Capital–Profitability Nexus in Indian Banking: A Simultaneous Equations Approach

Capital Adequacy and the Stability: Profitability Trade-off

Banks are required to maintain sufficient capital to absorb unexpected losses and safeguard systemic stability. The CAR serves as a crucial cushion against potential losses arising from various risks, thereby ensuring financial stability and protecting depositors’ interests (Fibriyanti & Nurcholidah, 2021; Rasyid et al., 2022). From a regulatory perspective, higher capital enhances resilience, whereas banks often perceive elevated capital requirements as constraining profitability and lending capacity. This divergence reflects the fundamental trade-off between prudential stability and profit maximization. When a bank’s CAR falls below the regulatory threshold, it is considered under distress, increasing the likelihood of systemic spillover (Acharya, 2009; Brownlees & Engle, 2017). Thus, theory predicts an inherently bidirectional relationship between capital adequacy and profitability, shaped by risk-taking incentives, regulatory constraints and market discipline.

Regulatory Reform and Capital Requirements

In response to the global financial crisis (GFC), regulators tightened capital norms under Basel III, effectively raising minimum requirements to 10.5% through the introduction of a 2.5% capital conservation buffer (BCBS, 2020). These reforms aimed to curb excessive risk-taking and improve banks’ loss-absorbing capacity. However, empirical evidence on the effectiveness and consequences of higher capital requirements remains mixed. Li et al. (2016) showed that most Taiwanese banks already exceeded Basel III thresholds, whereas Kartal (2019) reported that Turkish banks maintained unusually high CARs—around 19%. In the United States, Berger et al. (2008) demonstrated that high pre-crisis capitalization was not sufficient to shield banks from severe post-crisis losses, as mispriced risk-taking undermined the effectiveness of capital buffers. Similarly, Liu and Shim (2024) demonstrated that Chinese banks used off-balance-sheet or ‘shadow-loan’ channels to window-dress their capital positions.

Cross-country Evidence on CAR and Bank Performance

Cross-country findings remain equally inconsistent. Aktas et al. (2015) observed that profitability, liquidity and net interest margins increase CAR in Southeastern Europe, while leverage and size exert the opposite effect. In Vietnam, H. P. Nguyen (2019) reported a positive CAR–ROA relationship, but T. H. Nguyen (2020) showed this relationship holds good only for small banks. Abu Snobar and Al Hanini (2025) documented a similar positive association in Jordan, whereas Indriani et al. (2020) and Alnajjar and Othman (2021) identified negative effects in Indonesian and MENA banks, respectively. These contrasting results suggest that institutional quality, regulatory enforcement and banking structure critically mediate the capital–profitability nexus.

Evidence from India and the Role of Ownership Structure

The Indian banking system provides a particularly relevant context for examining these dynamics. The Reserve Bank of India (RBI) imposes a higher prudential standard than the Basel III minimum, requiring banks to maintain a CAR of 9% plus a 2.5% capital conservation buffer, resulting in an effective regulatory threshold of 11.5% (RBI, 2010, p. 253; 2021). This stricter standard reflects the RBI’s emphasis on resilience amid persistent credit-risk and asset-quality pressures.

India’s financial architecture comprises PSBs, PVBs and FBs—each with distinct governance frameworks and risk appetites. PSBs often implement government credit programmes and social-policy objectives that may constrain profitability and risk flexibility; PVBs operate under market discipline with efficiency-driven incentives; and FBs, though smaller in scale, typically maintain higher capital ratios. This structural heterogeneity suggests that the determinants of CAR and profitability are unlikely to be uniform across ownership types, underscoring the need for a disaggregated analytical approach.

Empirical evidence from India remains inconclusive. Das and Rout (2020) found a positive relationship between CAR and profitability as well as between CAR and non-performing assets (NPAs), implying that banks with higher capital may assume greater risk—a finding contrary to most global evidence. Similarly, Singh (2021) observed that CAR correlates positively with GDP growth but negatively with inflation, while Chaudhary and Kumar (2023) identified NPAs as a primary determinant of profitability. Such heterogeneity indicates that institutional structure, governance quality and regulatory stringency crucially shape the direction and strength of the CAR–profitability nexus. Marisetty and Shoeb (2024) further showed that although capital infusion into PSBs restored solvency, it also generated moral-hazard incentives that encouraged renewed risk-taking even outside crisis periods. Nevertheless, recapitalization can temporarily boost market capitalization and profitability (Bandyopadhyay, 2022), illustrating the inherent trade-off between prudential stability and profit maximization.

Research Gaps

Despite extensive literature, several gaps persist. First, ownership-specific dynamics among PSBs, PVBs and FBs have rarely been examined in a unified empirical framework. Second, most Indian studies rely on single-equation models that fail to account for endogeneity and bidirectional causality between CAR and profitability. Third, existing analyses largely overlook the post-2014 reform period, which includes the AQR, demonetization, GST implementation and the COVID-19 shock—events that significantly reshaped banks’ balance sheets and capital strategies (Chaudhary & Kumar, 2023; Das & Rout, 2020; Singh, 2021).

To bridge these gaps, the present study applies a 2SLS framework to panel data from 2005 to 2024, explicitly disaggregating banks by ownership type. This approach enables identification of how profitability, asset quality and macroeconomic conditions jointly determine capital adequacy—and how this interdependence has evolved in India’s post-reform period.

Research Philosophy and Research Design

This study assumes that relationships among economic and financial variables can be objectively measured and statistically tested. Empirical evidence derived from observed data forms the basis for validating or refuting theoretical propositions.

In line with this philosophy, the study employs a quantitative and explanatory research design. The design focuses on identifying determinants and directionality within the CAR–profitability nexus while controlling for macroeconomic and bank-specific factors. The quantitative approach enables reproducibility using secondary data from the RBI’s Database on the Indian Economy.

The explanatory nature of the design allows us to explore causal relationships through econometric modelling. Specifically, a simultaneous equation model estimated via the two-stage least squares (2SLS) method addresses potential endogeneity between CAR and ROA. This design is consistent with established practices in empirical banking research and ensures the robustness of causal inference.

Data and Variable Construction

The data are collected from the RBI’s Database on Indian Economy—a highly reliable source of information on Indian banks. The data set constitutes an unbalanced panel of 46 scheduled commercial banks comprising 21 PSBs, 18 private sector banks (PVBs) and 7 FBs from 2005 to 2024 (the latest year for which data are available). This panel structure enables the study to exploit both cross-sectional and temporal variation in capital adequacy and profitability. The study also includes the six PSBs whose mergers came into effect on 1 April 2020. A list of all the banks, along with the acronyms used in the study, is provided in the Appendix. Merged banks are suffixed with ‘_M’. Small finance banks and payment banks are excluded, as the regulatory requirements are not the same as those for commercial banks in India. Additionally, banks with extreme values are also excluded to avoid distortion of result. The study also excludes Tobin’s Q and other market ratios due to the absence of listings for all banks involved. The selection of variables is guided by the existing literature and a comprehensive understanding of the banking business with the aim of identifying the determinants of CAR and profitability.

To examine whether the relationship between CAR and profitability varies across PVBs, PSBs and FBs, two dummy variables representing bank ownership types are added. Additionally, a time dummy variable is also introduced to assess whether the relationship changed after 2015, following the regime change in mid-2014 and a series of structural reforms initiated thereafter. The following variables have been used in the study:

GDP (at constant price) and inflation numbers are taken from the RBI’s website. Since the data set spans 2005–2024, it covers the base year revision introduced in 2015, when the constant price series was shifted from 2004–2005 to 2011–2012 as the base year.

Exploratory Data Analysis

To examine how the variables evolve over time, CAR, ROA (a proxy for banks’ profitability) and other bank-specific indicators are plotted. Figure 1 illustrates the trends in CAR for each bank. The observations suggest that PSBs maintain the lowest CAR, followed by PVBs and FBs, which also show considerable variability. A slight increase in CAR is evident after 2008, coinciding with the introduction of Basel II requirements and the GFC. It also highlights that CAR has been the lowest between 2014 and 2018, possibly showing the impact of the rise in NPAs due to AQR, especially in the PSBs. The figure also indicates that, at times, some banks’ CARs fell below 10%. In contrast, after 2020, CAR has exhibited a steady upward trend across all banks, coinciding with the phased implementation of Basel III requirements, which were scheduled for full adoption in India in 2019 (RBI, 2014). However, the final tranche of the 0.625% capital conservation buffer was deferred and implemented only on 1 October 2021 (RBI, 2021). It is also noteworthy that FBs in India operate on a relatively smaller scale, typically through a limited branch network. Despite this, they consistently maintain CARs at an optimal level, suggesting greater efficiency in capital management.

Figure 2 presents the evolution of average CAR, ROA and NPAs over time for PSBs, PVBs and FBs. The plots highlight key differences in performance trajectories among bank groups, offering a visual overview of how capital adequacy and asset quality have evolved over time. It indicates that the average ROA for both PVBs and FBs remained relatively stable throughout the study period, with an exception of a modest decline for PVBs between 2015 and 2020. In contrast, PSBs experienced a much sharper decline in ROA, coinciding with a rise in their NPAs. NPAs have been increasing for both PSBs and PVBs since the GFC, but the increase was particularly pronounced for PSBs, especially after 2015, when the RBI initiated the AQR. The NPAs for PSBs peaked at 10% in 2018. The AQR compelled banks to recognize and report previously unacknowledged bad loans (Kaul, 2020). The surge in NPAs had a visible impact on CAR, particularly for PSBs and PVBs. While the PVBs continued to maintain CAR comfortably above the regulatory minimum despite rising NPAs, several PSBs experienced sharp reductions, prompting government-led recapitalization measures.

To better understand this relationship, Figure 3 plots CAR against NPAs at the bank level. The scales are adjusted at the entity level for more clarity. The results clearly highlight that the negative relationship between rising NPAs and declining CAR is more pronounced for PSBs. By contrast, PVBs and FBs generally maintain higher CARs relative to PSBs. Moreover, FBs sustain higher CARs and manage to contain their NPAs, making them appear relatively safer. Although Figure 2 shows that the average CAR across banks remained above 10%, Figure 3 reveals that some banks struggled to maintain the RBI’s minimum regulatory requirement of 9%.

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Figure 1.

Source: Authors’ graph using data from the Handbook of Statistics on the Indian Economy, Reserve Bank of India.

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Figure 2.

Source: Authors’ graph using data from the Handbook of Statistics on the Indian Economy, Reserve Bank of India.

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Figure 3.

Source: Authors’ graph using data from the Handbook of Statistics on the Indian Economy, Reserve Bank of India.

To complement these visual trends, Tables 1 and 2 reports descriptive statistics for the main variables. The summary provides a quantitative snapshot of the distribution, highlighting the variation in capital, profitability and risk exposures across bank. Table 1 presents the descriptive statistics of the entire data set, comprising 828 observations across 46 banks. The average value of CAR is 14.4%, which is well above the regulatory minimum in India of 9–1 percentage point higher than the BCBS requirement—plus an additional buffer of 2.5%, resulting in an effective benchmark of 11.5%. This figure indicates that, on average, Indian banks uphold a strong capital buffer, reflecting a generally robust financial position (Alnajjar & Othman, 2021). However, as discussed further below, PVBs and FBs tend to maintain significantly more capital than required, and their disproportionately high CARs can slightly overstate the average when all banks are given equal weight. Similarly, gross NPAs to advances have a mean of 5.2%, which does not appear very high and fails to indicate the poor management of advances by Indian PSBs that were highlighted by AQR. However, a large standard deviation in NPAs highlights greater variability among the banks.

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Table 1.

Descriptive Statistics at the Total Level.

Variable	Mean	Std. Dev.	Min.	Median	Max.
Total assets (In crores (₹))	273,058	547,302	978	112,988	6,179,694
CAR	14.3%	3.8%	5.6%	13.6%	56.4%
Gross NPA to adv.	5.1%	5.4%	0.0%	3.1%	36.4%
ROA	0.8%	1.1%	–5.4%	0.9%	9.6%
NII_II	17.4%	16.2%	–6.7%	14.6%	365.3%
Loan to TA	0.6%	0.1%	0.0%	0.6%	0.7%
Credit to dep	73.7%	14.2%	1.2%	72.2%	167.3%
Size (LN (assets))	11.6%	1.4%	6.9%	11.6%	15.6%
Leverage	13.9%	5.1%	1.4%	14.2%	30.7%
Exp to inc.	22.9%	6.5%	10.2%	22.1%	58.1%
Credit growth	0.3%	2.0%	–0.3%	0.2%	43.2%
GDP growth	6.8%	3.0%	0.2%	6.9%	13.3%
INFL	4.5%	3.9%	–3.7%	4.2%	13.0%

Source: Author’s calculations based on data from the Handbook of Statistics on the Indian Economy, Reserve Bank of India.

Note: Std. Dev. = Standard deviation; Min. and Max. refer to the minimum and maximum observed values, respectively.

Table 2 breaks down the descriptive statistics by bank ownership type: PSBs, PVBs and FBs. It reveals that the average CAR is more than 15.5% for FBs and PVBs, while for PSBs, it is at 12.7%. Additionally, FBs generally have smaller asset bases, while PSBs operate with substantially larger asset sizes. The standard deviation for CAR among PVBs is 4.8%, higher than that of FBs (3.2%) and PSBs (1.9%), highlighting the greater heterogeneity within PVBs.

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Table 2.

Descriptive Statistics: Bank Category-wise Breakup.

Entity	Stat.	CAR	ROA	TotalAssets (in Crores)	GrossNPAsto Adv.	Exp/Inc	LoanTA	NII_II	Credit/Dep	Credit Growth
Foreign banks (FB)	Count	131	131	131	131	131	131	131	131	131
	Min	9.9%	–3.1%	1,878	0.0%	14.7%	0.2%	–6.8%	1.2%	–0.3%
	Max	31.3%	9.6%	259,588	26.4%	58.1%	62.4%	356.3%	167.3%	43.2%
	Median	15.8%	1.6%	61,597	1.9%	27.4%	39.0%	25.9%	74.6%	0.1%
	Mean	15.7%	1.5%	83,832	3.3%	28.3%	38.2%	31.5%	76.3%	0.8%
	Std. Dev	3.2%	1.2%	64,952	4.1%	7.3%	10.9%	35.3%	26.0%	5.0%
Government banks (PSB)	Count	360	360	360	360	360	360	360	360	360
	Min	5.6%	–4.7%	19,043	0.6%	10.2%	41.8%	2.1%	47.0%	–0.2%
	Max	22.3%	1.7%	6,179,694	36.4%	44.1%	69.1%	32.8%	87.0%	0.9%
	Median	12.5%	0.6%	226,333	4.4%	19.6%	59.9%	12.8%	70.0%	0.2%
	Mean	12.7%	0.3%	418,730	7.3%	20.0%	59.0%	13.3%	69.5%	0.2%
	Std. Dev	1.9%	1.0%	711,133	6.7%	4.6%	5.5%	4.6%	7.2%	0.1%
Private banks (PVB)	Count	337	337	337	337	337	337	337	337	337
	Min	7.5%	–5.4%	978	0.1%	13.0%	39.7%	5.4%	53.2%	–0.3%
	Max	56.4%	2.6%	3,617,623	19.2%	45.5%	72.2%	50.4%	162.7%	2.2%
	Median	14.9%	1.1%	51,837	2.7%	23.1%	61.0%	15.5%	76.2%	0.2%
	Mean	15.5%	1.0%	191,000	3.4%	23.8%	60.5%	16.4%	77.2%	0.2%
	Std. Dev	4.8%	0.9%	389,680	2.8%	6.2%	5.3%	6.6%	12.0%	0.2%

Source: Author’s calculations based on data from the Handbook of Statistics on the Indian Economy, Reserve Bank of India.

Notes: Std. Dev. = Standard deviation; Min. and Max. refer to the minimum and maximum observed values, respectively.

Total assets are in crores (₹).

Similarly, the loans-to-total-assets ratio averages around 60% for both PVBs and PSBs, with a standard deviation of 5%. In contrast, FBs maintain a much lower ratio of 38%, accompanied by a larger standard deviation of 10%, reflecting their more conservative approach to lending in the Indian market. While the mean NPA-to-advances ratio is almost identical for FBs and PVBs (3.3% and 3.4%, respectively), PSBs show much higher NPAs at 7.3% when averaged across the period, indicating greater exposure to credit risk relative to their asset base.

These NPA figures paint a concerning picture of the Indian banking system, particularly highlighting the fragility of the PSBs. This situation is exacerbated by the fact that PSBs have historically struggled with asset quality, a challenge intensified by their lower profitability and efficiency compared to private and foreign counterparts. This increasing trend in NPAs for PSBs correlates negatively with their profitability, as evidenced by a decline in their ROA (Gaur & Mohapatra, 2021).

The mean value of NII_II is 31.5% for FBs, whereas it is much lower for PSBs and PVBs at 13.3% and 16.4%, respectively. This indicates FBs’ greater reliance on trading and fee-based income. The negative minimum value for FBs further suggests that trading activities can lead to losses and therefore do not necessarily contribute to a higher ROA. The non-interest income to interest income ratio that represents diversification shows that FBs rely more on dive. The credit-to-deposit ratio, reflecting a bank’s ability to convert deposits into loans, averages about 77% for PVBs and FBs, indicating a relatively more aggressive lending stance, whereas PSBs maintain a lower ratio of around 70%, consistent with their more conservative liquidity management. However, a greater standard deviation of 26% among the FBs shows greater variability in their lending behaviour. In summary, the descriptive analysis underscores clear ownership-specific patterns: PSBs struggle with persistently higher NPAs and weaker profitability, partly cushioned by government recapitalization; PVBs display greater variability, reflecting market-driven discipline and strategic differences; and FBs, despite their smaller scale, consistently maintain stronger capital ratios and lower NPAs. These contrasting profiles justify the need for disaggregated analysis, as pooled estimates risk masking crucial heterogeneity across bank types.

Model Specification

The established interdependence between CAR and profitability as documented in the existing literature suggests the existence of a two-way causal relationship that works as a feedback loop. In such cases, simultaneous equations are employed that jointly estimate endogenous and exogenous variables (Studenmund, 2014; Wooldridge, 2010).

Endogeneity is said to exist if an independent variable exhibits a correlation with the error terms. If endogeneity is found, ordinary least square (OLS) estimates become biased and inconsistent due to simultaneous bias. The issue can be corrected using the two-stage least squares (2SLS) method. In the first stage, the endogenous variable is regressed with instrumental variables (IV)—variables that are highly correlated with the endogenous regressor but uncorrelated with the error term—to obtain its predicted (fitted) values. In the second stage, these predicted values are substituted for the original endogenous variable in the structural equation to produce consistent estimates. Thus, the effectiveness of the 2SLS method hinges on the correct identification of strong and valid instruments. While the data set has a panel structure, firm and time fixed effects are not directly applied in the 2SLS estimation because the presence of endogenous regressors and instrumental variables makes within transformation inconsistent (Wooldridge, 2010).

To test for endogeneity, the Wu–Hausman test is conducted, which compares the consistency of the OLS and instrumental variable (IV) estimators. Under the null hypothesis, the OLS estimator is both consistent and efficient, implying the absence of endogeneity. Rejection of the null indicates that at least one explanatory variable is endogenous, necessitating the use of an instrumental variable approach such as 2SLS.

If the Wu–Hausman test indicates the endogeneity of an independent variable, it becomes necessary to ensure the instrument’s strength and validity using the F-test for instrument strength and the Sargan or J-test for overidentifying restrictions. To address the concern of weak instruments, limited information maximum likelihood and Fuller (1) estimators are employed, both of which are more robust to weak instruments. The results from these alternative estimators validate the reliability of the main 2SLS estimate.

The study uses the following two simultaneous equations, where ROA and CAR are treated as endogenous variables—ROA in Equation (1) and CAR in Equation (2). When estimating CAR (Equation (1)), ROA is treated as an endogenous variable via Equation (2). Conversely, when estimating ROA (Equation (2)), CAR is treated as the endogenous variable via Equation (1). This helps us in addressing RQ1, which focuses on identifying the individual determinants of each variable within the system.

Equations (1) and (2) examine the interdependence between CAR and ROA incorporating both bank-specific and macroeconomic variables. Here, β denotes the estimated coefficients, while subscripts i and t represent bank i and year t, respectively. Each construct is grounded in banking theory and prior empirical evidence, as outlined below.

To check how the relationship between CAR and ROA and other bank-specific variables changes across PVBs, PSBs and FBs, two entity-type dummy variables to the models are added. Dummy variables serve as a methodological tool to incorporate categorical factors into regression analysis, allowing us to capture shifts in the intercept across different categories (Gujarati & Porter, 2009). These dummy variables enable the model to account for systematic differences between bank groups that are not explained by other explanatory variables.

Furthermore, to explore whether there is any structural change in the relationships after the 2014 regime change, a time dummy variable is introduced. This variable takes the value 1 for years after 2014 and 0 for the rest, thus capturing the potential effect of policy reforms and macroeconomic changes initiated by the new government post-2014.

However, since dummy variables affect only the intercept and cannot fully capture differences in slope coefficients or structural behaviours, this study extends the analysis by splitting the data into three separate groups based on bank ownership—PVBs, PSBs and FBs. This study runs distinct sets of simultaneous equations for each group. This approach enables us to investigate whether the determinants of CAR and ROA differ significantly across these three categories of banks, beyond just a shift in intercept. However, equations and instrumental variable for each group are adjusted to ensure endogeneity and strong instrumental variable.

To ensure the reliability and robustness of our statistical inference, this study addresses potential issues of heteroskedasticity by reporting robust standard errors clustered at the bank level, which adjusts for intra-bank autocorrelation and ensures more accurate estimation of standard errors.

Theoretical Contributions

The findings offer several theoretical insights into the capital–profitability nexus within banking. First, the asymmetric relationship between ROA and CAR across ownership types challenges the traditional view that higher profitability universally leads to stronger capitalization through retained earnings. Instead, this study demonstrates that ownership structure mediates this link: PVBs exhibit behaviour consistent with buffer theory (banks build capital in anticipation of future shocks), whereas FBs align more closely with risk–return trade-off theory, using profitability to expand risk exposure rather than to build buffers. PSBs, meanwhile, reflect elements of regulatory capital dependence, where capital adequacy is externally maintained through policy intervention rather than internal earnings.

Second, the observed negative impact of NPAs on CAR reinforces the moral hazard and agency cost perspectives (Jensen & Meckling, 1979), highlighting how risk-taking behaviour and information asymmetry differ across ownership forms.

Collectively, these results contribute to a more nuanced understanding of the ownership-specific dynamics of capital adequacy, extending the theoretical discourse on bank behaviour under heterogeneous institutional settings.

Practical and Policy Contributions

From a practical standpoint, these findings have direct implications for bank managers, regulators and policymakers. For PSBs, profitability does not appear to translate into stronger capital adequacy, indicating a reliance on external recapitalization rather than internal capital generation. There is an urgent need to strengthen internal capital formation mechanisms and improve risk assessment frameworks. Enhancing profitability alone is unlikely to ensure financial resilience unless accompanied by reforms addressing structural inefficiencies and governance constraints. Furthermore, the Government of India’s ongoing plan to consolidate PSBs into a smaller number of large banks may not necessarily improve capital adequacy or profitability unless such mergers yield tangible cost efficiencies. Instead, PSBs should prioritize sustainable credit growth to enhance profitability while exercising caution in the rapid expansion of unsecured retail credit, consistent with the concerns raised by Das (2024).

For PVBs, the positive linkage between profitability and CAR indicates effective internal capital management. Policymakers could encourage this behaviour through incentive-based and principle-driven capital requirements, which reward proactive risk management and discourage regulatory arbitrage. As Rao (2024) notes, the regulatory framework itself must evolve from a rule-based to a principle-based approach as the financial system matures.

For FBs, the negative ROA–CAR link implies a greater tendency towards risk optimization. Regulators should therefore monitor FBs’ exposure to volatile earnings and ensure that capital adequacy reflects true risk-weighted exposures rather than global portfolio adjustments.

The post-2014 structural reforms appear to have had a stabilizing influence on capital adequacy, validating ongoing regulatory measures such as the AQR and recapitalization programmes.

In summary, the study contributes both theoretically and practically by showing that capital management behaviour is ownership-contingent, shaped jointly by internal profitability dynamics, external regulatory environments and macroeconomic conditions.