Advanced Macroeconomics I ECON 525a - Fall 2009 Yale University

Transcription

1 Advanced Macroeconomics I ECON 525a - Fall 2009 Yale University Week 7 - Reputation and Risk Taking

2 Motivation A sound banker, alas, is not one who foresees danger and avoids it, but one who, when he is ruined, is ruined in a conventional way along with his fellows, so that no one can really blame him J. M. Keynes, 1931

3 Motivation Reputation concerns may deter opportunistic behavior. Short-term opportunistic benefits vs. long-term reputational costs.

4 Motivation Reputation concerns may deter opportunistic behavior. Short-term opportunistic benefits vs. long-term reputational costs. Reputation has limits.

5 Motivation Reputation concerns may deter opportunistic behavior. Short-term opportunistic benefits vs. long-term reputational costs. Reputation has limits. In lending markets, borrowers whose actions are non-observable may take excessive risk...and reputation imposes self-discipline...with certain limits.

6 Question Aggregate effects of reputation incentives?

7 Question Aggregate effects of reputation incentives? In the aggregate, Identical borrowers with different reputation levels Conditions determine the temptation to take excessive risk.

8 Question Aggregate effects of reputation incentives? In the aggregate, Identical borrowers with different reputation levels Conditions determine the temptation to take excessive risk. How do borrowers with different reputation levels behave under same aggregate conditions? Effects of changes in aggregate conditions on aggregate behavior?

9 Question Aggregate effects of reputation incentives? In the aggregate, Identical borrowers with different reputation levels Conditions determine the temptation to take excessive risk. How do borrowers with different reputation levels behave under same aggregate conditions? Effects of changes in aggregate conditions on aggregate behavior? Why is this relevant? Reputation is at the core of lending relations, based on confidence. Reputation affects cost and availability of credit.

10 Answer Reputation is effective, but fragile Borrowers with intermediate and high reputation change risk-taking behavior under similar aggregate conditions. Small aggregate shocks may lead to clustering in risk-taking and confidence crises.

11 Answer Reputation is effective, but fragile Borrowers with intermediate and high reputation change risk-taking behavior under similar aggregate conditions. Small aggregate shocks may lead to clustering in risk-taking and confidence crises. Current crisis Market discipline failure. Excessive risk-taking. Confidence crisis on the reliability of ratings.

12 Road Map Model of reputation and risk-taking in lending markets. Diamond (89) and Mailath and Samuelson (01) Introduction of aggregate shocks. Selection of a unique equilibrium. Fragility of reputation and clustering in risk-taking. Sudden collapses in otherwise well-functioning lending markets.

13 Main Problem Firms borrow at a given interest rate to run a project. They decide to take safe or risky unobservable actions.

14 Main Problem Firms borrow at a given interest rate to run a project. They decide to take safe or risky unobservable actions. Typical moral hazard Short-term opportunistic benefits. Reputation concerns Long-term reputational cost.

15 Main Problem Firms borrow at a given interest rate to run a project. They decide to take safe or risky unobservable actions. Typical moral hazard Short-term opportunistic benefits. Reputation concerns Long-term reputational cost. How far reputation can go in reducing excessive risk-taking?

16 Example - Efficiency If actions of firms are observable. 1 1 Loan=1, R = 1, R s =, R r = Action Prob Payoff Payoff to lenders Payoff to firms Safe R s = Risky R r = Differential gains Safe 0.2 > SafeLoan=1, is efficient. R = 1, R, Action Prob Payoff Payoff to lenders Payoff to firms Safe

17 Safe R s = Example - Moral Hazard Risky R r = Differential gains Safe 0.2 > 0 If actions of firms are non-observable. 1 1 Loan=1, R = 1, R, Action Prob Payoff Payoff to lenders Payoff to firms Safe R R Risky R R Differential gains Safe R 1 1 Risky Loan=1, is preferred R = 1, R when, R > (Always) Action Prob Payoff Payoff to lenders Payoff to firms

18 Safe R R Example - Reputation Risky R R Two unobservable types, Strategic (choose) and Risky. Reputation φ is the probability the firm is strategic. Signals correlated to actions. Differential gains Safe R 1 1 Loan=1, R = 1, R, Action Prob Payoff Payoff to lenders Payoff to firms Safe < R R Risky < R R Differential gains Safe R Safe is preferred when R < 2.5 (Always)

19 A simplified two period model Timing Loan of 1 at R(φ) > 1 (decreasing in φ). Fundamentals θ N ( ) µ, 1 α are realized. Strategic firms decide safe (s) or risky (r) actions. Firm continues or die: (p s > p r ) Dies Gets 0. Defaults. Continues: Gets Π s if s or Π r = Π s θ if r. Repayment. No asset accumulation. Lenders update reputation based on continuation from φ to φ. Fixed payment V (φ ) (increasing in φ ).

20 - Differential gains from safe actions V s (φ, θ) = p s (Π s R(φ) + V (φ )) V r (φ, θ) = p r (Π s θ R(φ) + V (φ )) Short term Continuation Moral Hazard {}}{{}}{{}}{ (φ, θ) = (p s p r )Π s + p r θ + (p s p r )V (φ) (p s p r )R(φ) +(p s p r )[V (φ ) V (φ)] }{{} Reputation Formation

21 decreases with beliefs of risk taking x Define x(φ) the probability assigned by lenders to firms φ taking risk (φ, θ x) = (p s p r )Π s + p r θ+(p s p r )V (φ) (p s p r )R(φ) +(p s p r )[V (φ ) V (φ)]

22 decreases with beliefs of risk taking x (φ, θ x) = (p s p r )Π s + p r θ+(p s p r )V (φ) (p s p r )R(φ) +(p s p r )[V (φ x) V (φ)] Reputation 1 after continuation Updating ( x ˆ = 0 ) φ ' Updating ( x ˆ = 1) φ 45 0 φ φ 1 M Reputation before continuation

23 increases with fundamentals θ (φ, θ x) = (p s p r )Π s + p r θ+(p s p r )V (φ) (p s p r )R(φ) +(p s p r )[V (φ x) V (φ)] Limit of Reputation (φφ, θθ xx ) Risky Safe θθ

24 decreases with beliefs of risk taking x (φ, θ x) = (p s p r )Π s + p r θ+(p s p r )V (φ) (p s p r )R(φ) +(p s p r )[V (φ x) V (φ)] As xx decreases (φφ, θθ xx ) Risky Safe θθ

25 Cutoff Strategies s if θ > k(φ) a(φ, θ) = r if θ < k(φ) 0 if θ > k(φ) x(φ, θ, k(φ)) = 1 if θ < k(φ)

26 Multiple solutions when θ is observed (φφ, θθ xx = 0) (φφ, θθ xx = 1) θθ kk(φφ) θθ θθ

27 Uniqueness when θ is not perfectly observed New assumption about the information structure. Before production, all firms i observes a signal z i = θ + ɛ i where ( ) ɛ i N 0, 1 identically and independently distributed across i. β After production, lenders j observes a signal z j = θ + ɛ j where ( ) ɛ j N 0, 1 identically and independently distributed across j. β Alternative assumption: Lenders observe aggregate default rate by firms with reputation φ. Equilibrium strategies are redefined over signals. s if z > z (φ) a (φ, z) = r if z < z (φ)

28 Uniqueness when θ is not perfectly observed θ i = E(θ x i ) = αµ + βx i α + β ( 1 x j θ i N θ i, α + β + 1 ) β x(z i ) = Pr ( θj < θ ) [ ] i θ i = Φ γ( θi µ) where γ = α2 (α + β) β(α + 2β)

29 Uniqueness as β (φφ, θθ xx = 0) (φφ, θθ xx = 1) θθ μμ θθ θθ

30 Uniqueness as β E θ ( (φ, θ x) z ) = 0 As β, E(θ x i ) z and x 0.5 for all z i (p s p r ) (Π s R(φ) + V (φ x = 0.5)) + p r E(θ z ) = 0 z = p s p r p r (Π s R(φ) + V (φ x = 0.5))

31 Uniqueness as β (φφ, θθ xx = 0) (φφ, θθ xx = 0.5) (φφ, θθ xx = 1) θθ zz θθ θθ

32 Properties of Reputation Proposition Ex-ante probabilities of risk taking decrease with reputation dφ(z (φ)) dφ < 0 for all φ [0, 1] Interest rates decrease with reputation dr(φ) dφ < 0 for all φ [0, 1] Continuation values increase with reputation dv (φ) dφ > 0 for all φ [0, 1] Reputation concerns convexify the schedule of cutoffs z (φ). 2 z (φ) φ 2 > 0 for all φ [0, 1]

33 Risk Taking WITHOUT reputation formation φ 1 Safe actions Risky actions 0 * ( ) z φ (φ, θ) = (p s p r )(Π s (θ)+v(φ) R(φ) + p r θ

34 Reputation formation incentives φ ' 1 φ g Updating x=0 φ b 0 φ M 1 φ Benefits in reputation from good results 0 1 φ (φ, θ) = (p s p r ) (Π s +V(φ) R(φ)+[V (φ ) V (φ)]) + p r θ

35 Risk Taking WITH reputation formation φ 1 Safe actions φ M Risky actions 0 * ( ) z φ

36 Fragility of Reputation Proposition Selection: For β, small changes in θ around z (φ) induce sudden changes in risk-taking behavior among firms with the same φ. Learning: For β, as fundamentals decrease, an increasingly wider range of reputation levels φ decide to take risk.

37 Clustering in Risk Taking φ 1 Safe actions Risky actions 0 θ 1 θ 0 * ( ) z φ

38 Clustering in Risk Taking φ 1 Safe actions Risky actions 0 θ 1 θ 0 * ( ) z φ

39 Simulations - Example Value function iteration. Finite and large grid φ Assume Π s > 0, Π r = Π s + K ψθ, where ψ > 0 and θ N (0, 1) Parameters: β = 0.95, R = 1, Π s = 1.5, K = 0.4, ψ = 0.2, p s = 0.9, p r = 0.7, α s = 0.8 and α r = 0.4.

40 Simulations - Limits to Reputation Fundamental below which it is efficient to take risk Fundamentals below which firms take risk WITHOUT reputation formation 0.6 Reputation Fundamentals below which firms take risk WITH reputation formation Distribution of fundamentals (Standard Normal) Fundamentals

41 Simulations - Default Probabilities 0.5 Fundamentals Aggregate Default Probability 0.3 Efficiency Cutoff with Full Information Default Probability WITHOUT reputation formation Default Probability WITH reputation formation -2-4 Fundamentals Aggregate Default Probability Periods 0.1

42 Simulations - Net Returns to Lenders Aggregate Net Returns Aggregate Net Returns WITHOUT reputation formation Aggregate Net Returns WITH reputation formation 4 2 Fundamentals Fundamentals Periods -0.2

43 Introduction US Recession Model Quarters ( ) Fragility (percent) Simulations Evidence Final Remarks Terminal Rating Initial Rating AAA AA A BBB BB B CCC Default AAA AA A Clustering BBB in Corporate Default Rates BB B CCC Corporate default cluster in recessions. Duffie et al. (2007). 16 Corporate Default Rates Percen

44 Clustering in Risk Taking Behavior Idiosyncratic Risk cluster in recessions. Campbell et al. (2001). 1.6 Monthly Idiosyncratic Risk Idiosyncratic risk in selected industries Autos and Trucks

45 Conclusions Natural use of global games to select a unique equilibrium in reputational games. Fragility of reputation. Large change in aggregate risk-taking in response to small and non-obvious changes in aggregate fundamentals. Financial crises. Sudden raise in moral hazard vs. sudden weakening of reputation. Policy implications. Extensions. Basel II banking regulations. Credit bureaus. Reputation or Regulation?

46 Reputation or Regulation? Ben Bernanke, NY Times, Dec. 18, market discipline has in some cases broken down and the incentives to follow prudent lending procedures have, at times, eroded. Paul Krugman, NY Times, Dec. 21, 2007 Mr. Greenspan dismissed as a collectivist myth the idea that businessmen, left to their own devices, would attempt to sell unsafe food and drugs, fraudulent securities, and shoddy buildings. On the contrary, he declared, it is in the self-interest of every businessman to have a reputation for honest dealings and a quality product... Protection of the consumer by regulation is thus illusory, the only reliable protection the consumer has is competition for reputation. Charles Goodhart, FT, Jan. 31, 2008 Capital adequacy requirement on mortgage lending should be linked to the rise in both mortgage lending and housing prices...

47 Even more recent quotes NY Times, Oct. 3, 2008 (Stephen Labaton) About a 2004 rule change by the SEC that removed regulation of investment bank debt ratios, only for the largest firms We ve said these are the big guys...we foolishly believed firms had a strong culture of self-preservation and responsibility and would have the self-discipline not to be excessively borrowing. A similar laissez-faire philosophy has driven a push for deregulation throughout the government, from the CPSC and the EPA to worker safety and transportation agencies. NY Times, Oct. 2, 2008 (Joe Nocera) This is what a credit crises looks like...it s a loss of confidence in seemingly healthy institutions.