Spring 2010 Social Sciences 7418 University of Wisconsin-Madison. The Financial and Economic Crisis Interpreted in a CC-LM Model

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1 Publc Affars 854 Menze D. Chnn Sprng 2010 Socal Scences 7418 Unversty of Wsconsn-Madson The Fnancal and Economc Crss Interpreted n a CC-LM Model 1. Background: Typcal Fnancal Crss Source: Mshkn 2. Theory: Interacton between Fnancal Sector and Real Sector (CC-LM) Consder an economy where bank credt s mperfectly substtutable for bond fnance, as n Bernanke and Blnder (1988), augmented by allowng the credt supply to depend on a shft varable, the "rskness" of the margnal nvestment project. Banks hold labltes of deposts. On 1

2 the asset sde, the banks hold loans, reserves and ether domestc government debt. Loan demand s gven by: Loan supply s gven by: L d = L(,, y) (1) L s = λ( p,, ) D(1 τ ) (2) where s a measure of rskness of the margnal nvestment project, and τ s the reserve rato. The data generatng process of s not modelled explctly. The credt market equlbrum s gven by equatng loan supply and demand. The money market equlbrum s gven by equatng the demand for deposts wth the supply; hence the LM schedule s: D (, y) = mr (3) where m s the money multpler, and R s the stock of reserves. (Excess reserves are gnored n ths analyss.) The money multpler s assumed constant. Allowng t to depend postvely on the nterest rate does not change the qualtatve conclusons. The CC curve s a conventonal IS curve, except that t depends upon the bank lendng rate as well as the nterest rate: y = Y (, ) Substtutng money market equlbrum nto the loan market equlbrum yelds: (1) L (,, y) = λ(,, ) mr(1 τ ) (2) Solvng for the equlbrum loan rate,, one obtans: = ϕ(, y, R, ) (3) In ths formulaton, the spread between the bank loan rate and the rsk free rate, -, s a postve functon of, the rskness of the margnal project. The CC schedule s obtaned by substtutng (6) nto (4). To solve out the model analytcally, work wth the sem reduced form equaton representng the CC equaton s: 2

3 Takng the total dfferental yelds: y = Y (, ) (6 ) dy = Y d Y ( d dy dr d) (7) Y R Rearrangng: dy ( 1 Y ) = ( Y Y ) d Y dr Y d (8) Y R The LM curve s obtaned by dfferentatng (5): dd = m( dr) = D d D m D R Y dy (9) Solvng for the depost nterest rate: m( dr) DY dy d = D (10) Substtutng (10) nto (8): ( Y Y ) DY ( Y Y ) m dy 1 Y Y = Yñ R dr Y d D D (11) Solvng for ncome: dy 1 = ( Y Y ) m Y R dr Y d D (12.1) where ( Y Y ) DY 1 Y Y D (12.2) The comparatve statcs are summarzed n the table below. 3

4 Source: Bernanke and Blnder (1988) LM R 0, m 1 LM R 0, m 0 CC A 0, 0, R 0, m 0 CC A 0, 1, R 0, m 0 Y 1 Y 0 Y If rskness of the margnal nvestment project rses (), the CC curve shfts n. If the money multpler (m) falls, both the CC and LM curves shft n. If some fnancal nsttutons fal, both the CC and LM curves shft n. Here, we take as exogenous. But f depends upon the level of economc actvty, then one could have an adverse feedback loop, wheren the ntal shft nward of CC results n an addtonal ncrease n and hence further nward shft of CC. If ether fnancal nsttutons fal, or the monetary multpler falls, then the monetary authortes can ether ncrease Reserves, or drectly lend to the fnancal nsttutons. Ths s shown below as a shft outward of the LM curve, and of the CC curve (gray arrows). 4

5 LM R 0, m 1 LM R 1, m 1 LM R 0, m 0 CC A 0, 0, R 0, m 0 CC A 0, 1, R 0, m 0 Y 1 Y 0 Y 3. Actual Data and Thnkng about Balance Sheets A lttle more detal on the balance sheet of the Unted States pre-crss. 3.1 Readng Balance Sheets of a typcal bank before and after a negatve shock to assets Commercal Bank (Before) Assets Labltes Reserves $10M Deposts $90M Loans $90M Bank (Mortgages, Captal CRE) (or T-Blls equty Other bonds (GSEs) $10M Commercal Bank (After) Assets Labltes Reserves $10M Deposts $90M Loans $80M Bank (Mortgages, Captal CRE) (or T-Blls equty ) Other bonds (GSEs) $00M 5

6 3.2 Balance sheets of the fnancal sector before the collapse of Lehman Source: Greenlaw et al. (2008) 3.3 Loan loss magntudes Source: IMF, 2009, Global Fnancal Stablty Report (Washngton, DC: October). References Bernanke, B. and A. Blnder, 1988, "Credt, money, and aggregate demand," Amercan Economc Revew 78 (May): D. Greenlaw, J. Hatzus, A.K. Kashyap, H.S. Shn, 2008, Leveraged Losses: Lessons from the Mortgage Market Meltdown, mmeo (February). IMF, 2009, Global Fnancal Stablty Report (Washngton, DC: October), Box 1.3. Mshkn, F., 2006, The Economcs of Money, Bankng and Fnancal Markets (Addson-Wesley). Pa854_crss_s10,