactly the same way
as for linear models. These tests are only approximate because
of the approximation of the degree of freedom.
Perhaps the most useful aspect of semi parametric regres-
sion is that it allows us to test for nonlinearity by contrasting it
with a linear regression model. In general for semi parametric regression, if we are testing two nested models, we can con- struct the usual F-ratio as:
Where RSS0 is the residual sum of squares for the smaller model (linear model in our case), and RSS1 is that for the larg- er model (semi parametric univariate penalized spline smoothing). Also dfres, 0 is the degree of freedom for the RSS0 and dfres,1 is the degree of freedom for the RSS1 .
If p-value of F test is less than 0.05 then we conclude that there is no linear relationship between response and predictor variables.
In view of the relative importance of NPAs in banking sector in India in general with PSBs in particular, it is perceived that a comprehensive study in this area should be made. The pre- sent study is a humble endeavour to examine various aspects of NPAs in selected PSBs. The specific objectives embodied under the research are as follows:
i) to examine the overall trends of NPAs and to explore the dynamicity of NPA as the variable under study over time
been generated based on the said best fitted model as stated in objective number two.
Null Hypothesis (H0 ): There is no linear relationship between Non Performing Assets (response variable) and time (predic- tor variable).
Alternate Hypothesis (H1 ): There is a linear relationship be- tween Non Performing Assets (response variable) and time (predictor variable).
In view of the seriousness of the problem, numerous research studies have been conducted on different issues concerning credit risks including NPAs.
Berger and Young (1997) [13] develop an econometric mod- el for forecasting NPAs in a commercial bank, to test the hy- potheses regarding relationship among loan quality, cost effi- ciency and bank capital. The paper suggests that problem loans precede reductions in measured cost efficiency; that measured cost efficiency precedes reductions in problem loans; and that reductions in capital at thinly capitalized banks precede increase in problem loans. Hence, cost efficiency may be an important indicator of future problem loans and prob- lem banks.
Misra and Dhal (2001) [14] examine the factors responsible for increasing levels of NPAs and observes that NPLs are in- fluenced by three major sets of economic and financial factors, i.e., terms of credit, bank size induced risk preferences and macroeconomic shocks. A Panel Regression model for fore- casting Gross NPA Ratio has been developed. The empirical results from Panel Regression Models suggest that terms of credit variables have significant effect on the banks' non-
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performing loans in the presence of bank size induced by risk preferences and macroeconomic shocks. The study also ob- serves that factors like maturity of credit, better credit culture, favorable macroeconomic and business conditions lead to lowering of NPAs. Business cycle may have differential impli- cations adducing to differential response of borrowers and lenders.
Yao and Lee (2008) [8] states that:
“Due to its simplicity and effectiveness for handling
different semi parametric smoothing problems, penal-
ized spline regression has recently become a popular
tool for solving various estimation problems, ranging from environmental modeling (Wood and Augustin,
2002) to longitudinal and functional data analysis
(Harezlak, Ryan, Giedd & Lange, 2005; Yao & Lee,
2006) to remote sensing imaging (Clarke et al., 2006).
When comparing to smoothing splines, an attractive
property of penalized spline regression is the ease for
conducting statistical inference (Ruppert et al., 2003)”.
(p 259)
Salkowski (2008) [15] in his work has given examples of us-
ing spm function of the SemiPar package to fit the semipara-
metric model where temperature deviation is a function of the
year.
Ahmed (2010) [16] attempts to investigate empirically the
tive of the financiers. An econometric model has been cap- tured to predict NPAs, taking into account bank level micro economic variables in the sample banks. The study suggests a multi pronged approach for solution to the problem of NPAs by addressing policy issues, strategic issues, restructuring is- sues, legal issues, reporting issues, supervisory issues, opera- tional and procedural issues.
Rawlin and Sharan (2011) [19] make a sincere attempt to develop a forecasting model for the NPA percentage at both the gross and net level from the Total Assets of one of the In- dia’s largest PSB. A strong correlation is observed between gross and net NPA% and the total assets suggesting that the estimate of gross and net NPA can be made from total assets, by fitting to linear and non linear models. A non linear curve estimation model, is found best fit by virtue of best R2 value linking both gross and net NPA to advances provide the best curve fit and the least deviation from actual values. Thus by studying total assets an overall picture of the banks NPA level can be ascertained and effective strategy can be formulated to address the most formidable problem in the banking industry.
Thiagarajan et al. (2011) [20] in their empirical study make an attempt to predict the determinants of the credit risk ex- pressed in terms of NPA in the banking sector in India by us- ing an Econometric model. The study identifies both macro
economic as well as micro economic bank specific variables
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asset quality and loan recovery of Indian commercial banks
and establishes a relationship between growth in advance and
growth in NPA of a bank. The paper also examines various
factors that affect NPAs of a commercial bank and presents a
multi regression model in forecasting NPA of a bank with a
few strategic banking variables like Priority Sector Advances,
Credit Deposit Ratio, NPA to Advance Ratio as independent
variables. It is observed that Priority Sector Advances, Credit-
Deposit Ratio, Capital Adequacy Ratio and NPA to Advances
Ratio may not be considered as a very good determinant of
dependent variable, ie, Non Performing Assets. The researcher however concludes that NPA is an important parameter to assess the financial health of a banking company as it reflects asset quality, credit risk, and efficiency in the allocation of re-
sources in deficit sectors and therefore various initiatives have been taken to contain growth in NPAs.
Dash and Kabra (2010) [17] examine determinants of Non Performing Loans in India from both macro economic and strategic banking variables. With the help of regression analy- sis an econometric model is developed using a panel data set covering 10 years (1998-99 to 2008-09) to examine the relation- ship between non-performing loans and several key macroe- conomic and bank specific variables, for predicting future val- ue of NPA. The study observes that the real effective exchange rate and the changes in real income as reflected by growth in real GDP, have a significant positive and a significant negative relationship respectively with NPAs. It also finds that com- mercial banks that are aggressive and charge relatively higher interest rates incur greater NPLs.
Gupta and Jain (2010) [18] examine factors like credit spreads, collateral, long-term structures and commitments between borrowers and lenders over time, which are respon- sible for the cropping up of distressed asset from the perspec-
and observes a high R2 for both Public and Private Sector
Banks which is a reflection of the fitness of the model and its
predictability. For the purpose of the study descriptive statis-
tics including mean and standard deviation of the selected
variables have been captured. It is inferred by looking at the
graphical representation of non performing loans and the rate
of GDP Growth and inflation that there is an inverse relation-
ship between GDP Growth and NPA while a positive co-
relation between inflation and NPA for the recent past 2 years.
Siraj and Pillai (2012) [21] examine the impact of gross ad-
vance and total deposit on incremental NPA with the help of simple regression analysis. A multiple regression model has also been developed with NPA as a dependent variable with total deposits and total advances as independent variable to
examine the total effects of these variables in addition to NPAs of the bank.The study observe that increased level of addition to NPA still remain a major concern for banks in India.
Banking industry in India comprise of the PSBs and the Pri- vate Sector Banks (PrSBs). PSBs consists of the State Bank of India (SBI) and its five subsidiaries, collectively termed as the State Bank Group and nineteen nationalized banks, commonly referred to as Nationalised Bank Group and one other PSB, ie, IDBI Bank. The twenty PrSB’s are further subdivided into Old PrSB Group and New PrSB Group. In addition to these PrSB there exists thirty six Foreign Banks (FBs), privately owned with registrar office located abroad.
PrSBs and FBs are particularly excluded from the study, as they are not strictly comparable with PSBs and they account for less than 16% and 5.30% of Gross NPAs of banking system in India respectively, as on March 2012. The Regional Rural Banks (RRBs) are also excluded from the present study as their
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operations are confined to target groups in rural and semi ur- ban areas.
As the concept of NPA was first introduced in 1992, there- fore their post reform 1st balance sheets became available one year later ie, in, 1992-93. However NPA data of all PSBs are not available for 1992-93, 1993-94 and 1994-95 (only aggregate PSB figures are available since 1992-93). This provides justifi- cation for 1995-96 as the starting year in the present study. Further, the study covers the period upto 2011-12, i,e the lat- est year till the dataset is available.
For the purpose of the study, we have taken one large sized PSB {State Bank of India (SBI)}, two medium sized PSBs {Pun- jab National Bank (PNB) and Central Bank of India (CBI)} and three small sized PSBs {State Bank of Travancore (SBT), UCO Bank (UCO) and Syndicate Bank (SB)}.
The study makes an attempt to examine empirically trends of NPAs for six selected PSBs. However studies revealed macro economic factors like global recession, high rate of inflation have significant influence on NPAs of a bank which is beyond the scope of our study.
Time series GNPA data is available for seventeen years for six selected PSBs. Therefore the dataset can be said to be very small under any standard.
selected PSBs in India using semi parametric Penalized Spline technique.
Given the forecasting models, the paper is capable of providing insights into the stability of the financial system and is also of immense practical significance for policy mak- ers/regulators/financial engineers/researchers in terms of developing plans to minimise the volume of NPAs in the fu- ture. By examining trends in NPA time series data and fore- casting NPA for medium term in six selected PSBs, as at- tempted in the study, a bank will be in a position to initiate corrective actions as appropriate towards improving level of distress asset in the bank resulting in a great relief for the economy and society. Such forecasts enable the policy makers to judge whether it is necessary to take any measure to influ- ence the relevant economic variables. Given its association with bank failure and financial crisis, the evaluation of non- performing loans (NPLs) is of great importance and should therefore be of interest in a developing country like India. Ar- eas of future application of such modeling in the banking in- dustry are enumerated below:
i) Future values of GNPA, along with other strategic bank- ing variables, can be forecasted by other banks from the past performance using semi parametric approach which has been illustrated in the forecasting section of the re-
search paper.
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As the study is exclusively on secondary data, it is subject- ed to following shortcomings:
• The researcher has least control over how the data was
collected.
• There may be biases in the data that the researcher
doesn’t know about.
• Output from such dataset may not exactly fit the re-
searcher’s research questions.
Unimpressive asset quality is a matter of great concern to not only the lenders but also all concerned including the people at large (society). High level of NPA implies scarce resources of the bank get blocked, restricting the recycling of funds in the productive sectors of the economy. Once the credit to various sectors of the economy slows down, the economy is badly hit, resulting in increase in unemployment and poverty. Moreover mounting menace of NPA raises the cost of credit, makes banks more averse to credit risk and as a result, genuine small and medium entrepreneurs are denied of credit, which unfor- tunately, throttle their enterprising spirits as well.
Again, when a ‘NPA burdened PSB’ becomes sick with negative net worth, government comes forward to rescue by way of infusion of capital to the sick bank. Such financial as- sistance comes out of government’s budgetary resource which is contributed by the people in general, either in the form of tax revenues or from the hard earned savings of the investing public. In any case, the society is bearing the cost of these NPAs.
Despite the importance of monitoring non-performing
loans, forecasting on parameter GNPA have only received
moderate attention in literature. This study contributes to the
existing literature by modeling the parameter GNPA of six
ii) With the help of these forecasted values the banks can
formulate policy initiatives through planning and budg-
eting to bridge the gap between the tolerable level of
NPA and forecasted level of NPA.
iii) Such models can be used to mitigate risk associated with
credit portfolio as an early warning system.
iv) Such forecasts enable the policy makers to judge whether
it is necessary to take any measure to influence the rele-
vant economic variables.
v) Motivational schemes like promotion/ fringe benefits
can be employed through performance benchmarking based on forecasted value of GNPA.
vi) The models can be used as a performance measurement means for the selected PSBs. Some of the major areas are given as under:
a. Reviewing the profitability of the bank to reflect changes in policies and their underlying economics along with harmonization of these policies with risk management methods,
b. Determining the nature and impact of the critical factor that have greatest influence on the bank’s perfor- mance,
c. Redefining the profitability of the banks by effective management of NPA and harmonizing new policy ini- tiatives with NPA management, managing the criticali- ties to align the components of performance manage- ment processes with forecasting.
A number of factors make the NPAs in PSBs in India an inter- esting subject for study.
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First, during the 1990s, India underwent liberalization of the banking sector with the objective of enhancing effi- ciency, productivity, and profitability (India. RBI,
1991)[22].
Second, the banking sector underwent an important trans-
formation, driven by the need for creating a market-
driven, productive, and competitive economy in order to
support higher investment levels and accentuate growth
(India. GOI, 1998) [23].
Third, studies on NPAs in banking industry in emerging
economies like India has great relevance, as it dampens
the bottom-lines and thereby poses a serious threat to the very existence of the most important sector in propelling the desired growth and development of the economy.
In view of the seriousness of the problem, numerous re- search studies have been conducted on different issues con- cerning credit risks in banks including NPAs. However, em- pirical works on NPA problems in PSBs are inadequate. The exhaustive review of literature on NPA demonstrates that ma- jority of the research work has been undertaken on aggregate PSBs data with primarily focus on the following areas:
i) Chaitanya (2004) [24] and Reddy et al. (2006) [25] ex- amine the trends of NPA in PSBs.
ii) Berger and Young (1997) [13], Misra and Dhal, (2001)
[14], Ahmed (2010) [16], Dash and Kabra (2010) [17],
TABLE 1
SUMMARY STATISTICS FOR PENALIZED SPLINE MODELS
Note this includes 1 df for the intercept
The graphs and plots of the semi parametric models (smoothing by penalized spline) for six selected PSBs are giv- en below:
Gupta and Jain (2010) [18], Rawlin and haran (2011) [19], Thiagarajan et al. (2011) [20] and Siraj and Pillai (2012) [21] predict future value of NPAs with the help of simple/ multiple regression models. Graham and Humphrey (1978) [26] observe that forecasting NPA employing data of past loans are generally more accu- rate than less parsimonious models.
However empirical work on individual bank-wise trend study and modeling for the purpose of forecasting future val-
ue on NPA in PSB has seldom been attempted. It is against this backdrop that the present study is undertaken to fill up this gap and make a modest contribution in the field of man- agement of NPA in banks in India. Accordingly, examination of movement of NPA over time and forecasting the same for medium term with the help univariate time series data by em- ploying semi parametric (Penalised Spline Curve Fit) for six selected PSBs has been attempted in the paper.
The SemiPar package has algorithms for selecting knots, if knots are not provided by the user. The smoothness of the fit can also be left to SemiPar, but users can control smoothness in two ways. In a univariate fit, the smoothing parameter is the ratio of the smoothing variance to the error variance. Large values of the smoothing parameter (σ2 ε /σ2 u ) produce smooth- er functions. Alternatively, users can specify the degrees of freedom for the fit. The more degrees of freedom in the fit, the less smooth the function is.
Now the GNPA dataset as dependent variable with time (year as 1996,1997,1998….2012 taken as 1, 2, 3, ….17 respec- tively) as independent variable are processed through the SemiPar package of R software and summary statistics for non linear components are given below.
Fig.1. Penalized Spline on GNPA –SBI
Fig.2. Penalized Spline on GNPA –SBT
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Fig.3. Penalized Spline on GNPA –SB
Fig.6. Penalized Spline on GNPA –PNB
The GNPA and time (year) dataset are plotted on vertical axis and horizontal axis respectively. The findings from the above figures are detailed below:
1. The general diagonal orientations of the points sug- gest that GNPAs are highly correlated to Year for all the banks.
2. The curves follow the central tendency of the Y varia- ble’s (GNPA) values across the range of the X variable (Time). In doing so, the curvilinear nature of the rela- tionship between GNPAs and Time is revealed im- mediately.
3. These curves are obtained without any prior specifi- cation about the functional form of the relationship. Instead, the sigmoid (i.e. ‘S-like’) shape of the curve is produced by the semi parametric penalized spline re-
Fig.4. Penalized Spline on GNPA –UCO
gression procedure. The slopes of the fitted curves are negative at some Years on the horizontal axis.
4. These curves clearly show that a linear model would provide a misleading depiction of the relationship be- tween GNPA values and time (year).
Fig.5. Penalized Spline on GNPA –CBI
Fig.7. Residual vs Predictor Plot on GNPA – SBI
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Fig.8. Residual vs Predictor Plot on GNPA – SBT
Fig.9. Residual vs Predictor PloIt on GNJPA – SB
Fig.11. Residual vs Predictor Plot on GNPA – CBI
SEFig.12. Residual vRs Predictor Plot on GNPA – PNB
The dotted horizontal line is a visual baseline correspond- ing to residual value of zero. The above ‘Residual vs Predictor Plot’ (Fig. 7 to 12) shows that the residuals appear randomly scattered around zero indicating that the penalized spline model describes the data well. It can also be stated that the model provide adequate representation of the GNPA bi- variate dataset. Looking at the plots above we can say that for our GNPA dataset, the plots exhibit the absence of relation- ship between residual and predicted value and therefore it can be concluded that penalized spline model exhibiting simple curvelinear relationship is appropriate for our GNPA dataset.
Fig.10. Residual vs Predictor Plot on GNPA – UCO
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Fig.13. Quantile Comparison Plot on GNPA -SBI
Fig.16. Quantile Comparison Plot on GNPA -UCO
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Fig.17. Quantile Comparison Plot on GNPA -CBI
Fig.14. Quantile Comparison Plot on GNPA -SBT
Fig.15. Quantile Comparison Plot on GNPA -SB
Fig.18. Quantile Comparison Plot on GNPA -PNB
From the above figures it is evident that in case of CBI and PNB outliers are present. Rests of the banks (SBI, SBT, SB and UCO) are free from outliers.
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Fig.19. Normal Q-Q Plot on GNPA - SBI
Fig.22. Normal Q-Q Plot on GNPA - UCO
Fig.23. Normal Q-Q Plot on GNPA - CBI Fig.20. Normal Q-Q Plot on GNPA - SBT
Fig.21. Normal Q-Q Plot on GNPA - SB
Fig.24. Normal Q-Q Plot on GNPA - PNB
The q-q plot has been done to test the normal distribution of the residuals for all the banks. It may be observed that the residuals in respect of GNPA dataset of all banks with the ex- ception of SB and PNB follow approximately normal distribu- tion.
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R2 value and significance of F value generated by the software is given below.
TABLE 2
SUMMARY STATISTICS OF PRECISION CRITERIA FOR SELECTED
PSBS ON PARAMETER GNPA
From the above table it is apparent that R2 value is very high for SBI, SB, UCO and PNB while it is moderately high for for SBT and CBI. Hence we may say that the smooth curve summarizes nearly all of the total dispersion in the dependent variable.
The p-value of F test is less than 0.05 and therefore we may conclude that there is no linear relationship between response
serves immediate and serious attention on the part of the regulators to relook into the practices of credit appraisal and monitoring of credit in PSBs in India.
NPA is one of the most important banking parameters for de- termining soundness and efficiency of the monitory system in an economy. In an effort to examine trends in NPA and devel- op a forecasting model for the purpose of analysis and control of bad loans in selected PSBs, various approaches and tech- niques may be used by the researchers and experts. In this paper, penalized spline, a very popular semi parametric tech- nique has been fitted to GNPA data sets for six selected PSBs and it has been observed that these semi parametric models are very much relevant and useful as it enhances the precision level of the models in respect of parameter GNPA in six se- lected PSBs in India.
The study finds that NPA in PSB in India can be adequate- ly captured by semi-parametric regression (penalized spline). In future the researchers can use this study as a reference to examine the trend of NPA for other PSBs and PrSBs and de- velop appropriate forecasting models and further compare these results among different group of banks for examining the relative strengths and weaknesses of different banks. The
researchers may also explore multivariate modeling taking
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and predictor variables, which establishes the null hypothesis
that there is no linear relationship between Non Performing
Assets (response variable) and time (predictor variable).
TABLE 3
FORECAST VALUE FOR PARAMETER GNPA
Forecasted Values of GNPA for three years (2013, 2014 and
2015) of all the selected PSBs exhibit an alarming phenomenon
of continuous upward rise, which puts question mark on the
wisdom and integrity of the top management in PSBs in India
in handling credit portfolio. Such a situation undoubtedly de-
clue from this study which primarily focuses on univariate modeling.
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