Week 8

The Reserve Bank and the Economy Reference: Bernanke, Olekalns and Frank - Chapter 8 Key Issues Demand for money Bond prices and yields Money Market Cash Rate and Bond Rates PAE and the Real Interest Rate Policy Reaction Function

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Demand for Money How much of their wealth will an individual hold in the form of money? Portfolio allocation decision Given wealth of $50,000, how is this allocated among various assets? Money, Bonds, Equities, Housing, etc.

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Risk vs. Expected Return Risky assets need to pay a higher expected return to induce individuals to hold them. Benefits and Costs of Holding Money Main benefit from holding money is its usefulness in

making transactions – medium of exchange function Transactions demand for money can be affected by

financial innovation eg. credit cards

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Cost of Holding Money Many forms of money pay zero interest (currency) or very low rates of interest (transactions or demand accounts). There is an opportunity cost of holding money, which is the return that could have been earned by holding wealth in the form of other assets:

Bonds pay a fixed amount of interest each period Equities pay dividends

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Some Simplifying Assumptions Assume: Money pays a zero nominal interest rate The (expected) nominal return on other assets is

positive Represent the nominal interest rate on other assets by i

Other things equal, an increase in the nominal interest rate will raise the opportunity cost of holding money and reduce the amount demanded

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Influences on the Demand for Money The demand for money by households and firms is affected by three main factors: Nominal interest rate, (i) Money demand is negatively related to i

Real output (or GDP), (y) Money demand is positively related to y

Price level, (P) Money demand is positively related to P

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Money Demand Curve Nominal Demand Real Demand

),( yiLPM D ),( yiLP

M D

Interest rate i Money demand curve M

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A Fall in the Interest Rate Leads to an Increase in the Quantity of Money Demanded Interest rate i Money demand curve M

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Shifts in the Demand for Money Change in real income Change in price level (only if we measure nominal

money on the horizontal axis).

i Increase in P or y Md’ Md M

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Technological Change and Financial Innovation Both of these factors may produce shifts in the demand for money. Example: Development and spread of ATMs

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Supply of Money To complete the model of the money market we need to consider the supply of money. There are two polar cases that we can consider; The supply curve for money is vertical and its position

is determined by the actions of the RBA The supply curve for money is horizontal and the

RBA supplies money on demand (at a given i )

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Control of the Money Supply: Monetary Target Ms

i

0i Md 0M M RBA is able to control the money supply (currency and deposits) by OMO with the public

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Asset Prices and Yields The yield or return on a financial asset is inversely related to the asset’s price. Bond Principal = amount that is originally borrowed on the bond Coupon payment = regular dollar payment of interest on the bond Coupon rate = Coupon Payment Principal

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Bonds Continued Term of bond = length of time before bond has to be repaid (terms can range from 24 hours to 30 years) Principle (or face value) = $100 Term = 1 year Coupon = $5 per year Coupon rate = 5%

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Bond Prices and Interest Rates Bonds do not have to be held until maturity, but can be bought and sold on the bond market. What determines the price of a bond? Consider a two year bond with a face value (initial

price) of $1000. The annual coupon rate is 5%, implying there are two

annual coupon payments of $50.

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What is the price of this bond at the end of the first year? Bond price depends on the current interest rate Suppose that the market interest rate has risen to 10%. At the end of the year the owner of the two year bond will receive $1050 (principle plus coupon). Since new bonds are paying 10%, the bond price on the old bond must adjust so that its interest rate is 10%. Bond Price =

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Bond prices and interest rates are inversely related If market interest rates had stayed at 5% then,

Bond Price = but when they rise to 10%

Bond Price = The bond price falls.

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[SAMPLE MCQ QUESTION] One year before maturity, the price of a bond with a principal amount of $1000 and a coupon rate of 5% paid annually fell to $981. The one-year interest rate: A. rose to 8.5% B. rose to 7.0% C. rose to 6.0% D. remained at 5%

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Reduce Ms and Raise Interest Rate OMO: RBA sells bonds to the public in exchange for M

i M

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Adjustment Process At the initial interest rate their will be an excess

demand for money (and an excess supply of bonds) The excess supply of bonds will put downward

pressure on bond prices and as we have seen this will require a rise in interest rates

This process will continue until the demand for

money has been reduced to equal the lower supply

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Endogenous Money Supply: Interest Rate Target

i

0i Ms Md 0M M An alternative to controlling the money supply is for the RBA to target the interest rate (on bonds).

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Interest Rate Target Given the demand for money function, the RBA will supply whatever quantity of money that is required to achieve its target value 0i for the interest rate. Shifts in money demand are just accommodated by the RBA at the interest rate target. At any time the RBA can either control the money supply or set a value for the interest rate.

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Monetary Policy and the Money Market The above model indicates two ways in which the RBA might operate monetary policy via the money market. However in practice, we have seen in Week 7 lectures that the RBA: chooses to target a very short-term interest rate

(overnight interbank rate) and undertakes its OMO mainly with the banks

What are the implications of a cash rate target for longer-term interest rates?

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Market for 90-Day Bills 90-day commercial bill (short-term bond) price of Supply 90-day bill Demand Qty of bills

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Demand and Supply Supply curve indicates the willingness of firms to

supply bills (ie. to borrow for 90-days) Recall that when bill price is high, the interest rate on

bills is low so firms want to supply more bills (ie. borrow more).

Demand curve indicates the willingness to lend to

firms (ie. demand for 90-day bills) Recall that when bill price is high, the interest rate on

bills is low, so no one is willing to lend much (ie. demand for bills is relatively low).

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Equilibrium price of Supply 90-day bill Pe Demand Qe Qty of bills

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The Effect of an Increase in the Cash Rate on the 90-Day Bill Market In the previous figure Pe represents the equilibrium price for 90-day bills. This will also correspond to an equilibrium interest rate for 90-day bills. Now suppose the RBA raises its target level for the cash rate. How does this affect the market for 90-day bills? Banks (and some other financial institutions) are able to participate in both the overnight cash market and in the commercial bill market.

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When Cash Rate Increases…. The demand for commercial bills (the willingness to lend to firms) will tend to fall: Demand curve will shift to the left. This occurs because some lenders will leave the bill

market in favour of the higher returns in the overnight cash market.

The supply of commercial bills (the demand for 90-day loans) will tend to rise: Supply curve will shift outwards. Some borrowers in the overnight cash market will

now seek funds in the 90-day bill market, due to the higher cash rate

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The Price of 90-Day Bills Falls and Consequently the Interest Rate on 90-Day Bills Rises price of S0 90-day bill Pe D0 Qe Qty of bills

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Arbitrage While RBA targets a very short interest rate, changes in cash rate eventually lead to changes in longer-term interest rates.

Market Rates = Cash Rate + Premium Premium will tend to reflect risk or liquidity factors.

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Nominal and Real Rates Recall that: ir RBA has control of nominal interest rates, but it is the real rate that matters for saving and investment decisions. If inflation is sticky in the short-run, then RBA will be able to influence the real interest rate as well as the nominal rate. We assume this is the case in the following analysis.

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PAE and the Real Interest Rate In our model of income determination we have allowed PAE to depend on the level of real output. We now want to allow a role for the real interest rate to influence PAE. 2 main channels Higher real interest rates will lead households to defer

current consumption Higher real interest rates will raise the cost of capital

and reduce investment by firms

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Model for PAE Consumption rTYcCC )( Investment rII Assume (for simplicity) other variables are exogenous

GG XNNX

TT

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Planned Aggregate Expenditure rTYcCC )(

rII P GG

XNNX TT

NXGICPAE P Substitute and collect terms

cYrXNGITcCPAE ])([

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Implications cYrXNGITcCPAE ])([

Exogenous expenditure now depends on the real

interest rate For any given level of output, PAE will fall with a rise

in the real interest rate. If we assume that the RBA can set the real interest

rate, then we have a mechanism by which monetary policy can affect PAE and equilibrium output.

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Numerical Example Let: 500 XNGITcC , 1000)( and 8.0c

cYrXNGITcCPAE ])([ YrPAE 8.0]1000500[

If the RBA sets r=0.05 (5%)

YYPAE 8.04508.0)]05.0(1000500[ Equilibrium PAEY

YY 8.0450 eY

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Effect of a Rate Cut to r = 3%

YYPAE 8.04708.0)]03.0(1000500[ Equilibrium PAEY

YY 8.0470 e

newY Rate cut of 2 percentage points has increased equilibrium GDP by 100.

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Negative Output Gaps and Expansionary Monetary Policy PAE %)5( rPAE eY PY Y Contractionary Gap

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Negative Output Gaps and Expansionary Monetary Policy PAE %)3( rPAE %)5( rPAE eY PY Y RBA reduces real rate to close output gap

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Positive Output Gaps and Contractionary Monetary Policy PAE %)3( rPAE %)5( rPAE PY eY Y RBA raises real rate to close inflationary output gap

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[SAMPLE MCQ QUESTION] If planned aggregate spending in an economy can be written as PAE = 15 000 + 0.6Y – 20 000r, and potential output equals 36 000, what real interest rate must the Reserve Bank set to bring the economy to full employment? A. 0.02 B. 0.03 C. 0.04 D. 0.05

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Policy Reaction Function The above model suggests the RBA will set the level of the real interest rate as a function of the state of the economy. One way to characterise the behaviour of the RBA is with a policy reaction function. Example:

Taylor Rule ][5.05.001.0 P

P

yyyr

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A Policy Reaction Function for the RBA Assume (simplifying) that policy reaction function for the RBA only depends on inflation

r gr 02.0

0.04

0.02 0 0.01 0.02 0.03

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Note Equation indicates the level at which the RBA sets the

real interest rate for any given rate of inflation Positive slope implies that RBA raises the real rate as

inflation rises.