Financial Intermediation and Credit Policy in Business Cycle Analysis Mark Gertler and Nobuhiro Kiyotaki NYU and Princeton
Motivation Present a canonical framework to think about the current - nancial crisis and the nancial accelerator Disruption of Financial Intermediation More about nancing constraint of nancial intermediaries than non- nancial businesses and households Unconventional Monetary Policy Direct lending to non- nancial rms Liquidity facilities to nancial intermediaries Equity injections to nancial intermediaries
Federal Reserve Assets Trillions of Dollars 3 2.5 2 1.5 1 Repo Treasury Securities Other AMLF Maiden Lane I, II, III Other Credit (&AIG ext) PDCF, Other Broker-dealer TAF Primary Credit Currency Swaps Agency MBS Agency Debt TALF CPFF 3 2.5 2 1.5 1 Trillions of Dollars.5.5 Aug-7 Oct-7 Dec-7 Feb-8 Apr-8 Jun-8 Aug-8 Oct-8 Dec-8 Feb-9 Apr-9 Federal Reserve Liabilities 2.5 Treasury, SFA 2.5 2 1.5 1 Reserve Balances Treasury, ga Reverse Repo Other Currency 2 1.5 1.5 Source: H41, Bloomberg Aug-7 Oct-7 Dec-7 Feb-8 Apr-8 Jun-8 Aug-8 Oct-8 Dec-8 Feb-9 Apr-9.5
Model Goods producers dispersed across islands with perfectly mobile labor: Y t = A t K t L 1 t ; < < 1 Investment opportunity arrives to each island with prob i = - i:i:d: across island and time: K t+1 = t+1 [I t + (1 )K t ] + t+1 (1 )(1 )K t = t+1 [I t + (1 )K t ] Shocks to the quality of capital t+1 and productivity A t follow AR(1) Resource constraint Y t = C t + 2 6 41 + f B @ I t I t 1 13 C7 A 5 I t + G t
Each household consists of many members, 1 bankers f workers, f Workers supply labor and bring wages back to the household Each banker manages a bank, retains some earning and brings back the rest to the household Perfect consumption insurance within the household Each period, bankers exit to become workers and bring back the retained earning with prob 1 (1 ) f workers become bankers with fraction of total asset of the household as the start-up fund
The household chooses (C t ; L t ; D t+1 ) to maximize 2 X 1 E t t 4ln (C C 1 ) =t 1 + " L1+" subject to C t = W t L t + t T t + R t D t D t+1 The goods producer hires workers to produce! pro t per unit of capital: Z t = Y t W t L t K t = A L 1 t K t Goods producer sells security (equity) to banks of the same island in order to nance new investment. Each security pays dividend: t+1 Z t+1, (1-) t+1 t+2 Z t+2, (1-) 2 t+1 t+2 t+3 Z t+3... Capital goods producer chooses investment goods supply in order to maximize the pro t 3 5
Before the arrival of investment opportunity, each bank chooses an island to operate and raises funds from households by o ering non-contingent deposit contract d t After the arrival of the investment opportunity, the bank borrows (or lends) b h t in the interbank market in order to purchase the security of the goods producers of the same island: Q h t s h t = n h t + b h t + d t ; where h = i; n The net worth of the bank is n h t = Z t + (1 )Q h t ts t 1 R bt b t 1 R t d t 1
Beginning of the period Retail financial market Households Banks Deposit
During the period Investing regions Non-investing regions Bank with fund shortage Interbank market Banks with surplus fund New and old loans Old loans Firms with new investment opportunity Firms without new investment opportunities
The value of the bank at the end of period t is V t = V s h t ; b h t ; d t = Et 1 X =t+1 (1 ) t t; n h After the bank obtains funds, the banker may steal a fraction of "divertable" funds - total assets minus! fraction of interbank borrowing. The incentive constraint for the bank not to divert the asset is V s h t ; b h t ; d t Q h t s h t!b h t Case of! = 1 is no friction of interbank market. Case of! = is symmetric moral hazard between retail and interbank nancial markets
The security market equilibrium implies I t + i (1 )K t = St i = Spt i + Sgt i Q i tspt i!b t = i tnt i n (1 )K t = St n = Spt n + Sgt n Q n t Sn pt +!B t n t N n t The aggregate net worth of banks in islands of type h is Nt h = h ( + )[Z t +(1-)Q h t ] t S i pt 1 +Spt n 1 R t D t 1 The aggregate deposit D t is Q i ts i pt + Q n t S n pt = N i t + N n t + D t
Credit Policies Direct Lending: Central bank purchases a fraction ' h t of securities of goods producers of type h islands with the administrative cost of per unit Sgt h = ' h t St h ; where ' h t = v g Et R hh kt+1! The lending in investing islands expands R t+1 (R h k R) Discount Window Lending: Central bank lends to bank in the interbank market at interest rate R mt+1! To the extent that the central bank is better in preventing the diversion of asset, the central bank has to charge a rate R mt+1 > R bt+1 in order to keep the interbank market active.
ψ Figure 2. Crisis Experiment: Imperfect Interbank Market 5 x 1 3 r.6 spread.2.4.6 1 2 3 4.2.2.4.6.5.1.15.2.4.6 y 1 2 3 4 k 1 2 3 4 net worth 1 2 3 4 5 1 1 2 3 4.2.4.6 1 2 3 4.2.2 c labor 1 2 3 4 Imperfect Interbank Market (π i =.25) RBC Perfect Interbank Market.4.2 1 2 3 4 investment.1.1.2 1 2 3 4.5.5.1 q 1 2 3 4
ψ Figure 4. Lending Facilities: Imperfect Interbank Market r.1.6 spread.2.4.6 1 2 3 4.1.2 1 2 3 4.4.2 1 2 3 4 y c.1 investment.2.2.4.6 1 2 3 4.4.6 1 2 3 4.1.2 1 2 3 4 k labor.5 q.1.2 1 2 3 4.2.4.6 net worth.8 1 2 3 4.2.2.6.4.2 1 2 3 4 fraction of government assets 1 2 3 4.5.1 1 2 3 4 ν g = RBC ν g =1
Issues for Further Study Tightening margins Outside equity issue of banks Capital requirement and the other regulations Moral hazard from anticipated policy interventions