Determinants and Prediction Model for Rural Bank Sustainability in Indonesia Post-COVID-19

Abstract

This study investigates the key risk factors influencing the sustainability of rural banks in Indonesia following the COVID-19 pandemic. It develops a predictive model of rural bank sustainability using logistic regression analysis. The analysis identifies seven statistically significant financial indicators, and among the three models proposed, Model 3 demonstrates the highest predictive accuracy, both in-sample and out-of-sample. Robustness tests confirm the reliability of this model. The findings highlight the importance for rural banks to improve their financial management, particularly in liquidity, credit expansion, and operational efficiency, to achieve long-term sustainability in a post-crisis economic landscape.

1. Introduction

A growing body of research from 2020–2024 has focused on the sustainability of banking institutions during periods of crisis and recovery. Logistic regression provides empirical models to assess institutional resilience during the COVID-19 pandemic [1]. Lots of research highlight the challenges faced by banks in emerging economies during economic shocks [2]. Recent studies have increasingly focused on the role of digital transformation in enhancing rural banking resilience [3]. Profitability indicators such as ROA, NIM, and BOPO are closely tied to risk exposure and operational sustainability [4,5]. Furthermore, sustainability models post-COVID-19 highlight the importance of risk-based prediction frameworks tailored for small financial institutions [1,2,6]. It is essential to investigate the risk determinants and prediction frameworks tailored to the unique characteristics of Indonesian rural banks [6,7].

Further contributions from financial innovation literature and bank system journals confirm that capital adequacy, loan performance, and operational efficiency are key factors in banking sustainability [8]. It is important to provide the underlying financial theories that justify the use of these metrics [9]. These studies collectively reinforce the approach used in this research: employing a multifactor model grounded in financial performance to predict rural bank sustainability in a post-crisis context. This study not only seeks to address gaps identified in earlier works but also responds to the urgent need for practical, data-driven policy tools. By aligning predictive analytics with regulatory frameworks, it offers a direct application to Indonesia’s post-COVID financial recovery efforts, specifically for rural banks facing multidimensional pressures.

The sustainability of rural banks has become increasingly critical in the aftermath of the COVID-19 pandemic, especially in Indonesia where Bank Perekonomian Rakyat (BPR) plays a key role in local economic support and financial inclusion. To understand what drives the resilience of these institutions, this study is grounded in three complementary theoretical frameworks. First, signaling theory explains how well-capitalized and efficiently managed banks send positive signals to regulators and the market about their soundness, thus influencing investor and depositor confidence. Second, agency theory provides insights into the role of financial governance and performance indicators in mitigating conflicts of interest between bank managers and stakeholders, particularly in periods of financial stress. Third, intermediation theory emphasizes the function of rural banks as financial intermediaries that transform savings into productive credit, making liquidity and lending behavior essential indicators of sustainability. These theoretical foundations inform the selection of key financial ratios used in this study CAR, ROA, BOPO, and LDR and guide the formulation of hypotheses regarding their predictive power on institutional sustainability. Strong corporate governance is essential in minimizing agency conflicts and enhancing rural bank performance. However, the effectiveness of governance reforms may vary depending on institutional context [7]. Environmental, social, and governance (ESG) factors have become increasingly relevant in banking risk assessments, as elevated ESG risks are shown to undermine bank stability in emerging markets [10].

Given their critical role in supporting MSMEs and fostering local economic development, BPRs are seen as an essential part of Indonesia’s microfinance ecosystem [6]. They offer financing, enhance business capabilities, and contribute to local employment [7]. Despite this, they continue to face structural challenges. From 2008 to 2018, over 90 BPRs were liquidated, and the number of operational institutions decreased from 1800 in 2015 to 1631 in 2021, as depicted in Figure 1.

The pressing need to evaluate the sustainability of rural banks after the pandemic stems from their essential role in Indonesia’s financial framework. Previous research underscores the need to pinpoint early warning signs of potential bank failures and to establish solid risk management strategies. This research seeks to address this need by creating a predictive model based on financial performance metrics to evaluate the viability and sustainability of rural banks in the post-pandemic period.

This study adopts a quantitative research design using a logistic regression model to predict rural bank sustainability. The research is designed to address the following key question: Which financial ratios are significant predictors of sustainability in rural banks post-COVID-19? By analysing financial performance indicators and health ratings, the study systematically explores the impact of capital adequacy, profitability, efficiency, and liquidity on institutional resilience. In line with these theoretical considerations, this study develops the following hypotheses, grounded in prior empirical research:

Capital Adequacy Ratio (CAR) serves as a critical buffer that enhances a bank’s resilience in absorbing financial shocks. According to previous study, banks with higher CAR are better positioned to withstand unexpected losses and maintain solvency during periods of economic turbulence [11,12]. From a theoretical standpoint, capital adequacy supports the signaling theory, wherein stronger capitalization signals a bank’s financial strength and stability to external stakeholders. In the Indonesian context, rural banks with robust capital positions are more likely to be classified as sustainable by regulators, particularly when facing macroeconomic uncertainties such as those caused by the COVID-19 pandemic.

H1: 

Capital Adequacy Ratio (CAR) has a significant positive effect on rural bank sustainability.

Operational Efficiency (BOPO) reflects the bank’s ability to manage its cost structure effectively. Empirical studies emphasize that lower BOPO ratios correlate with higher levels of profitability and financial sustainability [4,5]. Efficient operations are key to sustaining performance in volatile environments. The agency theory suggests that inefficient operations often arise from poor internal controls or misaligned incentives, leading to higher operating costs and reduced performance. In rural banks, where margins are typically thin and competition is increasing, operational efficiency becomes a vital factor in maintaining viability. This aligns with governance challenges found in rural banks [12].

H2: 

Operational Efficiency (BOPO) has a significant negative effect on rural bank sustainability.

Return on Assets (ROA) is a widely accepted measure of a bank’s profitability and operational success. It indicates how effectively the bank utilizes its assets to generate net income. Prior research [7,9] has demonstrated that institutions with higher ROA tend to have more robust internal financial positions, enabling them to invest in risk management and growth. ROA is also consistent with the resource-based view (RBV), which posits that internally generated financial strength is a key driver of competitive advantage and long-term survival.

H3: 

Return on Assets (ROA) has a significant positive effect on rural bank sustainability.

Loan to Deposit Ratio (LDR) is an indicator of how effectively a bank transforms deposits into income-generating loans. While aggressive lending can increase risk exposure, moderate LDR values reflect healthy intermediation practices that support earnings generation. While aggressive lending increases exposure, moderate LDR levels reflect active intermediation and income generation [1,2]. However, this must be balanced against liquidity risk. From the perspective of intermediation theory, higher LDR levels when managed prudently indicate efficient functioning of a bank’s core operations.

H4: 

Loan to Deposit Ratio (LDR) has a significant positive effect on rural bank sustainability.

This research extends prior work by integrating multiple performance ratios into a unified predictive framework, applying robustness checks through in-sample and out-of-sample validation techniques. To strengthen the conceptual alignment between methodology and research problem, we ensured that each selected variable corresponded directly with a known challenge in rural banking—whether related to liquidity, credit quality, or efficiency. The structure of the models was designed to capture both standalone and interactive effects across variables, reflecting the multifaceted nature of sustainability.

2. Materials and Methods

This research employs a quantitative approach, specifically using logistic regression analysis, to assess the factors influencing the sustainability of rural banks in Indonesia post-COVID-19. Logistic regression was chosen due to the binary outcome of the dependent variable, distinguishing between sustainable and non-sustainable banks.

2.1. Data Collection and Sample Selection

The study used secondary data sourced from the audited financial statements of 203 rural banks (Bank Perekonomian Rakyat—BPR) throughout Indonesia. The data covers the years 2020 to 2022, reflecting the period of recovery after the COVID-19 crisis. The selection of these banks was based on the completeness and availability of their financial reports, as well as their presence in the health rating assessments by the Otoritas Jasa Keuangan (OJK).

The dependent variable in this study is the binary classification of bank sustainability based on the OJK’s composite health ratings. Independent variables include financial ratios such as Capital Adequacy Ratio (CAR), Operational Efficiency (BOPO), Return on Assets (ROA), and Loan to Deposit Ratio (LDR). Logistic regression is employed to estimate the probability of a bank being categorized as sustainable or not. The sample consists of 203 rural banks in Indonesia, selected using purposive sampling with criteria based on data availability, audit completeness, and operational continuity between 2020 and 2022.

2.2. Variables and Measurement

• Dependent Variable
  The sustainability status, which is binary. Banks labeled as ‘sustainable’ according to OJK health ratings received a code of 1, whereas those labeled as non-sustainable received a code of 0.
• Independent Variable
  Drawing on theoretical frameworks and regulatory standards, the study considered seven significant financial metrics:

  ▪

  Capital Adequacy Ratio (CAR)—an indicator of capital robustness.

  ▪

  Return on Assets (ROA)—a measure of profitability.

  ▪

  Operational Efficiency Ratio (BOPO)—an indicator of cost efficiency.

  ▪

  Loan to Deposit Ratio (LDR)—an indicator of liquidity risk.

  ▪

  Loan Growth—reflects efforts in expanding credit.

  ▪

  Liquidity (Current Ratio)—an indicator of short-term financial stability.

  ▪

  Non-Performing Loans (NPL)—a measure of credit risk.

These metrics were chosen due to their established importance in previous studies [4,13] and their alignment with the OJK’s criteria for financial health evaluation.

2.3. Model Specification and Estimation

To address concerns about model specification, the selection of variables for Model 1, Model 2, and Model 3 was guided by well-established theoretical frameworks and empirical research. Model 1 incorporates financial ratios drawn directly from the CAMELS framework, which is used by financial regulators such as the Indonesian Financial Services Authority (OJK) and Bank Indonesia to assess the health of financial institutions. This includes Capital Adequacy Ratio (CAR), Return on Assets (ROA), Operating Expenses to Operating Income (BOPO), and Loan to Deposit Ratio (LDR). These ratios reflect core dimensions of capital, earnings, and liquidity [14,15,16,17,18,19,20].

Model 2 builds upon this foundation by including variables that represent credit risk and liquidity support: Non-Performing Loan ratio (NPL), Current Ratio (CR), and Off-Balance Sheet exposures (OBS). These variables are aligned with risk-focused perspectives from the Basel Core Principles and reflect additional dimensions of asset quality and contingent risk exposure, supported by empirical findings studies [4,5].

Model 3 combines all the above variables to create a comprehensive framework for predicting sustainability, allowing for interaction effects and cumulative contributions to be evaluated. This layered model approach ensures both regulatory relevance and empirical robustness in the specification.

Three logistic regression models were developed:

• Model 1: Focuses on primary performance indicators (CAR, ROA, LDR, BOPO).
• Model 2: Includes additional risk and liquidity metrics (NPL, CR, OBS).
• Model 3: Combines all variables to create a thorough predictive model.

In addition to the theory-based variable grouping, we conducted a robustness check using backward stepwise logistic regression with Akaike Information Criterion (AIC) minimization. To examine multicollinearity among the independent variables, we conducted a Variance Inflation Factor (VIF) analysis. All VIF values were below the threshold of 5, indicating an acceptable level of collinearity and no significant distortion of the logistic regression estimates. The stepwise model confirmed that core variables such as CAR, BOPO, NPL, and ROA were consistently selected, aligning with the structure of Model 3.

2.4. Validation Strategy

The robustness and applicability of the models were tested by splitting the dataset into:

• In-sample data (2021–2022) used for model development.
• Out-of-sample data (2023) used for model testing.

The study used K-fold cross-validation and Hosmer–Lemeshow tests to confirm statistical reliability and assess model fit. The effectiveness of the models was measured using accuracy, specificity, sensitivity, McFadden R², AIC, SIC, and average error rates.

2.5. Ethical Considerations

This research did not involve human subjects or experimental manipulations. All data were anonymized and obtained from publicly available financial documents, adhering to the institution’s data usage guidelines.

3. Results

This research utilizes a quantitative method with logistic regression to evaluate the factors influencing the sustainability of rural banks in Indonesia post-COVID-19. The dataset includes audited financial statements from rural banks in different regions spanning from 2020 to 2022. Seven independent variables were chosen based on existing literature and their regulatory significance: Capital Adequacy Ratio (CAR), Return on Assets (ROA), Operational Efficiency Ratio (BOPO), Loan to Deposit Ratio (LDR), Loan Growth, Liquidity, and Non-Performing Loan (NPL). The dependent variable is a binary classification of sustainability, where sustainable banks are coded as 1 and non-sustainable banks as 0, according to the health rating criteria set by the OJK (Indonesia Financial Services Authority).

The presentation of the empirical results in this study has been refined to ensure clarity and accessibility. We begin by describing the characteristics of each variable using descriptive statistics, helping readers understand the general trends in the data. The correlation matrix then offers an overview of how the variables relate to one another before diving into the regression analysis. In the logistic regression output, we carefully present the coefficients, standard errors, significance levels, and odds ratios for each financial ratio. This structure allows for an easier and more intuitive interpretation of how each variable influences the likelihood of a rural bank being categorized as sustainable.

For instance, CAR shows a positive and significant relationship with sustainability, indicating that well-capitalized banks are more resilient—an insight aligned with theoretical expectations. On the other hand, BOPO has a negative and significant impact, showing how operational inefficiencies may weaken a bank’s stability. Similarly, ROA confirms that banks with stronger profitability are better positioned to remain sustainable in the long run. Lastly, LDR, while positively associated with sustainability, calls for careful interpretation. It’s essential to balance credit expansion with liquidity management. Overall, we have aimed to present the findings in a way that not only informs but also guides practical understanding. We hope this clarity strengthens the value of the study for both academic readers and financial practitioners.

For the development of the predictive model, we created three logistic regression models with various combinations of predictors. The performance of these models was assessed by their in-sample classification accuracy and their out-of-sample performance through cross-validation to determine their generalizability.

As indicated in Figure 2, in the period following the global health crisis, rural banks typically satisfied the minimum capital adequacy standards mandated by financial regulators, with Capital Adequacy Ratios (CAR) surpassing 37.84%. These high CAR figures seem to offset the substandard credit quality, evidenced by Non-Performing Loans (NPLs) over 5%, and point to less than optimal operational efficiency. This situation indicates that asset management strategies are not effectively producing sufficient profits, thus heightening the risk of collapse and jeopardizing the banks’ long-term viability. Detailed financial ratios by Jakarta Region are reported in Figure S1 (Supplementary Materials).

The average Net Interest Margin (NIM) for both categories of rural banks remains elevated, above 14%, signaling a substantial interest rate differential. This phenomenon is frequently seen in rural banks, where high interest on loans is necessitated by increased funding expenses and operational inefficiencies. Such a setup undermines the banks’ market competitiveness and attractiveness to clients, consequently impeding growth and expansion into new markets.

Operational efficiency, gauged by the ratio of operational costs to operational revenue (BOPO), falls between 77% and 88% for both categories. These numbers imply a reasonably efficient operation, particularly under the strenuous post-COVID-19 conditions. To uphold public trust, rural banks also maintain sufficient liquidity by keeping ample cash reserves. This is demonstrated by the average Current Ratio (CR), which is 23.49% for banks deemed non-sustainable and 25.63% for those considered sustainable. Both values greatly exceed the regulatory minimum of 6%, suggesting robust short-term liquidity. The high CR levels indicate that both groups can fulfill their short-term financial obligations with cash and equivalents, primarily due to cautious cash management and a low loan-to-deposit ratio.

Regarding intermediation performance in the post-COVID-19 era, both categories of rural banks show high liquidity risk, as reflected by Loan-to-Deposit Ratios (LDRs) over 100%. This scenario suggests that these banks are lending out more than the deposits they have on hand, which could lead to challenges in meeting withdrawal demands and liquidity strains. Liquidity issues continue to be a major worry for Indonesian banks post-crisis. High NPLs further complicate credit allocation, intensifying liquidity problems.

A comparison between the two bank groups shows a small variance in their average LDRs—81.97% for the group likely to sustain and 83.70% for the group less likely to sustain. Though the difference seems minor, statistical analysis confirms its significance at the 5% level (α < 0.05). Off-balance sheet (OBS) activities also display a statistically significant difference between the groups, with sustainable banks averaging 67.29% and non-sustainable banks at only 22.55% (α < 0.05). This indicates that sustainable rural banks engage more with off-balance sheet instruments, potentially improving financial flexibility and risk management.

In terms of credit expansion, both groups experienced moderate growth rates between 5% and 6%, reflecting continued efforts to perform their intermediation function despite external challenges. While rural banks vie with commercial banks and other financial entities for loan distribution, their strength lies in their localized strategies and deep customer connections, which are vital in underbanked regions.

During the stages of developing and validating the model, the data was split into two sets: one for estimating the model and another for validation. According to [14], it’s crucial to assess the model’s predictive accuracy using separate datasets for building and validating the model. This method helps maintain an unbiased error rate, provided the validation data is different from the data used to construct the classification or prediction model. For the post-COVID-19 analysis, model estimation used data from 2021 to 2023, and model validation was carried out with data from 2023.

This research assesses and compares the predictive accuracy of three different models (Model 1, Model 2, and Model 3) to identify the most precise model for evaluating rural bank sustainability post-COVID-19. After estimating the models, the next step involves analyzing the outcomes from the three models. The nature of the relationship between the dependent and independent variables (positive or negative) shows how changes in one variable affect the predicted result. A positive coefficient suggests an increased chance of sustainability, while a negative coefficient indicates a reduced likelihood of the predicted outcome. The estimation results, derived from in-sample data, along with the interpretation of each hypothesis tested across the three models, are shown in

Table 1. In Sample Logistic Regression Estimation Model Test Results.

Variable	Expected Sign	Model 1		Model 2		Model 3
		Coefficient	OR	Coefficient	OR	Coefficient	OR
CAR	(−) negative	−0.0095 ***	0.948			−0.029 ***	0.948
LDR	(+) positive	0.0346 ***	1060			0.003 ***	1034
ROA	(−) negative	−0.2139 ***	0.859			−0.026 *	0.815
CG	(−) negative	−0.6001 ***	1.001			−0.718 ***	1432
NIM	(−) negative			−0.0043	0.948	−0.003	1.002
NPL	(+) positive			0.1806 ***	1.141	0.168 ***	1.145
BOPO	(+) positive			0.0364 ***	1.019	0.020 **	0.976
CR	(−) negatif			−0.0127 ***	0.943	−0.006	0.965
OBS	(−) negatif			−0.0126 ***	0.831	−0.045 ***	0.888
C		−1.305 **		−74.113 ***		−0.751 **
McFadden R2 (%)	>70	86.95		86.09		92.03
H-L Statistic		31.75		27.53		33.00
Prob. Chi-Sq	α	0.081 **		0.080 **		0.030 ***
AIC	ε → 0	0.2481		0.281		0.221
SIC	ε → 0	0.2501		0.282		0.212
% Correct	ε → 100	96.82		96.45		98.86
%Incorrect	ε → 0	3.18		3.55		1.14

Information: ε → close value; OR = Odds Ratio; (***) significant alpha 0.01; (**) significant alpha 0.05; (*) significant alpha 0.10.

The analysis of Model 1 shows that all null hypotheses are dismissed. Each independent variable—Capital Adequacy Ratio (CAR), Loan-to-Deposit Ratio (LDR), Return on Assets (ROA), and Credit Growth—has a significant impact on the probability of bank unsustainability, with all results being statistically significant at the 1% level. Likewise, Model 2 reveals that Non-Performing Loans (NPL), Operational Efficiency (BOPO), Cash Ratio (CR), and Off-Balance Sheet (OBS) activities significantly affect the risk of bank default or unsustainability at a 1% significance level.

In contrast, Model 3 shows that while most variables significantly influence the dependent variable, Cash Ratio and Net Interest Margin (NIM) do not show a significant effect on the likelihood of a bank being unsustainable. The lack of significance of NIM is consistent with regulatory views, which do not consider NIM a primary factor in bank failure. However, this result differs from earlier research that found a strong positive correlation between NIM and bank sustainability [15]. While a higher NIM might enhance profitability, it could also increase borrowing costs for customers, potentially raising default risks and NPLs, thereby hindering sustainable growth.

Furthermore, the Cash Ratio was found to be an insignificant predictor of rural bank sustainability. This may be due to rural banks typically maintaining cash ratios at or above the regulatory minimum of 6%. Consequently, both unsustainable and default-prone banks usually meet this requirement, diminishing the predictive power of this variable. The next step involves assessing which model has the highest classification accuracy by examining prediction error values. The error value is determined as the difference between the actual data and the predicted probability.

Table 2. Comparison of Model Accuracy Based on Average Error Values between In Sample and Out-of Sample.

Category		Logit Score	Model 1		Model 2		Model 3		(I) Model	(J) Model	Anova Test Diff Mean Logit Score [1]	Model 1	Model 2	Model 3
			Avg Logit Score [1]	Avg Diff Logit Score [1]	Avg Logit Score [2]	Avg Diff Logit Score [2]	Avg Logit Score [3]	Avg Diff Logit Score [3]				Anova Test Diff Avg Logit [2]
		1	2	3	4	5	6	7	8	9	10	11
Bank Tend to Unsus-tain	Logit Score in-sample	0.9580	0.9646	0.0354	0.0319	0.9681	0.9697	0.0303	Model 1	Model 2	0.9327 **
										Model 3	−0.0050 **
									Model 2	Model 1	−0.9327 **
										Model 3	−0.9377 **
									Model 3	Model 1	0.0050 **
										Model 2	0.9377 **
	Logit Score out-of sample	0.9781	0.9636	0.0364	0.0307	0.9693	0.9690	0.0310	Model 1	Model 2	−0.9327 **	F Hit 1422149.703 Sig 0.000 **
										Model 3	0.0050 **
									Model 2	Model 1	0.9327 **
										Model 3	0.9377 **
									Model 3	Model 1	−0.0050 **
										Model 2	−0.9377 **
T-test [1]	t-stat		-50.220		75.402		−85.020
	Prob		0.1068		0.9374		0.342
Bank Not Tend to Sustain	Logit Score in-sample	0.6071	0.8553	0.1447	0.2333	0.7667	0.7326	0.2674	Model 1	Model 2	0.6220 **
										Model 3	0.1226 **
									Model 2	Model 1	−0.6220 **
										Model 3	−0.4993 **
									Model 3	Model 1	−0.1226 **
										Model 2	0.4993 **
	Logit Score out-of sample	0.6211	0.8901	0.1099	0.2040	0.7960	0.7693	0.2307	Model 1	Model 2	0.6220 **	F Hit 1818.037 Sig 0.000 **
										Model 3	0.1226 **
									Model 2	Model 1	−0.6220 **
										Model 3	−0.4993 **
									Model 3	Model 1	−0.1226 **
										Model 2	0.4993 **
T-test [2]	t-stat		−18.295		26.357		−27.856		T-test [3]	t-stat		−1.34	530.89	−1.22
	Prob		0.2337		0.2600		0.1806			Prob		0.179	0.000	0.222

Note: Logit score: overall sample logit value; Avg Logit Score [1] = Average value of logit score Model 1; Avg Logit Score [2] = Average value of logit score Model 2; Avg Logit Score [3] = Average value of logit score Model 3; Avg Diff Logit Score [1] = Average value of the difference between the actual value and predicted value and predicted value Model 1; Avg Diff Logit Score [2] = Average value of the difference between the actual value and predicted value and predicted value Model 2; Avg Diff Logit Score [3] = Average value of the difference between the actual value and predicted value and predicted value Model 3; Anova Test Diff Mean Logit Score [1] = The test result for difference in the average of the logit score difference between the actual value and the predicted value between models; Anova Test Diff Mean Logit Score [2] = The test result for difference in the average of the logit score difference between the actual value and the predicted value between models; T-test [1] = result of the test the difference in the average logit score between logit score between the in-sample and out-of sample logit scores in the bank unsustain category; T-test [2] = result of the test the difference in the average logit score between logit score between the in-sample and out-of sample logit scores in the bank sustain category; T-test [2] = The result of the difference in the average value on the magnitude of the error between model 1, model 2 and model 3; In-sample = estimated data year 2021 until 2023; out-of sample = estimated data year 2023; specification cut-off point Model 1 = 0.95; specification cut-off point Model 2 = 0.75; specification cut-off point Model 3 = 0.96; significant alpha 0.01; (**) significant alpha 0.05.

compares the accuracy of Models 1, 2, and 3 based on average error values, using both estimation (in-sample) and validation (out-of-sample) datasets. The dataset used in this study is available as Dataset S1 (Supplementary Materials).

This study uses a cut-off point based on the proportional distribution of sustainable and non-sustainable banks [16]. The selection of the cut-off point is crucial for determining prediction errors, as it affects classification results. Using the overall proportion of sustainable versus non-sustainable banks in the sample offers a balanced and objective method for setting the most suitable cut-off threshold.

In this research, Model 1 includes a sample where 5% of banks are deemed likely to be unsustainable, while 95% are considered sustainable (193 out of 203 banks). A cut-off point of 0.95 is used to represent this proportional split. In Model 2, 25% of banks are labeled as potentially unsustainable, and 75% as sustainable (153 out of 203 banks), which sets the cut-off at 0.75. In Model 3, 24% of banks are classified as potentially unsustainable, and 96% as sustainable (195 out of 203 banks), establishing a cut-off of 0.96.

As illustrated in Table 2, the mean logit scores for the category ‘tending to be unsustainable’ were computed using in-sample (estimation) data from 2021 to 2023. For Model 1, the mean logit score stands at 0.9646, surpassing the cut-off of 0.9506, which suggests robust classification accuracy for identifying unsustainable banks. In Model 2, the mean logit score is 0.0319, below the 0.75 cut-off, indicating poorer performance in classifying unsustainable banks. Conversely, Model 3 has a mean logit score of 0.9697, exceeding the cut-off of 0.9605, showing high accuracy in pinpointing banks likely to be unsustainable.

From these comparisons, it is evident that Models 1 and 3 have better accuracy in classifying banks that tend to be unsustainable, whereas Model 2 demonstrates reduced classification effectiveness, especially in identifying sustainable banks, as indicated by higher prediction errors. The same methodology was used to evaluate the average logit scores from out-of-sample (validation) data for 2023. Validation results for Model 1 indicate an average logit score of 0.9636, above the cut-off of 0.9506, showing strong classification accuracy for unsustainable banks. For Model 2, the average logit score is 0.0307, significantly below the 0.75 cut-off, suggesting a lower accuracy in predicting unsustainable banks. In contrast, Model 3’s average logit score of 0.9690 exceeds the 0.9605 threshold, confirming its effectiveness in predicting unsustainable banks. When assessing the three models’ out-of-sample prediction accuracy, Models 1 and 3 perform better at identifying banks at risk of unsustainability, while Model 2 shows the least predictive capability, as evidenced by its higher error rates. These outcomes are in line with the prediction and error values seen in the validation data for 2023.

Based on the average logit scores for the ‘tend to sustain’ category, the in-sample (estimation) results up to 2023 show that all three models successfully classify sustainable banks. In Model 1, the average logit score is 0.8553, below the cut-off of 0.9506, indicating effective classification of sustainable banks. Similarly, Model 2’s average logit score of 0.2333 is well below its cut-off of 0.75, reinforcing its accuracy in identifying sustainable banks. Model 3’s average logit score of 0.7326 falls below its cut-off of 0.9605, suggesting accurate estimation for this category. These results indicate that Models 1, 2, and 3 all perform well in estimating bank sustainability using in-sample data, as demonstrated by their average logit scores that appropriately correspond with the cut-off points set for each model.

According to the T [2] test results, comparing the logit scores from in-sample and out-of-sample data for banks categorized as ‘tending to sustain’ reveals the following insights:

• For Model 1, the T [2] test yields a p-value of 0.2337, surpassing the 5% significance level (α = 0.05). This suggests no statistically significant difference exists between the average in-sample (estimation) and out-of-sample (validation) logit scores for the ‘tend to sustain’ category. Therefore, it can be inferred that Model 1 is robust and dependable. The lack of significant variance between the estimation and validation outcomes indicates consistent predictive performance. This consistency is reinforced by the close match in average logit scores, demonstrating high accuracy in identifying banks likely to sustain.
• The T [2] test results for Model 2 indicate a p-value of 0.2600, above the 5% significance level (α = 0.05). This signifies no statistically significant difference between the average logit scores from in-sample (estimation) and out-of-sample (validation) data in the ‘tend to sustain’ category. Hence, Model 2 exhibits stable predictive performance. The nearness of logit scores between the estimation and validation periods, despite occasional slightly higher validation scores, indicates that the model is trustworthy in predicting sustainable banks.
• Likewise, the T [2] test for Model 3 produces a p-value of 0.1806, which is above the 5% significance level. This indicates no significant difference between the average in-sample and out-of-sample logit scores for the ‘tend to sustain’ group. Consequently, Model 3 is deemed stable and reliable, as the average logit scores during the validation phase closely reflect those during the estimation phase. The validation period is essential for evaluating the model’s future use, especially in accurately pinpointing banks at risk of becoming unsustainable.

Model 3 has been determined to be the most precise of the three models evaluated. This finding is backed by its average error value, which is nearest to zero, reflecting the smallest prediction error. Model 3 shows the least mean error, with Model 1 coming next, and Model 2 displaying the largest average error. Essentially, this indicates that Model 3’s predictions most accurately match the actual results. Nonetheless, it should be recognized that incorporating multiple model comparisons might result in estimation inflation, which could elevate the predicted probability and consequently decrease the overall confidence level. This inflation effect can alter the significance level (α), possibly leading to a Type I error.

The validation outcomes for Type I and Type II error analysis of Model 1 are as follows: the Type I error rate (false positive), which is the percentage of banks forecasted as sustainable but were actually unsustainable, was 12 out of 187, or 6.41%. The Type II error rate (false negative), indicating the percentage of banks predicted as unsustainable but were actually sustainable, was 8 out of 16, or 50%. The sensitivity of the model, or its effectiveness in correctly identifying unsustainable banks, was 75%. Its specificity, or the accuracy in pinpointing sustainable banks, was 96.25%. The model’s overall classification accuracy was 92.11%, demonstrating robust predictive capabilities. The classification accuracy of each model is presented in Table S1 (Supplementary materials). These findings are detailed in

Table 3. Type I and Type II Error Test Results.

Model 1 Y1_Observed		Y1_Predicted		Total	Percentage (%)
		Sustain	Unsustain	Observation
Type 1	Sustain	169	8	187	96.25
Type 2	Unsustain	4	12	16	75
Overall				203	92.11
Model 2 Y1_Observed		Y1_Predicted		Total	Percentage (%)
		Sustain	Unsustain	Observation
Type 1	Sustain	169	8	176	90.37
Type 2	Unsustain	12	15	27	55.55
Overall				203	86.69
Model 3 Y1_Observed		Y1_Predicted		Total	Percentage (%)
		Sustain	Unsustain	Observation
Type 1	Sustain	191	4	195	98.18
Type 2	Unsustain	1	7	8	87.5
Overall				203	96.05

Source: Processed research data, 2024.

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According to Table 3, Model 2 forecasted 27 banks as unsustainable, yet the actual data showed 15 banks as unsustainable and 12 as sustainable. The model’s sensitivity, or its accuracy in identifying unsustainable banks, was 15 out of 27, translating to 55.55%. For sustainable banks, the model predicted 176, with 169 confirmed to be sustainable, yielding a specificity of 169 out of 176, or 90.37%. The total accuracy of classification was 86.69%.

The Type I error rate (false positives), where sustainable banks were wrongly labeled as unsustainable, stood at 8 out of 176, or 4.54%. The Type II error rate (false negatives), where unsustainable banks were misidentified as sustainable, was 15 out of 27, or 55.55%. Despite a high specificity, the model’s sensitivity below 70% and a high Type II error rate suggest that Model 2 lacks reliability in pinpointing unsustainable banks.

On the other hand, Model 3’s validation results indicate superior performance. Its Type I error rate was merely 4 out of 195, or 2.05%, showing few sustainable banks were misidentified as unsustainable. The Type II error rate was 1 out of 8, or 12.5%, indicating high precision in identifying unsustainable banks. Sensitivity was 87.5%, and specificity was 98.18%. The overall classification accuracy reached 96.05%, affirming that Model 3 provides strong and dependable predictive capabilities.

Among the evaluated models, Model 3 showed the greatest predictive strength, achieving over 96% accuracy in both in-sample and out-of-sample tests. This model includes all relevant variables and provides the most solid structure for forecasting rural bank outcomes. The findings imply that a holistic strategy, encompassing capital strength, risk exposure, and operational efficiency, is crucial for enhancing resilience in rural banking.

These findings have profound implications for both regulators and practitioners. Policymakers should bolster supervisory frameworks to incorporate predictive analytics and early warning systems, whereas rural banks should focus on financial discipline, robust risk management, and capacity building to enhance sustainability in the post-COVID-19 era.

These findings bridge the gap between theoretical assumptions and empirical validation. The progression from individual ratio analysis to a comprehensive logistic model demonstrates how analytical rigor translates into actionable insight. Each step of the model construction from variable selection to validation was structured to directly address the problem of inconsistent bank performance in Indonesia’s rural banking sector.

4. Discussion

The application of backward stepwise selection based on AIC reinforced the relevance of the main predictors included in Model 3, supporting the robustness of the theory-driven model structure. The findings of this study provide substantial empirical support for the determinants of rural bank sustainability in Indonesia in the aftermath of the COVID-19 pandemic. The results affirm the theoretical propositions outlined in earlier sections and align with prior studies that emphasize the importance of capital strength, operational efficiency, profitability, and liquidity management in predicting bank sustainability.

Model 3, which integrates all significant variables, emerged as the most robust and accurate predictive model, as evidenced by its superior performance in both in-sample and out-of-sample validation. This reinforces the notion that multifactorial approaches incorporating capital adequacy, loan performance, and operational metrics offer a more comprehensive framework for assessing bank viability [11,13]. These results also extend the work by validating a predictive model specific to rural banks using logistic regression with contemporary post-crisis data [6].

The findings of this study provide critical insights into the sustainability of rural banks by empirically testing the predictive power of key financial ratios. The significant positive effect of Capital Adequacy Ratio (CAR) supports the signaling theory, as a higher CAR signals the bank’s financial strength to regulators and depositors, thereby enhancing stakeholder trust and long-term stability. This finding is consistent with prior research that underscores the importance of capital buffers in absorbing shocks and ensuring solvency. The positive association between Capital Adequacy Ratio (CAR) and sustainability underlines the protective role of strong capital buffers, consistent with the findings of [4,11,13], who argue that capital strength mitigates external shocks and reduces the risk of insolvency.

Similarly, the negative relationship between BOPO and sustainability affirms, who emphasize that operational efficiency is critical in maintaining profitability and navigating economic volatility [9]. Operational efficiency, as measured by BOPO, shows a strong negative association with sustainability. This aligns with agency theory, where inefficient cost structures may reflect managerial shortcomings and agency conflicts that erode institutional value. Highly efficient banks are better able to convert income into retained earnings, which in turn strengthens their resilience. The empirical findings are aligned with earlier studies suggesting that green banking instruments while boosting profitability do not necessarily contribute to institutional resilience in volatile markets [21].

Return on Assets (ROA), a proxy for profitability, also has a significant positive impact, confirming that sustainable banks are those that consistently generate adequate returns on their assets. This supports both agency and intermediation theories, highlighting that profitability not only reduces operational risk but also enhances a bank’s ability to fulfill its intermediation role. The role of Return on Assets (ROA) as a significant predictor is also congruent with [9], where high ROA is seen as an indicator of sound asset management and income-generating capability. Meanwhile, the significance of Loan to Deposit Ratio (LDR) resonates with the studies that suggesting prudent lending practices that balance liquidity and income generation are vital for long-term sustainability [1].

Interestingly, Loan to Deposit Ratio (LDR) was found to have a statistically significant positive impact on sustainability. This suggests that higher lending activity, when managed prudently, contributes to long-term viability by increasing interest income and reinforcing the bank’s function as a financial intermediary. However, excessive lending beyond prudent limits may lead to liquidity stress, indicating a trade-off that must be managed carefully.

Interestingly, Net Interest Margin (NIM) and Current Ratio (CR) were found to be statistically insignificant. While previously study shown that higher NIM contributes positively to profitability, these findings suggest a potential trade-off—high NIM may increase borrower burden, especially for rural clients, leading to rising default risk and higher Non-Performing Loans (NPL) [12,13]. The insignificance of CR can be attributed to regulatory constraints that ensure rural banks maintain minimum liquidity thresholds, thereby reducing its discriminative power. The non-significant relationship between certain financial ratios and sustainability scores may be influenced by internal leadership quality and technological readiness, as explored in recent studies on fintech adoption in rural banking [22].

To further explain the lack of statistical significance, we provide deeper theoretical and empirical insights specific to the context of rural banks. The insignificance of NIM and CR in the logistic regression models may be explained by sector-specific characteristics of rural banks. While high NIM typically suggests strong intermediation, in the BPR context, it often results from high funding costs and elevated lending rates, which may increase default risks. Likewise, CR, though above regulatory thresholds, lacks predictive value due to its limited reflection of maturity mismatches and the quality of liquid assets. These findings align with empirical studies that emphasizing the nuanced interpretation of these ratios in the microfinance banking sector [4,5].

Furthermore, the significance of Off-Balance Sheet (OBS) activities provides new insights. The greater involvement of sustainable banks in OBS activities supports [8], who posit that financial innovation and diversification enhance risk management and flexibility. This aspect adds a novel contribution to rural banking literature, particularly in highlighting the role of non-traditional activities in enhancing sustainability.

From a practical perspective, the study underscores the necessity for rural bank management to enhance profitability through better asset allocation (higher ROA), reduce inefficiencies (lower BOPO), and maintain healthy intermediation practices (moderate LDR). Regulators, particularly OJK, can adopt predictive modeling using financial ratios to design more proactive supervision frameworks, complementing traditional health rating assessments.

This study makes a multifaceted contribution to the literature on sustainability and risk management, particularly in the context of rural banking. First, it presents a validated logistic regression model tailored specifically for rural banks, which remains an underexplored segment in the broader financial risk modeling discourse. The development of this model is significant as it demonstrates that institutional sustainability in a post-crisis setting is best explained through a combination of internal performance indicators rather than isolated financial metrics. Second, the study provides empirical evidence supporting the use of performance ratios such as CAR, BOPO, ROA, and LDR as reliable predictors of sustainability, reinforcing their practical value for regulatory surveillance and internal risk assessment frameworks. Furthermore, by integrating variables across capital adequacy, profitability, operational efficiency, and liquidity dimensions, the model enhances the granularity and explanatory power of traditional health assessments. Third, the findings yield actionable insights for both policymakers and rural bank managers. For regulators, the model offers a complementary tool to health rating systems, enabling the deployment of early warning signals for financial distress. For practitioners, the study provides clear diagnostic guidance on which financial levers such as optimizing operating costs and strengthening capital buffers can be adjusted to bolster institutional resilience. Overall, this research bridges a theoretical gap by combining empirical rigor with practical applicability, and it lays a methodological foundation for future studies that seek to align financial sustainability with evidence-based decision-making.

Overall, the coherence between theoretical expectations and empirical findings enhances the robustness of this study. The results validate the selected financial ratios as reliable early-warning indicators for predicting institutional sustainability, especially in the vulnerable context of rural banks during post-pandemic recovery. The insights generated offer practical guidance for both regulatory oversight and internal bank management, emphasizing the importance of capital adequacy, cost control, asset profitability, and prudent lending in sustaining financial resilience.

4.1. Limitations of the Study

Despite its contributions, this study has several limitations that should be acknowledged to provide a realistic understanding of its scope. This study, while offering a robust predictive model for assessing rural bank sustainability in post-crisis conditions, is not without limitations. Firstly, the research is constrained by data availability, as it exclusively relies on audited financial statements from 203 rural banks over the period 2020–2022. Although these records are credible, they may not fully capture informal financial behaviors, regional regulatory disparities, or the qualitative attributes of bank governance and management. Secondly, the methodological framework employs logistic regression, which assumes linearity between predictor variables and the log odds of the dependent variable. Such an assumption may oversimplify the complex, dynamic interactions that exist within financial systems. Moreover, the binary classification of bank sustainability, based solely on OJK health ratings, may fail to reflect the continuum of financial health and institutional resilience. Thirdly, in terms of generalizability, the findings are context-specific to Indonesian rural banks and may not be directly transferable to other microfinance institutions operating in different regulatory or socio-economic settings. Finally, the study’s pooled cross-sectional design does not capture temporal dynamics or the evolution of sustainability indicators over time. Future studies might benefit from panel data analysis to explore time-varying effects and establish causal relationships more rigorously. Despite these limitations, the present research contributes significantly by laying a foundation for predictive risk modeling in the rural banking sector and highlighting key areas for future methodological refinement.

These limitations suggest caution in interpreting the findings and highlight opportunities for more comprehensive models that integrate qualitative data and broader institutional contexts in future research. Future work could leverage integrative ESG frameworks [20,23] and advanced boosting methods [22,24] with interpretable tools such as SHAP [16]. Future Research Directions could adopt and compare these machine learning techniques using comprehensive evaluation metrics such as AUC-ROC, F1-score, sensitivity, and specificity to validate and enhance predictive accuracy.

4.2. Future Research Directions

While this study provides a robust quantitative framework for predicting rural bank sustainability in the post-COVID-19 context, future research could extend this foundation through several complementary approaches. One promising direction involves the integration of Environmental, Social, and Governance (ESG) frameworks into predictive modeling. Incorporating ESG indicators would align sustainability assessments with global standards of responsible finance, and the use of advanced boosting techniques—such as XGBoost and Random Forest combined with interpretable tools like SHAP, could improve both model accuracy and transparency [16,20]. In addition, the inclusion of qualitative dimensions such as management quality, governance structures, and customer satisfaction could enrich the analytical scope and offer insights into non-financial determinants of resilience.

Comparative analyses between rural banks and other microfinance institutions across diverse organizational forms and regulatory environments could also validate the generalizability of the model and reveal sector-specific vulnerabilities. Moreover, longitudinal research spanning a longer post-pandemic recovery period would help capture the temporal dynamics of financial sustainability and track the persistence of predictive relationships over time. Spatial analyses leveraging geospatial tools may uncover regional disparities in bank performance and economic recovery, thereby informing more targeted policy interventions.

Stress-testing scenarios that simulate future economic shocks such as climate-related events or macroeconomic instabilities could further evaluate institutional resilience under adverse conditions. Methodologically, future research should consider benchmarking logistic regression against advanced classifiers like Support Vector Machines (SVM) and ensemble methods, using comprehensive metrics such as AUC-ROC, F1-score, and sensitivity-specificity to evaluate predictive performance. Furthermore, to address issues of multicollinearity and improve model parsimony, the application of regularized techniques such as Ridge and Elastic Net regression is recommended. The adoption of panel logistic regression models would allow for the investigation of both cross-sectional and temporal variation in sustainability drivers, while automated variable selection methods like LASSO or tree-based algorithms may enhance model efficiency and reduce overfitting in complex datasets. Collectively, these future directions offer a pathway toward more holistic, adaptable, and policy-relevant models for assessing the long-term viability of rural financial institutions. Future research could explore the moderating role of fintech leadership in rural banks, building on recent evidence that adaptive leadership styles influence digital transformation outcomes [25].

By exploring these areas, future research can offer a more holistic view of how rural financial institutions in developing economies can maintain resilience in the face of uncertainty. Future work could leverage integrative ESG frameworks [20,21] and advanced boosting methods [22,23] with interpretable tools such as SHAP [16]. This is consistent with findings on ESG-related risks [10].

These findings offer strong and meaningful insights into what drives rural bank sustainability in the post-pandemic era. Among the various financial indicators examined, CAR, BOPO, ROA, and LDR consistently stood out as significant predictors. This confirms not only the relevance of traditional financial health metrics but also aligns well with the practical frameworks widely used by regulators such as OJK.

The validation of Model 3 as the most reliable model further reinforces the idea that a comprehensive, theory-informed approach is essential. This model, which draws on multiple financial dimensions, reflects a growing consensus in the literature that sustainable bank performance is best assessed through a mix of capital adequacy, operational efficiency, profitability, and sound lending practices [10,11,13].

At the same time, the study does not overlook the variables that showed insignificant results like NIM and CR. Instead of disregarding them, we place these findings within the broader context of microfinance, where such indicators may behave differently due to the unique nature of rural banking. This balanced view adds depth to the analysis and strengthens the credibility of the study’s conclusions.

Notably, the importance of off-balance sheet (OBS) activities signals a shift in how we should think about innovation and sustainability. While these instruments are often overlooked in traditional analysis, our findings suggest they may play a growing role in helping rural banks adapt and thrive. For this reason, we believe that both policymakers and bank managers should expand their focus beyond just what appears on the balance sheet.