Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks

Gupta, Anupam Das; Sarker, Niluthpaul; Rahman, Mohammad Rifat Article Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks Cogent Economics & Finance Provided in Cooperation with: Taylor & Francis Group Suggested Citation: Gupta, Anupam Das; Sarker, Niluthpaul; Rahman, Mohammad Rifat (2021) : Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks, Cogent Economics & Finance, ISSN 2332-2039, Taylor & Francis, Abingdon, Vol. 9, Iss. 1, pp. 1-31, https://doi.org/10.1080/23322039.2021.1967575 This Version is available at: https://hdl.handle.net/10419/270143 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=oaef20 Cogent Economics & Finance ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/oaef20 Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks Anupam Das Gupta, Niluthpaul Sarker & Mohammad Rifat Rahman | To cite this article: Anupam Das Gupta, Niluthpaul Sarker & Mohammad Rifat Rahman | (2021) Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks, Cogent Economics & Finance, 9:1, 1967575, DOI: 10.1080/23322039.2021.1967575 To link to this article: https://doi.org/10.1080/23322039.2021.1967575 © 2021 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Published online: 22 Aug 2021. Submit your article to this journal Article views: 2739 View related articles View Crossmark data Citing articles: 2 View citing articles FINANCIAL ECONOMICS | RESEARCH ARTICLE Relationship among cost of financial intermediation, risk, and efficiency: Empirical evidence from Bangladeshi commercial banks Anupam Das Gupta 1 *, Niluthpaul Sarker 2 and Mohammad Rifat Rahman 3 Abstract: The global financial crisis and stiff market competition enhance risk exposures that raise debate on the cost of financial intermediation and the supremacy of banks’ efficiency. This study examines the concurrent effects of bank risk, efficiency and cost of financial intermediation of Bangladeshi commercial banks. The Two-Step System GMM (2GMM) estimators of unbalanced dynamic panel data of 32 commercial banks from 2000 to 2016 addresses key factors rigorously in the light of bank-level, industry-level, and macroeconomic-level phenomenon. Efficiency gains cost the spread of banks’ financial intermediation, and risk-taking negatively affects the return. Cost-efficient banks are taking more credit risk; however, more efficiency gains reduce banks’ risk substantially. Size (cost of intermediation) of banks positively (inversely) affect the risk-taking (efficiency) behaviour of banks. Market competition enhances the risk and efficiency and reduces banks’ Anupam Das Gupta ABOUT THE AUTHOR Dr. Anupam Das Gupta is working as an Associate Professor in the Department of Finance, University of Chittagong, Bangladesh. His current research focus is banking efficiency and risk management. Dr. Niluthpaul Sarker working as Associate Professor in the Department of Accounting & Information Systems, Jagganath University, Bangladesh. His current research is focused on risk, and disclosures. And 3 rd Author Mohammad Rifat Rahman is working as an Assistant Professor in the Department of Banking and Insurance, University of Chittagong, Bangladesh. His current area of interest is Risk, Capital regulations, and IT in Banking. All authors have published numerous academic papers in national and international peer-reviewed journals. This project is financed by Planning & Development Office, University of Chittagong, Chittagong-4331, Bangladesh, under University Revenue Budget of the Year 2018-2019 (code no. 5921, memorandum no. 246(17)/POU/7-37- (5)/2 nd /2019). Photograph of the Corresponding Author Dr. Anupam Das Gupta 1 st and Corresponding Author Associate Professor, Department of Finance, University of Chittagong, Bangladesh. Email: [email protected]. PUBLIC INTEREST STATEMENT This study explores the relationship of net interest margin, risk and efficiency of commercial banks in Bangladesh. This study’s findings examine that banks with low-interest margins are more efficient than banks with high-interest margins. Again, the risk of banks has a detrimental effect on the net interest margin. In the risk and efficiency relationship, we observe that efficient banks are taking more risk than inefficient counterparts. Moreover, size and market competition have an apparent effect on banks’ net interest, risk, and efficiency; and these effects are not similar over time. This research presents the simultaneous relationship between risk, efficiency and intermediation cost of banks as a sample developing country of Bangladesh with size and market competition effect Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 1 of 31 Received: 22 June 2020 Accepted: 9 August 2021 *Corresponding author: Anupam Das Gupta, Department of Finance, Faculty of Business Administration, University of Chittagong, Chittagong, Bangladesh E-mail: [email protected] Reviewing editor: David McMillan, University Of Stirling, Stirling United Kingdom Additional information is available at the end of the article © 2021 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. interest spread. Finally, the Nonlinear effect of size and market competition is heterogeneous on risk, efficiency, and financial intermediation cost that follows a U-shape curve. This study explicitly addresses two issues: simultaneous effect of financial intermediation, bank risk, and efficiency and validated the nonlinear relationship considering size and market competition effect. Subjects: Finance; Banking; Credit & Credit Institutions; Investment & Securities Keywords: Cost of financial intermediation; risk; efficiency; GMM estimators; market competition JEl classfications: C2; D61; G17; G21. 1. Introduction Commercial banks, the critical matchmakers of fund flow, intermediate capital from surplus to deficit units, and confirm the economic growth with their efficient intermediation (Demirguc-Kunt et al., 2003; Zheng et al., 2018b). However, a growing number of banks enhance the competition that force banks to ensure their efficiency. Numerous studies (Gupta & Moudud-Ul-Huq, 2020; Zheng et al., 2018a) show that the banks’ continuous regulatory pressure to control risk for keeping consistent growth is the prime concern of regulators and other stakeholders. Risk and efficiency are a longdebated issue in literature with bidirectional relationship examination (Zheng et al., 2017a, 2018b). The cost of financial intermediation (henceforth CFI), efficiency, and risk concern has examined empirically; but yet to be addressed their inter-dependencies in the literature. Thus, it becomes increasingly essential to delve into relationships among these commercial banks’ stimuli, i.e., CFI, risk, and banks’ efficiency, to gain new insights. This study investigates the concurrent relationship between the cost of financial intermediation, risk, and efficiency of Bangladeshi commercial banks and examines the intermediating effect of size and market competition. The term Cost of Financial intermediation (CFI) refers to the net interest margin between the income on loan and advance and cost paid to banks’ savers (Al-Jarrah, 2010; Bernanke, 1991). CIF is an increasingly important aspect that needs to address risk and efficiency, particularly in developing countries’ perspectives (Al-Jarrah, 2010). Al-Jarrah (2010) argues that the cost of financial intermediation has significantly contributed to improving market competitiveness and mobilizing efficiency in the financial system. Fair market competition will give market power to the highly capitalized and large-sized banks to crammed down the other counterparts and dominate in loan pricing due to their low cost of capital (Brock & Franken, 2002). The landmark initiative of the dealership model by Ho and Saunders (1981) mentions risk, market competition, transaction size, and interest rate fluctuation are significant determinants of the cost of financial intermediation. Therefore, from this debate, it is clear that financial intermediation’s cost has a significant association with the market competition, which simultaneously affects banks’ loan pricing and risk-taking. Furthermore, in such a condition, efficiency becomes an significant consideration as increasing market competition leads to reduce the investment in information acquisition (Hauswald & Marquez, 2006). Therefore, relationship among the CFI, risk, and efficiency demand the empirical examination having size and market competition effect. The growing number of banks increase market competition in Bangladesh, especially with banks’ inclusion in different generations. Moreover, over time, the increasing trends of bank’s size and solid capital base gave the extra pick to old generation banks to deal with competition and regulatory changes in the market. The increasing trend of net-interest margin (see Chart 1), the inconsistent growth of expenditure to income ratio (see Chart 2), and volatility in bank’s profit margin (ROA and ROE in Chart 3 and Chart 4 respectively) have a continuous improvement of NPLs (Non-Performing Loans) till 2011, and there-after NPLs moved with a growing tendency. The empirical evidence based on prior literature and numeric figures from the bank performance motivates us to research the bidirectional effect of CFI, risk, and commercial banks efficiency. Moreover, the performance gap between the State-owned Commercial Banks (SCBs) and the Private Commercial Banks (PCBs) clarifies Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 2 of 31 the relevance of banks’ efficiency, risk, and profitability through trend analysis. A synopsis of the performance of the banking industry of Bangladesh is depicting under section 2. The study is constructed based on the relevant issues to address the following questions: (i) Is there any association among CFI, banks’ risk and efficiency? (ii) Do nonlinear and quadratic effects of size and market competition valid in the examination of risk, cost of intermediation and efficiency relationship? The study encouraged to carry out the research work for the following reasons. Firstly, to shed light on bidirectional intermediation among risk, efficiency, and cost of financial intermediation to evident a new fact regarding Bangladeshi commercial banks. The existing literature does not sufficiently focus on the impact of the cost of financial intermediation in the risk-taking of commercial banks in developing countries like Bangladesh. Moreover, examining the simultaneous relationship of risk, efficiency, and cost of financial intermediation is not observed in the available literature. Secondly, to explore the size and competition effect on risk, efficiency, and cost of financial intermediation. Finally, extending the previous work of Rahman et al. (2018) by adopting performance measureefficiency and examining the nonlinear and quadratic effect, depicts new insights into the Bangladeshi banking industry. The rest of the study is organized as follows. Section 2 presents the institutional framework of the banking industry of Bangladesh, and Section 3 describes the relevant literature of the study; Sections 4 illustrates the data, variables description and empirical methodology of the study. Finally, Section 6 presents the empirical results explaining the relationship between risk, efficiency, and cost of financial intermediation with nonlinear and quadratic effects and Section 7 contains the concluding remarks. 2. Banking industry of Bangladesh Previous studies focus on the developing country context, primarily concentrating on the South Asian region’s emerging economies. Undoubtedly, Bangladesh is set its reflexive image in the marketplace due to rapid growth and higher potentiality in the regional economy. Till December 2016, the banking industry has operated with fifty-six (56) schedule banks, consists of six (6) state-owned commercial banks (SCBs), thirty-nine (39) private-commercial banks (PCBs), nine (9) foreign-commercial banks (FCBs) and two (2) development finance institutes (DFIs). The financial market (money market) of Bangladesh is under full supervision and control of Bangladesh Bank as per Bangladesh Bank Order, 1972. In Table 1, it is found that the state-owned commercial banks (SCBs) and private-commercial banks (PCBs) play a significant role in the market in terms of size (number of branches and asset holding) and also in deposits. From the year 2000 to 2016, it is found that PCBs generate more interest income than SCBs (Chart 1). The reason may be the efficient management of PCB through more inclusion of the ultimate consumers. Furthermore, SCBs are less efficient as they incur more expenditure compared Table 1. Banking system structure (Year 2016) (BDT. in billion) Bank types Number of Banks Number of branches % of industry assets % of deposits SCBs 06 3700 26.1 29 PCBs 39 4271 67 63.8 FCBs 09 75 4.5 4.3 DFIs 02 1407 2.5 2.9 Total 56 9453 100 100 Source: Bangladesh Bank annual report. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 3 of 31 to their income. The Expenditure-Income Ratio in Chart 2 below shows that PCBs always keep their ratio lower than the industry average. In contrast, SCBs exceed the line in all cases, which indicates their inefficiencies in operation. Return on Assets (ROA) and Return on Equity (ROE) are widespread measures of profitability. Chart 3 showed that the average ROA of Bangladesh’s banking industry from 2000 to 2016 fluctuates due to immense market pressure. The trend of ROA has drastically fallen in 2012 due to the world economic crisis in 2010. The SCBs performance worsens in contrast with PCBs. Similar results also found in the ROE case (Chart 4), where SCBs confirm their inefficiencies, which finally affect the bottom-line figure. The non-performing loan ratio (NPLTL) is the ratio between non-performing loans to total loans. Chart 5 below gives fascinating findings that the proper implementation of risk management guidelines (i.e., Basel I, II, and III) gradually reduces the NPLTL. The emergence of capital regulation plays a vital role in keeping the NPLTL minimum. However, PCBs show their efficiencies to maintain lower NPLTL in contrast with SCBs. The reason is that SCBs mainly granted their loans in the unproductive sectors for the welfare of society to keep the political promises of the government. 0 20 40 60 80 100 120 Percentage (%) Year SCBs PCBs Industry Average Chart 2 Expenditure-Income Ratio -100 0 100 200 300 400 BDT in Billion Year SCBs PCBs Industry Average Chart 1 Net Interest Income Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 4 of 31 3. Literature review A comprehensive survey of literature on the cost of financial intermediation, risk, and commercial banks’ efficiency is discussed in this section. At first, we investigate the studies relating to the cost of financial intermediation, and in the next, studies explaining the relationship between risk and efficiency are also discussed. -1 0 1 2 3 Percentage (%) Year SCBs PCBs Industry Average Chart 3 Return on Assets (ROA) -20 -10 0 10 20 30 Percentage (%) Year SCBs PCBs Industry Average Chart 4 Return on Equity (ROE) 0 10 20 30 40 50 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Percentage (%) Year Industry Average SCBs PCBs Chart 5 Non-performing loan ratio. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 5 of 31 3.1. Literature regarding the cost of financial intermediation The cost of financial intermediation refers to the benefit derived from the fund mobilization of a bank (Al-Jarrah, 2010). Thus CFI evaluation is related to the profitability and performance of banks. The concept of cost of financial intermediation discussed in the landmark initiative of Ho and Saunders (1981) in their dealership model (Islam & Nishiyama, 2016). Ho and Saunders (1981) argue that the net interest margin derived from banks’ intermediacy service. The net interest margin is the gap between the interest charged against loans and advances and the cost incurs against the deposit. The study of Ho and Saunders (1981) pinpoint four factors for the optimum level of cost of financial intermediation. These are the magnitude of banks’ risk-taking tendency, market power or competitive condition of the market, transaction size, and interest rate volatility. Extending Ho and Saunders (1981) models, Cruz-García and Fernandez de Guevara (2020) incorporate regulatory capital and deposit insurance as active determinants that positively influence the cost of financial intermediation of OECD countries. They also point out operating cost, market competition, efficiency as determinants of cost of financial intermediation. However, criticism also moves out, mentioning the limitations of Ho and Saunders (1981) model. Lerner (1981) slated the dealership model due to its failure to address cost inefficiency as a detrimental factor in the cost of financial intermediation. Based on the dealership model’s extension, Allen and Santomero (1998) opines that the interest rate spread depends on the loan portfolio’s heterogeneity and proper maturity intermediation of deposits. The author has addressed the portfolio effect in the margin determination of interest. Extending the dealership model on European countries, Maudos and Guevara (2004) incorporate the total operating cost and show the significant impact of the cost of intermediation in risk-taking of banks. Angbazo (1997) argues that financial intermediation’s benefit reflects both credit risk and interest rate risk premia of commercial banks. However, due to more concentration of short period asset exposures and off-balance sheet hedging instruments, interest margin is mainly affected by banks’ credit risk. From the literature, it is apparent that risk is a significant factor in determining the cost of financial intermediation. Literature digging the determinants of the cost of intermediation of banks is also observed apart from the relationship between risk and cost of financial intermediation. Working on lower-income countries, Poghosyan (2013) addresses the cost of financial intermediation through the netinterest margin. The author shows that the cost of mediation increases with the riskier loan portfolio and size. The inverse relationship between bank capitalization and interest margin is also evident in this study. The author points out that high market power, low level of competition, and institutional weakness play an active role in the higher financial intermediation cost. From the study of 142 Brazilian banks, Afanasieff et al. (2002) address both bank-level and macro-economic variables as determinants of interest margin spread. The authors address size, opportunity cost, operating cost as banks level variables, output growth, inflation, the market rate of interest, and the volatility of interest rate pointed out as macro-economic variables that affect the net interest margin. Khan and Jalil (2020) depict operating cost, tax, market competition, interest rate risk, and macroeconomic factors like money supply, risk-free return of the market, national saving positive association with cost of financial intermediation of banks. Whereas operational exposure, credit risk, inflation inversely affect the determination of the cost of financial intermediation. Therefore, industry conditions like the market power of banks and macroeconomic factors play an active role in determining the cost of financial intermediation. Sirait and Rokhim (2019) point out regulatory capital as a significant determinant of banks’ cost of financial intermediation and risk-taking. The authors assert that incremental regulatory capital requirement reduces the risk-taking and cost of financial intermediation of banks. Consideration of the cost of financial intermediation is also significant in determining the financial institution’s sound health and stability. Angori et al. (2019) mention the cost of financial intermediation as a gauge of banks protecting health and stability. They argue that regulatory and institutional settings also significantly affect market competition, efficiency level, risk, and Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 6 of 31 capitalization. Post arguments of the dealership model say Lerner (1981) justifies the relevance of efficiency in consideration of the cost of financial intermediation. 3.2. Literature regarding risk and efficiency of commercial banks Although literature stresses a diversified relationship between commercial banks’ risk and efficiencies, the general expectation against efficiency enhancement is that banks’ risk managing capacity will be accelerated (Zheng et al., 2017a). So, a negative relationship is expected to observe. An empirical investigation of H. T. Phan et al. (2019) on East Asian countries preaches that banks’ stability increases with efficiency enhancement. Berger and DeYoung (1997), Deelchand and Padgett (2009b), Fiordelisi et al. (2011), Nguyen and Nghiem (2015), and Kwan and Eisenbeis (1997), among others also point out the inverse association between risk and efficiency. Mentioning efficiency as a significant determinant of credit risk, Berger and DeYoung (1997) opine that administrative cost against loans and advances adversely affect banks’ cost efficiency. Again Kwan and Eisenbeis (1997) and Deelchand and Padgett (2009b) support the moral hazard hypothesis 1 for the adverse rapport between efficiency and risk. Keeping the “Bad Management” hypothesis 2 , Fiordelisi et al. (2011) opine that banks’ risk is subject to low cost and revenue efficiency. The “Bad Management” hypothesis is also evident in the study of Partovi and Matousek (2019). The authors stress the inverse effect of non-performing loan over the efficiency of banks. However, the efficiency of banks is not found homogeneous across different ownership structure. Similar outcomes also support the examination of intertemporal relationship risk and efficiency. Saeed et al. (2020) opine that the effect of efficiency on risk-taking is not homogenous across different banks’ ownership. They observe a positive impact of efficiency on Islamic banks’ risk-taking where inverse association with conventional banks. However, the authors mention capital as a dominant determinant in managing risk of commercial banks. Investigating Indian banks, Nguyen and Nghiem (2015) pinpoint the technological advancement behind banks’ cost efficiency. Salim et al. (2017) point out political interference as one of the significant reasons for loans becoming bad. They comment that although banks’ efficiency increases over time, the investment quality decreases due to political interference in the loan approval. Again bad loan is negatively related to the efficiency of banks. Industry-level variables like market competition and macroeconomic condition also mediate the relationship between risk and efficiency of banks. Validating the competition fragility view, Danisman and Demirel (2019) opine that superior market power inversely affects banks’ risk-taking tendency. Their study also supports regulatory capital restriction as a risk-mitigating tool. Harimaya and Ozaki (2021) examine the impact of diversification on the efficiency of banks. Opposing the market power, the authors opine that banks’ overemphasizing on loan and income concentration efficiency decreases. Therefore, portfolio diversification is playing a significant role in enhancing the efficiency of banks. Pointing differently, Chen and Lu (2021) focus on macroeconomic and regional disparities in determining the efficiency of commercial banks of China. The authors observe a significant impact of regions and macroeconomic factors like GDP per capita on cost and profit efficiency of commercial banks Previous literature covers the apparent effect of risk on the cost of financial intermediation. Studies also observed pointing out the relationship between risk and efficiency of banks. However, there is a scarcity of literature addressing the simultaneous examination of the cost of financial intermediation, risk, and commercial banks’ efficiency. To assess the relationship between CFI, risk, and efficiency, the relevant hypotheses are drawn: H 1 : There is an association between the cost of financial intermediation, bank risk-taking, and costefficiency. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 7 of 31 significance against the Fisher Type Augmented Dickey-Fuller test statistics. It refers that the series data does not possess any unit root. Table 5 shows Pearson’s correlation matrix to determine the relations between dependent and independent variables. The results are given below: The study conducts the correlation test to check the relationship between the variables, but it is challenging to conclude the independent variables’ multicollinearity. Therefore, the study also tests the Variance Inflation Factor (VIF) to address the model’s multicollinearity problem. The variance inflation factor (VIF) measures how often one predictor correlates with the other predictors in a model. Higher values indicate that determining the contribution of predictors to a model is complex. For each predictor in a predictive model, a VIF may be calculated. The predictor has a value of 1 if it does not correlate with other variables. The more significant the correlation between the variable and other variables, the higher the value. The value of correlation more than 0.90, and VIF value 10 refers to a very high degree of correlation between independent variables (Thompson et al., 2017). However, in Table 6, the value of VIF for each variable is below 5, and Pearson correlation coefficients between independent variables in Table 5 don’t show high degree correlation, which indicated no significant multicollinearity problems between the independent variables. 5.2. Determinants of risk and examination impact of the cost of financial intermediation and efficiency Table 7 depicts the effect of cost of financial intermediation and efficiency on the risk of banks along with other variables. In Table 7, we observe that with the increase in the cost of financial intermediation, the risk of banks managed substantially. This result is in line with the finding of (Rahman et al., 2018) and opposes the view of Angbazo (1997) mentions the cost of financial intermediation as a premium of risk-taking. The negative association of CFI 1 with Z-score in examining the cost of financial intermediation in risk shows that with the increase of net interest margin, the stability reduces having a significant improvement of credit risk-taking and overall bank risk. In efficiency concern, the efficiency of cost is negatively associated with all risk models. This result evident the “Bad Management” hypothesis. Thus, with the increase in cost efficiency, credit risk, stability, and overall bank risk decreases. The market competition measure Boone Indicator (BI) explores that increase market competition reduces the credit risk and overall bank risk significantly. It illustrates that a high degree of market competition reduces the risk-taking tendency of commercial banks. This result is in line with the outcome of Soedarmono et al. (2011) on Asian markets. However, the stability of banks also reduces in the competitive banking industry. As Boone indicators usually bear the negative sign, the sign of the Boone indicators’ coefficient will refer to the opposite meaning. Increased asset size induces banks in risk-taking as the coefficient of size shows a positive association with risk. Similar findings depicting a positive association of size and risk is also observed in Zheng et al. (2018a). In explaining other control variables, we observe that with the increase of capital, banks’ risk substantially reduces, and stability increases that depict ETA’s negative coefficient in NPLTL, LLPTA model, and positive coefficient of Z-score model. These findings also parallel with Zheng et al. (2017a) and Benes and Kumhof (2015). The industry level variable BSD shows a negative relationship with risk measures. It means that with the development of banking sectors, commercial banks are taking the calculative risk. Due to experience in the industry, the risk handling and managing capacity of banks increases. As debt servicing become more convenient for customers in economic progression (growth of GDP), the risk of banks reduces, and stability increases (Gupta & Moudud-UlHuq, 2020). LTA shows the negative, whereas inflation shows a positive association with risk measures. It refers that overall upward price moments of the market make the risk position of banks worse. In contrast, the mobilization of the loan in proportion to total assets reduces the risk significantly. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 14 of 31 5.3. Determinants of efficiency and examination of the impact of the cost of financial intermediation and risk Table 8 explains the effect of cost of financial intermediation, risk over the efficiency of banks using Equation (1) of the GMM estimator. The coefficients of risk (stability) depict the positive (negative) association with efficiency. It refers that cost-efficient commercial banks are taking more credit risk, and their stability is worse than the cost-inefficient counterparts. Supporting the previous findings of Chortareas et al. (2012), the negative association of CFI 1 with efficiency asserts that efficient banks have a low spread of interest than cost-inefficient counterparts. The Boone indicator’s positive coefficient (BI) depicts that the efficiency of cost decreases in increased market competition. This result is analogous to the finding of H. T. M. Phan et al. (2016). The coefficient of BSD reports a meaningful positive relationship with the efficiency of cost. It means that the efficiency of cost enhances with the development of Bangladesh’s banking sector (Gupta, 2018). A significant association with GGDP indicates that in economic progression, the efficiency of cost increases. Again in the rise of the overall market price (Inflation), the efficiency of cost decreases (Zheng et al., 2017a). Increase with assets size, the efficiency of cost decreases that denoted by the coefficient of size. With more dependency on depositm, increase the cost inefficiency of banks signified by the negative coefficient of DTA. This is because banks usually collect deposits short-term basis, but they also invest in longterm investment besides short term. Thus with the maturity gap of asset mobilization, the efficiency of cost decreases. ROA is significantly related to the efficiency of cost. It demonstrates that the profitability of banks provokes the efficiency of cost. With more exposure to non-traditional activities (off-balance sheet exposures), the efficiency of cost decreases. 5.4. Determinants of CFI and examination of the impact of risk and efficiency Table 9 presents the bidirectional effect of risk and efficiency on the cost of financial intermediation. Supporting the efficiency structure hypothesis, the negative coefficients of efficiency assert Table 6. Variance inflation factor Dependent Variables Base line equations Extended results Variable VIF (CFI) VIF (NPLTL) VIF (Eff_C) VIF(CFI) VIF(NPLTL) VIF(Eff_C) Dep(−1) 1.56 1.86 2.16 NPLTL 1.34 1.88 1.57 2.09 Eff_c 2.31 3.16 2.25 2.6 CFI 1.50 1.50 1.62 1.78 Size 3.42 3.29 2.44 Large 1.91 1.85 1.9 Small 1.44 1.41 1.45 Inlation 2.80 2.78 2.85 2.19 2.19 2.19 BI 2.48 2.38 2.42 2.88 2.75 2.84 GGDP 1.97 2.01 2.03 1.98 2.01 2.04 BSD 1.85 1.83 1.87 1.93 1.93 1.94 RD 1.12 1.16 LTA 1.73 1.93 ETA 1.33 1.44 ROA 1.42 1.45 DTA 1.13 1.14 OBSTA 1.13 1.19 Source: Authors’ Calculation through STATA Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 15 of 31 that efficiency gains result in low cost of financial intermediation (Chortareas et al., 2012). Risk coefficients are negatively related to the cost of financial intermediation. This result is in line with Chortareas et al. (2012). One of the possible reasons active behind this is that with most investment opportunity utilization, the interest spread reduces substantially. Moreover, financial literacy opposed the massive absorption of extravagant risk in triggering the quality of earnings. NPLTL model and LLPTA model present the positive association between market competition and the cost of financial intermediation. This result is similar to the finding of Chortareas et al. (2012) and evident the Structure-conduct-performance (SCP) 3 argument. The better macroeconomic environment creates an opportunity for higher CFI, depicted by the positive coefficient of GGDP; this is because, in economic progression, default risk reduces, and the average deposit collection cost also reduces since sufficient cash preserved by the corporate and private savers. However, inflation shows a mixed result with the cost of financial intermediation. It asserts a positive association in the Z-score model, whereas negatively related to CFI in the NPLTL model. Higher CFI is associated with bank size. It refers that size fuels banks to gain more interest spreads. This result is the opposite of the finding of Gelos (2009) on Latin American countries. BSD and RD are negatively related to CFI. With the growth of the industry, the opportunity of interest spread reduces as competition increases. Again revenue diversification minimizes the spread of interest margin because non-interest income is the proportion of total operating income that reduces the overemphasize to generate more income on interest (Rahman et al., 2018). The coefficients of lagged dependent variables are observed positive in all GMM estimates models, confirming the models’ dynamic nature and depicting dependent variables are persistently followed from year to year. The value of AR(1) and AR(2) reported in each equation’s regression tables validate the instrument of the lagged dependent variable. The Hensen test of J-statistics confirms the validity of the instruments of the models of the study. Table 7. Risk equation examining the effect of cost of financial intermediation and efficiency Variable NPLTL Z-score LLPTA Dep(−1) 0.547***(32.74) 0.655379***(117.85) 0.545***(39.95) CFI 1 −1.837***(−7.73) −4290.19***(−22.01) −0.168***(−2.83) Eff_C −0.308***(−14.29) −324.222***(−7.27) −0.055***(−7.01) BI 0.231**(2.64) 585.9426***(5.44) 0.100***(7.61) BSD −0.002***(−4.92) −0.622(−1.47) −0.001***(−9.33) GGDP −0.002(−1.08) 5.158037***(3.88) −0.002***(−5.57) Inflation 0.0001(0.17) 11.027***(5.63) 0.0004**(2.08) Size 0.028***(12.32) 11.16575**(2.75) 0.007***(7.89) LTA −0.206***(−12.39) −25.8488(−0.49) −0.019***(−3.50) ETA −0.301***(−9.68) 490.4179***(5.59) −0.159***(−24.27) Constant 0.393***(9.09) 340.417***(7.98) 0.063***(6.21) Hansen Test (P-value) 0.272 0.224 0.120 AR(1) (P-value) 0.011 0.014 0.004 AR(2) (P-value) 0.189 0.100 0.714 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers to significance at 10 %, 5 %, and 1 % level, respectively. Dependent variables are NPLTL, Z-score, and LLPTA as a proxy measure of Credit risk, Stability risk, and Overall bank risk, respectively. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 16 of 31 5.5. Robust check By interchanging the alternative selection of proxy variables, a robustness check of the risk equation is performed. For measuring the cost of financial intermediation, we change the proxy measure CFI 1 to CFI 2 in all models. Table 10 results confirm the validity of the risk equation model’s in examining the efficiency and cost of intermediation effect observed in Table 7. The other robust results observe in Tables 11–12 confirm similar findings present in Tables 8–9, respectively. The only exception is observed in variable inflation in Table 8 with the Z-score model, which is found significant; however, in robust check, it is observed insignificant in Table 11. 5.6. The nonlinear and quadratic effect of size & market competition Following Gupta and Moudud-Ul-Huq (2020), Kouki and Al-Nasser (2017), S. Kasman and Kasman (2015), and Jeon and Lim (2013), the squared term of Boone Indicator (BI) in equation (2) incorporate to examine the nonlinear effect. We extend the baseline model to delve into the nonlinear relationship between the dependent variables and market competition along with the size effect. Tables 13–18 presents the GMM estimators having a nonlinear impact by using Equation (2). Table 13 shows the nonlinear effect of size and market competition over the risk of banks. Empirical findings of Table 13 are in line with Gupta and Moudud-Ul-Huq (2020), Tabak et al. (2012) that depict the significant nonlinear effect of competition on risk-taking of banks. The square term of market competition (BI) 4 describes a significant negative (positive) association with credit and overall risk for large (small) banks and a positive (negative) relationship with stability. This result supports the “competition-stability” (competition-fragility) 5 view for large (small) banks and is in line with the finding of Gupta and Moudud-Ul-Huq (2020). However, the interim term of size and competition Table 8. Efficiency equation examining the effect of risk and cost of financial intermediation Variable Eff_C (with NPLTL) EFF_C(with Z-score) EFF_C(with LLPTA) Eff_C (−1) 1.11516***(1815.63) 1.114058***(1099.65) 1.11482***(1756.22) NPLTL 0.003436***(7.34) Z-score −1.1E-05***(−4.77) LLPTA 0.004225*(1.81) CFI 1 −0.007431***(3.28) −0.04085***(−4.57) −0.01023***(−3.91) BI 0.003522***(4.32) 0.008297**(2.73) 0.001701**(2.10) BSD 5.16E-06**(2.47) 1.79E-05*(1.91) −4.74E-06(−1.66) GGDP 6.88E-05***(8.47) 0.000114***(3.65) 5.03E-05***(4.89) Inflation −4.7E-05***(−6.39) −0.000079**(2.51) −6.3E-05***(−6.89) Size −0.00038***(−7.82) −0.00048***(−3.49) −0.00037***(−8.47) DTA −0.0008*(−2.00) −0.00302***(−2.77) −0.00153***(−3.38) ROA 0.000123***(8.47) 0.000186***(11.24) 9.31E-05***(4.86) OBSTA −0.00075***(−4.94) −0.00314***(−7.94) −0.00082***(−4.44) Constant −0.11285***(−177.92) −0.10717***(−90.13) −0.11074***(−141.71) Hansen Test (P-value) 0.242 0.283 0.237 AR(1) (P-value) 0.026 0.058 0.089 AR(2) (P-value) 0.251 0.480 0.245 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers significance at 10%, 5%, and 1% level respectively. The dependent variable is the efficiency of cost measure through SFA. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 17 of 31 Table 10. Equation risk examining the effect of efficiency and cost of intermediation Variable NPLTL Z-score LLPTA Dep(−1) 0.549***(31.40) 0.637378***(241.03) 0.545383***(39.97) CFI 2 −1.521***(−7.36) −746.177***(−6.16) −0.16131***(−3.35) Eff_C −0.305***(−13.94) −73.3607**(−2.48) −0.0569***(−7.08) BI 0.229***(2.70) 626.53***(7.13) 0.100449***(7.68) BSD −0.001**(−4.96) 0.649018(1.3) −0.00064***(−9.4) GGDP −0.001(−1.07) 2.445059**(2.19) −0.00148***(−4.92) Inflation 0.0001(0.33) 9.842193***(8.43) 0.000449**(2.23) Size 0.028***(14.40) 6.39585**(2.64) 0.007017***(7.94) LTA −0.204***(−11.33) −146.762***(−4.45) −0.01956***(−3.61) ETA −0.290***(−8.60) 210.6766***(4.81) −0.1581***(−23.64) Constant 0.372***(9.68) 216.0666***(5.24) 0.063655***(6.28) Hansen Test (P-value) 0.268 0.242 0.126 AR(1) (P-value) 0.012 0.065 0.004 AR(2) (P-value) 0.201 0.133 0.715 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers to significance at 10%, 5%, and 1% level respectively. Dependent variables are NPLTL, Z-score, and LLPTA as a proxy measure of Credit risk, Stability risk, and Overall risk, respectively. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation Table 9. Cost of financial intermediation equation examining the effect of risk and efficiency Variable CFI 1 (with NPLTL) CFI 1 (with Z-score) CFI 1 (with LLPTA) CFI 1 (−1) 0.425***(9.22) 0.481***(11.97) 0.533***(10.17) NPLTL −0.050***(−13.42) Z-score −0.0000106(−1.31) LLPTA −0.126***(−7.05) Eff_C −0.033***(−3.75) −0.056***(−8.79) −0.064***(−6.814) BI −0.041**(−2.62) −0.002(−0.08) −0.037**(−2.18) BSD −0.001***(−8.54) −0.0003***(−4.69) −0.001***(−7.14) GGDP 0.0005**(2.27) 0.001***(4.06) 0.001***(3.10) Inflation −0.0004***(−2.90) 0.0004**(2.72) −0.0001(−0.75) Size 0.003***(3.57) 0.003***(5.18) 0.005***(6.28) RD −0.129***(−6.27) −0.069***(−3.67) −0.127***(−6.90) Constant 0.051***(14.11) 0.051***(13.5) 0.055***(13.43) Hansen Test (P-value) 0.134 0.115 0.107 AR(1) (P-value) 0.000 0.000 0.000 AR(2) (P-value) 0.310 0.223 0.385 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers to significance at 10%, 5%, and 1% level respectively. The dependent variable is the cost of financial intermediation. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 18 of 31 Table 12. Cost of financial intermediation equation examining the effect of risk and efficiency Variable CFI 2 (with NPLTL) CFI 2 (with Z-score) CFI 2 (with LLPTA) CFI 2 (−1) 0.447***(9.95) 0.471***(10.07) 0.442***(10.84) NPLTL −0.054***(−13.95) Z-score −0.000015**(−2.15) LLPTA −0.142***(−10.76) Eff_C −0.043***(−4.53) −0.070***(−8.76) −0.067***(−7.30) BI −0.050***(−2.79) 0.0002(0.01) −0.033*(−1.97) BSD −0.0006***(−8.71) −0.0004***(−4.94) −0.001***(−7.44) GGDP 0.0006**(2.07) 0.001***(4.51) 0.001***(2.92) Inflation −0.0003***(−3.20) 0.0004**(2.40) −0.0002(−1.18) Size 0.003***(4.14) 0.004***(5.56) 0.005***(6.60) RD −0.152***(−7.79) −0.095***(−5.27) −0.119***(−5.61) Constant 0.057***(14.01) 0.061***(12.66) 0.060***(15.53) Hansen Test (P-value) 0.139 0.100 0.100 AR(1) (P-value) 0.000 0.000 0.000 AR(2) (P-value) 0.329 0.249 0.412 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers to significance at 10%, 5%, and 1% level respectively.The dependent variable is the cost of financial intermediation. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation. Table 11. Efficiency equation examining the effect of risk and cost of financial intermediation Variable Eff_C (with NPLTL) EFF_C(with Z-score) EFF_C(with LLPTA) Eff_C (−1) 1.114186***(1590.2) 1.114376***(1174.63) 1.114575***(1763.74) NPLTL 0.003623***(6.58) Z-score −1.5E-05***(−10.94) LLPTA 0.006457***(5.12) CFI 2 −0.00747***(−4.1) −0.03954***(−3.91) −0.01419***(−5.59) BI 0.003618***(4.9) 0.0089***(3.72) 0.001597**(2.11) BSD 6.20E-06**(2.19) 1.48E-05*(1.72) −7.57E-06(−2.33) GGDP 0.000101***(8.93) 0.000135*(4.87) 0.000066***(5.76) Inflation −2.2E-05***(−3.87) 8.34E-06(0.28) −6.6E-05***(−8.68) Size −0.00035***(−6.38) −0.00033***(−4.63) −0.00035***(−7.71) DTA −0.00142***(−4.45) −0.00307**(−2.46) −0.00161***(−3.63) ROA 0.000156***(9.15) 0.00019***(9.92) 0.000114***(8.45) OBSTA −0.00084***(−4.9) −0.00317***(−7.73) −0.0008***(−3.79) Constant −0.11164***(−213.2) −0.10836***(−67.64) −0.11061***(−160.94) Hansen Test (P-value) 0.186 0.324 0.209 AR(1) (P-value) 0.082 0.095 0.072 AR(2) (P-value) 0.216 0.905 0.375 Observations 480 480 480 Note: The values in parentheses are t-value; *, **, *** refers to significance at 10%, 5%, and 1% level respectively. The dependent variable is the efficiency of cost measure through SFA. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano–Bond order 1 (2) are tests for first (second) order correlation, asymptotically N (0, 1). These test the first-differenced residuals in the system GMM estimation. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 19 of 31 Table 13. Risk equation—Nonlinear effect of size and market competition on risk Variable NPLTL Z-score LLPTA Model I Model II Model I Model II Model I Model II NPLTL(−1) 0.5761002*** (30.83) 0.6073779*** (31.62) Z-score(−1) 0.531084*** (55.62) 0.647739*** (110.05) LLPTA(−1) 0.5414168*** (43.40) 0.587497*** (38.78) CFI 1 −0.6380638** (−2.68) −1.012678*** (−4.93) −4226.31*** (−7.20)) −2759.22*** (−11.35) 0.0670767 (1.34) 0.133039** (2.42) Eff_C 0.034306* (1.85) 0.0801584*** (4.38) 410.7304*** (4.28) −222.794*** (−5.11) 0.0355121*** (6.10) 0.050595*** (7.89) Large −2.71E-07*** (−14.32) 0.000442 (0.62) −9.03E-08*** (−9.44) Small 4.81E-07*** (2.83) −0.00163*** (−6.05) 1.01E-07** (2.39) BI −0.6211575 (−1.55) −2.328657*** (−7.9) −4510.49* (−1.81) 5226.275*** (4.52) −0.5459561*** (−4.67) −1.04534*** (−6.35) BI 2 −8.831444** (−2.60) −21.58409*** (−9.68) −42,647.70* (−1.80) 46,186.53*** (4.81) −5.920515*** (−5.74) −10.4636*** (−7.59) Large ×BI −0.0000114*** (−14.27) 0.064695** (2.61) −3.82E-06*** (−9.20) Small × BI 0.0000185** (2.46) −0.07424*** (−6.39) 4.43E-06** (2.51) Large × BI 2 −0.0000894*** (−11.31) 0.727755*** (3.37) −0.0000299*** (−8.58) Small × BI 2 0.0001438** (2.06) −0.74547*** (−6.52) 4.54E-05*** (2.92) BSD −0.0016815*** (−4.92) −0.0015729*** (−3.82) −2.00842*** (−2.84) 0.293584 (0.30) −0.000657*** (−6.57) −0.00073*** (−6.13) GGDP −0.0041321*** (−4.39) −0.0043238*** (−3.06) 0.290244 (0.12) 3.011385 (1.69) −0.0015355*** (−3.04) −0.00161** (−2.74) Inflation 0.0010858** (2.11) 0.0012325** (2.13) 3.625876* (1.78) 8.342811*** (5.27) 0.0002262 (1.03) 8.12E-05 (0.34) LTA −0.0895228*** (−3.84) −0.0355388** (−2.07) −12.619 (−0.13) −141.489** (−2.56) 0.0157527*** (2.87) 0.016125*** (3.30) ETA −0.2435876*** (−10.82) −0.1825525*** (−5.89) 377.8504** (2.12) 258.3677*** (4.15) −0.1314195*** (−15.87) −0.12986*** (−15.29) Constant 0.1630917*** (3.55) 0.0206707 (0.43) −393.125** (−2.22) 480.6397*** (6.36) −0.0121746 (−1.10) −0.04066*** (−4.04) Hansen Test (P-value) 0.305 0.356 0.176 0.382 0.519 0.217 AR(1) (P-value) 0.016 0.017 0.051 0.064 0.004 0.004 AR(2) (P-value) 0.216 0.236 0.160 0.132 0.924 0.996 Observations 480 480 480 480 480 480 Note(s): Empirical results of GMM panel estimator present in the table by using Equation (2). Risk is the dependent variable measured through NPLTL (credit risk), Z-score (Stability risk), LLPTA (overall risk). BI is the competition measures. Size of banks categorized by the small and large size of banks. Small × BI (Large × BI) and Small × BI 2 (Large × BI 2 ) denotes the quadratic term of size and market competition. The values show in parenthesis are t-values, ***, ** and * indicates significant at 1%, 5% and 10% respectively. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (overidentifying restrictions). Arellano-Bond order 1(2) is tested for the first(second)order correlation, asymptotically N (0,1). These test the first-differenced residuals in the system GMM estimation Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 20 of 31 shows the U-shaped shape curve proposed by Martinez-Miera and Repullo (2010). It means that initially, large (small) banks are taking more risk (less), but in the long run, they are taking calculative (more) risk. Banks’ stability is leading to the opposite direction of risk of banks for large and small banks. Table 14. Efficiency equation—nonlinear effect of size and market competition on efficiency Variable Eff_C (with NPLTL) Eff_C (with Z-score) Eff_C (with LLPTA) Model I Model II Model I Model II Model I Model II Eff_C (−1) 1.108606*** (1096.68) 1.111475*** (1683.07) 1.108889*** (1187) 1.112765*** (1128.91) 1.109032*** (1140.92) 1.111375*** (1578.86) NPLTL 0.0020567***(3.95) 0.005444***(9.48) Z-score 6.89E-07**(2.34) −8.07E-06*** (−5.39) LLPTA −0.00284**(−2.50) 0.004375*(1.83) CFI 1 0.0063782(1.58) −0.0059*(−1.73) −0.00203(−0.73) −0.03333***(−4.56) −0.00174(−0.77) −0.02422***(−6.52) large 2.45E-08***(9.46) 2.17E-08***(9.36) 2.39E-08***(8.79) Small −1.54E-08*** (−3.29) −1.44E-08*(−1.98) −9.64E-09**(−2.26) BI −0.0241289*** (−3.92) 0.019321**(2.29) −0.03262***(−5.45) −0.00302(−0.16) −0.03609***(−6.48) −0.00139(−0.16) BI 2 −0.2329476*** (−4.39) 0.036579(0.57) −0.3029***(−5.60) −0.1136(−0.66) −0.33993***(−6.69) −0.13207*(−1.97) Large × BI 6.29E-07***(10.65) 5.50E-07***(10.18) 6.01E-07***(10.71) Small × BI −3.25E-07*(−1.92) −4.81E-07(−1.52) −1.27E-07(−0.83) Large × BI 2 4.12E-06***(10.74) 3.57E-06***(10.01) 3.97E-06***(11.54) Small × BI 2 −4.08E-07(−0.32) −3.76E-06(−1.35) 8.46E-07(0.73) BSD −6.48E-06**(−2.12) −5.90E-06*(−1.73) −1.7E-05***(−4.00) −1.9E-05**(−2.28) −2.1E-05***(−5.51) −2.3E-05***(−5.17) GGDP 0.0000313***(2.86) 8.67E-05***(8.95) 9.25E-06(1.3) 8.54E-05***(4.00) 2.38E-06(0.32) 6.45E-05***(5.13) Inflation −0.0000687*** (−5.21) −0.0001***(−7.66) −9.7E-05***(−7.84) −9.4E-05***(−3.66) −0.0001***(−8.09) −0.00012***(−9.16) DTA −0.0009706** (−2.08) −0.00044(−1.12) −0.00173***(−5.12) −0.00198**(−2.40) −0.00199***(−5.13) −0.0017***(−3.77) ROA 0.0001166***(6.28) 0.000199***(9.62) 8.41E-05***(5.02) 0.000176***(6.34) 7.55E-05***(4.28) 0.000144***(7.18) OBSTA −0.000153(−0.69) −0.00041(−1.43) −0.00025(−1.61) −0.00156***(−3.08) −0.00029*(−1.98) −0.00102***(−3.31) Constant −0.1094461*** (−88.1) −0.11168*** (−133.78) −0.10823*** (−110.11) −0.1102*** (−77.85) −0.10794*** (−105.67) −0.10915*** (−128.27) Hansen Test (P-value) 0.387 0.225 0.373 0.370 0.353 0.253 AR(1) (P-value) 0.029 0.016 0.037 0.058 0.027 0.045 AR(2) (P-value) 0.184 0.259 0.054 0.239 0.100 0.242 Observations 480 480 480 480 480 480 Note(s): Empirical results of GMM panel estimator present in the table by using Equation (2). The cost efficiency is the dependent variable measured through SFA. Risk is measured through NPLTL (credit risk), Z-score (Stability risk), LLPTA (overall risk). BI is the competition measures. Size of banks categorized by the small and large size of banks. Small × BI (Large × BI) and Small × BI 2 (Large × BI 2 ) denotes the quadratic term of size and market competition. The values show in parenthesis are t-values, ***, ** and * indicates significant at 1%, 5% and 10% respectively. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (over-identifying restrictions). Arellano-Bond order 1(2) is tested for the first(second)order correlation, asymptotically N (0,1). These test the first-differenced residuals in the system GMM estimation Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 21 of 31 The relationship between market competition and efficiency portrays the opposite picture that observed with risk. From Table 14, it is noted that with the increase in market competition, the cost efficiency of large banks initially decreases then increases in the long run. Although small banks’ efficiency shows a positive association, however, in the long run, no significant relationship is observed. These findings are parallel to the finds of Gupta (2018). Table 15 summarizes the GMM estimates examining the effect of risk and efficiency over financial intermediation cost with a nonlinear effect of size and competition. The interim and square term of size and competition illustrates that in a competitive market, the interest spread of large (small) banks initially decreases (increases) and subsequently increases (decreases). This is because initially, the risk escalation of large banks reduces the cost of intermediation benefit. In contrast, broad asset exposure gives them extra benefits to adjust the risk and interest spread in a competitive market. 5.7. Robust check of the nonlinear and quadratic effect of size & market competition on risk, efficiency, and cost of financial intermediation Tables 16–18 reinforce the empirical outcomes of Tables 13–15. Adapting the cost of intermediation measures CFI 2 from CFI 1, we check the robustness of nonlinear and quadratic models. Few exceptions only observed in the level of significance in a different model. For example, GGDP have found insignificant in Table 13 at the Z-score model, whereas it observed significantly in Table 16 in robust checks. Thus, the empirical results are plausible, considering few exceptions between the actual results and robust check results. 6. Concluding remarks Bangladesh’s economic growth has not yet reached the projected levels. High margins may stifle savings, investment, and employment, negatively impacting economic growth. The study attempts to explain how efficiency and bank risk-taking behavior affect the cost of intermediation in the developing country context. Although liberalization and financial reforms have reduced intermediation costs due to legislative changes, this may be explained by a rise in the capital requirement, which makes it more expensive for banks, not to mention risk-taking. Furthermore, the findings reveal that efficiency, market concentration, non-performing loans, size, and macroeconomic factors have the greatest economic influence on intermediation. Taking the data together, it’s clear that the financial reform failed to accomplish its goal of increasing competition and efficiency across the banking industry, as seen by the variance in bank margins over time. There is a lot of room to lower interest margins in Bangladesh by promoting banking rivalry; therefore, measures to promote competition and efficiency are needed. On the regulatory front, loosening limitations on foreign entry may help reduce intermediation costs. Substantial changes in the country’s informational, contractual, and enforcement infrastructure are required to achieve the national goal. Furthermore, the government should encourage banks to participate in markets in order to boost economic growth in the country, as expenditures are passed on to the public at a lower rate. The banking sector of Bangladesh is tremendously affected by several risk factors that indulge in survival and develop a fragile financial system. Financial intermediation is broadening access to financial services and accelerating economic performance (Levine, 2005). Shreds of evidence of Beck et al. (2007), Demirgüç-Kunt and Levine (2009), and Levine (2005), among others, support that the extent of financial intermediation has a causal effect on poverty reduction, inequality elimination, and ultimately boosting the economic growth. The study conducted by Stiglitz and Weiss (1981) found that credit rationing is prioritized for a higher cost of financial intermediation results in a lower level of credit grant to borrowers. The cost of financial intermediation is higher for lower-income countries (Calice & Zhou, 2018), and hence the lower intermediation spread is driven as a causal factor for financial development. The study found similar results concerning the cost of financial intermediation, which is negatively associated with bank risk and cost-efficiency. Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 22 of 31 The cost of intermediation is lower for efficient cost management and inversely associated with risk of banks. Chortareas et al. (2012) opine that efficiency gains cost the low interest spread. It also shows that bank risk has negatively affect cost efficiency because non-performing loan or provisions for default is higher when banks are less efficient. This study also evident the linear and nonlinear impact of size and market competition on risk, efficiency, and cost of financial intermediation. In Bangladesh, most of the commercial banks face similar situations due to lack of Table 15. Cost of financial intermediation equation—nonlinear effect of size and market competition on the cost of financial intermediation Variable CFI 1 (with NPLTL) CFI 1 (with Z-score) CFI 1 (with LLPTA) Model I Model II Model I Model II Model I Model II CFI 1 (−1) 0.5230728*** (12.23) 0.453892*** (10.03) 0.558515*** (12.15) 0.572325*** (13.43) 0.547436*** (15.45) 0.498242*** (12.87) NPLTL −0.0418197*** (−8.76) −0.05209*** (−6.80) Z-score −1.7E-05(−1.31) −1.4E-05(−1.15) LLPTA −0.07478*** (−5.11) −0.11642*** (−4.82) Eff_C −0.0107975** (−2.05) −0.01628*** (−4.21) −0.01968*** (−4.38) −0.03321*** (−9.22) −0.02292*** (−5.05) −0.02972*** (−9.96) Large 6.84E-09(0.83) 2.21E-08**(2.72) 5.99E-09(0.56) Small 3.41E-08(0.71) −1.22E-07*** (−2.97) −4.27E-08(−0.95) BI 0.2726513*** (3.38) 0.258828(1.46) 0.525952***(5.61) 0.941394***(6.13) 0.517095***(7.2) 0.659211***(4.03) BI 2 2.961034***(3.78) 3.40354**(2.10) 5.242312***(5.83) 9.562024***(6.90) 5.203064***(8.03) 7.109628***(4.89) large× BI 5.55E-07(1.50) 1.41E-06***(3.91) 4.03E-07(0.81) small × BI 6.24E-08(0.03) −6.91E-06*** (−3.85) −3.01E-06(−1.43) large × BI 2 6.42E-06*(1.77) 1.34E-05***(3.32) 4.12E-06(0.81) small × BI 2 −2E-05(−0.97) −8.4E-05***(−4.56) −5E-05**(−2.38) BSD −0.0004905*** (−6.61) −0.00049*** (−5.72) −0.00027**(−2.64) −0.00026**(−2.42) −0.00037*** (−4.48) −0.00036*** (−4.46) GGDP 0.0007591*** (2.82) 0.000618**(2.12) 0.001272***(4.07) 0.001481***(4.49) 0.001042***(3.54) 0.00111***(3.66) Inflation −0.0001782(−1.34) 0.000243(1.50) 0.000354(1.49) 0.00062**(2.33) 0.000221(1.57) 0.000581***(3.09) RD −0.1495017*** (−6.69) −0.1517***(−6.08) −0.12483*** (−5.60) −0.10184*** (−4.60) −0.13533*** (−6.99) −0.15073*** (−6.14) Constant 0.0550617*** (8.28) 0.060435***(8.16) 0.053132***(9.13) 0.073431*** (10.53) 0.063361***(8.25) 0.073571*** (11.57) Hansen Test (P-value) 0.238 0.299 0.252 0.191 0.219 0.241 AR(1) (P-value) 0.000 0.000 0.000 0.000 0.000 0.000 AR(2) (P-value) 0.483 0.466 0.423 0.401 0.823 0.783 Observations 480 480 480 480 480 480 Note(s): Empirical results of GMM panel estimator present in the table by using Equation (2). The cost of financial intermediation is the dependent variable measured through Net interest margin to average total assets. Risk is measured through NPLTL (credit risk), Z-score (Stability risk), LLPTA (overall risk). BI is the competition measures. Size of banks categorized by the small and large size of banks. Small × BI (Large × BI) and Small × BI 2 (Large × BI 2 ) denotes the quadratic term of size and market competition. The values show in parenthesis are t-values, ***, ** and * indicates significant at 1%, 5% and 10% respectively. J-statistic refers to the p-value of the Hansen test. The Hansen test’s null hypothesis depicts that the instruments used are not correlated with residuals (overidentifying restrictions). Arellano-Bond order 1(2) is tested for the first(second)order correlation, asymptotically N (0,1). These test the first-differenced residuals in the system GMM estimation Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 23 of 31 Psychology, 39(2), 81–90. https://doi.org/10.1080/ 01973533.2016.1277529 Yesmin, A. (2018). Do competition and development indicators heterogeneously affect risk and capital? Evidence from Asian banks. International Journal of Financial Engineering, 05(3), 1850017. https://doi.org/ 10.1142/S2424786318500172 Zheng, C., Gupta, A. D., & Moudud-Ul-Huq, S. (2017a). Do market competition and development indicators matter for banks’ risk, capital and efficiency relationship? International Journal of Financial Engineering, 4(02n03), 1750027. https://doi.org/10. 1142/S242478631750027X Zheng, C., Gupta, A. D., & Moudud-Ul-Huq, S. (2018a). Do human capital and cost efficiency affect risk and capital of commercial banks? An empirical study of a developing country. Asian Economic and Financial Review, 8(1), 22–37. https://doi.org/10.18488/journal. aefr.2018.81.22.37 Zheng, C., Gupta, A. D., & Moudud-Ul-Huq, S. (2018b). Effect of human capital efficiency on bank risk-taking behavior and capital regulation: Empirical evidence from a developing country. Asian Economic and Financial Review, 8(2), 231–247. https://doi.org/10.18488/journal.aefr. 2018.82.231.247 Zheng, C., Rahman, M. M., Begum, M., & Ashraf, B. N. (2017b). Capital regulation, the cost of financial intermediation and bank profitability: Evidence from Bangladesh. Journal of Risk and Financial Management Science Letters, 10(2). https://doi.org/ 10.3390/jrfm10020009 Appendix A Determination of Cost Efficiency Using Stochastic Frontier Analysis (SFA) The stochastic frontier analysis originated by (Aigner et al., 1977) is used to calculate each bank’s efficiency based on the production frontier. On this production frontier model, the stochastic cost frontier model was developed (For details, see Kwan and Eisenbeis (1997), Schmidt and Knox Lovell (1979)). According to this methodology, due to inefficiency and random noise, a bank’s observed cost is formulated to deviate from the cost-efficient frontier (Deelchand & Padgett, 2009a). For the nth Bank, Ln TCn¼f ln Qi;lnPj  �þεn(1A) TC n represents total operating cost including financial costs; Q i indicates two outputs, i.e. Q 1 = Gross loans and advances, Q 2 = Other earning assets. Pj stands for three input prices, i.e. P 1 = Price of the fund, the ratio of total interest expenses to total deposit, P2 = Price of physical capital, which is non-interest expenses to fixed assets P 3 = Price of labour, which is total personnel expenses. ε n shows the deviation of the actual total cost of a bank from the cost-efficient frontier, and it has two disturbance terms given as below: εn¼VnþUn Where V n is the random error term, and we assume that this is independent and identically distributed N (0,σ2 v). U n represents cost inefficiency and assumed to be distributed independently of V n and a half-normal distribution, i.e. N (0,σ2 u). By using the intermediation approach (Sealey & Lindley, 1977) and by following (Deelchand & Padgett, 2009a), we have developed the following multiproduct translog cost function to specify the cost function: Ln TC ¼αþ∑ i αilnQiþ∑ j βjlnPjþ1= 2∑ i ∑ k γiklnQilnQk þ1=2∑ j ∑ h δjhlnPjlnPhþ∑ i ∑ j λijlnQilnPjþε(2A) According to Jondrow et al. (1982), the expected value of U n, on conditional ε n, represents the cost-inefficiency of bank n (which is defined as C n ). Cn¼EUn=εn¼ ½σλ=ð1þλ2Þ�½φ εnλ=σð Þ=ϕ εnλ=σð Þþεnλ=σ�(3A) Das Gupta et al., Cogent Economics & Finance (2021), 9: 1967575 https://doi.org/10.1080/23322039.2021.1967575 Page 30 of 31 Where λ is the ratio of the standard deviation of U n to standard deviation of V n , φ is the cumulative standard normal density function, and ϕ is the standard normal density function. C n can be estimated by using Equation (3A). © 2021 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. You are free to: Share — copy and redistribute the material in any medium or format. Adapt — remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. 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