Central Banks

Macro - Adjustment Strategies

Central Banks & Exchange Rate Regimes

Flexible Fixed Managed Floating

Flexible Exchange Rate

Exchange rates are freely determined by the demand & supply of currencies.

Increase in Demand for £ Under Flexible Exchange Rate

D£

S£

e$/£

Q£

D£’

e

e’

Fixed Exchange Rate Gold standard (up to 1914)

Peg currency to gold at a mint parity. ($20.67/ounce of gold, £4.25/ounce of gold).

Fixed Exchange Rate Gold standard Pegged rate system

Peg is the central value of exchange rate around which the government maintains narrow limits. (Haitian Gourde = $.20 since 1907 for a long period of time).

Government intervenes in foreign exchange markets to maintain the exchange rate within prescribed limits.

Increase in Demand for £ Under Pegged Rate System

D£

S£

e$/£

Q£

S£’

D£’

ē

Fixed Exchange Rate Devaluation

Peg is increased. • £ was devalued in Nov. 1967 from $2.80/£ to

$2.40/£ . Revaluation

Peg is decreased.

Managed Floating

Government intervenes in the foreign exchange market to influence the exchange rate, but does not commit itself to maintain a certain fixed rate or some narrow limits around it.

Goods Market Equations

Y = C + I + G0 + NX (Equim condition)  C = C0 + cYd (Consn function)  Yd = Y – T + R0 (Disposable

income)  T = T0 + tY (Tax function)  I = I0 – br (Investment

function)

Goods Market Equations

Parameters

c: MPC t: Personal Tax Rate b: Interest Sensitivity of I

C0 : Exogenous Component of C

I0 : Exogenous Component of I

G0 : Government Expenditure

R0 : Transfer Payments

T0 : Fixed personal tax revenue

Endogenous Variables

Y: National Income C: Consumption Yd: Disposable Income T : Personal Tax Revenue I : Investment

Goods Market Equilibrium:IS Curve (General form) Goods market equilibrium condition:

AS = ADÞ Sn – I = NXÞ - A0 + br + sY = NX0 – mYÞ r = (A0 + NX0)/b – (s + m)/b*Y

= (A0 + NX0)/b – 1/αb*Y where

A0 = C0 + c(R0 – T0) + I0 + G0

NX0 = X0 – Q0 + (g + j)eP*/P

α = 1/[1 – c(1 – t) + m]

Goods Market Equilibrium:IS Curve (Particular form)

r = A0 =

Open economy multiplier 1/(s+m) =

IS Curve

Y

r

S

I[A0 + NX0/b

-1/b

Assets Markets

Markets in which money, bonds, stocks, real estate & other forms of wealth or stores of value are exchanged.

We consider two types of assets domestic bonds domestic money

Total Real Wealth in the Economy Supply of real wealth

W/P = M/P + VS whereW : Nominal wealthP : General price levelVS: Stock of bonds

Demand for real wealth W/P = L + V

L: Demand for moneyV: Demand for bonds

In equilibrium L + V = M/P + VS

Or (L - M/P) + (V - VS) = 0

Walras law

As long as money market is in equilibrium (i.e. L = M/P), bond market will also be in equilibrium.

Money Market Equations

L = M/P (Money market equim condition)

L = L0 + kY – hr (Money demand)

M = uH (Money supply)

H = IR + CBC0 (High Powered

Money)

IR = IR-1 + BP-1 (Int. Reserves adjustment)

Money Market Equations

Endogenous Variables

L: Liquidity Demand r: Real interest Rate M: Nominal Money Supply H: High-Powered Money IR: International Reserves P: General Price Level CBC0: Central Bank Credit

Exogenous Variables

k: Income Sensitivity of L h: Interest Sensitivity of L u: Money Multiplier L0: Exogenous component of L

Demand for Money

The demand for money can be linearized to:

L = L0 + kY – hr

Supply of Money

MS = Cp + CD

Cp: Currency (coin, dollar notes) in the

hand of the publicCD: Checkable deposits

M = H where : the money multiplier H: the high powered money (monetary base)

Central Bank’s Balance Sheet Assets = IR + CBC Liabilities = Cp + RE

IR + CBC = Cp + RE = H H is created when the Central Bank acquires

assets in the form of international reserves, IR (foreign exchange & gold), & Central Bank credit, CBC (loans, discounts & government bonds).

Simplified Central Bank Balance Sheet

 

Assets Claims

International Reserves $100b

Central Bank Credit $200b

   High Powered Money $300b

Currency $240b

Cash in vaults $20b

Currency in the hand of the public $220b

Deposits at the central bank $60b

 High Powered Money $300b

Effects of Open Market Purchase on Central Bank’s Balance Sheet Central bank purchase of securities (increase in

CBC). Central bank check is deposited in the

commercial bank. If the commercial bank decides to convert the

check into cash, the currency in vault (RE) increases.

If commercial bank deposit the check at the central bank, commercial bank deposit (RE) increases.

Effects of a Drain of International Reserves on Central Bank’s Balance Sheet

IR decreases & Commercial bank deposit decreases. A BP deficit (surplus) decreases (increases) H &, therefore, tends to decrease (increase) MS.

Money Market Equilibrium: The LM Curve

MS/P = L0 + kY – hr

r = (L0 - MS/P)/h + k/h Y Particular: r =

LM Curve

Y

r

L

M

[L0-MS/p]/h

k/h

Immediate-run Equilibrium Immediate-run equilibrium is obtained when

both the product & the money markets are in simultaneous equilibrium. It occurs for a given level of fixed MS.

Immediate-run Equilibrium

Y

r

S

I

L

M

YE

rE

Foreign Trade Equations

BP = 0 (Foreign sector equim condition)

BP = NX + CF (Balance of Payments)

NX = X – Q (Net Export function)

X = X0 + gePW/P (Export function)

Q = Q0 + mY – jePW/P (Import function)

e = e-1 – qBP (Exchange Rate adjustment)

CF = f(r – rW) (Capital Flow equation)

Foreign Trade Equations

Endogenous Variables

NX : Net Exports (Trade Surplus) X : Value of Exports Q : Value of Imports BP : Balance of Payments

Surplus CF : Capital Flow (KAB Surplus) e : Exchange Rate (Domestic/Foreign Currency)

Exogenous Variables

g : Exchange Rate Sensitivity of X

m : Marginal Propensity to Imp.

j : Exch. Rate Sensitivity of Q

f : Capital Mobility Coefficient

q : Exchange Rate Coefficient

rW : World Interest Rate

X0 : Exogenous Component of X

Q0 : Exogenous Component of Q

Foreign Trade Sector Equilibrium: The BP Curve BP = 0 => NX + f (r – rW) = 0 With no capital mobility (f = 0)

NX = NX0 - mY = 0

Y = NX0/m

With perfect capital mobility r = rW

With imperfect capital mobility NX0 – mY + f (r – rW) = 0

=> r = [rW - NX0/f] + m/f * Y

BP with No Capital Mobility

Y = NX0/m

In particular form: Y =

BP Curve with No Capital Mobility

Y

r BP

NX0/m

BP Curve with Perfect Capital Mobility

Y

r

BPr = rW

BP Curve with Imperfect Capital Mobility

Y

r

BP

Short-run Equilibrium An immediate-run equilibrium sustaining a BP

deficit & losses of international reserves leads to a decline in MS & a leftward shift of the LM curve.

A short-run equilibrium exists when all the three markets are in equilibrium.

Short-run Equilibrium withNo Capital Mobility

Y

r

S

I

L

M

YE

rE

BP

Short-run Equilibrium withPerfect Capital Mobility

Y

r

S

I

L

M

YE

rE BP

Short-run Equilibrium with Imperfect Capital Mobility

Y

r

S

I

L

M

YE

rE

BP

Sterilization Operations

Operations carried out by the Central Bank in order to neutralize the effects that its intervention in foreign exchange markets has on H.

H = IR + CBC = 0or CBC = - IR