Mergers and Acquisitions’ Moderating Effect on the Relationship Between Credit Risk and Bank Value: A Quantile Regression Approach

1

Introduction part is roughly designed. I recommend the authors to follow the academic style of writing the introduction. For this, I recommend to ensure the presence of rationale of study, background, summary of results, theoretical, empirical, and practical contributions.

We rewrote the introduction to ensure the presence of:

A)    Background – First and second paragraphs: concise overview of credit risk, bank value and M&A and their importance in banking sector.

B)     Rationale of study –

Third paragraph: concise the credit risk, bank value and M&A relationships.

Fourth paragraph: highlight the research motivation in a quantile-based framework.

Fifth paragraph: research gap.

Sixth paragraph: objective.

C)     Novel contribution- Seventh paragraph: theoretical, empirical, and practical contributions.

D)    Summary of results – Eighth paragraph: concise summary of results.

E)     Implications – Nineth paragraph: refined with more actionable points.

The new introduction:

Since the global financial crisis (GFC) of 2007-2008, credit risk topic has become a greater concern in the financial industry. The high financial leverage nature of banks makes credit risk management a top priority. Unlike other institutions, banks adapt traditional asset and liabilities management into asset default and liabilities default management. Liquidity monitoring focuses on preventing liquidity defaults. Profitability is a key consideration, assessed primarily from the perspective of economic default (Chen & Kuei, 2024). The consequences of the GFC on the global economy were initially reflected in the collapse of the value of institutions operating in the banking sector, demonstrating the importance of understanding the factors that influence banks’ value, which is commonly linked to stock price (Amimakmur et al., 2024).

Worldwide, the phenomenon of M&A in the banking sector has been constantly increasing. While in the year 1985 there were only 247 deals, the number peaked in the year 2018, reaching over 2,000 deals (Statista, 2024). M&A benefit banks by raising capital, expanding, achieving a competitive advantage, enhancing financial operating performance and bringing financial stability (Chakraborty & Das, 2024).

Montgomery and Takahashi (2014) find that M&A lead to an increase in both shareholders’ wealth and the credit risk of banks involved in such transactions. Hassan and Giouvris (2020) observe that local bank-to-bank M&A create shareholders wealth, with local M&A associated with a reduction in credit risk, while cross-border M&A are linked to an increase in risk. Both papers rely on traditional conditional mean analysis techniques, including multivariate regression, robust regression, maximum likelihood regression and weighted least squares regression. However, Wang et al. (2024) clarify that these methods rely on assumptions of normality and homoscedasticity, which are often not met in real-world financial data. Given the high volatility and non-normal distribution of such data, these methods may be inadequate for estimation.

An alternative approach, quantile regression, offers more robust estimates and provides a comprehensive analysis of business performance changes in response to specific events. Especially, when Pop and Pop (2024) observe that markets price risk differently for banks in the upper locations of the spread distribution, where market discipline being more tougher for risker banks. Similarly, Fich et al. (2018) find that the characteristic related to the acquiring banks have varying effects on the distribution of abnormal returns. To understanding complex predictor-response relationships, Cunningham et al. (2020) consider quantile regression an ideal analytical tool, as it captures variations in predictor effects across different response quantiles.

While the traditional conditional mean models can address the question “how horizontal M&A affects the relationship between credit risk and bank value”, they cannot answer an equally important question “how horizontal M&A moderates this relationship across different quantiles of the bank value distribution.”

Therefore, this paper investigates the moderating effect of horizontal M&A on the relationship between credit risk and bank value within a quantile-based framework.

Current literature provides explanations about the relationship of credit risk with value in the context of M&A within banking industry. Our paper offers a deeper theoretical understanding of this relationship by capturing the heterogeneity in predictor-response relationship across the distribution of response, providing a novel contribution to the theoretical literature. Empirically, our novel results cannot be captured using standard conditional mean estimations. We introduce quantile regression to uncover how lower-valued banks and higher-valued banks exhibit different sensitivities to credit risk in M&A activities, effectively addressing challenges related to violations of normality and homoscedasticity in the financial data. Practically, our novel findings guide investors in identifying rewarding investment opportunities, assist bank managers in balancing risk and value creation during M&A, and inform policymakers about regulating credit risk exposure in M&A activities within the banking sector.

The results of this paper reveal that credit risk has a significant negative effect on bank value across the entire distribution, with magnitude of this effect decreasing from lower to upper locations. This indicates lower-valued banks are more vulnerable to a steeper decline in value as a result of credit risk, compared to higher-valued banks. Horizonal M&A exhibit a stable and significant positive effect on bank value across the entire distribution, suggesting that horizontal M&A consistently enhance bank value, regardless of the bank’s valuation. However, the moderating effect of horizontal M&A significantly magnifies the negative impact of credit risk on bank value across the entire value distribution, but without statistically significant differences observed from lower to upper locations of the distribution. This implies that horizontal M&A amplifies the adverse effect of credit risk on bank value uniformly, across banks, regardless of their valuation, assuming other factors remain constant.

Our results encourage investors to invest in banks that intend to merge and acquire, as such activities increase their wealth. However, simultaneously, they should carefully consider the credit risk profile of these banks because credit risk plays a significant counterfactor to value creation, especially for low-valued banks. We advise investors to utilize recent machine learning techniques, such as Decision Trees, to classify and categorize these investment opportunities based on credit risk and bank value. This will exclude investing in banks that are willing to M&A with other banks when they are low-valued and experience high credit risk, and prioritize those that are high-valued and experience low credit risk, as these represent the best investment opportunities. Additionally, for investors who hold a portfolio of bank stocks, we advise them to incorporate a fundamental-based diversification strategy, where they overweight banks actively involved in horizontal M&A and underweight low-valued, high-credit risk banks, as these are more vulnerable to significant declines in value. This enables investors to maximize their portfolio value while minimizing exposure to the adverse effects of credit risk and M&A activities.

For practitioners, the paper’s findings advise board of directors in the banking sector to consider horizontal M&A as a growth strategy, as it enhances value across the entire banking sector. However, the findings emphasize the importance of implementing tailored risk management strategy for lower-valued banks during M&A processes to minimize the adverse effects of credit risk. This approach ensures that M&A activities leverage the positive effects to the interest of shareholders. Additionally, the findings suggest that board of directors utilize a credit risk–bank value monitoring tool that tracks both credit risk exposure and value simultaneously. This tool should adjust credit risk exposure based on the bank’s value, tightening exposure when value is low and loosening it when value is high, thereby balancing risk and reward more effectively.

Policymakers can benefit from our results by establishing a supportive framework that encourages healthy M&A activities in the banking sector, ensuring these activities contribute to growth while maintaining financial stability. We also suggest developing regulatory frameworks that address the impact of credit risk exposure on the banking sector, recognizing the increased vulnerability of lower-valued banks to greater declines in value due to credit risk; a vulnerability that becomes even more pronounced during M&A transactions. Approvals for M&A should be conditioned on banks demonstrating a low credit risk profile and/or strong valuation. Regulators should establish a dynamic capital buffer that calibrated to credit risk exposure and bank value parameters, along with introducing event-specific capital buffers during M&A activities to safeguard against foreseen and unforeseen credit risks. Additionally, policymakers can establish a monitoring mechanism to track credit risk exposure and bank value simultaneously, ensuring that banks to adhere to strict credit risk policies when their value fall below specified levels.

2

In introduction, please replace the outdated references with recent ones.

The new introduction has now 10 references, 6 of them are new and from year 2024. We could not replace the rest which are 2 from year 2020, 1 from year 2018 and 1 from year 2014.

3

In literature review, I see many outdated studies. Please ensure that at least 35 % references are from the year 2024. Please update the literature.

The literature review originally contained 67 references, while the entire paper had 112 references. The second reviewer raised concerns about the large number of references. To address your both suggestions, we removed around 20% of the total references (22 references), reducing the literature review to 43 resources. The removal was based on eliminating redundant content or references deemed less important. I then replaced 35% of the remaining 43 sources with newer 2024-year references, ensuring they either shared similar content or added value to the research objectives. Note that one 2024 reference was already there, and a one new 2024 reference was used twice; thus, I added new 13 references.

Original removed or replaced references:

(Abedifar et al., 2018; Akhtaruzzaman et al., 2021; Altunbaş & Marqués, 2008; Amel & Rhoades, 1989; Andreou et al., 2021; Beaver et al., 1989; Beccalli & Frantz, 2009; Bernad et al., 2010; Chen & Vashishtha, 2017; Cornett & Tehranian, 1992; Dimitropoulos et al., 2010; DoĞAn & Yildirim, 2017; Du & Sim, 2016; Ekinci & Poyraz, 2019; Elsas, 2004; Feldman & Hernandez, 2021; Hansen & Lott, 1996; Hassen et al., 2018; Kim, 2023; Lu, 2023; Madugu et al., 2020; Madura & Wiant, 1994; Mirzaei et al., 2013; Moeller et al., 2004; Naceur & Omran, 2011; Ngo, 2019; Papadimitri et al., 2019; Rahman et al., 2016; Salas & Saurina, 2003; Sapienza, 2002; Seth, 1990; Taylor, 2022; Turk Ariss, 2010; Vallascas & Hagendorff, 2011; Widjaja & Ariefianto, 2022).

Year 2024 references:

(Amimakmur et al., 2024; Arbolino et al., 2024; Chakraborty & Das, 2024; Chen et al., 2024; Cobbinah et al., 2024; Dinger et al., 2024; Ishu & Mallik, 2024; Jou et al., 2024; Kaur & Bala, 2024; Kiosses et al., 2025; Na & Shimizu, 2024; Sghaier & Hamza, 2024; Takahashi & Vasconcelos, 2024; Wang, 2024)

4

Please add the rationale for sampling the BHC and span.

We rewrote the 2.1. Data and Sample Description in Methodology as below:

The data for this paper are compiled on an annual basis, and are obtained from several sources. M&A data, and the FR Y-9C reports, which offers consolidated financial statements, are both retrieved from the Federal Financial Institutions Examination Council (FFIEC). Market-related data are acquired from the YCharts platform. Macroeconomic data are obtained from the International Monetary Fund (IMF).

The data focus on BHC within the U.S. banking industry. This focus is justified by the fact that the U.S. banking sector has witnessed over 10,000 M&A transactions since 1980 (Adams, 2012), making it an ideal field for M&A research. Additionally, approximately 80% of U.S. banks are part of a BHC structure, meaning that BHCs represent the banking industry in U.S. environment (Fed Partnership, 2024).

Our sample includes 110 BHC, spanning the period from 2000 to 2022, covering 23 years. This combination of cross-sectional (BHC) and time spans (Years) data forms a panel dataset, resulting in 2,530 observations.

At the end of 2000, there were 5,845 active U.S. BHC, but by the end of 2022, this number had decreased to 3,713. This paper uses two specific selection criteria to construct the sample: BHC maintained publicly traded and consistently submitted the FR Y-9C report throughout the analysis period. Only 110 BHC met these criteria.

The choice of the time span is driven by several reasons. First, data collection and analysis conducted in mid-2023, meaning the most recent available financial data at that time were from the end of 2022. Second, the rationale for this time span is based on technical considerations associated with the quantile analysis of Machado and Santos Silva (2019). In this quantile regression estimators are biased when the number of BHC (n) is large relative to the number of time periods (T), with a general recommendation that n/ T≤10. For clarification, dividing 110 BHC by 10 years (2013-2022) results in a ratio of 11, which would provide biased estimators. To avoid such bias, the maximum available time span provided by FFIEC dataset, starting from the year 2000, was selected.

5

Policies should be results oriented. 

The results are about how credit risk affects bank value, how M&A affects bank value, and how M&A moderate how credit risk affects bank value. Therefore, we rewrote implications part of introduction where:

Policies are refined in Ninth, Tenth and Eleventh paragraphs:

A)    Investors: Decision trees for choosing best investment opportunities, and fundamental-based diversification and tailored risk management strategy for portfolio optimization.

B)     Practitioners: M&A as growth strategy for leveraging positive effects to the interest of shareholders, credit risk–bank value monitoring tool to adjust exposure and balancing risk and reward more effectively.

C)     Policymakers: Frameworks encourage M&A and manage credit risk for growth and stabilize financial system, such conditional approvals, capital buffers and monitoring mechanism.

1

Clearly highlight the novel contributions of the study

It is highlighted in Seventh paragraph as theoretical, empirical, and practical contributions.

“Current literature provides explanations about the relationship of credit risk with value in the context of M&A within banking industry. Our paper offers a deeper theoretical understanding of this relationship by capturing the heterogeneity in predictor-response relationship across the distribution of response, providing a novel contribution to the theoretical literature. Empirically, our novel results cannot be captured using standard conditional mean estimations. We introduce quantile regression to uncover how lower-valued banks and higher-valued banks exhibit different sensitivities to credit risk in M&A activities, effectively addressing challenges related to violations of normality and homoscedasticity in the financial data. Practically, our novel findings guide investors in identifying re-warding investment opportunities, assist bank managers in balancing risk and value creation during M&A, and inform policymakers about regulating credit risk exposure in M&A activities within the banking sector.”

2

Refine implications for investors, practitioners, and policymakers with more actionable points.

We refined implications with actionable points in Ninth, Tenth and Eleventh paragraphs, as below:

A)    Investors: Decision trees for choosing best investment opportunities, and fundamental-based diversification and tailored risk management strategy for portfolio optimization.

B)     Practitioners: M&A as growth strategy for leveraging positive effects to the interest of shareholders, credit risk–bank value monitoring tool to adjust exposure and balancing risk and reward more effectively.

C)     Policymakers: Frameworks encourage M&A and manage credit risk for growth and stabilize financial system, such conditional approvals, capital buffers and monitoring mechanism.

3

Strengthen the motivation for the study, especially regarding the importance of examining credit risk, M&A, and bank value in a quantile-based framework.

The rationale of study was rewritten. While Fourth paragraph highlights the research motivation in a quantile-based framework, Fifth paragraph highlights research gap related to quantile-based framework.

In summary, quantile-based framework overcome outperforms traditional conditional analysis in addressing the high volatility and non-normal distribution of real-world financial data; it provides a comprehensive analysis of business performance changes in response to specific events; it is ideal tool for complex relationships; captures variations in predictor effects across different response quantiles.

While the traditional conditional mean models can address the question “how horizontal M&A affects the relationship between credit risk and bank value”, they cannot answer an equally important question “how horizontal M&A moderates this relationship across different quantiles of the bank value distribution.”

4

Establish how this research builds on and goes beyond existing literature.

It is established in Seventh paragraph:

“Current literature provides explanations about the relationship of credit risk with value in the context of M&A within banking industry. Our paper offers a deeper theoretical understanding of this relationship by capturing the heterogeneity in predictor-response relationship across the distribution of response, providing a novel contribution to the theoretical literature.”

For “Current literature” I put two references in the beginning of Third paragraph that explain the relationship of credit risk with value in the context of M&A within banking industry.

5

Ensure clarity and logical flow in presenting the relationships between credit risk, M&A, and bank value.

We adjusted the literature review by removing 33% of its current literature as it redundant or deemed less important. We also updated 35% of it but replacing the outdates studies with new 2024 references that either share same similar content or adds value to the research objective.

6

Refine the justification for using the Quantiles via Moments estimator, emphasizing its superiority over other methods.

We refined the justification in 2.3. Empirical Analysis in Methodology as below:

“The MM-QR model shows its superiority over other quantile regressions with fixed effects method in four ways. First, it shares most of robustness properties of Koenker and Bassett (1978) quantile regression, yielding the same inherently robust conditional quantiles estimators. Second, it is well-suitable for panel data analysis, as it allows methods limited to conditional means regression-such as incorporating individual fixed effects-to be applied in a quantile regression framework. Third, it avoids incidental parameter bias when including fixed effects in the quantile regression model. Fourth, it is simple to implement, as it does not require additional complex techniques such as penalizing, smoothing and jackknifing to yield consistent estimates”

7

Including detailed explanations of robustness checks performed and any alternative approaches tested.

1)      We wrote this paragraph at the end of 3. Empirical Results and Discussion section to summarize the detailed explanations of robustness checks performed.

“The robustness of our MM-QR results is validated through a series of multiple checks: variables validity, conditional quantile validity, fixed effects validity, bootstrapping and consistency validity. First, we confirm that the variables are free of multicollinearity and unit root issues, as addressed in Table 3, Table 4 and Figure 1, using correlation matrix and VIF (Belsley, 1980), Pesaran's CD test (Pesaran, 2021), average line graphs (Wang et al., 2018), and The K&T test (Karavias & Tzavalis, 2014). Second, we illustrate that conditional quantile regression of Koenker and Bassett (1978) outperforms conditional mean regression by effectively handling the non-Gaussian residuals (Royston, 1983), heteroskedasticity (Cook & Weisberg, 1983), and autocorrelation (Drukker, 2003) in OLS and LSDV regressions, as presented in Table 5. Third, using Wald test (F-Statistic), we reveal in Table 5, the necessity of including individual fixed effects to the conditional quantile regression of to avoid issues in endogeneity and omitted variable bias. Such, necessity cannot be directly implemented in Koenker and Bassett (1978) model due to incidental parameter bias (Koenker et al., 2017); Therefore, we introduce MM-QR of Machado and Santos Silva (2019), which can include individual fixed effects into the quantile regression model without such bias. Fourth, all results presented in Table 6 and Table 8 are derived via bootstrapping, ensuring robust estimates (Efron & Tibshirani, 1994). Furthermore, the partially consistency of MM-QR results in Table 8 with those from Koenker and Bassett (1978) quantile regression in Table 6, as well as the OLS and LSDV results in Table 5, along with similar outcomes of hypotheses testing using Wald test in Table 7 and Table 9, further validate the robustness of our results.”

2)      Our analysis has two alternative approaches and each approach has two alternative methods. we compared between all of them to find the best model as what discussed above

A)    Approach one is Conditional mean approach: Sub approaches are OLS and LSDV regressions.

B)    Approach two is Conditional Quantile approach Sub approaches are Koenker and Bassett (1978) regression and Machado and Santos Silva (2019) regression.

8

The number of sources (references) is quite high, 112

The literature review originally contained 67 references, while the entire paper had 112 references. we removed around 20% of the total references (22 references), reducing the literature review to 43 resources. The removal was based on eliminating redundant content or references deemed less important. I then replaced 35% of the remaining 43 sources with newer 2024-year references, ensuring they either shared similar content or added value to the research objectives. Note that one 2024 reference was already there, and a new 2024 reference was used twice; thus, I added new 13 references.

Original removed or replaced references:

(Abedifar et al., 2018; Akhtaruzzaman et al., 2021; Altunbaş & Marqués, 2008; Amel & Rhoades, 1989; Andreou et al., 2021; Beaver et al., 1989; Beccalli & Frantz, 2009; Bernad et al., 2010; Chen & Vashishtha, 2017; Cornett & Tehranian, 1992; Dimitropoulos et al., 2010; DoĞAn & Yildirim, 2017; Du & Sim, 2016; Ekinci & Poyraz, 2019; Elsas, 2004; Feldman & Hernandez, 2021; Hansen & Lott, 1996; Hassen et al., 2018; Kim, 2023; Lu, 2023; Madugu et al., 2020; Madura & Wiant, 1994; Mirzaei et al., 2013; Moeller et al., 2004; Naceur & Omran, 2011; Ngo, 2019; Papadimitri et al., 2019; Rahman et al., 2016; Salas & Saurina, 2003; Sapienza, 2002; Seth, 1990; Taylor, 2022; Turk Ariss, 2010; Vallascas & Hagendorff, 2011; Widjaja & Ariefianto, 2022).

Year 2024 references:

(Amimakmur et al., 2024; Arbolino et al., 2024; Chakraborty & Das, 2024; Chen et al., 2024; Cobbinah et al., 2024; Dinger et al., 2024; Ishu & Mallik, 2024; Jou et al., 2024; Kaur & Bala, 2024; Kiosses et al., 2025; Na & Shimizu, 2024; Sghaier & Hamza, 2024; Takahashi & Vasconcelos, 2024; Wang, 2024)

1

Quantile regression outperforms the conditional mean function as it is robust over a wide class of non-Gaussian error distributions. Throughout the manuscript, there are no evidence or verification to check the M/B, NCO and MA for the data suit the condition from Koenker and Bassett (1978).

In Table 2. Descriptive Statistics, we report that all variables exhibit significant skewness and kurtosis, therefore they are non-Gaussian. This gives an early indicator that the distributions of error term after doing the linear regression may be non-Gaussian. Thus, the data will be suit for Koenker and Bassett (1978) model after approve that the error term is non-Gaussian, not the variables.

In Table 3. Cross-sectional Dependence and Stationarity Tests, we show that all variables are stationary. This ensures that there are no unit roots or trends in the data, thus, the variables are suitable for modeling.

In Table 4. Correlation Matrix and VIF, we demonstrate the absence of multicollinearity among regressors, thus, the variables are suitable for modeling.

In line with your comment(s), we cannot write an additional explanation in Methodology and Results because it is already explained.

2

The Quantile Regression (QR) proposed by Koenker and Bassett (1978) uses an asymmetric loss function, what the lose function do you use in this manuscript?

Machado and Santos Silva (2019) combine the location and scale functions to propose an estimator of the conditional quantiles (stated at the first paragraph of their paper).

In line with your comment(s), we will state this sentence, as below, in section 2.3. Empirical Analysis

“Machado and Santos Silva (2019) introduce the Quantiles via Moments estimator (MM-QR), which combines the location and scale functions. This method identifies the same conditional quantiles as those estimated using the usual asymmetric loss function of Koenker and Bassett (1978)”

3

With the linear model for M/B, NCO and MA, is the error distribution non-Gaussian? If it is not non-Gaussian, there is serious flaw in applying quantile regression approach to gain convincing conclusions.

The error distribution of M/B, NCO, MA, NCOMA and controls is non-Gaussian.

In Table 5. Linear Regressions, we present the results of Shapiro-Francia W’ test for non-normality (Royston, 1983), the Breusch–Pagan/Cook–Weisberg test for heteroskedasticity (Cook & Weisberg, 1983), and the Wooldridge test for autocorrelation (Drukker, 2003). The Shapiro-Francia W' test strongly rejects the null hypothesis of normality in the residuals, indicating a non-Gaussian error distribution. The Breusch–Pagan/Cook–Weisberg test reveals significant heteroskedasticity in the residuals, and the Wooldridge test confirms the presence of autocorrelation. Therefore, the non-Gaussian nature of the residuals, alongside evidence of heteroskedasticity and autocorrelation, justifies the use of Quantile Regression in this study.

Additionally, If the error distribution is Gaussian, we can justify our interest in QR by our research theoretical contribution “Current literature provides explanations about the relationship of credit risk with value in the context of M&A within banking industry. Our paper offers a deeper theoretical understanding of this relationship by capturing the heterogeneity in predictor-response relationship across the distribution of response, providing a novel contribution to the theoretical literature.

In line with your comment(s), we cannot write an additional explanation in Methodology and Results because it is already explained.

4

The manuscript takes bank value from the market-to-book ratio, and credit risk from the ratio of net charge-offs, and M&A activities using a dummy variable set to one for bank engaged as bidders in M&A transactions and only for the years in which those transactions are completed. The data includes 110 active BHC from 2000 to 2022 with only 23 years. what is your time lag? how many M/B values in your empirical analysis? If the time lag is in year, there are only 23 M/B values. The quantiles does not seem make any sense.

Since we analyze panel data, we have 2,530 of M/B values (23 years × 110 BHCs).

In line with your comment, we will write the below paraph in section 2.1. Data and Sample Description

“Our sample includes 110 BHC, spanning the period from 2000 to 2022, covering 23 years. This combination of cross-sectional (BHC) and time spans (Years) data forms a panel dataset, resulting in 2,530 observations.”

5

Line 283 - line 297: Quantile regression outperforms the conditional mean function as it is robust over a wide class of non-Gaussian error distributions. Throughout the manuscript, there are no evidence or verification to check the M/B, NCO and MA for the data suit the condition from Koenker and Bassett (1978). The Quantile Regression (QR) proposed by Koenker and Bassett (1978) uses an asymmetric loss function, what the lose function do you use in this manuscript? With the linear model for M/B, NCO and MA, is the error distribution non-Gaussian? If it is not non-Gaussian, there is serious flaw in applying quantile regression approach to gain convincing conclusions.

These comments were answered previously from point 1 to 3

6

Lines 402-404, Does the quantile regression only involved with NCO and M/B for the first part of Table 9? Or some quantile regression formula did not show up before (certainly cannot be formula (1) and formula (2))? Same confusions for the other parts.

Our Quantile regression involve M/B as dependent variable, NCO, MA, NCOMA + Controls. (This set of variables is present in both equations without any difference.) See lines 292-298, and 329

We have two formulas of Quantile regression:

Formula (1) employes the method of Koenker and Bassett (1978). See line 291.

Formula (2) employes the method of Machado and Santos Silva (2019). See line 326

Our primary focus is on Formula (2), not Formula (1) because Formula (2) is better for our data. If we do not add fixed effects to the Quantile model, we will have endogeneity results from omitted variable bias. With 110 BHC in the sample, we will have 110 dummy fixed effect variables. If we include these 110 variables to Koenker and Bassett (1978) model, we will have incidental parameter bias. Therefore, we use  Machado and Santos Silva (2019) as it overcomes both issues omitted variable bias and incidental parameter bias. See lines 306-326

Table 9 is Coefficients Equality Test; it examines the equality of quantile coefficients of Table 8. We need Table 9 to examine if we reject or accept our research hypotheses. See lines 299-305

For illustration:

Our H1: the effect of credit risk on bank value varies significantly across quantiles of bank value.

Our Machado and Santos Silva (2019) Quantile regression results.

You see that NCO coefficient at p10 (21.64) differs than p20 (19.44) and differs than p30 (17.85) … etc. This is not enough to clarify that they differ, thus we accept H1. You need statistical test to reach this conclusion which is Walid test (Cameron & Trivedi, 2022).

Wald test’s H0: the difference between the coefficient estimates at different quantiles equal to zero. Between p10 and 20, we confirm there is difference. Between p10 and p30, we confirm there is difference… and so on.

We repeat the same thing MA and NCOMA as they represent Hypothesis 2 and Hypothesis 3

In line with your comment(s), we cannot write an additional explanation in Methodology and Results because it is already explained.

7

Lines 416-423: The statement is lack of evidence to conclude. Table 9 may build on the non-verifi
ed quantile regression
first, or M&A success or failure can be predicted by linear (additive) model without too many control variables. The sentence of Gauss theorem is not violated, is not being speci
fied. What exactly do you refer here? for error term or for M/B?

In line with your comment(s), we wrote supportive sentences, as below, after the specified lines

“The findings of MA in Table 8 are consistent with those in Table 9. Bank value is positively affected by horizontal M&A. However, the magnitude of this effect remains positive and is relatively stable across all M/B percentiles. Thus, the posed H₂: the effect of horizontal mergers and acquisitions on bank value varies significantly across quantiles of bank value, cannot be supported, suggesting that the linear prediction of the success or failure of M&A is adequate as long as the Gauss theorem is not violated. The magnitude of the effect of horizontal M&A on bank value appears to be influenced by factors beyond the M/B of the acquiring banks, such as the size of acquirer. Alexandridis et al. (2017) show that the dynamics of wealth creation in M&A change based on acquirer size, with smaller banks outperform large banks in wealth creation. This is supported by DeYoung et al. (2009), who suggest that the primary cause for large bank to engage in M&A is for building an empire, rather than wealth creation.”

However, we cannot state that that our model may be built on non-verifi
ed quantile regression
first, or M&A success or failure can be predicted by linear (additive) model without too many control variables because of several reasons.

First, we reported our results as what they are. The robustness of our MM-QR results is validated through a series of multiple checks: variables validity, conditional quantile validity, fixed effects validity, bootstrapping and consistency validity.

Second, we reviewed literature as much we can to include 13 control variables. Even with these 13 control variables, they were not enough to avoid endogeneity in omitted variable bias. We cannot control all factors in real world; thus, we included fixed effects as a replacement for adding more controls.

In line with your comment(s), we will not specify which is not violated in Gauss theorem, error term or M/B.

Because the Gauss theorem pertains exclusively to the error. It is neither reasonable, possible, and correct to refer to the Gauss theorem in relation to the variables. Therefore, there is no need to specify whether the violation is for a variable or an error term.

8

Based on the conclusions, Hypothesis H2 and H3 are not supported by quantile regression, supposed that the rest of work is proper. Does that mean quantile regression with data you have is not suitable for the empirical analysis? This draw back to my earlier question on whether the conditions for applying Koenker and Bassett (1978) is satisfied.

The quantile regression and data used are suitable for the empirical analysis.

A)    First, we have 2,530 observation which is sufficient enough. 2.1. Data and Sample Description

B)     Second, we proved that the variables are stationary and free of multicollinearity. Table 4.

C)     Third, we proved that the error term of linear regression is non-Gaussian. The 3^ed, 4^th and 5^th tests in Table 5.

D)    Forth, we proved that we need fixed effects to avoid endogeneity, thus we used the quantile regression of Machado and Santos Silva (2019). The 3^ed, 4^th and 5^th tests for the need of quantile regression and 6^th tests in Table 5 for the need of including fixed effects.

Our focus is on Machado and Santos Silva (2019) quantile regression (Quantiles via Moments), not Koenker and Bassett (1978). We reference Koenker and Bassett (1978) to maintain the logical flow of the research. OLS regression shows that we need quantile regression, thus we need employ Koenker and Bassett (1978). Then LSDV regression shows that we need fixed effects, thus we need employ Machado and Santos Silva (2019). We cannot just introduce Machado and Santos Silva (2019) in our research without first addressing the foundational literature and the theoretical and empirical justifications of using it. See 2.3. Empirical Analysis

The rejection of H2 and H3 does not diminish the research contribution because H1 is accepted. The three hypotheses should be viewed together in a moderating framework. The variation in the effect of NCO on M/B across quantiles indicates that the credit risk–bank value relationship is not uniform across different bank value levels. Therefore, even if the effects of MA and NCOMA on M/B are stable, the inclusion of NCO necessitates analyzing these effects across the quantiles of M/B.

We mentioned this in another way in section 3. Empirical Results and Discussion, lines 438-442

“Despite the lack significant heterogeneity in the slopes of the moderator and the interaction term, and assuming the Gauss theorem holds, examining the posed H3 in a quantile regression method is deemed more superior than linear methods due to the strong slope heterogeneity exhibited by the NCO.”

, 4. Conclusion, lines 482-490 and 474-479

“The findings indicate a significant variation in the effect of credit risk on bank value across the entire distribution of bank value. However, the results failed to provide statistical evidence to support a significant variation in the effect of horizontal M&A on bank value, as well as in their moderating effect on the relationship between credit risk and bank value, across the entire distribution of bank value. Given the significant non-linear behavior in credit risk-bank value relationship, evaluating it within the scope of horizontal M&A using quantile analysis enhances the precision and accuracy for decision-making. This remains valid despite the linearity nature of M&A’s direct and moderating effects, as well as deviations from the Gauss theorem.”

“To our knowledge, the existing literature has not provided an explanation of the credit risk and bank value relationship in the context of horizontal M&A that accounts for the potential non-linear behavior and the variability across different quantiles of bank value. This research bridges this gap adopting a distinctive approach that utilize revolutionary the Quantiles via Moments estimator to address endogeneity concerns, ensuring the robust-ness of our findings.”

In line with your comment(s), we will write another justifiable paragraph, as below, in section 3. Empirical Results and Discussion

“The rejection of H2 and H3 does not diminish the research contribution because H1 is accepted. The three hypotheses should be viewed together in a moderating framework. The variation in the effect of NCO on M/B across quantiles indicates that the credit risk–bank value relationship is not uniform across different bank value levels. Therefore, even if the effects of MA and NCOMA on M/B are stable, the inclusion of NCO necessitates analyzing these effects across the quantiles of M/B. Furthermore, the non-Gaussian nature of the error term distribution, along with evidence of heteroskedasticity, autocorrelation, and fixed effects, justifies the use of Quantiles via Moments in this study.”

9

Based on the above questions, the manuscript does not present clearly the results and methods. It is hard to recommend it for the journal.

Our methods are well-presented and well-cited in a separate sub-section named Empirical Analysis in Methodology. Our methodology follows a smooth flow. It begins in demonstrating that quantile regression is better than linear regression when error term violates Gauss theorem. Then it lists which test is used to check the violation such as normality, homoscedasticity and autocorrelation. After this is lists the test to make sure that variables are suitable for analysis such as multicollinearity and stationarity. Then it shows Koenker and Bassett (1978) quantile regression, its formula and how we will test our research hypothesis via Wald test. After that, it talks about omitting fixed effects will cause endogeneity issue, and how we test if we need fixed effects or not. Then, it presents the Quantiles via moments of Machado and Silve (2019, its formula and how we will test the research hypotheses using Wald Test. It also presents why Quantile via moments is superior over other quantile regression that use fixed effects.

We understand that the methodology is bit complicated because it mixes between quantile analysis and moderating analysis.  It includes 2 main approaches, under each approach there is two sub approaches. Conditional mean approach using OLS and LSDV approaches. Conditional Quantile approach using Koenker and Bassett (1978) and Machado and Santos Silva (2019) approaches.

Therefore, and in line with your comment(s), we wrote this paragraph at the end of 3. Empirical Results and Discussion section to summarize the detailed explanations of our analysis. We want from this paragraph to easily present our methodology, but we cannot clarify more than is already clarified in section 2.3. Empirical Analysis

“The robustness of our MM-QR results is validated through a series of multiple checks: variables validity, conditional quantile validity, fixed effects validity, bootstrapping and consistency validity. First, we confirm that the variables are free of multicollinearity and unit root issues, as addressed in Table 3, Table 4 and Figure 1, using correlation matrix and VIF (Belsley, 1980), Pesaran's CD test (Pesaran, 2021), average line graphs (Wang et al., 2018), and the K&T test (Karavias & Tzavalis, 2014). Second, we illustrate that conditional quantile regression of Koenker and Bassett (1978) outperforms conditional mean regression by effectively handling the non-Gaussian residuals (Royston, 1983), heteroskedasticity (Cook & Weisberg, 1983), and autocorrelation (Drukker, 2003) in OLS and LSDV regressions, as presented in Table 5. Third, using Wald test (F-Statistic), we reveal in Table 5, the necessity of including individual fixed effects to the conditional quantile regression of to avoid issues in endogeneity and omitted variable bias. Such, necessity cannot be directly implemented in Koenker and Bassett (1978) model due to incidental parameter bias (Koenker et al., 2017); Therefore, we introduce MM-QR of Machado and Santos Silva (2019), which can include individual fixed effects into the quantile regression model without such bias. Fourth, all results presented in Table 6 and Table 8 are derived via bootstrapping, ensuring robust estimates (Efron & Tibshirani, 1994). Furthermore, the partially consistency of MM-QR results in Table 8 with those from Koenker and Bassett (1978) quantile regression in Table 6, as well as the OLS and LSDV results in Table 5, along with similar outcomes of hypotheses testing using Wald test in Table 7 and Table 9, further validate the robustness of our results.”

Additionally, and in line with your comment(s) we rewrote our introduction to clearly present our contribution, results and implications.

“Current literature provides explanations about the relationship of credit risk with value in the context of M&A within banking industry. Our paper offers a deeper theoretical understanding of this relationship by capturing the heterogeneity in predictor-response relationship across the distribution of response, providing a novel contribution to the theoretical literature. Empirically, our novel results cannot be captured using standard conditional mean estimations. We introduce quantile regression to uncover how lower-valued banks and higher-valued banks exhibit different sensitivities to credit risk in M&A activities, effectively addressing challenges related to violations of normality and homoscedasticity in the financial data. Practically, our novel findings guide investors in identifying rewarding investment opportunities, assist bank managers in balancing risk and value creation during M&A, and inform policymakers about regulating credit risk exposure in M&A activities within the banking sector.

The results of this paper reveal that credit risk has a significant negative effect on bank value across the entire distribution, with magnitude of this effect decreasing from lower to upper locations. This indicates lower-valued banks are more vulnerable to a steeper decline in value as a result of credit risk, compared to higher-valued banks. Hori-zonal M&A exhibit a stable and significant positive effect on bank value across the entire distribution, suggesting that horizontal M&A consistently enhance bank value, regardless of the bank’s valuation. However, the moderating effect of horizontal M&A significantly magnifies the negative impact of credit risk on bank value across the entire value distribution, but without statistically significant differences observed from lower to upper locations of the distribution. This implies that horizontal M&A amplifies the adverse effect of credit risk on bank value uniformly, across banks, regardless of their valuation, assuming other factors remain constant.

Our results encourage investors to invest in banks that intend to merge and acquire, as such activities increase their wealth. However, simultaneously, they should carefully consider the credit risk profile of these banks because credit risk plays a significant counterfactor to value creation, especially for low-valued banks. We advise investors to utilize recent machine learning techniques, such as Decision Trees, to classify and categorize these investment opportunities based on credit risk and bank value. This will exclude in-vesting in banks that are willing to M&A with other banks when they are low-valued and experience high credit risk, and prioritize those that are high-valued and experience low credit risk, as these represent the best investment opportunities. Additionally, for investors who hold a portfolio of bank stocks, we advise them to incorporate a fundamental-based diversification strategy, where they overweight banks actively involved in horizontal M&A and underweight low-valued, high-credit risk banks, as these are more vulnerable to significant declines in value. This enables investors to maximize their portfolio value while minimizing exposure to the adverse effects of credit risk and M&A activities.

For practitioners, the paper’s findings advise board of directors in the banking sector to consider horizontal M&A as a growth strategy, as it enhances value across the entire banking sector. However, the findings emphasize the importance of implementing tailored risk management strategy for lower-valued banks during M&A processes to minimize the adverse effects of credit risk. This approach ensures that M&A activities leverage the positive effects to the interest of shareholders. Additionally, the findings suggest that board of directors utilize a credit risk–bank value monitoring tool that tracks both credit risk expo-sure and value simultaneously. This tool should adjust credit risk exposure based on the bank’s value, tightening exposure when value is low and loosening it when value is high, thereby balancing risk and reward more effectively.

Policymakers can benefit from our results by establishing a supportive framework that encourages healthy M&A activities in the banking sector, ensuring these activities contribute to growth while maintaining financial stability. We also suggest developing regulatory frameworks that address the impact of credit risk exposure on the banking sec-tor, recognizing the increased vulnerability of lower-valued banks to greater declines in value due to credit risk; a vulnerability that becomes even more pronounced during M&A transactions. Approvals for M&A should be conditioned on banks demonstrating a low credit risk profile and/or strong valuation. Regulators should establish a dynamic capital buffer that calibrated to credit risk exposure and bank value parameters, along with introducing event-specific capital buffers during M&A activities to safeguard against fore-seen and unforeseen credit risks. Additionally, policymakers can establish a monitoring mechanism to track credit risk exposure and bank value simultaneously, ensuring that banks to adhere to strict credit risk policies when their value fall below specified levels.”