The bank-lending channel: The IS-BL model Christian Groth - PowerPoint PPT Presentation

The bank-lending channel: The IS-BL model Christian Groth University of Copenhagen November 21, 2016 C. Groth (University of Copenhagen) 11/2016 1 / 10

directly granted f inancial saving credit credit indirect credit intermediated credit Banks End-users: gov- withdrawals long-term Households (transform liquid deposits ernment, borrow- interest incl. into long-term loans) ing households and firms. profit profit Figure: A stylized financial system. C. Groth (University of Copenhagen) 11/2016 2 / 10

i B = bond interest rate (one-period bonds) i L = bank lending interest rate (the “lending rate”), D = deposits of the non-bank private sector (a stock, earns no interest), ρ = required reserve-deposit ratio, ρ ∈ [ 0 , 1 ) , exogenous, M 0 = monetary base, mm = the money multiplier, M 1 ≡ mm · M 0 = money supply in the sense of demand deposits in banks (a stock, earns no interest), E ≡ M 0 − ρ D = excess reserves (a stock, like ρ D earning no interest), L s = supply of bank loans, σ = perceived riskiness of offering bank loans, a shift parameter, B = value of the stock of government bonds held by the private sector, B b = value of government bonds held by the banks, B n = value of government bonds held by the non-bank public, W ≡ M 0 + B = aggregate nominal financial wealth of private sector, P = price level, exogenous, P = 1 , Y = real aggregate output, G = real government spending on goods and services, a policy parameter, τ = “fiscal tightness”, a policy parameter. C. Groth (University of Copenhagen) 11/2016 3 / 10

Table 2. Balance sheet of the central bank (CB). Assets Liabilities Currency (here = 0 ) ¯ B − B = gov. bonds held by CB Deposits held by banks (here = M 0 = ρ D + E ) Gold Net worth Total (= D ) Total = Table 3. Merged balance sheet of the commercial banks. Assets Liabilities M 0 = ρ D + E = reserves (in CB) D = liquid deposits held by the non-bank public L s = loans to the non-bank public Long-term debt (here = 0) B b = value of gov. bonds held by Net worth (here = 0 ) commercial banks Total = Total C. Groth (University of Copenhagen) 11/2016 4 / 10

The supply of bank loans M 0 + L s + B b ≡ D . Subtract required reserves, ρ D , to get disposable deposits: M 0 − ρ D + L s + B b ≡ E + L s + B b ≡ ( 1 − ρ ) D , 0 ≤ ρ < 1 . e ( i B ) = desired fraction of disposable deposits held as excess reserves. Assume: e � ( i B ) < 0 . E = e ( i B )( 1 − ρ ) D , Supply of bank loans: L s = � ( i B , i L , σ )( 1 − ρ ) D , � � i B < 0 , � � i L > 0 , � � σ < 0 . The remainder placed in government bonds: B b = ( 1 − ρ ) D − ( E + L s ) . C. Groth (University of Copenhagen) 11/2016 5 / 10

The supply of broad money Currency is ignored. The monetary base is M 0 = banks’ reserves held in the CB = ρ D + E . The inverse of money multiplier = reserve-deposit ratio: D = ρ D + E mm = M 0 1 = M 0 1 = ρ + e ( i B )( 1 − ρ ) ≡ mm ( i B ) . M s D 1 The money supply then is M s mm � ( i B ) > 0 . 1 = D = mm ( i B ) M 0 > M 0 , C. Groth (University of Copenhagen) 11/2016 6 / 10

Demand for broad money Table 4. The balance sheet of the non-bank private sector. Assets Liabilities L d = bank loans D = bank deposits B n = gov. bonds held by non-bank public W = net worth Total = Total L d L � Y > 0 , L � i B > 0 , L � = L ( Y , i B , i L ) , i L < 0 , M d M � Y > 0 , M � = M ( Y , i B ) , i B < 0 , 1 L d + W − M d B n = 1 , W ≡ M 0 + B b + B n ≡ M 0 + B . C. Groth (University of Copenhagen) 11/2016 7 / 10

General equilibrium Equilibrium in the three asset markets. Walras’ law of stocks. Equilibrium in the output market: D = C ( Y p , i B , i L , W , τ ) + I ( Y , i B , i L ) , 0 < C Y p ≤ C Y p + I Y < 1 , Analysis Let M 0 be given (monetary policy instrument). Derivation of MP curve. Derivation of IS curve: combine equil. in output market and market for bank loans. C. Groth (University of Copenhagen) 11/2016 8 / 10

i B IS MP Y i B IS σ , , M G 0 MP 0 M Y Figure: The IS-MP cross (for fixed M 0 , σ , τ , and G ) . A higher σ shifts the IS curve to the stippled position. Suppose σ (the perceived riskiness of supplying bank loans) goes up: � i L − i B ↑ σ ↑⇒ i L ↑⇒ i B ↓ (for fixed Y ) ⇒ IS curve ↓⇒ . Y ↓ C. Groth (University of Copenhagen) 11/2016 9 / 10

Expansionary monetary policy: ∆ M 0 = − ∆ B > 0 . Affects output through two channels: The credit channel : � Y ↑ bank loans ↑⇒ i L ↓⇒ D ↑⇒ IS curve rightward ⇒ i B ↑ The interest rate channel : M 1 ↑⇒ i B ↓ (for fixed Y ) ⇒ MP curve ↓⇒ Y ↑ . Total effect: ∆ M 0 = − ∆ B > 0 ⇒ i L ↓ and Y ↑ while sign of effect on i B ambiguous. C. Groth (University of Copenhagen) 11/2016 10 / 10