Bank Competition and Financial Stability: A General Equilibrium Exposition

1. Bank Competition and Financial Stability: A General Equilibrium Exposition Discussion Gabriella Chiesa University of Bologna

2. Review of the literature • conventional wisdom: competition in banking results in ceteris paribus greater instability (more failures)

3. Competition for deposits: ↑“debt burden” (risk-shifting incentives) Keeley(1990), Allen and Gale (2000, 2004), Hellmann, Murdock and Stiglitz (2000), Repullo(2004) - • Competition for loans: worsening of borrowers pool- winner curse under adverse selection - Broecker (1990), Chiesa (1998) – • Liquidity shortage (contagion) more likely with non-oligopolistic bks: a price-taker bk does not internalize the effects of its actions on the price of liquidity → insufficient liquidity provision Allen-Gale (2003, 2004) ■ Scope for regulation: capital req.s, liquidity regulation..

4. This Paper • analyses the issue of bank competition for funds (deposits) and financial stability within a "bank moral hazard" framework (a framework that supports convent. wisdom) but it extends the analysis to: • General eq. aspects → Conclusion: Competition is Pareto Optimal Key: a competitive structure minimizes «bk equity waste»

5. Model • Continuum of risk-neutral agents [0,A], each endowed with one unit of resources. Storage techn. yields a gross return , available to all. • At date 0 an agent chooses to invest his endowment in: • bk deposit : become a depositor and earn the deposit rate; • bk equity (become a bk shareholder)

6. Bk shareholdings • benefit: sharing the bk profits (which depends on the mkt structure, comp. versus monopoly) • cost of becoming a bk shareholder is the waste of the endowment key assumption that drives GE results

7. Bank • Coalition of bk shareholders - objective function: = [P(X-R)]Z - C(P)Z - C(Z) Z = operating capacity = deposits raised (bk shareholders’ endow.s are lost) C(P)= effort cost ; m.c. of effort: P/α C(Z) = private cost ofsetting upcapacity; mc Z/ → Effort (success prob): • P* = (X-R) (1) → Operating capacity • Z*=[P*(X - R)-C(P*)] (2)

8. Deposit Rate • Competitive bk: R : max [P*R + (1-P*)g] Using (1): Rc= (X+g)/2 Pc*= (X-g) / 2 (decreasing in g) Zc*= [(X-g)2 / 8] Result: Competitive banks: Deposit insurance leads to greater failure risk, smaller bank size and profits

9. Monopolistic bk • Depositor’s payoff equals outside option : RM: [PM*RM + (1-PM*)g] = PM* = (X-RM) > Pc* • Monopolistic Bank is safer than a competitive bank • Deposit insurance lowers monop. bk’s failure risk, and leads to greater bank size and profits (by ↓RM ) Partial eq.- analysis: Standard – conventionalwisdom - results

10. General Equilibrium • Assumption: two locations (mkts): C, M. • An agent that chooses to be a depositor will be locked in to C with prob. , in to M with residual prob. 1- .Expected payoff to a depositor is r(,g) =D* +(1-) • An agent that chooses to be a bk shareholders can freely choose between C or M (share the profits of a competit. bk or those of a monopolistic bk)

11. Characterization of equilibrium • ABmeasure of bk shareholders : total resources invested in bk equity (A-ABin deposits) • x AB equity investment in the competitive bk sector/region C ((1-x) ABin M) • nc number of banks in C, nMnum. of banks in M which implies: - equity investm per bk in C : x AB /nc (ec ) - equity investm per bk in M: (1-x) AB /nM(eM )

12. Equil: AB , x AB , ncsuch that • return to a bk shareholder is the same in C, M: → eM is the amount of resources wasted per monopolistic bk, and → Welfare is maximized for =0 (No monopoly bk)

13. Interesting and intriguing analysis • Possible simplifications ( no C(Z)) • Less drastic assumption about «cost of providing equity»