Do Intermediation Returns and Concentration Increase Banking ...

Do Intermediation Returns and Concentration Increase Banking Stability? Marcella Lucchetta∗ October 29, 2007

Abstract This work presents a general setting to analyze the linkages between entry, concentration and regulation of the banking sector when banks are heterogeneous. Agents decide endogenously whenever to run a bank, i.e. entry, or to be a depositor. I show that when the intermediation return is high the economy reaches an inefficient equilibrium having agents with lower probability of project success running a bank. In an unregulated environment, this equilibrium makes banks unsolvable due to the lack of capital. However, capital requirement may prevent such an equilibrium and ensure banks solvability. Finally, the level of capital has to increase as bank margins and banking concentration raise. These results substantially contrast with respect to the previous literature on this topic. ∗

Ente Luigi Einaudi, Via Due Macelli 73, Roma - University of Verona and SAFE

Center, Dipartimento di Scienze Economiche, Giardino Giusti 2, Verona - Italy

1

Marcella Lucchetta

1

Introduction

The relation between bank competition and risk-taking is often defined as a trade-off balancing, on one hand, efficiency gains arising from a competitive bank management and, on the other hand, greater risk-taking due to the erosion of bank margins. The goal of this paper is to show that this is not always the case. Moreover, some of the previous literature doesn’t consider bank entry, whilst entry matters to asses banking sector peculiarity. Indeed, there are conditions that allow the entry into the market of inefficient banks. In the present paper, I show that the minimum bank capital requirement can be designed to prevent the entry of riskier banks. I develop a general setting to analyze the linkages between concentration in the banking sector, risk-taking and regulation with bank heterogeneity. The heterogeneity regards the probability of realization of a project that each agent has. Then, each agent decides according to his probability of success to be a banker or to be a depositor. To generalize, the decision to be a banker can be seen as the choice to undertake or not an investment by an already existing bank. Therefore, in this environment regulation has a role on agents’ decision which traduces in the entry into the banking sector, i.e. to invest or not in a given project. I show that bank intermediation margin increases risk-taking. In this economy two equilibria are feasible: one efficient when intermediation margins are low and one inefficient when intermediation margins are above a threshold value. The inefficient equilibrium has agents with lower probability of project success running a bank. Indeed, an agent with high expected value project exploits an effort proportional to the project success and to the intermediation return. Thereby, when the intermediation return is high, it may not be profitable to undertake the good project because of the greater effort. However, capital requirement may avoid this equilibrium and ensure

Do Intermediation Returns and Concentration Increase Banking Stability?

2

Marcella Lucchetta

banks solvability. I find that the capital requirement increases as the intermediation return and banking concentration raise. This work substantially differs with respect to the previous literature about bank risk-taking and competition. It finds opposite results with respect to the “traditional” literature predicting an higher bank risk-taking as the margin of bank diminishes (Repullo 204). It differs also with respect to the recent one (Boyd and De Nicolò 2005) which links higher interest rates, due to bank market power, applied to firms with greater entrepreneurial risks. While in the present paper, the risk-taking of bank increases because high intermediation return makes attractive for banks to undertake less profitable projects. In other terms, this is an incentive to undertake riskier investments. The fact that intermediation returns increases bank risk-taking contrasts also with the common view that deposit interest rate ceiling is effective in reducing risk as in Hellmann, Murdock and Stiglitz (2000). Moreover, the finding that minimum regulatory capital for solvability must increase as banking concentration raises, suggests a careful reconsideration of restrictions on bank entry (Alhadeff 1962). The academic literature stated to focus on the linkages between competition and stability in banking about 20 years ago. The interest in this issue has been attracted by the seminar article of Michael Keeley (1990), claiming that bank failures had been caused, in some cases, by deregulations and market changes that reduced monopoly rents. The author provides a theoretical framework and empirical evidence that such deregulation in the U.S. had increased competition and reduced banks’ profits threatening financial stability. On the same flavor, Edwards and Mishkin (1995) prove that excessive risk taking is a banks response to the erosion of profits in a competitive financial market. As pointed out in Vives (2001), in the recent history of banks it is possible to distinguish between two periods: one of strong regulation, intervention, and stability, lasting from the 1940s up to 1970s, and


3

Marcella Lucchetta

subsequently, one marked by liberalization and greater instability. Then, in the earlier literature, the common view is that an increase in bank competition that erodes banks’ margins reduces their incentive to behave behave prudently. Thereafter, economists and policy makers reexamine this relation and try to answer the questions: is there effectively a trade-off between competition and stability in banking? Should banking sector be regulated? Indeed, some researchers are less confident on the trade-off between competition and banking stability and their regulation. Then, the view of the literature starts to be mixed. Following, I review some of the most relevant papers in chronological order. Allen and Gale (2004) underline that in the banking sector competition policy must take account of the interaction between competition and financial stability. Therefore, greater competition may be good for efficiency, but bad for financial stability. They use a variety of models to address the problem and find that different models provide different results suggesting a high degree of complexity in the relationship between competition and financial stability. Shy and Stenbacka (2004) show that the introduction of competition into the banking industry can only improve social welfare. The authors demonstrate that increase in competition leads bank to invest in less risky asset portfolios in an environment where risk averse depositors can choose in which bank to make their deposits based on their knowledge of the risk included in the banks’ portfolios in addition to deposit rate comparison. On regulation, Chiesa (2001) observes that we do not learn why the banking system should be regulated at all as opposed to being disciplined by market forced, or how regulation should be designed in terms of its relationships to interbank competition and the business cycle. Her paper develops a model in which the intensity of competition, the role of capital requirements, and bank profits are all endogenously determined. The results are that the social-welfare-maximizing capital requirements are lowered in reces-


4

Marcella Lucchetta

sion, are higher the more fragmented the banking sector, and are increased when anti-competitive measures are removed. Then, Chiesa predicts that a less concentrated banking sector implies higher capital requirements. While, I shows the opposite: the optimal capital requirement is lower when the number of banks increases. The “traditional” view of a trade-off between competition and banking stability is recovered in Bolt and Tieman (2004). They state that increased competition in the banking industry leads to riskier bank behavior. Moreover, they show that risk-adjusted regulation is effective to reduce bank risktaking. These results are achieved in a model of competition between two banks which operate for T periods and the loans of the two banks are imperfect substitute. The same intuition is in Repullo (2004). The author presents a dynamic model of imperfect competition where banks can invest in a prudent or a gambling asset. He shows that if intermediation margins are small, in absence of regulation, only a gambling equilibrium will exist. Then, this result confirms the hypothesis that bank competition reduces banks’ incentives to behave prudently. Boyd and De Nicolò (2005) consider the optimal contracting problem between the bank and firms that borrow from it. They show that in this case as markets become more competitive the risk of bank failure declines. Then, the authors demonstrate that the conclusion of previous theoretical research were fragile, depending on the assumption that competition is only allowed in deposit markets but suppressed in loan markets. Boyd, De Nicolò and Jalal (2006) study two new models in which banks face a non-trivial asset allocation decision. The first model predicts a negative relationship between banks’ risk of failure and concentration. The second model predicts a positive relationship, suggesting that increased competition doesn’t mean financial instability. They test empirically these two models to find that the relationship between banks’ risk of failure and concentration is positive. Thus, the risk


5

Marcella Lucchetta

prediction of the second model are not rejected. Beck, Demirgüç-Kunt and Levine (2006) study the impact of national bank concentration, bank regulations, and national institutions on the likelihood of a country suffering a systemic banking crisis. Using data on 69 countries from 1980 to 1997, they find that crises are less likely in economies with more concentrated banking systems. The linkages between competition and banking regulation is highlighted in Guiso, Sapienza and Zingales (2006). They use exogenous variation in the degree of restrictions to bank competition across Italian provinces to analyze both the effects of a bank regulation and the impact of deregulation. They find that where entry was more restricted the cost of credit was higher and access to credit lower. Moreover, they shows that the pre-existing conditions severely impact the effect of liberalization: in provinces where restrictions to bank competition were most severe, the proportion of bad loans after deregulation raises above the level present in more competitive markets. Finally, they find that competition does not impact the quality of loans. Then, economic theory and empirical results provide conflicting predictions about the relationship between competition and banking system fragility. The aim of this work is to analyze the issue taking into account also bank heterogeneity. Section 2 defines the model which is designed in a simple framework. Equilibria are analyzed in section 3. Here, I show that the intermediation return increases risk-taking through the entry into the banking sector of agents with low probability of success of their projects. Section 4 defines the behavior of agents without regulation. It demonstrates that bankers may hold not enough capital. Then, at section 5 I derive the optimal capital regulation to achieve banks’ solvability and to reach the efficient equilibrium. Section 6 concludes.


6

Marcella Lucchetta

2

Model Features

In this section I define the features of the model. In order to disentangle the key effects of bank intermediation return and regulation on risk-taking, I design a simple framework which allows a straightforward analysis. I assume a one period society with a continuum of risk-neutral agents indexed by i. Each of them is endowed with one unit of good and he may invest in a project having returns at the end of the period S > 1 with probability q in case of success or D < 1 with probability 1 − q in case of default. To undertake the project, each agent must invest his own endowment of one and may collect in form of deposits the other agents endowment. Agents differ with respect to the project’s probability of success, qi , which is uniformly distributed on the interval (0, 1), and is a private information. An agent has an higher project success because he exploits effort at a cost e. Such a cost is greater than one and is multiplied by the probability of realization of the project, so that effort is proportional to the project success.1 Then, each agent may invest in his own project (collecting at least one good from another agent) and become a bank, delegate another agent to invest his good, and finally consume his good at the end of the period.2 The number of bankers is denoted N , and the number of depositors is denoted M . Whenever an agent intermediates the endowment of other agents in form of deposits he receives, in case of success at the end of the period, an intermediation return B for each unit intermediated. I suppose that S − B > 1 and B < 1.3

The effort that the agent exploits is proportional to this intermedia-

tion return, so that each unit of deposit yields B(1 − Beqi ). In excess of his own unit that the banker invest as capital, he can be asked by an external regulator to raise (k − 1) as further capital. The cost of 1

The cost of effort can be seen as a cost of monitor whenever one structures the model as an agent that engages an outside project. 2 The choice to consume one at the end of the period implies no intermediation. 3 The assumption B < 1 is important to avoid banal results. Do Intermediation Returns and Concentration Increase Banking Stability?

7

Marcella Lucchetta

this capital is T . Assumptions on T are not needed, as I will show later on. While, I suppose that in the event of default the bank assets are shared across depositors and in this case depositors will receive an amount not greater than one, i.e. the initial endowment. Close to real economy, I suppose that, except qi , all the other parameter are common knowledge, i.e. returns and intermediation return, number of bankers, and bank’s capital.

3

Equilibria

To analyze the equilibria in the economy, I structure the agents’ payoffs accordingly to the possible choices. Therefore, each agent i will be a banker if his qi belongs in the interval of solutions qˆ that solves the following inequality, πb ≥ πd

qˆ(Sk + B(1 − Beˆ q)

⇒

M M ) + (1 − qˆ) max[0, Dk + (D − 1) ] − T (k − 1) ≥ N N

D( M 1+M 1+M N + k) (S − B) + (1 − ) min[1, ], M 2 2 N

(1)

where the first part is the payoff of a banker, πb , the second part is the payoff of a depositor, πd , and

M N

is the amount of deposits that each bank raises.

These payoffs are shortly explained. On the first part of inequality (1), the payoff of a banker entails, with probability qˆ, the return in the event of success, S times the banker capital, k,

plus the intermediation return, B(1 − Beˆq), times the amount of deposits,

M N

. With probability 1 − qˆ, the banker defaults, and in this event he earns the

maximum between zero and the assets excess after refunding the depositors. The depositor payoff, on the second part of inequality (1), is given by the project expect return in the event of success minus the intermediation fee, B , Do Intermediation Returns and Concentration Increase Banking Stability?

8

Marcella Lucchetta

owed to the banker with probability

1+M 2

, and by the expected return in the

event of default with probability 1 − 1+M 2 . Therefore, when the bank defaults assets are shared across depositors. Inequality (1) must be combined with the intermediation existence condition: π d ≥ 1.

(2)

Indeed, the depositors’ payoff should be greater or equal to the initial endowment to ensure the existence of an intermediation economy. The competition effect arises from the magnitude of B M N . Therefore, each banker collects as deposits an amount equal to

M N

. As the number of bankers

increase with respect to depositors, the term B M N diminishes. From this point of view, the optimal degree of competition is a “system outcome”: it results from the aggregation of agents’ behavior.

Figure 1: Graph of inequality (1) with respect to q.


9

Marcella Lucchetta

Figure 1 shows the behavior of (1) with respect to q. The difference πb −πd increases as the probability of project success raises when the intermediation return is low. An agent is a banker if his probability of project success is grater than qˆ∗ . While, when the intermediation return is high, only agents with lower probability of success find profitable to be a banker. In this case an agent is a banker if his probability of project success belongs between qˆ1 and qˆ2 . This equilibrium is inefficient. Since the cost of effort is proportional to the intermediation return and to the probability of success, worse projects are undertaken because they are cheeper than better projects. This result is puzzling and it explains why an inefficient bank enters the market when returns are high. Proposition 1 An increase of the intermediation return, B , raises bank risktaking. Proposition 2 There exist a level B ∗ of the intermediation return such that when B > B ∗ the only possible equilibrium is the one where agents with lower probability of project success, qi , are bankers, i.e. qˆ1 ≤ qi ≤ qˆ2 with qˆ2 < qˆ∗ . Propositions 1 and 2 formalize the result obtained. Detailed proofs are in the appendix. The level of risk increases as the intermediation return raises. This result differs with respect to the previous literature: with respect to the “traditional” view that there is a tradeoff between competition and bank risktaking, i.e. Keeley (1990), and with respect to the new view predicting lower bank risk-taking as competition raises because of the reduced entrepreneurial risks associated with a lower interest rate applied to firms, i.e. Boyd and De Nicolò (2005). Here, risk-taking raises because high intermediation margins make profitable to undertake projects that otherwise a bank would not finance at all.


10

Marcella Lucchetta

4

Banks Behavior without Regulation

In this section I describe banks behavior without regulation. Then, k is determined by the profit maximizing agent. This requires to differentiate the discontinuous profit function, πb , of the banker. the derivative with respect to k is ∂πib ∂k

=

   qi S + (1 − qi )D − T  

qi S − T

which is negative whenever qi

M N

otherwise,

when D( M N + k) >

M N

(3)

, and when qi
S

while, when each bank’s deposits,

if M N

M S > , N 2B 2 eq − B

(4)

, are lower than such amount, banks’

capital is equal to one. When regulator has solved the allocation problem, then the number of banks into the market is 1 − qˆ∗ and the number of depositors is qˆ∗ . Then, the solvability problem can be written as the following stability condition ∗

qˆ P ( 1−ˆ q∗ + k )D qˆ∗ 1−ˆ q∗

≥ 1,

(5)

where the optimal capital is subject to the lower bound k¯ necessary to ensure the efficient equilibrium. Proposition 5 Capital requirement, kP , to ensure bank solvability increases with market concentration. Proposition 5 contrasts with the common idea that a concentrated banking sector is more solvable and therefore capital requirements can be relaxed. Do Intermediation Returns and Concentration Increase Banking Stability?

12

Marcella Lucchetta

The economic intuition relies on the increase of bank rents due to market concentration. From proposition 1, higher bank rents increases risk-taking and, therefore, the optimal capital required for solvability. An other interesting analysis is the sensitivity of kP with respect to the intermediation return, B .

Figure 2: Capital requirement for solvability, kP , with respect to B at different values of q. Figure 2 shows that when intermediation return B is low, then the minimum capital for solvability has to be higher for q big. While, when the intermediation return raises, the capital for solvability increases rapidly for q

small. This feature can be explained in light of agents behavior. Indeed,

from proposition 2 when B is low, agents with lower probability of success do not enter the banking sector. When B is high, precisely B > B ∗ , worse agents enter the banking sector and this requires an higher level of capital for solvability. Stated in other terms, since the intermediation return raises Do Intermediation Returns and Concentration Increase Banking Stability?

13

Marcella Lucchetta

risk-taking, then as B increases kP must in turn increase. Proposition 6 Capital for solvability increases as the intermediation return raises and it increases more rapidly for the banks with low probability of success projects. Propositions 5 and 6 predict different results with respect to the “traditional” view that capital requirement for solvability must increase as anticompetitive measures are removed. Here, competition and low margins allows to impose less restrictive capital requirements. The story is as follows: whenever the regulator ensures the level of capital necessary to avoid inefficient banks entry, then in a competitive environment capital does’t need to be high.

6

Conclusion

This work provides a general model to analyze the linkages between concentration and regulation with bank heterogeneity. I show that the traditional view predicting higher bank risk-taking as intermediation margins declines is not generally verified. Indeed, intermediation returns allow the entry into the banking sector of agents with lower project probability of success. Here, regulation has a role to ensure banks solvability in the event of default and to avoid the inefficient equilibrium having agents with low probability of success project running a bank. In other terms, I show that capital requirement has the two crucial purposes: the efficient bank entry into the market and the solvability aim. Finally, the increase of intermediation returns and banking concentration requires an higher regulatory capital. These results contrast with the previous literature. They differ with respect to the traditional literature predicting an higher bank risk-taking as the profit of bank diminishes. They differ also with respect to the recent one Do Intermediation Returns and Concentration Increase Banking Stability?

14

Marcella Lucchetta

(Boyd and De Nicolò 2005) which links higher interest rates, due to bank market power, applied to firms with greater entrepreneurial risks. Here, the risk-taking of bank increases because high intermediation return makes attractive for banks to undertake less profitable projects. In other terms, this is an incentive to undertake more riskier investments. Regarding the regulation issue, the literature predicts higher capital requirement when competition into the banking sector is high (Chiesa 2001). While, I show that a less concentrated market implies a low capital requirement with respect to a concentrated banking sector.


15

Marcella Lucchetta

Appendix Proof of Proposition 1 Solving equations (1) and (2), there are two solutions qˆ1 = −

r

(

1 2 2M NB e

−

M M B − kS + max[0, (D − 1) + Dk]− N N

M M M M B + kS − max[0, (D − 1) + Dk])2 + 4 B 2 e(T − 1 − kT + max[0, (D − 1) + Dk]) , N N N N

and qˆ2 = − r

(

M M 1 − B − kS + max[0, (D − 1) + Dk]+ M 2 N N 2N B e

M M M M B + kS − max[0, (D − 1) + Dk])2 + 4 B 2 e(T − 1 − kT + max[0, (D − 1) + Dk]) . N N N N

These solutions belong on the interval (0, 1) when B is greater than a certain level, otherwise, the only admissible solution is qˆ2 that will be called qˆ∗ . • for B high, N = qˆ2 − qˆ1 , M = 1 + qˆ1 − qˆ2 , • for B low, N = 1 − qˆ∗ , M = qˆ∗ .

Proof of Proposition 2 To find the value of B such that as q increases πb − πd increases, I compute the following first order derivative: M M M ∂(π b − π d ) = − B 2 eq + B(1 − Beq) + kS − max[0, (D − 1) + Dk] ∂q N N N

which has to be solved for the value of B for that is positive. There are two results 1 1 B< + 4eq 4

s

M N

+ 8ekqS M 2 2 Ne q

if 0 < D

S 2B 2 eq−B

.

To avoid negative values, it must be checked that 2Beq − 1 > 1. This traduces in proving that q>

1 2eB

⇒

qˆ1 >

1 , 2eB

this ensures that the banks in the market satisfy the above condition. 1 The difference qˆ1 − 2eB gives

1 M kS − max[0, (D − 1) + Dk]+ M 2 N 2N B e


17

Marcella Lucchetta

r

(

M M M M B + kS − max[0, (D − 1) + Dk])2 + 4 B 2 e(T − 1 − kT + max[0, (D − 1) + Dk]) > 0. N N N N

The difference is positive since kS − max[0, M N (D − 1) + Dk] > 0. This proves that S > 0. 2B 2 eq − B

Therefore, when banking market is concentrated, the capital to ensure the efficient equilibrium must be higher than when the market is more competitive. The second inequality is redundant with respect to the one analyzed, since the outcome in case of default is higher and then it is satisfied with the above conditions.

Proof of Proposition 5 Solving equation (5) with respect to kP , kP ≥

qˆ∗ (1 − D) , D(1 − qˆ∗ )

and combining with the lower bound k¯ determined at proposition 4, the results are • kP ≥

qˆ∗ (1−D) D(1−ˆ q∗ )

if

M N

qˆ∗ (1−D) D(1−ˆ q∗ )

if

M N

=

q(DS−S) BD−BDq−2B 2 eDq+2B 2 eDq2

;

• kP >

2B 2 M eq−B M N N S

if

M N

>

q(DS−S) BD−BDq−2B 2 eDq+2B 2 eDq2

This implies that concentration, i.e. high deposits

. M N

for bank, requires an

higher capital requirement to ensure banks’ solvability.


18

Marcella Lucchetta

References [1] Alhadeff, David A. “A Reconsideration of Restrictions on Bank Entry”. The Quarterly Journal of Economics, May, 1962, 76 (2), pp. 246263. [2] Allen, Franklin, and Gale, Douglas “Competition and Financial Stability”. Journal of Money, Credit and Banking, June 2004, 36 (3), pp. 453-480. [3] Beck, Thorsten, Demirgüç-Kunt, Asli, and Levine Ross “Bank Concentration, Competition and Crises: First Results”. Journal of Banking and Finance, May 2006, 30 (5), pp. 1581-1603. [4] Bolt, Wilko, and Tieman, Alexander F. “Banking Competition, Risk and Regulation”. Scandinavian Journal of Economics, 2004, 106 (4), pp. 783-804. [5] Boyd, John H., and De Nicolò Gianni “The Theory of Bank Risk Taking and Competition Revisited”. The Journal of Finance, June 2005, 60 (3), pp. 1329-1343. [6] Boyd, John H., De Nicolò Gianni, and Jalal, Abu M. “Bank RiskTaking and Competition Revisited: New Theory and New Evidence”. IMF Working Paper, December 2006, WP/06/297. [7] Chiesa, Gabriella “Incentive-Based Lending Capacity, Competition and Regulation in Banking”. Journal of Financial Intermediation, January 2001, 10 (1), pp. 28-53. [8] Edwards, Franklin R., and Mishkin, Frederic S. “The Decline of Traditional Banking: Implications for Financial Stability and Regulatory Policy”. Federal Reserve Bank of New York Economic Policy Review, January 1995, (1), pp. 27-45. Do Intermediation Returns and Concentration Increase Banking Stability?

19

Marcella Lucchetta

[9] Guiso, Luigi, Sapienza, Paola, and Zingales, Luigi “The Cost of Bank Regulation”. CEPR Discussion Paper, October 2006, n. 5864. [10] Keeley, Michael C. “Deposit Insurance, Risk and Market Power in Banking”. The American Economic Review, December 1990, 80 (5), pp. 1183-1200. [11] Hellmann, Thomas F., Murdock, Kevin C., and Stiglitz, Joseph E. “Liberalization, Moral Hazard in Banking, and Prudential Regulation: Are Capital Requirement Enough?”. The American Economic Review, March 2000, 90 (1) pp. 147-165. [12] Repullo, Rafael “Capital Requirements, Market Power, and RiskTaking in Banking”. Journal of Financial Intermediation, April 2004, 13 (2), pp. 156-182. [13] Shy, Oz, and Stenbacka, Rune “Market Structure and Risk Taking in the Banking Industry”. Journal of Economics, July 2004, 82 (3), pp. 249-280. [14] Vives, Xavier “Competition in the Changing Word of Banking”. Oxford Review of Economic Policy, Winter 2001, 17 (4), pp. 535-547.


20