The regulator’s trade-oﬀ: bank supervision vs. minimum capital

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The regulator’s trade-off: bank supervision vs. minimum capital

Florian Buck & Eva Schliephake

University of Munich & Otto-von-Guericke University

Workshop “Understanding Macroprudential Regulation”

Norges Bank, Oslo

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Stability of the banking sector responds to changes in theminimum capital requirement regulation(Barth et al. 2004; Laeven and Levine 2009) and to changes indomestic supervision(Buch and DeLong, 2008).

The Basel Accords focus on the regulation of capital and liquidity standards, whereas there are considerable variations in supervisory standards in

jurisdictions that are adopting the Basel framework.

De factooutcome of international banking regulation depends on both capital regulation and national effort that is spent on supervision.

Florian Buck The regulator’s trade-off

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Motivation

The Research Question

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Motivation:

How to ensure financial intermediation?

A Small Model: Optimal Regulation in Closed Economies Lemons equilibrium in an unregulated banking sector

The effect of capital standards The effect of ex-ante supervision

Regulator’s preferences on the mix of both instruments

Outlook: Optimal Regulation with International Spillovers The club view: observable domestic supervision

International deposit rates: unobservable supervision Conclusion and Discussion

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A small model: an unregulated banking sector

Banks finance projects with deposits (at r_D) and costly capital (atr_D+ρ) where projects return eitherR (success) with probabilityp_L or 0 (failure).

Unregulated banks do not hold any capital.

A natural fractionθⁿ∈[0,1) of banks isefficienthaving a monitoring technology; the other banks (1−θ) are said to begoofy.

Using the monitoring technology at costmincreases the probability of the high returnR of the project up topH=pL+4p>pL.

Depositors, endowed with 1, either invest in a riskless storage technology with a return ofγ≥1 or in an opaque bank at a deposit rate ofr_D.

Asymmetric informationon bank quality andno deposit insurance.

Goofy banking is inefficient:R·pH> γ >R·pL.

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Efficient Bank’s “Monitoring condition”

Fractionθof banks will choose to monitor their projects if (R−rD(1−k)) (pL+4p)−m≥(R−rD(1−k))pL. The incentive constraint of monitoring banks:

rD≤rD^MICk:=R−_4p^m

(1−k) >rD^MIC. (1)

IfrD>r_D^MIC: unconditional probability that project succeeds ispL.

Depositors Participation Constraint

WithrD<r_D^MIC depositors are willing to deposit their endowments if (rD)·(pL+θ4p)≥γ.

With perfect competition, depositors participate if

r_D^PCD:=

( _γ

p_L γ p_L+θ4p

iffrD>r_D^MIC,

iffrD≤r_D^MIC. (2)

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When does financial intermediation take place?

Definition

In order to satisfy both constraints simultanously the natural fraction of efficient banks needs to be large enough: θⁿ<θˆ:= _4pR−m^γ −_4p^p^L .

Otherwise: Ifθⁿ<θ, it follows thatˆ _p ^γ

L+θⁿ4p >R−_4p^m : depositors correctly foresee that no bank monitors.

The financial market is unable to channel funds effictively to those who have the most productive investment opportunities.

This market inefficiency caused by asymmetric information could be eleviated by the introduction of aminimum capital requirement(CR).

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Figure: Banking region for a given pool qualityθⁿ<θ˜

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The effects of capital regulation

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The effects of capital regulation

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Bank’s profits decrease in capital standards!

Efficient Bank’s Participation condition Condition with non-negative profits is given by (R−rD(1−k))pH−m−ρk≥0 and, hence:

rD≤:=R−^m+ρk_p

H

(1−k) . (3)

Since we assumedρ >pH·R, the minimum capital requirement must be small enough to keep efficient banks operating: k<^p^H^R−m_ρ . A fully equity financed bank will never participate.

Goofy Bank’s Participation condition

Goofy banks will make non-negative profits whenever (R−rD(1−k))pL−ρk>0,

rD≤rD^PCG:= R−^ρk_p

L

(1−k). (4)

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Figure: Introducing the exit-option for efficient banks

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The effects of capital regulation

Figure: Introducing the exit-option for goofy banks

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Figure: Introducing the exit-option for banks

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The feasible set of capital standards

Figure: An Economy with a high fraction of efficient banksrD[θⁿ]>rD

hkˆi

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Figure: An Economy with a low fraction of efficient banksrD[θⁿ]<rD

hkˆi

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The Story so far

In a world without capital regulation

Ifθⁿ<θ, depositing is on average less productive than investments in the˜ storage technology. The banking market breaks down (lemons equilibrium).

Capital requirements can decrease this critical fraction of efficient banks.

Only for a sufficiently high natural proportion of efficient banks where rD[θⁿ]<rD

hˆki

, there exists acontinuum of minimum capital requirement ratesk∈h

k^∗,ˆk_ei

that solves the moral hazard problem.

Otherwise, capital requirements alone cannot guarantee financial intermediation,k ∈[∅].

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Costly supervisory technology

Supervisory officers, watchdog institutions and specialised equipment (institutional costs)

Screening and auditing banks and license applicants (structural costs) Disclosure requirements (costs of compliance)

Fraction of efficient banks as the output of supervision.

The pool quality of banksθ(e) is a function of costly supervisory effort e∈[0,e^max], withθ(e) =f[e],θ(0) =θⁿ<θ.ˆ

Every jurisdiction has a specific cost function of supervisory effort with c(0) = 0,c(e^max) =∞,c⁰(0) = 0,c⁰(e)>0,c⁰⁰(e)>0.

Costs are born by taxpayers (Masciandao et al. 2007)

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The effects of supervisory effort

Figure: Lower refinancing cost for a given capital standard ¯k

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costs.

She cares about the rent of domestic efficient banks (φ) and taxpayers (1−φ).

Linear increasing function of supervisory effort: c[e] =^c₂·θ².

Maximisation problem of the regulator maxU(e,k)

e,k

=φ· {pH·(R−rD[θ,k]·(1−k))−m−ρ·k}

| {z }

rent of the banking sector

−(1−φ)·c

2·θ². (5)

s.t.

rD[θ] =_p ^γ

L+θ4p, k≥1−

R−^m

∆p

r_D , k≤^p^H^(R−r_ρ−p^D^)−m

Hr_D

0≤k≤1, 0≤θ≤1.

Cost of capital can be interpreted as crowding out of deposits: The higher CRs, the lower depositing.

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The regulator’s cost minimisation problem

Figure: Optimal mix of CR and supervision

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The regulator’s cost minimisation problem

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The regulator’s cost minimisation problem

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Who has a preference for loose capital standards?

e c

[e ]

ρ m 4p

k^∗

- + - + -

Within the feasible set capital standards and supervision are substitutes: A jurisdiction in which highsupervisory efforte is spent, has lower optimal capital standardsk^∗.

Lowercost efficiency in supervisory effortc[e] lead to higherk^∗. Lowercost of capitalρwill increasek^∗.

Highermonitoring costmdecrease the profit of efficient banks which lowers the optimal effort level thereby increasingk^∗.

The lessvalue added by monitoring4p , the less likely theMIC of efficient banks holds. In terms of our model lower profits justify higherk^∗.

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The game of regulatory competition

Consider two identical countriesA,B that are linked through perfect bank mobility.

Regulators in each country differ w. r. t the supervisory efficiency, where cA<cB resulting inθ^∗_A> θ^∗_B.

The respective optimal national minimum capital requirements are k_A^∗(θ^∗_A)<k_B^∗(θ_B^∗).

With differentiated regulatory “products” national banks will shift to the most appropriate regulator.

A bank of typei∈[E,G] that is settled in countryB will move whenever Πⁱ(A)−ϑ >Πⁱ(B).

As long as ˆk>k^∗, efficient banks are able to generate higher marginal profits than goofy banks.

What is the outcome of systems competition?

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Complete information for all market participants regarding the quality and the cost of banking supervision.

Re-allocation of banks

Migration of banks to the less regulated economyA: lower CRs and lower deposit rates strictly enhance the profits of banks: Πⁱ(B)<Πⁱ(A).

For sufficient low moving costs, financial intermediation in jurisdictionB breaks down.

Feedback effect on the optimal policy mix in A Depositors in countryAdemand higher deposit rates.

The regulator inAhas to adapt the optimal policy mix (increasek ore).

With convex effort costs,Awill gradually increase the capital requirement compared to autarky (redistribution).

Welfare-loss: Both countries lose in welfare terms compared to autarky.

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Case B: International deposit rates

Asymmetric information makes it hard for depositors to distinguish regulatory sytems: rD[θ_A^∗]<r¯D<rD[θ^∗_B].

Re-allocation of banks

InB banks benefit from lower overall lending rates.

InAa higher deposit rate prevents efficient banks from monitoring,i.e., k_A^∗(θ^∗_A) is too low to satisfy the monitoring incentive constraint.

Banks move to countryAwhere the financial sector does not monitor.

Feedback effect on the optimal policy mix

Dilemma: Regulators do not benefit from an increase in CRs, since depositors do not punish non-monitoring efficient banks.

It is individual rational to decrease CRs, but this implies thebreakdown of the global financial market.

Incentives to harmonise regulatory policy

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Figure: Pooling of deposit rates creates an unstable global economy

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Conclusion and discussion

Regulators seek to prevent the breakdown of the financial sector at lowest costs.

Direct forms of regulation (supervision) enhances the average ability of banks to control risk.

Indirect regulation via capital requirements incentives monitoring activity by banks.

The expected costs of a breakdown are minimised with a mix of both instruments.

Once we allow for cross-boder banking, the optimal policy is not feasible.

If domestic supervision is not observable, without collusion our model predicts a global financial breakdown.

Countries are better off by harmonising regulation.

Problem: non-contractability of supervision.

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Thank you very much for your questions!

Further comments please send to florian.buck@lmu.de

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What will happen with deposit insurance?

With a risk-adjusted deposit insurance scheme, we get the same results; only the composition of costs differs

Depositors will get their outside option, regardless of the risk behaviour of banks;

theirPCDwill not change

rD=_p ^γ

L+θ4p_L

.

Now, banks have to pay a risk-premiumρ[p] that is equal to the value at risk with probabilityp.

The new deposit rate (that equals theMIC)isr_D=γ+ρ[p, θ].

All participation constraints and the monitoring incentive constraint remain the same.

The deposit insurance policy is welfare-neutral resulting in the same allocation of banks.

The effect of subsidized deposit insurance is benign (Morrison, White, JBF 2011) Requiring banks to contribute part of their capital to a deposit insurance fund reduces the banker’s stake in any investment of a given size.

More deposit insurance reduces the interest rate that bankers have to pay to entice depositors to deposit, and so increases the share of any given return from a successful project that a banker can extract.

The optimal level of deposit insurance (safety net) varies inversely with the quality

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Figure: Deposit rates and capital regulation

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Optimal regulation in closed economies

Figure: Feasible policies

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The regulator does not care about profits

(φ = 0)

If thePCof banks never becomes binding before theMIC,i.e., ˆk= _∆p^p^L ·^m_ρ >1, the regulator just setsk= 1 ande= 0;

Otherwise, he setsk= ˆkande=f^-1

θ= _4pR−m^γ·(1−^ˆ^k) −_4p^p^L

>0.

The regulator cares about the profits of efficient banks

(φ > 0)

A “captured” regulator implements θ^∗=

1 2

^q

(1−φ)²·p²_L−φ·^4·^pH·∆p(R·∆p−m) c

(1−φ)·∆p −_∆p^p^L

,and

k(θ^∗) = 1−_γ¹(pL+θ^∗4p)

R−_∆p^m .

Taking the partial derivative of the regulator’s optimal supervisory effort w.r.t. k,gives _∂k∂θ^∂²^U =−φ

p_H∆pγ (p_L+θ4p)²

<0.

Capital requirements and supervision aresubstitutes(higher optimalk, lower optimal efforte,vice versa).

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Calculating the critical moving costs

The efficient bank will move toAwhenever Π^E(A)−ϑ >Π^E(B). pH((R−rA)(1−kA))−m−ρ·kA−νM>pH((R−rB)(1−kB))−m−ρ·kB.

We can derive the moving condition for goofy banks:

νM < νM^G :=pl((R−rA)(1−kA)−(R−rB)(1−kB)) +ρ·(kB−kA).

Since efficient banks are more productive than goofy banks, the critical cost is greater for efficient banks than for goofy banks:

ν^E_M−ν_M^G = ∆p·((R−rA)(1−kA)−(R−rB)(1−kB)).

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Figure: Choice of jurisdiction for banks

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Divergence in supervisory regulation

Figure: What was the global relative budget (in $ per 100.000 $ Assets) for supervision of banks in 2005?

0 20 40 60 80 100 120 140 160

Germany United Kingdom France Ireland Luxembourg Portugal South Africa Brazil Poland United States

Relative Budget

Source: World Bank 2008

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The implementation of the Basel Accord agreements into national law allows for some discretion of national regulators.

“Supervisors should have the discretion to use the tools suited to the circumstances of the bank and its operating environment.”

(Basel II Accord, Supervisory Review Process, Section 759)

National regulators have two choice parameters:

(1) a preferred

capital requirement

(equity to deposit ratio) and (2) a

level of effort spend on sophisticated supervision

(monitoring), represented by the average banking pool quality.

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Bank’s Profits in Equilibrium

The optimal policy mix leaves banks with refinancing cost where marginal benefits of higher capital equal the marginal costs. Accordingly, the profits are:

Π^E(θ^∗,k^∗) = pH·

R− 1

2 ρ pH

(1−k^∗)

−ρ·k^∗,

Π^G(θ^∗,k^∗) = pL·

R− 1

2 ρ pH

(1−k^∗)

−ρ·k^∗.

The profits are decreasing in the capital requirement.

The profits of efficient banks are less sensitive to higher CRs, since they benefit more from saved cost of fincial intermediation.

The regulator can setθ^∗,k^∗ such that goofy banks find it not profitable to participate in financial intermediation.

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Efficient Bank’s Participation condition

Condition of non-negative profits: (R−rD)pH−m≥0and hence:

rD≤r_D^PCE :=R− m pH

. (6)

The lower bound on the deposit rate of the efficient bank’s

participation is always above the incentive constraint, sincep_H >∆p.

Goofy Bank’s Participation condition

Goofy banks will make non-negative profits whenever(R−rD)pH>0,

rD≤rD^PCG:=R. (7)

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The regulator’s trade-oﬀ: bank supervision vs. minimum capital

The regulator’s trade-off: bank supervision vs. minimum capital

Florian Buck & Eva Schliephake

Workshop “Understanding Macroprudential Regulation”

Norges Bank, Oslo

Motivation

The Research Question

A small model: an unregulated banking sector

When does financial intermediation take place?

Definition

The effects of capital regulation

The effects of capital regulation

Bank’s profits decrease in capital standards!

The effects of capital regulation

The feasible set of capital standards

The Story so far

In a world without capital regulation

The effects of supervisory effort

The regulator’s cost minimisation problem

The regulator’s cost minimisation problem

The regulator’s cost minimisation problem

Who has a preference for loose capital standards?

[e ]

- + - + -

The game of regulatory competition

Case B: International deposit rates

Conclusion and discussion

Thank you very much for your questions!

Further comments please send to florian.buck@lmu.de

What will happen with deposit insurance?

Optimal regulation in closed economies

(φ = 0)

(φ > 0)

Calculating the critical moving costs

Divergence in supervisory regulation

The implementation of the Basel Accord agreements into national law allows for some discretion of national regulators.

National regulators have two choice parameters:

(1) a preferred

(equity to deposit ratio) and (2) a

(monitoring), represented by the average banking pool quality.

Bank’s Profits in Equilibrium

End

Thank you very much for your questions!

Further comments please send to florian.buck@lmu.de