theory of Macroeconomics

ECON5002 – Macroeconomic Theory

Week 10: Open economy II – IS-LM-IP model Reading: Blanchard chapter 20 (excluding 460-464) and chapter 21 (excluding 471-480)

Dr Kim Hawtrey

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› money market equilibrium - open economy ! in a closed economy, recall (Week 2) that the LM relation captures

equilibrium between demand and supply of money M, where: - the supply of money is measured in real terms (M/P) and is given

exogenously by policymakers - the demand for money YL(i) is measured in real terms and depends on

transactions (proxied by output Y) and on opportunity cost (= a function of i, interest rate on bonds B, the opportunity cost of holding M)

! Q: does the LM equation change in the open economy? A: no - demand for M is still determined by domestic residents because

foreigners have no daily use for Australian dollars, and supply of M is still determined by Australia’s central bank

" the open economy LM equation remains unaltered: M/P = YL(i) .. no foreign variables appear in the LM relation

! for simplicity, we will assume that monetary policy follows Rule 2 .. the central bank sets the interest rate at a target value, say i = i0

Open economy LM curve

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› IS-LM-IP equilibrium - open economy (algebraic) ! by solving the IS (Week 9) and LM (slide 2) equations simultaneously for

(i,E) we can determine the ISLM equilibrium for open economy IS: Y = C (Y-T) + I(Y, i) + G + NX [Y, Y*, ((1+i)/(1+i*))Ee]

the open economy IS relation between the interest rate and output is derived for given values of T, G, Y*, i*,and Ee .. it is still a downward sloping curve because ­i leads to ¯Y, but in the open economy this now occurs via two channels, direct (¯I) and indirect (¯NX)

LM: M/P = YL(i) the open economy LM relation is exactly the same as in the closed economy and is derived for a given value of (M/P) .. it is still an upward sloping curve because ­Y leads to higher M demand which would require ­i, but we are assuming i = i0 and so money supply M must adjust endogenously (and LM shift up/down) to maintain money market equilibrium at i0

Open economy IS-LM-IP model

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› IS-LM-IP equilibrium - open economy (geometric)

Open economy IS-LM-IP model

The equilibrium interest rate occurs i0, at the intersection of the downward sloping IS curve and upward sloping LM curve.

Projecting across to panel (b) at equilibrium interest rate i0, the interest parity relation implies equilibrium exchange rate E.

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› IS-LM-IP equilibrium - open economy ! the procedure for the economy to be at equilibrium is:

- with the central bank choosing the interest rate i0, equilibrium output Y0 is determined from the IS curve Þ the quantity of money M adjusts endogenously so that the LM curve goes through the point (i0,Y0)

- given the foreign interest rate i* and the expected future exchange rate Ee, the equilibrium interest rate (i0) determines the equilibrium exchange rate (E0)

! the equilibrium will be altered by changing the given variables:

Open economy IS-LM-IP model

eg. - a domestic monetary policy contraction, which is an increase in the Australian interest rate, will increase the demand for Australian bonds Þ as investors switch from foreign currency to $A, the Australian dollar appreciates

- a foreign monetary contraction, which is an increase in the foreign interest rate, will increase the demand for foreign bonds Þ as investors switch into the foreign currency from the $A, the Australian dollar depreciates

- if investors’ expectation of the future value of the Australian dollar increases, this will increase the demand for Australian bonds and the $A appreciates

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› effect of policy - open economy (short run) ! domestic fiscal expansion - ­G

Open economy IS-LM-IP model

An increase in domestic government spending leads to an increase in output. If the central bank keeps the interest rate constant, the LM curve shifts right to go through A′, with no effect on E. If the central bank raises the interest rate, say to i″, equilibrium is at A″ with Y″<Y′ and the exchange rate appreciating to E″.

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› effect of policy - open economy (short run) ! Q: what if i rises?

A: an ­G leads to ­Y .. as output increases, the central bank may be prompted to ­i to prevent overheating .. the ­i will result in ­E, both of which will dampen the demand for goods, offsetting some of G effect

! Q: what is the effect on domestic investment? A: because I = (Y,i) the ­G may lead to two conflicting effects, with an increase due to ­Y but a decrease due to ­i if the central bank raises the interest rate .. if so, the net effect on I may well be ambiguous

! Q: what is the effect on the domestic trade balance? A: because NX = NX(Y,Y*,E) the ­G will unambiguously result in ¯NX because higher output means ­IM and the appreciation means ¯X as well as ­IM .. this relationship – that higher fiscal deficits lead to a wider trade deficits is known as the ‘twin deficit’ hypothesis

Open economy IS-LM-IP model

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› effect of policy - open economy (short run) ! domestic monetary contraction - ­i

Open economy IS-LM-IP model

A domestic monetary policy contraction – rise in the interest rate - leads to a decrease in output, and an appreciation. The increase in the interest rate affects neither the IS curve nor the position of the interest-parity curve.

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› effect of policy - open economy (short run) ! Q: what happens to IS, LM and IP?

A: at a given level of output, the increase in interest rate to i’ requires open market operations to shift the LM curve from LM to LM’ .. because money does not directly enter the IS relation, the IS curve does not shift .. the economy slides along the IS curve to A’ .. causing an appreciation

! Q: why does the ­i cause an appreciation? A: the ­i makes domestic bonds more attractive, triggering a sell of foreign currency and a buy of the home currency

! Q: how well does this experiment fit the facts? A: for the most part, very well the ISLM model for the open economy is known as the Mundell-Fleming model .. it is the main model in use today .. it implies that an economy cannot simultaneously maintain a fixed exchange rate, free capital movement, and independent monetary policy (the ‘policy trilemma’)

Open economy IS-LM-IP model

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› effect of policy - open economy (short run) ! foreign fiscal contraction - ¯G*

Open economy IS-LM-IP model

A decrease in foreign government spending leads to a decrease in domestic output, an ambiguous effect on the trade balance, and a depreciation. The ¯G* affects the IS curve. There is no direct effect on the position of LM or IP.

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› effect of policy - open economy (short run) ! Q: what happens to IS?

A: the IS curve shifts left because the foreign fiscal contraction is likely to decrease home output Y, but the ¯Y is limited by ¯i as well ¯E

! Q: why does the domestic interest rate i fall? A: a reduction in the domestic interest rate i is required to restore goods market equilibrium when the ¯Y occurs (we are assuming no policy response from the central bank)

! Q: what is the effect on the domestic trade balance? A: it depends on the net effect from opposing forces .. exports will fall due to ¯foreign demand but imports will also fall with ¯Y .. NX improve with ¯E

! Q: why does the exchange rate depreciate? A: using the IP line, ¯i translates into a fall in E

Open economy IS-LM-IP model

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› effect of policy - open economy (short run) ! foreign monetary contraction - ­i*

Open economy IS-LM-IP model

A foreign monetary policy contraction – rise in the interest rate - leads to an increase domestic output, and a depreciation. The ­i* affects the position of the domestic IS and IP curves.

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› effect of policy - open economy (short run) ! Q: what happens to IS, LM?

A: the IS curve shifts right because the rise in i* tends to create a depreciation of the home currency, thereby increasing net exports and domestic output .. LM is unaffected .. the increase in Y is limited by the interest rate rise and will depend on the relative size of the exchange rate fall (E depreciation is stimulatory) versus the interest rate rise (­i is contractionary)

! Q: why does the domestic interest rate i rise? A: the ­i* requires a rise in the domestic interest rate i to maintain international parity

! Q: what is the effect on IP? A: the IP line rotates anticlockwise and becomes steeper with ­i* because for any given E, an increased domestic i is required to maintain parity

Open economy IS-LM-IP model

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› interest rate risk premia ! so far, we have developed the Mundell-Fleming model assuming

riskless international bond markets .. but in reality we need to take account of imperfect substitutability between domestic and foreign bonds

! recall (week 9 slide 28) the international forward arbitrage relation (1+it) = (1+i*t) [Et/Eet+1]

and the closely allied interest parity relation Et = [(1 + it)/(1 + i*t)] Eet+1] this was developed under a working assumption of perfect bond substitutability where international investors were not concerned about foreign risks such as default risk, currency risk, liquidity, macro slump, or unstable political system, that can affect the return on foreign bonds

! when comparing bonds from two countries with differing risk characteristics investors will demand a risk premium be added to the interest rate of the riskier country, in order to remain indifferent between the two bonds in equilibrium

Open economy IS-LM-IP model

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› interest rate risk premia ! define r = risk premium attached to the home country bond ! then the interest parity relation becomes

Et = [(1 + it)/(1 + i*t)(1 + rt)] Eet+1 this effectively ‘discounts’ the return on the home country bond for the perceived extra risk it entails the value of r can vary over time and so we give it a time subscript if investing in the domestic bond is seen as riskier than the foreign bond, then r > 0 (and vice versa) .. if r = 0 the two are perfect substitutes

! suppose r > 0 and interest rates are set by the respective central banks and assume Eet+1 is given (= Ee) Þ then ­r means E must immediately fall

conclusion: ­r acts like an ­i* .. the IP curve will rotate anticlockwise (like the diagram on slide 12) .. E will depreciate .. IS shifts right .. ­Y

Open economy IS-LM-IP model

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› interest rate risk premia the risk premium is subjective, and will undulate over time

Open economy IS-LM-IP model

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› exchange rate dynamics ! so far, we have developed the Mundell-Fleming model assuming

instant macro adjustment .. but in reality we need to take account of exchange rate adjustment responses and lags

! recall (slide 14) the international forward arbitrage relation (1+it) = (1+i*t) [Et/Eet+1]

and write it as Et = [(1+it)/(1+i*t)] Eet+1 (1)

which says the exchange rate this year depends on the one-year domestic interest rate, the one-year foreign interest rate, and the exchange rate expected for next year

! we no longer assume Eet+1 is given and constant .. in fact this is not likely to hold, because if we consider the equation .. it is clear that the exchange rate for next year will depend on next year’s i and i* .. as well as the E expected for the following year .. and so on ..

Open economy IS-LM-IP model

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› exchange rate dynamics ! that is, any change in expectations of future domestic and/or foreign

interest rates, as well as future exchange rates, will affect E today ! for year 2 the equation is

Et+1 = [(1+it+1)/(1+i*t+1)] Eet+2 which says the exchange rate next year (t+1) depends on the domestic interest rate and foreign interest rate for t+1 and Ee for t+2 .. .. so the expectation for the t+1 exchange rate .. held as of year t .. is

Eet+1 = [(1+iet+1)/(1+i*et+1)] Eet+2 and using this to replace Eet+1 in equation (1) gives

Et = [(1+it)(1+iet+1)] / [(1+i*t)(1+i*et+1)] Eet+2 which says: the current exchange rate depends on this year’s domestic and foreign interest rates, next year’s domestic and foreign interest rates, and on the expected exchange rate two years from now

Open economy IS-LM-IP model

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› exchange rate dynamics ! continuing to solve forward in time until (say) year n gives

Et = [(1+it)(1+iet+1)..(1+iet+n)] / [(1+i*t)(1+i*et+1) ..(1+i*et+n)] Eet+n (2) which tells us that the current E depends on two sets of drivers: - current and expected future interest rates over the next n years - the expected exchange rate n years from now the linkages across time are recursive, a continual process of intertemporal arbitrage

! an implication of equation (2): any factor that moves these two sets of drivers will move the current exchange rate

eg. if investors this year expect domestic i to rise next year (relative to foreign rates) the current E rate will appreciate this year .. if next year investors expect domestic i to fall the following year, then the E rate at that time will depreciate

therefore it’s not surprising if Et changes even if today’s i rates don’t

Open economy IS-LM-IP model

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› exchange rate dynamics for example, the $A is known as a ‘commodity currency’ and often moves based on news of world commodity prices, even if today’s i is unchanged

Open economy IS-LM-IP model

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› exchange rate dynamics ! another implication of equation (2): exchange rates will exhibit continual

short term volatility as market expectations shift around eg. suppose the central bank cuts the current interest rate .. financial markets need to assess whether this signals a major shift in monetary policy stance (implying the cut is the first of many future cuts) or if this cut is just a temporary movement in interest rates .. .. using the n-year equation (slide 19) and assuming Eet+n = 1 and that all interest rates equal 5%, then the current E rate is given by

Et = (1.05)n/(1.05) n x 1 = 1 next, consider a monetary expansion which decreases the current domestic interest rate from 5% to 3% and compare two scenarios scenario 1 – the ¯i is seen as temporary for only one year .. so E’t = (1.03)(1.05)n-1/(1.05) n x 1 = (1.03)/(1.05) = 0.98 (ie 2% depreciation)

scenario 2 – the ¯i is seen as persisting for five years .. so E’t = (1.03)5(1.05)n-5/(1.05) n x 1 = (1.03)5/(1.05)5 = 0.90 (ie 10% depreciation)

Open economy IS-LM-IP model

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› exchange rate dynamics for example, the chart shows constant gyrations in the US$/$A exchange rate over a period of one month, even within the daily trading range

tradingeconomics.com

Open economy IS-LM-IP model

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› exchange rate dynamics ! a further implication of equation (2): exchange rates will overshoot

suppose the central bank announces a 2% increase in the policy interest rate and that remain it will two percent higher for the next 5 years Q: what will be the effect on the exchange rate today? A: we work backwards in time .. start five years in the future

- because it doesn’t alter expectations of interest rates beyond 5 years, there is no change in the expected interest rate five years from now

- it follows that the announcement doesn’t change expectations of the medium run E rate either (E5=E0)

- from interest parity i-i*=2% for the next 5 years implies expected depreciation each year of 2%, or 5x2=10% over 5 years

- so the exchange rate today must appreciate by enough so that 10% cumulative depreciation over 5 years gets the E rate back to E0

with a tighter monetary policy both Et and Eet+1 rise - but Et rises more at t

Open economy IS-LM-IP model

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› exchange rate dynamics the example illustrates exchange rate overshooting

after 5 years i and E return to their pre-announcement values .. but in the interim the exchange rate overshot its medium run value

Open economy IS-LM-IP model

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› open economy comprehensive model ! we combine the IS-LM-IP model and the AS-AD equations with P level

dynamics (Weeks 5-6) and E rate dynamics (Weeks 9-10) to understand the economy’s response in the short-to-medium run

! the comprehensive chart on the next slide has 3 panels: - ISLM panel: the central bank has set the interest rate at in according to the interest rate rule i = in+a(P–PT) (week 5 slide 8) .. output is at the natural level Yn (determined by the long run economic growth model at the steady state) .. price level is at its target level PT0, so i = in .. the open economy IS and LM curves are as per slide 4 …

- IP panel: the interest rate in is associated with exchange rate E0 .. in the medium run equilibrium E0 = Eet+n and both are constant .. and i = i*

- AS-AD panel: output is at Yn and price level is PT0 which is the policy target .. the AS curve is unchanged from the closed economy .. the open economy AD curve extends the closed AD relation by adding a second channel for P effects (­P ® ­e ® ¯NX, ¯I ) and is flatter

Open economy IS-LM-IP-AS-AD model

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› open economy comprehensive equilibrium (geometric)

Open economy IS-LM-IP-AS-AD model

In medium-run equilibrium, output is at the natural level, the interest rate equals the foreign rate, and the price level equals the target.

Q: can you guess what the 4th quadrant must show? A: axes are (E,P), downward-sloping curve, e held fixed (s6 wk9)

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› open economy comprehensive dynamics ! monetary policy contraction - ¯PT (short run)

Open economy IS-LM-IP-AS-AD model

Short run effect - a monetary policy contraction leads in the short run to an increase in the interest rate, a fall in output, a small fall in the price level, and an overshooting appreciation of the nominal exchange rate beyond the medium-run effect. Q: from the 4th quadrant, what is the policy’s short run effect on e? A: curve briefly shifts right, e temporarily rises

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› open economy comprehensive dynamics ! Q: where is the economy in the short run, after the monetary contraction?

A: at point B ! Q: what happens to IS and LM in the short run?

A: as soon as the central bank announces the lower target PT1 it begins increasing the interest rate to iB .. this requires open market operations to shift LM up to LMB .. the higher E (see below) sees IS shift left to ISB

! Q: what happens to AS and AD in the short run? A: the lower PT (and higher Ee) require a leftward shift in AD to AD1 .. raising the interest rate generates a cyclical output slump to YB in the short run .. this is just like in the closed economy, but in the open economy there is an additional reason, an overshooting E rate that goes to EB

! Q: what happens to IP in the short run? A: since P is lower, the nominal exchange rate E must appreciate Þ Ee1 must also rise Þ IP shifts right and becomes flatter but goes too far to IPB

Open economy IS-LM-IP-AS-AD model

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› open economy comprehensive dynamics ! monetary policy contraction - ¯PT (medium run)

Open economy IS-LM-IP-AS-AD model

Medium run outcome - a monetary policy contraction is a reduction in the price level target, which leads to a stronger nominal exchange rate but no real effects in the medium run.

Q: from the 4th quadrant, what is the policy’s medium run effect on e? A: curve shifts back again, e unaffected

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› open economy comprehensive dynamics ! Q: is the effect of a monetary contraction on medium run real variables

in the open economy different to the closed economy? A: no – the medium run real effects are neutral .. Y returns to Yn and e to e0

! Q: what happens to AS and AD in the medium run? A: after PT falls to PT1 AS shifts right (because Pe falls) and AD shifts left (P must fall at any given Y level) to go through A1 at the lower price level

! Q: what happens to IS and LM in the medium run? A: as the P level reaches the lower target in the medium run, the interest rate set by the central bank returns to in .. with Yn and e0 unchanged, the IS and LM curves return to their original positions

! Q: what happens to IP in the medium run? A: since e ends unchanged while P is lower, the nominal exchange rate E must appreciate to E1 Þ so Ee1 must also rise Þ IP shifts right and becomes flatter Þ new equilibrium is A1 with in = i* and E1 = Ee1

Open economy IS-LM-IP-AS-AD model

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overview - open economy comprehensive model our model combines the IS-LM-IP model and the AS-AD model to give a

comprehensive framework for the economy in the short-to-medium run the key equations

IS: Y = C(Y-T) + I(Y,i) + G + NX(Y,Y*,EP/P*) LM: M/P = YL(i) monetary policy rule: i = in + a(P – PT) IP: E = (1 + i)Ee/(1 + i*) AS: P = Pe(1 + m) F[(1-Y/L),z] AD: Y = Y(P,G,T)

this set of equations summarises our short-to-medium run open economy model developed over Weeks 1-10

Open economy IS-LM-IP-AS-AD model

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Short-to-medium run macroeconomy - empirical view (Australia real GDP growth, quarterly %)