Abstract
The Reserve Bank of India has put 11 public sector banks under prompt corrective action and is planning to put three more where public sector banks constitute 68.9% of the total asset of the Indian banking industry based on 2018 figures; this raises a genuine concern for the financial health of the Indian banking sector as a whole. Under these considerations, this study is conducted to estimate the survival of banks based on ownership and size and uses the Cox proportional hazards model. This study has not found any significant difference in the failure risk of both public and private sector banks based on ownership. However, the study found a significant difference in the failure risk of banks based on size. The smaller banks are indeed at a higher risk of failure than larger banks. The findings of this study can be used to create an early warning system for smaller banks in India.
1 Introduction
The Reserve Bank of India (RBI)^{[1]} has put 11 banks under prompt corrective action (PCA) out of 27 public sector banks (PSBs). Notably, Indian PSBs constitute 68.9% of the total assets of the Indian banking industry as a whole, based on figures obtained from 2018. Further, it is indeed worrisome that RBI is planning to put three more PSBs under PCA. Generally, RBI initiates PCA proceedings for banks with a capital adequacy ratio below 9% or nonperforming assets (NPAs) above 10%. Acharya (2018) argued that PCA is an essential and important step taken by RBI to restore financial stability in the Indian banking system. A bank’s capital is a critical indicator of loss absorption adequacy. Therefore, it becomes imperative for bank supervisors to intervene in weak banks before the capital is completely eroded. Notably, banks under PCA are restricted on dividend distribution, branch expansion, and management compensation.
Further, they are asked to infuse more capital by their owners/promoters in addition to higher provisioning requirements. In 2015, the Government of India (GOI), Ministry of Finance, announced the “Indradhanush” plan for revamping PSBs, a sevenpart plan, suggested mainly by the “P J Nayak” committee. The sevenpart plan includes appointments, bank board bureau, capitalization, destressing, empowerment, framework of accountability, and governance reforms (ABCDEFG).
In R. K. Talwar Memorial Lecture (2017), Dr Viral V. Acharya (Deputy Governor of RBI) had raised concerns about the unfinished agenda of restoring PSBs’ health in India.^{[2]} He pointed out that Indian banks’ credit growth and transmission are weak. Moreover, their gross NPA ratios have been increasing at one end, while the growth in advances (% YoY) has been decreasing significantly in the case of Indian PSBs from 2008 to 2018. The RBI has been taking constant steps to address the stressed assets problem of Indian banks by creating a Central Repository of Information on Large Credits, Asset Quality Review in 2015, Enactment of Insolvency, and Bankruptcy Code (IBC) for referring large aged NPA. In addition, it has asked the Government of India to infuse more capital to meet the recapitalization needs of PSBs. Based on RBI’s recommendation, the Government of India announced a recapitalization package for PSBs in October 2018 of Rs. 2.11 trillion, comprising Rs. 1.53 trillion of government capital infusions and the balance raised from market funding by March 2019.
2 Indian Banking Structure
Indian financial system has scheduled commercial banks and cooperative banks. Scheduled commercial banks are further 27 in number for PSBs, 21 for private sector banks, 49 foreign banks, and 56 regional rural banks as per the financial year 2017 data. PSBs dominated Indian banks till 1990. Beginning from muchcontrolled environments such as restrictive entry, regulated interest rate, credit dispersal, and high reserve requirement, the Indian banking system has come a long way through various reforms that were introduced through recommendations of various expert committees formed at different periods. The most prominent reforms were the Narsimham Committee (1991) reforms that deregulated the interest rates and other issues like income recognition and disclosures transparency. These reforms have increased the competition of nationalized banks from private and foreign banks (Aßmuth, 2020; Kaur & Kaur, 2020). PSBs and private sector banks highly concentrate the Indian banking system; even though the number of private (foreign) banks is large, still foreign banks comprise only 5.7% of the total asset of the banking industry as per the estimates of 2007 (Table 1).
Banks  %  2017  %  2018 

Foreign banks  6.2  8,144,577  5.7  8,095,272 
Nationalized banks  47.3  62,064,503  45.3  64,124,272 
Private sector banks  24.0  31,467,338  25.4  36,015,123 
State Bank of India and its associates  22.6  29,616,465  23.5  33,231,911 
Small finance banks  0.0  0.1  119,662  
All scheduled commercial banks  100.0  131,292,882  100.0  141,586,239 
Source: Statistical tables relating to banks in India (RBI website).
Considering the present state of the Indian banking industry, it would be useful to know the probability of bank failure or survival. This study proposes to use Cox proportional hazards model to estimate the survival of Indian banks, both ownership and sizewise. The study is organized as follows: Section 1 presents the introduction, Section 2 describes the Indian banking structure, Section 3 presents the literature review and develops hypotheses in accordance, Section 4 includes the methodology, Section 5 presents data description and descriptive statistics, Section 6 presents the empirical results, and finally, Section 7 presents conclusions and implications of the study.
3 Literature Review and Hypothesis Development
To carry out the literature review, we followed stepwise filtering of literature search in three major reputed databases (ABI/INFORM, Science Direct, and Emerald) using keywords “Survival Analysis of firms” OR “Survival Analysis of Banks,” restricting the date range to 1991–2020. Notably, only research and review articles in journals have been considered for bibliometric and content analyses. First, in our bibliometric analysis, we have identified 998 articles from 1991 to 2020 based on the survival or failure of firms. These research articles are gathered from the Science Direct, Emerald, and ProQuest databases. Table 2 summarizes published articles, and Figure 1 shows the pattern of articles published by year on the survival of firms.
Publication years  1991–2020 
Citation years  29 (1991–2020) 
Papers  998 
Citations  71,578 
Citations/year  2468.21 
Citations/paper  71.72 
Authors/paper  2.80 
hindex  120 
Gindex  256 
As it is evident from Figure 2, between 2004 and 2013, maximum articles were published on the survival of firms. Probably, this was the time when the market was more uncertain, and the risk was high for firms. The authors have formulated a word cloud for the title of the research articles using text mining as shown in Figure 2.
The word cloud of the abstract extracted from all 998 articles shows that most research articles represent the survival of either financial firms or banks globally. The top12 most cited research papers based on search are listed in Table 3.
Number of citation  Authors  Title 

851  Wheelock and Wilson (2000)  Why do banks disappear? The determinants of US bank failures and acquisitions 
254  Bellotti and Crook (2009)  Credit scoring with macroeconomic variables using survival analysis 
154  Giovannetti, Ricchiuti, and Velucchi (2011)  Size, innovation, and internationalization: a survival analysis of Italian firms 
134  Glennon and Nigro (2005)  Measuring the default risk of small business loans: a survival analysis approach 
98  Evrensel (2008)  Banking crisis and financial structure: a survivaltime analysis 
96  Carlson (2004)  Are branch banks better survivors? Evidence from the depression era 
94  Leung, Rigby, and Young (2003)  Entry of foreign banks in the People’s Republic of China: a survival analysis 
88  LeClere (2000)  The occurrence and timing of events: survival analysis applied to the study of financial distress 
86  Halling and Hayden (2006)  Bank failure prediction: a twostep survival time approach 
81  Pappas, Ongena, Izzeldin, and Fuertes (2017)  A survival analysis of Islamic and conventional banks 
The literature section is classified into two parts: ownership versus bank stability and size versus bank stability.
3.1 Ownership and Bank Stability
PSBs dominated Indian banks till 1990. Acharya and Kulkarni (2010) found that performancewise, profitability (net profit/assets) of private sector banks surpassed that of PSBs from 2005 to 2006, wherein the quality of assets (NPA/total assets) was lower for PSBs. However, after the financial crisis, PSBs outperformed private sector banks. The argument in favor of PSBs can be both implicit and explicit, whereby the government has been backing the PSBs. Based on crosscountry data, La Porta, LopezdeSilanes, and Shleifer (2002) found that higher government ownership of banks in the 1970s was associated with slower subsequent financial development and lower per capita income and productivity growth, thereby supporting “political” theories of the effects of government ownership of firms. Dewenter and Malatesta (2001) found that stateowned firms do display low profitability. Altunbas, Evans, and Molyneux (2001), based on the German banking market for 1989–1996, found that PSBs and mutual banks have a slight cost and profit advantage over their privatesector competitors. Bonin, Hasan, and Wachtel (2005), based on transition countries Bulgaria, Czech Republic, Croatia, Hungary, Poland, and Romania, found that governmentowned banks are less efficient than privatized banks and foreignowned banks. Sathye (2003), based on data from 1997 to 1998, found that PSBs were more efficient than the private sector and foreign commercial banks in India. Das and Ghosh (2006), based on data from 1992 to 2002, found that PSBs were more efficient than their private counterparts.
Crosscountry findings of Caprio and Peria (2002) reported that nationalized banks are generally less efficient because of the requirement of pursuing multiple goals at the same time; for instance, in addition to profit maximization, it needs to encourage the employment of lowskilled workers, open branches in rural areas to promote job opportunities, and also focus on priority sector lending (i.e., being lent at belowmarket rates, yield a low return on advances). Kumbhakar and Sarkar (2003), based on data from 1985 to 1996, found that postderegulation of the Indian financial markets, private sector banks have improved their performance in terms of total factor productivity, but PSBs have not responded well to the deregulation measures. Beck, DemirgüçKunt, and Maksimovic (2004), based on a dataset from 74 countries, found that restrictions on a bank’s activities, including more government interference in the banking sector as a whole, coupled with a large share of governmentowned banks in themselves, do increase the obstacles further for obtaining financing especially if the banks are largely more concentrated.
The Indian Bank Nationalization Act provides an explicit guarantee that the government would fulfill all obligations of PSBs in the event of a failure (Acharya & Kulkarni, 2010), which leads to our first hypothesis of the study.
H1. Public sector banks have a higher probability of survival than private sector banks
Even though the Indian banking sector has scheduled commercial banks consisting of public sector banks, private sector banks, and foreign banks, public sector banks and private sector banks contribute 94.4% of total assets under the banking industry (Bandick, 2020; Kaur & Bapat, 2021). Considering the percentage of assets represented by public and private sector banks, this study only focuses on these banks.
3.2 Size and Bank Stability
There are arguments both in favor and against whether the size increases or decreases financial fragility. Uhde and Heimeshoff (2009) found that larger banks in concentrated banking sectors reduce financial fragility through five channels that include
Large banks may increase profits, building up high “capital buffers,” thereby making them more secure from liquidity and macroeconomic shocks.
Supervisory authorities find it easier to monitor large and fewer banks.
Large banks provide credit monitoring services.
Large banks have higher economies of both scale and scope, along with the potential to diversify loan portfolio risks efficiently and geographically through crossborder activities (Mirzaei, Moore, & Liu, 2013).
Arguments claiming that the banking sector increases financial fragility (Gavilá Alcalá, Maldonado GarcíaVerdugo, & Marcelo Antuña, 2020; Giovannelli, Iannamorelli, Levy, & Orlandi, 2020; Uhde & Heimeshoff, 2009) are as follows:
Moral hazards because large banks are too big to fail (Mishkin, 1999).
Larger banks charge higher loan interests because of their market power; the borrower may be compelled to undertake risky projects to pay off the loans, which may, in turn, increase the risks of defaults.
Risk diversification in assets and liabilities may deteriorate in a concentrated banking market, causing high operational risk (Mirzaei et al., 2013).
De Haan and Poghosyan (2012), based on banks in the United States from 1995 to 2010 found that a bank’s size typically reduces volatility with a nonlinear effect. In other words, when a bank’s size exceeds a particular threshold, it is positively related to earnings volatility. Laeven, Ratnovski, and Tong (2014), based on data from 52 countries, found that larger banks, on average, create more risks than smaller banks. On the bais of data from the EU banking sector for 2002–2011, Köhler (2015) reported that the bank size has a significant negative effect on bank stability, indicating that larger banks are generally less stable than smaller banks.
However, Altaee, Talo, and Adam (2013) have tested the stability of banks in the Gulf Cooperation Council (GCC) countries and found that the size (represented by total assets) has no statistically significant effect on a bank’s stability. On the basis of ownership and size, Kaur and Kaur (2020) found that PSBs and larger private/international banks are more aggressive in substituting their noninterest income if there is a change in that front. However, Das and Ghosh (2006), based on the bank size, found that both small (assets up to Rs. 50 billion) and large banks (assets exceeding Rs. 200 billion) do witness the highest efficiency. Hence, there is no conclusive evidence on the effect of size on the stability of banks, especially in the context of developing markets like India, where one of the recommendations of the Narasimham Committee (1998) was to set up a threetier banking structure. This comprises three large banks of international size, 8–10 national banks, and a large number of regional banks. This study looks to explore the impact of size (based on total asset) on bank stability with the following premise:
H2. Large banks have a higher probability of survival than smaller banks
4 Methodology
4.1 Survival Analysis and Censoring
Cox proportional hazards model has been used in this study to measure the survival of the banks. Interestingly, however, previous studies were based on discriminant analysis, binary logit model, or some conventional classification techniques. The survival analysis estimates the expected timetofailure for an event, whereby the parameters are estimated using the partial maximum likelihood. The survival method deals with censored and complete lifetime data easily. The complete lifetime data, in turn, are very interesting because they imply that the survival analysis naturally controls for the fact that the observation period may not necessarily represent an entire lifetime. Further, because the models effectively exploit information on survival time, defined as the actual number of years, especially when a bank has been in business, left censoring is naturally avoided. However, on the other hand, a bank could remain in business beyond the end time, known otherwise as “right censoring,” whereby the survival models are formulated to deal with the rightcensored data explicitly.
Censoring generally is of two types, i.e., right and left. If an individual is followed up from a time of origin T_{0} up to some later time point T_{C} and has not observed the event of interest, this is known as right censoring. This may occur due to an individual dropping out of a study even before the event of interest occurs. Left censoring is a situation in which an individual is known to have had the event before a specific time or a starting time, but that could be any time before the censoring time. The survival method aims to estimate survival times in different categories and inspect how much predictors affect the risk of events (Chart 1).
Banking failure studies through the survival analysis follow two strands; the first is a semiparametric Cox proportional hazards model (Cox, 1972; Lane, Looney, & Wansley, 1986) that does not require any distributional assumption on the hazards function. Lane et al. (1986) applied this method to investigate the prediction of failure for USbased banks. Whalen (1991) and Wheelock and Wilson (2000) extended the study by Lane et al. (1986) in terms of the sample size. Yet, in another setting, Dabos and SosaEscudero (2004) examined the failure of Argentinean banks using the banks’ accounting information. Caporale, Pittis, and Spagnolo (2006), Cole and Wu (2009, April), GomezGonzalez and Kiefer (2009), Molina (2002), Platt and Platt (2002), and Whitaker (1999) also used the Cox model to assess conventional bank and corporate failures.
The second relies on a parametric survival model (Evrensel, 2008; Männasoo & Mayes, 2009; Sales & TannuriPianto, 2007), which imposes several distributional assumptions (e.g., exponential, Weibull) over the hazards functions. Each of these studies accepts a different distribution for the baseline hazards that illustrate the potential misspecification problem. We use a Cox proportional hazards model, where T ∈ [0, ∞) denotes the timetofailure, which in itself is a random variable with the probability density function f(t) and the cumulative density function F(t) as follows:
The survival function S(t) gives the probability of survival for banks beyond year t under the condition that banks have survived until time t. Hazards rate h(t) is an immediate risk of the disappearance in year t under the condition that banks have survived till time t. These two functions mathematically can be formalized as follows:
Furthermore, the hazards rate that is always nonnegative gives a timevarying risk of a bank’s failure. This study uses the unconditional Kaplan and Meier (1958) methods to estimate the survival function using data containing information on whether a bank has failed over the observation window, vis a vis the time when the bank’s failure effectively occurred. The null hypothesis in the unconditional Kaplan and Meier (1958) estimator is the equality of the unconditional survival rates for the two bank types, whereby the significance is checked using a logrank test statistic.
The Cox model is expressed by the hazards function h(t) and can be interpreted as the risk of failure at time t. The mathematical form of Cox model can be written as follows:
Here, t is the survival time, h(t) is the hazards function estimated by p predictors (y _{1}, y _{2},…,y _{ p }), and the coefficients (a _{1 },a _{2},…,a _{ p }) measure the impact of predictors.
The term h _{0} is called baseline hazards. It gives the value of the hazards when all the predictors are zero. The exponent of coefficients (a _{1}, a _{2},…,a _{ p }) are called hazards ratios (HRs). A value of an estimated coefficient (a _{1}, a _{2},…,a _{ p }) greater than zero or an HR greater than 1 shows that as the value of the jth predictor variable increases, the hazards increases, and thus, the length of survival time decreases. The Cox proportional hazards model assumes that the hazards curve for the groups of records should be proportional and cannot cross. In this study, due to two types of predictors, timedependent and timeindependent predictors, we have used an advanced form of Cox proportional hazards model that deals with both, and its mathematical formulation is given as follows:
where h(ty,z(t)) is the hazards rate.
The coefficients β
_{1},…,β
_{
p1} and δ
_{1},…,δ
_{
q
} are estimated using the partial maximum likelihood. A value β
_{
j
} >0 indicates that by increasing the jth predictor variable, failure risk increases and survival time decreases.
4.2 Why Survival Analysis?
The first reason to use survival analysis is that it uses the actual timetofailure as the primary observable variable. Herein, the survival functions give the probability of survival beyond a certain number of years, which could also help identify the determinants of the differential failure risk profiles associated with the two bank groups. The second reason is the presence of censoring data. In survival techniques, the inferences are based on surviving and failed banks, which could have started operating at different times, thereby eliminating any unaccounted for survivorship bias that earlier statistical methods like discriminant analysis or logit model suffer from. The third reason is that it does not impose any distributional condition concerning the baseline hazards function.
5 Data Description and Descriptive Statistics
Considering that approximately 94% of total assets are covered by public^{[3]} and private^{[4]} sector banks in India (Table 1), this study focuses on data collected from 2000 to 2018 for public and private sector banks in India from the Reserve Bank of India’s website (RBI, 2018). The target variable in the Cox model is the time a bank takes to fail after its inception. Herein, the variable equals zero for the surviving banks in all the sample years. A bank generally fails (Pappas et al., 2017) when any conditions such as bankruptcy, dissolution, negative assets, merger, or acquisition occur.
Table 4 provides descriptive statistics for the variables considered for this study. The study is based on 56 Indian banks (i.e., both public and private) and covers 2000–2018. All quantitative variables except ratios are in a million. As it is clear from Table 4, the standard deviation of variables and ratios are high, indicating the significant difference in bank profiles. For a basic comparison of the banks, we summarize the descriptive statistics of their accounting profile in Table 5, from columns I–VI. The statistics shown in columns I and II indicate that PSBs are bigger than private sector banks in terms of total assets (1,448,182 million against 723,978 million), equity (82,287 million against 71,079 million), and net interest revenue (34,236 million against 21,662 million). Importantly, in a country like India, PSBs capture 70% of the banking assets compared to private banks, which comprise only 25% of banking assets as of 2018 (Table 1).
Bankspecific variables  Definitions  Mean  Max  Min  Std. Dev.  N 

Status  Survived (0) or failed (1)  0.03  1  0  0.16  838 
Size  Total assets  0.62  1  0  0.49  825 
Bank type  Public sector banks as 1 and private sector banks as 0  0.64  1  0  0.48  838 
Profit after tax  Operating profits ± other incomes  8,268  145,496  −60,892  19,077  823 
Total assets  Current assets + advances + investment + fixed assets + others  1,185,955  27,059,663  0.5  2,239,587  823 
Total capital  Equity + reserves and surplus  4,371  45,739  0.5  5646.94  822 
Deposits  Demand + saving + term deposits  952,140  20,447,514  866  1,725,551  814 
Loans and advances  Loans and advances  705,731  15,710,784  763  1,381,711  821 
Return on assets  Net profit/total assets  0.85  4.46  −6.5  0.81  794 
Gross tierI capital  Shareholder’s fund plus perpetual, noncumulative preference shares as a percentage of riskweighted assets and offbalance sheet risks  79710.38  434042.7  0  87351.47  190 
Return on net worth  Net profit/net worth  12.37  64.18  −392.33  24.93  814 
Net interest revenue  Gross interest and dividend income minus total interest expense  29703.24  625,481  −14063.9  58665.92  821 
Other operating income  Any other sustainable income that is related to the company’s core business  103652.6  2075392.8  79.5  187286.5  822 
Overheads  Personnel expenses and other operating expenses  61682.34  1139568.9  34.3  105937.9  821 
LLR/loans ratio  Loan loss reserve/loan ratio  0.04  0.52  0  0.04  670 
Total capital/asset ratio  Total capital/asset ratio  0.01  0.95  −50.6  1.77  823 
Total capital/net loans  Total capital/net loans  0.15  11.43  −0.12  0.45  821 
Total capital/deposits  Total capital/deposits  0.1  11.68  −0.06  0.43  814 
Total capital/liability ratio  Total capital/liability ratio  0.11  19.86  −0.98  0.77  823 
Net loan/asset ratio  Net loan/asset ratio  0.54  0.74  0  0.11  823 
Net interest margin  Net interest income expressed as a percentage of earning assets  0.03  0.68  0  0.04  814 
Cost/income ratio  Cost/income ratio  1.64  22.75  0.92  0.78  821 
Zscore  (Return on assets (ROA) + equity/asset)/σ (return on assets)  2.29  11.46  −3.27  2.05  792 
Microeconomics variables  
Inflation CPI  Inflation at the consumer price index  6.92  14.97  2.23  3.24  675 
GDP at market prices  Gross domestic product at market price  71,389  151,837  25,363  39,582  675 
GDP growth  GDP growth  0.13  0.2  0  0.04  675 
Market structure variables  
C3 all  Percentage of total assets held by the big three banks of total assets of the banking industry  0.25  0.32  0  0.11  675 
C5 all  Percentage of total assets held by the big five banks of total assets of the banking industry  0.33  0.41  0  0.14  675 
I  II  III  IV  V  VI  

Variables  Public  Private  Smaller  Bigger  Survive  Fail 
Number of banks  33  24  25  32  36  21 
Profit after tax  7,684  9,297  2,250  11,984***  10017.56  2,066*** 
Total assets  1,448,182  723,978***  236,517  1,768,470***  1,435,595  300,492** 
Return on net worth  13  11  7.9  15***  0.92  0.58*** 
Equity  82,287  71,079**  19,007  114,769***  95,788  15,946*** 
Liabilities  1,365,895  652,898***  217,509  1,656,742***  1339806.8  284545.6*** 
Total provision  40,188  13,710***  4,325  44,010***  35391.59  6,797*** 
Loans  1,003,488  484,460***  172,875  1,149,979***  935,094  246,853*** 
Net interest revenue  34,236  21,662***  6,605  43,855***  35,929  7686.814 *** 
Other operating income  123,634  68,330***  22,893  153,304***  125,046  27,887*** 
Growth overheads  0.31  0.20***  0.25  0.30***  74,247  17,252*** 
LLR/loans ratio  0.04  0.03**  0.04  0.04***  0.03  0.04 
Equity/asset ratio  0.06  −0.08  −0.09  0.06  −0.01  0.06 
Equity/net loans  0.14  0.16  0.21  0.10***  0.13  0.21 
Equity/deposits  0.09  0.12  0.16  0.07**  0.09  0.14 
Equity/liability ratio  0.08  0.15  0.18  0.06**  0.1  0.12 
Net loan/asset ratio  0.54  0.53  0.52  0.55***  0.55  0.49 
Net interest margin  0.03  0.04***  0.04  0.04***  0.03  0.03 
Cost/income ratio  1.62  1.67**  1.7  1.6  1.61  1.72 
Zscore  1.75  3.25***  2.49  2.2**  2.34  2.13** 
Inflation CPI  6.98  6.79  6.74  7  6.98  6.6 
C3 all  0.25  0.25  0.24  0.26  0.26  0.22*** 
GDP growth  0.13  0.13  0.123  0.13  0.13  0.12 
***, **, and * imply significance at 1, 5, and 10%, respectively.
In columns III and IV, we have compared the accounting profiles of both small and big banks. The difference between both is noticeable from the total assets (236,517 million against 1,768,470 million), equity (19,007 million against 114,769), and loans (172,875 million against 1,149,979 million). In columns V and VI of Table 5, the comparison is made between surviving and failed banks. In terms of size and turnover, the failed banks are significantly smaller than the surviving banks. The equity and net income for failed banks are 15,946 and 2066, while for surviving banks, the equity and net income are 95,788 and 1,435,595, respectively.
Moreover, the financial position of failed banks is significantly worse when compared to the surviving banks (−0.01 against 0.06). Hence, the critical conditions for the failed banks show up in their accounting information. Overall, this table indicates that the surviving banks have a stronger financial profile than the failed banks.
Table 6 represents the correlation between various features used in the survival model, and it is evident that some of them have a statistically significant correlation, while some have insignificant. We have classified banks into smaller and bigger banks using the medians of their asset distributions and denoted by size (0, 1), where 1 represents bigger banks, and 0 represents smaller banks. The explanation of all the above features are presented in Table 4.
Variables  Size  Profit after tax  Return on assets  Gross Tier I capital  Return on net worth  Net interest revenue  Overheads  LLR loans ratio  Equity asset ratio  Equity net loans  Equity liab ratio  Netloanasset ratio  Net interest margin  Costincome ratio  Z score 

Size  1  0.21**  0.073  0.013  0.10*  0.21**  0.32**  0.037  0.34**  0.31**  0.34***  0.05  0.058  0.149  0.077 
Profit after tax  0.21**  1  0.25**  0.68**  0.13*  0.81***  0.7**  0.19*  0.02  −0.02  −0.01  0.23**  0.04  0.05  0.12* 
Return on assets  0.073  0.25**  1  0.03  0.67**  0.02  −0.1  −0.36**  0.25**  0.06  0.05  0.08  0.27**  0.15**  0.64*** 
Gross Tier I capital  0.013  0.68**  0.03  1  −0.03  0.95***  0.88***  0.23**  −0.01  −0.05  −0.02  0.09  0.24**  0.36**  −0.06 
Return on net worth  0.10*  0.13*  0.67**  −0.03  1  −0.01  −0.1  −0.27**  0.03  0.01  0  0.01  0.06  0.2**  0.39*** 
Net interest revenue  0.21**  0.81***  0.02  0.95***  −0.01  1  0.96***  −0.01  0.02  −0.03  −0.01  0.27**  0.01  0.01  0.1 
Overheads  0.32**  0.7**  −0.07  0.88***  −0.05  0.96***  1  0.01  −0.01  −0.05  −0.02  0.32**  −0.04  −0.04  −0.01 
Total capital asset ratio  0.08**  −0.24 **  −0.014  0.01  0.10**  0.20**  −0.01  0.012*  0.01  0.03  0.02  0.023  0.09  0.12**  0.17** 
Total capital liability ratio  0.023  0.012  0.014  −0.01  −0.23**  0.01  0.043  −0.17**  0.021  0.23**  −0.09*  0.011  0.01  0.09  0.12** 
LLR loans ratio  0.037  0.19*  −0.36**  0.23**  −0.27**  −0.01  0.01  1  −0.03  0.13**  −0.02  −0.42**  −0.04  −0.02  −0.27** 
Equityasset ratio  0.34**  0.02  0.25**  −0.01  0.03  0.02  0  −0.03  1  0.8**  0.07  0.17**  0.61**  0.65**  0.08 
Equitynet loans  0.31**  −0.02  0.06  −0.05  0.01  −0.03  −0.1  0.13**  0.8**  1  0.94***  −0.27**  0.5**  0.86***  0.01 
Equity liab ratio  0.34***  −0.01  0.05  −0.02  0  −0.01  0  −0.02  0.07  0.94***  1  −0.22**  0.51**  0.95***  −0.03 
Net loan asset ratio  0.05  0.23**  0.08  0.09  0.01  0.27**  0.32**  −0.42**  0.17**  −0.27**  −0.22**  1  −0.05  −0.18**  0.07 
Net interest margin  0.058  0.04  0.27**  0.24**  0.06  0.01  0  −0.04  0.61**  0.5**  0.51**  −0.05  1  0.56**  0.13* 
Cost income ratio  0.1  0.05  0.15**  0.36**  0.2**  0.01  0  −0.02  0.65**  0.86***  0.95***  −0.18**  0.56**  1  0.09 
Z score  0.077  0.12*  0.64***  −0.06  0.39***  0.1  0  −0.27**  0.08  0.01  −0.03  0.07  0.13*  0.09  1 
***, **, and * imply significance at 1, 5, and 10%, respectively.
6 Empirical Results
6.1 Survival Function Estimates (Unconditional)
The dependent variable in the first survival estimate (Figure 3) is the observed failure event: the failure indicator is a binary dummy variable that takes the value one in the year immediately before the actual failure and zero else. This variable equals zero for the surviving banks in all of the sample years. The independent variable in the first unconditional survival model (baseline of the model) is the Bank_Type that is equal to one in the case of public sector banks and zero in the case of private banks.
Figure 3 represents the unconditional survival function to test the hypothesis of equal survival rates for public and private sector banks using the Kaplan–Meier estimator. Figure 3 also shows 95% confidence interval bands of banks’ survival for 18 years. The survival rate is 70% for private banks and 63% for public sector banks beyond 18 years. Notably, the 95% confidence interval for survival overlaps, and a logrank pvalue of 0.44 shows no statistically significant difference in the survival of private sector banks versus public sector banks. Furthermore, since the Indian regulatory system is proactive, it may be a primary reason why we have not found any statistically significant difference in the failure risk of both public and private banks ownerwise.
The dependent variable in the second unconditional survival estimate (Figure 4) is the observed failure event as in the first case, but the independent variable is the bank size (bigger and smaller) equal to one in the case of bigger banks and zero in the case of smaller banks. Later, we have used bankspecific variables, macroeconomic variables, and market structure variables to estimate the banks’ survival guided by the literature.
Here, size = 0 indicates a smaller bank, and size = 1 is a bigger bank. To check whether the bank size matters in the survival of banks, we classify all banks into small and large using the medians of their asset distributions. We check the hypothesis of equal survival rates for both small and bigger banks. Figure 4 shows the unconditional survival function S(t), t = 1…18 years estimated using the Kaplan–Meier model. The 95% confidence interval band shows that the survival of larger banks is significantly different from smaller banks, as indicated from the nonoverlap of confidence intervals. The same conclusion may also be supported by the logrank pvalue of 0.0017. Therefore, the survival probabilities are approximately 50% for smaller banks and 90% for bigger banks beyond 18 years.
6.2 Survivor Function Estimates (Conditional)
As discussed in Section 6.1, the dependent variable in the survival model is the time, a bank takes to fail after its inception. The main independent variable of interest is size, a dummy variable that takes the value one in the case of bigger banks and zero for smaller banks. Further, we have also considered bankspecific, macroeconomic, and market structure variables based on previous studies as follows.
Bankspecific variables: The study conducted by Lane et al. (1986) provides evidence that accounting information such as capital ratios, earnings, and liquidity is an essential feature in predicting the banks’ failure. Another study conducted by Männasoo and Mayes (2009) shows that high leverage levels and operating costs are significantly connected with a higher threat of bank failure. We have included information from the balance sheet and the income statement in also the survival model. Overall, the set of variables included in the survival model is broader than those used in the previous studies, allowing us to capture the failure risk more precisely. We have shown a list of bankspecific variables in Table 4, the profile comparison in Table 5, and the correlation between them in Table 6.
Macroeconomic variables: DemirgüçKunt and Detragiache (1998) and Männasoo and Mayes (2009) have shown that economic downturns affect banks’ financial stability. Motivated by the outcome of these two studies, we have included real GDP growth and inflation as macroeconomic variables in the survival model. The descriptive statistics of macroeconomic variable is given in Table 4 and profile comparison in Table 5.
Market structure variables: A study conducted by Mishkin (1999) shows that a more concentrated banking atmosphere increases the chance of failure risk. Allen and Gale (2004) resist that larger profits in more concentrated banking sectors moderate the banks’ risktaking behavior. Matutes and Vives (2000) and Beck et al. (2006) show that intense banking competition increases the chance of bank failure. This study has taken C3_All (percentage of total assets held by the big three banks of the total banking industry assets) as an independent market structure feature in the survival model.
The dependent variable and the complete set of independent variables considered for the survival model are listed in Table 4.
The survival model is presented as follows:
Here, the coefficient “ai” variables are time dependent and take the different values for different banks in the same year. The coefficients “bi” variables are time independent, and the values are the same for all banks in the same year. We have used the iterative process to formulate the statistically significant model. The likelihoodratio test, Wald test, and score logrank statistics are the three methods to check the significance of the survival model. These three methods are asymptotically equivalent. For large enough N, they will give similar results. For small N, they may differ somewhat. The likelihoodratio test shows better behavior for small sample sizes, so it is generally preferred. The highly correlated features (Table 6) may inflate the value of coefficients, and to avoid this, this analysis applies the selection of conditioning factors based on a backward approach. After including all combinations of independent features given in equation 7, we have selected only those that offer the model’s global statistical significance. (The pvalue of the likelihoodratio test is less than 0.5) (Cox, 1972; Shrivastav, 2019; Shrivastav & Ramudu, 2020.) The final output of the survival model is given in Table 7. The pvalue of all these three tests is less than 0.05, indicating that the overall model is statistically significant.
Parameter  Parameter estimate  Standard error  Pr > Chisq. 

Size  −1.89**  0.74  0.0103 
Cost income ratio (cost/income ratio)  −0.53  0.13  0.7098 
Profit after tax  −0.52**  0.43  0.028 
Equity assets ratio (equity/asset ratio)  5.29  4.94  0.2844 
Net interest margin  −3.26**  0.14  0.028 
Zscore  −0.64**  0.22  0.0038 
Testing the global null hypothesis: alpha = 0  

Test  Chisq.  Pr > chisq.  
Likelihoodratio  26.19  0.005  
Score  54.05  <0.0001  
Wald  27.92  0.0002  
PH test (chisquare)  1.37  — 
Criterion  Without covariates  With covariates 

−2λογΛ  136.008  109.818 
AIC  136.008  123.818 
SBC  136.008  130.051 
R ^{2}  0.38  0.36 
***, **, and * imply significance at 1, 5, and 10%, respectively.
The value of R ^{2} without covariates is 0.38 and with covariates is 0.36. In the multivariate Cox analysis, the covariates size (bigger or smaller), Zscore, net interest margin, and profit after tax are statistically significant in the model, as pvalues are less than 0.05. However, the other remaining covariates are not significant, as the pvalue is greater than 0.05. The negative coefficient of the size indicates that smaller banks’ survival is less than bigger banks, and the same result is obtained with the Kaplan–Meier method (Figure 4).
The coefficient estimate of the size variable is −1.89, and the hazards rate of size is exponential (−1.89) or 0.17. The expected hazards rate is 0.17 times lower in bigger banks as opposed to smaller banks or bigger bank reduces the hazards by a factor of 0.17 or 83%, holding other predictive variables constant, and so, the bigger banks have a survival probability higher than the smaller ones, a result that confirms our hypothesis 2. The negative sign of the Zscore indicates that as the Zscore increases, the survival probability of the bank increases. The coefficient estimate of the Zscore is −0.64, with a hazards rate of 0.53. Holding the other covariates constant, increasing one unit of Zscore decreases the hazards by a factor of 0.53 or 47%. The cox survival model has a proportionality assumption, and it is tested and depicted in Table 8.
Variables  Rho  Chisq.  p 

Size  0.716  0.5811  0.59 
Zscore  0.415  0.803  0.6 
Net interest margin  −0.397  0.973  0.324 
Profit after tax  0.605  0.4301  0.381 
Global  NA  2.84  0.45 
From Table 8, it can be seen that the proportionality test is not statistically significant for each of the covariates (pvalue is greater than 0.05) and the global test is also not statistically significant. Therefore, the model satisfies the assumption of the proportional hazards for the cox model.
7 Conclusions and Implication of the Study
The unconditional survival functions based on the nonparametric Kaplan–Meier model indicate that the failure risk of smaller banks is significantly higher than the bigger banks. We have not observed any statistically significant difference in survival between private and public sector banks. Hence, this study rejects the first hypothesis that public sector banks have a higher probability of survival and accepts the second hypothesis that large banks have a higher probability of survival than smaller banks. The conditional survival function, estimated using the advanced Cox model, which includes the size as a predictor variable, shows that smaller banks have higher hazards than bigger ones. From Table 7 and based on the aforementioned discussion, it is evident that if all the predictor variables are constant except size, bigger banks reduce the chance of failure by 83% with respect to smaller banks. Furthermore, our study found a statistically significant relationship between the failure of banks and their accounting information such as the Zscore, net interest margin, and profit after tax, which in turn may prove helpful to quantify the financial stress of banks.
It has been found that overall bank credit growth and transmissions are weak in Indian Banks. In R. K. Talwar Memorial Lecture (2017), Dr. Viral V Acharya (Deputy Governor, Reserve Bank of India) raised concerns about the unfinished agenda of restoring Public Sector banks’ health in India.^{[5]} He pointed out that gross NPA ratios are increasing on the one side, and the growth in advances (% YoY) is decreasing for public sector banks in India for 2008–2017. The study conducted by Kaur and Kaur (2019) based on data from 2005 to 2018 found no significant difference in essential parameters of public sector banks with or without PCA. This study highlights the concern that the overall health of public sector banks needs attention rather than a few, and there is a problem of “Toomanytofail” rather than “ToobigtoFail” in the Indian Banking Industry. During the 2008 financial crisis, it was thought that the Indian banking system was shielded from the global financial crisis owing to heavy public ownership and conservative management. It was a surprise for the bank management to see the high deposit in some banks, especially toward the public sector banks in India. Later, it was realized that the people had shifted their money into the large public sector banks for security reasons. They were under the impression that the smaller and private banks may face a financial crisis in the future (Mohan, 2008). This study also verifies the reason for shifting the money to bigger banks from smaller banks, and probably, the fear of depositors was right during the global crisis (Subbarao, 2009). The financial crisis has affected not only the United States but also the European Union and Asia. The crisis has also impacted the Indian economic system to some extent. It is difficult to quantify the impact of the crisis on India. It is felt that certain sectors of the economy would be affected by the spillover effects of the financial crisis.
The study helps to carry out comparative analyses of the survival of banks. It has significant implications for the decisions of various stakeholders such as shareholders, management of the banks, analysts, and policymakers. This study also indicates that the design and implementation of early warning systems for bank failure should distinguish the different risk profiles of the banks based on the size and ownership.

Conflict of interest: Authors state no conflict of interest.
References
Acharya, V. V. (2018). Prompt corrective action: An essential element of financial stability framework. Current Statistics, 67, 1.10.4135/9789354792595.n4Search in Google Scholar
Acharya, V. V., & Kulkarni, N. (2010). State ownership and systemic risk: Evidence from the Indian financial sector during 2007–09, Unpublished paper. New York: NYU–Stern.Search in Google Scholar
Allen, F., & Gale, D. (2004) Competition and financial stability. Journal of Money, Credit and Banking, 36, 453–48010.1353/mcb.2004.0038Search in Google Scholar
Altaee, H. H. A., Talo, I. M. A., & Adam, M. H. M. (2013). Testing the financial stability of banks in GCC countries: Pre and postfinancial crisis. International Journal of Business and Social Research, 3(4), 93–105.Search in Google Scholar
Altunbas, Y., Evans, L., & Molyneux, P. (2001). Bank ownership and efficiency. Journal of Money, Credit and Banking, Vol. 33, No. 4, pp. 926–954.10.2307/2673929Search in Google Scholar
Aßmuth, P. (2020). Stock price related financial fragility and growth patterns. Economics, 14(1), 1–33.10.5018/economicsejournal.ja.202010Search in Google Scholar
Bandick, R. (2020). Global sourcing, firm size and export survival. Economics, 14(1), 1–29.10.5018/economicsejournal.ja.202018Search in Google Scholar
Beck, T., DemirgüçKunt, A., & Merrouche, O. (2013). Islamic vs conventional banking: Business model, efficiency and stability. Journal of Banking & Finance, 37, 433–44710.1596/181394505446Search in Google Scholar
Beck, T., DemirgüçKunt, A., & Maksimovic, V. (2004). Bank competition and access to finance: International evidence. Journal of Money, Credit and Banking, Vol. 36, No. 3, 627–648.10.1353/mcb.2004.0039Search in Google Scholar
Bellotti, T., & Crook, J. (2009). Credit scoring with macroeconomic variables using survival analysis. Journal of the Operational Research Society, 60(12), 1699–1707.10.1057/jors.2008.130Search in Google Scholar
Bonin, J. P., Hasan, I., & Wachtel, P. (2005). Privatization matters: Bank efficiency in transition countries. Journal of Banking & Finance, 29(8–9), 2155–2178.10.1016/j.jbankfin.2005.03.012Search in Google Scholar
Caporale, G. M., Pittis, N., & Spagnolo, N. (2006). Volatility transmission and financial crises. Journal of Economics and Finance, 30(3), 376–390.10.1007/BF02752742Search in Google Scholar
Caprio, G., & Peria, M. S. M. (2002). Avoiding disaster: Policies to reduce the risk of banking crises. Monetary policy and exchange rate regimes: Options for the Middle East (pp. 193–230). Egypt: The Egyptian center for economic studies Cairo.Search in Google Scholar
Carlson, M. (2004). Are branch banks better survivors? Evidence from the depression era. Economic Inquiry, 42(1), 111–126.10.1093/ei/cbh048Search in Google Scholar
Cole, R. A., & Wu, Q. (2009, April). Predicting bank failures using a simple dynamic hazards model. In 22nd Australasian Finance and Banking Conference (pp. 16–18).Search in Google Scholar
Cox, D. R. (1972). Regression models and life‐tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187–202.10.1007/9781461243809_37Search in Google Scholar
Dabos, M., & SosaEscudero, W. (2004). Explaining and predicting bank failure using duration models: The case of Argentina after the Mexican crisis. Revista de AnálisisEconómico, 19(1), 31–49.Search in Google Scholar
Das, A., & Ghosh, S. (2006). Financial deregulation and efficiency: An empirical analysis of Indian banks during the post reform period. Review of Financial Economics, 15(3), 193–221.10.1016/j.rfe.2005.06.002Search in Google Scholar
De Haan, J., & Poghosyan, T. (2012). Size and earnings volatility of US bank holding companies. Journal of Banking & Finance, 36(11), 3008–3016.10.1016/j.jbankfin.2012.07.008Search in Google Scholar
DemirgüçKunt, A., & Detragiache, E. (1998). The determinants of banking crises in developing and developed countries. IMF Staff Papers, 45, 81–10910.5089/9781451947175.001Search in Google Scholar
Dewenter, K. L., & Malatesta, P. H. (2001). Stateowned and privately owned firms: An empirical analysis of profitability, leverage, and labor intensity. American Economic Review, 91(1), 320–334.10.1257/aer.91.1.320Search in Google Scholar
Evrensel, A. Y. (2008). Banking crisis and financial structure: A survivaltime analysis. International Review of Economics & Finance, 17(4), 589–602.10.1016/j.iref.2007.07.002Search in Google Scholar
Gavilá Alcalá, S., Maldonado GarcíaVerdugo, A., & Marcelo Antuña, A. (2020). The Banco de España inhouse credit assessment system. Financial Stability Review, 38(Spring 2020), 95–122.Search in Google Scholar
Giovannelli, F., Iannamorelli, A., Levy, A., & Orlandi, M. (2020). The Inhouse credit assessment system of Banca d’Italia (No. 586). Bank of Italy, Economic Research and International Relations Area.Search in Google Scholar
Giovannetti, G., Ricchiuti, G., & Velucchi, M. (2011). Size, innovation and internationalization: A survival analysis of Italian firms. Applied Economics, 43(12), 1511–1520.10.1080/00036840802600566Search in Google Scholar
Glennon, D., & Nigro, P. (2005). Measuring the default risk of small business loans: A survival analysis approach. Journal of Money, Credit and Banking, Vol. 37, No. 5, 923–947.10.1353/mcb.2005.0051Search in Google Scholar
GomezGonzalez, J. E., & Kiefer, N. M. (2009). Bank failure: Evidence from the Colombian financial crisis. The International Journal of Business and Finance Research, 3(2), 15–31.Search in Google Scholar
Halling, M., & Hayden, E. (2006). Bank failure prediction: A twostep survival time approach. Available at SSRN 904255.10.2139/ssrn.904255Search in Google Scholar
Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.10.1007/9781461243809_25Search in Google Scholar
Kaur, N., & Kaur, P. (2019). Why me? The Saga of public sector banks under prompt corrective action. The Saga of Public Sector Banks under Prompt Corrective Action (July 18, 2019).10.2139/ssrn.3421917Search in Google Scholar
Kaur, N., & Bapat, D. (2021). Income Diversification and Riskadjusted Returns for Indian Banks. Economic & Political Weekly, 56(14), 10–14.Search in Google Scholar
Kaur, N., & Kaur, P. (2020). Ownership structure, size, and interest income substitution by banks: An exploratory study in the Indian context. Australian Economic Paper, 59(3), 279–301.25.10.1111/14678454.12181Search in Google Scholar
Klein, J. P., Van Houwelingen, H. C., Ibrahim, J. G., & Scheike, T. H. (Eds.). (2016). Handbook of survival analysis. Boca Raton, FL: CRC Press.10.1201/b16248Search in Google Scholar
Köhler, M. (2015). Which banks are more risky? The impact of business models on bank stability. Journal of Financial Stability, 16, 195–212.10.1016/j.jfs.2014.02.005Search in Google Scholar
Kumbhakar, S. C., & Sarkar, S. (2003). Deregulation, ownership, and productivity growth in the banking industry: Evidence from India. Journal of Money, Credit and Banking, Vol. 35, No. 3, 403–424.10.1353/mcb.2003.0020Search in Google Scholar
La Porta, R., LopezdeSilanes, F., & Shleifer, A. (2002). Government ownership of banks. The Journal of Finance, 57(1), 265–301.10.3386/w7620Search in Google Scholar
Laeven, M. L., Ratnovski, L., & Tong, H. (2014). Bank size and systemic risk (No. 14). France: International Monetary Fund.Search in Google Scholar
Lane, W. R., Looney, S. W., & Wansley, J. W. (1986). An application of the Cox proportional hazards model to bank failure. Journal of Banking & Finance, 10(4), 511–531.10.1016/S03784266(86)800036Search in Google Scholar
LeClere, M. J. (2000). The occurrence and timing of events: Survival analysis applied to the study of financial distress. Journal of Accounting Literature, 19, 158.Search in Google Scholar
Leung, M. K., Rigby, D., & Young, T. (2003). Entry of foreign banks in the People’s Republic of China: A survival analysis. Applied Economics, 35(1), 21–31.10.1080/00036840210148030Search in Google Scholar
Männasoo, K., & Mayes, D. G. (2009). Explaining bank distress in Eastern European transition economies. Journal of Banking & Finance, 33(2), 244–253.10.1016/j.jbankfin.2008.07.016Search in Google Scholar
Matutes, C., & Vives, X. (2000) Imperfect competition, risk, and regulation in banking. European Economic Review, 44, 1–3410.1016/S00142921(98)000579Search in Google Scholar
Mirzaei, A., Moore, T., & Liu, G. (2013). Does market structure matter on banks’ profitability and stability? Emerging vs. advanced economies. Journal of Banking & Finance, 37(8), 2920–2937.10.1016/j.jbankfin.2013.04.031Search in Google Scholar
Mishkin, F. S. (1999). Financial consolidation: Dangers and opportunities. Journal of Banking & Finance, 23(2–4), 675–691.10.3386/w6655Search in Google Scholar
Mohan, R. (2008). Global financial crisis and key risks: Impact on India and Asia. RBI Bulletin, 2003–2022.Search in Google Scholar
Molina, C. A. (2002). Predicting bank failures using a hazards model: The Venezuelan banking crisis. Emerging Markets Review, 3(1), 31–50.10.1016/S15660141(01)000292Search in Google Scholar
Narasimham, M. (1998). Report of the committee on banking sector reforms. Government of India.Search in Google Scholar
Pappas, V., Ongena, S., Izzeldin, M., & Fuertes, A. M. (2017). A survival analysis of Islamic and conventional banks. Journal of Financial Services Research, 51(2), 221–256.10.1007/s1069301602390Search in Google Scholar
Platt, H. D., & Platt, M. B. (2002). Predicting corporate financial distress: Reflections on choicebased sample bias. Journal of Economics and Finance, 26(2), 184–199.10.1007/BF02755985Search in Google Scholar
RBI. (2018). Statistical tables relating to banks in India. https://dbie.rbi.org.in/DBIE/dbie.rbi?site=publications.Search in Google Scholar
Sales, A. S., & TannuriPianto, M. (2007). Identification of monetary policy shocks in the Brazilian market for bank reserves. Banco Central do Brasil WPS, 1–54.Search in Google Scholar
Sathye, M. (2003). The efficiency of banks in a developing economy: The case of India. European Journal of Operational Research, 148(3), 662–671.10.1016/S03772217(02)00471XSearch in Google Scholar
Shrivastav, S. K. (2019). Measuring the determinants for the survival of indian banks using machine learning approach. FIIB Business Review, 8(1), 32–38.10.1177/2319714519825939Search in Google Scholar
Shrivastav, S. K., & Ramudu, P. J. (2020). Bankruptcy prediction and stress quantification using support vector machine: Evidence from Indian banks. Risks, 8(2), 52.10.3390/risks8020052Search in Google Scholar
Subbarao, D. (2009, February). Impact of the global financial crisis on India: Collateral damage and response. In: Speech delivered at the Symposium on The Global Economic Crisis and Challenges for the Asian Economy in a Changing World (Vol. 18). Tokyo: Organized by the Institute for International Monetary Affairs.Search in Google Scholar
Uhde, A., & Heimeshoff, U. (2009). Consolidation in banking and financial stability in Europe: Empirical evidence. Journal of Banking & Finance, 3(7), 1299–1311.10.1016/j.jbankfin.2009.01.006Search in Google Scholar
Whalen, G. (1991). A proportional hazards model of bank failure: An examination of its usefulness as an early warning tool. Economic Review, 2(1), 21–31.Search in Google Scholar
Wheelock, D. C., & Wilson, P. W. (2000). Why do banks disappear? The determinants of US bank failures and acquisitions. Review of Economics and Statistics, 82(1), 127–138.10.1162/003465300558560Search in Google Scholar
Whitaker, R. B. (1999). The early stages of financial distress. Journal of Economics and Finance, 23(2), 123–132.10.1007/BF02745946Search in Google Scholar
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