Monetary Macroeconomics & Central Banking Lecture /

Transcription

1 Monetary Macroeconomics & Central Banking Lecture /

2 Outline 1 IS LM with banks 2 Bernanke Blinder (1988): CC LM Model 3 Woodford (2010):IS MP w. Credit Frictions

3 Literature For Sections 1 and 2, see Bernanke & Blinder (1988), for Section 3 read Woodford (2010), see also Curdia & Woodford (2010).

4 IS LM with banks We stick to the Keynesian IS LM framework. However, we explicitly introduce banks into the model. We begin with modeling banks in a rather simplistic way. Households do not hold money, M, directly, but demand deposits D with banks. 1 / 30

5 Household deposit demand Suppose deposits can be equally well used for transaction purposes as money balances. Households allocate their wealth between deposits and bonds. Bonds are synonymous for all other types of fixed income financial assets. All fixed income assets are viewed as perfect substitutes. Household s demand for deposits D D p = D(Y, i) (1) with D Y > 0 and D i < 0. 2 / 30

6 Banks are assumed completely passive. Banks Issue deposits, hold bonds (of firms and government) and reserves. Bank s balance sheet reads R + B D b = D S, with R being central bank reserves, Bb D total bond demand from banks and D S bank s issuance of deposits. Assume money multiplier, R = µd S D S = R µ where µ (0, 1) denotes the reserve ratio. 3 / 30

7 Aggregate production Labor demand Consumption Investment Output use Portfolio balance Structural equations Y = F(K, N ) (2) w p = F N (K, N ) (3) C = C(Y T, i π) (4) I = I (i π) (5) Y = C + I + G (6) R = µpd(y, i) (7) 4 / 30

8 Complete model The model contains eight exogenous variables {G, T, K, R, B, π, w, µ} and six endogenous variables {Y, N, C, p, i, I } which are determined by equations (2) (7). 5 / 30

9 Solving the model The model is identical to the previous IS LM, except we assume the existence of financial intermediaries called banks, M /p replaced by R/pµ, we carry an additional parameter, µ, the reserve ratio. Otherwise, solution exactly the same, all comparative static results carry over. 6 / 30

10 CC LM Model Banks provide funding by supplying loans. In contrast to previous model, loans and bonds are imperfect substitutes. Bank balance sheet R + L S + B D b = D S, where L S is loan supply. Still the sin, mechanistic money multiplier, D S = R/µ. Thus, L S + B D b = 1 µ µ R. Allocation of loanable funds from bank s portfolio optimization: L S = l(i B, i L )R and B D b = β(i B, i L )R, where l( ) + β( ) = 1 µ µ, r L is loan rate and l ib < 0 < l il and β il < 0 < β ib. 7 / 30

11 Investment and Loan Demand Investment depends on bond rate i B and loan rate i L, I = I (i B, i L ) = BF(i S B, i L ) + L D (i B, i L ) (8) with I ib, I il < 0, Li D L < 0 < Li D B and Bi S B < 0 < Bi S L. Equation (8) replaces (5). Furthermore, we add the loan market to the model. Loan market equilibrium L D (i B, i L ) = l(i B, i L )R 8 / 30

12 Structural equations Structural equations are given by (2) (4) plus (6) and (7) We replace equation (5) with I = I (i B, i L ), (9) which depends negatively on bond and loan rates. We add the equilibrium condition for the loan market, L D (i B, i L ) = l(i B, i L )R (10) Model displays interdependencies among all variables. Analyze by using LM and CC curves. 9 / 30

13 LM Curve The LM curve is an equilibrium locus. It shows combinations of r B and Y where demand and supply of real balances are equal, given that production function and labor demand equation hold. The LM curve is determined by ( D Y R/µp + F NN F 2 N ) dy = dµ µ dr R + dw w + D i B R/µp di B, (11) Its slope is given by dr B dy = LM ( F NN F 2 N ) R µp D Y > 0. D ib 10 / 30

14 CC Curve The CC curve is an equilibrium locus. It shows combinations of i B and Y where goods and credit markets are in equilibrium. Derivation of CC curve: Take total differential of S(Y, i B ) = Y C(Y, i B ) = I (i B, i L ) + G, Note, for simplicity: π = 0. (1 C Y ) dy + C Y dt C ib di B = I ib di B + I il di L + dg... and use total differential of equation (10), 1 ( ) di L = l il R Li D (Rl ib Li D B )di B + ldr, L to get equation determining the CC curve, (1 C Y ) dy + C Y dt dg = ( = I ib + C ib I i B (Rl ib Li D ) B ) I il l l il R Li D di B L l il R Li D dr L 11 / 30

15 CC Curve Slope of CC curve given by di B 1 C Y dy = < 0, CC I ib + C ib I i L (Rl ib Li D ) B l il R Li D L... because numerator (1 C Y ) > 0, and denominator strictly negative, I ib < 0, C ib < 0, I il < 0, Rl ib L D i B < 0 and l il R L D i L > / 30

16 Monetary transmission Increase in monetary base, dr > 0. As in previous version: Portfolio balance disturbed, i B declines and investment increased (LM curve moves rightwards). Additional channel: Loan supply increases, i L decreases, investment rises further. (CC curve moves rightwards.) Opposing effect on i B. Lower loan rate stimulates demand for bonds, i B increases. Total effect on i B ambiguous. But total effect on Y positive, thus total effect on i L must be negative. Punchline: Monetary policy can effectively stimulate aggregate output without strong effect on bond rates. 13 / 30

17 i B LM 0 LM 1 i B1 i B0 CC 0 CC 1 Y 0 Y 1 Y 14 / 30

18 Critique Several points of criticism: 1 Demand deposits are not remunerated. 2 Households also borrow. 3 Lending is risky. 4 Central banks do not use the monetary base as instrument. They use a short term interest rate. We consider a model by Woodford (2010) that accounts for these points. 15 / 30

19 IS MP w. Credit Frictions For simplicity we dispense with the production side and the labor demand equations. We further assume the price level to be exogenously given and we fix it at p = 1. The remaining structural equations for the real economy are an investment equation like (5), a consumption function like (4) and the goods market equilibrium (6). Moreover, we dispense with the assumption that the central bank can control the money supply and assume instead that the central bank controls an interest rate (more on that later). 16 / 30

20 Financial Intermediation & Interest Rates Households save and borrow. Firms pay surpluses to households in form of dividends and borrow to make investment into fixed capital (δ = 0, no inventory investment etc.). Households do not lend directly, but via financial intermediaries (banks, investment banks, mutual funds, trusts, mortgage institutions are assumed to be identical). Nominal borrowing rate denoted i B nominal rate paid to savers denoted i S. Again, set π = 0. Thus r B = i B, and r S = i S. The spread between deposit and lending rate is denoted ω, i.e. ω = i B i S. 17 / 30

21 Consumption and Investment Since households save and borrow, consumption function becomes C = C(Y, i S, i B ) with C Y > 0, C is, C ib < 0. Using i S = i B ω, consumption function becomes Since firms only borrow, which we write as C = C(Y, i B ω, i B ) (13) I = I (Y, i B ) with I Y > 0, I ib < 0, I = I (Y, i B ). (14) Note that here investment also depends on Y. 18 / 30

22 Goods Market Equilibrium Equilibrium in the goods market obtains if, S = Y C = I + G. i.e. S = Y T C = I + G T. By using the respective functions, S(Y, i S, i B ) = I (Y, i B ) + G. (15) Endogenous variables are (Y, i S i B ω). ω will be determined on the loan market. 19 / 30

23 i S, i B I (i B ) S(i B, i S ) i B0 ω i S0 I, S 20 / 30

24 Financial Intermediation Consider demand and supply for financial intermediation. Saving households do not lend directly but via the financial sector. Financial intermediation is costly. Financial intermediaries take savings and use them to produce loans. Input factors are monitoring skills and expertise, screening skills, loss absorption capacity etc. The supply of financial intermediation is given by L S = L S (Y, ω, σ) with L S Y > 0, L S ω > 0, L S σ < / 30

25 Demand for credit is given by sum of household and firm demand. Suppose fraction (1 η) of households saves and fraction η dissaves. Dissaving households consume C dis (ηy, i B ). Their marginal propensity to consume out of income is C dis Y = 1. Aggregate demand for credit becomes L D (Y, i B ) = C dis (ηy, i B ) ηy + I (Y, i B ). 22 / 30

26 Credit Market Equilibrium Equating demand and supply for financial intermediation, L S (Y, ω, σ) = L D (Y, i B ) = L D (Y, i S + ω). Solve for ω, ω = ω(y, i S, σ) with ω Y 0, ω is < 0, and ω σ > 0. Sign of ω Y deserves comment. Determined by I Y L S Y, which is positive if we assume that a marginal increase in income leads to marginal increase in investment demand larger than what financial intermediaries are willing to finance (at the given interest rate). We henceforth assume ω Y > / 30

27 IS curve We can use ω(y, i S, σ) to derive an IS curve (actually rather a CC curve) that is the locus of combinations of Y and i S where the goods and the credit market are in equilibrium. Substituting i B by i S + ω(y, i S, σ) in equation (15) yields S(Y, i S, i S + ω(y, i S σ)) = I (Y, i S + ω(y, i S, σ)) + G. (16) The slope of the IS curve is given by di S dy = (1 C Y I Y ) ω Y (C ib + I ib ) < 0. IS C is + C ib + I ib 24 / 30

28 Monetary Policy Note that we have not talked about the money market so far. We abandon the assumption that the central bank can control the money supply M. Rather, we assume that central bank targets rate i S, by using a Taylor Rule, i S = φ Y (Y Ŷ ) + φπ (π e ˆπ), where Ŷ is the natural level of output, ˆπ the inflation target, Φ Y > 0 and φ π > / 30

29 Digression on the Taylor Rule In 1993, John Taylor proposed that US monetary policy can best be described by an interest rate feedback rule of the form i = π +.5y +.5(π 2) + 2, where π is the inflation rate, y is the deviation of output from a target. Taylor s proposal had a considerable impact on economists thinking about monetary policy as well as on the conduct of monetary policy by central banks. On positive grounds, Taylor claimed that his rule captured FED s actions during On normative grounds, Taylor argued that his rule fitted actual policy during a period where US monetary policy was quite successful. 26 / 30

30 Twenty years after Taylor s proposal, his rule and variants of it have standard in macroeconomic monetary models. Central banks have almost never used the money supply as an instrument. They exercise control over an interest rate (usually a very short-term rate). Taylor rule describes active stabilization policy, i.e. responses it describes serve to stabilize inflation and output gap. Stabilization of both variables is in general desirable. Following the rational expectations revolution and the expanding literature on time consistency, a rule based approach to policy has become central tenet of macroeconomic policy prescriptions. (More on this later!) 27 / 30

31 ...back to model We use a variant of the Taylor rule, i S = φ Y (Y Ŷ ) + φπ (π e ˆπ), which allows to derive an MP curve (rather than an LM curve). The slope of the MP curve is given by di S dy = φ Y > 0. MP That φ π > 1 is important and will be covered in the next lecture. 28 / 30

32 i S IS MP i S0 Y 0 Y 29 / 30

33 Comparative Statics Comparative statics and the mechanics of the model are left for the exercise. 30 / 30