Bank Risk Taking and Competition Revisited: New Theory and New Evidence

1. Bank Risk Taking and Competition Revisited: New Theory and New Evidence John Boyd, Gianni De Nicolò and Abu Al Jalal The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF or the Federal Reserve System.

2. Questions • Is there a trade-off between competition and stability in banking? • The existing empirical evidence is mixed and theory has produced conflicting predictions. • What are the implications of market structure for bank asset allocations? • To date, neither theory nor evidence • We address these important policy questions bringing to bear new theory and new evidence.

3. New Theory: bank asset allocation • Banks face botha “portfolio allocation problem” and an “optimal contracting problem” • They acquire bonds and other traded securities (they are price takers) andthey lend in environments with private information. • A causal relationship from market structure to asset portfolio allocation is of more than theoretical interest (what is special about banks?)

4. New Theory: bank asset allocation • We model both decisions by allowing banks to invest in a default-risk- free government bond. • We get a good deal of increased complexity for two reasons: A) Banks’ investment in bonds can be viewed as a choice of “collateral” (indeed, the risk-free bond becomes a risky asset....) B) The asset allocation between bonds and loans becomes a “strategic variable”

5. Two New Models • The (CVH) model : a) competition in deposit, but not in loan, markets, and b) no contracting problem (e.g. Keeley, 1990, Hellman, Murdoch and Stiglitz, 2000, Repullo, 2004) . • Our model (BDN): a) competition in both loan and deposit markets, and b)contracting problem (Boyd and De Nicolo’ (2005). • In both models, lower concentration (more banks) means more competition

6. New Theory: Predictions • Both models yield a negative relationship between loan-to-asset ratios and concentration... BUT • CVH model : negative relationship between concentration and bank’s probability of failure • BDN model: positive relationship between concentration and bank’s probability of failure

7. New Evidence • We explore the predictions of the models empirically using two data sets: • U.S. sample: 2003 cross-sectional sample of about 2,500 U.S. banks • International sample: panel data set with bank-year observations ranging from 13,000 to 18,000 in 134 non-industrialized countries for the period 1993-2004.

8. Empirical Results • A measure of bank probability of failure is positively and significantly related to concentration. • The risk implications of the CVH model are rejected, those of the BDN model are not. • The implications of both models for asset allocations are not rejected, as loan-to-asset ratios are negatively and significantly associated with concentration.

9. Implications • No trade-off between banking stability and competition • The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking • Many positive and normative analyses of regulation based on CVH-type models should be re-examined.

10. CVH Model (1) • Bank Problem • NMH and MH strategies

11. CVH Model (2) • No-moral-hazard (NMH) strategy (max{.}>0) • Moral-hazard (MH) strategy (max{.}=0) • Banks may or may not endogenously choose to be default risk-free even though they have the option of risk shifting. • Focus on symmetric Nash equilibria in pure strategies

12. CVH Model (3) Proposition 1 • (a) Either the unique equilibrium is MH (loans/assets=1) or • (b) Unique NMH if N<N(1), multiple equilibria (NMH or MH) if N(1)<N<N(2), and unique MH if N>N(2) • Risk of failure increases in N • In (b), loans/assets move from 0 to 1 as N increases

13. BDN Model (1) • Entrepreneurs: Given a loan rate , entrepreneurs solve: • Banks: Each bank solves

14. BDN model (2) • As before, NMH and MH strategies • But NOW, NMH strategies need to be distinguished in two categories: • No provision of credit (if this is an equilibrium outcome, we have CREDIT RATIONING) • Some provision of credit

15. BDN Model (3) Propositions 2, 3 and 4 • (a): There exists economies for which for N<N(1) the unique equilibrium is a CREDIT RATIONING equilibrium (no lending) • (b) For N>N(2), the unique equilibrium is MH • Risk of failure decreases in N • Loans/assets increases in N for N>N(3)

16. Evidence: Theory and Measurement Measure of Bank Risk • Theory: probability of bank failure • Measurement: Z-score (distance-to-default) Measure of Competition • Theory: Number of banks (homogenous firms) • Measurement: Hirschmann-Hirfendahl Indices (HHIs).

17. Evidence: U.S. Sample • About 2500 U.S. banks that operate only in rural non-Metropolitan Statistical Areas • Cross-section for one period only, June, 2003. • The FRB defines a competitive market as a county and maintains and updates HHI Indices • Within each market area the FRB defines a competitor as a “banking facility,” which could be a bank or a bank branch.

18. U.S. sample • The U.S. sample has an important, interesting and unique feature. We asked the FRB to delete from the sample all banks that operated in more than one market area. • Thus, we are able to better match up competitive market conditions as represented by the HHI and individual bank asset allocations as represented by balance sheet data. • Disadvantage : exclusion of many banks (all in HHI)

19. International sample • Panel data set of about 2700 banks in 134 countries excluding major developed countries over the period 1993 to 2004 (Bankscope). (Bank-year observations range from more than 13,000 to 18,000, depending on variables’ availability). • Disadvantage: bank market definitions are necessarily imprecise, since it is assumed that the market for each bank is defined by its home nation. • We did not include in the sample banks from the U.S., Western Europe and Japan, since defining the nation as a market is problematic.

20. U.S. Sample Regressions • Dependent variables: • Z-score, • loans/assets, and • Z-score components, regressed on: county HHI, county/state specific and bank specific controls • Robust OLS and GMM IV estimation

21. Results • Bank risk of failure positively related with concentration • The ratio of loans to assets negatively related to concentration • The positive relationship between bank risk of failure and concentration mainly driven by the positive relationship between concentration and ROA volatility

22. Z-score regressions

23. Loans/Assets regressions

24. ROA regressions

25. Equity/Asset regressions

26. ROA volatility regressions

27. International Sample Regressions • Z-score is defined at each date • Panel regressions with a) Z-score, b) loans/assets and c) Z-score components as dependent variables, regressed on: • country’s HHIs (Asset, Loans, Deposits) • country-specific and bank-specific controls. • Robust country fixed effects and firm fixed effects panel regressions • All explanatory variables are lagged one year

28. Results • Bank risk of failure positively related with concentration • The ratio of loans to assets negatively related to concentration • The positive relationship between bank risk of failure and concentration driven by the negative relationship between capitalization and concentration, and the positive relationship between ROA volatility and concentration

29. Dependent Variable: Z-score(t)

30. Dependent Variable: LGLTA(t)

31. Components of the Z-score(t)

32. Conclusion • No trade-off between banking stability and competition • The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking • Many positive and normative analyses of regulation based on CVH-type models should be re-examined.