Topic 4: Financial markets and the macroeconomy Part 2: The portfolio model with money. Øystein Børsum, Temporary lecturer, University of Oslo

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1 Sub-topics: Topic 4: Financial markets and the macroeconomy art 2: The portfolio model with money Øystein Børsum, Temporary lecturer, University of Oslo The extended portfolio model: Money and the exchange rate. Money supply: Definition and its role in monetary and exchange rate policy. Exchange rate policy/monetary policy regimes. Reading: OEM Ch. 3.1, B&W ch April 1, Model specification Two simplifications compared to Ch 1.1: Sectors: rivate investors, government and foreign investors Financial assets: Domestic bonds and foreign assets. Domestic money paying no interest. Held for transaction purposes. Foreign investors only demand USD assets (not kroner bonds nor money) Domestic investors are the only ones to hold domestic money rivate Government Foreign Sum Money (kr) M M 0 0 Kr bonds B B 0 0 USD assets F p F g F 0 Net assets M + B + EF p EF g M B EF 0 Tabell 1: Balance sheet with money (Tab 3.1 in OEM)

2 Endogenous: W g,w p,w,f, F p,r,e e +3depending on regime. B + M + EF p M B + EF g F = B 0 + M 0 + EF p0 = M 0 B 0 + EF g0 = W p (3.1) = W g (3.2) = F 0 = W (3.3) r = i i e e (3.4) e e = e e (E) e 0 e < 0 (3.5) M = m(i, Y ) m i < 0 m Y > 0 (3.6) B = W p f(r, W p ) m(i, Y ) (3.7) EF p = f(r, W p) f 0 r < 0 f 0 W > 0 (3.8) F g + F p + F =0 (3.9) (note: 10 endogenous variables, not 12, since only 10 independent equation, explained on page 65 in OEM). Exogenous: i,y,,, M 0,B 0,F p0,f go, F +2depending on regime. Regime-dependent variables: E,F g,m,b,i Equlibrium in the market for foreign exchange Theroleofmoneysupply Consider F g exogenous to find the properties of the supply curve from F g = F F p (3.10) F g = F 0 E f(i i e e (E), B 0 + M 0 + EF p0 ) (Insert (3.1), (3.4), (3.5) and use F = F 0 to obtain 3.10) M B + EF g = M 0 B 0 + EF g0 = W g At the time of a trade dw g =0and de =0, so the central bank s trading constraint is: (3.11) dm = EdF g db The slope of the supply curve is: (3.11) S E = F g E = 1 E [F p0(1 f W )+f r e 0 e] S E > 0 under the same set of condition as in the first model. where dm = M M 0, df g = F g F g0 and db = B B g0. Fundamental money-supply function of an open economy. It links a change in the money supply to changes in other stocks.

3 Sterilisation The degree of sterilization in monetary policy denotes how much B is changed when there is a change in F g.coefficient of sterilisation: s = db EdFg s =1: Full sterilisation. s =0: No sterilisation. No sterilisation: The link df g dm is not sterilized by bonds sales. db =0 equivalent with dm =1 EdF g EdF g Full sterilisation: The link is broken (df g 9 dm). Domestic money supply is insulated from foreign exchange interventions. db =1 equivalent with dm =0 EdF g EdF g Overview of key policy regimes Exchange rate No sterilisation Full sterilisation Fixed rate Regime II: (E,B) exogenous. Regime III: (E,M) exog. Monetary policy must accomodate exchange rate policy Sterilisation enables independent monetary policy Floating Regime V: (F g,b) exogenous. Regime VI: (F g,m) exog. rate Choice of portfolio has full effect Monetary policy has no effect on monetary policy and on foreign exchange reserves theexchangerate Tabell 2: olicy regimes (Tab 3.2) Regime V and VI are equivalent as long the there is a clean float df g =0. "Left-out" regime: (E,F g ) exogenous. Fixed exchange rate with fixed foreign reserves. Monetary policy must accomodate exchange rate policy through the use of i(m). Exogenous variables are either monetary or exchange rate policy targets, or instruments set aside to attain other target variables (not specified in this model). Solving the model Two-step procedure: 1. Determine the interest rate. 2. Given the solution for the interest rate, find the solution for E or F g from the equilibrium in the market for foreign exchange.

4 Step 1: Determining the interest rate When M is exogenous: i is determined in the money market (3.6). This is the case for regime III, and for V and VI with clean float. Also relevant for "left out" regime where i determines M. (Remember: Y and are exogenous and constant in the short run) When M is endogenous: i is determined in the domestic bond market (3.7). This is the case for regime II. Equilibrium in the domestic bond market (insert (3.1), (3.4), (3.5) and (3.6) into (3.7) to obtain 3.12): (3.12) B = M 0 + B 0 + EF p0 f(i i e e (E), M 0 + B 0 + EF p0 ) m(i, Y ). M = m(i, Y ) M = 1 m i < 0. B = (f r + m i ) > 0 Demand for foreign exchange and demand for money are decreasing in i. Remaining wealth is in bonds, so demand for bonds is increasing in i. Step 2: Solving for E or F g from the foreign exchange market equilibrium Example of monetary policy analysis in regime III: Fixed exchange rate with sterilisation Fixed rate regime: E is constant. Derivation of (3.14) gives F g = E f r > 0 Floating rate regime (clean float): F g is constant. Implicit derivation of (3.14) gives E = f r < 0 (1 f W )F p0 + e 0 ef r Suppose the government wants monetary expansion (increase M 1 billion kroner) to stimulate the real economy. Uses market operations (M is exogenous, the instrument B is endogenous). Effect on i from money market equilibrium (3.12): M = 1 < 0. m i Effect on B from the money supply function. db = EdF g dm implies: db dm = E df g dm 1

5 As the interest rate falls, the central bank must sell foreign currency to support the exchange rate (the supply curve of foreign currency is shifted leftwards): df g dm = F g M = E f 1 r = 1 f r < 0 m i E m i This means that db/dm < 1: The central bank must buy bonds for more than 1 billion in order to increase M by 1 billion since reserves are worn down. Role of capital mobility: df g dm = 1 E f r m i fr Clean and managed float Clean float (df g =0): dm > 0 is achieved by market operations db = dm. Effect: i & (money market) and E % (market for foreign exchange). Effect on E depends on degree of capital mobility: de di = f r (1 f W )F p0 + e 0 ef r fr 1 e 0 e Full sterilization is impossible when capital mobility is perfect: The central bank cannot control the money supply. Managed float (float with interventions): An important left out regime Regime V (interventions without sterilisation): dm = EdF g > 0 and db =0. Leadstoi & and E %. Foreign exchange market: Negative horizontalshiftinthes-curve,anddemandincreases. Bothimplyhigher E (depreciation). The policy work also with high capital mobility, since i is affected. Regime VII (sterilised interventions): db = EdF g > 0, dm =0. No change in i. E % since F g increases (demand for foreign exchange). erfect capital mobility takes away the effects of sterilized interventions. Characterised Sweden and Norway in the 1990s + several other countries. Both F g and E exogenous with i and M endogenous. Allows a fixed exchange rate while freezing F g at a certain level. Monetary policy accomodates the exchange rate policy. dm is achieved by market operations db = dm. High (short-term) interest rates may be necessary to fend off speculative attacks. In the model, i is determined by the equilibrium condition for the market for foreign exchange. Graphically, the regime can be analysed using the Ei-curve along with a the money-market graph.

6 Model formulation with perfect capital mobility ossible regimes: No separate asset demand functions. ALL capital flows to where expected returns are highest. The model reduces to: M = m(i, Y ) (3.13) (0.1) r = i i e e (E) =0 1. Use the interest rate to target E (given e 0 e 6= 0) 2. Clean float with M targeting 3. Clean float with i-targeting (e.g. inflation targeting with i as instrument) Note: The central bank can set reserves wihtout any effect on the exchange rate. Fixed rate regime: i and M endogenous. Floating rate regime: i and E endogenous. What is money? Next time: Fixed income assets (bonds) and the term structure of interest rates Several possible definitions. i) Stock of base money,m0: Notes and coins issued by the central bank ii) Through private banks money creation process: Reason as if M in the economic model corresponds to a broader definition of money, M1,M2 or M3. Builds on the money (and credit) multiplier: Each time a bank issues a loan, reserve requirements also creates a deposit. In the portfolio model: "Money" is a non-interest bearing asset (like M 0). "Kroner bonds" are not actually bonds but an interest bearing bank deposit (included in M2).

7 TheslopeoftheEi-curve Calculation of the partial derivative E/ from (3.14): " f(r, Wp ) E 0= + ½ f E 2 r (1 e 0 E e E )+f W F p0 ¾ # E SimplifybyusingF p = f(r, W )/E. Set F p = F p0 (since both F g and F are constant). Solve for E/: E = f r < 0. (1 f W )F p0 + e 0 ef r Interpretation in terms of a coefficient of capital mobility and a portfolio rebalance effect: γ =(1 f W ) EF p0, κ = f r, E κ = E (1 f W )F p0 E e0 eκ κ = γ 1 E e0 eκ 1 = γ κe e0 e The effect of selling bonds under a fixed exchange rate The money supply is not controlled (M is endogenous). The central banks buys bonds from the public ( open market operation ) hence increasing money supply (monetary expansion). Corresponds to regime II. The effect on i is found from (3.13) di db = 1 (f r + m i ) < 0 minus, since dm = db, from the money demand function (3.10), dm > 0= db < 0. The market equilibrium glides down along the B d -curve in Figure 3.2 in OEM. Assume that the initial increase in M was 1billion (if db = 1bill). In the new equilibrium: dm db = m 1 i (f r + m i ) = m i (fr + m i ) < 1 since F g is reduced to restore equilibrium in the market for foreign exchange. df g db = [dm db +1]= [ (f r + m i ) ] < 0. (Supply of foreign currency is reduced by i &. In order to keep E constant, F g must fall by the same amount). In the analysis of Regime III, full sterilization, we saw that monetary policy had no effect on the interest rate if capital mobility is perfect. f r

8 How is the regime with no attempt to sterilise affected? From (3.17) dm db = m i (f r + m i ) 0. f r since f r means that F g falls by the same amount as Bs. From (3.18): E df g db = [ f r (f r + m i ) ]= [ 1 (1 + m i /f r ) ] 1. f r Hence, again as a result of the link between foreign currency reserves and the money supply, perfect capital mobility makes monetary policy ineffective also in Regime II. Formally: di db = 1 (f r + m i ) 0 f r