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penn101_09s11GT - Two Models of Bank Run Asymmetric...

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Two Models of Bank Run Asymmetric Information Econ 101: Intermediate Microeconomics Topics in Game Theory Jing Li Department of Economics University of Pennsylvania April 22, 2009 Jing Li Intermediate Microeconomics
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Two Models of Bank Run Asymmetric Information Banking Industry as Financial Intermediary The Role of Higher-Order Beliefs: Global Games The Diamond-Dybvig model (1983) Main idea: banks create liquidity for investors who may need cash at a random date. This service in essence helps investors to pool their risks and hence improve welfare of the entire economy, however, the essence of this service makes banks subject to runs. Essential elements: Mismatch of liquidity: bank’s liabilities are more liquid than its asset; A coordination component of the investors: it is profitable to leave money in the bank only if others do. Jing Li Intermediate Microeconomics
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Two Models of Bank Run Asymmetric Information Banking Industry as Financial Intermediary The Role of Higher-Order Beliefs: Global Games A simple numerical example: set-up Three periods: 0, 1, 2 Period 0: investment decisions are made, 100 investors, each endowed with $1 at period 0: Risk-averse expected utility maximizer: u ( c ) = 1 - 1 c ; 25 are type 1 and have to eat in period 1; 75 are type 2 and can eat in either period 1 or 2; Each investor is privately informed of their type at the beginning of period 1. Illiquid investment project: R 1 = 1 , R 2 = 2; Jing Li Intermediate Microeconomics
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Two Models of Bank Run Asymmetric Information Banking Industry as Financial Intermediary The Role of Higher-Order Beliefs: Global Games A simple numerical example: creation of the bank Benchmark: if invest in the illiquid asset: . 25 ( 1 - 1 1 ) + . 75 ( 1 - 1 2 ) = . 375 Let’s create a bank: Let the bank pay r 1 , r 2 respectively; 25 type 1 take out cash in period 1 and 75 type 2 leave money until period 2. max r 1 , r 2 . 25 ( 1 - 1 r 1 ) + . 75 ( 1 - 1 r 2 ) Subject to: r 2 2 ( 100 - 25 r 1 ) 75 Optimal deposit interest rate: r 1 = 1 . 28 , r 2 = 1 . 813. If deposit in the bank: . 25 ( 1 - 1 1 . 28 ) + . 75 ( 1 - 1 1 . 813 ) = . 391 > . 375 Jing Li Intermediate Microeconomics
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Two Models of Bank Run Asymmetric Information Banking Industry as Financial Intermediary The Role of Higher-Order Beliefs: Global Games A simple numerical example: bank run Suppose the bank exists. A coordination game for type 2 investors in period 1: Each player decides whether to withdraw the deposit; Bank liquidates the asset to satisfy demand for cash. Multiple equilibria: Simplified version of the game. ( r 1 = 1 . 5 , r 2 = 1 . 6 , R 2 = 2) W N W (1,1) (1.5, .8) N (.8, 1.5) (2,2) Equilibrium 1: no one withdraws; Equilibrium 2: everybody withdraws – bank run! Public information as the coordination/selection device.
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