ee =θ(e – e), 0 <θ<1 Equation (2)
Next, the equilibrium in the money market requires the real money supply m-p to equal real money demand which depends positively on real income, here assumed to be constant at the natural rate of output y, and negatively on the interest rate:
m – p = ky –λr, k,λ> 0 Equation (3)
Consider domestic aggregate demand, which is assumed to be a function of the domestic interest rate, a domestic autonomous expenditure term g and the real exchange rate e+p*-p, which amounts to Ep*/p in non-log terms, a measure of the international competitiveness of domestic output affecting net exports:
y = -γr +δ(e + p* - p) + g Equation (4)
Finally, assume that domestic output is fixed at some natural level y and inflation is a function of excess demand:
p =φ(y – y) Equation (5)
In the long run, the exchange rate is at its long run level e and the domestic interest rate is equal to the foreign interest rate. While income is as always in this model at the natural level y, the exogenous domestic money supply must determine the equilibrium price level and so does the exchange rate. This also shows that money is neutral in the long run. In addition, the long-run equilibrium levels of the exchange rate and the price must be proportionally related. The model therefore incorporates what is called relative purchasing power parity in the long run, which states that the exchange rate between two currencies depends upon the purchasing power of each currency in its country of origin (More detailed algebras are shown in appendix).
Short run equilibrium in asset markets requires that UIP holds and the money market clears. By substituting and rearranging (details are shown in appendix), the relationship between the short-run price level and the exchange rate in terms of the long-run levels is:
p – p = -λθ(e – e)p = p +λθ(e – e) Equation (10)
or alternatively e = e + (p – p)/λθ Equation (11)
Equations (10) and (11) make clear two things: there is an inverse relationship between the actual price and the exchange rate; and when either of these two variables is at its long-run equilibrium level, the other must be so too. The AA curve in Figure 3 represents this diagrammatically.
The short-run goods market equilibrium is found by setting inflation equal to zero (see appendix):
Equation (14)
The relationship between price and exchange rate in terms of deviations from the long-run equilibrium, given what was said above about equation (10), shows that long-run equilibrium in both asset and goods markets occurs at the point (p, e). Equation (14) can also be differentiated to find the relationship between p and e:
Short run goods market equilibrium requires that for a higher exchange rate the price must be higher but not as much. A rise in e improves competitiveness and raises aggregate demand; a rise in p reduces competitiveness and raises the interest rate via the money market, reducing aggregate demand in both ways. Thus, for aggregate demand to remain equal to output, a rise in e must be accompanied by a smaller rise in p. The GG curve in Figure 3 represents this and the AA and GG curves interest on the 45 line at the long-run equilibrium levels e and p.
Figure 3
P AA
GG (p = 0)
e e
In Figure 4, above the e = 0 schedule the price is above its long-run equilibrium, so the interest rate is above the foreign level and the exchange rate is depreciating. These movements are indicated by the horizontal arrows. To the left of the p = 0 schedule the exchange rate is below the level where aggregate demand equals output, therefore there is excess supply and the price is falling. These movements are indicated by the vertical arrows. The AA schedule then can be seen as the locus of the points at which the left-right and up-down movements combine to bring about a movement towards the full equilibrium. This is the “saddle path”, which is the unique stable path along that full equilibrium can be approached in rational expectations models, and it is assumed that the economy ‘jumps’ on to such a path.
Figure 4
AA GG (p = 0)
When money supply increases, the GG schedule shifts up to GG’ in Figure 5. The long-run equilibrium price and exchange rate are both increased by the same amount. The AA schedule therefore shifts out to the right so that it intersects GG’ at E’ on the 45 line. In the short run, the price level is fixed at p0 so the exchange rate jumps from e0 to e1 on AA’. From there the economy gradually moves along AA’ until it reaches the new long-run equilibrium point E’ with the price and the exchange rate at p1 and e1 respectively.
Figure 5 p AA
E’ GG’
GG
E
0 e0 e
So the monetary expansion brings about a higher domestic price and a depreciated exchange rate in the long run. In the short run because of the price stickiness, the interest rate falls and this requires an expectation of appreciation. Therefore, the exchange rate, as shown in Figure 6, overshoots in the short run.
Figure 6
On the other hand, when there is fiscal expansion, ie, an increase in g, the GG curve shifts upwards to GG’ in Figure 7. It does not affect the equilibrium price but shifts upwards the 45 line. Since the new long-run equilibrium is at point E’, the AA curve shifts down to AA’ and the exchange rate moves directly to e1, without any overshooting and any change in the price level.
Figure 7
p
0 e
The underlying behaviour is as follows: the larger fiscal deficit boosts aggregate demand but this is offset in the long run by the appreciation of the exchange rate which reduced international competitiveness. Since the price does not have to change, its stickiness does not slow down the adjustment, the economy moves to the new full equilibrium at once.
In Dornbusch overshooting model, exchange rates overshoot in response to monetary, but not fiscal policy changes. The key reason for this result is the assumption that financial markets clear quickly but goods markets slowly.
It can be seen that the Mundell-Fleming model is well in line with the Dornbusch model, both suggesting that monetary and fiscal policy have indeed played different roles in exchange rate movements. Is there any positive empirical evidence in recent history?
Let us look behind the strong appreciation of dollar in the 1980s as an example. Since 1980 the dollar had undergone a massive appreciation in world currency markets.
By the late 1970s, the chairman of the Fed, Paul Volcker, concluded that US inflation was too high and had to be reduced. He started a sharp monetary contraction in late 1979. Interest rates, both nominal and real, increased sharply. In 1986, US interest rates exceeded those in Germany or Japan by more than 250 basis points. The long-term interest differential between the US and Germany or Japan exceeded 400 basis points. These differentials would imply a really huge incentive to hold US securities, leading to a large dollar appreciation.
The change in fiscal policy was triggered by the election in 1980 of Ronald Reagan, who promised a scaling down of taxation and the government’s role in economic activity. However, big tax reductions were accompanied by increasing government spending, and resulted a steady increase in budget deficits. Table 1 shows data on that the US has shifted dramatically toward a deficit while Germany and Japan have moved in the opposite direction with as much vehemence. From 1982 on, the economy was dominated by the effects of the fiscal expansion which leaded to even higher interest rates and further dollar appreciation.
Table 1 Government budget trends (percent of GDP)
Thus, the strong dollar in 1980s can be seen primarily as a reflection of monetary and fiscal policies in the US and abroad.
Another example is the rise of the sterling since 1996. The Bank of England raised interest rates and the market expected future rises, which was the main reason behind sterling’s rise. But in 1998 the sterling kept rising while the interest rates remained stable and the difference between UK and other interest rates had reduced.
Sterling’s continued strength was a surprise over a period where the UK economy has begun to slow and interest rate expectations have been scaled back. However, this is consisted with the delayed overshooting model: the currency tends to carry on reacting to monetary policy shocks after the event. In this model, the exchange rate does not jump instantaneously to a new equilibrium level, but it continues to move for some time after the change in monetary policy. Individuals face a signal extraction problem when observing a monetary shock and they must infer whether the policy change is permanent. Given imperfect information, the only way to do so is to apply a filtering rule which suggests an increased probability that a monetary policy is persistent the longer it lasts. Under this framework, the exchange rate adjusts slowly to a monetary shock as agents only slowly realize that the shock is persistent.
Figure 7 Exchange rate overshooting models
However, some economists argued that so little of the post-1995 appreciation was explained by the change in monetary policy by using UIP-based methodology and they believed the behaviour of sterling during that time was puzzle. There are also many alternative explanations such as that the real exchange rate was low by historical standards in early 1996; and the German unemployment increased sufficiently relative to UK unemployment which resulted a further appreciation.
To sum up, both the Mundell-Fleming model and the Dornbusch model indicate that a contractive monetary policy or an expansionary fiscal policy will lead an appreciation and vice versa. However, the exchange rates only overshoot under monetary policy. The rise of dollars in 1985 was due to the mixture of monetary and fiscal policy, and the appreciation of sterling since 1996 was also due to the tight monetary policy. Therefore, these theories do explain exchange rates fluctuations with relatively strong evidence.
Bibliography
Dornbusch, “Expectations and Exchange Rate Dynamics”, Journal of Political Economy 1976
Blanchard, Macroeconomics, Chapter 21, Appendix, p418-420
Gartner, Macroeconomics, Chapter 5, section 5
Cobham, Macroeconomics Analysis, Chapter 18
Dornbusch, Dollars, Debt and Deficits (1986), Chapter 1
Breedon and Michaelides, ‘Sterling’s Rise: A Case of Delayed Overshooting?’, Economic Outlook, May1998
Wadhwani, ‘Sterling’s Puzzling Behaviour’, Bank of England Quarterly Bulletin, Nov. 1999
Appendix
In the long run
In the long run, e = e, r = r* and y = y. Substituting equation (1) and (2) in (3) gets:
m – p = ky –λr* Equation (6)
The right-hand side of this equation is given, so that the exogenous domestic money supply must determine the equilibrium price level p:
p = m – ky +λr* Equation (7)
Long run equilibrium also requires that aggregate demand is equal to output, ie:
-γr* +δ(e + p* - p) + g = y
which applies e = p – p* + (y +γr* - g)/δ Equation (8)
As y, p* and r* are exogenous, once p is determined from equation (7), e is determined as well.
Short run assets market equilibrium
The short run asset markets equilibrium can be found by substituting from equation (1) and (2) in (3):
m – p = ky –λ[r* +θ(e – e)] = ky –λr*-λθ(e – e) Equation (9)
Rearranging equation (7) for the long-run equilibrium as m – p = ky -λr* and subtracting it from (9) gives the relationship between the short-run price level and the exchange rate in terms only of the long-run levels.
Short run goods market equilibrium
From equation (5) zero inflation requires that aggregate demand is equal to output: δ(e + p* - p) –γr + g = y. In the short run the domestic interest rate is not equal to the foreign rate but is determined from equation (3). Substituting from there and rearranging gives: δ(e + p* - p) –γ+ g = y
Equation (12)
The long-run equilibrium of (12) is:
Equation (13)
and subtracting from (12), we get the relationship between price level and exchange rate more simply in terms of deviations from the long-run equilibrium.