Chapter 4: Exchange rates II: the asset approach in the short run

Goals: Understanding how the exchange rates are determined in the short run.

4-1

The long run monetary-approach model assumes that price is flexible, and uses the purchasing power parity to determine the exchange rate.

Empirical researches support PPP in long run, but find significant deviation from PPP in short run.

One of the reasons for the failure of PPP in short run is due to sticky price. This chapter considers a different model to explain the behavior of exchange rate in short run.

Basic idea:

The short run asset-approach model treats the exchange rate as the price of an asset, the foreign exchange.

In asset market the price is determined by the no-arbitrage condition. That is, the price is determined in such a way that expected returns of two assets in different currencies are equal.

Recall that the no-arbitrage condition in the foreign exchange market implies the uncovered interest parity (UIP).

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The annual return of a US deposit is 1+i$, where i$ is the annual nominal interest.

One can alternatively convert US dollars into euros, invest in a euro deposit that pays annual interest rate of i€, and at the end of one year convert euro returns back to US dollars. The annual return is__________________.

No-arbitrage requires that the two returns are equal, i.e., UIP holds:

1+i$=(1+i€ )E$ /€

e

E$ /€ (2-2) Uncovered Interest Parity (UIP)

Please see figure 2-10 for a quick review of UIP.

Exercise: rewrite (2-2) using the exchange rate expressed as E€ /$

Algebra rearrangement of (2-2) leads to

i$ ≈ i€+E$ /€

e −E$ /€

E$ /€ (4-1) an approximation of UIP

(4-1) is an approximation of (2-2).

(4-1) implies that if the US interest rate i$ is greater than the euro rate i€, then E$/€

e should be (greater or less) than E$/€, or US dollar is expected to (appreciate or depreciate).

This result is intuitive. If a US deposit pays a higher rate than a euro deposit, then investors will not consider euro deposits

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unless they expect that euro will (appreciate or depreciate), or conversely, dollar will (appreciate or depreciate), in the future.

Exercise: if a US deposit pays a lower rate than a euro deposit, then dollar is expected to (appreciate or depreciate) in the future.

(Optional) Derivation of (4-1)

Chapter 4 is based on (4-1).We can rearrange (4-1) and get

E$/€=E$ /€

e

(1+i $−i€ ) (4-1b)

which clearly shows that we can solve for E$/€ if we know all the three variables on the right hand side of (4-1b). (4-1b) is the basis for the short run asset-approach model for exchange rate. According to (4-1b), everything else equal, E$/€ will rise (so dollar will depreciate) if

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(1) i€ goes (up or down)

(2) E$/€e goes (up or down)

(3) i$ goes (up or down)

The intuition is, if euro deposit is expected to pay a higher rate or euro is expected to appreciate, either one makes the euro deposit more attractive. People will convert dollars to euros and move to euro deposit now. Selling dollars causes the depreciation of dollars.

A dollar deposit with a lower interest rate also makes the euro deposit more attractive.

The equilibrium condition for foreign market, equation (4-1), is graphically illustrated in figure 4-2. That figure shows the foreign exchange market reaches equilibrium (no-arbitrary condition is satisfied) when the domestic return line (DR) and the foreign return (FR) line cross at point 1.

The variable on the horizontal line (X-variable) is ____________________

The variable on the vertical line (Y-variable) is _______________________

DR line is horizontal because ________________________

FR line is (upward or downward) sloping because __________________

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Intuitively FR line is downward sloping because when E$/ € rises one can convert one dollar to (more or less) euros, and so have (lower or higher) return from holding a euro deposit.

(1) To the left of point 1 such as at point 2, (dollar or euro) deposit is more attractive. People will convert ________ to __________, and dollar will ____________ and E$/€ will go (up or down).

(2) To the right of point 1 such as at point 3, (dollar or euro) deposit is more attractive. People will convert ________ to __________, and dollar will ____________ and E$/€ will go (up or down).

So when the market is out of equilibrium at the beginning, the market force will push the market back to equilibrium.

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Exercise:Rising US interest rate will shift __________ line ____________Rising Euro interest rate will shift _______________ line ________________Rising E$/€

e will shift _______________ line ________________We move along the FR line when____________________________

4-2

In order to use (4-1b) to determine the interest rate E$/€ we need to know

(1) E$/€e , which is determined by PPP over long run

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(2) i$

(3) i€

In the long-run monetary-approach model, the nominal interest equals the sum of real interest rate and expect inflation rate. See the two equations on page 95. However, the real interest parity is derived from PPP, which is invalid in short run because of sticky prices.

Instead, the short run asset-approach model uses the equilibrium in money market to determine the nominal interest rate.

MUS

PUS=L(i $)Y US (4-2)

M EUR

PEUR=L(i€)Y EUR (4-3)

Note in short run we assume sticky prices, so P is a constant. This implies that the short run money-market equilibrium is achieved via the adjustment of nominal interest rate, instead of the price.

L(i) is a decreasing function of nominal interest: the opportunity cost of holding cash rises when nominal interest rate rises, so people will convert cash to interest-bearing assets and the demand for money falls.

According to (4-2), everything else equal, i$ will go down if

(1) M US goes (up or down)7

(2) Y US goes (up or down)

Graphically, we can use the real money balance as the X-variable, and the nominal interest rate as the Y-variable. Then the money supply curve is a vertical line (why?), and the money demand curve is downward sloping (why?). The money market is on equilibrium when the two lines cross.

Exercise

Use the graph to show the effect on i$ when8

(1) M US goes up(2) Y US goes up

Please compare your graphs to Figure 4-6.

4-3

Now we can complete the short run asset-approach model by considering the equilibriums in both foreign exchange market and money market.

Short run policy analysis can be done using the short run asset-approach model.

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Short run policy analysis

(1) Temporary increase in M US

In words, rising US money supply lowers the dollar interest rate, makes euro deposit more attractive, and causes dollar to depreciate. Note FR line is fixed because both E$/€

e and i€ are unchanged.

(2) Temporary increase in M EUR

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In words, rising EUR money supply lowers the euro interest rate, makes euro deposit less attractive, and causes dollar to appreciate.

Exercise: please show graphically how a temporary decrease in M EUR affectsE$/€.

A real-data check of the short run asset-approach model

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4-4

Long-run policy analysis

Long Run Short RunPrice flexible fixedNominal Interest Rate

Fixed (due to π targeted )

flexible

Money Market Price adjusts Nominal interest rate adjustsForeign Exchange PPP applies UIP applies

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MarketSpot Exchange Rate

Moves by same proportion as price level

Overshoots its long-run level

Expected Exchange Rate

Moves by same proportion as price level

Moves by same proportion as price level

In order to analyze the effect of permanent policy shocks, we must solve backward from the future to the present:

Step 1: use the long run monetary-approach model to determine the expected exchange rate.

Step 2: use the short run asset-approach model, along with the expected exchange rate obtained in step 1, to determine the exchange rate in short run.

Example

Consider the effect on exchange rate when US money supply increases by 3% permanently. We will show that the short-run effect differs from the long-run effect.

In long run:In the money marketNominal interest rate remains unchanged at level of itargeted=r ¿+π targeted. Real income remains unchanged (no growth)

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Price is flexible, and price rises by the same proportion as money supply to clear the money market:

MUS

PUS=L (itargeted ) Y US →∆ PUS %=∆ M US %

PPP implies that exchange rate will rise by the same proportion as price:

E$/€=PUS

PEUR→ ∆ E$ /€ %=∆ PUS%

So in long run, dollar will depreciate by 3%.

In short runIn the money marketPrice is fixed; while nominal interest rate adjusts to clear the money market.

MUS

PUS=L (iUS ) Y US

So M US↑ →iUS ↓

In the foreign exchange market falling iUS shifts the DR line down, while rising E$/€

e shifts the FR line up.

In the long run, DR line moves back to its original place (why?) while FR line remains at its higher position (why?).

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The short-run equilibrium exchange rate is higher than the long-run equilibrium exchange rate. This phenomenon is called overshooting. To see this recall UIP:

i$=i€+E$ /€

e −E$ /€

E$ /€

In long run i$ remains unchanged, so E$/ €e and E$/€ must rise

by the same proportion of 3%.

In short run i$ falls and E$/€e rises by 3%. Then E$/€ must

rise by more than 3% to ensure UIP.

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Short-run equilibrium is located at point 2’ in panel (b) Long-run equilibrium is located at point 4’ in panel (d)

Did you see a typo in (d)?Exercise: please draw the time path for the real exchange rate

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