# Pvs 1W

while in Europe,

As before, we have used the symbol Ms to stand for a country's money supply and L(R, K) to stand for its aggregate real money demand, which decreases when the interest rate rises and increases when real output rises.2

Equations (15-3) and (15-4) show how the monetary approach to the exchange rate comes by its name. According to the statement of PPP in equation (15-1), the dollar price of a euro is simply the dollar price of U.S. output divided by the euro price of European output. These two price levels, in turn, are determined completely by the supply and demand for each currency area's money: The United States' price level is the U.S. money supply divided by U.S. real money demand, as shown in (15-3), and Europe's price level similarly is the European money supply divided by European real money demand, as shown in (15-4). The monetary approach therefore makes the general prediction that the exchange rate, which is the relative price of American and European money, is fully determined in the long run by the relative supplies of those monies and the relative real demands for them. Shifts in interest rates and output levels affect the exchange rate only through their influences on money demand.

In addition, the monetary approach makes a number of specific predictions about the long-run effects on the exchange rate of changes in money supplies, interest rates, and output levels:

1. Money supplies. Other things equal, a permanent rise in the U.S. money supply M£s causes a proportional increase in the long-run U.S. price level Pvs, as equation (15-3) shows. Because under PPP, Ey% = PUS/PE, however, Em also rises in the long run in proportion to the increase in the U.S. money supply. (For example, if rises by 10 percent, Pus and Em both eventually rise by 10 percent as well.) Thus, an increase in the U.S. money supply causes a proportional long-run depreciation of the dollar against the euro. Conversely, equation (15-4) shows that a permanent increase in the European money supply causes a proportional increase in the long-run European price level. Under PPP, this price level rise implies a proportional long-run appreciation of the dollar against the euro (which is the same as a proportional depreciation of the euro against the dollar).

2. Interest rates. A rise in the interest rate /?\$ on dollar-denominated assets lowers real U.S. money demand L{R\$, Kus). By (15-3) the long-run U.S. price level rises, and under PPP the dollar must depreciate against the euro in proportion to this U.S. price level increase. A rise in the interest rate R£ on euro-denominated assets has the reverse longrun exchange rate effect. Because real European money demand L(7?e, YE) falls, Europe's

2To simplify the notation, we assume identical money demand functions for the United States and Europe.

price level rises, by (15-4). Under PPP, the dollar must appreciate against the euro in proportion to Europe's price level increase.

3. Output levels. A rise in U.S. output raises real U.S. money demand L(R%, Kus), leading by (15-3) to a fall in the long-run U.S. price level. According to PPP, there is an appreciation of the dollar against the euro. Symmetrically, a rise in European output raises L{RKh) and, by (15-4), causes a fall in Europe's long-run price level. PPP predicts that this development will make the dollar depreciate against the euro.

To understand these predictions, remember that the monetary approach, like any longrun theory, essentially assumes that price levels adjust as quickly as exchange rates do— that is, right away. For example, a rise in real U.S. output raises the transactions'demand for real U.S. money balances. According to the monetary approach, the U.S. price level drops immediately to bring about a market-clearing increase in the supply of real balances. PPP implies that this instantaneous American price deflation is accompanied by an instantaneous dollar appreciation on the foreign exchanges.

The monetary approach leads to a result familiar from Chapter 14, that the long-run foreign exchange value of a country's currency moves in proportion to its money supply (prediction 1 above). The theory also raises what seems to be a paradox (prediction 2). In our previous examples, we always found that a currency appreciates when the interest rate it offers rises relative to foreign interest rates. How is it that we have now arrived at precisely the opposite conclusion—that a rise in a country's interest rate depreciates its currency by lowering the real demand for its money?

At the end of Chapter i 3 we warned that no account of how a change in interest rates affects the exchange rate is complete until we specify exactly why interest rates have changed. This point explains the apparent contradiction in our findings about interest and exchange rates. To resolve the puzzle, however, we must first examine more closely how monetary policies and interest rates are connected in the long run.

Ongoing Inflation, Interest Parity, and PPP

In the last chapter we saw that a permanent increase in the level of a country's money supply ultimately results in a proportional rise in its price level but has no effect on the long-run values of the interest rate or real output. The conceptual experiment of a onetime, stepwise money supply change is useful for thinking about the long-run effects of money, but it is not too realistic as a description of actual monetary policies. More often, the monetary authorities choose a growth rate for the money supply, say, 5 or 10 or 50 percent per year, and then allow money to grow gradually, through small but frequent increases. What are the long-run effects of a policy that allows the money supply to grow smoothly forever at a positive rate?

The reasoning in Chapter 14 suggests that continuing money supply growth will require a continuing rise in the price level—a situation of ongoing inflation. As firms and workers catch on to the fact that the money supply is growing steadily at, say, a 10 percent annual rate, they will adjust by raising prices and wages by the same 10 percent every year, thus keeping their real incomes constant. Full-employment output depends on supplies of productive factors, but it is safe to assume that factor supplies, and thus output, are unaffected over the long run by different choices of a constant growth rate for the money supply. Other things equal, money supply growth at a constant rate eventually results in ongoing price level inflation at the same rate, but changes in this long-run inflation rate do not affect the full-employment output level or the long-run relative prices of goods and services.

The interest rate, however, is definitely not independent of the money supply growth rate in the long run. While the long-run interest rate does not depend on the absolute level of the money supply, continuing growth in the money supply eventually will affect the interest rate. The easiest way to see how a permanent increase in inflation affects the long-run interest rate is by combining PPP with the interest rate parity condition on which our previous analysis of exchange rate determination was built.

As in the preceding two chapters, the condition of interest parity between dollar and euro assets is

(recall equation (13-2), page 342). Now let's ask how this parity condition, which must hold in the long run as well as in the short run, fits with the other parity condition we are assuming in our long-run model, purchasing power parity. According to relative PPP, the percentage change in the dollar/euro exchange rate over the next year, say, will equal the difference between the inflation rates of the United States and Europe over that year (see equation (15-2)). Since people understand this relationship, however, it must also be true that they expect the percentage exchange rate change to equal the U.S.-Europe inflation difference. The interest parity condition written above now tells us the following; If people expect relative PPP to hold, the difference between the interest rates offered by dollar and euro deposits will equal the difference between the inflation rates expected, over the relevant horizon, in the United States and in Europe.

Some additional notation is helpful in deriving this result more formally. If/*' is the price level expected in a country for a year from today, the expected inflation rate in that country, n1', is the expected percentage increase in the price level over the coming year,

If relative PPP holds, however, market participants will also expect it to hold, which means that we can replace the actual depreciation and inflation rates in equation (15-2) with the values the market expects to materialize;

By combining this "expected" version of relative PPP with the interest parity condition

and rearranging, we arrive at a formula that expresses the international interest rate difference as the difference between expected national inflation rates:

If, as PPP predicts, currency depreciation is expected to offset the international inflation difference (so that the expected dollar depreciation rate is - 71^), the interest rate difference must equal the expected inflation difference.

### The Fisher Effect

Equation (15-5) gives us the long-run relationship between ongoing inflation and interest rates that we need to explain the monetary approach's predictions about how interest rates affect exchange rates. The equation tells us that all else equal, a rise in a country's expected inflation rate will eventually cause an equal rise in the interest rate that deposits of its currency offer. Similarly; a fall in the expected inflation rate will eventually cause a fall in the interest rate.

This long-run relationship between inflation and interest rates is called the Fisher effect The Fisher effect implies, for example, that if U.S. inflation were to rise permanently from a constant level of 5 percent per year to a constant level of 10 percent per year, dollar interest rates would eventually catch up with the higher inflation, rising by 5 percentage points per year from their initial level. These changes would leave the real rate of return on dollar assets, measured in terms of :U.S. goods and services, unchanged. The Fisher effect is therefore another example of the general idea that in the long run, purely monetary developments should have no effect on an economy's relative prices.3

The Fisher effect is behind the seemingly paradoxical monetary approach prediction that a currency depreciates in the foreign exchange market when its interest rate rises relative to foreign currency interest rates. In the long-run equilibrium assumed by the monetary approach, a rise in the difference between home and foreign interest rates occurs only when expected home inflation rises relative to expected foreign inflation. This is certainly not the case in the short run, when the domestic price level is sticky. In the short run, as we saw in Chapter 14, the interest rate can rise when the domestic money supply falls because the sticky domestic price level leads to an excess demand for real money balances at the initial interest rate. Under the flexible-price monetary approach, however, the price level would fall right away and thus make the interest rate change unnecessary.

We can better understand how interest rates and exchange rates interact under the monetary approach by thinking through an example. Our example illustrates why the monetary approach associates sustained interest rate hikes with current as well as future currency depreciation, sustained interest rate slumps with appreciation.

Imagine that at time t0 the Federal Reserve unexpectedly increases the growth rate of the U.S. money supply from iz to the higher level n + An. Figure 15-1 illustrates how this change affects the dollar/euro exchange rate Eye, as well as other U.S. variables, under the assumptions of the monetary approach. To simplify the graphs we assume that in Europe the inflation rate remains constant at zero.

Figure 15-la shows the sudden acceleration of U.S. money supply growth at time /0. (We have scaled the vertical axes of the graphs so that constant slopes represent constant proportional growth rates of variables.) The policy change generates expectations of more rapid currency depreciation in the future: Under PPP the dollar will now depreciate at rate % + An rather than at the lower rate n. Interest parity therefore requires the dollar interest rate to rise, as shown in Figure 15-lb, from its initial level R]s to a new level that reflects the extra expected dollar depreciation, R^ = + An (see equation (15-5)). Notice that this

3The effect is named after Irving Fisher, one of the great American economists of the early twentieth century. The effect is discussed at length in his book, The Theory of Interest (New York: Macmillan, 1930). Fisher, incidentally, gave an early account of the interest parity condition on which our theory of foreign exchange market equilibrium is based.

igure l-^Run Time Paths of U.S. Economic Variables after a ¿»nent Increas| (JiS (growth Rate of the U.S. Money Supply