Financial Intermediation and Credit Policy in Business Cycle Analysis Gertler and Kiotaki 2009 Professor PengFei Wang Fatemeh KazempourLong 1
Motivation Bernanke, Gilchrist and Gertler (1999) studied great depression and the crisis in the past quarter of centuries The recent crisis has featured a significant disruption of intermediation Providing a framework to study dynamic through which disruption of financial intermediate which propagate to real activities The role of Central bank and Treasury intervention to mitigate the crisis, a significant break from tradition which was effective for recovery Crisis could be mitigated through liquidity and equity injection 2
New Features in Study Disruption of intermediaries can create a crisis Credit policy introduced by banks can mitigate it Agency problem between borrowers and lenders induce wedge between cost of internal and external finance which increase borrowing cost This premium will depend on borrower’s balance sheet and their share in project In equilibrium a financial accelerator strengthens balance sheet and controls the problems of external finance A mutual feedback between real and financial part of economy 3
Set Up • At the beginning of the period each bank raises deposits from households in the retail financial market at the deposit rate R t • Two investment and non-investment island • A fraction of non-financial firms have access to project and a fraction of them have no access • Then investment opportunities for non-financial firms arrive randomly only in investment Island • Financial friction only happens when banks collects deposit from households or get loan from other banks • No friction between bank and non-financial firms • Bank only can make loan in to financial market in the same Island • Instead of the loans, firms offer equity (a perfectly state-contingent debt) 4
Other Assumptions • Financial intermediaries ( banks) are skillful and efficient in credit allocation • Household deposit their money before banks • Agency problem limits the ability of banks to raise money from households and other banks • when incentive constraint can bind, deterioration of balance sheet induces a wedge between the loan rate and deposit rate • This wedge widens during crisis causing non-financial borrowers face with limited external funding and higher cost of credit • This limitation affect real activities too 5
Crisis • Sharp deterioration of borrower’s balanced sheet • Borrower bank can lend less and may have do fire sale • Possibly associated with a sharp deterioration in asset price captured by an exogenous variable called quality of capital • External finance premium jumps
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Physical Setup Law of motion of capital Capital depreciation Crisis is an exogenous source of variation in quality of capital 8
Physical Set up is physical adjustment cost 9
Household 10
Household
The Problem of Households 12
Financial Intermediary 13
Intermediaries 14
Intermediaries 15
Households and Banks Retail financial market at the beginning of period Household Deposit Bank Rt+1 & dt 16
No friction between a bank and nonfinancial firm in the same island Firms are able to offer perfectly state-contingent debt After the bank knows about its lending opportunities decides the volume of loans accordingly decides about interbank loans is the market price of the loan or the price of bank’s claim for one unite of capital in non -financial firms and d epends on the opportunities a bank faces Financial frictions affect real activity in our Framework via the impact on funds available to the banks 17
Assumptions 18
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Source of Friction and Borrowing constraint • Bank can divert a fraction of divertible assets which consist Nt net a fraction • If a bank diverts then it defaults on its debts and creditors take • Friction also exist for interbank loan • With banks recover their assets from other banks frictionlessly, so no constraint for interbank loan • With banks are like retail market in recovering their debt • Banks make its decision whether to default or not at the end of each period after the realization of the idiosyncratic risk which determines its type • Incentive constraint for deviation: value of the bank for entrepreneur should exceeds the gain from cheating: 20
Bank value at the end of period t-1 Bellman equation CONJUNCTURE: 21
First Order Condition: Marginal value of Assets is higher than interbank loan Agency problem creates endogenous 22 balance sheet constraint
Further Explanation 23
Bank cannot divert asset in interbank market and interbank market is frictionless Marginal value of asset equalize marginal cost of borrowing on interbank market Perfect arbitrage equalize the shadow value of assets and asset price in each market 24
Given that banks are constrained in retail market : • SINCE INTERBANK MARKET IS FRICTIONLESS, THE CONSTRAINT APPLIES T O ASSETS INTERMEDIATED MINUS INTERBANK BORROWING • HOW TIGHTLY THE CONSTRAINT BINDS, DEPENDS ON THE DEVIATION FACT OR • ALSO THE HIGHER EXCESS RETURN MEANS THE GREATER FRANCHISE VALUE OF THE BANK AND THE LESS LIKELY IT DEVIATES, THEREFORE THE HIGHER WOULD BE THE AGGREGATE INTERBANK ASSETS 25
Bellman Equation CONJUNCTION: Marginal Value of net worth is a weighted average of marginal Value for exiting and for continuing bank Rtk tk+1 is is th the e gr gross rate of of retu turn on on assets ts 26
Marginal Value of net worth is a weighted average of marginal value for exiting and for continuing bank If a continuing bank has an additional net worth it can save the cost of deposits and can increase assets by leverage ratio Bank’s balance sheet constraint
Interbank loan and deposits become perfect substitute If the constraints on interbank borrowing binds, bank in non-investing island only finance their own old project Hence banks in non-investing Island are likely to get zero return This friction lowers asset price in investing island 29
• Type of Island matters • The banks in non-investment Island give less loan than they afford through their net worth 30
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Equilibrium: Market Clearing for security market The market price of capital in each island depend on the situation of bank in the same Island. 35
Equilibrium: Market Clearing for labor market 36
Crisis and Impact on balance sheet effect 37
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Credit policy: Direct lending • Fed directly acquire high quality private securities • Fed is not balance sheet constrained and guarantee repayment so can borrow from public • Fed can reach all markets • Less efficient in monitoring and incurs a cost of T • In recent crisis fed issued government debt from treasury and then used interest bearing reserves • Total amount of assets intermediated in the market increase , but no subsidized rate • Equilibrium rate of lending falls • Asset price goes up 40
Credit policy: Direct lending Total Intermediated Asset Increases 41
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Discount window lending ( case of symmetric friction w=0) • The Fed dir irectly le lends to banks to enable th their le lending to fir firms • Offering at penalty rate driven by distressed borrower’s unusual high excess return • CB offers dis iscount win indow cr credit in in non-contingent in interest rate Rmt+ t+1 to banks who borrow on in interbank market. Here governmental debt is is a perfect substitute for household deposit • CB better enforces repayment th than th the household 43
Discount window lending ( case of symmetric friction w=0) 44
The condition that both bank borrowing and discount window borrowing become used Total Assets Intermediated Increases 45
Equity Injection: Equity Injection Fiscal authority coordinate with monetary authority to acquire ownership in bank • Efficiency costs with government acquiring equity • Equity injection is slower than direct lending • Bank inject equity at the beginning of period before investment opportunities arrive • Perfect interbank lending • Government receive the equity value after liquidation of bank or upon passing crisis sell off its holding at this value before the bank exits 46
Equity Injection 47
• Equity Sharing expands private bank net worth which in turn expand asset demand by multiple equal to leverage • Risk absorption for high risks involved in the crisis 48
The doted line is the model without financial friction. 49 The negative shock has a much modest effect compared to the friction case
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