Ch. 11: Exchange Rates in the Short Run: The Asset Approach

Based on Feenstra and Taylor, Chapter 15 (KOM chapters 14 and 16). There are no lecture slides for this topic on the site yet; check against the lecture when it is given.

The previous two chapters gave us two building blocks. Chapter 7 (interest parity) explained the spot exchange rate today, given interest rates and the expected future exchange rate. Chapter 8 (the long-run monetary approach and PPP) explained where the exchange rate goes in the long run, when prices are fully flexible. This chapter puts the two together into the asset approach to exchange rates in the short run. The key assumption is that in the short run prices are sticky: the price level P does not jump when the money supply changes. Interest rates and the exchange rate do the adjusting instead. The chapter has five parts: (1) the forex market in the short run (UIP as a diagram); (2) the money market in the short run; (3) the asset approach, with temporary policy shocks; (4) the complete theory, with permanent shocks and overshooting; and (5) fixed exchange rates and the trilemma.

Why a separate short-run theory?

PPP and the monetary approach work reasonably well over long horizons (ten years or more) and in high-inflation countries, but they fail badly in the short run. Month to month, nominal exchange rates of floating currencies move by several percent, while consumer price indices move by a fraction of a percent. Because prices barely move, almost all of the movement in the nominal exchange rate shows up as movement in the real exchange rate. This is the main evidence for sticky prices: when a country switches from a floating to a fixed exchange rate, the volatility of its real exchange rate drops sharply (FT show this for Slovakia when it pegged to the euro). If prices were flexible, the regime should not matter for the real exchange rate.

So in the short run we treat the price level P as fixed (predetermined), and we treat output Y as given in this chapter (output is made endogenous in Chapter 12). The variables that move instantly are financial: the interest rate and the exchange rate. These are asset prices, which is why this is called the asset approach.

Part 1: The forex market in the short run (UIP)

Take the United States as home and the euro area as foreign. Investors can hold dollar deposits or euro deposits. Under uncovered interest parity, the expected returns, measured in the same currency (dollars), must be equal:

The FX diagram. FT draw the forex market with the spot rate E $/€ on the vertical axis and rates of return (in dollars) on the horizontal axis.

• The domestic return line is vertical at i $: it does not depend on E.
• The foreign return curve slopes downward. A higher spot rate E today (a weaker dollar now), with E e unchanged, means less expected future depreciation of the dollar, so the expected return on euro deposits falls. Intuition: if the euro is already expensive today, there is less room for it to rise further.
• Equilibrium is where the two cross: the spot rate at which investors are indifferent between the two currencies.

Worked example (FT numbers). Let i $ = 5%, i € = 3% and E e $/€ = 1.224. Try different spot rates:

The equilibrium spot rate is 1.20. If E is above equilibrium, dollar deposits pay more, investors buy dollars and the dollar appreciates (E falls) until UIP holds again. The forex market clears almost instantly because traders arbitrage continuously.

Shifts in the FX diagram

Read every shift as: which return line moves, and what must happen to E to restore equality.

• Rise in i $ (home interest rate): the domestic return line shifts right. At the old E, dollar deposits pay more, so the dollar appreciates: E $/€ falls.
• Rise in i € (foreign interest rate): the foreign return curve shifts right (up). Euro deposits become more attractive, the dollar depreciates: E $/€ rises.
• Rise in E e $/€ (expected future dollar depreciation): the foreign return curve shifts right (up). Investors expect the euro to gain, so they buy euros today and the dollar depreciates now: E $/€ rises. Expectations are self-fulfilling in this sense.

Part 2: The money market in the short run

Where does i $ come from? In the short run it is set in the home money market. From Chapter 8, real money demand is proportional to real income and falls with the nominal interest rate (the opportunity cost of holding money):

In the long run (Chapter 8) the interest rate was pinned down by the Fisher effect and P adjusted to clear the market. In the short run it is the other way around: P is sticky and Y is given, so the interest rate adjusts to equate real money demand with real money supply.

The money market diagram. Interest rate i $ on the vertical axis, real money balances M/P on the horizontal axis. Real money supply MS is a vertical line at M/P. Real money demand MD slopes downward (higher i, lower desired real balances). Equilibrium: the interest rate where the two meet. If i is above equilibrium there is excess supply of money: people try to buy interest-bearing bonds, bond prices rise and i falls.

Example. Suppose M rises 5% and P is stuck. Real money supply M/P rises 5%. To make people willing to hold 5% more real balances, L(i) must rise 5%, which requires a lower interest rate. The size of the fall depends on how interest-sensitive money demand is: the flatter MD, the smaller the drop in i.

The same logic holds in Europe: M EUR / P EUR = L(i €) Y EUR determines i €. Monetary policy abroad therefore moves the foreign return curve in our FX diagram.

Part 3: The asset approach: putting the two markets together

The asset approach links the two diagrams. FT draw the money market (panel 1) and the FX market (panel 2) side by side, with the interest rate as the common axis: the equilibrium interest rate from the money market is the domestic return line in the FX market.

The key distinction for policy analysis is whether a shock is temporary or permanent, because that decides whether expectations E e change.

Temporary monetary expansion at home

A temporary shock does not affect the long run, so it leaves the long-run price level and therefore E e unchanged. Steps:

1. Money market: M US rises, P fixed, MS shifts right, i $ falls.
2. FX market: the domestic return line shifts left. The foreign return curve does not move (i € and E e unchanged).
3. At the old E, euro deposits pay more, so investors sell dollars: the dollar depreciates, E $/€ rises.

Numbers. Start at i $ = i € = 5% and E = E e = 1.00. A temporary expansion lowers i $ to 3%. UIP: 3% = 5% + (1.00 minus E)/E, so (1.00 minus E)/E = minus 2% and E = 1.00/0.98 = 1.020. The dollar depreciates by about 2% today. Investors are willing to hold dollar deposits at a 2% lower interest rate only because they now expect the dollar to appreciate back by 2%.

A temporary foreign monetary expansion works in reverse: i € falls, the foreign return curve shifts left, the dollar appreciates (E $/€ falls).

Application: the rise and fall of the dollar, 1999 to 2004

In the early years of the euro, US interest rates were above euro area rates and the dollar appreciated strongly against the euro (the euro fell from about $1.18 in 1999 to below $0.90 in 2000 to 2001). From 2001 the Federal Reserve cut interest rates aggressively (down to 1% by 2003), far below the European Central Bank's rates. The dollar then depreciated, and the euro rose to around $1.30 by 2004. The movements of the interest differential i $ minus i € and of the exchange rate match the asset approach prediction: a relatively higher home interest rate goes with home appreciation. The fit is not perfect, since expectations also moved, but the direction is what the model predicts.

Part 4: A complete theory: permanent shocks and overshooting

Now combine the short run (asset approach) with the long run (monetary approach). The long-run model tells investors what the exchange rate will be in the future, which is exactly the E e they use today.

Permanent monetary expansion at home

Suppose the Fed raises M US permanently by 10%. In the long run (Chapter 8), money is neutral: P US rises 10%, and by PPP the exchange rate E $/€ also rises 10%. Investors know this, so E e rises 10% immediately. Now there are two effects in the short run:

1. Money market: M rises with P sticky, i $ falls (domestic return line shifts left), as in the temporary case.
2. FX market: E e rises, so the foreign return curve shifts right (up).

Both effects push the dollar down, so the short-run depreciation is larger than for a temporary shock of the same size.

Numbers. Start at i $ = i € = 5%, E = E e = 1.00. M rises permanently by 10%, so the new long-run rate is 1.10 and E e = 1.10. In the short run i $ falls to 3%. UIP: 3% = 5% + (1.10 minus E)/E, so (1.10 minus E)/E = minus 2% and E = 1.10/0.98 = 1.122.

Overshooting

The exchange rate jumps to 1.122, above its new long-run level of 1.10, and then gradually appreciates back toward 1.10 as prices adjust. This is exchange rate overshooting, first explained by Rudiger Dornbusch (1976): the short-run response of the exchange rate to a monetary shock is greater than its long-run response.

Why it happens. Prices are sticky, so the money increase first lowers the interest rate. For investors to hold dollar deposits paying a lower interest rate, they must expect the dollar to appreciate over the adjustment period (UIP). The only way the dollar can be expected to appreciate toward its new long-run level of 1.10 is if it first depreciates beyond 1.10. Overshooting requires sticky prices: with flexible prices, P would jump to 110 at once, M/P would not change, i would not fall, and E would move straight to 1.10.

The time path after a permanent monetary expansion (FT figure in words):

• M: jumps up once at time T and stays higher.
• i: drops at T, then rises back to its old level as P climbs and real money balances M/P shrink back.
• P: unchanged at T, then rises gradually to its new level (10% higher).
• E: jumps up at T by more than 10%, then falls back gradually to the new long-run level (10% above the start).
• Real exchange rate q = EP*/P: rises at T (real depreciation) because E jumps and P is stuck, then returns to its original level (PPP holds in the long run).

Overshooting helps explain why floating exchange rates are so volatile: monetary news moves the exchange rate more than the fundamentals change in the long run. In practice, big overshooting episodes follow sharp monetary policy changes, for example when a country abandons a peg or a central bank makes a surprise switch in policy.

Temporary versus permanent: summary

KOM view of the same model

KOM (chapters 14 and 16) use the same two diagrams, with one twist in presentation: they stack the money market below the FX market, with real money supply measured downward from the origin, so that the equilibrium interest rate can be read off directly. The results are identical: an increase in the home money supply lowers the home interest rate and depreciates the home currency; a permanent increase does so more strongly and produces overshooting. KOM also stress that in the long run a permanent money increase raises P in proportion and leaves the interest rate and output unchanged.

Part 5: Fixed exchange rates and the trilemma

So far the exchange rate floated. Now suppose the home country pegs: it fixes E at a central value, and the peg is credible, so investors expect it to last. Then E e = E, the expected depreciation is zero, and UIP reduces to:

Consequence for the money market: since i is fixed at i*, and P and Y are given, money demand L(i*)Y is fixed, so the central bank must supply exactly M = P × L(i*) × Y. The money supply becomes endogenous: the central bank cannot set it independently. If it tried to expand M, i would start to fall below i*, investors would sell home currency, and the central bank would have to buy home currency with its foreign reserves, reducing M again. Monetary policy autonomy is lost.

Example: Denmark. Denmark pegs the krone to the euro (within the ERM II arrangement). Danish interest rates closely follow ECB rates; when the ECB changes its policy rate, the Danish central bank follows. Denmark has capital mobility and a fixed exchange rate, so it gives up independent monetary policy.

The policy trilemma

A country can have at most two of the following three goals at the same time:

1. A fixed exchange rate (stability for trade and investment).
2. International capital mobility (open financial markets).
3. Monetary policy autonomy (setting i to stabilize the home economy).

The logic comes straight from UIP. With capital mobility, UIP holds. With a fixed rate, the expected depreciation is zero. Then i = i*, so there is no autonomy. To regain autonomy you must drop one of the other two: either let the currency float (then i can differ from i* because E e can differ from E), or impose capital controls (then UIP need not hold).

FT draw the trilemma as a triangle: each corner is a goal and each side a regime; a country can only be on one side. Most countries make middle-ground choices (managed floats, partial capital controls), but the constraint still binds at the margin.

Application: the trilemma in Europe

In Europe the choices differ. The euro area members gave up their own currencies and their national monetary policy entirely. Denmark keeps its own currency but pegs to the euro, so it imports ECB policy. Sweden and the United Kingdom float and keep monetary autonomy. A typical FT exercise: compare how closely each country's interest rate follows the German (later euro) interest rate. Pegged countries track it almost exactly; floating countries do not. The data show the trilemma at work: the more a country fixes its exchange rate with an open capital account, the more its interest rate moves one for one with the base country's rate.