Download Pugel Chapter 19 Problems What Determines Exchange Rates ?

Pugel Chapter 19 Problems
What Determines Exchange Rates ?
Problem 1. Do trade flows determine exchange rates?
Remember the BIS figures on foreign exchange transactions -- 1.8 trillion a DAY in 2004.
Total US trade in 2004 was not 1.8 trillion a YEAR, and total world trade accounts for less than
two weeks worth of foreign exchange transactions.
Look ahead to the Mexican 1994 crisis (p. 493). The Mexican peso appreciated strongly in the early
1990s due to the expectation that it would soon join NAFTA. US firms increased investment in Mexico
(for example, Chrysler moved engine production for many models to Mexico), and so did Japanese firms
anxious for a foothold within NAFTA. Meanwhile, the Mexican government was making appropriate
macroeconomic policy reforms (lower inflation, more balanced budget,etc.) which encouraged foreign
purchase of Mexican stocks, and when the US Federal Reserve cut US interest rates in 1991-2 due to the
US recession, it further encouraged financial capital flows to Mexico, with higher interest rates. What was
a small portfolio adjustment (increase holdings of Mexican stocks) to US investors was a big capital
inflow to Mexico -- but once US portfolios were adjusted, the capital inflow dried up. Despite reasonably
sound economic fundamentals (inflation in Mexico was fairly low, Mexican foreign debt was not
excessive, NAFTA was passed and trade with the US was increasing), the Mexican peso lost half its
value.
Problem 2. Uncovered interest parity
If uncovered interest parity (UIP) holds, the expected future spot rate will play the same role as the
forward rate in covered interest arbitrage. Note that changes in the expected future spot rate can drive
changes in the current spot rate or in interest rates. Problems 2 and 3 in Pugel focus attention on the
current spot rate, but it is surely the case that investors will demand higher interest rates to protect
themselves against an expected depreciation, and with high capital mobility this may be the primary
channel of adjustment.
Spot rate: 1 dollar per euro.
Expected future (180 days in the future) spot exchange rate: 1.005 per euro:
hence there is a half-percent expected appreciation of the euro for half a year,
or a one percent expected appreciation for the year.
[Note: expected appreciation plays the same role here as the forward premium
in talking about covered interest arbitrage].
Annual US dollar interest rate: 4 percent
Annual euro interest rate: 3 percent
Since the expected appreciation is (on an annualized basis) approximately enough to compensate
risk-neutral investors in European securities for the lower interest rate.
If the interest rate on dollar bonds fell to match the euro interest rate, the spot and forward rates would
also have to match -- the spot exchange rate would rise right now to $ 1.005 per euro.
More interesting variation: suppose the dollar were expected to depreciate more against the Euro. For
example, suppose the expected future spot rate (in 180 days) moved to $ 1.01 per euro, for an annualized
2 percent expected depreciation of the dollar. If the current spot rate did not change, the interest rate
differential between the dollar and the euro would have to widen to 2 percent -- US investors, buying
European bonds, would drive euro interest rates down, and European investors would not buy US bonds
unless dollar interest rates rose.
Problem 3. Uncovered Interest Parity again.See text answer p. 697.
Problem 4. Uncovered Interest Parity One More Time
a. Since there is no interest differential between US and Japanese bonds, there should be no difference
between the current spot rate and the expected forward rate.
b. Expected dollar appreciation (it will cost less to buy one yen -- not one cent but 0.95 cents) is more
considerable than the fourth decimal place makes it looks. This is five percent in 90 days, or 20 percent
on an annualized basis. This would force:
i. an immediate adjustment of the spot rate to 0.95 if interest rates did not move.
ii. a fall of Japanese interest rates as investors stop buying Japanese bonds.
Since Japanese interest rates could not fall 20 percent (to minus 16 percent), at least some
of the adjustment would fall on the spot rate and US interest rates.
iii. a rise in US interest rates as investors bid up the price of US bonds (to 24 percent if only US
interest rates were to change).
Problem 5. Forming expectations of the future spot rate.
a. What do you expect the future trade pattern to be? If the demand for a country's exports
increase more than its demand for your imports , this will increase demand for their currency and lead to
their currency appreciating against yours. Given NAFTA, bet on the peso's rise against the dollar.
b. what do you expect the future returns on investment in that country to be? If there are real
resources to be developed (Mexico's offshore Cantarell oil fields; Australia's iron ore) or a country has a
comparative advantage in a rapidly growing industry (US information technology in the 1990s), expect
the demand for their currency to increase, and their currency to appreciate.
c. what do you expect future government policy to be? If you see a prospect of high inflation,
expect future depreciation (purchasing power parity does work in the longer run).
With these principles in mind, the answer to the questions is simple:
a. if you expect Mexico's Cantarell oil fields to run out (see the Wall Street Journal, 5 April
2007), expect a fall in the peso as the demand for pesos drops.
b. if you expect inflationary policies from the Social Credit Party, expect investors to avoid
Canada and expect Canadians to invest in the US. Note: the Wikipedia entry on the Socreds note that,
although the party had electoral strength from the 1930s through the 1960s (especially in Western
Canada), it has since almost disappeared (largely into alliance with the Conservatives).
c. if the Swiss tax interest payments to foreigners, demand for Swiss bonds could be expected to
drop -- and so will demand for Swiss francs to buy the bonds with.
Problem 6. Big Macs, gold and the Law of One Price.
The law of one price should apply better to gold, which is a uniform product traded on
international markets, than to Big Macs. Beef and sesame seeds may be traded, but the labor that goes
into the service component is not. See the articles by Pakko and Pollard on my international website for
more on Big Macs.
Problem 7. Undervaluation and vacations.
If (say) the rupee is undervalued against the dollar, that means that it costs (for example, but the
example is close to the Penn World Table latest estimates) only 7 rupees to obtain a bundle of goods and
services which would sell for a dollar in the US, but it costs 45 rupees to buy a dollar. It would be better
to buy rupees in the US, take your vacation in India, and enjoy a standard of living 6 times that in the US
(warning: this would not necessarily apply to the prices of international hotels; a single in the Grand Hyatt
Mumbai goes for $ 317 a night, according to Priceline.com on 16 April 2007).
Problem 8. Purchasing Power Parity and Exchange Rates – the Mark and the Pound.
The Purchasing Parity Exchange rate of the mark against the dollar, as given in Penn World Tables 6.1 is
graphed against the actual exchange rate below. The PPP exchange rate is the smoother line in red; the
blue line is the actual exchange rate.
Note that in 1970 (as Bretton Woods was breaking down) it actually cost 3.66 marks to buy a
dollar, but it only cost 2.68 marks to buy a dollar's worth of goods and services.
Was the mark overvalued or undervalued?
The second graph shows inflation for Germany (compared to the US inflation rate) against the
depreciation rate of the mark. The PPP inflation rate is the smooth red line (usually less than zero, since
German inflation was usually less than American, but never varying very much); the actual depreciation
rate the very irregular blue line, showing that the mark depreciated by over 20 percent in 1981 (as US
interest rates shot up) and appreciated more than 20 percent in 1986 (as a result of the Plaza agreement to
bring down the dollar).
Problem 8 (continued)
The graph for the PPP value of the pound in the United Kingdom and the actual pound/dollar exchange
rate shows again a general correspondence, but not a close short-run relationship:
Note the undervaluation of the pound in 1977, its overvaluation in 1980 (North Sea oil discovered),
and its sharp undervaluation in 1985 (when it cost only about half a pound to buy a dollar's worth of
goods and services, but more than three-quarters of a pound to buy a dollar).
Again the relation between inflation and depreciation is not very close: the depreciations of 1968 and
1993 are associated with problems in maintaining fixed exchange rates (in 1993 the European Exchange
Rate Mechanism was in crisis, see page 476 of Pugel), and the pound appreciation of 1985 shows the
impact of the Plaza Agreement – not of British inflation or deflation.
Problem 9. Mexican inflation.
In the early 1990s, Mexico reduced its inflation rate from 100 percent (1988) to 20 percent
(1994). Capital inflows had risen in anticipation of NAFTA, and Mexico wanted to fix the exchange rate
against the dollar to encourage the flows to continue, as well as to make trade within NAFTA easier.
Purchasing Power Parity implies that Mexico would have to bring domestic inflation to the same
rate as US inflation to hold the exchange rate steady. In general, the Mexican exchange rate has tracked
inflation differentials with the US, but a close examination of the PPP inflation rate (in red) with the peso
exchange rate indicates that the exchange rate often overshot PPP inflation rates – especially during the
“tequila crisis” of 1982 and the crisis of 1994-95.
The quantity theory equation M = kPY may be familiar to some in the form MV = PY, where V is
velocity of circulation. If we use the second form and denote percent change by a small letter, we have:
m + v = p + y where: (m = growth rate of the money supply)
(p = inflation rate)
(v = percent change in velocity of circulation, assumed to be zero here)
( y = real GDP growth rate)
To target a 3 percent increase in prices with 6 percent real GDP growth, a money supply growth rate of
9 percent is appropriate.
Problem 10. Quantity Theory. Given the two percent higher growth rate of the money supply, we
should expect a two percent greater inflation rate and hence a two percent higher depreciation rate of the
currency. It should be noted that quantity theory relations are long term at best (and in the 1980s and
1990s, when the velocity of money in many countries changed dramatically, not very reliable).
Problem 11. Purchasing Power Parity. See answer in text, p. 697. If the initial price levels in 1975 are
both taken to be 100, and if in 2005 the Pugelovian price level of 390 is well above the price level of 260
in the United States, the pnut should depreciation. If in 1975 it took 1 pnut to buy a dollar, in 2005 it
should take 390/260 = 1.50 pnuts to buy a dollar. If in fact it takes only 1 pnut to buy a dollar, the pnut is
overvalued.
Problem 12. If you are tempted to try it, use arc percentage changes (divide change by average value)
and you will get the approximate result that the text assumes. No problem modeled on this will appear on
any exam.
United States
Pugelovia
--------------In 1975 ----------Real
Money
GDP
CPI
20
800
100
10
200
100
The quantity theory predicts that m + v =
------------- In 2005 -------------Real
Money
GDP
CPI
65
1,000
260
58.5
300
390
p + y where the lower case letters = percent changes.
The percentage change of the US money supply = 65 – 20 / 42.5 = 1.06 or 106 percent.
The percentage change in US real GDP = 1000 – 800 / 900 = .22 or 22 percent.
Percentage change in CPI expected to be 106 – 22 = 84 percent; but note that the percentage change
formula is approximate and not exact.
The percentage change in the US CPI = 260 – 100 / 175 = .91 or 91 percent.
Quantity equation in percent change form: m + v = p + y = 106 + 0 = 22 + 91.
Similarly, for Pugelovia:
Percentage change in money = 58.5 – 10 / 34.25 = 142 percent.
Percentage change in Pugelovian real GDP = 300 – 200 / 250 = 20 percent.
Percent change in CPI = expected at 122 percent; calculated as 390 -100 / 245 = 118 percent.
If you begin by noting that the real GDP in 1975 equals the nominal GDP in 1975, we have a
velocity of money of 800 / 20 = 40 for the US and 200 / 10 = 20 for Pugelovia
(Actually, the M1 velocity for the US is approximately 12 for the US).
Translate the CPI of 100 to 1.0 to find that MV = PY since 20*40 = 800 for the US in 1975.
For Pugelovia in 1975, MV = PY implies 10*20 = 200.
In 2005, MV = PY with unchanged V implies = 65 * 40 = 2.60 * 1000 = 2600 for the US
and for Pugelovia MV = 58.5 * 20 = 1170
and PY = 3.9 * 300 = 1170.
The numbers given are consistent with the quantity equation.