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Chapter 3:

4. Here’s the data you’re given (Actual, June), along with the relevant info from table 3-1
(note that India is listed in the table in the question, but isn’t in table 3-1):
Country     Over (+)    predicted      Actual,   Actual,   Actual
Under (-)   direction      7/2009    1/2010    change
Australia          -6   Appreciate        1.29       0.9   Appreciate
Brazil             13   Depreciate           2      1.74   Appreciate
Canada             -6   Appreciate        1.16      1.04   Appreciate
Denmark            55   Depreciate        5.34      5.17   Appreciate
Eurozone           29   Depreciate        0.72      0.69   Appreciate
Japan              -3   Appreciate        92.6     93.05   Depreciate
Mexico            -33   Appreciate        13.8     12.92   Appreciate
Sweden             38   Depreciate         7.9      7.14   Appreciate

PPP predicts that currencies that were undervalued in January should appreciate, and vice
versa. All of these exchange rates are expressed in local currency per dollar, so an
appreciation is a drop in the exchange rate. For example, the Australian dollar
appreciated, since the price of a US dollar went down (\$A1.29 to 0.90). In fact, all of
these currencies except the Yen appreciated against the dollar over this time period. So
the theoretical result and the actual result coincide for Australia, Canada, and Mexico.
For the others, the PPP-based predictions were incorrect.
Reasons for the incorrect predictions would include things like the importance of non-
traded goods like labor in the local Big Mac price, differing regulatory regimes, etc.
5. We’re given the following:
E 2
P  \$100
US

EP  \$120
UK

 US  2%
e

 UK  3%
e

Also, the convergence to PPP happens at 15% per year. The nominal exchange rate is in
dollars per pound.
a) This is just -1%; UK inflation is predicted to be 1% per year higher than in the US.
b) The real exchange rate formula is
EP
q        UK
PUS

so in this case q = 120/100 = 1.2. Notice that you’re given the dollar price of a UK basket
of goods.
c) The dollar is 20% undervalued. PPP predicts a real exchange rate equal to 1, which
means one US goods basket (1 keg Bud Lite) trades for 1 UK goods basket (1 keg
Newcastle Brown Ale). But here we have to give up 20% more of one of our kegs in
order to get one in return.
d) This is where we use the convergence rate to PPP. If q is currently 20% too high, then
15% of that difference will disappear over the next year (q will move 15% of the way to
1). So 20%*0.15 = 3% of the difference will disappear, leaving a 17% overvaluation. Of
course, 85% of the overvaluation will persist for longer than a year: 20%*0.85 = 17%.
Either way, the predicted value of q a year from now is 1.17.
e) The expected real depreciation is

q   e
q          
1.17  1.2           0.025,
q                       1.2
which is a 2.5% real appreciation (negative depreciation = appreciation).
f) Use our “fun math facts” to write the growth rate version of the real exchange rate:
EP
q      UK
, so
PUS

q e E e
       UK   US
q    E
E e
2.5              3  2,
E
so we’d expect a 3.5% nominal appreciation. In the second equation above, I’ve just
written π for the percentage changes in the price levels (ie, the inflation rates).
g) The current level of the exchange rate is \$2/pound, and we’re looking at a 3.5%
appreciation, so the rate in a year will be 3.5% lower (pounds will be cheaper). So
2*0.965 = \$1.93/pound. Or, the price will fall by 2*0.035 = 0.07, or 7 cents.
7. The key relationships here are, first, the quantity theory of money, relating the growth
rate of the money supply (µ) to inflation (π) and the growth rate of GDP (g) (assuming
constant velocity of money):
   g
and second, relative PPP, which relates the percentage change in the exchange rate to the
two inflation rates:
E e
  K   JP .
E
a) We’re given g JP  1%, g K  6%,  JP  2%, and K  12%. Use these in the quantity
theory equation to solve for the inflation rates, and you should get 6% in Korea and 1% in
Japan.
b) Now use the relative PPP equation. The expected depreciation of the won against the
Yen is just 6% - 1% = 5%; The won is expected to fall in value by 5% over the coming
year.
c) The increased rate of money growth in Korea will raise its inflation rate to 15% - 6% =
9%.
d) You should get a picture (or series of pictures) like figure 3-6. This is the simple
version of the money demand function, so there’s no change in real money demand when
the interest rate drops (ie, when the money supply growth rate increases).
e) If Korea pegs the won to the Yen, then the expected depreciation term becomes 0
(because E can’t change anymore). In that case, Korean inflation would have to be equal
to Japanese inflation of 1%, implying money supply growth of 7%.
f) In order for the won to appreciate against the Yen, Korean expected inflation would
have to be less than Japanese expected inflation. We’d need an inflation rate of less than
1%, which means a money supply growth rate below 7%. Notice that values of µK less
than 6% (the output growth rate) would imply deflation in Korea.
8. Now we’re using the more general money demand equation, where higher interest
rates mean less money demand.
a) Using the approximate expression for UIP, along with the depreciation rate implied in
part (b) of the last question, we get
E e
iK  iJP 
E
 3%  5%
 8%
b) The two real interest rates are 8% - 6% = 2% for Korea, and 3% - 1% = 2% for Japan.
c) Once again we get an increase in Korean inflation from 6% to 9%. The nominal
interest rate on Korean deposits will increase from 8% to 11%. Remember that the
nominal interest rate is a price, and all prices are going up by 3 percentage points.
Another way to see this is that the real interest rate should still be 2% after the change.
d) Now the higher interest rate lowers real money demand, so you get the situation in
figure 3-14 (14-14).
9. This question is about different possible nominal anchors.
a) Swiss inflation will be 8% - 3% = 5% with the given information. Using the money
growth rate to target an inflation rate of 2% would require the Swiss Central Bank to
decrease µ to 5% (assuming output growth stays at 3%).
b) Since the real interest rate in NZ will equal the world real interest rate, we have
iNZ  rNZ   NZ , so  NZ  iNZ  rNZ  6%  1.5%  4.5%. To get inflation under 2.5%
would require interest rates of no higher than 1.5% + 2.5% = 4%.
c) The two sides of the band are 3.4528*0.85 = 2.9349 and 3.4528*1.15 = 3.9707 litas
per euro. The expected rate of depreciation is equal to Lithuanian inflation minus euro
zone inflation, which is 5% - 2% = 3%. How long Lithuania will be able to maintain its
band depends on where the exchange rate is at the moment. Suppose that it’s currently at
the bottom end of the band, at 2.9349 ltias per euro (ie, the lita is at its most valuable).
For the lita to reach the other end of the band would be a depreciation of about 35.3%
(3.9707/2.9349 – 1). To find out how long this would take at a depreciation rate of 3%
per year, we need to solve the following equation for X:

2.9349 * 1.03  3.9707 .
X

Using our friend the natural logarithm, we get
ln(2.9349)  X ln 1.03   ln(3.9707), so
ln(3.9707)  ln(2.9349)
X=
ln 1.03
 10.23 years.
Of course, if we start somewhere else in the band it would take less time to get to the
other side.
For the last question, let’s assume the ECB’s definition of “price stability” is a 2%
inflation rate in all (current and future) euro zone countries. The numbers above suggest
that a member country’s inflation rate could be substantially higher than this for an
extended time period, even with an exchange rate band. So the band is not a sufficient
condition (the presence of the band doesn’t guarantee low inflation). It’s also not a
necessary condition. Lithuania could switch to an inflation target or money growth target
in order to reduce inflation to 2%.
11. Current inflation is 4% and needs to be reduced to 2.5%. We currently have g = 3%
and r* = 1.5% (the world interest rate).
a) Adopting a nominal anchor would allow the central bank to influence investors’
expectations about inflation. Assuming that the anchor is credible, investors would begin
to expect inflation equal (or near) the target rate, and this would help get actual inflation
lower. The drawback is that commitment to a (long run) rule, such as a target money
growth rate, means the central bank gives up some short-run flexibility (for example, the
ability to stimulate the economy if there’s a fall in aggregate demand).
b) The money growth rate (assuming the quantity theory holds and velocity is constant) is
µ = π + g = 4% + 3% = 7%. A money growth target that delivers a 2.5% inflation rate
would be 5.5%.
c) The exchange rate is currently expected to depreciate by 2% per year. In order to get
inflation from 4% to the US level of 2.5%, we’d need to slow the rate of depreciation to
0.5% per year. The lira will depreciate against the dollar, but more slowly than before.
The relevant formula is   E e / E   US , with “home” inflation of 4% or 2.5% and US
inflation at 2%.
d) The current nominal interest rate is i =r* + π = 1.5% + 4% = 5.5%. In order to get to
2.5% inflation the neutral interest rate would have to be 4%.

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