✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 117 — #129 ✐ ✐ ✐ ✐ ✐ ✐ MACROECONOMIC SHOCKS AND BANKING SUPERVISION 117 Therefore, W =  +∞ 0 {(1 −q)qR +qx(ρ)(pR −ρ) −1}L(ρ) dF +V( ¯ L), (4.5) where ¯ L =  +∞ 0 L(ρ){1 −q + qx(ρ)}dF. (4.6) The optimal regulatory contract is obtained by choosing x(·) and L(·) that maximize W under the budget constraint (4.4) of each bank. Proposition 4.2. In the presence of macroeconomic shocks, the optimal regulatory contract is characterized by a separation of banks into two categories: • The banks such that ρ  ρ ∗ = 1/(1 − q) (small exposure to macroshocks) are rescued in the case of a crisis, but they are subject to a higher capital ratio (than in the absence of macroshocks). This capital ratio increases with their exposure ρ to macroshocks: k 1 (ρ) = E L(ρ) = 1 − p  R − B ∆p  +qρ. (4.7) • The banks such that ρ>ρ ∗ (large exposure to macroshocks) are closed in the case of a crisis and are subject to a flat capital ratio: k 0 = E L 0 = 1 − (1 − q)p  R − B ∆p  . (4.8) Proof of proposition 4.2. Given that there is a separate budget constraint for each ρ (condition (4.4)), we can solve for L(ρ) and maximize with respect to x the following quantity: U(x,ρ) = (1 −q + qx)(pR + V  ( ¯ L)) −qxρ − 1 1 −(1 −q + qx)p(R − B/∆p) +qxρ (E has been omitted because it only appears multiplicatively and there- fore does not influence the optimal value of x(ρ)). The expression of U can be simplified as follows: U(x,p) =−1 + (1 −q + qx)(V  ( ¯ L) +pB/∆p) 1 +qxρ − (1 − q +qx)p(R − B/∆p) , =−1 + V  ( ¯ L) +pB/∆p (1 +qxρ)/(1 −q + qx) −p(R − B/∆p) . ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 118 — #130 ✐ ✐ ✐ ✐ ✐ ✐ 118 CHAPTER 4 For a given ρ, this expression is monotonic in x: increasing if ρ<1/(1 − q), decreasing if ρ>1/(1 − q). Thus the optimal regulatory contract involves x(ρ) = ⎧ ⎪ ⎨ ⎪ ⎩ 1ifρ  1 1 −q ≡ ρ ∗ , 0ifρ>ρ ∗ . The corresponding capital ratios are deduced from constraint (4.4): k(ρ) ≡ E L(ρ) = 1 −{1 −q + qx(ρ)}p  R − B ∆p  +qρx(ρ), by replacing x(ρ) by its optimal value found above. Proposition 4.2 adopts a normative viewpoint, i.e., it characterizes the optimal closure rule for banks in the presence of macroeconomic shocks. We now adopt a positive viewpoint and compare the optimal closure rule with the effective closure rules implied by two institutional arrangements: pure private contracting between the banks and the DIF on the one hand, and pure public supervision on the other hand. Proposition 4.3. A purely private organization of the banking sector leads to too many closures in the event of a recession: indeed, a bank is closed whenever ρ  ρ 0 = p  R − B ∆p  <ρ ∗ . Proof. In the absence of a public intervention, the only way in which a bank can obtain liquidity at the interim date t = 1 2 is by borrowing from other banks (or issuing new CDs). The maximum amount of cash that can be raised in the way is equal to the collateral value of the bank’s assets, i.e., the maximal expected payment that can be obtained from bankers while preserving incentive compatibility: ρ 0 ≡ p  R − B ∆p  L. Assumption 4.2 states that ρ 0 < 1, which implies that ρ 0 <ρ ∗ = 1/(1 − q). Therefore, all the banks with an intermediate exposure to macroshocks (ρ ∈ ]ρ 0 ,ρ ∗ [) should be allowed to continue, but would be closed in the absence of a public intervention. Proposition 4.3 shows the need for the CB acting as an LLR: by provid- ing liquidity assistance to the banks characterized by ρ ∈ ]ρ 0 ,ρ ∗ [, the CB improves upon the purely private organization discussed in propo- sition 4.3. However, there is also a problem with public intervention. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 119 — #131 ✐ ✐ ✐ ✐ ✐ ✐ MACROECONOMIC SHOCKS AND BANKING SUPERVISION 119 Indeed, once a bank has granted a certain volume of loans, its social continuation value is positive as long as ρ<pR+V  ( ¯ L) ≡ ρ 1 , which is larger than ρ ∗ = 1/(1 − q) by assumption 4.3. If the bank authorities are subject to political pressure, it will be impossible for them to limit liquidity assistance to the banks such that ρ  ρ ∗ , since it is ex post optimal to also let all the banks such that ρ ∈ ]ρ ∗ ,ρ 1 [ continue. This not only implies too few closures (regulatory forbearance) but also overinvestment at t = 0, since bankers anticipate this forbearance. This is explained in the next proposition. Proposition 4.4. Prudential regulation by a public authority leads to forbearance: all banks such that ρ  ρ 1 receive liquidity support during a recession. In this case, the only thing regulatory authorities can do is to impose on these banks a flat capital ratio: 15 k 0 = 1 − (1 − q)p  R − B ∆p  . Comparing with the optimal contract characterized in proposition 4.2, we see that this leads to overinvestment by these banks, who thus exploit this anticipated regulatory forbearance. Proof of proposition 4.4. We have already seen that it is ex post optimal for the government to provide liquidity assistance to all banks such that ρ  ρ 1 = pR + V  ( ¯ L) (positive social continuation value). When ρ<ρ 0 (solvent banks) this liquidity support is fully collateralized and the central bank does not lose any money. However, when ρ ∈ ]ρ 0 ,ρ 1 ], the central bank loses (ρ −ρ 0 )L in expectation, but seizes maximum income (R −B/∆p)L = D in the case of success. From the DIF point of view the cost of deposit insurance becomes [(1 −q)(1 −p) +q]D. The associated capital ratio is k 0 = E L = 1 + P −D L = 1 − (1 − q)p  R − B ∆p  . It is smaller than the efficient capital ratio characterized in proposi- tion 4.2: k 0 <k 1 (ρ) = 1 −p  R − B ∆p  +qρ. This is because ρ>ρ 0 = p(R − B/∆p). Thus there is overinvestment. Finally, notice that, from an ex ante view point, the marginal social value 15 Banks such that ρ  ρ 0 are subject to the same capital ratio as in proposition 4.2. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 120 — #132 ✐ ✐ ✐ ✐ ✐ ✐ 120 CHAPTER 4 Need for a lender of last resort Exposure to macroshocks ρ Regulatory forbearance Banks that are closed if a macroshock occurs ρ Solvent banks 0 ρ * ρ 1 Figure 4.3. The fundamental problem faced by prudential supervision. of loans made by a bank such that ρ ∈ ]ρ 0 ,ρ 1 ] is equal to (ρ 1 − ρ), which is nonnegative. This means that it would be inefficient ex ante to restrict further the volume of credit granted by such banks. Thus the government cannot compensate for its lack of commitment power by an increase of capital ratios. We see this as the fundamental problem faced by prudential supervi- sion: public intervention is needed 16 in order to avoid too many bank closures, but since governments are subject to commitment problems, public supervision alone leads to too few bank closures and overinvest- ment. By analogy with Dewatripont and Maskin (1995), we call this a soft budget constraint (SBC) phenomenon. 17 This problem is summarized by figure 4.3. We discuss in section 4.6 a possible organization of banking super- vision that could solve this problem. For the moment, we see how introducing market discipline by private investors modifies the picture. 4.5 Is Market Discipline Useful? Proponents of market discipline for banks have argued that private investors might have to play a part complementary to public supervisors in the monitoring of commercial banks. In order to discuss the potential monitoring role of private investors, we now introduce an external monitor, who can reduce the unit private benefit of commercial bankers from B to b<Bby exerting a monitoring activity of unit cost γ. The regulation contract has to stipulate the amount D M that the external monitor is required to invest at t = 0 (interpreted as subordinated debt) and the repayment R M L, he receives in the case of success. 16 Holmström and Tirole (1998) show that, when ρ corresponds to a diversifiable shock, private arrangements between firms and banks (namely private lines of credit) can be enough to implement the (second best) optimum. However, when there are macroshocks, public provision of liquidity is needed. 17 Notice, however, that the mechanism that underlies the SBC in Dewatripont and Maskin (1995) is different. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 121 — #133 ✐ ✐ ✐ ✐ ✐ ✐ MACROECONOMIC SHOCKS AND BANKING SUPERVISION 121 The optimal regulation contract for a bank with a macro-exposure ρ is thus obtained by maximizing W(ρ)= L{(1 − q)ρ + qx(ρ 1 −ρ) −1 −γ}. (4.9) The policy variables are D  0, L  0, D M  0, R M  0, and x ∈ [0, 1]. They have to satisfy the following constraints: L[1 +qxρ] −E − D M  (1 − q + qx)pD, (4.10) {(1 −q + qx)pR M −γ}L  D M , (4.11) R M  γ ∆p , (4.12) (R −R M )L −D  bL ∆p , (4.13) where as before ρ 1 = pR + V  ( ¯ L). The objective function of this program is the net social surplus W(ρ) produced by the bank, modified to take into account the cost of monitor- ing γL. Condition (4.10) is the breakeven constraint for the DIF, modified to take into account the amount D M brought by market investors. Con- dition (4.11) is the participation constraint of these market investors. Conditions (4.12) and (4.13) are respectively the incentive compatibility constraint of market investors and that of the banker. Again all the constraints bind at the optimum. Thus, R M = γ ∆p ,D=  R − γ +b ∆p  L, D M =  (1 −q + qx)p γ ∆p −γ  L. Plugging this into the budget constraint (4.10), we see that the problem reduces to ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ max L{(1 −q)ρ 1 +qx(ρ 1 −ρ) −1 −γ}, under the constraint L  1 −(1 −q + qx)p  R − b ∆p  +qρx + γ   E. The solution of this program is given in the next proposition. Proposition 4.5. The presence of external monitors increases the opti- mal closure threshold: ρ ∗ (γ) = 1 +γ 1 −q >ρ ∗ . In the absence of commitment power by the government, the effective closure threshold remains unchanged at ρ 1 . Capital requirements are then reduced, due to the decrease in bank moral hazard, but the impact on social surplus is ambiguous. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 122 — #134 ✐ ✐ ✐ ✐ ✐ ✐ 122 CHAPTER 4 Need for a lender of last resort Exposure to macroshocks ρ Regulatory forbearance Banks that are closed if a macroshock occurs ρ Solvent banks 0 ρ * ρ 1 ρ * γ ( ) Figure 4.4. The impact of market discipline (ρ ∗ is increased to ρ ∗ (γ) but ρ 1 is unchanged). Proof of proposition 4.5. Using the same reasoning as in the proof of proposition 4.2, the optimal x(ρ) can be obtained by maximizing the expression, U 1 (x, ρ) = (1 −q)ρ 1 +qx(ρ 1 −ρ) −1 −γ 1 −(1 −q + qx)p(R − B/∆p) +qxρ − γ , which can be simplified into U 1 (x, ρ) =−1 + V  ( ¯ L) +pb/∆p (1 +qxρ + γ)/(1 − q +qx − p)(R − B/∆p) . For a given ρ, this expression is monotonic in x: increasing if ρ< 1 +γ/(1 −q), decreasing if ρ>1 +γ/(1 −q). Thus the optimal closure threshold is ρ ∗ (γ) = 1 +γ/(1 − q). However, if the government cannot commit, the effective closure threshold is still ρ 1 = pR + V  ( ¯ L). The capital requirement becomes k  0 = 1 − (1 − q)p  R − b ∆p  <k 0 . It is thus reduced by market discipline. However, since market discipline is costly, the overall impact on social welfare is ambiguous. The impact of market discipline is summarized in figure 4.4. Therefore, if we compare it to the optimal contract with commit- ment, the use of an external monitor is not necessarily beneficial. More importantly, market discipline does not completely solve the commit- ment problem, except if the external monitor cannot exert pressure on politicians. Suppose indeed that the market debt D M is held by foreign investors, as suggested in Calomiris (1999), and suppose that these foreign investors cannot lobby 18 the national regulator. In this case, the commitment problem of the latter will be reduced, since the ex post 18 This is probably questionable, given the internationalization of capital markets and the huge size of the major investors, who are typically multinational firms. ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 123 — #135 ✐ ✐ ✐ ✐ ✐ ✐ MACROECONOMIC SHOCKS AND BANKING SUPERVISION 123 socially optimal continuation threshold will be reduced to ρ  1 = ρ 1 −pR F , where R F is the promised repayment to foreign investors in the case of success. An adequate choice of R F will give ρ  1 = ρ ∗ (γ). Therefore, the main interest of using foreign investors as external monitors of national banks is to solve the commitment problem of the regulator. By pledging future income to outsiders (who cannot lobby political authorities), the regulator becomes tougher. However, the expected surplus is not necessarily increased, especially if foreign investors are characterized by high monitoring costs γ and low monitoring effectiveness B − b. An alternative solution to the commitment problem exists, which does not have all these drawbacks: requiring independency and accountability of banking supervisors, as has been done for monetary policy. We now conclude by examining how this reform could be organized, taking into account the need for an LLR. 4.6 Policy Recommendations for Macroprudential Regulation We conclude this paper by offering some reflections on the ways in which the optimal contract characterized in section 4.4 can be implemented by an adequate design of the supervisory–regulatory system. As we saw in section 4.4, two crucial elements are needed: • Intervention of the CB as an LLR for providing liquidity assistance, in the case of a recession, to the banks characterized by ρ  ρ ∗ . • Preventing extension of this liquidity assistance to the banks char- acterized by ρ ∗ <ρ ρ 1 , for which ex post continuation value is positive (from a social point of view) but bailing them out would be welfare decreasing from an ex ante perspective. We claim that these two elements can only be reconciled if the CB is made independent from political authorities, as has been done for monetary policy. To ensure accountability of the CB in its role as an LLR, a precise agenda has to be defined ex ante, namely providing liquidity assistance to a subset of banks (those for which ρ  ρ ∗ ) that would be backed by the supervisors (or the DIF). To ensure that the DIF selects properly the banks that can be assisted, we require that the liquidity loans granted by the CB (acting as an LLR) would be backed by the DIF. In other words, those loans would be insured by the DIF: the CB would be completely protected against credit risk and no taxpayer money would be involved. The next proposition summarizes the proposed organiza- tion of the regulatory system. Proposition 4.6. The optimal contract (characterized in proposition 4.2) can be implemented by the following organization of the regulatory system: ✐ ✐ “rochet” — 2007/9/19 — 16:10 — page 124 — #136 ✐ ✐ ✐ ✐ ✐ ✐ 124 CHAPTER 4 • For each commercial bank, the supervisory authorities evaluate ρ, the bank’s exposure to macroeconomic shocks, which determines the treatment of the bank by regulators. • Banks with a small exposure, ρ  ρ ∗ , are backed by the DIF and, in the case of a macroshock, receive liquidity assistance by the CB. They face a capital adequacy requirement k(ρ) and a deposit insurance premium P(ρ) that increase with ρ: k(ρ) = 1 −p  R − b ∆p  +qρ, P(ρ) = D  1 −p +pq ρ ρ 0  . Banks with a large exposure to macroshocks (ρ>ρ ∗ ) are not backed by the DIF: they do not receive liquidity assistance by the CB. They face a capital requirement k 0 and a deposit insurance premium P 0 that do not depend on ρ: k 0 = 1 − (1 − q)p  R − b ∆p  , P 0 = D(1 −p + pq). The LLR activities of the CB are made independent from political powers: the CB exclusively provides liquidity assistance to the banks that are backed by supervisory authorities. Central bank loans are fully insured by the DIF. This organization can be summarized by figure 4.5. References D’Amato, L., E. Grubisik, and A. Powell. 1998. Contagion, banks fundamentals or macroeconomic shocks. Bank of Argentina Discussion Paper. Basel Committee on Banking Supervision. 1988. 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[...]... expect, the study on the borrowing bank side is similar to that of the autarky case, for distribution F1 (ρ1 ) The following proposition and the next are proved in the appendix Proposition 5. 1 (borrowing bank) Under optimal interbank lending: (i) the continuation decision and the welfare of the borrowing bank do not depend on the liquidity shock facing the lending bank; (ii) the borrowing bank is closed... that the bank (a banking entrepreneur) privately chooses the probability p that the project succeeds The bank can either “behave” or “shirk.” One interpretation of this “effort choice” might be the intensity of the bank s monitoring of its commercial loans If the bank behaves, the probability of success is pH (high) If the bank shirks, the probability of success is pL (low), where pH −pL ≡ ∆p > 0, and. .. while a “liquidity bank (such as the German Likobank) is able to achieve the social optimum; and (ii) in the presence of macroeconomic shocks, the government has a role in creating and managing liquidity in the economy 5. 1.4 The Role of Banking Regulation in Our Framework The optimal allocation described in sections 5. 1.1 and 5. 1.2 can be implemented through a contract between the bank and its investors... recourse to other banks) The key difference with the interbank-loan institution is that the deposits made at the originating bank would, except to the eyes of the depositors, become deposits of the receiving bank So, if the latter defaulted, losses would be borne by the deposit insurance fund, and not by the originating bank We conclude that a mere specialization of banks into deposit-taking banks and actively... liquidity shock” ρ21 , which must correspond to the credit loss incurred at date 1 on the interbank market: ˆ ρ2 ≡ ρ2 + ρ21 The harder the liquidity shock hitting bank 1, the lower the value of the interbank loan and the higher the overall liquidity shock of bank 2 While the qualitative features of the implementation of the optimum are clear, the exact details of this implementation depend on a number i... loans 5. 2.2 Intuition and Implementation The lending bank s closure decision should be linked with the performance of the borrowing bank Bank 2’s closure is more likely, the higher the liquidity shock faced by bank 1 The natural vehicle for this linkage is the credit risk on the interbank loan We defined bank 2’s overall liquidity shock (per unit of illiquid asset) as the sum of ρ2 and the “interbank... which no bank fails, a small increase in a bank s liquidity shock can trigger the closure of all banks Section 5. 4 summarizes the main insights and discusses alleys for research 5. 1 Benchmark: No Interbank Lending 5. 1.1 The Model The benchmark model is adapted from Holmström and Tirole (19 95) , to which we refer the reader for more detail There are n banks, and three periods, t = 0, 1, 2 Banks and investors... health of its monitors 5. 2 5. 2.1 Date-0 Monitoring and Optimal Interbank Loans The Two -Bank Case: Optimal Allocation with Peer Monitoring In this section, we analyze in detail the simplest example of peer monitoring, that involving a borrowing bank (bank 1) and a lending bank (bank 2) In this situation, only one bank (bank 2) has an incentive to monitor the other bank 14 14 In this section (and the next)... SHOCKS AND BANKING SUPERVISION i 127 Sharpe, S 1990 Asymmetric information, bank lending and implicit contracts: a stylized model of customer relationships Journal of Finance 45: 1069– 85 Sironi, A 2000 An analysis of European bank SND issues and its implications for the design of a mandatory subordinated debt policy Journal of Financial Services Research 19:233–66 Solow, R 1982 On the lender of last resort... see, imply closing the lending bank when it itself is solvent but near insolvency In such cases, however, it is not “ex post optimal” for the central bank to adhere to the stated resolution method The solvency of 7 For simplicity, this paper does not make a distinction between the deposit insurance fund, banking supervisors, and the several departments of the central bank 8 Interbank loans might conceivably . between the banks and the DIF on the one hand, and pure public supervision on the other hand. Proposition 4.3. A purely private organization of the banking sector leads to too many closures in the. purchased at the price of government exposure and bank 6 There is ample evidence on the existence and relevance of peer monitoring in the banking industry. For example, in their study of the Suffolk. capital regulation and risk taking: a note. Journal of Banking and Finance 13:883–91. Gorton, G., and A. Santomero. 1990. Market discipline and bank subordinated debt. Journal of Money, Credit and Banking