Lectures 5-6 Lecture 5: Flexible prices - the monetary model of the exchange rate Lecture 6: Fixed-prices - the Mundell- Fleming model Chapters 5 and 6 in Copeland
IS-LM revision Exchange rates and Money With a pure floating exchange rate, official financing is not used to manipulate the exchange rate because This means that the money stock can be controlled by the government (maybe?). It is an instrument With a fixed exchange rate, foreign reserves are used to fix the exchange rate FX 0 Therefore, the government looses control of the money supply since it is in part endogenous determined by the factors determining the BOP FX 0
4.1.2 Money market: LM curve Equilibrium in the money market when S=D Equation (4.9) means M s d / P0 M / P ky lr k, l 0 (4.12) Fix P P 0 ky lr M s / P k, l 0 0 0 (4.13) which has the same general form as the equation of the IS curve in that there are now 2 unknowns, y and r. On a given LM curve: at a lower r - money demand>money supply so the lower r needs to be offset by a lower income y to reduce money demand, for the money market to clear
4.1.2 Money market: LM curve Figure 4.3 the LM curve Issue 1: a given LM curve is upward sloping; Issue 2 an increase in M or a decrease in P shifts the LM curve to the right
IS-LM We can now put the IS and LM curves together to produce a unique solution for y and r And changes in things such as G or money will change the equilibrium of the system
Aggregate Demand We can then see how the IS-LM equilibrium varies as the price level changes This gives the aggregate demand (AD) curve
4.1.3 Aggregate demand Figure 4.4 derivation of the aggregate demand curve; and the effects of a higher price level
Aggregate supply We have an aggregate demand curve, if we face this with an aggregate supply curve we can then derive the full solution to the system Two extreme assumptions: Classical flexible prices Keynesian fixed prices
Classical flexible prices Supply is determined by firms and the production function Production is a function of employment Employment is determined by the labour market which fixes the real wage (at the MP of labour) to make demand and supply equal So the AS curve is vertical at the long-run/trend level since the nominal wage adjusts to price changes to keep the real wage constant no money illusion Prices are determined by the AD curve
Figure 4.5 derivation of the classical aggregate supply curve; & response to P
Keynesian fixed nominal wages The extreme Keynesian assumption is that nominal wages will not respond: they are fixed Due to contracts, unions So the effective labour supply curve is horizontal at a given nominal wage rate But firms continue to react to price changes So as prices change, the real wage changes and firms change their production levels Prices and quantity are determined by AD
Figure 4.6 derivation of the Keynesian aggregate supply curve; & response to P
A compromise case Sticky prices Wages and prices are fixed in the short-run (as in the Keynesian case) but wages and prices do adjust eventually (as in the Classical case) so that real variables do not change So the AS curve gets steeper as time passes This analysis underpins the Dornbusch exchange rate model
4.2.3 A compromise: sticky prices Figure 4.7 the sticky price aggregate supply curve
Chapter 5 Flexible Prices: the Monetary Model
Monetary Model: General Features Originates from Hume s Theory of Price-specie Flow in 1741 Links exchange rate movements to balance of payments equilibrium Dominant theory of the 1970s Still used for medium- to long term forecasting
5.1 the simple monetary model of a floating exchange rate 5.1.1 Setting The Monetary model rests on three assumptions: 1. the aggregate supply curve is vertical 2. the demand for real money balances is a stable function of only a few domestic macroeconomic variables using the Cambridge quantity equation (4.7), in equilibrium: s d M M kpy ky k 0 where y is real national income 3. PPP obtains at all times
4.2.3 A compromise: sticky prices Figure 4.7 the sticky price aggregate supply curve
Nominal income Y, which is constant along AD 0, is measured by the area of the rectangle between any point and the axis e.g. P 0 Ay 0 0 = P 2 Dy 1 0. P Aggregate demand with the quantity equation P 1 B P 0 A C P 2 D AD 1 (M s 1) y 0 y 1 AD 0 (M s 0) y
Disturbance (quantitative easing): M 0 s increases to M 1 s Result: AD 0 shifts to AD 1 How big is this shift? Compare points A and B. P 1 must be higher than P 0 by the same proportion as M 1 s is greater than M 0 s e.g. if money supply doubles, so must aggregate demand. With constant real income and output, this must imply a doubling of the price level But PPP must be preserved; so exchange rate will adjust
Leads to a depreciation (S ) in proportion to the money supply increase. This depreciation is needed to restore competitiveness, given that P Left panel is locus of points that satisfy PPP Right panel shows AD-AS given M, P* and y Figure 5.2 effects of a money supply increase under floating rates
5.1.2 Equilibrium Combining Equations 2.4 (PPP) and 5.1, M s kpy ksp * y (5.2) which is solved for S as: S M s / * kp 0 y (5.3) The exchange rate is the ratio of the money stock to the demand, measured at the foreign price level.
Predictions of the Monetary Model Home currency will depreciate (S will increase) whenever: Home money stock increases Home real income decreases Foreign price level falls fall
Contracts (Mundell-Fleming) idea that real income rises suck in imports and hence leads to a depreciation. This is because the excess demand for money, due to income increasing, means less demand for goods and therefore a lower P. With P* fixed this implies S (an appreciation) 5.1.4 Real income increase under floating exchange rates Figure 5.3 real income increase under floating exchange rates implies S (appreciation)
5.1.5 Foreign price increases under floating exchange rates Figure 5.4 foreign price increases under floating rates P* increases gradient of PPP line: so the appreciates to restore competitiveness and there are no other effects on the domestic economy (right hand side panel is unchanged) So world inflation does not affect domestic economy; P determined as in closed economy model by AD-AS, with domestic policymaker able to control domestic inflation
5.1.6 Two-country model of a floating exchange rate But what can have caused P* to rise? Presumably the same factors that determine P So consider the foreign-country version of the quantity equation (4.7): * * M d k P * y * (5.4) d * - foreign demand for money, M, proportional to foreign nominal income P * y * Dividing the UK demand for money equation (4.7) by (5.4) and setting the demands for money equal to supply in each country, M s s* * * * / M kpy / k P y 0 0 (5.5)
5.1.6 Two-country model of a floating exchange rate (continued) Under PPP, P/ P * S, and (5.5) can be rewritten as: M / M k. Sy / k y s s* * * 0 0 (5.6) Solving for S, S M / M * ky / k y * * (5.7) - the exchange rate equals the ratio of the relative money stocks to the relative real money demands Therefore, it is relative movements in both the money supply and real incomes that matter
What about the monetary model with fixed exchange rates? Important to clarify what is exogenous Money stock is endogenous, since monetary policy needs to defend the fixed exchange rate, S Money stock contains FX component which increases (decreases) when there is excess demand (supply) for domestic currency, so domestic credit is the monetary policy instrument not the money supply as a whole Endogenous: P, FX Exogenous: y, P* (determined by foreign money supply) and DC (domestic credit: recall FX+DC=money supply)
Figure 5.5 domestic credit increase, DC0 to DC1, under fixed rates ( M s P 0 0 is neutralised by a fall in the foreign reserves FX due to the temporary BOP deficit which progressively reduces the money supply and reduces P 1)
5.2.1 Money supply increase If reserves = FX 0 Money stock: (5.9) 0 FX0 DC0 M s Under a fixed exchange rate regime, the policy variable for the money supply is domestic credit, DC 0 Recall in a floating exchange rate regime, unlike a fixed regime, the BOP=0; the authorities do not use foreign currency reserves to intervene in the currency markets so that: s FX 0 and M DC
5.2.1 Money supply increase (continued) If the exchange rate is pegged at S 0, under PPP, P S P * 0 (5.10) M d ks * s 0P y M FX DC0 (5.12) FX ks * 0P y DC0 (5.13) The foreign currency reserves must be equal to the gap between - given demand for domestic money - supply generated by the local banking system.
Conclusions re. Fixed Exchange Rates: In a fixed exchange rate system, the (change in the) stock of reserves simply fills the gap between the demand for money and the domestically generated supply (DC) Domestic credit expansion changes nothing, except composition of money stock: increase (decrease) in DC offset by fall (rise) in reserves, so post-expansion money stock is: M s 1 = FX 1 +DC 1
Q. What happens if authorities prevent money stock returning to its previous level by further increasing DC? Sterilisation can only work in the short run, if at all. Pushing the M s curve up again simply repeats the same process of balance of payment deficits followed by reserve loss The longer the policy is sustained, the greater the domestic credit component of M s and the smaller the stocks of foreign reserves At some point, the fall in the reserves leads to collapse of the fixed exchange rate regime as speculators sell the domestic currency anxious to convert while they can (see Chapter 17)
Change in real income under fixed exchange rates Initial situation: M s 0 = P 0 = 1 ky 0 = 1, since M s 0 = kp 0 y 0 Disturbance to income: rightward shift to AS-curve Causes P as public spend less to raise their money balances. This leads to a BOP surplus and an increase in FX which increases M s and restores P0 AS M s 0 AS 1 P P FX+DC 0 P = SP 0 * P 1 P 0 P 0 =1 M s 1 P 1 M s 0 M s 1 M s 0 S Y r 0 Y r 1 Y r DC 0 FX 0 FX 1 FX
5.2.4 Devaluation under fixed exchange rates Imagine a one-off devaluation designed to eliminate a BOP deficit Figure 5.6 devaluation under fixed rates ( M s P 0 0 Move from S0 to S1 with P and P* fixed in the very short run means we move from A to C, where S is over-competitive. This leads to BOP surplus and FX ; and move from G to H and then upward shift of AD curve as M s increases. So there s inflation until we reach B 1)
Conclusion re. devaluation Devaluation raises domestic competitiveness creating temporary balance of payments surplus and consequent reserve increase, until money stock increases in same proportion as devaluation J-curve effect could mean that the devaluation will, in fact, be initially followed by an increase in the deficit, before it s reversed, as each unit of exports earns less but imports cost the same (as the devaluation affects the $ price of exports but not imports in the SR) Final outcome: higher domestic price level with cheaper domestic currency means real exchange rate (competitiveness) unchanged, balance of payments back in balance Only change: one-off increase in reserves
5.3 Interest rates in the monetary model Extend Cambridge quantity equation to allow for interest rates M s Figure 5.7 interest rate increase (could be relative to abroad) under floating exchange rates: from a to c (where P ) to b, where S has depreciated Changes in r are not exogenous; expectations about S cause immediate changes in r
Fig 5.8 UK Money, Income and Exchange Rate 1975-99 1995 = 100 150.0 140.0 UK M1/USM1 UKGDP/USGDP per $ 130.0 120.0 110.0 100.0 90.0 80.0 70.0 60.0 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Year
Figure 5.9 German Money, Income and Exchange Rate 1975-99 1995 = 100 250.0 230.0 210.0 German M1/USM1 German GDP/US GDP DM per $ 190.0 170.0 150.0 130.0 110.0 90.0 70.0 50.0 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Year
Figure 5.10 Japanese Money, Income and Exchange Rate 1975-99 1995 = 100 500.0 450.0 400.0 Japanese M1/USM1 Japanese GDP/US GDP Yen per $ 350.0 300.0 250.0 200.0 150.0 100.0 50.0 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Year
Conclusion The basic monetary model has been outlined In practise this does not seem to explain anything but very long run fluctuations in the exchange rate For the class, read Meese & Rogoff (1983) Journal of International Economics; available at: http://www.le.ac.uk/economics/teach/ec7075/ec7075.html
Chapter 6 Fixed Prices: the Mundell-Fleming Model
Introduction The Mundell-Fleming model is the opposite extreme to the monetary model It adheres to the Keynesian tradition with prices fixed (AS curve is horizontal), y is determined by the AD curve; and we need only consider the IS-LM model May be used for fixed and floating exchange rates Very popular in 1960s/70s
6.1 Setting: Assumptions 1. The aggregate supply curve is flat (i.e. prices/wages fixed, as in Keynesian paradigm). Set domestic and foreign price level = 1 (for simplicity), so Q = SP*/P = S; and M denotes real and nominal money stocks 2. Short run view: instead of PPP, current account equilibrium condition: B 0 (6.1) B B( y, Q) B( y, S) 0 - the current account surplus (B) depends: positively on the real exchange rate (competitiveness) negatively on real income via consumption effect (contrasts with the monetary model where if domestic income rises the exchange rate appreciates as M d causing P ) y 3. Exchange rate expectations are static 4. Capital mobility is less than perfect, so interest rate differential in favour of domestic country causes finite capital inflow - could be down to risk aversion B s
Values of y and r satisfying (6.4) for two different values of S are plotted in the BP lines in Figure 6.1(b): BP line is upward sloping, since as y (at a given S) the current account deteriorates as imports. To preserve equilibrium, the capital account must improve so r (perfect capital mobility implies a flat BP line). A rise in S (depreciation) implies BP shifts down and to the right except when BP is flat and unaffected by changes in S 6.1 setting (continued) Pure floating exchange rate regime requires balance of payments (BP) to be in equilibrium at all times: i.e., B( y, S) K( r r*) 0 (6.3) (strictly FX=0), where B is current account surplus and K is capital account surplus. i.e. capital account surplus (deficit) must offset current account deficit (surplus) Home country s capital account surplus positively (negatively) related to home (foreign) interest rate Taking the foreign interest rate r* as given: F( y, S, r) 0 0 0 0 F y F s F r (6.4)
Diagrammatic Apparatus: IS-LM-BP Figure 6.1: Monetary Expansion under a Float NW corner: FF line plots r, S combinations consistent with balance of payments equilibrium (equation (6.4)) slopes down: lower interest rate smaller capital inflow smaller current account deficit/larger surplus greater exchange rate (cheaper currency) NE corner: IS-LM plus BP line plotting r, y combinations consistent with balance of payments equilibrium (equation (6.4)) slopes up: lower interest rate smaller capital inflow smaller current account deficit/larger surplus lower income level (lower net imports) SW corner: TT line plots S, y combinations consistent with balance of payments current account equilibrium (equation (6.1)) slopes up: higher income level smaller current account deficit/larger surplus higher exchange rate (cheaper currency) SE corner: 45 0 line
Figure 6.1 (real=nominal) monetary expansion under floating rates in the M-F Model. LM shifts to the right, so r. But we don t move all the way from A to C as the lower r induces a current & capital a/c deficit. So S and IS shifts to the right too. Current a/c ends up at F, in surplus
6.3 Conclusion: Monetary expansion with a floating exchange rate Proposition 6.1 In the M-F model of a floating exchange rate, money supply increase causes: a depreciation in the exchange rate an increase in income a fall in the interest rate, provided capital is not completely mobile an improvement in the current account of the balance of payments
6.4 Fiscal expansion with a floating exchange rate Figure 6.2 fiscal expansion under floating rates in the M-F model IS shifts to the right as the gov must finance its increased spending not by increasing money (printing money) but by borrowing it can access these funds only by raising r. But C is inconsistent with BOP equilibrium as higher r leads to capital inflow and an insufficient outflow due to imports rising. So S and IS shifts back to B and F (a current a/c deficit due to y and S ). When capital is mobile both LM and BP are fixed, so IS can move only temporarily S moves to offset increased G crowding out
6.5 Fiscal expansion with a floating exchange rate Proposition 6.2 In the M-F model of a floating exchange rate, fiscal expansion causes: an appreciation in the exchange rate an increase in income provided capital is not completely mobile a rise in the interest rate provided capital is not completely mobile a deterioration in the current account of the balance of payments
Fiscal Expansion With A Floating Exchange Rate And Perfect Capital Mobility IS 1 (G 1, S 0 ) IS(G 0, S 0 ) LM 0 r = r* BP(S 0 ) = BP(S 1 ) y 0 All of the increase in G is neutralised by a reduced demand from the external sector as the exchange rate appreciates. This is because r is pegged by the international capital markets; so the burden of adjustment falls on S monetary policy is more effective than fiscal policy y
6.5 Monetary expansion with a fixed exchange rate Figure 6.3 monetary expansion under fixed rates in the M-F model DC causes LM to shift down so current a/c worsens at F. So to maintain S, FX so money supply contracts and LM curve returns to initial position
6.5 Monetary expansion with a fixed exchange rate: in sum Proposition 6.3 In the M-F model of a fixed exchange rate, a money supply increase causes: In the short term (and provided capital is not completely mobile, if so SR=LR) a fall in the interest rate a rise in income a deterioration of the balance of payments on both current and capital accounts In the long term a fall in the foreign currency reserves and a rise in DC no change in income, the interest rate or the balance of payments
6.6 Fiscal expansion with a fixed exchange rate Figure 6.4 fiscal expansion under fixed rates in the M-F model IS shifts to the right and r. But C is above the BP line: capital a/c improves by more than the current a/c deteriorates. So FX as foreigners buy as r is high. So money supply increases and LM shifts down and external balance is restored at J with a current a/c deficit at D
6.6 Fiscal expansion with a fixed exchange rate: in sum Proposition 6.4 In the M-F model of a fixed exchange rate, fiscal expansion causes the following changes: In the short run a rise in the interest rate and income an overall surplus on the balance of payments (net reserve gain) In the long run a further increase in income a fall in the interest rate a fall in the balance of payments surplus to zero, leading to a substantial current account deficit
6.7 The Monetary model and the M-F model compared The M-F model, in contrast to the monetary model - emphasises the level of activity and interest rates rather than the price level In the monetary model changes in real income can only be exogenous events. Increases in income increase Md and hence S. In the M-F model they are endogenous and (i) raise Md; (ii) raise C and (iii) worsen the current a/c so S In the monetary model r determined by loanable funds market and r*. So P does the adjusting. In M-F, UIRP does not hold and r clears both the money and goods markets - concentrates on flows of spending and capital rather than on stocks of assets - gives a central role to the crowding-out mechanism
Conclusion Neither the monetary nor the M-F model provide a good account of real world events They are however two extreme versions of how the world might work and provide a good starting point to understand exchange rates more fully