Banking, Liquidity and Bank Runs

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Banking, Liquidity and Bank Runs in an In…nite Horizon Economy Mark Gertler and Nobuhiro Kiyotaki NYU and Princeton University May 2012

Abstract We develop a variation of the macroeconomic model of banking in Gertler and Kiyotaki (GK2011) that allows for household liquidity risks and bank runs as in Diamond and Dybvig (DD1983). As in GK, because bank net worth ‡ uctuates with aggregate production, the spread in the expected rates of return on bank credit and deposit ‡ uctuates countercyclically. However, because bank assets have a longer maturity than deposits, bank runs are possible as in DD. Whether a bank run equilibrium exists depends on the condition of bank balance sheets and an equilibrium liquidation price for bank assets. Thus in normal times a bank run equilibrium may not exist, but the possibility can arise in a severe recession. Overall, the goal is to present a framework that synthesizes the macroeconomic and microeconomic approaches to banking and banking instability. Thanks to Francesco Ferrante and Andrea Prespitino for outstanding research assistance, well above the call of duty.

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Introduction

There are two complementary approaches in the literature to capturing the interaction between banking distress and the real economy. The …rst, summarized recently in Gertler and Kiyotaki (2011), emphasizes how the depletion of bank capital in an economic downturn hinders banks ability to intermediate funds. Due to agency problems (and possibly also regulatory constraints) a bank’ ability to raise funds depends on its capital. Portfolios losses exs perienced in a downturn accordingly lead to losses of bank capital that are increasing in the degree of leverage. In equilibrium, a contraction of bank capital and bank assets raises the cost of bank credit, slows the economy and depresses asset prices further. The second approach, pioneered by Diamond and Dybvig (1983), focuses on how maturity mismatch in banking, i.e. the combination of short term liabilities and partially illiquid long term assets, opens up the possibility of bank runs. If they occur, runs lead to ine¢ cient asset liquidation along with a general loss of banking services. In the recent crisis, both phenomena were clearly at work. Depletion of capital from losses on sub-prime loans and related assets forced many …nancial institutions to contract lending and raised the cost of credit they did o¤er. (See, e.g. Adrian, Colla and Shin, 2012, for example.) Eventually, however, weakening …nancial positions led to classic runs on a number of the investment banks and money market funds, as emphasized by Gorton (2010) and Bernanke (2010). The asset …resale induced by the runs ampli…ed the overall …nancial distress. To date, macroeconomic models which have tried to capture the e¤ects of banking distress have emphasized balance-sheet and …nancial accelerator e¤ects, but not captured bank runs. Most models of bank runs, however, are typically quite stylized and not suitable for quantitative analysis. Further, often the runs are not connected to fundamentals. That is, they may be equally likely to occur in good times as well as bad. Our goal is to develop a simple macroeconomic model of banking instability that features both balance-sheet and …nancial accelerator e¤ects and bank runs. Our approach emphasizes the complementary nature of these mechanisms. Balance sheet conditions not only a¤ect the cost of bank credit, they also a¤ect whether runs are possible. In this respect one can relate the possibility of runs to macroeconomic conditions and in turn characterize how runs feed back into the macroeconomy. For simplicity, we consider an in…nite horizon economy with a …xed supply 2

of capital, along with households and bankers. It is not di¢ cult to map the framework into a more conventional macroeconomic model with capital accumulation. The economy with a …xed supply of capital, however, allows us to characterize in a fairly tractable way how...
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