Faculty of Social Sciences - econ.ku.dk · PDF file... On dynamic IS-LM: Floating exchange...

Faculty of Social Sciences

Adv. Macro 2 ExercisesWeek 10

23th of November 2011 (week 10)Slide 1/30

Adv. Macro 2Exercises

Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Outline

1 Introduction

2 Exercise 4.34.3.14.3.24.3.3

3 Exercise 4.44.4.14.4.24.4.3

23th of November 2011 (week 10) — Slide 2/30


Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Outline

1 Introduction

2 Exercise 4.34.3.14.3.24.3.3

3 Exercise 4.44.4.14.4.24.4.3



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Introduction• We have two exercises today:

• 4.3: On dynamic IS-LM: Floating exchange rate.• 4.2: On dynamic IS-LM: Fixed exchange rate.

• Important stuff for the exam.

• Exercise on the bank lending channel is postponed until further notice.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Outline

1 Introduction

2 Exercise 4.34.3.14.3.24.3.3

3 Exercise 4.44.4.14.4.24.4.3



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.1We consider a small open economy (SOE) satisfying (approximately):

• Perfect mobility across borders of financial capital, but no mobility of labour.• Domestic and foreign financial claims are perfect substitutes.• Domestic and foreign output goods are imperfect substitutes.

Yt = λ(D(Yt , rt ,xt ,ω) + G−Yt ) λ > 0, 0 < DY < 1, Dr < 0, Dx > 0, Dω > 0Mt

Pt= L(Yt , it ), LY > 0, Li < 0

π∗t = πt = 0

it = i∗+X e

t

Xt

rt ≡ it −πet

xt =Xt P∗t

Pt

• We assume that expectations are rational and speculative bubbles neveroccur.

• The money stock is assumed to be constant.23th of November 2011 (week 10) — Slide 6/30


Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.2 aa) Briefly interpret the model.• Answer: It is the Blanchard-Fischer version of Dornbusch’s ”overshooting”

model, i.e., a dynamic IS-LM model for a SOE with a floating exchangerate.

• Inflation (foreign and domestic) is constant and zero.• Money demand is Keynesian.• Output is demand determined. Dx > 0 because the Marshall-Lerner

condition is implicitly assumed satisfied so that net exports depend positivelyon the real exchange rate x ≡ XP∗/P.

• SOE⇒ UIP: it = i∗+ Xte

Xt. Domestic and foreign financial assets pay the

same expected rate of return when measured in the same currency.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.2 b Ib) Draw the phase diagram in (Y ,X)-space and illustrate the path that the

economy follows. Comment.• IS-relationship

• Rational expectations⇒ πet = πt = 0→ rt = it .

• MP = L(Yt , it )→ it = i(Yt ,M/P)where iY =−LY /Li > 0 and iM/P = 1/Li < 0.

• IS-relationship: Yt = λ(D(Yt , i(Yt ,M/P),Xt P∗/P,ω) + G−Yt ).

• LM-relationship• Rational expectations⇒ Xe

t = Xt .

• UIP: it = i∗+ XtXt

• LM-relationship: Xt = (i(Yt ,M/P)− i∗)Xt



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.2 b IIIS-relationship: Yt = λ(D(Yt , i(Yt ,M/P),Xt P∗/P,ω) + G−Yt )LM-relationship: Xt = (i(Yt ,M/P)− i∗)Xt

b) Draw the phase diagram in (Y ,X)-space and illustrate the path that theeconomy follows. Comment.

• IS-curve• Y = 0 for D(Y , i(Y ,M/P),XP∗/P,ω) + G = Y .• Take the total differential on both sides wrt. Y and X.• (DY + Dr iY )dY + Dx

P∗P dX = dY → dX

dY

∣∣Y=0 = 1−DY−Dr iY

Dx P∗/P > 0.

• LM-curve• X = 0 for i(Y ,M/P) = i∗.• The value of Y satisfying this equation is unique (because iY 6= 0).• LM-curve is vertical.

• Standard saddle point stable system.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.2 b III



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 aSuppose that the SOE is initially in steady state. Then, unexpectedly, a recession in the leadingeconomies in the world comes about and gives rise to an offsetting monetary policy in thesecountries. As a crude representation of these events vis-a-vis our SOE we ”translate” them into twounanticipated parameter shifts occurring at time t0 > 0: a shift in the demand shift parameter toω′ < ω and a shift in the world interest rate to i∗

′< i∗

′, where i∗

′is close to zero.

a) Suggest an interpretation of the fall in the demand shift parameter.

• Answer: The recession in the leading economies in the world implies lessexports from our SOE to these countries. The change in the demandparameter to ω′ < ω can be seen as reflecting this. The whole setup mightbe interpreted as a crude description of, for example, the Swiss or theSwedish economy in the present situation of an almost global recession.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 b IIS-curve: D(Y , i(Y ,M/P),XP∗/P,ω) + G = Y .LM-curve: i(Y ,M/P) = i∗.

Assume that after time t0 the public in the SOE rightly expects that the mentioned two newparameter values (i∗

′< i∗

′and ω′ < ω) will remain in force for a long time and that no policy change

in the SOE will occur.

b) Illustrate how the SOE evolves for t ≥ t0, using a phase diagram as well asa figure with time profiles of Yt , Xt , and rt , presupposing that the sign of thelong-run effect on Xt is dominated by the influence from the fall in the worldinterest rate. Explain the economic intuition.

• Answer:• ω′ < ω: IS-curve upward. The interpretation is that a fall in ω induces a

lower output demand; then, for demand to still match the fixed Y , adepreciation (higher X ) is needed.

• i∗′< i∗

′: LM-curve left. The interpretation is that a lower i∗ requires a lower

domestic interest rate for UIP to hold with X = 0. In turn, given M/P, a lowerdomestic interest rate requires a lower transaction demand for money, i.e., alower output level.

• The new steady is South-West of the old.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 b II• Adjustment: The long-run effect of the two shocks is thus an economic

recession in the SOE combined with (in the present case) appreciation ofits currency. The impact effect on the exchange rate is, however, a largerappreciation than in the long run - the phenomenon called ”overshooting”.Then Yt gradually falls in response to the low output demand generated bythe low real exchange rate xt (low competitiveness); along with the fallingYt the interest rate gradually falls as well, because of lower demand fortransaction balances (M is unchanged). During the adjustment we haveit > i∗

′with interest parity maintained through gradual depreciation of the

exchange rate until the new steady state is ”reached”.

• Intuition: The downward jump in the world interest rate triggers an inflowof financial capital sufficiently large to cause immediate appreciation of thedomestic currency to a level from which it is expected to depreciate at asufficient rate to re-establish and maintain interest parity. Very fastarbitrage brings about the new short-run equilibrium where the demand fordomestic bonds is again satisfied by the given supply because the higherdomestic interest rate is counterbalanced by expected depreciation.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 b III



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 ci(Y ,M/P) = i∗

D(Y , i(Y ,M/P),XP∗/P,ω) + G = Y

As an alternative scenario imagine that at time t1 ≥ t0 the monetary and fiscal authorities in theSOE find the situation unsatisfactory and contemplate monetary and fiscal measures to stimulateeconomic activity. It is soon realized, however, that neither conventional monetary policy (upwardshift in M) nor conventional fiscal policy (upward shift in G) will work.

c) Give plausible reasons for this unfavorable outlook.

• Conventional monetary policy: Under ”normal circumstances” anupward shift in M would stimulate output demand by lowering the interestrate and triggering off a depreciation. But we are told that i∗′ is close tozero. ”Liquidity trap”.

• Conventional fiscal policy. When capital mobility is perfect and domesticand foreign bonds are perfect substitutes, as assumed by the model, thenexpansionary fiscal policy is immediately counteracted by appreciation ofthe domestic currency. The role of a higher G is simply the opposite of thatof a lower ω.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 c Bonus• There might be multiple equilibria.

• Money market: Because we for i ′′ = i∗′ ≈ 0 have Li =−∞ we have

M ′ > M→ Y ′′ ≥ Y ′.• Goods market: This requires X ′′ ≥ X ′. Xt will therefore jump to X ′′

immediately and output will begin to increase.• During adjumstent: it = i ′′ = i∗

′.

• Problem: No economic mechanism for Y ′′ > Y ′, except maybe a peg.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.3.3 dd) If international coordination of fiscal policy is possible, can this then

improve the outlook? Why or why not?

• Answer: Yes, the outlook is improved if international coordination ofexpansionary fiscal policy is possible. Then one can regard theinternational economy as a large closed economy, where the problem ofoffsetting appreciation does not arise.

• There is a further advantage of a coordinated fiscal stimulus. A unilateralfiscal stimulus in a small open economy (even under a fixed exchange rate)faces the problem that a lot of the stimulus goes to other countries throughthe imports leakage. This restrains the spending multiplier and can makethe needed fiscal expansion problematic for a country with already highpublic debt or current account deficit problems. With a coordinated fiscalexpansion these problems are eased.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Outline

1 Introduction

2 Exercise 4.34.3.14.3.24.3.3

3 Exercise 4.44.4.14.4.24.4.3



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.1We consider a small open economy (SOE) satisfying (approximately):

• Perfect mobility across borders of financial capital, but no mobility of labour.

• Domestic and foreign financial claims are perfect substitutes.

• Domestic and foreign output goods are imperfect substitutes.

• Nominal prices are fixed.

Y dt = D(Yt ,Rt ,XP∗t /Pt ,τ) + G

Yt = λ(Y dt −Yt ), λ > 0

π∗t = πt = 0

it = i∗

Mt

Pt= L(Yt , it ), LY > 0, Li < 0

Rt =1qt

1 + qet

qt= rt

rt ≡ it −πet

• The initial value, Y0, of Y is predetermined.

• We assume that expectations are rational and speculative bubbles never occur.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.2 aa) Briefly interpret the model.• Answer: The model is Blanchard’s dynamic IS/LM model extended to a

SOE with a fixed exchange rate• Inflation (foreign and domestic) is constant and zero.• Money demand is Keynesian.• Output is demand determined. Dx > 0 because the Marshall-Lerner

condition is implicitly assumed satisfied so that net exports depend positivelyon the real exchange rate x ≡ XP∗/P.

• SOE⇒ UIP: it = i∗. Domestic and foreign financial assets pay the sameexpected rate of return when measured in the same currency and X isconstant.

• The internal rate of return of the consol is: qt =∫

∞

t 1 ·e−Rt (s−t)ds = 1/Rt .



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.2 b Ib) Draw the phase diagram in (Y ,R)-space and illustrate the path that the

economy follows. Comment.• IS-relationship: Given directly Yt = λ(D(Yt ,Rt ,XP∗/P,τ) + G−Yt ).

• Y = 0 for D(Y ,R,XP∗/P, ,τ) + G = Y .• DY dY + DRdR = dY → dR

dY

∣∣Y=0 = 1−DY

DR< 0.

• LM-relationship:• Rational expectation I:⇒ πe

t = πt = 0→ rt = it = i∗ > 0.• Rational expectation II: qe

t = Et qt = qt .

• 1+qet

qt= rt → 1/qt + q/q = Rt − Rt/Rt = rt .

• Ordering gives: Rt = (Rt − i∗)Rt .• R = 0 for R = i∗

• Standard saddle point stable system.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.2 b II



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.2 cIS-curve: D(Y ,R,x ,τ) + G = Y .LM-curve: R = i∗.

c) Determine the long-term real interest rate in steady state.

• Answer: R = R = i∗



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.2 dIS-curve: D(Y ,R,x ,τ) + G = Y .LM-curve: R = i∗.

d) How does Y in steady state depend on i∗ and G?

• Answer: Steady state D(Y , i∗,XP∗/P,τ) + G = Y .

• Total differentiation implies: DY dY + DRdi∗+ dG = dY .

• Result 1: ∂Y∂i∗ = DR

1−DY< 0

• Result 2: ∂Y∂G = 1

1−DY> 0



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 a IIS-curve: D(Y ,R,x ,τ) + G = Y . LM-curve: R = i∗.Suppose that the economy has been in its steady state until time t0. At time t0 an unanticipatedupward shift in the foreign short-term nominal interest rate occurs. But after this shift everybodyrightly expects the foreign short-term nominal interest rate to remain unchanged for a very long time.

a) Illustrate by a phase diagram and by graphical time profiles what happensto Rt , Yt , rt and Mt for t ≥ t0. Comment.

• Answer: IS-curve unaffected. The LM-curve moves upwards.• The long-term interest rate jumps to the higher level Rt = i∗1 and stays

there. The upward shift in Rt reduces output demandand so Yt begins togradually fall towards the new steady-state level, Y ′.

• The upward shift in i∗ causes a downward jump in the money supply.Financial investors instantaneously rush to convert home currency toforeign currency to buy foreign bonds and take advantage of the higherforeign interest rate. After time t0, when output gradually falls, so doesmoney demand (reduced transaction motive). The lower money demandgenerates an incipient tendency for the home nominal short-term interestrate, i , to fall. But this tendency is immediately counteracted by a decline inMt due to financial investors converting home currency to foreign currencyto take advantage of the slightly higher foreign interest rate.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 a II



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 b IIS-curve: D(Y ,R,x ,τ) + G = Y . LM-curve: R = i∗.Assume instead that at time t0, people in the SOE become aware that a monetary tightening in theleading countries in the world economy is underway. As a crude representation of this, suppose theagents rightly expect an upward shift in the foreign short-term nominal interest rate to take place attime t1 > t0. But after this shift everybody rightly expects the foreign short-term nominal interest rateto remain unchanged for a very long time.

b) Illustrate by a phase diagram and by graphical time profiles what happensto Rt , Yt , rt and Mt for t ≥ t0. Comment.

• At announcement, t0: The real long-term rate jumps upward, anticipatingthe later permanent increase in the short-term rate. This dampensdemand, and output begins to fall already. Dynamics is determined by theold phase diagram. Because Rt can be seen as an average of the future ofrt it must be rising until t0, so the jump must be to a point below the newsteady state. Due to no-arbitrage equilibrium on the currency market, thisimplies falling a money stock.

• At implementation, t1: The stable arm of the new phase diagram isreached without a jump (otherwise infinite arbitrage) and output keepsdecreasing. Due to no-arbitrage equilibrium on the currency market, theincreased i∗ implies a jump down in money stock and then a falling moneystock.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 b II



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 c IIS-curve: D(Y ,R,x ,τ) + G = Y . LM-curve: R = i∗.Now imagine the scenario is somewhat different from the one just described. Until time t2 > t1everything is as described above. But at time t2, due to now foreseeable unemployment problems,the government of the SOE credibly announces an upward shift in G to take place at time t3 > t2.After this shift everybody rightly expects G to remain unchanged for a very long time. The size of theshift in G is such as to reestablish, in the long run, an output level equal to that attained at time t1.

c) Illustrate by a phase diagram and by graphical time profiles what happensto Rt , Yt , rt and Mt for t ≥ t0. Comment.

• Curves: The IS-curve shifts to the right.

• At announcement, t2: Nothing because the forward looking variable Rt isnot affected.

• At implementation, t3: The IS-curve shifts to the right. Yt begins toincrease gradually due to the extra demand. Due to no-arbitrageequilibrium on the money market, implies rising money stock.



Introduction

Exercise 4.3

4.3.1

4.3.2

4.3.3

Exercise 4.4

4.4.1

4.4.2

4.4.3

Exercise 4.4.3 c II


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