The Encyclopedia of Economic Principals

Chapter 59

Exchange Rates, Capital Flows, Crises, and Open-Economy Policy

Trace exchange rates through interest parity, productivity and the trade balance.

Four of the chapter's worked examples, made interactive: overshooting after a monetary expansion, covered interest parity, the Balassa-Samuelson effect and the J-curve. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

The exchange rate jumps past its target

Why can a monetary expansion push the currency beyond its long-run value on impact?

With sticky goods prices the domestic rate falls, and investors hold domestic assets only if they expect the currency to appreciate. That requires the spot rate to jump past its long-run value and then drift back.

Equation, written in LaTeX: 1+i=(1+i^*)\frac{E_tS_{t+1}}{S_t}.

Equation, written in LaTeX: E_tS_{t+1}=1.15(\frac{1.01}{1.05})\approx1.1062.

Equation, written in LaTeX: \frac{1.1062}{1.15}-1\approx-3.81\%.

Scroll sideways for the whole equation

S is domestic currency per unit of foreign currency, so a higher S is depreciation. The long-run rate after the expansion is 1.10. The foreign rate i* stays at 5 percent; i is the domestic rate after easing and S_t the impact rate.

Predict first. After the jump to 1.15 with i = 1 percent, is the currency expected to depreciate further or appreciate?

Your prediction

Choose an example

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Figure: The exchange rate jumps past its target. Exchange rate path: 1.00 before the shock, a jump to 1.15, an expected 1.1062 a year later and the long-run 1.10.
Impact exchange rate (assumed): 1.15, Domestic rate after easing: 1%
Constructed example: the chapter's hypothetical shock (S0 1.00, long run 1.10, i* 5 percent, i 1 percent, impact 1.15); impact rates 1.10 and 1.20 and domestic rates 3 and 5 percent are added.

Calculated values

Expected S next year
1.1062
Expected change from impact
-3.81%
Overshoot beyond 1.10
5 points

E S = 1.15 x 1.01 / 1.05 = 1.1062, so the expected move is 1.1062 / 1.15 - 1 = 1.01 / 1.05 - 1 = -3.81%, an expected appreciation of 3.81 percent. The impact rate 1.15 lies 5 points beyond the long-run 1.10: the rate overshoots.

Worked steps

  1. 1 + i = 1.01, 1 + i* = 1.05
  2. E S = 1.15 x 1.01 / 1.05 = 1.1062
  3. Expected change = 1.1062 / 1.15 - 1 = 1.01 / 1.05 - 1 = -3.81%
  4. Overshoot = (1.15 - 1.10) x 100 = 5 points

Use the idea

After a monetary shock, read a sharp move in the exchange rate as possibly temporary, and check the interest differential for the implied path back.

Where the conclusion applies

Exact uncovered parity, perfect capital mobility, a known long-run rate and the impact rate taken as given; the model does not pin down the jump without more structure.

Check your understanding: If i = 3 percent with S_t = 1.15, what is expected S next year?
1.15 x 1.03 / 1.05 = 1.1281.

Chapter 59 source: section "Dornbusch overshooting".

Demonstration 2 of 4

Locking in the forward rate

When does a quoted forward rate leave a riskless profit?

Selling the euros forward removes all exchange-rate risk, so the two routes must pay the same or traders borrow in the cheap route and lend in the dear one until prices move back.

Equation, written in LaTeX: F=1.20(\frac{1.05}{1.02})\approx1.2353

Equation, written in LaTeX: 0.85\times1.2353\approx1.05

Equation, written in LaTeX: 0.85\times1.26=1.071.

Equation, written in LaTeX: 1.071-1.05=0.021

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S = 1.20 domestic dollars per euro is the spot rate, i_d the domestic deposit rate, i_f = 2 percent the euro rate and F the one-year forward rate. The parity forward rate makes both locked routes pay the same.

Predict first. At F = 1.26 with the book's rates, should a trader borrow dollars and invest in euros?

Your prediction

Choose an example

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Figure: Locking in the forward rate. Two bars: the home deposit returns 1.0500 and the covered euro route 1.0500 at a forward rate of 1.2353.
Quoted forward rate: Parity rate, Domestic rate: 5%
Constructed example: the chapter's hypothetical quotes (spot 1.20, rates 5 and 2 percent, forward 1.26); a forward of 1.20 and domestic rates of 3 and 7 percent are added for comparison.

Calculated values

Parity forward rate
1.2353
Home payoff
1.0500
Euro route payoff
1.0500
Covered profit per dollar
0.0000
Trade
none

Parity F = 1.20 x 1.05 / 1.02 = 1.2353. One dollar buys 1 / 1.20 = 0.8333 euros, which grow to 0.8333 x 1.02 = 0.8500, worth 0.8500 x 1.2353 = 1.0500 dollars against 1.0500 at home. The two routes pay the same, so there is no covered arbitrage.

Worked steps

  1. F parity = 1.20 x 1.05 / 1.02 = 1.2353
  2. 1 / 1.20 = 0.8333 euros, x 1.02 = 0.8500
  3. Euro route = 0.8500 x 1.2353 = 1.0500
  4. Profit = 1.0500 - 1.0500 = 0.0000

Use the idea

Compare a quoted forward with S(1 + i_d)/(1 + i_f); a gap smaller than spreads, collateral and capital charges is not a usable arbitrage.

Where the conclusion applies

No transaction costs, no default risk and free borrowing at the quoted rates.

Check your understanding: What profit per borrowed dollar does F = 1.26 give?
(1 / 1.20) x 1.02 x 1.26 = 1.071, minus 1.05 = 0.021.

Chapter 59 source: section "Covered interest parity".

Demonstration 3 of 4

Productive traders, pricier haircuts

Why do countries with productive traded sectors have higher price levels?

Traded productivity sets the wage; labor mobility carries that wage into services, whose productivity did not change, so services get dearer and the overall price level rises.

Equation, written in LaTeX: w_0=P_TA_T=1(20)=20

Equation, written in LaTeX: P_{N,0}=\frac{w_0}{A_N}=\frac{20}{10}=2.

Equation, written in LaTeX: P_0=1^{0.5}2^{0.5}=\sqrt{2}\approx1.414.

Equation, written in LaTeX: P_1=1^{0.5}3^{0.5}=\sqrt{3}\approx1.732,

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P_T = 1 is the world price of the traded good, A_T and A_N are output per worker in traded goods and local services, w the common wage and P_N the service price. The index weights both at 0.5. The comparison is always against the starting point A_T = 20, A_N = 10.

Predict first. When traded productivity rises from 20 to 30, do traded goods get dearer?

Your prediction

Choose an example

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Figure: Productive traders, pricier haircuts. Grouped bars before and after: the traded price stays at 1, the service price moves from 2 to 3.000 and the index from 1.414 to 1.732.
Traded productivity: 30, Service productivity: 10
Constructed example: the chapter's hypothetical economy (P_T 1, A_T 20 then 30, A_N 10, equal shares); traded productivity 25 and 40 and service productivity 15 and 20 are added.

Calculated values

Wage
30
Service price P_N
3.000
Price index
1.732
Index change
+22.5%
Real exchange rate change
-18.4%

w = 1 x 30 = 30, so P_N = 30 / 10 = 3.000 and P = sqrt(1 x 3.000) = 1.732, against sqrt(2) = 1.414 before. The index changes 1.73205 / 1.41421 - 1 = +22.5%, and with E and P* fixed the real exchange rate changes 1.41421 / 1.73205 - 1 = -18.4% (real appreciation). The traded price stays at 1.

Worked steps

  1. w = 1 x 30 = 30
  2. P_N = 30 / 10 = 3.000
  3. P = 1^0.5 x 3.000^0.5 = 1.732
  4. Index change = 1.73205 / 1.41421 - 1 = +22.5%
  5. q change = 1.41421 / 1.73205 - 1 = -18.4%

Use the idea

When comparing price levels across countries, expect richer, high-productivity traders to look expensive in services even with a fair nominal exchange rate.

Where the conclusion applies

One mobile labor input, a world traded price, competitive pricing at wage over productivity and a fixed nominal exchange rate and foreign price level.

Check your understanding: If service productivity also rose to 15, what is P_N?
30 / 15 = 2, so the index stays at sqrt(2) = 1.414.

Chapter 59 source: section "Balassa-Samuelson effect".

Demonstration 4 of 4

Worse before better

Why does a depreciation often worsen the trade balance before it improves it?

Prices adjust before quantities. The valuation effect makes the balance worse at once; only later do export and import volumes respond, and if they respond enough the balance ends above its start.

Equation, written in LaTeX: TB_0=100(10)-100(10)=0.

Equation, written in LaTeX: TB_1=100(10)-100(12)=-200.

Equation, written in LaTeX: TB_4=1{,}375-840=535.

Equation, written in LaTeX: TB=100(11)-90(12)=20.

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TB is export receipts minus import spending in domestic currency. The country starts at 100 exports and 100 imports, both priced 10. After a 20 percent depreciation the import price passes through to 12 (or 11 with half pass-through), and from quarter 4 exporters earn 11 a unit.

Predict first. Right after the depreciation, does the trade balance improve?

Your prediction

Choose an example

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Figure: Worse before better. Trade balance path: 0 in quarter 0, -200 in quarter 1 and 535 in quarter 4.
Volume response strength: Strong (125, 70), Import price after depreciation: 12
Constructed example: the chapter's hypothetical country (100 exports and imports at 10, import price 12, strong response 125 and 70, weak response 100 and 90); the no-response case and half pass-through to 11 are added.

Calculated values

TB quarter 0
0
TB quarter 1
-200
TB quarter 4
535
Shape
a J: worse first, then above the start

TB0 = 100 x 10 - 100 x 10 = 0. Quarter 1: TB1 = 100 x 10 - 100 x 12 = 1,000 - 1,200 = -200. Quarter 4: TB4 = 125 x 11 - 70 x 12 = 1,375 - 840 = 535. The path is a J: worse first, then above the start.

Worked steps

  1. TB0 = 100 x 10 - 100 x 10 = 0
  2. TB1 = 1,000 - 100 x 12 = -200
  3. Exports in quarter 4 = 125 x 11 = 1,375
  4. Imports in quarter 4 = 70 x 12 = 840
  5. TB4 = 1,375 - 840 = 535

Use the idea

Judge a depreciation by the trade balance several quarters out, and check whether volume responses are large enough to deliver the upward arm.

Where the conclusion applies

Contracted volumes in quarter 1, a fixed export price of 11 from quarter 4 and the stated volume responses; none of these is guaranteed.

Check your understanding: With the weak response, what is the quarter-4 balance?
100 x 11 - 90 x 12 = 1,100 - 1,080 = 20.

Chapter 59 source: section "J-curve effect".