1.2 - Monetary model

Floating ER - assumptions

AS curve vertical

• price is flexible

• Supply Side factors which make up AS not modelled (tech or K accumulation)

Small local economy

• Foreign variables taken as given

Simple Demand for money

• Not dependent on interest rates

• Only depends on real income

PPP holds

• SP* = P

demand for real money balance - equation

M^d / p = kY

• kY - Share of total output

Money market equilibrium

M^S = M^d  

Simple AD relation - equation

M^S = kPY

• M^d / P = kY → M^d = kPY

• M^S = M^d  

Simple AD relation - graphically

PPP holds - graph

Monetary model equilibrium

Using AD-AS relation

• M^S = M^D = kPY → P = M^S / kY

PPP holds by assumption

• P = SP*

M^S / kY = SP* → S = M^S / kP*Y

What changes Model equilibrium

If M^S rises, S rises (depreciation)

If output (Y) rises, S falls (appreciation)

If foreign price (P*) rises, S falls (appreciation)

Money Supply increase effects on equilibrium - graph + explanation

If M^S increases (treat M^S as exogenous):

At initial p (p⁰ = S₀P*) there is excess D for goods

• Since Y fixed (Y0), p rises → dom goods now relatively more expensive

• D for H goods & H currency falls

• Dom currency depreciates to keep competitiveness for PPP to be preserved

  • decrease proportional to increase in M^S

Income increase effects on equilibrium - graph + explanation

Income (Y) increases (Y exogenous in model):

• At original p (p⁰) there is excess supply

• p falls to keep money market in equilibrium

• Exchange rate appreciates (S falls) – to restore competitiveness of F goods

Balance sheet of a Central Bank (CB)

Assets

• Domestic-currency bonds (D)

• Foreign exchange reserves (F)

Liabilities

• High powered money (H)

M^s in a fixed ER

M^s = hH = h(F+D)

• h - money multiplier

• assume h = 1 (Money consists of currency only)

• If CB holding of D increases -> monetary base increases -> M^S increases through the money multiplier (expansionary MP)

M^s = F+D

Fixed ER assmptions

Dom Output (Y) + Foreign price (P*) - Exogenous

M^S no longer exogenous

• CB adjusts Foreign reserves (F) to preserve ER

• When other exogenous variables change (shock)

Money supply increase (↑ in D) - graph + explanation

An increase in govt bonds (D) leads to increase in M^S (expansionary MP)

Shifts AD upwards from the excess demand -> increases P (domestic price index)

Dom goods become under-competitive → Which leads to demand falling + D for dom currency falls

Without CB intervention, dom currency would depreciate to correct competitiveness (floating ER)

To preserve fixed exchange rate, CB buys dom currency using Foreign reserves (F)

F falls till competitiveness restored

• An increase in D is exactly offset by a decrease in F (M^S falls so movement along AS curve)

  • F = kS₀P*Y – D

Asset composition changes (F falls but D increases)

PPP doesn’t shift at all so p & output (Y) doesn’t change

Income increase with fixed ER - G + E

Shock to income (Y)

• dont need M^S diagram as assumed kY = 1 implicitly (so always consistent)

Y increases due to supply side shock → AS curve shifts right

At initial price (p0) there is excess supply → Dom price falls and dom goods become over-competitive as they are cheaper

Demand for home currency increases -> Without CB intervention Dom currency would appreciate to correct competitiveness

CB increases F reserves (F) -> Issue dom currency & buy F currency to keep exchange rate constant

F increases for given D → M^S increases → AD shifts upwards until PPP restored

Output (Y) increase BUT price fixed + CB now hold more F

Asset price approach

Dynamic version of the model with nominal exchange rate viewed as an asset price

• PPP still holds

Money demand function with nominal interest rate - dynamic

PPP in logs - dynamic

Rational expectations

Rational expectations use all information available

• Peoples subjective expectations conditional on all information available today

UIP with expectation

Combine UIP with logs equation

Difference in H & F interest rate should be equal to expectation of depreciation rate

What does γ_t equal

Combined equation - s_t

law of iterated expectations

Expanded s_t with 1 level of expectations

Expanded using Law of iterated expectations

Expanded s_t with all levels of expectations & iteration

Asset bubble restriction (on iteration)

The assumption rules out a bubble situation where p keeps increasing at a fast rate

• limit of present discounted value of terminal ERs

Non-bubble condition hold if s increasing at slower rate than (n/1+n)^t inverse

Final s_t equation

Exchange rate today is a function of:

• Expectation of future money S + output in the future + future foreign interest rate + future foreign p