Bank Competition and Financial Stability: A General Equilibrium Exposition

1
Bank Competition and Financial Stability A
General Equilibrium Exposition

• Gianni De Nicolò
• International Monetary Fund and CESifo
• Marcella Lucchetta
• University of Venice, Department of Economics
• The views expressed in this paper are those of
  the authors and do not necessarily represent
  those of the IMF.

2
Motivation

• The issue of whether bank competition should be
  restrained has a long history in the bank
  regulatory debate, and has resurfaced in the
  aftermath of the recent financial crisis
• The existing theoretical banking literature does
  not offer much guidance to this debate, since
• a) it is based on partial equilibrium
• b) focuses on the relationship between banks
  risk of failure and competitive conditions

3
The inconclusive results of the partial
equilibrium literature (1)

• When banks are modeled as limited liability firms
  raising funds from insured depositors, choose the
  risk of their investment, and this choice is
  unobservable (moral hazard), then the standard
  risk-shifting argument applies
• More competition for funds implies a higher risk
  of bank failure
• Many contributions Keeley (1990), Hellmann
  Murdock and Stiglitz, (2000), etc.

4
The inconclusive results of the partial
equilibrium literature (2)

• When banks are modeled a la Cournot as limited
  liability firms raising funds from insured
  depositors and lending to entrepreneurs under
  moral hazard, then
• More competition (an increase in the number of
  banks) implies a LOWER risk of bank failure if
  project risks are perfectly correlated (Boyd and
  De Nicolò, 2005), or a U-shaped relationship
  between the number of banks and bank risk of
  failure (Martinez-Meira and Repullo, 2010) if
  project risks are not perfectly correlated

5
General equilibrium

• Restraining bank competition seems at odds with
  the implications of some general equilibrium
  models
• Allen and Gale (2004) perfect competition is
  Pareto optimal under complete markets, and
  constrained Pareto optimal under incomplete
  markets, with financial instability as a
  necessary condition for optimality
• Boyd, De Nicolò and Smith (2004) analogous
  results in a general equilibrium monetary economy
  with aggregate liquidity risk under low
  inflation.
• Yet, these papers do not model bank risk choices
  under moral hazard, which we introduce in general
  equilibrium.

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The key unanswered normative question is

• Is there a trade-off between bank competition and
  financial stability?
• Is a lower level of risk of bank failure
  necessarily desirable in a welfare sense?
• In this paper we address the following question
• What is the welfare-maximizing level of
  competition and the associated optimal level of
  bank risk of failure?

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Key features of our model

• We introduce all features of partial equilibrium
  models that find that competition increases
  banks risk of failure
• Agents occupational choices between being
  bankers or depositors determine endogenously the
  allocation of resources to productive activity
  and bank intermediation
• We consider no deposit insurance and deposit
  insurance How the presence of deposit insurance
  affects the welfare ranking of competitive
  conditions?

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Key Result

• Perfect bank competition is
• constrained Pareto optimal.
• This result holds without and with deposit
  insurance
• It holds even though competitive banks risk of
  failure is higher than banks enjoying monopoly
  rents
• It holds under any social cost function
  associated with costs of banks failures not
  internalized by banks that are consistent with
  essential bank intermediation.
• There is no trade-off between bank competition
  and financial stability
• WHY?

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The key resource re-allocation mechanism at work
The general equilibrium effect of bank
competition

• As bank competition for funds increases, the
  relative return of intermediated investment
  (deposits) relative to shares of bank ownership
  increases.
• This causes a shift of resources from investment
  in costly bank intermediation to investment in
  productive assets intermediated by banks.
• The resulting increase in expected output (net of
  monitoring and production costs) is large enough
  to offset any reduction in the expected return on
  investment due to the higher risk of failure of
  banks operating under more intense competition.

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Plan

• The model
• Equilibrium
• Definition of competition
• Deposit insurance
• Welfare
• Welfare implications
• Conclusion

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The Model Time, Endowments and Preferences

• There are 2 dates 0 and 1
• A continuum of risk neutral agents on
• Every agent has an endowment of 1 of date 0
  goods
• All agents have access to a risk-free technology
  which yields per unit invested.
• At date 0 agents decide either to become bankers
  or depositors.

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Banks (1)

• If an agent chooses to become a banker, she
  forgoes her initial endowment in exchange of the
  ability to form coalitions, called banks, which
  operate a risky project
• The project is indexed by the probability of
  success
• An investment in a risky project yields
  with probability P, and 0 otherwise
• Banks choose P and operating capacity z (or
  demand for funds) at an effort cost.

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Banks (2)

• Bank effort cost function is given by
• The transformation of effort into productive
  capacity is simply a standard production
  technology. The effort cost of setting up
  operating capacity z is

14
Competition

• Agents who have chosen to be bankers can move at
  no cost to one of two unconnected locations,
  labeled M and C
• Each bank in M acts as a monopolist and in C as a
  perfect competitive bank
• there is free entry in the monopolistic and
  competitive banking sectors
• project risks are independent across locations,
  but perfectly correlated within locations. Denote
  with and the risk choices
• If an agent chooses to be a depositor, he will
  move to location C with probability
  (switching costs)

15
Deposit insurance

• Deposit insurance (DI) is pre-funded by taxation
  of initial resources A
• The tax revenues are invested in the safe
  technology that yields
• Let denote the tax rate. The total
  end-of-period assets of the deposit insurance
  fund (DIF) are equal to
• Denote with and total investment
  (deposits) and the guarantee per unit
  of deposits

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Contracts and sequence of decisions

• Depositors finance the bank with simple debt
  contracts that pay a fixed amount R per unit
  invested
• Moral hazard is introduced by assuming that bank
  choices of P are not observable by depositors
• Denote with x the fraction of bankers in C, with
  the measure of bankers, with the number
  of banks, with bank size (capacity), and
  with the deposit rates, for

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Sequence of decisions and determined variables
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Bank Problems

• We solve backward, starting with the competitive
  and monopolistic bank problems
• Competitive banks choose P to maximize
• 
  (1)
• With solution
• 
  (2)

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Competitive banks

• Bertrand competition implies that maximizes
  depositors expected return
• 
  (3)
• Then

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Monopolistic banks

• The representative monopolistic bank chooses
• to maximize expected profits
• (9)
• subject to the depositors participation
  constraint
• 
  (10)

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Monopolistic banks

• where is given by
• 
  (11)
• And
• 
  (14)

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Monopolistic banks

• The optimal risk choice of the monopolistic bank
  is thus
• 
  (15)
• Using (14) and (15), the expected profits of the
  monopolistic bank are
• 
  (16)

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Comparing bank optimal choices
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Equilibrium (1)
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Equilibrium (2)
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Welfare
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Social costs of bank failures
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Conclusion

• General equilibrium modeling of intermediation
  appear an essential tools to throw light on the
  desirable level of systemic risk in the economy,
  and how it could be attained