Bank regulation when both deposit rate control and capital requirements are socially costly

• Published date: 01 June 2018
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/ijet.12150

doi: 10.1111/ijet.12150

Bank regulation when both deposit rate control and capital

requirements are socially costly

Carsten Krabbe Nielsen∗and Gerd Weinrich†

The bank regulation reforms in the 1980s and 1990s saw deposit rate ceilings being replaced

by minimum capital requirements. However, there seem to be no theoretical studies supporting

these reforms; either the two instruments are considered for all practical purposes equivalent,

or the conclusion is in favor of deposit regulation. In our model there is a real tradeoff between

the two: capital regulation is costly because the opportunity costs of capital are higher than the

return from normal banking activities, while deposit rate ceilings may result in an inefficiently

large number of banks. We show that, depending on the opportunity costs of banking capital

and on the severity of the moral hazard problem they seek to address, each of the two regulatory

instruments may welfare-dominate the other.

Key wor ds banking regulation, moral hazard, deposit rate control, capital requirement, Salop

model

JEL classification D43, D82, G21, G28

Accepted 11 July2016

1 Introduction

Deposit rate ceilings were commonly used in banking regulation until the 1980s when, as part of

a wave of regulatory reforms, they were replaced by capital requirements stipulating that parts of

bank investment funds be supplied by bank owners.1Despite this dramatic change in regulatory

policies, there is, to the best of our knowledge, so far no theoretical model that, contrasting the two

*Department of Economics and Finance, Catholic University of Milan, Milan,Italy.

†Department of Mathematical Disciplines, Mathematical Finance and Econometrics, Catholic Universityof Milan, Milan,

Italy.Email: gerd.weinrich@unicatt.it

We are grateful for comments from participants at the following conferences: Italian Economic Association, Annual

Conference 2013; European Economic Association, Annual Meeting 2013; InternationalFinance and Banking Societ y,

Annual Conference2013; Associazione per la Matematica Applicata alle Scienze Economiche e Sociali, Annual Conference

2013; XXII International Conference on Money,Banking and Finance, Rome 2013. Financial support from the Italian

national research project “Local interactions and global dynamics in economics and finance: models and tools”, PRIN-

2009, and from the Catholic University’sresearch projects “Teoriee modelli matematici per le scienze economiche”,UCSC

D.1,and “ The challenges of the crisis: Rethinkingmicroeconomic and macroeconomic policies”,UCSC D3.2, is gratefully

acknowledged.

1All three Basel accords focus on reducingr isk-taking bybanks, and in doing so rely heavily on capital requirements as the

regulatory instrument. The third Basel accord is characterized by a tightening of control and supervision, exemplified by

an increase in capital requirements and a return to more objective standards for defining the riskiness of the individual

bank’s assets.

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International Journal of Economic Theory

Capital requirements deposit rate ceilings Carsten Krabbe Nielsen and Gerd Weinrich

regulatory regimes, comes out in favor of capital requirements.2The purpose of our contribution is

to formalize a tradeoff between the two regimes, which has at least implicitly been recognized in the

literature, and compare their consequential welfare properties. This is done in a setting where, due

to moral hazard, there is a real need for regulation, since without it banks would take on too much

risk.

Capital requirements are costly because bank capital is costly (this is why bank owners in general

seek to limit their contribution of capital) and these costs are ultimately borne by depositors in

the form of lower deposit rates.3Deposit rate ceilings, on the other hand, depress competition (for

depositors) and increase profits for existing banks. These excess profits, attracting newcomers, lead

to a bloated banking sector, which is also costly to society. This cost, in the form of excess entry,

is widely acknowledged by regulators and is also confirmed by empirical evidence (as we briefly

show later). Nevertheless, no theoretical study seems to have taken it into account in a comparison

of the two regulatory regimes, which is essentially why none have concluded against deposit rate

ceilings.

Since neither type of regulation is without its costs, any comparison of their welfare consequences

should explicitly take them into consideration, as we do here. In particular, taking these costs into

account, it could conceivably be better to not regulate at all. It is therefore important to identify, as

we shall in our analysis, conditions under which either type of regulation leads to higher welfare than

laissez-faire.

Our model, which builds on Hellmann et al. (2000) and Repullo (2004), assumes a continuum of

potential depositors on the unit circle `alaSalop, served by a finite number of imperfectly competitive

banks and covered by deposit insurance. When investing the deposits received, banks may choose

between a risky (“gambling”)asset and a non-r isky (“prudent”)asset, with the former having positive

probability πof a non-positive net return and consequent bankruptcy of the bank, and the latter

having a higher expected return, α, thus being the socially optimal choice. Due to moral hazard prob-

lems (the non-observability of the investment choices of banks), an unregulated banking industry

may end up in a gambling equilibrium (where all banks choose the risky asset) rather than a prudent

equilibrium.4We retain the assumption of Hellmann etal . (2000) and Repullo (2004) that capital

requirements are socially costly since the capital provided by owners has a higher opportunity cost,

denoted ρ, than what it can earn when employed in normal banking activities. The novelty of our

model, which otherwise follows that of Repullo (2004) rather closely, is to allow for an endogenous

determination of the number of banks assuming that these have setup costs C.5Deposit rate ceilings

tend to lead to excess profits (for empirical documentation of this, see, for example, Berger et al.

1995), which in turn leads to the entry of new banks. Like Chiappori et al. (1995), we assume that

banks are free to enter and will do so until profits (including setup costs) are driven down to zero.

Together with the assumption that depositors pay for deposit insurance via taxes, this assumption

2The few theoretical models that do consider both instruments either come out in favor of deposit rate ceilings or take a

neutral stance. We arereferr ing toBhattachar ya (1982), Hellmannet al . (2000), Matutes and Vives (2000) and Repullo

(2004), which we discuss further below.

3Besanko and Thakor (1992, p. 911) were probably the first to observe this: “raising the capital standard is virtually

isomorphic to reimposing Reg Q ceilings on deposit interest rates.”

4This formalization of moral hazard in banking goes back to at least Bhattacharya (1982).

5Besanko and Thakor (1992) also studied the effects of varying the number of banks in a Salop-type model. Chiappori

et al. (1995) study the costs, in terms of an increased number of banks, under deposit rate regulation, in a Salop model

with setup costs. However, they do not explicitly considerthe benefits of banking regulation. Gehrig (1995) studies the

welfare consequences of free (and restricted) entry in a model quite different from ours: the model does not consider

moral hazard issues and has only one period.

140 International Journal of Economic Theory 14 (2018) 139–178 © IAET

Carsten Krabbe Nielsen and Gerd Weinrich Capital requirements deposit rate ceilings

leads to a simplification of the welfare analysis: to compare the different regulatory regimes we only

need to compare the welfare of the (average) depositor. The possibility of an excess entry of banks at

a cost to society then establishes a tradeoff, as measured by dead-weight costs, between using deposit

rate ceilings and capital requirements as regulatory instruments.

We show that the number of banks in a prudent equilibrium cannot be lower (and may be

higher) in a regulatory regime of deposit rate control than in a regime with capital requirements,

which, in turn, is higher than the optimal number of banks, which then establishes that deposit rate

ceilings carry a social cost. As was observed by Chiappori et al. (1995), the inefficiency associated

with an excessive number of banks may as well be interpreted as an inefficiency due to non-price

competition in the form of product differentiation, that is, of attracting customers by other means

than the deposit rate.6

Our main result finds that when ρis close to α(meaning that capital requirements are not too

socially costly) capital requirements, as a regulatory instrument, dominate deposit rate ceilings.

This is not a surprising conclusion, although the picture is rendered more complicated by the fact

that ρalso plays the role of discount factor and as such influences the franchise value (equal to the

discounted value of future profits) of any bank. On the other hand, we show that, as πincreases,

deposit rate ceilings overtake capital requirements in terms of consumer welfare. We interpret this

as saying that, when the moral hazard problem is severe in the sense of a low probability of default,

making the risky asset more attractive, deposit rate ceilings are an insufficient regulatory tool and

capital requirements are needed.7We provide a numerical example showing that in the case where

deposit rate regulation is welfare optimal, the deposit rate ceiling may or may not be binding in

equilibrium.

1.1 Related literature

The two studies (that we know of) which explicitly compare deposit rate ceilings and capital re-

quirements, Hellmann et al. (2000) and Repullo (2004), both come out in favor of the former as a

measure for preventing moral hazard by banks. The study by Hellmann et al. (2000) finds that while

deposit rate ceilings alone can implement a subset of the (constrained) efficient allocations, capital

requirements always need to be combined with deposit rate control to do so. In fact Hellman et al.

(2000, p. 156) interpret their main proposition as stating that “the current policy regime practiced in

most countries around the world (i.e. using just a capital requirement with no deposit-rate control)

is a Pareto-inferior policy choice.”

Repullo (2004) provides an examination of the results of Hellmann et al. (2000) in a general

equilibrium framework where banks maximize profits over an infinite horizon.8The conclusions

of Hellmann et al. (2000) are to a large extent confirmed: deposit rate ceilings are effective (in

eliminating excessive risk-taking by banks) whenever capital requirements are effective, while the

opposite is not the case (Repullo, 2004, p. 175). However, since in the models of Repullo and

(disregarding financial repression) of Hellman et al. capital requirements are socially costly, while

6VanHoose (2010, pp. 76–80) provides a review of the existing literature on non-price competition in the banking sector.

He cites several studies that find that the number of branches or ATMsystems are used by banks to boost the demand for

their products. See also Berger et al. (1995, p. 79) and Hammond and Knott (1988, p. 15).

7Complementing this result, Nielsen (2012) showshow capital control may become ineffective as the riskiness of the risky

asset increases.

8An interesting contribution by Niu (2008) uses the model of Repullo (2004) to study the effects of subordinated debt

requirements assuming the number of banks fixed.

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