International Monetary Policy - LSEpersonal.lse.ac.uk/PIFFER/Lecture Slides for Shanghai/13...

International Monetary Policy13 IS-LM Model in Open Economy 1

Michele Piffer

London School of Economics

1Course prepared for the Shanghai Normal University, College of Finance, April 2011Michele Piffer (London School of Economics) International Monetary Policy 1 / 50

Lecture topic and references

I In this lecture we extend the IS-LM model to an open economy andunderstand the different effectiveness of economic policies acrossdifferent monetary regimes

I No reference, sorry

Michele Piffer (London School of Economics) International Monetary Policy 2 / 50

Review from previous lecture

I Under fixed exchange rates we have

BP > 0→ DDc > SDc i.e. DFc < SFc → Dc would appreciate →→ IR ↑→ MB ↑→ Ms ↑

BP < 0→ DDc < SDc i.e. DFc > SFc → Dc would depreciate →→ IR ↓→ MB ↓→ Ms ↓


IS curve in Open Economy

I Remember, equilibrium on the goods market requires

Y as = Y ad

I We defined aggregate demand as

Y ad = C + I + G + CA

withI C = ConsumptionI I = InvestmentI G = Government SpendingI CA = Current Account



I What we need to do is assume some meaningful expression for CA

I We saw that CA = X − IM, and we assumed

X = X (ε+

)

IM = IM(ε−,Y

+)

I Given the real exchange rate as a measure of domestic goodscompetitiveness, exports increase as the domestic currencydepreciates. Imports increase as the domestic currency appreciates,and increase if the domestic economy has a higher national income



I It follows that the net export increases as the domestic currencydepreciates and decreases as the domestic economy increases inoutput.2 Specifically, we will assume

CA(ε,Y ) = X0 + x · ε− z · Y

I Note, CA increases as domestic currency depreciates, and as Yincreases

2To be precise, this is not always the case, since there are both price and incomeeffects: as the domestic currency depreciates the price of imports increases, so CA movestemporarily into deficits until quantities imported decrease and quantities exportedincrease. We will assume that the Marshall-Lerner conditions are satisfied, so that thecurrent account increase as the domestic currency depreciates. Don’t worry about this



I At this point we simply need to derive the new IS curve

Y = a + mpc · (Y − T ) + I0 − b · r + G0 + X0 + x · ε− z · Y

I Factorizing Y we obtain

Y ∗ =1

1−mpc + z· (a + I0 − b · r + (1−mpc) · G0 + X0 + x · ε)



I Rewrite the above expression in a more convenient form and obtainthe IS curve in Open Economy

Y ∗ =1

1−mpc + z· (A− b · r + x · ε) (IS)

with A = a + I0 + (1−mpc) · G0 + X0, defined as the autonomousaggregate demand in open economy



I Note, under closed economy the IS curve was defined as thecombinations of interest rate and output that guarantee equilibriumon the goods market

I The key difference here is that we have an extra variable, the realexchange rate! As ε increases the domestic currency depreciates, netexports increase and the aggregate demand increases

I Similarly, as ε decreases the domestic currency appreciates, netexports decrease and the aggregate demand decreases



I This means that here we define the IS curve as the combinations ofinterest rate, output and real exchange rate so that the goods marketis in equilibrium

I Having three variables instead of two, how do we represent the curvegraphically?

I It turns out that it is convenient to represent it on the (r ,Y ) spaceand to parametrize the curve at different possible values of ε


IS Curve in Open Economy

I For each level of the exchange rate, the IS curve is negatively slopedon the the space (r ,Y ): higher interest rate reduces investments,aggregate demand and hence equilibrium output

I Above the curve we have excess supply of goods; equilibrium outputwill decrease since firms realize that they are producing too much

I Below the curve we have excess demand of goods; equilibrium outputwill increase since firms realize that they are producing too little





I For given level of interest rate, a higher level of ε means that thecurrent account is higher as the domestic currency is depreciated

I Hence equilibrium output will be higher, otherwise there would be anexcess demand in the goods market




LM curve in Open Economy

I Nothing is different in the derivation of the LM curve. Remember, wehad

Ms

P= L(Y

+, r) (LM)

I The LM curve captures all combinations of income and interest ratethat allow for the equilibrium in the money market

I There is going to be a unique key difference here. Under fixedexchange rate the nominal money supply cannot be any given value,but must be the one that guarantees the equilibrium in the exchangerate. We will get back to this point


LM curve


BoP Equilibrium

I What we are missing is an equilibrium condition for the third marketconsidered by the model, the forex market

I We saw that the forex market is in equilibrium when the currentaccount and the capital account sum up to zero

I When BoP > 0, it means that the overall demand for domesticcurrency exceeds the overall supply for domestic currency, leading toan exchange rate appreciation

I When BoP < 0, it means that the overall demand for domesticcurrency runs short of the overall supply for domestic currency,leading to an exchange rate depreciation


BoP Equilibrium

I Remember, BoP = CA + KA = ∆ · IR

I In our model, CA = X0 + x · ε− z · Y

I Assume that the capital account is uniquely determined by theinterest rate spread between the two countries according to the factorθ. This implies

BoP = X0 + x · ε− z · Y + θ · (r − rw ) = ∆ · IR

where rw is equal to the world interest rate


BoP Equilibrium

I The forex market is in equilibrium when the combination of ε, r ,Y isso that

X0 + x · ε− z · Y + θ · (r − rw ) = 0

I Having represented the IS curve on the (r ,Y ) space, it is convenientto do the same for the BoP curve


BoP Equilibrium

I Factorize the interest rate to recover the BoP curve:

r = rw +1

θ· (z · Y − X0 + x · ε) (BoP)

I This expression detects the BoP curve: combinations of exchangerate, interest rate and output so that the forex market is inequilibrium

I The BoP curve is positively sloped on the (r ,Y ) space: an increase inthe interest rate determines a higher capital inflow and a higherdemand for domestic currency. Holding the exchange rate constantone needs a higher equilibrium output to increase imports, increasesupply of domestic currency and avoid exchange rate movements


BoP Equilibrium


BoP Equilibrium

I The BoP curve is parametrized at different values of the exchangerate: given an interest rate, higher values of ε imply a higher level ofequilibrium output

I This is because, given the interest rate, the demand and supply ofcurrency from the capital account is unchanged. As the domesticcurrency depreciates we have a disequilibrium in the forex marketresulting from the increase in net exports. To offset this we need anincrease in output to boost imports and hence the supply of domesticcurrency


BoP Equilibrium


BoP Equilibrium

I We will consider only the special case of Perfect Capital Mobility:there is no friction in the international capital flows, so that anydifference in the interest rates across countries causes capital inflowsof infinite amount

I This coincides with taking the limit of the parameter θ up to infinity.The BoP curve becomes

r = rw (BoP)


BoP Equilibrium

I Note, this means that the equilibrium in the forex market isdetermined uniquely by the capital account. Any minimum spreadbetween domestic and foreign interest rates creates excesses ofdemands and supplies that cannot matched by any current accountposition

I This means that in equilibrium the domestic interest rate mustcoincide with the foreign interest rate. The capital inflows andoutflows that take place in equilibrium are the ones required tobalance the current account position (investors are perfectlyindifferent between investing in the domestic or in the foreign country)


BoP Equilibrium under Perfect Capital Mobility


The IS-LM Model in Open Economy

I To sum up, the model studies three markets, goods, money andexchange markets

I Hence, it has three variables, respectively output, interest rate andexchange rate

I The model is hence given by three equations in three unknowns


The IS-LM Model in Open Economy

I IS curve

Y ∗ =1

1−mpc + z· (A− b · r + x · ε) (in (Y,r, ε))

I LM curveMs

P= L(Y , r) (in (Y,r))

I BoP curver = rw (in (r))

I The equilibrium interest rate is always pinned down by the BoP curve.The determination of the remaining variables depends crucially on theexchange rate regime


Flexible Exchange Rates

I Under flexible exchange rate, the exchange rate is an endogenousvariable determined by market forces. Money is exogenouslydetermined, as it simply reflects the monetary stance that the CBfollows

I Solve the model recursively:

1. Determine r∗ from the BoP curve2. Given r∗ and Ms , determine Y ∗ from the LM curve3. Given r∗ and Y ∗, determine ε∗ from the IS curve

I Let’s see this graphically






Monetary Policy under Flexible Exchange Rates

I What happens if the CB increases money supply?

I The LM curve shifts right, the money market is now in disequilibriumand the excess of money supply generates a decrease in the interestrate

I While increasing investments, the reduction of the interest rate causesa capital outflow due to the lower return offered by domestic savingpossibilities



I The capital outflow triggers a depreciation in the domestic currency,shifting the IS curve to the right

I The overall increase in output increases money demand, leading theinterest rate back to rw . The current account is undetermined, do tothe combination of higher domestic input and depreciation

I Monetary policy is even more effective under flexible exchange rate,due to the effect on net exports






Fixed Exchange Rates

I Under fixed exchange rate, the exchange rate is an exogenous variabledetermined by the CB (call it ε′). Money is endogenously determined,as it the money supply that the CB must guarantee usinginternational reserves interventions to stabilize the exchange rate atthe desired level

I Solve the model recursively:

1. Determine r∗ from the BoP curve2. Given r∗ and ε′, determine Y ∗ from the IS curve3. Given r∗ and Y ∗, determine Ms from the LM curve

I Let’s see this graphically






Monetary Policy under Fixed Exchange Rates

I What happens if the CB increases money supply?

I The LM curve shifts right, the money market is now in disequilibriumand the excess of money supply generates a decrease in the interestrate

I While increasing investments, the reduction of the interest rate causesa capital outflow due to the lower return offered by domestic savingpossibilities



I The capital outflow triggers a depreciation in the domestic currency.But the CB cannot accept this as it has committed to a fixed ε′

I In response it will contrast the excess of demand of foreign currencyby supplying its own international reserves to the forex market. Bydoing this it reduces the monetary base. The LM curve shifts back

I Monetary policy is ineffective under fixed exchange rate. Under fixedexchange rate you loose one channel of economic policy






Fiscal Policy under Flexible Exchange Rates

I How about fiscal policy? Start from the case of flexible exchangerates

I When G increases the IS curve shifts to the right. This leads firms toproduce more. At the same time the excess money demand producedby this will increase the interest rate



I As r increases the inflow of capital will increase the international valueof the currency through an appreciation of the domestic currency.This shifts the IS curve back through a decrease in the trade balance

I Under a flexible exchange rate, the crowding out effect of fiscal policyis complete and it occurs through the contraction in net exports






Fiscal Policy under Fixed Exchange Rates

I Consider now the case of fixed exchange rates

I When G increases the IS curve shifts to the right. This leads firms toproduce more. At the same time the excess money demand producedby this will increase the interest rate



I As r increases the inflow of capital will increase the internationalvalue of the currency through an appreciation of the domesticcurrency. The CB cannot accept this and will react by accumulatinginternational reserves

I This will increase the money supply and shift the LM curve to theright

I Under a fixed exchange rate, the crowding out effect of fiscal policy iszero since monetary policy is used to avoid an increase in interest rate






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