4 A Complete Theory: Unifying the Monetary and Asset Approaches

In this section, we extend our analysis from the short run to the long run, and examine permanent as well as temporary shocks. To do this, we put together a complete theory of exchange rates that couples the long-run and short-run approaches, as shown schematically in Figure 4-11:

• We need the asset approach (this chapter) — short-run money market equilibrium and uncovered interest parity:

  

• There are three equations and three unknowns (two short-run nominal interest rates and the spot exchange rate). The future expected exchange rate must be known, as must the current levels of money and real income. (The price level is also treated as given.)
• But to forecast the future expected exchange rate, we also need the long-run monetary approach from the previous chapter—a long-run monetary model and purchasing power parity:

  

• There are three equations and three unknowns (two price levels and the exchange rate). Note that all variables here have a superscript e to denote future expected values or forecasts. We assume that forecasts of future money, real income, and nominal interest rates are known. This model can then be applied to obtain price forecasts and, hence, a forecast of the future expected exchange rate.2

Figure 4-11 sums up all the theory we have learned so far in the past two chapters. It shows how all the pieces fit together. In total we have six equations and six unknowns.

It is only now, with all the building blocks in place, that we can fully appreciate how the two key mechanisms of expectations and arbitrage operate in a variety of ways to determine exchange rates in both the short run and the long run. Ensure you are comfortable with all of the building blocks—how they work individually and how they connect.

After all our hard work, we have arrived at a complete theory to explain exchange rates in the short run and the long run. The model incorporates all of the key economic fundamentals that affect exchange rates and, in practice, although forex markets exhibit a great deal of turbulence and uncertainty, there is evidence that these fundamentals play a major role in shaping traders’ decisions (see Side Bar: Confessions of a Forex Trader).

Long-Run Policy Analysis

When and how can we apply the complete model? The downside of working with the complete model is that we have to keep track of multiple mechanisms and variables; the upside is that the theory is fully developed and can be applied to short-run and long-run policy shocks.

The temporary shocks we saw in the last section represent only one kind of monetary policy change, one that does not affect the long-run nominal anchor. The fact that these shocks were temporary allowed us to conduct all of the analysis under the assumption that the long-run expected level of the exchange rate remained unchanged.

When the monetary authorities decide to make a permanent change, however, this assumption of unchanged expectations is no longer appropriate. Under such a change, the authorities would cause an enduring change in all nominal variables; that is, they would be electing to change their nominal anchor policy in some way. Thus, when a monetary policy shock is permanent, the long-run expectation of the level of the exchange rate has to adjust. This change will, in turn, cause the exchange rate predictions of the short-run model to differ from those made when the policy shock was only temporary.

These insights guide our analysis of permanent policy shocks. They also tell us that we cannot approach such analysis chronologically. Before we can figure out what happens in the short run, we have to know expectations, that is, what is going to happen in the long run. Thus, we have to use a technique that is common in forward-looking economic problems: we must solve backward from the future to the present. (This ordering mirrors the presentation of the material in this textbook—we must understand the long run before we can understand the short run.)

A Permanent Shock to the Home Money Supply We start our analysis of the Home (U.S.) and Foreign (Europe) economies with each economy currently at a long-run equilibrium in which all variables are steady. In this equilibrium, we assume that each country has a fixed real income, a fixed money supply, and a zero rate of inflation. Hence, there is a zero rate of depreciation because the equilibrium is characterized by purchasing power parity, and interest rates in each country are the same because the equilibrium is characterized by uncovered interest parity.

Our analysis is shown Figure 4-12. Panels (a) and (b) show the short-run impacts of a permanent increase in the money supply in the home (U.S.) money and FX markets; panels (c) and (d) show the long-run impacts and the adjustment from the short run to the long run.

As shown in panels (a), (b), (c), and (d), we suppose the home economy starts with initial equilibria in the home money and FX markets shown by points 1 and 1′, respectively. In the money market, in panels (a) and (c), at point 1, the home money market is initially in equilibrium: MS₁ corresponds to an initial real money supply of ; given real money demand MD, the nominal interest rate is . In the FX market, in panels (b) and (d), at point 1′, the domestic return DR₁ is the nominal interest rate . Given the foreign return curve FR₁, the equilibrium exchange rate is . If both economies are at a long-run equilibrium with zero depreciation, then this is also the expected future exchange rate .

We now start to figure out what happens after the policy shock hits today, working backward from the future to the present.

The Long Run Refer to panels (c) and (d) of Figure 4-12. In the long run, we know from the monetary approach that an increase in the money supply will eventually lead to a proportionate increase in the price level and the exchange rate. If the money supply increases from to today, then the price level will eventually increase by the same proportion from to , and, to maintain PPP, the exchange rate will eventually rise by the same proportion (and the dollar will depreciate) from to its long-run level , in panel (d), where . (We use “4” to denote long-run exchange rate values because there will be some short-run responses to consider in just a moment.)

Thus, in the long run, in panel (c), if money and prices both rise in the same proportion, then the real money supply will be unchanged at its original level , the real money supply curve will still be in its original position MS₁, and the nominal interest rate will again be . In the long run, the money market returns to where it started: long-run equilibrium is at point 4 (which is the same as point 1).

In the FX market, however, a permanent money supply shock causes some permanent changes in the long run. One thing that does not change is the domestic return DR₁, since in the long run it returns to . But the exchange rate will rise from the initial long-run exchange rate , to a new long-run level . Because is a long-run stable level, it is also the new expected level of the exchange rate that will prevail in the future. That is, the future will look like the present, under our assumptions, except that the exchange rate will be sitting at instead of . What does this change do to the foreign return curve FR? As we know, when the expected exchange rate increases, foreign returns are higher, so the FR curve shifts up, from FR₁ to FR₂. Because in the long run is the new stable equilibrium exchange rate, and is the interest rate, the new FX market equilibrium is at point 4′ where FR₂ intersects DR₁.

The Short Run Only now that we have changes in expectations worked out can we work back through panels (a) and (b) of Figure 4-12 to see what will happen in the short run.

Look first at the FX market in panel (b). Because expectations about the future exchange rate have changed with today’s policy announcement, the FX market is affected immediately. Everyone knows that the exchange rate will be in the future. The foreign return curve shifts when the expected exchange rate changes; it rises from FR₁ to FR₂. This is the same shift we just saw in the long-run panel (d). The dollar is expected to depreciate to (relative to ) in the future, so euro deposits are more attractive today.

Now consider the impact of the change in monetary policy in the short run. Look at the money market in panel (a). In the short run, if the money supply increases from to but prices are sticky at , then real money balances rise from to . The real money supply shifts from MS₁ to MS₂ and the home interest rate falls from to , leading to a new short-run money market equilibrium at point 2.

Now look back to the FX market in panel (b). If this were a temporary monetary policy shock, expectations would be unchanged, and the FR₁ curve would still describe foreign returns, but domestic returns would fall from DR₁ to DR₂ as the interest rate fell and the home currency would depreciate to the level . The FX market equilibrium, after a temporary money supply shock, would be at point 3′, as we have seen before.

But this is not the case now. This time we are looking at a permanent shock to money supply. It has two effects on today’s FX market. One impact of the money supply shock is to lower the home interest rate, decreasing domestic returns in today’s FX market from DR₁ to DR₂. The other impact of the money supply shock is to increase the future expected exchange rate, increasing foreign returns in today’s FX market from FR₁ to FR₂. Hence, the FX market equilibrium in the short run is where DR₂ and FR₂ intersect, now at point 2′, and the exchange rate depreciates all the way to .

Note that the short-run equilibrium level of the exchange rate () is higher than the level that would be observed under a temporary shock () and also higher than the level that will be observed in the long run (). To sum up, in the short run, the permanent shock causes the exchange rate to depreciate more than it would under a temporary shock and more than it will end up depreciating in the long run.

Adjustment from Short Run to Long Run The arrows in panels (c) and (d) of Figure 4-12 trace what happens as we move from the short run to the long run. Prices that were initially sticky in the short run become unstuck. The price level rises from to , and this pushes the real money supply back to its initial level, from MS₂ back to MS₁. Money demand MD is unchanged. Hence, in the home money market of panel (c), the economy moves from the short-run equilibrium at point 2 to the long-run equilibrium, which is again at point 1, following the path shown by the arrows. Hence, the interest rate gradually rises from back to . This raises the domestic returns over in the FX market of panel (d) from DR₂ back to DR₁. So the FX market moves from the short-run equilibrium at point 2′ to the long-run equilibrium, which is again at point 4′.

An Example Let’s make this very tricky experiment a bit more concrete with a numerical example. Suppose you are told that, all else equal, (i) the home money supply permanently increases by 5% today; (ii) prices are sticky in the short run, so this also causes an increase in real money supply that lowers domestic interest rates by four percentage points from 6% to 2%; (iii) prices will fully adjust in one year’s time to today’s monetary expansion and PPP will hold again. Based on this information, can you predict what will happen to prices and the exchange rate today and in a year’s time?

Yes. Work backward from the long run to the short run, as before. In the long run, a 5% increase in M means a 5% increase in P that will be achieved in one year. By PPP, this 5% increase in P implies a 5% rise in E (a 5% depreciation in the dollar’s value) over the same period. In other words, over the next year E will rise at 5% per year, which will be the rate of depreciation. Finally, in the short run, UIP tells us what happens to the exchange rate today: to compensate investors for the four percentage point decrease in the domestic interest rate, arbitrage in the FX market requires that the value of the home currency be expected to appreciate at 4% per year; that is, E must fall 4% in the year ahead. However, if E has to fall 4% in the next year and still end up 5% above its level at the start of today, then it must jump up 9% today: it overshoots its long-run level.

Overshooting

Compared with the temporary expansion of money supply we studied before, the permanent shock has a much greater impact on the exchange rate in the short run.

Under the temporary shock, domestic returns go down; traders want to sell the dollar for one reason only—temporarily lower dollar interest rates make dollar deposits less attractive. Under the permanent shock, domestic returns go down and foreign returns go up; traders want to sell the dollar for two reasons—temporarily lower dollar interest rates and an expected dollar depreciation make dollar deposits much less attractive. In the short run, the interest rate and exchange rate effects combine to create an instantaneous “double whammy” for the dollar, which gives rise to a phenomenon that economists refer to as exchange rate overshooting.

To better visualize the overshooting phenomenon, we show in Figure 4-13 the time path over which the key economic variables change after the permanent shock we just studied using Figure 4-12. We see the following:

• The nominal money supply is subject to a one-time increase at time T.
• Real money balances rise instantaneously but revert to their initial level in the long run; the nominal interest rate falls instantaneously but reverts to its initial level in the long run.
• The price level is sticky in the short run but rises to a new higher level in the long run, increasing in the same proportion as the nominal money supply.
• The exchange rate rises (depreciates) to a new higher level in the long run, rising in the same proportion as the nominal money supply. In the short run, however, the exchange rate rises even more, overshooting its long-run level, then gradually decreasing to its long-run level (which is still higher than the initial level).

The overshooting result adds yet another argument for the importance of a sound long-run nominal anchor: without it, exchange rates are likely to be more volatile, creating instability in the forex market and possibly in the wider economy. The wild fluctuations of exchange rates in the 1970s, at a time when exchange rate anchors were ripped loose, exposed these linkages with great clarity (see Side Bar: Overshooting in Practice). And new research provides evidence that the shift to a new form of anchoring, inflation targeting, might be helping to bring down exchange rate volatility in recent years.3