3-equation model open economy PDF

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Summary

3-equation open economy model Supply and demand shocks and policies (independent of exchange rate regime) determine the medium-run exchange rate  Medium-run inflation rate:o Fixed exchange rate: πMRE=π¿o Flexible exchange rate: πMRE=πT We assume that home’s CB chooses πT=π¿i.∆ee= 0 in MRESummary:...

Description

3-equation open economy model  

Supply and demand shocks and policies (independent of exchange rate regime) determine the medium-run exchange rate Medium-run inflation rate: o Fixed exchange rate: π MRE =π ¿ o Flexible exchange rate: π MRE =π T



We assume that home’s CB chooses

¿

π T =π i . e .

∆e =0 in MRE e

Summary: Check (5) in notes  Demand side represented by AD curve  Supply side represented by ERU curve, incorporates  In MRE, economy is: o On an AD curve and on an ERU curve o Inflation is constant o Real exchange rate is constant ¿ o r=r

WS = PS

Why the ERU is vertical  Neither WS nor PS depend on q Why q is constant on the ERU curve at MRE E ¿  Given r=r , Real UIP tells us that q t+1=qt ;

q is constant

Recall the closed economy: 3 equations: 1. IS: y t =A −a r t−1 ; y e = A −a r s 2. PC: 3. MR:

π e =π E +α( y t − y e ) y t − y e =−αβ (π t −π T )

Minimise L=( y t− y e )2+ β(π t −π T )2 Parameters: a , α , β

Structure of the 3-equation closed economy model 

CB minimises its loss function, which expresses its objectives:

Min L=( y t − y e )2 +β (π t −π T )2 Subject to the constraint from the supply side, in the Phillips curve:

π t= π E +α ( y t − y e ) Which produces the monetary rule function that pins down the optimal output gap:

y t − y e =−αβ (π t −π T ) Which is implemented in closed economy through choice of r

y t =A−a r t−1

→ y t − y e =− a(r t −1−r s)

using the IS equation (best-response Taylor Rule):

The open economy 

One obvious change in the open economy is in IS:

y t =A−a r t−1 + b q t−1

Inflation shock in closed economy 1. 2. 3. 4.

Start in MRE Show the shock Solve the constrained opt. problem (find best-response output gap Use the IS to find r 0

Check (6) in notes

The structure of the 3-equation open economy model 

CB minimises the loss function, which expresses its objectives:

Same as closed economy Subject to the constraint from the supply side, in the Phillips curve:

same as closed economy Which produces the optimal monetary rule function that pins down the optimal output gap:

same as closed economy Which is implemented through choice of r looking forex market

using the IS equation & taking account of the reaction of the forward-

Comparing an inflation shock in closed & open economies 

Check (7) in notes



Before the CB even acts, the IS already shifts to left because of the appreciated exchange rate o Forward-looking actors in the market already know that the CB will increase the interest rate to dampen inflation, so the exchange rate will appreciate o So less work will be needed to be done on the interest rate by the CB because of this



During that period of time on the path back to equilibrium, the exchange rate will begin to depreciate again and so the IS curve will shift to the right Eventually, we will go back to the original IS curve with the original exchange rate



The RX curve 

In the closed economy: o The optimal monetary rule function pins down the optimal output gap, which is implemented through choice of r using the IS equation



In the open economy: o The optimal monetary rule function pins down the optimal output gap, which is implemented through choice of r using the IS equation & taking account of the reaction of the forward-looking forex market o We use the RX curve to calculate q 0

Modelling forward-looking behaviour How does forex market analyse the CB’s optimal reaction? And vice versa?  Use intuition from RUIP condition for every period E ¿ r−r =qt +1−qt ¿

As we move to point Z on the IS curve diagram, r >r – the RUIP condition must still hold during this period  Therefore, there must be an expected depreciation ¿  For r >r , expected depreciation every period → can calculate immediate appreciation via ↓ et 

Both CB and forex market solve the same model in terms of Real UIP ( r , q ); implemented by action of CB (change in iP ) and in forex (jump in e ) that produce required change in r and jump in q

↓ et



The CB raises r



Both solve the same problem, use the same model, and the model assumes both have rational expectations o Modellers at BoE o Profit-seeking behaviour in forex market

(by its choice of i ) and the q jumps via

Demand & supply shocks 

We know that: o Permanent demand & supply shocks affect medium-run real exchange rate, q´ o Supply shocks also affect equilibrium output, y e Check (8) in notes

y e for the output gap



CB and forex market need to calculate new MRE q



Behaviour of UK exchange rate in context of global financial crisis suggests forex market saw a specific problem for the UK: o The permanent disappearance of some domestic & foreign demand (revealed as unsustainable) – view of over-expansion of financial sector + of consumption o Need for permanent shift toward tradeables (net exports) o Not just a temporary crisis-related negative demand shock – permanent; ∆ q´ → depreciated

q´

and new

Central bank reaction to a permanent negative demand shock Steps: 1. Use AD-ERU model to work out equilibrium

q

2. Use 3-equation model to work out CB’s policy response & dynamic adjustment to shock

Check (9) in notes...