Economics 302 001 Spring 2011 University of Wisconsin Madison Menzie D Chinn Social Sciences 7418 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 1 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 ld 0 1 2 i 3Y P 1 0 1 2 i 3 Z D 1 ls P P 2 Loan supply is given by where Z is a measure of riskiness of the marginal investment project and is exogenous D is deposits and 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 0 Y hi 1 R P 3 where 1 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 i 0 1 1 R 1 Y h h P h 4 The CC curve is a conventional IS curve except that it depends upon the bank lending rate as well as the interest rate Y 0 b2 i b3 Where 5 1 1 c1 1 t1 b1 To determine what is one has to substitute money market equilibrium into the loan market equilibrium to obtain 2 0 1 2 i 3Y 0 1 2 i 3 Z D 1 P 6 Solving for the equilibrium loan rate one obtains the following relationship where linearity is assumed for simplicity 1 R 1 4Z P 0 1i 2 Y 3 7 Where 0 depends negatively on 0 which is the constant in the loan or credit supply equation and 0 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 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 Instead of working this out just note that the factors that increase 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 1 1 R 1 Y 1 c1 1 t1 b1 0 b2 0 Y b3 0 1i 2Y 3 1 R 1 4 Z h h P h 8 Notice the R is still present on the RHS and so the LM curve has to be substituted in again 1 1 R 1 Y 1 c1 1 t1 b1 0 b1 0 Y h h P h 1 1 R 1 b3 0 1 0 Y 2Y 3 1 R 1 4 Z h h P h Notice Y shows up two places on the RHS and 1 R in two places Factoring and solving for Y b b3 1 b b3 1 b b3 1 0 1 R b3 2 Y 2 b3 3 1 r b Y 1 b 1 t b1 0 2 b3 4 Z 2 h P h h Bringing the Y terms over to the LHS and then solving yields 3 Y0 1 b2 b3 1 1 R b2 b3 1 0 b3 3 1 b3 0 b3 4 Z 0 h h P 10 b b3 1 Where 1 c1 1 t1 b1 2 b3 2 h The multipliers are given below b2 b3 1 b3 3 1 h Y 1 For a change in real reserves 0 1 R P b2 b3 1 h 2 For a change in real money demand Y 0 Note Y b3 0 0 3 For a change in real credit supply Y Y 0 0 0 0 4 For a change in real credit demand Y Y 0 0 0 0 Y 1 GO 5 For a change in commodity demand gov t spending 0 since 0 0 0 0 0 since 0 0 1 0 b2 b3 1 1 c1 1 t1 b1 b3 2 h An additional multiplier is for a change in the risk of the marginal investment project Y b3 4 0 Z 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 4 In the Figure below shocks to the riskiness of the marginal investment project Z increases or to the money multiplier 1 and hence 1 R declines are shown LM R0 1 i LM R0 0 CC 0 Z0 R0 0 CC 0 Z1 R0 0 Y1 Y Y0 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 0 falls and the CC shifts in If the money multiplier 1 falls both the CC and LM curves shift in Here we take Z as exogenous But if Z depends upon the level of economic activity then one could have an adverse feedback loop wherein the initial shift inward of CC results in an additional increase in Z and hence further inward shift of CC If either financial institutions fail or the monetary multiplier …