Exogenous Money supply Endogenous Money supply The determination of the interest rate

Macroeconomic CSI: Instruments of monetarypolicy

Rodolphe Desbordes

http://www.rodolphedesbordes.com/

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Table of Contents I

1 Exogenous Money supply

2 Endogenous Money supply

3 The determination of the interest rate

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Textbook theory and economic reality

We have seen in the previous lecture that a policy tool to stabilise the economyis the manipulation of the interest rate r .

That is what Central Banks do! For instance, you can read the following on theBank of England’s website

The Bank of England’s Monetary Policy Committee today voted tomaintain the official Bank Rate paid on commercial bank reservesat 0.5%. (http://www.bankofengland.co.uk/publications/news/2010/068.htm)

However, in most textbooks, the story is less straightforward. We usually read

We have described the central bank as choosing the money sup-ply and letting the interest rate be determined at the point wheremoney supply equals money demand. (Blanchard Olivier, AlessiaAmighini and Francesco Giavazzi (2010). Macroeconomics, a Eu-ropean Perspective. Essex: Pearson Education Limited. p. 68)

The question is then: do central banks set the interest rate or money supply?

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Textbook story

1 The central bank sets the supply of money (Ms) to its preferred value.The volume is fixed

Ms = Ms

2 There is a demand for money in the economy (Md ) which dependspositively on prices P and real income Y (you need more money to domore transactions and/or when prices increase) and negatively on theinterest rate i (which is the opportunity cost of holding money):

Md = P×(kY − hi); k > 0, h > 0

3 There is a market for money, and as usual i is the outcome of theinteraction between Ms and Md such as Ms = Md

Ms = Md

Ms = P(kY − hi)

i =kh

Y − 1h

Ms

P

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The money market

Money Supply Ms

Interest rate i

Money

Money demand

i*

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Exogenous money supply and the quantity theory ofmoney

What I have just described is a regime of exogenous money: the central bankcontrols the money supply and let the interest rate be determined by the mar-ket.

Such a regime would fit well with monetarists, who believe that erratic changesin the money supply is the main cause of business cycles.

They advocate a simple rule based on the quantity equation, which relates thequantity of money to nominal income :

M︸︷︷︸ × V︸︷︷︸ = P︸︷︷︸ × Y︸︷︷︸Money supply Velocity Price level Real income

V is the velocity of money, i.e. the average number of times a unit of money isused in transactions over the course of the year.

Now if you believe as monetarists do, that a rise in M causes a rise in P, thenit makes sense to manipulate M such as you reach a particular inflation target,i.e. increase in P, given the growth rate of Y and constant V .BUT, if V is not constant, a given rise in M may not lead to the target rise in P.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Exogenous money supply and the velocity of moneyThe quantity theory tells us how much money is held for a given amount ofaggregate income, so you can interpret it as a theory of the demand for money:

Md V = PY

Md =PYV

V =PYMd

velocity is constant only if the money demand is stable. That would be thecase if

1 the rise in demand for money was proportional to the rise in incomespending.

2 the sensitivity of the demand for money to the interest rate was verylow, or at least constant.

3 no financial or technological innovations occurred (e.g. withdrawingcash using an ATM from a saving account).

If V is not constant, the central bank runs into troubles since it may over- orunder- supply the ‘correct’ amount of Ms.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The velocity of the monetary aggregate M2

http://research.stlouisfed.org/fred2/series/M2V

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Monetary targeting and money demand shocksMoney Supply Ms

Interest rate i

Money

Money demand

i*

Positive shock to Money demand

Negative shock to Money demand

i+

i-

With monetary targeting, the money supply is fixed and the interest rateis determined by the intersection of money supply with money demand.

Shocks to money demand will lead to rises and falls of the interest rate,creating large fluctuations in income (remember i influences I).

Hence monetary targeting can create undesirable fluctuations in theeconomy, especially when the economy is dominated by money shocks.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Interest rate targeting and money demand shocksMoney Supply Ms

Interest rate i

Money

Money demand

i*

Positive shock to Money demand

Negative shock to Money demand

M*M- M+

With interest rate targeting, the interest rate is fixed and money supplyis determined by the intersection of money demand with the interestrate line.Shocks to money demand will lead the central bank to actively decreaseor increase the money supply, but there will be no fluctuations inincome.Hence interest rate targeting can stabilise output, especially when theeconomy is dominated by money shocks.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Endogenous money story

1 The central bank sets the interest rate (i) to its preferred value.2 This interest rate determines the money commercial banks have to pay

to borrow base money (reserves R) from the central bank.3 Commercial banks want to make a profit. Hence their loans rate (rL) is a

mark-up over i

rL = (1 + m)×(i)

4 Commercial banks are willing to meet any demand for loans. Hence thebank credit supply (money supply) is perfectly elastic.

5 The demand for bank credit (money demand) depends on prices P,income Y and the loans rate rL:

Md = P×(kY − hrL)

6 Bank loans create bank deposits BD, which need to be backed up bymandatory or precautionary reserves supplied.

R = c×(BD)

7 The central bank will supply any base money required to meet thereserve demands of the banking system.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The endogenous money supply process

Whatever the money demand, the interest rate will remain the same.

However, the money supply will change according to the fluctuations incommercial banks’ demand for reserves.

Total money supply is thus governed by the demand for and supply ofcredit in the private sector.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The objectives of a Central Bank

A central bank usually cares about a) Inflation b) Output growth/Unemployment.

The Bank’s monetary policy objective is to deliver price stability –low inflation – and, subject to that, to support the Government’seconomic objectives including those for growth and employment.Price stability is defined by the Government’s inflation target of 2%.

http://www.bankofengland.co.uk/monetarypolicy/framework.htm

The Federal Reserve sets the nation’s monetary policy to promotethe objectives of maximum employment, stable prices, and moder-ate long-term interest rates.

http://www.federalreserve.gov/pf/pdf/pf_2.pdf

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Targeting the interest rate: The Taylor ruleThe economist John Taylor has suggested that his ‘Taylor rule’ provides a gooddescription of the behaviour of the Fed:

Interest rate target = Stabilising real interest rate

+Inflation + 0.5(Inflation gap) + 0.5(Output gap)

i0 = rs + π0 + 0.5(π0 − πT ) + 0.5(Y0 − Ye

Ye)

This rule tells us that1 If the economy is in equilibrium (no inflation or output gaps), the real

interest rate (r0 = i0 − π0) ought to be equal to the stabilising real rate ofinterest (r = rs) .

2 the Taylor rule is an activist rule. Positive inflation or output gap, ceterisparibus, leads to setting a higher real interest rate.

3 The presence of both gaps suggest that the behaviour of the centralbank is consistent with its two main objectives, to which it gives equalweight (0.5): price stability and minimising business cycle fluctuations ofoutput around its potential.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

Actual U.S. interest rate and the Taylor rulerecommendation

http://research.stlouisfed.org/publications/mt/20100901/mt_20100914.pdf

The Taylor rule describes reasonably well the behaviour of the Fed.It seems to be a reasonably good approximation of how a central bankacts.There are nevertheless some +/- divergences, which suggest overlyexpansionary or restrictive monetary policies.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The logic behind the Taylor rule I

IS curve: it showed that there was a negative relationship between thereal interest rate r and output Y .

So if the Central Bank raises the real interest rate r following a positiveinflation (π) gap, Y will fall.

The purpose of increasing r is to tame inflationary pressures. Thereforewe need to find a link between Y and π:

1 Okun’s Law: a fall in the output gap Y0−YeYe

will lead to a risein the unemployment gap U0 − Ue:

U0 − Ue = −ωY0 − Ye

Ye

2 A rise in unemployment means that workers have lessbargaining power. Hence, they will not be able to secure thesame nominal wage W0 =

W0−Wt−1Wt−1

increase as last year

(Wt−1).

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The modern (inertia-augmented) Phillips curveWe have seen that current wage inflation (W0) depends on

1 previous money wage increase.2 The level of unemployment U0.

We can write a wage inflation equation

W0︸︷︷︸ = ˆWt−1︸ ︷︷ ︸ − γ (U0 − Ue)︸ ︷︷ ︸Current inflation Past inflation Unemployment gap

Now, if we assume that firms increase their prices such as P0 = W0:

P0 = ˆPt−1 − γ(U0 − Ue)

π0 = πt−1 − γ(U0 − Ue)

And if we make use of Okun’s Law, we can write the modern Phillips curve:

π0︸︷︷︸ = πt−1︸︷︷︸ + αY0 − Ye

Ye︸ ︷︷ ︸Current inflation Past inflation Output gap ,and α = ω × γ

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The logic behind the Taylor rule IIThe Phillips curve tells us that a negative output gap (Y0 < Ye) needs to becreated to lower inflation.

π0 = πt−1 + αY0 − Ye

Ye

The Taylor rule tells us that a positive inflation gap requires a rise in real inter-est rate r0 above its stabilising level rs:

1 A rise in r0 has a negative impact on investment I1. y2 I1 falls, Aggregate Demand AD1 falls. y3 AD1 falls, output Y1 falls. y4 Y1 falls, unemployment U1 rises. y5 U1 rises, workers accept a lower wage increase W1 < W0. y6 Lower W1 leads to a lower price rise π1 < π0.

Hence, there is a negative relationship between i and π because the rise in Utriggered by the rise in r leads to lower π over time.

Exogenous Money supply Endogenous Money supply The determination of the interest rate

The output cost of disinflation: the sacrifice ratio

Ball Laurence, 1993. “What Determines the Sacrifice Ratio?” NBER Working Papers no 4306. The sacrifice ratio is

the percentage of cumulative output lost (∑ Y0−Ye

Ye) for each 1 pt reduction in the inflation rate over a disinflation

period.