Bank Competition and Financial Stability: A General Equilibrium Expositi on

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): analogousresults 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.

6. 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?

7. Key features of our model We introduce all features of partial equilibrium models that find that competition increases bank’s 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?

8. Key Result Perfect bank competition is constrained Pareto optimal. This result holds without and with deposit insurance It holds even though competitive bank’s 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?

9. 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.

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

11. 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.

12. 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.

13. 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

16. Contracts and sequence of decisions • Depositors finance the bank with simple debt contractsthat 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

17. Sequence of decisions and determined variables

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

19. Competitive banks • Bertrand competition implies that maximizes depositors’ expected return (3) • Then:

20. Monopolistic banks • The representative monopolistic bank chooses to maximize expected profits: (9) • subject to the depositors’ participation constraint (10)

21. Monopolistic banks • where is given by: (11) And (14)

22. 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)

23. Comparing bank optimal choices

24. Equilibrium (1)

25. Equilibrium (2)

26. Welfare

27. Social costs of bank failures

28. 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