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Presentation Bank Liquidity Interbank Markets and Monetary Policy Interbank Rates

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Presentation Bank Liquidity Interbank Markets and Monetary Policy  Interbank Rates Powered By Docstoc
					                  Conference on

      “Liquidity and Liquidity Risks”
      Frankfurt am Main, 23-24 September 2010

                 Xavier Freixas
             University Pompeu Fabra


                 Presentation to

“Bank Liquidity, Interbank Markets and
            Monetary Policy“

                 www.bundesbank.de
Introduction        Model          Results        Central bank       Financial fragility   Conclusion




                      Bank Liquidity, Interbank Markets,
                           and Monetary Policy1

                  Xavier Freixas             Antoine Martin         David Skeie
                         UPF                   FRB NY               FRB NY


                            “Liquidity and Liquidity Risks”
                      23-24 September 2010, Frankfurt/Germany



           1 The views expressed herein are those of the authors and do not necessarily re‡ect

       the views of the Federal Reserve Bank of New York or the Federal Reserve System.
Introduction        Model       Results    Central bank    Financial fragility   Conclusion




Main question



               What should be the interest rate policy of a central bank
               during a banking crisis?

               Standard view:
                   Monetary policy only plays a role if a …nancial disruption
                   directly a¤ects in‡ation or the real economy
                   No role for alleviating …nancial distress
                   Separation between prudential regulation and monetary policy
                   should be implemented
Introduction        Model       Results      Central bank   Financial fragility   Conclusion




Recent experience



               The fed funds rate was cut well below the Taylor Rule
               (measured by the current output gap and headline CPI
               in‡ation)
               Interest rates were cut to help reduce stress in the banking
               system
               Interest rates were also cut in previous …nancial disrutpions

                   1987 stock market crash
                   1998 LTCM
                   9/11
Introduction        Model      Results     Central bank    Financial fragility   Conclusion




Monetary policy, banking crises and interbank markets




               Interbank lending markets are a critical source of external
               liquidity for banks during …nancial turmoil
               Interbank interest rates are the fundamental instrument of
               monetary policy
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




Our paper




               We study the role of optimal central bank interest rate policy
               in interbank markets during liquidity shocks
               We provide a justi…cation for central bank policies in recent
               crises
               We show that monetary policy has a direct role by helping
               redistribution of liquidity in a crisis
Introduction        Model       Results      Central bank    Financial fragility   Conclusion




Main results



               Interbank market is an optimal institutional arrangement
               Central banks should use di¤erent tools to respond to
               idiosyncratic and aggregate shocks
                   Lower interest rate in case of idiosyncratic shock
                   Inject liquidity in case of aggregate shock
               Failure to implement optimal policy can lead to …nancial
               fragility
Introduction        Model       Results      Central bank     Financial fragility   Conclusion




Two concepts of liquidity


               Two types of liquidity:

                   Bank liquidity provision: Optimal holding of reserves. Held to
                   provide risk-sharing. The amount depend upon the expected
                   monetary policy.
                   Interbank market liquidity: Ease of distributing liquidity
                   between banks a¤ected by di¤erent liquidity shocks


               De…nition: In a crisis banks have high uncertainty about their
               liquidity needs
Introduction        Model       Results     Central bank     Financial fragility   Conclusion




The e¤ect of interbank rates



               Ex ante high rate promotes depositor risk-sharing
                   Banks hold more liquidity because it is expensive to acquire it
                   in the interbank market


               Ex post low rate promotes interbank risk-sharing
                   Redistribution of liquidity between banks is done more
                   e¢ ciently when interbank rates are low
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




Optimal central bank (CB) policy



               The CB can choose interbank rates

               CB will set average rates so as to promote optimal liquidity
               insurance between depositors.
               To promote risk-sharing between banks, CB must set low rate
               during a crisis
               Therefore CB must set high rates in normal times
Introduction        Model       Results     Central bank    Financial fragility   Conclusion




Literature


               Prudential/Monetary policy separation
                   Goodhart-Shoenmaker (1995)
                   di Giorgio and di Noia (1999)
               IB market not part of optimal arrangement
                   Bhattacharya and Gale (1987)
                   Freixas and Holthausen (2005)
                   Freixas and Jorge (2008)
                   Heider, Hoerova, and Holthausen (2008)
               IB market part of optimal arrangement
                   Allen, Carletti, and Gale (2008)
                   Our paper
Introduction        Model      Results     Central bank    Financial fragility   Conclusion




Literature (cont.)



               Trade-o¤ between holding liquidity ex ante and acquiring
               liquidity ex post

                   Diamond and Rajan (2008): Lower rates are bene…cial during
                   a crisis but CB may be ine¤ective because of Ricardian
                   equivalence
                   Bolton, Santos, and Scheinkman (2008): Timing of central
                   bank intervention is key
                   Our paper: Focus on level of interbank rates. CB can
                   implement the e¢ cient allocation
Introduction        Model        Results         Central bank   Financial fragility   Conclusion




Model



               Three dates: t = 0, 1, 2

               Multiple competitive banks, each with a unit mass of
               consumers who deposit

                        s
               Consumer’ private liquidity shock type

                       u ( c1 )            with prob λ            (impatient depositors)
               U=f
                       u ( c1 + c2 )       with prob 1      λ     (patient depositors)
Introduction        Model         Results      Central bank      Financial fragility   Conclusion




Liquidity shocks

               Liquidity shock state of nature i

                              1   with prob ρ                 (crisis)
                     i=f
                              0   with prob 1       ρ         (normal times)

                    s
               Bank’ private liquidity shock type j
                                                   1
                                  h    with prob   2          (high shock)
                            j=f                    1
                                  l    with prob   2          (low shock)

               Bank j has λij impatient consumers

                                  λ + iε    for j = h          (high shock)
                      λij = f
                                  λ iε      for j = l          (low shock)

               ε is the size of liquidity shock
               Liquidity shocks are bank-speci…c, not aggregate
Introduction        Model      Results      Central bank        Financial fragility         Conclusion




Endowments and Technologies



               Consumers have one unit of good at date 0




                                   Date :           t=0          t=1                  t=2
                 Storage (liquid asset) :                  1 ——>1
                                                                      1 ——>1
           Investment (illiquid asset) :                   1 — — — — — — –> r
Introduction       Model         Results       Central bank       Financial fragility   Conclusion




Timeline

               Date 0
                   Consumers deposit endowment
                   Bank invests α, stores 1 α
               Date 1
                   Shock state i = 0, 1
                   Consumers learn type, impatient withdraw c1
                   Bank learns type j = h, l, pays λij c1 , borrows interbank loan
                   f ij
                     I ιi is the interbank interest rate in state i
               Date 2
                                                ij
                   Patient consumers withdraw c2
                                       ij
                   Bank pays (1 λij )c2 , and repays interbank loan f ij ιi
Introduction        Model      Results     Central bank    Financial fragility   Conclusion




Assumptions




               Liquidity shock state i is observable but not veri…able

               c1 is non-contingent

               CRRA > 1. Banks provide liquidity insurance

               No sunspot driven bank runs
Introduction        Model       Results       Central bank             Financial fragility   Conclusion




First best


               The full-information …rst best is (α , c1 , c2 ) chosen by the
               planner who observes consumer types to maximize

                                     λu (c1 ) + (1      λ ) u ( c2 )

               subject to

                                            λc1              1    α
                                      (1   λ ) c2            αr
                                               α             1
Introduction        Model         Results              Central bank         Financial fragility   Conclusion




Bank optimization


                                      ij
               Bank chooses (α, c1 , c2 , f ij ) to maximize consumer’ EU
                                                                     s
                                                        0j
                   EU       = λu (c1 ) + (1 ρ)(1 λ)u (c2 )
                                  h                                      i
                              +ρ (1 λ1h ) 2 u (c2 ) + (1 λ1l ) 1 u (c2 )
                                            1   1h
                                                               2
                                                                     1l


               subject to bank budget constraints

                                             λij c1              1    α + f ij
                                                  ij
                                  (1        λij )c2              αr    ιi f ij
Introduction        Model        Results     Central bank   Financial fragility   Conclusion




Where are we now?




               Introduction
               Model: idiosyncratic shocks
               Results
               Central bank role
               Financial fragility
               Conclusion
Introduction         Model        Results          Central bank              Financial fragility   Conclusion




First order conditions
               Euler equation:
                                                                   ij  ij
                                       u 0 ( c1 ) = E [ ι i u 0 ( c2 ) λ ]
                                                                       λ

               No-arbitrage condition:
                                                 ij               ij
                                     E [ιi u 0 (c2 )] = rE [u 0 (c2 )]
               Market clearing: f ih =         f il for i = 0, 1
                                               α  1
                                 c1 ( α ) =
                                            λ
                                            i εc1    for j = h
                               f ij (α) = f
                                               i εc1 for j = l
       Remarks:
           1   Inelastic supply and the demand for liquidity f il , f ih
           2   Two FOC equations in three unknowns α, ι1 , ι0
Introduction        Model          Results        Central bank      Financial fragility   Conclusion




Multiple ex-post interest rates

           1   Inelastic supply and the demand for liquidity

               Low-shock liquid banks will lend f 1l = εc1 at ι1                   1

               High-shock illiquid banks will borrow f 1h = εc1 at
                                    0j
                            (1 λ)(c2 c1 )
               ι1   1+           εc1
                               1h
                    Such that c2             c1


               Result: There are multiple ex-post interbank market rates
                                                              0j
                                                      (1 λ)(c2 c1 )
                                       ιi 2 [1, 1 +        εc1      ]
Introduction        Model      Results     Central bank    Financial fragility   Conclusion




Multiple ex-post interest rates



               The level of the interbank market rate determines how gains
               from trade are shared

               High (low) rates bene…ts liquid (illiquid) banks

               Multiple equilibria studied before by Allen and Gale (2004)

               Empirically plausible: “open mouth operations”
Introduction        Model          Results       Central bank      Financial fragility           Conclusion




Results for ρ = 0 or "never a crisis case"


               Expansion of FOCs:
                                                                                     0j
                                ρ[ 1 u 0 (c2 ) + 2 u 0 (c2 )]ι1 + (1
                                   2
                                           1h    1       1l
                                                                          ρ ) u 0 ( c2 ) ι 0
                                                                                   0j
                            = ρ[ 2 u 0 (c2 ) + 2 u 0 (c2 )]r + (1
                                 1       1h    1       1l
                                                                        ρ ) u 0 ( c2 ) r

                                    1h
                                                   λ1l 0 1l                                0j
                u 0 ( c1 ) = ρ [ λ u 0 ( c2 ) +
                                 2λ
                                          1h
                                                   2λ
                                                      u (c2 )]ι1   + (1         ρ ) u 0 ( c2 ) ι 0

               FOCs imply ι0 = r
                   Indeterminate ι1 is extraneous
               Equilibrium allocation is optimal because no interbank lending
               needed (Diamond Dybvig)
Introduction        Model          Results        Central bank      Financial fragility           Conclusion




Results for ρ = 1 or "always a Crisis" case

               Expansion of FOCs:
                                                                                      0j
                                ρ[ 1 u 0 (c2 ) + 2 u 0 (c2 )]ι1 + (1
                                   2
                                           1h    1       1l
                                                                           ρ ) u 0 ( c2 ) ι 0
                                                                                    0j
                            = ρ[ 2 u 0 (c2 ) + 2 u 0 (c2 )]r + (1
                                 1       1h    1       1l
                                                                         ρ ) u 0 ( c2 ) r

                                    1h
                                                    λ1l 0 1l                                0j
                u 0 ( c1 ) = ρ [ λ u 0 ( c2 ) +
                                 2λ
                                          1h
                                                    2λ
                                                       u (c2 )]ι1   + (1         ρ ) u 0 ( c2 ) ι 0

                                             c2
               FOC implies ι1 = r >          c1

                   Indeterminate ι0 is extraneous


               Patient depositors face risk because interbank lending rate
                        c
               ι1 = r > c2 (Bhattacharya and Gale case)
                            1
Introduction        Model       Results     Central bank    Financial fragility   Conclusion




Results for ρ = 1


               Next, optimizing over α gives in equilibrium α > α

               Banks increase patient depositors’expected consumption to
               compensate them for their consumption risk

               There is too little liquidity held for impatient depositors

               There is less than optimal consumption sharing for depositors
               with liquidity shocks, and among depositors without liquidity
               shocks
Introduction        Model          Results       Central bank      Financial fragility           Conclusion




For 0 < ρ < 1: Multiple Rational Expectations Equilibria

           1   Two equations in three unknowns α, ι1 , ι0

               The FOCs can be rewritten as
                                                                                     0j
                                ρ[ 1 u 0 (c2 ) + 2 u 0 (c2 )]ι1 + (1
                                   2
                                           1h    1       1l
                                                                          ρ ) u 0 ( c2 ) ι 0
                                                                                   0j
                            = ρ[ 2 u 0 (c2 ) + 2 u 0 (c2 )]r + (1
                                 1       1h    1       1l
                                                                        ρ ) u 0 ( c2 ) r

                                    1h
                                                   λ1l 0 1l                                0j
                u 0 ( c1 ) = ρ [ λ u 0 ( c2 ) +
                                 2λ
                                          1h
                                                   2λ
                                                      u (c2 )]ι1   + (1         ρ ) u 0 ( c2 ) ι 0


               Many pairs of fι0 , ι1 g that satisfy the FOCs support an REE
               Result: There exist multiple REE
Introduction        Model       Results      Central bank    Financial fragility   Conclusion




Results for 0 < ρ < 1




               In this case, the allocation is a “weighted average” of the
               cases shown previously
               Most equilibria are suboptimal

               A …xed interest rate r = ι1 = ι0 is a suboptimal equilibrium
                   This also occurs if rates are not state-contingent
Introduction        Model        Results       Central bank             Financial fragility   Conclusion




Results for 0 < ρ < 1
               There exists a …rst best equilibrium with allocation α , c1 , c2 :

                    Interest rate must be low in a crisis for e¢ cient interbank
                    lending:
                                                   c
                                             ι1 = 2 < r ,
                                                   c1

                    Interest rates must equal r in expectation for banks to have
                    incentives to hold liquidity
                    The weighted-average interest rate equals r :
                                           X ι0 + (1       X ) ι1 = r
                    Combining the two we obtain:
                                                   ρ              c2
                                   ι0 = r +                   r              >r
                                               1       ρ          c1
                    In good times the rate must be high
Introduction        Model        Results     Central bank   Financial fragility   Conclusion




Where are we now?




               Introduction
               Model: idiosyncratic shocks
               Results
               Central bank role
               Financial fragility
               Conclusion
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




CB chooses ι1 and ι0 to select optimal REE



               The role of the CB is to choose the rate on the interbank
               market optimally by promising to borrow and lend at a given
               rate

               Optimal CB rate is state-contingent

               Looks like a corridor system with a corridor of zero width

               The CB selects the optimal REE among multiple REE
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




The market equilibrium equals the CB policy rate



               If market rate would be higher than CB rate, then all buyers
               prefer to trade with the CB

               If market rate would be lower than CB rate, then all sellers
               prefer to trade with the CB

               In either case, all trades end up taking place at the CB chosen
               rate but CB does not trade
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




Extension: Liquidation



               Suppose banks can liquidate the long-term technology and get
               s < 1 unit of good at date 1

               This puts a ceiling on the rate in the interbank market:
                    r
               ιi < s . Otherwise banks liquidate

               If s is high, it may not be possible to implement a high
               enough rate in good times to achieve the …rst best equilibrium
Introduction        Model      Results    Central bank   Financial fragility   Conclusion




Extensions and Robustnes




               Extension to aggregate shocks
               Extension to …at model
               Extension to the case of N states
               Elastic demand for funds in the interbank markets
Introduction        Model       Results      Central bank     Financial fragility   Conclusion




Idiosyncratic and aggregate shocks



               The CB has two instruments for two di¤erent kind of shocks

               CB must:

                   Lower rates if idiosyncratic shock occurs: uncertain liquidity
                   needs
                   Inject liquidity— stored goods— if aggregate shock occurs
                   (looks like …scal policy)
                   Do both when they occur simultaneously
Introduction        Model      Results       Central bank   Financial fragility   Conclusion




Where are we now?




               Introduction
               Model: idiosyncratic shocks
               Results
               Central bank role
               Financial fragility
               Conclusion
Introduction        Model      Results    Central bank   Financial fragility   Conclusion




CB policy and panics




               If the CB does not follow the optimal policy, then bank runs
               could occur

                                            1h
               A bank panic occurs if c1 > c2

               Patient depositors in banks that have many impatient
               depositors prefer to withdraw early
Introduction        Model      Results     Central bank   Financial fragility   Conclusion




If CB sets r = ι1 = ι0




                                           1h
               If ε and λ are large, c1 > c2 can occur

               Banks do not choose a “run-preventing” contract if ρ is
               su¢ ciently small

               Equilibrium allocation tends to e¢ cient allocation as ρ ! 0
Introduction        Model       Results       Central bank     Financial fragility   Conclusion




Conclusion



               Crises are periods during which banks are uncertain about
               their liquidity needs
               Central banks can help by setting interest rates appropriately

                   Low rates in crises help redistribution of liquidity

                   High rate otherwise provide incentives to hold optimal
                   investment portfolio (enough liquid assets)

				
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