Ownership Structure, Size, and Banking System Fragility in India: An Application of Survival Analysis

3.1 Ownership and Bank Stability

PSBs dominated Indian banks till 1990. Acharya and Kulkarni (2010) found that performance-wise, 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 cross-country data, La Porta, Lopez-de-Silanes, 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 state-owned 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 private-sector competitors. Bonin, Hasan, and Wachtel (2005), based on transition countries Bulgaria, Czech Republic, Croatia, Hungary, Poland, and Romania, found that government-owned banks are less efficient than privatized banks and foreign-owned 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.

Cross-country 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 low-skilled workers, open branches in rural areas to promote job opportunities, and also focus on priority sector lending (i.e., being lent at below-market 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, Demirgüç-Kunt, 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 government-owned 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

1. Large banks may increase profits, building up high “capital buffers,” thereby making them more secure from liquidity and macroeconomic shocks.

2. Supervisory authorities find it easier to monitor large and fewer banks.

3. Large banks provide credit monitoring services.

4. Large banks have higher economies of both scale and scope, along with the potential to diversify loan portfolio risks efficiently and geographically through cross-border activities (Mirzaei, Moore, & Liu, 2013).

Arguments claiming that the banking sector increases financial fragility (Gavilá Alcalá, Maldonado García-Verdugo, & Marcelo Antuña, 2020; Giovannelli, Iannamorelli, Levy, & Orlandi, 2020; Uhde & Heimeshoff, 2009) are as follows:

1. Moral hazards because large banks are too big to fail (Mishkin, 1999).

2. 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.

3. 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 three-tier 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

4.1 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 time-to-failure 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 right-censored data explicitly.

Censoring generally is of two types, i.e., right and left. If an individual is followed up from a time of origin T₀ 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).

Chart 1

Types of survival analysis. Source: Klein, Van Houwelingen, Ibrahim, and Scheike (2016).

Banking failure studies through the survival analysis follow two strands; the first is a semi-parametric 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 US-based 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 Sosa-Escudero (2004) examined the failure of Argentinean banks using the banks’ accounting information. Caporale, Pittis, and Spagnolo (2006), Cole and Wu (2009, April), Gomez-Gonzalez 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 & Tannuri-Pianto, 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 time-to-failure, 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 time-varying 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 log-rank 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, time-dependent and time-independent 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(t|y,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. e β j is the hazards rate, and 100 × ( e β j − 1 ) gives the expected percentage increase in failure risk for one unit increase in the jth predictor variable.

4.2 Why Survival Analysis?

The first reason to use survival analysis is that it uses the actual time-to-failure 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.

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

Unconditional survivor function estimates for Bank_Type (public and private sector banks) (Bank_type = 0 indicates private bank and Bank_type = 1 public sector 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 log-rank p-value 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 owner-wise.

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 bank-specific variables, macroeconomic variables, and market structure variables to estimate the banks’ survival guided by the literature.

Figure 4

Unconditional survivor function estimates for bigger and smaller banks.

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 log-rank p-value 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 bank-specific, macroeconomic, and market structure variables based on previous studies as follows.

Bank-specific 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 bank-specific variables in Table 4, the profile comparison in Table 5, and the correlation between them in Table 6.

Macroeconomic variables: Demirgüç-Kunt 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’ risk-taking 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 likelihood-ratio test, Wald test, and score log-rank 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 likelihood-ratio 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 p-value of the likelihood-ratio 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 p-value of all these three tests is less than 0.05, indicating that the overall model is statistically significant.

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), Z-score, net interest margin, and profit after tax are statistically significant in the model, as p-values are less than 0.05. However, the other remaining covariates are not significant, as the p-value 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 Z-score indicates that as the Z-score increases, the survival probability of the bank increases. The coefficient estimate of the Z-score is −0.64, with a hazards rate of 0.53. Holding the other covariates constant, increasing one unit of Z-score 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.

From Table 8, it can be seen that the proportionality test is not statistically significant for each of the covariates (p-value 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.