1Economics 302-001 Menzie D. Chinn Spring 2011 Social Sciences 7418 University of Wisconsin-Madison The Financial and Economic Crisis Interpreted in a CC-LM Model (rev’d) Summary: In this handout, the importance of the banking (as well as the overall financial) system is discussed. First, some historical context is provided. Second, a formal model incorporating a credit channel is provided. Third, bank losses in the current financial crisis are discussed in the context of bank balance sheets. 1. Schematic: Typical Financial Crisis Source: Mishkin (2006). 2. Theory: Interaction between Financial Sector and Real Sector (CC-LM) Consider an economy where bank credit is imperfectly substitutable for bond finance, as in Bernanke and Blinder (1988), augmented by allowing the credit supply to depend on a shift variable, the "riskiness" of the marginal investment project. The key is to make the real side of the economy depend upon both the interest rate on deposits (which will equal essentially the interest rate set by the Federal Reserve, and be denoted by the familiar variable i), and the interest rate at which banks lend, or the lending rate, denoted by a new variable ρ.2 In order to accomplish the goal of modeling a role for the lending interest rate, we will need to model the banking sector more closely than what was laid out in the textbook. 2.1 Loan demand and supply Banks hold liabilities of deposits. On the asset side, the banks hold loans, reserves and either domestic government debt. Loan demand is given by: Loan supply is given by: where Z is a measure of riskiness of the marginal investment project, and is exogenous, D is deposits, and θ is the reserve ratio. The credit market equilibrium is given by equating loan supply and demand. The money market equilibrium is given by equating the demand for deposits with the supply; hence the LM schedule is: where (1/θ) is the money multiplier, and R is the stock of reserves. (Excess reserves are ignored in this analysis.) The money multiplier is assumed constant. Allowing it to depend positively on the interest rate does not change the qualitative conclusions. 2.2 LM curve and CC curve Notice that (3) leads to a slightly different formulation of the LM curve than before: The CC curve is a conventional IS curve, except that it depends upon the bank lending rate as well as the interest rate: Where 111)1(11btc −−−=γ To determine what ρ is, one has to substitute money market equilibrium into the loan market equilibrium to obtain: YiPd3210Ω+Ω+Ω−Ω=ρl (1) PDZiPs)1()(3210θλλρλλ−−−+=l (2) PRhiY /)/1(0×=−+θμ (3) YhPRhhi1)/1(10+⎟⎠⎞⎜⎝⎛−=θμ (4) )(320ργbibY−−Λ= (5)3Solving for the equilibrium loan rate, ρ, one obtains the following relationship, where linearity is assumed for simplicity: Where 0ϕdepends negatively on 0λ, which is the constant in the loan, or credit, supply equation, and 0Ω, which is the constant in the loan, or credit, demand equation. In this formulation, the spread between the bank loan rate and the risk free rate, ρ-i, is a positive function of Z, the riskiness of the marginal project. The CC schedule (commodity and credit equilibrium) is obtained by substituting (7) into (5), which is the IS curve, allowing a role for interest rates (and implicitly, the determinants of the lending rate, ρ). Instead of working this out, just note that the factors that increase ρ according to equation (7) decrease Y according to equation (5). Hence, an increase in i or Z will, ceteris paribus, decrease output. Notice that i and Y are in (7), so the CC curve only represents equilibrium (in this case both the goods and credit markets, instead of just the goods market, as in the IS curve). 2.3 Solving for equilibrium income Let’s substitute the LM curve in (4) as well as (7) into (5). First, rearrange (5): Notice the R is still present on the RHS, and so the LM curve has to be substituted in again: Notice Y shows up two places on the RHS, and (1/θ)R in two places. Factoring, and solving for Y: Bringing the Y terms over to the LHS, and then solving yields: PDZiYi)1()(32103210θλλρλλρ−−−+=Ω+Ω+Ω−Ω (6) ZPRYi43210)1()/1(ϕθθϕϕϕϕρ+⎟⎠⎞⎜⎝⎛−−++= (7) ))]1()/1[((1)/1(1))1(1(432103020111ZRYibYhPRhhbbtcYϕθθϕϕϕϕθμ+−−++−⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛−−Λ=−−− (8) ))]1()/1[(1)/1(1(1)/1(1))1(1(4320103010111ZRYYhPRhhbYhPRhhbbtcYϕθθϕϕθμϕϕθμ+−−+⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛−+−⎟⎟⎠⎞⎜⎜⎝⎛+⎟⎠⎞⎜⎝⎛−−Λ=−−− ⎢⎣⎡++−−⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛−+++⎟⎠⎞⎜⎝⎛++−Λ=−−−013243331322313201)()/1()1()())1(1(μϕϕθϕϕϕϕbhbbZbPRrbhbbYbhbbbtbY4Where ⎟⎠⎞⎜⎝⎛+++−−−=Θ23132111)())1(1(ϕϕbhbbbtc. The multipliers are given below: 1. For a change in real reserves: 0)1(]/)/1[(33132>Θ⎟⎠⎞⎜⎝⎛−++=ΔΔθϕϕθbhbbPRY 2. For a change in real money demand: 0132<Θ⎟⎠⎞⎜⎝⎛+−=ΔΔhbbYϕμ Note: 030<Θ−=ΔΔbYϕ 3. For a change in real credit supply: 00000>⎟⎟⎠⎞⎜⎜⎝⎛ΔΔ×⎟⎟⎠⎞⎜⎜⎝⎛ΔΔ=ΔΔλϕϕλYY since 000<⎟⎟⎠⎞⎜⎜⎝⎛ΔΔλϕ 4. For a change in real credit demand: 00000<⎟⎟⎠⎞⎜⎜⎝⎛ΔΩΔ⎟⎟⎠⎞⎜⎜⎝⎛ΔΔ=ΔΩΔϕϕYY since 000>⎟⎟⎠⎞⎜⎜⎝⎛ΔΩΔϕ 5. For a change in commodity demand/gov’t. spending: 0)()1(11123132111>+++−−−≡Θ=ΔΔϕϕbhbbbtcGOY An additional multiplier is for a change in the risk of the marginal investment project: 043<Θ=ΔΔϕbZY Comparative statics (i.e., for the impacts on the 5 shocks above, on four variables, namely Y, M, L, and R) are summarized in the table below. Source: Bernanke and Blinder (1988) ⎩⎨⎧⎥⎦⎤⎢⎣⎡++−−⎟⎠⎞⎜⎝⎛⎟⎠⎞⎜⎝⎛−+++ΛΘ=030132433313200)()/1()1(1ϕμϕϕθθϕϕbhbbZbPRbhbbY (10)5 In the Figure below, shocks to the riskiness of the marginal investment project (Z increases) or to the money multiplier ((1/θ) and hence (1/θ)R declines) are shown: • If riskiness of the marginal investment project rises (Z), the CC curve shifts in. • If some financial institutions fail, or wish to lend less, then λ0 falls, and the CC shifts in. • If the money multiplier (1/θ) falls, both the CC and LM curves shift in. Here, we take Z as exogenous. But if Z