THE RELATIONSHIP BETWEEN HOLDING CAPITAL AND BANKS’ COST AND PROFIT EFFICIENCY: RISK-BASED CAPITAL RATIOS AND UNWEIGHTED LEVERAGE

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A.H. (Amarins) Smits (s1975404)

Study program: MSc International Financial Management; Other UoG program: MSc International Business and Management; Faculty of Economics and Business, University of Groningen, the Netherlands.

Supervisor: M.A. (Martien) Lamers

Co-assessor: P.J. (Paulo) Marques Morgado

Article information Abstract

Article history: Draft: 12-12-15

Received feedback: 16-12-15 Final: 08-01-16

Policymakers focus with financial regulation on increasing financial stability, but they overlook the effect of banks’ efficiency on stability. With this study, I investigate the discussion in literature about the impact of risk-based and unweighted capital on banks’ efficiency. With a sample of 318 EU and US banks over the period 2005-2014, I find that unweighted leverage affects pure cost efficiency negatively, but both types of capital influence profit efficiency positively. Moreover, unweighted leverage has a stronger effect on both efficiency types, which is robust for revenue efficiency. Future research may investigate the optimal level of capital buffers. JEL classification: G21 G28 Keywords: Cost efficiency Profit efficiency Risk-based capital Unweighted leverage Word count: 17.441

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Amarins Smits | The relationship between holding capital and bank’s cost and profit efficiency: risk-based capital ratios and leverage 2

I. PREFACE

The fall of Lehman Brothers and Bear Stearns in 2008 was only the beginning of the worldwide liquidity crisis. Policymakers have constantly focused on regulation for recovering and improving the stability in the financial system. With this thesis, I am focusing on an overlooked effect of regulation that impacts financial stability as well: banks’ efficiency. When banks are efficient, they contribute to stability in the financial system. With investigating the relationship between holding capital and cost and profit efficiency, I hope to provide insights in the trade-off between stabilizing the financial system and banks’ efficiency when assessing the impact of financial requirements. Writing this thesis was the last step I took in the journey of preparing myself for the labor market. The opportunities I got during my whole studies have made me the person I am today. Therefore, I want to thank several people.

First of all, I want to thank Martien Lamers for the valuable feedback I received during the writing process of my thesis. You provided me useful comments through which have improved my thesis substantially. I also want to thank Paulo Marques Morgado for being my co-assessor. Moreover, I thank EY Amsterdam for providing me the opportunity to write my thesis at their office. Especially, I want to thank Henk-Jan Nanninga for his ideas regarding my thesis. Furthermore, I want to thank Jacqueline Schijven for her econometrical knowledge: you know how to make statistics interesting. Here I only mention two people of an amazing team. Everyone of FAAS FSO has contributed to making my thesis an interesting and fun project: either in discussing about my topic or providing me knowledge about the projects of EY. Last but not least, I want to thank my family and friends, who supported me during my whole studies.

The combination of writing my thesis and being an intern at EY have prepared me in the right way for the labor market: this was the last step I needed to take before I am going to start my first job.

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II. CONTENTS

I. PREFACE 2

II. CONTENTS 3

1. INTRODUCTION 4

2. LITERATURE REVIEW 7

2.1 Cost and profit efficiency 7

2.2 Financial regulation 8

2.3 Bank’s compliance with regulation: decisions on different levels 11 2.4 Trade-off between stability and efficiency: risk-taking and insolvency 13

2.5 Increased capital costs: agency theory 14

2.6 Hypotheses development 15

3. METHODOLOGY 18

3.1 Sample selection 18

3.2 Method and measurement 18

3.2.1 Measurement of dependent variables 18

3.2.2 Measurement of independent and control variables 20

3.3 Research design 22

4. DATA 24

5. ANALYSIS 29

5.1 Results regression analyses: cost efficiency 29

5.2 Results regression analyses: profit efficiency 33

5.3 Robustness checks 35

5.3.1 Revenue efficiency 35

5.3.2 Sample split: US, EU, pre- and post-crisis 36

5.3.3 Unweighted leverage: bank size and efficiency 37

6. CONCLUSION 38

7. RECOMMENDATIONS FOR MANAGEMENT 40

8. LIMITATIONS 41

9. REFERENCES 43

10. APPENDICES 49

A Variable description 49

B Sample composition 50

C Frontier analysis: SFA vs. DEA 51

D Evolution of capital ratios 52

E Robustness check one: revenue efficiency 55

F Robustness check two: sample split 56

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CHAPTER ONE INTRODUCTION

Since the financial crisis, financial regulators are more than ever focused on increasing the stability in the financial system. Policymakers realized that the financial system was subject to contagion after the collapse of Lehman Brothers in 2008. The whole financial system became unstable and caused the worldwide liquidity crisis. After the crisis, new financial regulation was introduced because Basel II needed to be improved: banks held too little high quality capital, insufficient liquid funds and were too highly leveraged, i.e. they took on too many assets relative to capital (Haan, Oosterloo, & Schoenmaker, 2012). Regulators focus with Basel III on increasing the stability of the financial system, by not only requiring banks to hold a certain amount of capital reduced for risk-weights, but also maintaining an amount of leverage that is unweighted.

Policymakers are constantly seeking for ways to improve the financial stability by imposing requirements for banks’ capital. However, when they look at increasing the financial stability for banks, they should also consider the effect on banks’ efficiency: efficient banks are less likely to fail, which contributes to a more stable financial system (Wheelock & Wilson, 2000). Where financial regulators consider higher capital requirements for increasing stability, they overlook the influence on banks’ efficiency. Too little capital may increase the risk of bank failure, but excessive capital reduces the efficiency in the financial system as it increases costs on banks and their customers (Lee & Chih, 2013). This trade-off between stability and efficiency is important to take into account.

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Amarins Smits | The relationship between holding capital and bank’s cost and profit efficiency: risk-based capital ratios and leverage 5 reduce insolvency risk of banks. In contrast, Admati and Hellwig (2014) criticize risk-based capital as they perceive the risk-weights as manipulative and subject to moral hazard. This discussion in literature is relevant as the European Systemic Risk Board (2014) found a negative correlation between risk-based and unweighted capital. By comparing risk-based and unweighted capital, I offer useful insights to management in two ways. First, financial regulation is a highly dynamic field in which requirements are constantly subject to change. Banks are seeking for ways to comply with the regulations, and need to be able to adjust to the upcoming requirements announced by the regulator. Second, financial regulation is subject to countries’ as well as banks’ individual decision-making: even though the Basel Committee on Banking Supervision (2009) has stated a certain threshold for the ratios, many banks hold their ratios above this required minimum. By measuring the RBC ratios and leverage ratio at margin, I overcome not only the possible changes in regulation, but I also provide insights to banks of what the implications are for their cost and profit efficiency of holding higher capital levels than the minimum required.

With my paper, I contribute to the discussion in literature by investigating the effect of increasing banks’ capital on bank efficiency and in turn the stability in the financial system, but as well I make a distinction between the impact of risk-based and unweighted capital. I consider a sample of 318 banks in the US and EU during 2005 to 2014. Including the years 2005 to 2014 allow me to investigate the effect pre- and post-crisis. Moreover, I include pre- and post-years of the Basel III implementation, which started in 2010. I choose US and EU banks, because those banks have a long-time experience with financial regulation. My main research question is:

“How does risk-based and unweighted capital affect banks’ cost and profit efficiency?”

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Amarins Smits | The relationship between holding capital and bank’s cost and profit efficiency: risk-based capital ratios and leverage 6 Margaritis & Staikouras, 2011). Where these papers are based on absolute efficiency scores, I look at the impact in efficiency of capital requirements. Second, I compare the two types of capital, as there is no consensus in literature about the effectiveness of risk-based or unweighted capital. Therefore, my second research question is “How is risk-based and unweighted capital related?”. Where Admati and Hellwig (2014) state that risk-based capital is subject to manipulation and moral hazard, Kim and Santomero (1988) find unweighted capital insufficient for covering unexpected losses of banks. I find a low correlation, indicating that regulators really focus on two different capital requirements with the risk-based and equity-to-assets ratio. I find that unweighted capital has a stronger effect on my pure cost efficiency measure and on profit efficiency. Furthermore, my study provides the following contributions. First, holding capital affects banks’ profit efficiency positively. Here, in line with Berger and DeYoung (1997), I assess the effect of moral hazard: an increase in capital leads to reduced risk-taking by banks and a decrease in moral hazard. Moreover, an increase in capital decreases bank’s insolvency risk (Kim & Santomero, 1988). This reduced moral hazard and insolvency risk affect profit efficiency positively. Second, unweighted capital affects pure cost efficiency negatively. An increase in own capital leads to increased agency costs to monitor the interests of shareholders and managers (Berger & Bonaccorsi di Patti, 2006). These increased costs reduce banks’ cost efficiency. Last, I find results in line with Kamarudin et al. (2014) that revenue efficiency is the main driver for profit efficiency when holding unweighted capital.

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CHAPTER TWO LITERATURE REVIEW

In this part, I describe the relevant literature regarding my subject. First, I define the concepts of cost and profit efficiency, whereafter I assess the correlation of risk-based capital and unweighted leverage. Additionally, I link these concepts to important theories in finance related to asymmetric information: moral hazard and the agency theory. Finally, I summarize the findings in literature, which leads to the formulation of the hypotheses.

2.1 COST AND PROFIT EFFICIENCY

Where technical efficiency focuses on the use of technology, cost and profit efficiency are both based on a different type of economic optimization (Berger & Mester, 1997). The difference in economic optimization becomes clear when we look at the different definition of both types of efficiency. First, the definition of cost efficiency is:

“(…) how close a bank’s cost is to what the optimal bank’s costs would be for producing the same output under the same conditions.” (Berger & Mester, 1997: p. 898).

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Amarins Smits | The relationship between holding capital and bank’s cost and profit efficiency: risk-based capital ratios and leverage 8 “(…) how close a bank is to generating maximum profits regarding its output levels rather than its output prices.” (Berger & Mester, 1997: p. 901-902).

Next to overcoming the possible scale bias by making use of the alternative approach, another advantage of this definition is that it incorporates product quality. With the standard definition, output prices may be an arbitrary measure: some banks are better able to be competitive in output prices due to their country’s market structure, regulation and quality of banking services provided (Berger & Mester, 1997). Therefore, I do not consider output prices, but I evaluate banks on their output levels which gives a more proper comparison as I can measure the additional revenue that higher quality output can generate (Berger & Mester, 1997).

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TABLE 1

Efficiency: Differences in Focus

Inputs Input Prices Outputs Output prices

Cost efficiency Minimizing Minimizing Stabilizing x

Standard profit efficiency Minimizing Minimizing Maximizing Maximizing

Alternative profit efficiency Minimizing Minimizing Maximizing x

Revenue efficiency Stabilizing Stabilizing Maximizing Maximizing

Technical efficiency Minimizing x Maximizing x

Note: Alternative profit efficiency is more appropriate under different market structures, regulation and quality of banking services provided. Source: Berger and Mester (1997) and Kamarudin et al. (2014)

Now I have assessed that cost and profit efficiency are different types of economic optimization regarding their different definitions and banking strategies, important to note is the shift in efficiency focus by banks. Where many research found that cost efficiency has been superior to profit efficiency for pre-crisis years (Maudos et al., 2002; Yildirim & Philippatos, 2007; Pasiouras, Tanna & Zopounidis, 2009), research based on samples for post-crisis years show a decrease in cost efficiency and increase in profit efficiency (Alam, 2012; Andrieş & Căpraru, 2014; Galavas & Syriopoulos, 2014). The reason for this shift is that profit efficiency turned out to be more important to banks than cost efficiency during the crisis: banks that were more profit efficient were better able to absorb bad debts and to prevent themselves to unexpected events (Koutsomanolli-Filippaki et al., 2011). Here, a focus on diversification turned out to be a more appropriate strategy: according to Beltratti and Stulz (2009), banks that held more liquid assets and had more loans performed significantly better during the month after the Lehman bankruptcy. This reason explains the shift in efficiency focus by banks: they evaluated that profit efficiency was more useful for survival than cost efficiency.

2.2 RISK-BASED AND UNWEIGHTED CAPITAL: ARE THEY RELATED?

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Amarins Smits | The relationship between holding capital and bank’s cost and profit

efficiency: risk-based capital ratios and leverage 10 customers, which in turn decreases financial stability (Lee & Chih, 2013). Literature is

divided about the effect of capital on bank efficiency, by which they have different evaluation of the distinction of risk-based and unweighted capital. The risk-based capital (RBC) ratios require an amount of capital that a bank must have at risk: the ratios include assets that are adjusted to their risk-weights, which provide owners and managers with incentives to take less risk (Chortareas, Girardone & Ventouri, 2012). High risk-weightings are assigned to risky assets, which will lower the RBC ratios. Safer assets will receive low weightings, which increase the RBC ratios. The idea behind the RBC ratios is that when banks have more risk-based capital, the gains they may receive from their increased risk-taking will be equalized by the potential loss of their capital (Barth, Lin, Ma, Seade & Song, 2013b).

The Basel Committee on Banking Supervision (2009) requires banks to maintain their capital ratios above a certain threshold, but many banks have higher ratios due to their individual decision-making. In this way, it is possible for me to investigate the different effect between banks of holding different levels of capital. The Basel Committee on Banking Supervision (2009) requires that the Total RBC ratio should be at a minimum of 8% in 2019. Total RBC consists of Tier 1 and Tier 2 capital and can be described as ‘going concern’ loss absorbing capacity adjusted for items as intangible assets and unrealized gains or losses (Hogan, 2015). Tier 1 capital is required to be 6% in 2019 and includes Common Equity Tier 1, i.e. common equity and retained earnings, and additional Tier 1 capital, i.e. contingent convertible instruments that meet certain criteria. Tier 2 capital incorporates specific types of going concern instruments such as loan loss provisions that can absorb losses once common equity and additional Tier 1 equity are spent. The Common Equity Tier 1 capital is a part of Tier 1 capital and needs be 4.5% in 2019, but I will not analyze this due to a lack of available data. (Basel Committee on Banking Supervision, 2009; Haan et al., 2012) In Appendix A, I give a comprehensive overview of the variables.

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efficiency: risk-based capital ratios and leverage 11 The European Systemic Risk Board (ESRB) (2014) evaluated the correlation of RBC

ratios and leverage and found a diverging trend. In the 1990s, these variables were highly correlated. However, this correlation started to decrease in the 2000s, becoming negative in 2006. Also after the crisis, this correlation remained negative. This negative correlation implies that when banks hold higher RBC ratios, their leverage ratio will be lower. (ESRB, 2014)

2.3 BANKS’ COMPLIANCE WITH REGULATION: DECISIONS ON DIFFERENT LEVELS

In order to increase the stability in the financial system, the Basel Committee on Banking Supervision (2009) designed the regulatory standards of Basel III. The standards are not only subject to changes in requirements, but also additional requirements are imposed. For instance, the Financial Stability Board released in consultation with the Basel Committee on Banking Supervision at the end of 2014 a proposed standard for all systemic banks to maintain a certain level of Total Loss Absorbing Capacity, also known as TLAC (FSB, 2015). After this, also in the end of 2014, the European Banking Authority announced additional loss-absorbing capacity requirements for all European banks of which the implementation starts in 2016: the Minimum Requirement for own funds and Eligible Liabilities (MREL). MREL is designed for banks to maintain additional capital in the form of bail-in capital. When banks face financial distress, they can utilize their own MREL buffer as bail-in capital. This is an additional tool to increase the financial stability as banks do not need a bail-out in order to recover from their losses. (BBVA RESEARCH, 2015; EBA, 2014) These two extra requirements are only examples of how dynamic financial regulation is. Banks should realize that this is not only because of changing requirements imposed by the regulator, the standards are also subject to country-level decisions: countries can impose higher ratios for their national banks. This shows that financial regulation is a dynamic field: banks need to be able to comply with the (upcoming) requirements of the regulators as well as the national governments.

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efficiency: risk-based capital ratios and leverage 12 risk (Dash & Pathak, 2011). When designing their ALM, they take into account the

adjustment rate, asset volatility and the target capital buffer in order to compensate for unexpected events (Memmel, & Raupach, 2010). De Jonghe and Öztekin (2015) assess the behavior of banks when they need to increase their capital ratios to reach the target level as:

“Banks increase their capital ratios through external capital management rather than through a substantial change in the asset base: (…) they focus on equity growth rather than asset liquidation” (De Jonghe & Öztekin, 2015: p. 175)

This shows that banks accept the higher costs involved in raising equity. However, when raising new capital is too costly, it is more cost-efficient to liquidate assets rather than increase equity. Banks’ ALM should then consider whether banks can reduce their assets, depending on their maturity and whether they will lose capital resulting from selling off illiquid, nonmaturing assets (De Jonghe, & Öztekin, 2015; Memmel & Raupach, 2010).

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efficiency: risk-based capital ratios and leverage 13

2.4 TRADE-OFF BETWEEN STABILITY AND EFFICIENCY: RISK-TAKING AND INSOLVENCY

The main purpose of financial regulation is to improve banks’ liquidity and solvency (Lee & Chih, 2013). Basel III focuses on requiring higher buffers for individual banks in order to prevent systemic contagion as happened in 2007-2008 (Haan et al., 2012). Before the crisis, a well-known type of risk, associated with the asset side of the balance sheet, was credit risk: the risk of loss because of a counterparty’s failure to perform according the contractual arrangement, for instance due to a defaulting borrower (Haan et al., 2012; Memmel & Schertler, 2012). During the crisis another type of risk, i.e. liquidity risk, turned out to be crucial to the operations of banks: they had insufficient liquid resources to meet the liquidity demand (Haan et al., 2012). This type of risk is associated with the asset and liability side, respectively reflecting bank’s investment and funding decisions (Memmel & Schertler, 2012). Basel II assumed that a one-year maturity asset was funded with a one-year maturity debt. In contrast, banks funded long-term assets partly with short-term deposits that were withdrawable on demand (Dermine, 2015). This maturity mismatch caused bank runs by uninsured depositors, with the example of banks Bear Stearns and Lehman Brothers during the financial crisis (Dermine, 2015). Therefore, Basel III focuses with the RBC ratios on constraints on liquid assets and maturity mismatches, and thereby preventing situations in which risky long-term assets are financed by short-term deposits (Dermine, 2015). The regulations have the overall objective to strengthen the financial stability in the financial system and thus reduce the individual financial institutions’ risk-taking (Schmaltz, Pokutta, Heidorn & Andrae, 2014).

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efficiency: risk-based capital ratios and leverage 14 but on the other hand banks should maintain a stable level of efficiency as efficient banks are

less likely to fail (Haan et al., 2012; Wheelock & Wilson, 2000).

Due to the presence of information asymmetry, Hogan (2015) is skeptical about the effect of RBC on banks’ risk-taking: the correspondence of RBC with actual risk was weak in Basel I and II. Friedman (2011) shows that American banks circumvented the Basel I RBC requirements by obtaining assets that were rated as safe in the risk-weighting system, but involved actually much risk. In this way, banks were incentivized to acquire assets that were mis-rated by the supervisor (VanHoose, 2007). Where regulators did not notice it, banks had information about the mis-ratings and thus seemed compliant to the regulations, but could take more risks than their assets would be able to cover in case of losses. This fact shows another classical issue in the banking industry: moral hazard. Here, banks are incentivized to take excessive risks as they have access to government deposit insurance and other safety net protections (Berger & Bonaccorsi di Patti, 2006; Berger & DeYoung, 1997). Moreover, moral hazard will increase with inadequate prudential supervision and when banks have the possibility to obtain government support (ESRB, 2014). The moral hazard hypothesis assumes that banks with relatively low capital engage in higher risk-taking activities compared to banks with more capital: a less efficient firm may take higher risks to compensate for the lost returns (Berger & DeYoung, 1997). The adoption of capital reduces moral hazard and risk-taking behavior: banks that are restricted by capital requirements take less risks (Hermes & Meesters, 2015). Thus, a safer asset portfolio reduces excessive risk-taking by banks. Moreover, De Jonghe and Öztekin (2015) find that the adoption of more capital reduces bank’s insolvency risk. A decrease in the overall riskiness of banks increases its ability to allocate resources efficiently (Hermes & Meesters, 2015): banks that are more cautious in their risk-taking have higher efficiency scores (Staub, da Silva e Souza & Tabak, 2010).

2.5 INCREASED CAPITAL COSTS: AGENCY THEORY

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efficiency: risk-based capital ratios and leverage 15 the costs of outside equity. This will increase firm value by encouraging managers to act more

in the interests of shareholders, as they feel the threat of failure because of a higher share of debt which may cause personal losses in salary or reputation. (Berger & Bonaccorsi di Patti, 2006) However, the effect is nonmonotonic: when the debt-to-equity ratio becomes too high, the risk of financial distress arises, because it leads to higher agency costs in increased interest expenses for compensating the expected losses of debt holders. Thus, relatively low levels of debt-to-equity increase incentives for managers to act in the interest of the shareholders, and thereby reducing agency costs of outside equity. However, at some point, the agency costs of outside debt outweigh the agency costs of outside equity, which results in higher agency costs. (Berger & Bonaccorsi di Patti, 2006)

I follow the definition of unweighted leverage of Berger and Bonaccorsi di Patti (2006) as the equity to assets ratio. De Jonghe and Öztekin (2015) show that banks increase their capital ratio by increasing equity rather than shrinking their assets. A higher equity share implies that the agency costs will increase, because investors are putting more effort into aligning the interests of themselves with their managers’ interests. The increased agency costs will result in lower cost efficiency.

2.6 HYPOTHESES DEVELOPMENT

On the basis of the literature review, I formulate several hypotheses. Before I formulate the hypotheses, I give a short summary of the literature on which the hypotheses are based.

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efficiency: risk-based capital ratios and leverage 16 Hypothesis 1a: The Tier 1 capital ratio influences cost efficiency negatively.

Hypothesis 1b: The Total RBC ratio influences cost efficiency negatively. Hypothesis 1c: Unweighted leverage influences cost efficiency negatively.

Hypothesis 1d: The RBC ratios affect cost efficiency differently than unweighted leverage.

The literature review shows that cost and profit efficiency move in the opposite direction: they focus on a different type of economic optimization (Berger & Mester, 1997). According to Kamarudin et al. (2014), revenue efficiency is a trigger for profit efficiency rather than cost efficiency. The financial crisis seems to be the trigger for banks to focus more on profit efficiency, as more profit efficient banks were in a better financial position to survive. However, banks face regulatory and market constraints when designing their ALM. When they hold more capital, their credit and insolvency risk will reduce: while they take less risks, they will attract safer assets. Moreover, moral hazard will decline as banks have fewer incentives to take risks when their assets are covered by own high-quality capital. Hermes and Meesters (2015) state that banks with reduced risk-taking have a more efficient allocation of resources. Therefore, I formulate the following hypotheses regarding profit efficiency:

Hypothesis 2a: The Tier 1 capital ratio influences profit efficiency positively. Hypothesis 2b: The Total RBC ratio influences profit efficiency positively. Hypothesis 2c: Unweighted leverage influences profit efficiency positively.

Hypothesis 2d: The RBC ratios affect profit efficiency differently than unweighted leverage. A summary of the variables can be found in Appendix A.

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FIGURE 1 Conceptual Framework H2b + Net loans to total assets H2c + H2a + H1a - H1b - H1c -

Bank size Equity

Inflation

rate GDP growth Deposit coverage Capital stringency Tier 1 ratio Total RBC ratio Unweighted leverage Cost

efficiency Profit efficiency

H1d: RBC ≠ Unweighted leverage on cost efficiency H2d: RBC ≠ Unweighted leverage on profit efficiency

Controls have an effect on the relationship between independent and dependent variables as depicted by:

Bank-specific controls: Country-specific controls:

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CHAPTER THREE METHODOLOGY

In this section, I explain the way I conduct the research. First, I explain the sample composition and how I select the necessary data for this research. Then, I elaborate on the measurement of the dependent, independent and control variables. Finally, I explain my decision for the empirical model and give the econometric definitions which I use for the regression analyses in order to test the hypotheses.

3.1 SAMPLE SELECTION

I obtain the data necessary for this research from the Bureau Van Dijk Bankscope database. The sample selection process consists of three steps. First, I select banks with consolidation codes C1 and C2 that are located in the European Union and in the United States. I choose this location, because these countries have long-term experiences with regulations and transparency, which increases the data availability. The consolidation codes C1 and C2 reflect holding companies. This threshold results in 2711 banks. Second, I only maintain banks that have total assets above 4 billion USD in 2014 in the sample. I choose the threshold of the year 2014 to reduce the effect of the financial crisis on banks: in years before, the crisis may still have had its effect on the banks’ performance. This results in 573 banks. Finally, since I use Data Envelopment Analysis (DEA), I need to have a balanced panel on the inputs and outputs for measuring efficiency. Therefore, I exclude banks from the sample that have a lack of available data on inputs, input prices or outputs during the period 2005 to 2014. I choose 2005 to 2014 as sample period in order to assess both pre- and post-crisis period, together with years before and after the implementation of the Basel III capital requirements. This final threshold results in a sample of 318 banks in total, of which 101 are located in the US and 217 in the EU.

3.2 METHOD AND MEASUREMENT 3.2.1 Measurement of Dependent Variables

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efficiency: risk-based capital ratios and leverage 19 the Return on Assets (ROA) as the first measure of profit efficiency: net income divided by

total assets (Maudos et al., 2002). Both ratios are easily calculated for banks and provide a proper benchmark to compare their efficiency with the competition. However, I complement the accounting ratios with a best-practice frontier method in order to increase the generalizability of the research, as Berger and Mester (1997) state that using frontier efficiency as a measurement tool is superior to traditional accounting ratios such as the cost-to-income ratio. The efficiency scores obtained from the frontier analyses are more pure measures compared to the accounting ratios. The two most common frontier measurement methods for efficiency are Stochastic Frontier Approach (SFA) and Data Envelopment Analysis (DEA). Both methods make use of the selection of input-output combinations and determine a best-practice frontier of optimal efficiency, where deviations from this frontier represent inefficiencies (Pevcin, 2014; Cook & Seiford, 2009). However, there are also several differences which I list in Appendix D. I use the DEA approach to complement the accounting ratios. DEA has different specifications for its calculation of inefficiencies, which I show in Table 2.

Additionally, when using frontier analysis, it is useful to control for national characteristics by drawing a frontier for every country (Chortareas et al., 2012). However, my sample consists of certain small countries in which not enough banks operate to be able to obtain a proper national best-practice frontier. Therefore, I estimate one frontier for the EU and one for the US for cost efficiency, and one frontier for the EU and one for the US for profit efficiency. As a result, I perform 16 regression analyses to test the four hypotheses with two measures for cost as well as two measures for profit efficiency.

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efficiency: risk-based capital ratios and leverage 20 interest expenses on customer deposits plus other interest expenses divided by deposits, and

the price of fixed assets, i.e. operating expenses divided by fixed assets. Finally, I use loans and income as outputs. (Berger & Mester, 1997; Lee & Chih, 2013; Kamarudin et al., 2014; Bonaccorsi di Patti & Hardy, 2005).

TABLE 2

Econometric Definitions of Cost and Profit Efficiency DEA Definition Equation Cost functiona _{ln(𝐶) = 𝑓(𝑤, 𝑦, 𝑧, 𝑣) + ln(𝑢 ) + ln (𝜀 )} ₍₉₎ Cost definitionb 𝐶𝑂𝑆𝑇𝐸𝐹𝐹 =𝐶 . 𝐶 = exp[𝑓(𝑤 , 𝑦 , 𝑧 , 𝑣 )] ∗ exp ln (û ) exp[𝑓(𝑤 , 𝑦 , 𝑧 , 𝑣 )] ∗ exp ln(û ) (10) Profit functiona _{ln(𝜋 + 𝜃) = 𝑓(𝑤, 𝑦, 𝑧, 𝑣) + ln(𝑢 ) + ln (𝜀 )} ₍₁₁₎ Profit definitionc 𝑃𝑅𝑂𝐹𝐸𝐹𝐹 = 𝜋 𝜋 = {exp[𝑓 (𝑤 , 𝑦 , 𝑧 , 𝑣 )] ∗ exp[ln (û )]} − 𝜃 {exp[𝑓 (𝑤 , 𝑦 , 𝑧 , 𝑣 )] ∗ exp[𝑙𝑛(û )]} − 𝜃 (12) Description of coefficients C Variable costs f Functional form

w Vector of prices of variable inputs

y Vector of quantities of variable outputs

z Quantities of any fixed netputs (inputs or outputs)

v Vector of control for environmental or market variables

ln(uC) or ln(uπ) Control for inefficiencies that reduce costs or profits

ln(εC) or ln(επ) Random error term

i Banks in sample

uC Inefficiency factor that may raise costs above the best-practice level

εC Random error term for measurement error and luck

ûCmin Minimum observed cost efficiency of all banks in the sample

π Variable profits of the bank

θ Constant that is added to every bank’s profit to create positive numbers for the natural

logarithm

ûπmax Maximum observed profit efficiency of all banks in the sample

Notes:

a_{Cost/profit function shows that costs/profits are affected by input prices, output quantities, fixed netputs}

(off-balance-sheet guarantees, physical capital, and financial equity capital), and environmental and market variables plus two error terms, one correcting for inefficiencies that reduce costs/profits and on for random errors.

b_{Cost definition: “Bank i’s estimated costs to produce bank i’s output if the bank was as efficient as the}

best-practice bank in the sample facing the same (w ,y ,z ,v) variables, divided by the actual cost of bank i” (Berger & Mester, 1997: p. 899)

c_{Profit definition: “The ratio of predicted actual profits to the predicted maximum profits that could be earned if}

bank I was as efficient as the best-practice bank in the sample facing the same (w, y, z, v) variables” (Berger & Mester, 1997: p. 899-900).

3.2.2 Measurement of Independent and Control Variables

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efficiency: risk-based capital ratios and leverage 21 define unweighted leverage as the equity-to-assets ratio following the Basel III definition (Dermine, 2015). Important to take into account is that I do not consider the minimum requirements of the Basel III, i.e. a 6%, 8% and 3% minimum level for Tier 1, Total RBC and unweighted leverage respectively, but I compare these values among banks: in this way I can evaluate the effect of a higher or lower capital ratio.

Additional to the dependent (cost and profit efficiency) and independent variables (capital measures), I add control variables to obtain a proper analysis of the relationship. I divide the control variables into bank- and country-specific variables. The bank-specific variables are bank size, bank’s financing activities and equity. When banks are bigger, they tend to be more efficient due to scale economies (Altunbas, Carbo, Gardener & Molyneux, 2007; Barth et al., 2013b). I calculate bank size as the natural logarithm of total assets (Barth et al., 2013b). The bank’s financing activities are reflected in the ratio of net loans to total assets (Altunbas et al., 2007). Net loans reflect performing loans, by which I correct for non-performing loans (Altunbas et al., 2007). Altunbas et al. (2007) argue that when banks experience rapid growth in performing loans, they may increase their risk-taking and affect hereby efficiency negatively. The subtraction of non-performing loans corrects for negative shocks that may affect banks (Berger & Mester, 1997). Additionally, performing loans are perceived as the main source of revenue and expected to affect performance negatively: banks with a lower net loans to total assets ratio tend to be more efficient in profits as they take less risk (Altunbas et al., 2007). The last bank-specific variable is the natural logarithm of equity. Berger and Mester (1997) advocate that not controlling for equity will give biased results when measuring efficiency. Large banks tend to have lower shares of equity and have thus higher interest expenses on their debt. In contrast to dividends, interest expenses are seen as costs that lead to cost scale diseconomies. This decreases cost and profit efficiency (Berger & Mester, 1997).

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efficiency: risk-based capital ratios and leverage 22 Additionally, I use the research of Barth et al. (2013a) to obtain data on capital stringency,

and the paper of Demirgüç-Kunt et al. (2005) for deposit coverage. De Jonghe and Öztekin (2015) found that banks make faster capital structure adjustments in countries with stricter capital requirements. Higher capital stringency limits bank runs and thus may increase banks’ efficiency (Barth et al., 2013a). Finally, governments use deposit insurance schemes in order to protect depositors from incurring large losses in cases of bankruptcy. This will result in less systemic shocks to the financial system, affecting bank efficiency positively (Demirgüç-Kunt et al., 2005). Finally, I control for bank- and year-fixed effects.

3.3 RESEARCH DESIGN

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efficiency: risk-based capital ratios and leverage 23 index for the evolution over a large time-span, which may not have been up-to-date anymore

due to events as the financial crisis in 2007-2008.

Now I explained which statistical model I use for testing the hypothesis, I elaborate on the econometrical approach of the tests. The econometric definitions for the hypotheses regarding cost efficiency are:

𝐶𝑂𝑆𝑇𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑁𝐸𝑅𝐵𝐶 + 𝛾𝑋 + 𝜇 +𝜆 + 𝜀 (1) 𝐶𝑂𝑆𝑇𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑇𝑅𝐵𝐶 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (2) 𝐶𝑂𝑆𝑇𝐸𝐹𝐹 = ∝ + 𝛽 𝑈𝑁𝐿𝐸𝑉 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (3) 𝐶𝑂𝑆𝑇𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑇𝑅𝐵𝐶 + 𝛽 𝑈𝑁𝐿𝐸𝑉 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (4)

For cost efficiency, I use cost-to-income and Cost efficiency DEA as measures. However, important to take into account is that a lower cost-to-income indicates higher cost efficiency: banks are able to generate more income with less costs. Therefore, a significant positive coefficient for β1TONERBCit, β2TOTRBCit or β3UNLEVit on cost-to-income does not reject

hypothesis 1a, 1b or 1c, respectively. In contrast, a significant negative coefficient for β1TONERBCit, β2TOTRBCit or β3UNLEVit on Cost efficiency DEA does not reject

hypothesis 1a, 1b or 1c, respectively. In order to test hypothesis 1d, I perform two F-tests: (1) H0: β2TOtRBCit = 0 and (2) H0: β3UNLEVit = 0. When one F-test is significant, and the other

is not significant, the ratio with a significant F-statistic has a stronger effect on the regression analysis. When both F-tests are significant, both null hypotheses are rejected: then, both ratios have a significant influence in the regression analysis. A higher coefficient shows then which ratio has a stronger effect on the regression analysis.

The econometric definitions for the profit efficiency hypotheses are:

𝑃𝑅𝑂𝐹𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑁𝐸𝑅𝐵𝐶 + 𝛾𝑋 + 𝜇 +𝜆 + 𝜀 (5)

𝑃𝑅𝑂𝐹𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑇𝑅𝐵𝐶 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (6)

𝑃𝑅𝑂𝐹𝐸𝐹𝐹 = ∝ + 𝛽 𝑈𝑁𝐿𝐸𝑉 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (7)

𝑃𝑅𝑂𝐹𝐸𝐹𝐹 = ∝ + 𝛽 𝑇𝑂𝑇𝑅𝐵𝐶 + 𝛽 𝑈𝑁𝐿𝐸𝑉 + 𝛾𝑋 + 𝜇 + 𝜆 + 𝜀 (8)

In contrast to the cost efficiency measures, for both profit efficiency a higher value indicates higher profit efficiency. Here, a positive coefficient for β1TONERBCit does not reject

hypothesis 2a, a positive coefficient for β2TOtRBCit does not reject hypothesis 2b, and a

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efficiency: risk-based capital ratios and leverage 24 negative values for these coefficients, I reject the hypotheses. When one measure for profit

efficiency finds a significant positive coefficient and the other measure is not significant, I reject the hypothesis partially. In order to test hypothesis 1d, I perform two F-tests: (1) H0:

β2TOtRBCit = 0 and (2) H0: β3UNLEVit = 0. When one F-test is significant, and the other is

not significant, the ratio with a significant F-statistic has a stronger effect on the regression analysis. When both F-tests are significant, both null hypotheses are rejected: then, both ratios have a significant influence in the regression analysis. A higher coefficient shows then which ratio has a stronger effect on the regression analysis.

In the econometrical definitions, the coefficients reflect: Dependent and independent variables

COSTEFFit vector of cost efficiency for bank i at time t;

PROFEFFit vector of profit efficiency for bank i at time t;

TONERBCit Tier 1 capital ratio for bank i at time t;

TOTRBCit: Total RBC ratio for bank i at time t;

UNLEVit unweighted leverage ratio for bank i at time t;

Control and additional variables

Xit vector of control variables, for bank i at time t;

α constant;

β regression coefficient; γ regression coefficient;

µi the vector of entity fixed-effects;

λt the vector of period fixed-effects;

εit the error term.

In Appendix A, I give an overview of the used variables in the models.

CHAPTER FOUR DATA

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efficiency: risk-based capital ratios and leverage 25 variables. Here, I highlight the low correlation between risk-based and unweighted capital,

and I explain my decision to drop bank size as control variable due to multicollinearity issues.

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TABLE 3 Descriptive Statistics

N Mean

Std.

Dev. Median Min. Max.

Efficiency measures

Cost-to-income (%) 3170 61.85 16.08 61.19 5.49 109.90

Cost efficiency (DEA) (%) 3180 16.14 20.50 6.30 0.00 100.00

Return on assets (%) 3043 65.79 79.87 60.30 -303.40 301.90

Profit efficiency DEA (%) 3180 48.39 34.21 44.35 0.40 100.00

Capital ratios Tier 1 RBC ratio (%) 2767 11.78 4.19 11.12 0.60 24.90 Total RBC ratio (%) 2877 14.18 4.11 13.50 0.90 26.70 Unweighted leverage (%) 3174 8.32 3.70 7.92 0.86 19.87 Control variables Ln(total assets) 3180 17.32 1.74 16.99 13.29 22.06

Net loans to total assets (%) 3180 59.79 17.70 63.51 0.94 96.64

Ln(equity) 3174 19.33 1.62 19.03 15.69 23.92

Inflation (% growth) 3180 2.27 1.50 2.12 -4.48 15.40

GDP (% growth) 3172 0.68 2.74 1.30 -13.86 12.65

Notes:

- The values reported are the descriptives after the correction of the cost-to-income, return on assets and capital ratios: observations that were excessive outliers (observations with a values of more than 3 times standard deviation from sample mean) were deleted from the sample.

- Std. Dev., Min., and Max. are abbreviations for Standard Deviation, Minimum, and Maximum respectively. - Total observations are 101 banks in the US, and 217 in the EU over 2005-2014.

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efficiency: risk-based capital ratios and leverage 27 years of the sample, I find higher average efficiency scores than before the crisis. When

comparing cost efficiency measures with the mean over 2005 to 2014, cost-to-income in 2014 shows a lower cost efficiency than the mean over 2005 to 2014. This is in line with research of e.g. Andrieş, & Căpraru (2014), who found a decreased cost efficiency after the crisis: in my sample, the values are relatively stable from 2009 to 2014. In contrast, even though Cost efficiency DEA shows a decrease from 2011 to 2014, its level is still above the average of 2005 to 2014.

TABLE 4

Evolution of Cost and Profit Efficiency

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Mean

Cost-to-income (%) _{59.85 58.56 59.44 65.66 61.55 60.70 62.91 63.24 62.20 62.35 61.85}

Cost efficiency DEA (%) _{17.03 17.70 11.86 12.20 13.80 18.10 15.29 19.11 18.08 18.22 16.14}

Return on Assets (%) _{105.72 108.91 94.63 48.57 47.21 51.12 48.15 40.16 58.18 55.23 65.79}

Profit efficiency DEA (%) _{49.83 46.71 46.69 43.59 49.76 47.13 45.64 47.77 51.36 50.45 48.39}

Notes: Cost-to-income and Cost efficiency DEA are measures of cost efficiency, Return on Assets and Profit efficiency DEA are indicators of profit efficiency.

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efficiency: risk-based capital ratios and leverage 28 profit efficiency is shown to be useful for protection to systemic shocks, banks in my sample

were on average not able to maintain such a high return on its assets as before the crisis. Next to the evolution of the dependent variable, I assess the changes in the RBC and unweighted leverage (See Appendix D). As Meunier (2013) and Koutsomanolli-Filippaki et al. (2011) highlight, the US had more buffers during the financial crisis and therefore less American banks needed a bailout. As shown in Appendix D, comparing the three capital measurements between the US and the EU over time shows that the US had higher risk-weighted buffers on average than the EU from 2005 to 2013. Just before the crisis in 2006, both experience a decline in Tier 1 and Total RBC ratio. After the crisis, an increase is visible for both. These ratios increase in the EU until 2014, while in the US there is again a decline in 2011 in both ratios. This indicates that the Basel III implementation in 2010 has a higher impact in the EU than the US. When analyzing unweighted leverage, the US has higher unweighted leverage than the EU during the whole period: in general, American banks maintain a higher equity-to-assets ratio than European banks. Moreover, where unweighted leverage does not reduce for US banks during the crisis, there is a decline in unweighted leverage for EU banks in 2007, after which they are able to increase their unweighted capital.

In Table 5, I show the correlation matrix of the independent variables. With analyzing the correlations, it is possible to detect the presence of multicollinearity in the independent variables. I find near multicollinearity between total assets and equity with a correlation of 0.96. Therefore, I drop total assets in order prevent the data from multicollinearity, which may have caused the regressions becoming very sensitive to small changes in the specification (Brooks, 2008). I take this decision to drop bank size, because Berger and Mester (1997) state that not controlling for equity will give biased results when measuring efficiency. After the drop of bank size as a control variable, there is only a high correlation between Tier 1 RBC and Total RBC, which is not surprising as Basel’s total capital is calculated as Tier 1 and Tier 2 capital. Therefore, multicollinearity is not an issue.

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efficiency: risk-based capital ratios and leverage 29 correlation between Tier 1 ratio and unweighted leverage is low with 0.29. Therefore, Tier 1

adjusted to its risk-weights cannot be perceived as the same as unweighted equity-to-assets.

TABLE 5 Correlation Matrix (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Tier 1 RBC ratio (%) 1.00 Total RBC ratio (%) 0.92 1.00 Unweighted leverage (%) 0.29 0.21 1.00 Total capital (%) 0.80 0.81 0.75 1.00 Ln(total assets) -0.14 -0.06 -0.34 -0.24 1.00

Net loans to total assets (%) -0.15 -0.18 0.14 -0.07 -0.22 1.00

Ln(equity) -0.09 -0.02 -0.08 -0.07 0.96 -0.19 1.00

Inflation (% growth) -0.08 -0.07 0.02 -0.03 -0.12 0.06 -0.12 1.00

GDP (% growth) 0.00 -0.01 0.09 0.04 -0.10 -0.05 -0.08 0.30 1.00

Notes: Multicollinearity is not severe or nonexistent:

- The variable Ln(total assets) is dropped in the regressions to prevent multicollinearity: 1. Berger and Mester (1997) advocate that Ln(equity) is crucial as a control variable;

- Only a high correlation between Tier 1 RBC and Total RBC is shown as Total RBC is computed by Tier 1 RBC and Tier 2 capital, and therefore no reason to be concerned about the high correlation.

- The general correlation between the other independent variables is low.

- The low correlation between Tier 1 ratio and unweighted leverage and Total RBC ratio and unweighted leverage shows that risk-based capital is not equal to unweighted leverage.

CHAPTER FIVE ANALYSIS

In this section, I evaluate the results I obtained from the regression analyses. First, I show the results of the regression analyses testing the hypotheses for cost efficiency, while I compare these findings with literature. Second, I assess the regression analyses results testing the hypotheses for profit efficiency. I compare these results with the findings in literature as well.

5.1 RESULTS REGRESSION ANALYSES: COST EFFICIENCY

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efficiency: risk-based capital ratios and leverage 30 perform F-tests to consider whether these ratios have a different effect on cost efficiency

(Table 7).

I find a significant negative coefficient for Tier 1 ratio with the cost-to-income as dependent variable. However, there is no significant effect with Cost efficiency DEA as dependent variable. When considering the other risk-based measure, Total RBC ratio, I find similar results: a significant negative coefficient for the cost-to-income as dependent variable, but no significant effect for the Cost efficiency DEA. Important to take into account is that a lower cost-to-income ratio implies a higher cost efficiency. Therefore, my cost-to-income regression analyses show that risk-based capital has a positive effect on cost efficiency. For unweighted leverage, I find a negative coefficient on cost-to-income as well. This shows that both types of capital have a positive effect on cost efficiency with cost-to-income as dependent variable: banks are better able to generate higher income while minimizing their costs. In contrast, I find a negative effect of unweighted leverage on Cost efficiency DEA. This is in line with my expectations based on agency theory. De Jonghe and Öztekin (2015) find that banks increase their equity-to-assets ratio mainly by expanding their equity: banks accept the higher costs involved in this equity expansion. Berger and Bonaccorsi di Patti (2006) link the increased equity costs to agency theory: when unweighted leverage increases, i.e. the share of equity capital expands, banks will face higher agency costs in order to monitor the increased amount and thus more different interests of shareholders. However, this theory is not in line with my cost-to-income measure. In contrast, I find that holding capital results in a lower cost-to-income, indicating that efficiency increases. An explanation for the different effect between both cost efficiency measures may be that cost-to-income does not solely look at minimizing costs, but also at maximizing income. Therefore, in contrast to Cost efficiency DEA, cost-to-income is not a pure cost efficiency measure as it focuses on maximizing rather than stabilizing outputs (See Table 1).

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efficiency: risk-based capital ratios and leverage 31 When assessing the country-specific control variables, I find a significant negative effect of

inflation on cost-to-income. However, the results of the Cost efficiency DEA do not support this, as I no significant effect. GDP shows a significant positive effect on both efficiency measures. This is in line with e.g. Claessens et al. (2001), who state that an increase in GDP improves quality and skills of institutions, which enhances cost efficiency.

To summarize, I find mixed results for my cost efficiency measures. On the one hand, for my pure cost efficiency measure, I find that unweighted leverage affects Cost efficiency DEA negatively, but I find no significant effects for risk-based capital on Cost efficiency DEA. On the other hand, with the cost-to-income ratio as dependent variable, I find that holding capital, either risk-based or unweighted, enables banks to generate higher income while having less costs. As I find mixed results for the relationship between the two risk-based capital ratios and two measures of cost efficiency, I reject hypotheses 1a and 1b. I find inverse results for unweighted leverage on cost efficiency, and therefore I reject hypothesis 1c partially. I reject hypothesis 1c for cost-to-income as dependent variable as I find that capital decreases cost-to-income. I do not reject hypothesis 1c for Cost efficiency DEA as I find a negative effect.

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TABLE 6

Coefficient Estimates from Regression Analyses Results Cost Efficiency Measures

Dependent variable Cost-to-income ratio Cost efficiency DEA

(1) (2) (3) (4) (5) (6) (7) (8) Constant 99.36*** 95.91*** 80.99*** 96.69*** 129.77*** 129.24*** 126.12*** 133.44*** (5.30) (5.14) (4.45) (5.25) (5.57) (5.55) (5.02) (5.60) Tier 1 ratio -0.84*** 0.03 (0.09) (0.10) Total RBC ratio -0.68*** -0.71*** 0.06 -0.08 (0.09) (0.09) (0.10) (0.10) Unweighted leverage -0.27*** 0.11 -0.35*** -0.58*** (0.11) (0.12) (0.12) (0.12)

Net loans to total

assets -0.17*** -0.16*** -0.13*** -0.17*** -0.11*** -0.11*** -0.09*** -0.13*** (0.02) (0.01) (0.02) (0.02) (0.02) (0.02) (0.02) (0.02) Ln(equity) -1.48*** -1.32*** -1.09*** -1.35*** -5.90*** -5.89*** -5.82*** -6.04*** (0.19) (0.18) (0.17) (0.19) (0.20) (0.20) (0.19) (0.20) Inflation -0.66** -0.57** -0.56** -0.55** -0.09 -0.17 -0.17 -0.06 (0.28) (0.25) (0.25) (0.25) (0.40) (0.40) (0.40) (0.41) GDP 0.42*** 0.32** 0.34** 0.32** 1.11*** 0.96*** 0.94*** 0.93*** (0.16) (0.15) (0.16) (0.15) (0.24) (0.23) (0.22) (0.23)

Year-fixed effects Yes Yes Yes Yes Yes Yes Yes Yes

Bank-fixed effects Yes Yes Yes Yes Yes Yes Yes Yes

R2 _0.21 _0.21 _0.18 _0.21 _0.31 _0.31 _0.30 _0.31 Adjusted R2 _0.20 _0.20 _0.16 _0.19 _0.30 _0.30 _0.29 _0.30 F-statistic 17.99 18.39 16.40 17.99 29.71 30.67 32.00 30.73 P-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 N 2752 2858 3157 2858 2757 2865 3166 2865 Notes:

- Columns (1) and (5) show the testing of hypothesis 1a, testing the effect of Tier 1 ratio on cost efficiency. Columns (2) and (6) show the results for testing hypothesis 2a, testing the effect of total RBC ratio on cost efficiency. Columns (3) and (7) show the results for testing hypothesis 3a, testing the effect of unweighted leverage on cost efficiency. Columns (4) and (8) show the regression results for hypothesis 4a, testing whether there is different degree of the effect of risk-based or unweighted capital on cost efficiency;

- White standard errors are presented in parentheses; - *** significant at 1 percent

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TABLE 7 F-test Results

Cost efficiency Profit efficiency

Cost-to-income Cost efficiency DEA Return on Assets Profit efficiency DEA

F-statistic (1) 53.34*** 0.73 4.66** 1.62

F-statistic (2) 0.83 21.57*** 24.35*** 13.29***

Degrees of freedom (1,2815) (1,2822) (1,2713) (1,2822)

Notes:

- F-test (1) tests whether the effect of TotRBC in the regression analysis is equal to zero.: H0: β2TOtRBCit = 0

- F-test (2) tests whether the effect of unweighted leverage in the regression analysis is equal to zero. H0 :

β3UNLEVit = 0.

- *** significant at 1 percent - ** significant at 5 percent; - * significant at 10 percent;

5.2 RESULTS REGRESSION ANALYSES: PROFIT EFFICIENCY

Columns (1) to (4) of Table 5 show the regression analyses results of the Return on Assets as dependent variable. Columns (5) to (8) show the results with the Profit efficiency DEA measure as dependent variable. With all regressions, year- and bank-fixed effects are included. Columns (1) and (5) show the regression analyses for testing hypothesis 2a. Columns (2) and (6) show the regression analyses for testing hypothesis 2b. Columns (3) and (7) show the regression analyses for testing hypothesis 2c. Additionally, in columns (4) and (8) the regression analyses results of the Total RBC and Leverage are shown, on which I again perform two F-tests to compare the effect of risk-based and unweighted capital to test hypothesis 2d.

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TABLE 8

Coefficient Estimates from Regression Analyses Results Profit Efficiency Measures

Dependent variable Return on Assets Profit efficiency DEA

(1) (2) (3) (4) (5) (6) (7) (8) Constant 51.78** 58.85** 82.32*** 82.42*** 147.97*** 142.76*** 151.51*** 148.30*** (23.77) (23.63) (20.85) (23.45) (10.07) (9.86) (9.03) (9.91) Tier 1 ratio 1.80*** 0.26* (0.36) (0.15) Total RBC ratio 1.71*** 0.80** 0.39*** 0.20 (0.40) (0.36) (0.15) (0.15) Unweighted leverage 3.95*** 3.49*** 0.66*** 0.77*** (0.64) (0.71) (0.18) (0.21)

Net loans to total assets 0.16* 0.14* -0.01 -0.00 -0.21*** -0.19*** -0.23*** -0.22***

(0.09) (0.09) (0.08) (0.09) (0.04) (0.03) (0.03) (0.04) Ln(equity) -0.89 -1.13 -1.44* -1.90** -5.64*** -5.61*** -5.82*** -5.82*** (0.88) (0.86) (0.81) (0.86) (0.41) (0.39) (0.38) (0.40) Inflation 5.39*** 3.60** 4.08** 3.98** -0.64 -0.64 -0.47 -0.49 (1.95) (1.81) (1.75) (1.81) (0.59) (0.58) (0.56) (0.58) GDP 7.11*** 6.13*** 5.31*** 5.53*** -0.56 -0.82** -0.78** -0.81** (118) (1.16) (1.12) (1.15) (0.37) (0.37) (0.35) (0.37)

Year-fixed effects Yes Yes Yes Yes Yes Yes Yes Yes

Bank-fixed effects Yes Yes Yes Yes Yes Yes Yes Yes

R2 _0.27 _0.26 _0.23 _0.27 _0.39 _0.38 _0.37 _0.38 Adjusted R2 _0.26 _0.24 _0.22 _0.25 _0.38 _0.37 _0.36 _0.37 F-statistic 23.47 22.79 22.14 23.44 43.20 42.41 45.02 42.00 P-value 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 N 2653 2760 3029 2756 2757 2865 3166 2865 Notes:

- Columns (1) and (5) show the tests of hypothesis 1b, testing the effect of Tier 1 ratio on profit efficiency. Columns (2) and (6) show the results for testing hypothesis 2b, testing the effect of total RBC ratio on profit efficiency. Columns (3) and (7) show the results for testing hypothesis 3b, testing the effect of leverage on profit efficiency. Columns (4) and (8) show the tests of hypothesis 4b, testing the different effect of risk-based capital or non-risk based capital on profit efficiency.

- White standard errors are presented in parentheses; - *** significant at 1 percent

- ** significant at 5 percent; - * significant at 10 percent;

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efficiency: risk-based capital ratios and leverage 35 significant negative values for equity for all four regressions of Profit efficiency DEA, which

is supported by Berger and Mester (1997). For inflation, a positive significant effect is found on ROA. For GDP, I find significant positive effects on ROA, but significant negative effects on Profit efficiency DEA.

To summarize, a decreased risk-taking and reduced insolvency risk affect profit efficiency positively. I find similar results for both profit efficiency measures: risk-based as well as unweighted capital has a positive effect on profit efficiency. Therefore, I do not reject hypothesis 2a, 2b and 2c.

When taking a look at the F-tests, which I perform in order to test hypothesis 2d (See Table 7), I find that Total RBC and unweighted leverage are both significant in the F-test for the regression analysis on ROA. The coefficient of the second F-test is higher. Therefore, I conclude that unweighted leverage has a stronger impact than risk-based capital, supporting Admati and Hellwig (2014) that unweighted leverage is a better measure than risk-based capital. In contrast, I do not find a significant coefficient when testing Total RBC being equal to zero, and therefore I do not reject that null hypothesis. This finding also supports Admati and Hellwig (2014) that risk-based capital ratios are not as effective as unweighted capital. When comparing both profit efficiency measures, I conclude that unweighted capital has a stronger effect on profit efficiency. Therefore, I do not reject hypothesis 2d.

5.3 ROBUSTNESS CHECKS 5.3.1 Revenue Efficiency

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efficiency: risk-based capital ratios and leverage 36 confirm the different effect of unweighted leverage on cost and profit efficiency: revenue

efficiency is here the main driver (Kamarudin et al., 2014). Additionally, I perform an F-test on the regression analysis incorporating Total RBC and unweighted leverage. I find significant F-statistics for both F-tests, indicating that both ratios have a non-zero impact on revenue efficiency. As the F-statistic for unweighted leverage is higher, I conclude that unweighted leverage has a stronger impact on the regression analysis than risk-based capital, which confirms Admati and Hellwig (2014). Therefore, the results of unweighted leverage on revenue efficiency are robust for the profit efficiency results in my research.

5.3.2 Sample Split: US, EU, Pre- and Post-crisis

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efficiency: risk-based capital ratios and leverage 37 significant effect for Tier 1 and Total RBC. When assessing unweighted leverage, I find a

negative significance for EU and US post-crisis. In contrast to my whole sample results, I find a significant positive effect on unweighted capital pre-crisis in the US. The post-crisis results for EU and US unweighted leverage are robust for the whole sample. When assessing profit efficiency, I find that both risk-based unweighted capital affects ROA positively post-crisis for EU and US, which is in line with my whole sample results. However, pre-crisis years do not show this effect: only Total RBC in the US and unweighted leverage in the EU have a significant positive effect. When taking into account Profit efficiency DEA as a measure of profit efficiency, I find a significant positive effect of unweighted leverage for the EU post-crisis. In contrast, for the US I find a significant positive effect of both risk-based measures post-crisis. Therefore, I can state that there are differences pre- and post-crisis in capital buffers. However, because my pre-crisis period only contains three years, I cannot draw proper conclusions on this pre-crisis analysis.

TABLE 9 Summary of Results

Whole sample: EU, US, pre- and post-crisis

Cost-to-income Cost DEA Return on Assets Profit DEA

Tier 1 - x + + Total RBC - x + + Unweighted leverage - - + + Pre-crisis EU US EU US EU US EU US Tier 1 - - x + x x x x Total RBC - - - + x + x x Unweighted leverage - - x + + x x - Post-crisis EU US EU US EU US EU US Tier 1 - - x x + + x + Total RBC - - x x + + x + Unweighted leverage - x - - + + + x