✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 213 — #225 ✐ ✐ ✐ ✐ ✐ ✐ SYSTEMIC RISK, INTERBANK RELATIONS, AND LIQUIDITY PROVISION BY THE CENTRAL BANK213 Consider now the case of credit chains. Still assuming λ = 1, the balance sheet equations give D i = 1 2 [R i +D i+1 ], i = 1, 2, 3. (7.11) We can compute the losses experienced by each bank (with respect to the promised returns R) and it is a simple exercise to check that the only solution is D 1 = 3 7 R; D 3 = 5 7 R; D 2 = 6 7 R. (7.12) Therefore, bank 1 is able to pass on a higher share of its losses than in the diversified lending case, which explains the lower exposure of the interbank system to market discipline in the credit chain system. The results of this section highlight another side of interbank markets in addition to their role in redistributing liquidity efficiently, as studied by Bhattacharya and Gale (1987). Interbank connections enhance the “resiliency” of the system to withstand the insolvency of a particular bank. However, this network of cross-liabilities may loosen market dis- cipline and allow an insolvent bank to continue operating through the implicit subsidy generated by the interbank credit lines. This loosening of market discipline is the rationale for a more active role for monitoring and supervision with the regulatory agency having the right to close down a bank in spite of the absence of any liquidity crisis at that bank. The effect of a central bank’s guarantee on interbank credit lines would be that x = (1, ,1) is always an equilibrium, even if one bank is insolvent. The stability of the banking system would be preserved at the cost of forbearance of inefficient banks. 7.4 Closure-Triggered Contagion Risk 7.4.1 Efficiency versus Contagion Risk We now turn to the other side of the relationship between efficiency and stability of the banking system, and investigate under which conditions the closure at time t = 1 of an insolvent bank does not trigger the liquidation of solvent banks in a contagion fashion. Suppose indeed that bank k is closed at t = 1. Assumption 7.2 implies that X k = 0 and D k = 0. Closing bank k at t = 1 has two consequences. First, we have an unwinding of the positions of bank k since π ki D k assets and π ki D i liabilities disappear from the balance sheet of bank k. In a richer setting this is equivalent to a situation in which the other banks have reneged on their credit lines toward bank k, possibly as a result of the arrival of negative signals on its return. Second, a proportion π ik of travelers going to location k will be forced to withdraw early the amount π ik D 0 and bank ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 214 — #226 ✐ ✐ ✐ ✐ ✐ ✐ 214 CHAPTER 7 i will have to liquidate the amount π ik D 0 /α.Ifπ ik D 0 /α is sufficiently large, bank i is closed at t = 1; otherwise the cost at t = 2 of the early liquidation is π ik ((D 0 /α)R −D i ). Notice that if π ik D 0 /α  1, then X i = 0, i.e., bank i is liquidated simply because there are too many depositors going from location i to location k, the bank is closed at t = 1. The type of contagion that takes place here is of a purely mechanical nature stemming simply from the direct effect of inefficient liquidation. Since this case is straightforward let us instead concentrate on the other case, namely π ik D 0 /α < 1. Because of unwinding and forced early withdrawal, the full general case is more complex. Since x k = 0, we have to suppress all that concerns bank k from the equations (7.5). We obtain X i(k) R i +  j≠k π ji D j x i =   j≠k π ij x j +  j≠k π ji x i  D i , (7.13) where X i(k) = max  1 − π ik D 0 α −  j≠k π ji (1 − x j ) D 0 α , 0  . (7.14) We now have to check whether x ij ≡ 1 for all i, j ≠ k can correspond to an equilibrium. In this case, X i(k) = max[1 − π ik D 0 /α, 0] and system (7.13) becomes R i =   j≠k π ij +π ji X i(k)  D i −  j≠k π ji X i(k) D j . (7.15) Since by assumption R i ≡ R for all i ≠ k, (7.15) becomes  1 − π ik D 0 α  R +  j≠k π ji D j = (2 −π ik −π ki )D i . (7.16) This allows us to establish a result analogous to proposition 7.2. Proposition 7.5 (contagion risk). There is a critical value of the smallest time t = 2 deposits below which the closure of a bank causes the liquidation of at least another bank. This critical value is lower in the credit chain case than in the diversified lending case. The diversified lending structure is always stable when the number N of banks is large enough, whereas N has no impact on the stability of the credit chain structure. Proof. This follows the same structure as the proof of proposition 7.2. Denoting by M k the inverse of the matrix defined by system (7.16), ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 215 — #227 ✐ ✐ ✐ ✐ ✐ ✐ SYSTEMIC RISK, INTERBANK RELATIONS, AND LIQUIDITY PROVISION BY THE CENTRAL BANK215 stability is equivalent to ⎛ ⎜ ⎝ D 1 . . . D N ⎞ ⎟ ⎠ = RM k ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ >D 0 ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ (7.17) One can see that all the elements of M k are nonnegative 19 , thus stability obtains if and only if D 0 /R  ψ k , where ψ k denotes the minimum of the components M k ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ . The computation of ψ k is cumbersome in the general case but easy in our benchmark examples (where, because of symmetry, k does not play any role). One finds Ψ cre = 1 −λ  D 0 α −1  and Ψ div = 1 −λ  D 0 /α − 1 N − 1 −λ  (7.18) in the credit chain example and in the diversified lending case, respec- tively. It is immediate from these formulas that Ψ cre <Ψ div (for N  2) and that Ψ div tends to 1 when N tends to infinity while Ψ cre is independent of N. 7.4.2 Comparison with Allen and Gale (2000) It is useful to compare our results with those of Allen and Gale (2000). Proposition 7.2 establishes that systemic crises may arise for funda- mental reasons, as in Allen and Gale. However, the focus of the two papers is different. Allen and Gale are concerned with the stability of the system with respect to liquidity shocks arising from the random number of consumers that need liquidity early in the absence of aggregate uncertainty. They show that the system is less stable when the interbank market is incomplete (in the sense that banks are allowed to cross-hold deposits only in a credit chain fashion) than when the interbank market is complete (in the sense that banks are allowed to cross-hold deposits in a diversified lending fashion). In our paper interbank links instead arise from consumers’ geographic uncertainty and we focus on the implications of the insolvency of one bank in terms of market discipline and the stability of the system. In par- ticular in proposition 7.4 we show how the structure of interbank links 19 The fact that the matrix M k has nonnegative elements follows from a property of diagonal dominant matrices (see, for example, Takayama 1985, p. 385). ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 216 — #228 ✐ ✐ ✐ ✐ ✐ ✐ 216 CHAPTER 7 allows the losses of one bank to be spread over other banks. We show that a diversified lending system is more exposed to market discipline (i.e., less resilient) than a credit chain system because in the latter the insolvent bank is able to transfer a larger fraction of its losses to other banks, thus reducing the incentives for its own depositors to withdraw. In proposition 7.5 we are concerned with the stability of the system with respect to contagion risk triggered by the efficient liquidation at time t = 1 of the insolvent bank. 7.5 Too-Big-to-Fail and Money Center Banks Regulators have often adopted a too-big-to-fail (TBTF) approach in deal- ing with financially distressed money center banks and large financial institutions. 20 One of the reasons is the fear of the repercussions that the liquidation of a money center bank might have on the corresponding banks that channel payments through it. Our general formulation of the payments needs, where the flow of depositors going to the various locations is asymmetric, offers a simple way to model this case and to capture some of the features of the TBTF policy. We interpret the TBTF policy as designed to rescue banks which occupy key positions in the interbank network, rather than banks simply with large size. 21 Consider, for example, the case where there are three locations (N = 3). Locations 2 and 3 are peripheral locations and location 1 is a money center location. All the travelers of locations 2 and 3 must consume at location 1, and one-half of the travelers of location 1 consume at location 2 and the other half at location 3. That is, t 12 = t 13 = 1 2 and t 21 = t 31 = 1, t 23 = t 32 = 0. 22 This implies that X 1 = max  1 − D 0 α  1 − (1 −λ)x 1 −λ  x 2 +x 3 2  ;0  (7.19) and X 2 = max  1 − D 0 α [1 − (1 −λ)x 2 −λx 1 ];0  , X 3 = max  1 − D 0 α [1 − (1 −λ)x 3 −λx 1 ];0  . ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ (7.20) Suppose now that one of these banks (and only one) is insolvent (this is known at t = 1). The next proposition illustrates how the closure of a 20 See, for example, the intervention of the monetary authorities in the Continental Illinois debacle in 1984 and, to some extent, in arranging the private-sector rescue of Long Term Capital Management. 21 The failure of Barings in 1996 is an example of the crisis of a large financial institution that did not create systemic risk. 22 Note that we now abandon assumption 7.3 (the symmetry assumption). ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 217 — #229 ✐ ✐ ✐ ✐ ✐ ✐ SYSTEMIC RISK, INTERBANK RELATIONS, AND LIQUIDITY PROVISION BY THE CENTRAL BANK217 bank with a key position in the interbank market may trigger a systemic crisis. Proposition 7.6. (i) If λ>µ= α(1/D 0 − 1/R), the liquidation of bank 1 triggers the liquidation of all other banks (too-big-to-fail). (ii) If λ>2α/D 0 , liquidation of banks 2 or 3 does not trigger the liquidation of either of the other two banks. Proof. To prove (i) notice that if bank 1 is closed then X 1 = 0 and x 1 = 0. Then D 2 = X 2 R = (1 − (D 0 /α)λ)R. Thus x 2 = 0if(1 − (D 0 /α)λ)R < D 0  λ>α(1/D 0 − 1/R). To prove (ii) notice that if bank 2 is closed then x 2 = 0. If (1, 0, 1) is an equilibrium, when D 0 λ/α < 2 the balance sheet equations become D 1  1 − λ 2 D 0 α +λ  =  1 − D 0 α λ 2  R 1 +λD 3 , D 3  1 + λ 2  = R 3 + λ 2 D 1 . ⎫ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎭ (7.21) If R 3 = R 1 = R, this yields D 3 = D 1 = R. This implies that x = (1, 0, 1) is an equilibrium whenever D 0 λ/α < 2. Our last result concerns the optimal attitude of the central bank when the money center bank becomes insolvent (R 1 = 0). When D 0 /R is low, no intervention is needed. When D 0 /R is large, the central bank has to inject liquidity. More precisely, we have the following proposition. Proposition 7.7. When R 1 = 0, x = (1, 1, 1) is an equilibrium if D 0 /R is sufficiently low (no central bank intervention is needed). In the other case, the cost of bailout increases with D 0 /R. Proof. When R 1 = 0, x = (1, 1, 1) can be an equilibrium if D >D 0 ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ . When x = (1, 1, 1), the balance sheet equations (7.5) become R 1 +(D 2 +D 3 ) = 3D 1 , (7.22) R 2 + 1 2 D 1 = 3 2 D 2 ,R 3 + 1 2 = 3 2 D 3 . (7.23) ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 218 — #230 ✐ ✐ ✐ ✐ ✐ ✐ 218 CHAPTER 7 Table 7.1. Summary of central bank interventions. Type of central Problem bank intervention Costs Results Speculative Coordinating role of Never used in Proposition 7.1 gridlock central bank equilibrium; no • guarantee credit lines cost apart from • deposit insurance moral hazard Insolvency in Ex ante monitoring Imperfect monitoring Proposition 7.2 a resilient and supervision leads to forbearance interbank and moral hazard market Insolvency Orderly closure of No cost, apart from Proposition 7.5; leading to insolvent bank moral hazard and Proposition 7.6 contagion and arrangement money center banks; of credit lines in the case of money to bypass it center banks it may be too costly or even impossible to organize orderly closure Bailout Transfer of Proposition 7.7 taxpayer money Solving (7.22) and (7.20) when R 1 = 0, R 2 = R 3 = R yields D 1 = 4 7 R, D 2 = D 3 = 6 7 R, which is an equilibrium if and only if D 0 /R < 4 7 . The cost of bailout is 0 if and only if D 0 /R < 4 7 ,itisD 0 − 4 7 R if and only if 4 7 <D 0 /R < 6 7 . When D 0 /R > 6 7 , the central bank also has to inject liquidity in the solvent banks. The total cost to the central bank becomes 3D 0 − 16 7 R. 7.6 Discussions and Conclusions We have constructed a model of the banking system where liquidity needs arise from consumers’ uncertainty about where they need to consume. Our basic insight is that the interbank market allows the minimization of the amount of resources held in low-return liquid assets. However, interbank links expose the system to the possibility that a num- ber of inefficient outcomes arise: the excessive liquidation of productive investment as a result of coordination failures among depositors; the reduced incentive to liquidate insolvent banks because of the implicit subsidies offered by the payments networks; the inefficient liquidation of solvent banks because of the contagion effect stemming from one insolvent bank. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 219 — #231 ✐ ✐ ✐ ✐ ✐ ✐ SYSTEMIC RISK, INTERBANK RELATIONS, AND LIQUIDITY PROVISION BY THE CENTRAL BANK219 7.6.1 Policy Implications We use this rich setup to derive a set of policy implications (summarized in table 7.1) with respect to the interventions of the central bank. First, the interbank market may not yield the efficient allocation of resources because of possible coordination failures that may generate a “gridlock” equilibrium. The central bank thus has a natural coordination role to play which consists of implicitly guaranteeing the access to liquidity of individual banks. If the banking system as a whole is solvent, the costs of this intervention is negligible and its distortionary effects may stem only from moral hazard issues (proposition 7.1). Second, if one bank is insolvent, the central bank faces a much more complex trade-off between efficiency and stability. Market forces will not necessarily force the closure of insolvent banks. Indeed, the resiliency of the interbank market allows it to cope with liquidity shocks by providing implicit insurance, which weakens market discipline (proposition 7.2). The central bank therefore has the responsibility to provide ex ante monitoring of individual banks. However, it is the responsibility of the central bank to handle systemic repercussions that may be caused by the closure of insolvent banks (proposition 7.5). In this case two courses of action are available: orderly closure or bailout of insolvent banks. Given the interbank links, the closure of an insolvent bank must be accompa- nied by the provision of central bank liquidity to the counterparts of the closed bank. 23 This is what we call orderly closure. Assuming that this is possible, theoretically it entails no costs apart from moral hazard. However, the orderly closure might simply not be feasible for money center banks (proposition 7.6) in which case the central bank has no choice but to bail out the insolvent institution, with the obvious moral hazard implications of the TBTF policy. Our model can be extended in various directions, some of which are discussed below. 7.6.2 Imperfect Information on Banks’ Returns In reality, both the central bank and the depositors have only imperfect signals on the solvency of commercial banks (although the central bank’s signals are hopefully more precise). Therefore, the central bank will have to act knowing that with some probability it will be lending to (guarantee- ing the credit lines of) insolvent institutions and with some probability it will be denying credit to solvent institutions. Also, depositors may run on all the banks which have generated a bad signal. 23 For instance, in the credit chain case, if bank k is closed the central bank can borrow from bank k − 1 and lend to bank k + 1, thus allowing the interbank arrangements to function smoothly. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 220 — #232 ✐ ✐ ✐ ✐ ✐ ✐ 220 CHAPTER 7 The consequences are different depending on the structure of the interbank market. In the credit chain case, the central bank will have to intervene to provide credit with a higher probability than in the diversified lending case. Therefore in the credit chain case the central bank has a higher probability of ending up financing insolvent banks. Ex ante, therefore, the central bank intervention is much more expensive in the credit chain case, so that in this case a fully collateralized payments system may be preferred. 7.6.3 Payments among Different Countries Systemic risk is often related to the spreading of a financial crisis from one country to another. Our basic model can be extended to consider various countries instead of locations within the same country. When depositors belong to different countries, travel patterns that generate a consumption need in another location have the natural interpretation of demand of goods of other countries, i.e., import demand. Goods of the other country can be purchased through currency (like in autarky in the basic model) or through a credit line system whereby the imports of a country are financed by its exports. Our results extend to the model with different countries but the role of the monetary authority is somewhat different. While in our setup the lending ability of the domestic monetary authority was backed by its taxation power, the lending ability of an international financial organization is ultimately backed by its capital. Hence the resources at its disposal are limited and in the case of aggregate uncertainty its ability to guarantee banks’ credit lines is limited. 24 7.7 Appendix: Proof of Proposition 7.1 Notation Define M(λ) ≡ [2I −Π  ] −1 = [(1 +λ)I − λT  ] −1 = 1 1 + λ  I − λ 1 + λ T   −1 , (7.24) where I is the identity matrix. We first need a technical lemma. Lemma 7.1. All the elements of M(λ) are nonnegative: m ij (λ)  0 for all i, j. Moreover, for all i,  j m ij (λ) = 1. As a consequence, if R i >D 0 24 See the role of the IMF in the 1997 Asian crises and the 1998 Russian crisis. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 221 — #233 ✐ ✐ ✐ ✐ ✐ ✐ SYSTEMIC RISK, INTERBANK RELATIONS, AND LIQUIDITY PROVISION BY THE CENTRAL BANK221 for all i, then M(λ)R >D 0 ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ . (7.25) Proof. M(λ) = (2I − Π  ) −1 . Since Π  is a Markov matrix (because of assumption 7.3), all its eigenvalues are in the unit disk and M(λ) can be developed into a power series: M(λ) = 1 2 (I − 1 2 Π  ) −1 = +∞  k=0 Π k 2 k+1 . (7.26) This implies that M(λ) has positive elements. Moreover, ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ being an eigenvector of Π  (for the eigenvalue 1), it is also an eigenvector for M(λ). Proof of proposition 7.1. (i) Because of assumption 7.2, D i = 0 when x ij = 0 for all j. Therefore, x ∗ ij ≡ 0 is always an equilibrium. (ii) x j = 1 ⇒ X j = 1. Using the assumption that  j π ji = 1 equation (7.5) becomes 2D = R + Π  D. (7.27) For x j = 1 to be an equilibrium for all j, it must be D = [2I − Π  ] −1 R = M(λ)R  D 0 ⎛ ⎜ ⎝ 1 . . . 1 ⎞ ⎟ ⎠ . (7.28) This is an immediate consequence of the above lemma, which implies that x = (1, ,1) is always an equilibrium when all banks are solvent. There are no other equilibria when α = D 0 . Indeed, if x i = 0, then equation (7.5) implies that X i = 0orD i = R i . But X i cannot be zero (unless all x j are also zero) and D i = R i >D 0 contradicts the equilibrium condition. Notice, however, that when α<D 0 , X i can be zero even if some of the x j are positive, which implies that other equilibria may exist. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 222 — #234 ✐ ✐ ✐ ✐ ✐ ✐ 222 CHAPTER 7 Before establishing proposition 7.3, we have to compute the expres- sion of matrix M(λ) in the two cases of credit chain and diversified lending. Consider the credit chain case first, where the matrix T is given by T = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 01 0··· 0 ··· ··· 0 ··· 01 10··· 00 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . (7.29) Therefore T N = I, so that T k = T k+N = T k+2N ···. Now M(λ) =  1 1 + λ  ∞  k=0 (θT  ) k , (7.30) where λ/(1 + λ) ≡ θ. Let Θ ≡{1 + θ +θ N +θ 2N ···}. Thus M(λ) ≡ Θ 1 + λ [I + θT  +(θT  ) 2 +···+(θT  ) N−1 ] = 1 − θ 1 − θ N A, (7.31) where A ≡ [I + θT  +···+(θT  ) N−1 ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1 θ N−1 ··· ··· θ 2 θ θ 1 θ N−1 ··· ··· θ 2 ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· 1 θ N−1 θ N−1 ··· ··· θ 2 θ 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . (7.32) Consider now the diversified lending case, where the matrix T is given by T = 1 N − 1 ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 01··· ··· 1 101··· 1 ··· ··· ··· ··· ··· 1 ··· 101 1 ··· ··· 10 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ . (7.33) It follows that T = T  . Now M(λ) = 1 1 + λ  I − λ 1 + λ T   −1 = (1 −θ) ∞  k=0 (θT  ) k . [...]... notably Koehn and Santomero (1 980 ) and Kim and Santomero (1 988 ) It is adapted from the portfolio model of Pyle (1971) and Hart and Jaffee (1974) Banks are supposed to behave as competitive portfolio managers, in the sense that first they take prices (and yields) as given, and second that they choose the composition of their balance sheets (including liabilities) so as to maximize the expectation of some (ad... remarks, and mathematical proofs are gathered in two appendixes 8. 2 The Model It is a static model with only two dates: t = 0, where the bank chooses the composition of its portfolio; and t = 1, where all assets and liabilities are liquidated There are only two liabilities: equity capital K0 and deposits D In most of the paper, K0 is exogenously fixed but D is chosen by the bank, taking into account the. .. CHAPTER 8 The paper is organized as follows The model is presented in section 8. 2 Section 8. 3 is dedicated to the behavior of banks in the complete markets setup The portfolio model is introduced in section 8. 4, and the behavior of banks without capital requirements is examined in section 8. 5 Capital requirements are introduced in section 8. 6, and limited liability in section 8. 7 Section 8. 8 contains some... regulation (the so- called Cooke ratio) adopted earlier (December 1 987 ) by the Bank of International Settlements I try to examine here what economic theory can tell us about such regulations, and more specifically: • Why do they exist in the first place? • Are they indeed a good way to limit the risk of failure of commercial banks? • What consequences can be expected on the behavior of these banks? In fact, the. .. Modigliani–Miller indeterminacy principle: the market value of the bank is completely independent of any of its actions If we introduce a reorganization cost g supported by the bank in the case of failure, as in Kareken and Wallace (19 78) , then (8. 7) becomes V = K0 p(ω) g, ω∈ΩF where ΩF denotes the set of states of nature in which the bank fails V is then maximum for any choice of x and D that prevents this failure,... 1977; Koehn and Santomero 1 980 ; Kim and Santomero 1 988 ), who made the same assumption as Hart and Jaffee (1974) There is an exogenous price for equity capital, and the bank chooses ∆K in a competitive fashion Since we are concerned with failure possibilities, it does not seem reasonable to assume that the price of capital is independent of the investment policy of the bank However, again because of our incomplete... sets of assumptions In the first setup, financial markets are supposed to be complete and depositors are perfectly informed about the failure risks of banks Then the Modigliani–Miller indeterminacy principle applies and the market values of banks are independent of the structure of their assets portfolio, as well as their capital to assets ratio However, when a bankruptcy cost is introduced, as in Kareken... depend on the bank s investment policy • Secondly, banks behave as if they were fully liable! In other words, although the regulation under study is precisely motivated by the default risk of commercial banks, this is not taken into account by the banks themselves Thus I do essentially two things in this paper: • I reexamine the conclusions of Koehn and Santomero (1 980 ) and Kim and Santomero (1 988 ) in... in the Global Economy: Risks and Opportunities, Proceedings of the 34th Annual Conference on Bank Structure and Competition Federal Reserve Bank of Chicago Freeman, S 1996a Clearinghouse banks and banknote over-issue Journal of Monetary Economics 38: 101–15 Freeman, S 1996b The payment system, liquidity, and rediscounting American Economic Review 86 :1126– 38 Freixas, X., and B Parigi 19 98 Contagion and. .. banking arrangements American Economic Review 81 :497–513 Calomiris, C W., and J R Mason 1997 Contagion and bank failures during the Great Depression: the June 1932 Chicago banking panic American Economic Review 87 :86 3 83 De Bandt, O., and P Hartmann 2002 Systemic risk: a survey In Financial Crises, Contagion, and the Lender of Last Resort A Reader (ed C Goodhart and G Illing) Oxford University Press i i . now turn to the other side of the relationship between efficiency and stability of the banking system, and investigate under which conditions the closure at time t = 1 of an insolvent bank does not. paper interbank links instead arise from consumers’ geographic uncertainty and we focus on the implications of the insolvency of one bank in terms of market discipline and the stability of the system by the closure of insolvent banks (proposition 7.5). In this case two courses of action are available: orderly closure or bailout of insolvent banks. Given the interbank links, the closure of