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Uncertainty in an Interconnected Financial System, Contagion, and Market Freezes

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Uncertainty in an Interconnected Financial System, Contagion, and Market Freezes Q ED Queen’s Economics Department Working Paper No. 1308 Uncertainty in an Interconnected Financial System, Contagion, and Market Freezes Mei Li Frank Milne University of Guelph Queen’s University Junfeng Qiu Central University of Finance and Economics Department of Economics Queen’s University 94 University Avenue Kingston, Ontario, Canada K7L 3N6 5-2013 Uncertainty in an Interconnected Financial System, Contagion, and Market Freezes Mei Li, Frank Milne, Junfeng Qiu∗ May 13, 2013 Abstract This paper studies contagion and market freezes caused by uncertainty in fi- nancial network structures and provides theoretical guidance for central banks. We establish a formal model to demonstrate that, in a financial system where financial institutions are interconnected, a negative shock to an individual financial institu- tion could spread to other institutions, causing market freezes because of creditors’ uncertainty about the financial network structure. Central bank policies to allevi- ate market freezes and contagion, such as information policy, bailout policy and the lender of last resort policy, are examined. Keywords: Interconnection, Market Freezes, Contagion, Financial Crises JEL Classifications: D82 G2 ∗Mei Li: Department of Economics and Finance, College of Management and Economics, Uni- versity of Guelph, Guelph, Ontario, Canada N1G 2W1. Email: [email protected]. Frank Milne: Department of Economics, Queen’s University, Kingston, Ontario, Canada K7L 3N6. Email: mil- [email protected]. Junfeng Qiu: China Economics and Management Academy, Central Uni- versity of Finance and Economics, 39 College South Road, Beijing, China 100081. Email: qiujun- [email protected]. 1 Introduction An important contagion mechanism emerged in the recent subprime mortgage crisis: with the rapid expansion of credit derivatives, financial institutions are interconnected through an increasingly complicated financial network. Consequently, when one of the financial institutions goes bankrupt, general uncertainty about the losses of other financial insti- tutions in the network arises. This is because the complexity of the financial network makes it difficult for market participants to assess these losses. As a result, market par- ticipants can stop lending to one another; in other words, all the financial markets freeze. This contagion mechanism played an important role in the recent crisis following Lehman Brothers’ bankruptcy. Market participants stopped lending to one another, as they were all perceived to have been exposed to some counterparty risk because of Lehman Brothers’ bankruptcy. This paper establishes a formal model of this phenomenon. In our model, financial institutions are interconnected through interbank loans.1 Meanwhile, these financial in- stitutions are financing their long-term investments through short-term liabilities. As a result, there is a maturity mismatch between their assets and liabilities, which could potentially lead to bankruptcy of these institutions resulting from a lack of liquidity. We demonstrate that, due to short-term creditor uncertainty about the interconnections among these financial institutions, a negative shock to one financial institution can spread to all the other financial institutions in the system, leading to systematic market freezes. To illustrate the mechanism in the most transparent fashion, we assume that all fi- nancial institutions are divided into an equal number of borrowers and lenders. Each borrower is linked to a single lender, and each lender has only one borrower. (Later in the paper this assumption can be modified in a more realistic fashion.) Short-term creditors do not have perfect information about the financial institution lending network. Instead, they believe that each lending institution could lend to each of the borrowing institutions in the system with an even probability. This assumption introduces uncertainty about interconnections among financial institutions into the model and plays a key role in our contagion mechanism. In addition, we assume that a negative shock hits the long-term investments of one of the borrowing institutions that we call the distressed institution. 1Here we alter the commonly understood definition of “interbank loans” and use it to refer instead to financial transactions between any financial institutions that are not necessarily commercial banks. 1 The shock spreads to the rest of the financial institutions in the following way: First, the financial institution that has lent to the distressed institution may suffer a loss because its interbank loans may default. Second, short-term creditors of the lending institutions may charge a higher interest rate (we call this case a partial market freeze) or even refuse to roll over their short-term loans (we call this case a complete market freeze) because of their concern that the financial institution they are lending to may be the one lending to the distressed institution and may thus fail to repay its debts. As a result, the lending institutions may be forced to liquidate their long-term investments and recall their interbank loans. Third, due to the interbank loan recall of the lending institutions, the healthy borrowing institutions unaffected by the shock could incur a loss. As a result, their short-term creditors may refuse to roll over their loans, forcing the borrowing institutions to liquidate part or all of their long-term investments. Our model produces the following major results: First, depending on the magnitude of the negative shock to the distressed institution, the severity of market freezes varies. When the negative shock is large enough, a sys- tematic collapse can happen where complete market freezes occur in all the short-term markets. When the negative shock is moderate, partial market freezes may occur to some financial institutions. When the negative shock is low enough, a market freeze may not happen at all. Second, in our model, contagion occurs among financial institutions who need not be interconnected through actual financial transactions. Instead, as long as a financial insti- tution is perceived by the market to be connected to the distressed institution, it becomes part of the contagion. Thus, our model reveals that short-term creditor uncertainty over network structures can significantly increase the magnitude of contagion compared to a situation where there is no short-term creditor uncertainty. Third, our model reveals that a small loss to an individual financial institution can be magnified through the contagion mechanism and can lead to a large social loss. Fourth, we find that the maximum total social loss has a non-monotonic relationship with the number of financial institutions in the network. This is because of the trade-off between the number of financial institutions affected by contagion and the loss of each affected institution when the number of institutions in the network increases. When the number is small, complete market freezes are more common, leading to a higher loss 2 for each individual institution. However, a small number of affected institutions lowers the total social loss. When the number is large, partial market freezes tend to happen, leading to a lower loss for each institution. However, a large number of affected institutions increases the total social loss. Moreover, our model produces the following major policy implications. First, we examine the information policy of a central bank. In a perfect information case where the central bank, because of its close cooperation with the prudential regulator, can signal credibly to short-term creditors that there is only one distressed bank, we find that contagion can be effectively prevented. The crucial assumption here is that the markets are confident that the central bank is fully informed and credible. In an imperfect information case where the central bank does not know for sure the identity of the distressed institution, we find that more information provided by a central bank, to reduce the number of financial institutions that might be connected to the distressed institution, does not necessarily improve social welfare. Second, we examine bailout policies and find that both direct guarantees for the dis- tressed institution and injections of capital to all the lending institutions can alleviate market freezes if the moral hazard problem is ignored. Third, we examine the Lender of Last Resort (LOLR) policy and find that a central bank loan with an interest rate lower than the prevailing market rate will lower the market rate, and makes complete market freezes less likely. Our paper is most closely related to Caballero and Simsek (2009) and Pritsker (2010), two studies that examine financial contagion caused by uncertainty in an interconnected financial system. However, both papers resort to the concept of Knightian uncertainty. In addition, the basic setup of their models is quite different from ours. For example, our model assumes that financial institutions finance their long-term investments through both interbank loans and small short-term creditors. As a result, one of the important theoretical contributions of our paper is to introduce a large creditor in the presence of a continuum of small creditors to a Diamond and Dybvig bank run model. Consequently, our model can provide insights into how the presence of a large creditor will affect bank run dynamics. Moreover, our paper contributes to the literature on financial contagion. The exist- ing literature on financial contagion focuses mainly on two contagion mechanisms. The 3 first works
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