سرایت مالی و نقش بانک مرکزی

We investigate the role of a central bank (CB) in preventing and avoiding financial contagion. The CB, by imposing reserve requirements on the banking system, trades off the cost of reducing the resources available for long-term investment with the benefit of raising liquidity to face an adverse shock that could cause contagious crises. We argue that contagion is not due to the structure of the interbank deposit market, but to the impossibility to sign contracts contingent on unforeseen contingencies. As long as incomplete contracts are present, the CB may have a useful role in curbing contagion. Moreover, the CB allows the banking system to reach first-best allocation in all the states of the world when the notion of incentive-efficiency is considered. If the analysis is restricted to constrained-efficiency, the CB still avoids contagion without, however, reaching first-best consumption allocation. The model provides a rationale for reserve requirements without the presence of fiat money or asymmetric information.

Various theoretical interpretations have been proposed in order to give a rationale for financial contagion. Financial systems seem to be particularly vulnerable to systemic risk given their characteristics: the structure of bank balance sheets, the network of exposure among financial institutions, and the character of financial contracts. Although a general paradigm has not yet emerged, we have a better understanding of the propagation of shocks in the banking and payment system.1 In this paper, we focus the attention on financial institution linkages, in particular the interbank deposit market, that are able to generate the possibility of contagion. In this context, we analyze the possible role for the central bank (henceforth CB) in preventing and avoiding bank crises and contagion. From the early contribution by Diamond and Dybvig (1983), there is a shared view of banks as providers of liquidity. Banks, in this context, are ‘pools of liquidity’ and their existence is not rooted in the presence of information asymmetries in credit markets.2 However, the Diamond–Dybvig model treats the whole banking industry as a single entity. In reality there are many banks in different regions, and problems arising in one bank can spread through the entire banking system. Financial contagion can be induced by an information-based mechanism. Difficulties in one bank may cause depositors to suspect that the whole bank industry is under pressure. For example, Jacklin and Bhattacharya (1988) argue that bank runs are triggered by asymmetry between the banks’ knowledge about its depositor’s liquidity needs and the depositor’s information about the bank’s asset. Chen (1999) argues that information externalities are important in causing contagious bank runs, since they force depositors to respond to noisy information such as failures of other banks. However, financial contagion is possible even without the presence of asymmetric information. Allen and Gale (2000) provide an explanation of financial contagion as a phenomenon that emerges in the banking system of a multi-region economy. Contagion can be the equilibrium outcome in which, after the distress of a region due to an adverse shock on agents’ preferences, there is the possibility of a spillover in other regions because of the presence of cross-holding interbank deposits. The interbank deposit market is able to provide insurance to the different regions against asymmetric liquidity needs, thus allowing the economy to reach first-best allocation in a decentralized setting. However, this arrangement is vulnerable to financial contagion if the unexpected liquidity shock occurs. Then we can ask the following question: Is there any instrument that is able to avoid contagion in the most efficient way? We show that the CB could offer a solution. The intervention of the CB takes the form of reserve requirements, which are a fraction of the amount of the bank’s deposits. The reserve requirements imposed on the banking system imply that less resources can be allocated in long-term productive activities. However, the reserves give the opportunity for the CB to face the adverse liquidity shock. Then the problem of the CB is to choose the optimal fraction of reserve requirements that, on the one hand, ensures enough liquidity in case of an aggregate liquidity shortage occurs and, on the other hand, does not divert too many resources from profitable investment opportunities. The intervention of the CB allows the decentralized banking system to reach first-best allocation when contingent contracts are considered. Indeed, when there is no shortage of aggregate liquidity, the imposition of reserve requirements delivers the efficient consumption allocation, making the payment to early (late) consumers higher (lower) than what the decentralized banking system alone would offer. When the unexpected shortage of aggregate liquidity occurs, and consequently the possibility of contagion arises, the CB intervenes declaring the insolvency of the banking system, and guarantees first-best consumption level with the liquidity collected by means of reserve requirements. If we restrict attention to non-contingent contracts, consequently shifting from the notion of incentive-efficiency to constrained-efficiency, reserve requirements alone allow the CB to avoid contagion when the aggregate liquidity shortage occurs. No declaration of insolvency is needed. However, in this case it is impossible to achieve first-best consumption allocation. The underlying assumption is that the CB has a different a-priori about the possibility of the occurrence of the aggregate liquidity shortage. While depositors and commercial banks give a probability zero to this event to happen, the CB attaches to the occurrence of this event its true (small) probability. The reason to assume a different a-priori is because it makes depositors and banks to sign incomplete deposit contracts, that is they do not take into account the liquidity shock, which appears to be a widespread characteristic of real world deposit contracts. The CB, observing this contract incompleteness, and being worried by the occurrence of an aggregate liquidity shortage, can take the appropriate action. Allen and Gale (2000) claim that the possibility of contagion is related to the structure of the interbank deposit market. The more complete is the structure of the interbank deposit market, the more difficult it is for contagion to occur. This may incorrectly suggest that a complete interbank deposit market may essentially eliminate contagion, thus, reducing the need for a CB. It will be argued that contagion is not rooted in the structure of the interbank deposit market, but in the impossibility for agents to sign contracts contingent on unforeseen contingencies. This result is consistent with Dasgupta (2004), who also argues the necessity of a CB despite a complete structure of the interbank deposit markets. In this paper, the CB does not find its rationale on the failure of the ex-post loan market, as in Bhattacharya and Gale (1987). The CB’s role is rooted in the bad distribution of liquidity among different regions, and its intervention is designed to avoid a coordination problem in the same fashion as Diamond and Dybvig (1983), i.e., one that is caused by an aggregate liquidity shock. There is, however, a distinction between the two models. In Diamond and Dybvig (1983) the intervention of the CB takes the form of deposit insurance since this is enough to avoid the bad equilibrium (i.e., the bank runs) in the presence of multiple equilibria. In this model, the intervention of the CB needs to be more explicit through reserve requirements. There is an authoritative doctrine claiming that reserve requirements are useless, at least from the point of view of monetary policy (Sargent and Wallace, 1982). However, various monetary models have provided a rationale for reserve requirements. For example, they reduce the nominal instability generated by a monetary policy that targets interest rate stabilization. In this context, reserve requirements are a useful ‘companion’ to interest rate stabilization (Lorenzoni, 2001). Moreover, reserve requirements make the money market multiplier more stable and predictable, thus helping to control money and credit expansion (Brunner and Meltzer, 1990). Alternatively, a scope for a regulatory intervention by means of reserve requirements can derive from the fact that banks are characterized by costly state verification (Di Giorgio, 1999). In our model, there is no need of fiat money injections in order to rationalize the presence of reserve requirements. Consequently, a rationale for the introduction of a legal reserve requirement is obtained in a ‘real’ (non-monetary) model. Moreover, in our model banks do not face asymmetric information problems on the activities side of their balance sheets since they invest directly in productive assets. Finally, since the CB successful intervention does not rely on liquidity creation, no direct transfers from taxpayer are necessary in order to bail out the distressed region (contrary to Freixas et al., 2000). In our model, the cost is represented by the missed long-term investment opportunity. The paper is organized as follows. In Section 2, we present the model, which builds on Allen and Gale (2000). In Section 3, we characterize the optimal risk-sharing solution obtained by the social planner. In Section 4, the decentralized economy with the CB is analyzed. In Section 5, we compare the financial fragility of the decentralized economy with and without the intervention of the CB. In Section 6, we restrict the analysis to non-contingent contracts, considering then the notion of constrained-efficiency, rather than incentive-efficiency, as the benchmark. Finally, we draw the conclusions.

Various theoretical interpretations have been proposed in order to give a rationale for financial contagion. Financial systems seem to be particularly vulnerable to systemic risk given their characteristics: the structure of bank balance sheets, the network of exposure among financial institutions, and the character of financial contracts. Although a general paradigm has not yet emerged, we have a better understanding of the propagation of shocks in the banking and payment system.1 In this paper, we focus the attention on financial institution linkages, in particular the interbank deposit market, that are able to generate the possibility of contagion. In this context, we analyze the possible role for the central bank (henceforth CB) in preventing and avoiding bank crises and contagion. From the early contribution by Diamond and Dybvig (1983), there is a shared view of banks as providers of liquidity. Banks, in this context, are ‘pools of liquidity’ and their existence is not rooted in the presence of information asymmetries in credit markets.2 However, the Diamond–Dybvig model treats the whole banking industry as a single entity. In reality there are many banks in different regions, and problems arising in one bank can spread through the entire banking system. Financial contagion can be induced by an information-based mechanism. Difficulties in one bank may cause depositors to suspect that the whole bank industry is under pressure. For example, Jacklin and Bhattacharya (1988) argue that bank runs are triggered by asymmetry between the banks’ knowledge about its depositor’s liquidity needs and the depositor’s information about the bank’s asset. Chen (1999) argues that information externalities are important in causing contagious bank runs, since they force depositors to respond to noisy information such as failures of other banks. However, financial contagion is possible even without the presence of asymmetric information. Allen and Gale (2000) provide an explanation of financial contagion as a phenomenon that emerges in the banking system of a multi-region economy. Contagion can be the equilibrium outcome in which, after the distress of a region due to an adverse shock on agents’ preferences, there is the possibility of a spillover in other regions because of the presence of cross-holding interbank deposits. The interbank deposit market is able to provide insurance to the different regions against asymmetric liquidity needs, thus allowing the economy to reach first-best allocation in a decentralized setting. However, this arrangement is vulnerable to financial contagion if the unexpected liquidity shock occurs. Then we can ask the following question: Is there any instrument that is able to avoid contagion in the most efficient way? We show that the CB could offer a solution. The intervention of the CB takes the form of reserve requirements, which are a fraction of the amount of the bank’s deposits. The reserve requirements imposed on the banking system imply that less resources can be allocated in long-term productive activities. However, the reserves give the opportunity for the CB to face the adverse liquidity shock. Then the problem of the CB is to choose the optimal fraction of reserve requirements that, on the one hand, ensures enough liquidity in case of an aggregate liquidity shortage occurs and, on the other hand, does not divert too many resources from profitable investment opportunities. The intervention of the CB allows the decentralized banking system to reach first-best allocation when contingent contracts are considered. Indeed, when there is no shortage of aggregate liquidity, the imposition of reserve requirements delivers the efficient consumption allocation, making the payment to early (late) consumers higher (lower) than what the decentralized banking system alone would offer. When the unexpected shortage of aggregate liquidity occurs, and consequently the possibility of contagion arises, the CB intervenes declaring the insolvency of the banking system, and guarantees first-best consumption level with the liquidity collected by means of reserve requirements. If we restrict attention to non-contingent contracts, consequently shifting from the notion of incentive-efficiency to constrained-efficiency, reserve requirements alone allow the CB to avoid contagion when the aggregate liquidity shortage occurs. No declaration of insolvency is needed. However, in this case it is impossible to achieve first-best consumption allocation. The underlying assumption is that the CB has a different a-priori about the possibility of the occurrence of the aggregate liquidity shortage. While depositors and commercial banks give a probability zero to this event to happen, the CB attaches to the occurrence of this event its true (small) probability. The reason to assume a different a-priori is because it makes depositors and banks to sign incomplete deposit contracts, that is they do not take into account the liquidity shock, which appears to be a widespread characteristic of real world deposit contracts. The CB, observing this contract incompleteness, and being worried by the occurrence of an aggregate liquidity shortage, can take the appropriate action. Allen and Gale (2000) claim that the possibility of contagion is related to the structure of the interbank deposit market. The more complete is the structure of the interbank deposit market, the more difficult it is for contagion to occur. This may incorrectly suggest that a complete interbank deposit market may essentially eliminate contagion, thus, reducing the need for a CB. It will be argued that contagion is not rooted in the structure of the interbank deposit market, but in the impossibility for agents to sign contracts contingent on unforeseen contingencies. This result is consistent with Dasgupta (2004), who also argues the necessity of a CB despite a complete structure of the interbank deposit markets. In this paper, the CB does not find its rationale on the failure of the ex-post loan market, as in Bhattacharya and Gale (1987). The CB’s role is rooted in the bad distribution of liquidity among different regions, and its intervention is designed to avoid a coordination problem in the same fashion as Diamond and Dybvig (1983), i.e., one that is caused by an aggregate liquidity shock. There is, however, a distinction between the two models. In Diamond and Dybvig (1983) the intervention of the CB takes the form of deposit insurance since this is enough to avoid the bad equilibrium (i.e., the bank runs) in the presence of multiple equilibria. In this model, the intervention of the CB needs to be more explicit through reserve requirements. There is an authoritative doctrine claiming that reserve requirements are useless, at least from the point of view of monetary policy (Sargent and Wallace, 1982). However, various monetary models have provided a rationale for reserve requirements. For example, they reduce the nominal instability generated by a monetary policy that targets interest rate stabilization. In this context, reserve requirements are a useful ‘companion’ to interest rate stabilization (Lorenzoni, 2001). Moreover, reserve requirements make the money market multiplier more stable and predictable, thus helping to control money and credit expansion (Brunner and Meltzer, 1990). Alternatively, a scope for a regulatory intervention by means of reserve requirements can derive from the fact that banks are characterized by costly state verification (Di Giorgio, 1999). In our model, there is no need of fiat money injections in order to rationalize the presence of reserve requirements. Consequently, a rationale for the introduction of a legal reserve requirement is obtained in a ‘real’ (non-monetary) model. Moreover, in our model banks do not face asymmetric information problems on the activities side of their balance sheets since they invest directly in productive assets. Finally, since the CB successful intervention does not rely on liquidity creation, no direct transfers from taxpayer are necessary in order to bail out the distressed region (contrary to Freixas et al., 2000). In our model, the cost is represented by the missed long-term investment opportunity. The paper is organized as follows. In Section 2, we present the model, which builds on Allen and Gale (2000). In Section 3, we characterize the optimal risk-sharing solution obtained by the social planner. In Section 4, the decentralized economy with the CB is analyzed. In Section 5, we compare the financial fragility of the decentralized economy with and without the intervention of the CB. In Section 6, we restrict the analysis to non-contingent contracts, considering then the notion of constrained-efficiency, rather than incentive-efficiency, as the benchmark. Finally, we draw the conclusions.