“Commercial banks’ capital structure and performance in Vietnam: Panel data model approach”

The study delves into the factors that influence the capital structure of commercial banks in Vietnam. Capital structure, measured by the net debt-to-asset ratio, is a key indicator of bank leverage. The study uses pooled OLS, fixed effects, and random effects models to analyze the impact of factors such as net interest-earning rate, Corporate Income Tax rate, and liquidity on commercial banks’ profitability and their capital structure. Data from 26 banks during the 2010–2022 period in Vietnam was collected for the analysis. The results indicate that factors such as Tax, ROA, growth, and liquidity have significant impacts on the capital structure of the banks. Specifically, Tax has a beta coefficient of –0.05967, ROA has a beta of –0.01796, growth has a beta of 0.000509, and liquidity has a beta of –0.00045. The study found that ROA, Tax, and liquidity are negatively related to the capital structure of Vietnamese commercial banks, meaning that an increase in these factors leads to a decrease in the banks’ total debt-to-total assets and vice versa. The empirical results suggest that commercial banks can manage their capital structure through these factors to reduce their debt-to-asset ratio, resulting in reduced credit risk, improved asset quality, and increased business efficiency. However, lowering the debt-to-asset ratio may also lead to reduced profits from lending activities, particularly when interest rates are high.


INTRODUCTION
Competition among businesses in the market economy is becoming increasingly fierce.Therefore, optimizing a company's capital structure is an essential task for financial managers; simultaneously, the banks' capital structure has a significant impact on their capacity to implement company plans, achieve economic efficiency, and promote sustainable growth.The issue of actively selecting a proper capital structure of equity and debt capital to optimize bank value has become increasingly pressing.This study examines the impact of various factors on a bank's capital structure using the GLS regression model.It identifies size, profitability (ROA), leverage, liquidity, risk, and net profit margin (NIM) as explanatory factors for banks.Additionally, macroeconomic variables such as economic growth, price inflation, real interest rates, equity market index volatility, deposit insurance, and governance index are incorporated into the model to regulate macroeconomic policies.
The data for this study were collected from 26 banks in the Vietnamese stock market from 2010 to 2022, with a focus on major banks that have a significant impact on the economy.The empirical results derived from this analysis can be used as a reference for banks to develop their business strategies and provide a basis for macroeconomic policymakers to formulate appropriate monetary policies for the economy.
The empirical research findings demonstrate that a bank's competitive strategies and effectiveness are significantly influenced by key factors, such as return on assets (ROA), leverage, liquidity, net profit margin, and risk.These factors play a crucial role in determining the competitive advantage of a bank and its ability to achieve strategic objectives.ROA is an important metric that measures how efficiently a bank utilizes its assets to generate profits.Similarly, leverage and liquidity ratios are vital indicators of a bank's financial health, whereas the net profit margin measures the profitability of a bank's operations.Lastly, risk is a critical consideration for banks, as it determines the likelihood of potential losses due to market fluctuations or other external factors.Understanding the impact of these factors on a bank's strategy is therefore essential for banks seeking to maintain their competitive edge in the financial industry (Jadah et al., 2020;Khan et al., 2021).Environmental factors such as the economic growth rate, Vietnam's volatility in the stock market index, deposit insurance ratio, and governance all significantly influence the economy's development and stability.Empirical data suggest that capital structure is now a key problem, not only in firms but also in banks.Empirical results also show that the banking system shows that banks face an imbalance in the structure of capital and assets when using short-term capital for long-term loans, increasing liquidity risk, leading to a high rate of bad debt, affecting the banking system in particular and the Vietnamese economy in general.
A well-crafted plan and a finely tuned capital structure are critical for ensuring a bank's profitability.This requires careful alignment and adjustment of the investment structure, which is essential for success.Investors must make educated judgments on capital investment plans, as mistakes can have a substantial influence on the overall balance of the investment structure.Modigliani and Miller's (1958) paper introduced capital structure theory, also known as M&M theory.This theory has since evolved into other theories like equilibrium, pecking order, market regulation, and management structure (Modigliani & Miller, 1958;Aji & Adawiyah, 2021).Gropp and Heider (2010) show that between 1991 and 2004, deposits were the most important determinants of the capital structure and leverage of large US and European banks.There was a shift from deposits to non-deposit liabilities in the banks' liability structure.The impact of bank deposits on a bank's capital structure and leverage remained consistent over time.

LITERATURE REVIEW
In addition, there is literature mentioning capital structures, such as Khaki and Akin (2020) and Aulia (2020) identifying factors affecting capital structures; the results show that firm size, loan tangibles and opportunities, and loan growth positively impact financial leverage.They studied the correlation between capital structure parameters, such as profitability, business size, non-debt tax shield, growth, and business risk, and the financial leverage ratio (Kim & Berger, 2019;Cruijsen & Knoben, 2021;Kim et al., 2010;Park & Kim, 2003).Besides, Doliente (2006) showed the factors that influence the net profit margin (NIM) of banking institutions in four Southeast Asian nations using a linear regression model, and the results show that a bank's NIM depends on the structure of the bank, such as operating costs, capital, loan quality, collateral, and liquid assets.Although NIM exhibits sensitivity to fluctuations in interest rates for short-term loans, they are still major based on the insufficiently competitive organization of the banking system in the region.Allen et al. (2015), Horst et al. (2006), and Dinh (2020b) also showed that with the inappropriate use of capital, the business may go bankrupt, affecting the deposit and equity markets, they used the endogenous variable model to evaluate capital structure and costs and equity capital from bank deposit financing.The results show that capital structure affects expected returns and that equity generates higher returns than direct investment in risky assets.Dinh (2021) analyzed the relationship between risk and return and found that the higher the profit, the greater the risk by approaching the bias model, such as standards, variances, coefficients of various methods, and matrix functions to measure risk.Thus, banks must have a reasonable capital structure to generate profits and minimize risk.
Following these studies, the factors that determine companies' capital structure were analyzed.Although they are not banks, companies' capital structure is similar to that of banks (Neves et al., 2020;Shi et al., 2020;Liu et al., 2022).However, banks' capital is mainly mobilized from the outside, so it has a high risk.Thus, the empirical results show that capital structure plays an important role in deciding an appropriate investment policy to minimize risk.In addition, Dong and Robin (2018) and Teoh et al. (2013) investigate the possibility of effective capital allocation and risk management by analyzing the relationship between capital structure and portfolio risk level and consider the relationship between capital structure and portfolio risk by analyzing banks' ownership categories.The empirical results show that better-performing banks raise their capital holdings and take on more credit risk while lowering their riskier assets.Wojewodzki et al. (2020) examined the impact of the capital structure of banking enterprises and the adjustment of the capital structure according to the target to meet enterprise loan sources.The empirical findings show that credit ratings have a significant impact on economic growth based on banks' level of capital structure adjustment.The credit rating required for companies to adjust the appropriate capital structure of banks has affected the cash flow of the economy because commercial banks are financial intermediaries that regulate the economy and prompt economic development.Sheikh and Qureshi (2017) investigated how commercial banks analyzed the impact of the capital system on economic development by providing capital to the economy.The empirical results show that large commercial banks have more leverage than small intermediary financial institutions, as well as being more profitable and having a more secure income than small commercial banks; thus, profitability and structure of capital are closely related.It is well understood that saving an enterprise's capital structure is inextricably linked to the capital structure of banks, as banks' job is to mobilize capital and lend to companies.Kumar et al. (2017) examined enterprises' structure of capi-tal using a theoretical model of capital organization and found that enterprises' capital organization affects commercial banks' capital organization, and evidence that the structure of capital is related to financial leverage, which also shows the advantage of the theory of capital organization in discussing commercial banks' profits both theoretically and statistically.Although the results of these studies have different scopes and objectives, they also have different meanings.The empirical findings indicate that the structure of capital has a detrimental impact on bank performance; that is, if the structure of capital is not appropriate, commercial banks' profits decrease (Siddik et al., 2017;Qayyum & Noreen, 2019;Jadah et al., 2020).The majority of the study's findings suggest that banks that achieve success through earnings from assets have a significant positive relationship with the ratio of equity to assets, percentage of liabilities to assets, and bank size (Ghosh & Chatterjee, 2018;Lama et al., 2014;Ayalew & McMilla, 2021).Furthermore, the ratios of shortterm debt to property, longer-term obligations to total assets, and total liabilities to the total value of assets significantly and negatively affect bank profitability.The studies also aim to evaluate the impact of banking and environmental factors on the capital adequacy ratio of banks in Southeastern Europe (Schepens, 2016;Diamond & Rajan, 2002;Harding et al., 2013).
This study has reviewed the literature mentioned earlier and formulated hypotheses based on the information gathered from those sources.Additionally, the study has carefully analyzed previously conducted research and developed proposed hypotheses that align best with the findings and conclusions of the cited literature.
Based on the literature review, this study will test and evaluate the hypotheses to gain insights and draw forecast models.The hypotheses of the model were constructed as follows: H1: The relationship between return on assets (ROA) and bank capital structure in the Vietnam Stock Market.
H2: The connection between the net interest income rate (GROW) and bank capital structure in the Vietnam Stock Market.

METHODOLOGY
The study used Pooled OLS, FEM, and REM models and tested the data using the Likelihood Ratio and Housman methods to eliminate redundant variables (Qian, 1999), which is also consistent with previous studies such as the model of Myers and Majluf (1984)  In which.Total Debt includes all short-term and long-term debt, including short-term loan payables and long-term debt due to borrowing or issuing long-term bonds.Total assets: all assets of the bank.where μ it = ε i + u it ; ε i -Random error with mean 0 and variance ∂ 2 ; u it -Error in the combined evaluation of individual qualities based on the object being evaluated or over a certain period.

Independents variables
The random-effects model assumes that the error component μ it is not connected with any of the explanatory factors.Unobserved time constant qualities provide random effects that are corrected for serial correlation.
A fixed-effects model is a type of statistical model where the model parameters are considered nonrandom or fixed.In contrast, random-and mixedeffects models include some or all of their parameters as random variables.The fixed-effects model can be symbolized as: The pooled OLS model is a regression method used to estimate the coefficients of the selected variables based on the data.Determining variable correlation is essential to selecting the appropriate model for panel data analysis and eliminating multicollinearity.To select these two hypotheses, they are based on probability value as follows: • If the test Prob value < α (5%), H 0 is rejected, H 1 is accepted, and the model has autocorrelation.
• If the test Prob value > α (5%), H 0 is accepted, the model has no autocorrelation.
Further, the FGLS stochastic estimation method was used in this study to control variable variance and autocorrelation, so these models estimate the model randomly and correct errors that may arise from the OLS method.The objective was to test the factor's impact on the capital structure of banks, with statistical significance levels set at 1%, 5%, and 10% to consider whether the pooled OLS model is more efficient than the FEM or REM model and vice versa .
This study aims to explore the influence of commercial banks' capital structure in Vietnam and determine the relationship between macro and endogenous factors of commercial banks on capital structure.The study proposes fiscal policies suitable for Vietnam's economic conditions and long-term strategies and investigates the correlation between profitability and capital structures.1).

Descriptive
The coefficient of the correlation matrix represents the link between the two variables in the model, so this shows the correlation coefficients between the dependent and independent variables in the model (Dinh, 2020a).To test whether there was a correlation between the variables, the data were tested using a correlation coefficient matrix (Table 2).All variables with a P-value < 0.05 were considered statistically significant, with an alpha significance level of 5%.Besides, the mean squared error (MSE) of an estimate is calculated as the average of the squared errors, which is the difference between the estimate and the actual value being evaluated.MSE is a risk function that corresponds to the expected value of the squared error loss or quadratic loss.The difference can occur due to chance or because the estimates do not take into account information that could lead to a more accurate estimate (see Table 3).
Furthermore, the results show that the ROA, TAX, and LIQ variables have a negative relationship with the TLEV variable.This means that as these factors increase, the TLEV decreases.On the other hand, the GROW variable has a positive relationship with the TLEV variable.Therefore, when the GROW variable decreases, it leads to a decreased TLEV variable, so these results are consistent (see REM and random effects models are two approaches for data analysis.In REM, differences between units relate to explanatory variables.In random effects, differences between units are random.REM assumes that the cutoff value of cross-units is randomly drawn from a larger total sample, expressed as a deviation from the mean (Bollen & Brand, 2010; Dinh, 2022).
The REM regression analysis shows that independent variables have a close relationship with the dependent variable (R-squared = 62.34%).The model fits well with Prob > F = 0.0000 < 5%.ROA is not statistically significant (P-value = 0.290 > 0.05), while the remaining variables are significant (P-value < 0.05).TAX and LIQ have negative coefficients, while GROW has a positive coefficient, implying that an increase in profitability leads to an increase in capital structure (see Table 5).This empirical result is similar to the literature (Sufian & Habibullah, 2014; Agusman et al., 2014).
To analyze the impact of factors on the capital structure of 26 Vietnamese banks listed from 2010 to 2022, the study used panel data analysis with pooled OLS, FEM, and REM.
This study used statistical tests to compare different models and evaluate multicollinearity.The F-test and Hausman test were used to compare OLS and FEM models, while VIF was used to check for multicollinearity (see table 6).Additionally, the study applied FGLS estimates to the model with heteroskedasticity.
After conducting the Hausman test, it was found that the probability value was less than 0.05, spe- cifically 0.0001.Therefore, the null hypothesis H 0 was rejected.This implies that the FEM model fits the data sample better than the REM model.Additionally, the FEM model was tested for ho-mogeneity, autocorrelation between residuals, and multicollinearity, and it was found to be a good fit model.Hence, the FEM model was selected as the goodness-of-fit model.Note: (***) P-value coefficient < 0.01, (**) the significance level coefficient < 0.05, and (*) the p-value coefficient < 0.1.
The Wooldridge test showed a P-value of 0.1103 > 0.05 (significant level 5%), which means that hypothesis H 0 cannot be rejected.Therefore, it can be concluded that the model does not have serial autocorrelation.The study then tested for variable variance based on the results of the F-test (see Table 7), which showed a p-value of 0.000 < 0.05.This means that H 0 should be rejected, and the FEM model is more efficient than the OLS Poole model.
The Breusch-Pagan LM test showed that the model had a P-value of 0.000 < 0.05 (significant level 5%), which means that H 0 was rejected, and H 1 was accepted, so this indicates that the model has the variable variance phenomenon.
E mpirical findings show that the TAX variable, which has a beta coefficient of -0.05967, has a negative relationship with a bank's capital structure, so the tax index helps banks avoid tax costs, but, on the contrary, reduces banks' profits and capital struc-ture.Therefore, the manager considers taxation cost, which affects the bank's profitability and capital structure.The GROW variable has a beta coefficient of 0.000509, which has a positive relationship with banks' capital structure; thus, when banks' revenue increases, the banks' profits and capital structure increase.The LIQ variable, which has a beta coefficient of -0.00045, has a negative relationship with banks' capital structure; thus, when banks' debt increases, their capital structure decreases.Therefore, bank managers need to increase their current assets and reduce their debt to improve their capital structures.
The ROA variable, which has a negative relationship with a commercial bank's capital structure, has a beta coefficient of -0.01796, so, the higher the bank's profit, the higher its profitability.that the higher the income tax, the more detrimental its effect on their capital structure.Therefore, commercial banks need to constantly improve their internal control systems to identify risks, including financial ones.When promptly identifying risks, commercial banks take many measures to adjust operations and develop short-, medium-, and longterm financial planning goals for their capital source policies.
Commercial banks should improve their business performance because the ROA factor has a strong impact on capital structure and a positive relationship with capital structure (beta = 0.01693).Therefore, commercial banks can enhance their strengths and seek capital to achieve high business performance.However, commercial banks that need to mobilize capital must have specific plans to minimize bad debt.When commercial banks perform well, instead of making loans, they can utilize financial and capital resources from retained earnings, which are less expensive than debt charges, to issue new shares.However, commercial bank financial management must assess the dividend payment ratio and retained earnings to guarantee that shareholders' interests are balanced with optimal capital usage.Furthermore, when commercial banks do well in business, they can improve their credit ratings in the financial market, allowing them to raise cash from creditors and investors at a cheaper cost.
The empirical results also show that the net interest income rate (GROW) has a positive relationship with commercial banks' capital structure, meaning that commercial banks' growth is mainly based on the net interest income from lending to individuals and economic organizations.Therefore, commercial banks that want to grow quickly must increase their lending to individuals and economic entities.
Liquidity is negatively related to capital structure, although its impact on capital structure is very small, with a beta coefficient of -0.00055, indicating that commercial banks need to improve their liquidity and ensure debt from funding sources and shortterm capital sources, avoiding the situation in which commercial banks are insolvent, which adversely affects capital structure.Risk managers need to manage liquidity well and simultaneously have measures to coordinate the liquidity management of assets and liabilities and asset liquidity management to take advantage of cash in the treasury and ensure mobilized capital in the economy to increase liquidity.Managers should be aware of liquidity safety risks, especially credit risk.Loan risk and liquidity risk are interconnected, as are loan growth rates.Banks have recently paid more attention to liquidity risk management.Empirical results show that three factors, GROW, TAX, and LIQ, are statistically significant in the OLS, REM, and FEM models for the ROA factor.
The FEM model has some defects, such as multicollinearity, series correlations, and heteroskedasticity errors, which are difficult to overcome (see Table 7).

CONCLUSION
In the realm of commercial banking, there is a significant focus on capital structure and efficiency.The primary objective of this study is to identify ways to optimize capital use and maximize profits.This involves a range of considerations, such as determining the ideal capital size to ensure stability and control capital mobilization costs.Additionally, the study aims to increase operational efficiency, which can lead to enhanced profitability and ensure the safety of investments.By analyzing and optimizing the capital structure of commercial banks, this study identifies ways to improve long-term financial stability and growth.Empirical results based on factors affecting twenty-six commercial banks' capital structure in the 2010-2022 period, with a total of 156 observations, show that the sample size is appropriate and reliable and that the empirical results can be applied to all domestic and foreign commercial banks for reference.Although many other factors can affect capital structure, this study selected basic factors that have a major influence on capital structure.In addition, the models were also applied to choose the best model with the most accurate forecast results, and through the above-mentioned criteria, the FEM model was selected for forecasting.
Based on the capital structure methodology and empirical research in the globe and Vietnam as a foundation for building a model suitable for the research objectives, four factors affecting capital structure were identified.Bank capital in Vietnam's stock market includes tax rate (TAX), bank profitability (ROA), net interest income (GROW), and liquidity (LIQ).The empirical results suggest policies on risk management, profit growth, etc., and the study has clarified the methodology of capital structure in general, its general influencing factors, and the factors that influence commercial banks' capital structure in the Vietnamese stock market.
The empirical results are particularly useful for bank managers in Vietnam's stock market, and this study's empirical findings have significant consequences for bank managers in building an optimum capital structure.Banks in Vietnam's stock market should prioritize retained earnings or equity overborrowing.On the other hand, the experimental results show that, in addition to the above factors, 2.1 ROA: Bank profitability and it is calculated byReturn on Assets.
2.2 GROW: Net Interest Margin (NIM) reflects the growth rate of interest income relative to the growth rate of expenses (%), (Next year's net interest income minus that of the previous year's net interest income) divided by the previous year's net interest income multiplied by 100 percent.2.3 TAX: Corporate income tax rate (%), It is important to consider the calculation of corporate income tax on profits.Corporate income tax directly affects and reflects the bank's business situation.In addition, the bank's performance and the overall state of the economy also have a significant impact on corporate income tax.2.4 LIQ: Liquidity, customer's account outstanding (before provision) divided by the customer's deposit.other words, a regression model with fixed crosseffects builds on the assumption of different origins between diagonal units, but the slope is constant, the REM model is: Banks and Bank Systems, Volume 19, Issue 2, 2024 http://dx.doi.org/10.21511/bbs.19(2).2024.10 To decide between H 1 or H 0 , use a probability value test as: If the test value Prob < α (5%), H 0 is rejected, and H 1 is accepted.If the test value was Prob > α (5%), H 0 is accepted.If the test value Prob > α (5%), H 0 is accepted, and the model has homoscedasticity.Autocorrelation test: The autocorrelation test helps to detect whether the research model is autocorrelated.For the autocorrelation test, there will also be two hypotheses: H 0 : The model has no autocorrelation, and H 1 : The model has autocorrelation.
Tests such as the F-test, Breusch-Pagan Lagrangian, and Hausman were used to select the best-fit model.• If the test value was Prob < α (5%), H 0 is rejected, H 1 is accepted H 1 , and the model has a heteroskedasticity.Banks and Bank Systems, Volume 19, Issue 2, 2024 http://dx.doi.org/10.21511/bbs.19(2).2024.10• statistics summarize data samples and parameters.The most common types are mean, median, and mode.They provide statistical indices like standard deviation.

Table 2 .
Correlation variables analysis Source: Stata software.

Table 1 .
Descriptive statisticsTherefore, the F-test result is F(4, 151) = 15.13.The F index is 15.13, which shows that the R-square in the Poole OLS model is statistically significant.With a prob > F of 0.0000 < 5%, it can be concluded that this regression model is reliable.

Table 4 .
Regression results according to the FEM model Source: Stata software.

Table 5 .
Regression results by the REM model

Table 6 .
Regression results of models, including Pooled OLS, FEM, and REM Source: Stata software.

Table 7 .
Test results