Integrated
Markets
Part III
It’s the real thing
Real Interest Parity
Real interest rate (r)
Nominal interest rate (i)
i$ = r$ + p$e, p$e =
expected inflation, and
i¥ = r¥ + p¥e
Don’t You Just Love
Math!
If (i$
- i¥) = 4%, as before
Then, r$ + p$e - r¥ - p¥e = 4%
Or, (r$ - r¥) + (p$e - p¥e) = 4%
So, (r$ - r¥) = 4% - (p$e - p¥e)
What are
e
p$ &
e
p¥ ?
p$e  2%
Jpn inflation rate: p¥e  - 2%
Therefore,
(r$ - r¥)  (2 – (-2) - 4
And r$ - r¥  0
US inflation rate:
Just What the Doctor
Ordered
Note that uncovered
interest parity has to be
true for real interest parity
to hold
If real interest parity does
not hold, and capital is
mobile, real interest parity
will hold
Purchasing Power Parity
 The Law of One Price (LOOP)
 Gold, silver, oil, and securities with
identical risk & return each have the
same price everywhere
 That’s common sense
 Actual applications may require
considerable disentangling of tariffs
& local taxes, transportation costs
Weaker
 For real estate it clearly does not
work in any absolute sense
 But, if humans were perfectly mobile,
would real estate prices become
uniform everywhere?
 People are already very mobile;
comparable units in major cities have
become comparably expensive. How
about comparable rural locations?
Back to PPP
 PPP is also common sense, but isn’t
that simple
 What is a “representative market
basket of goods?”
 Absolute PPP: ER = relative prices
 Very strong assumption.
ER(¥/$) = P¥/P$
ER(¥/$) = P¥/P$
 If ER = 110, as it does now
 A New York salary of $100 a day is as
livable as a Tokyo salary of ¥11,000 a
day
 An Alaska salary of $500.00 per week
is equivalent a Hokkaido salary of
¥55,000
 A one week $3000 ecotourism
package in Maui should be identical
or similar to a ¥330,000 package in
Okinawa
Relative PPP
 Using the above equation and a little




mathematics,
Ln(¥/$) = ln(P¥) – ln(P$),
Taking derivatives with respect to time,
%Δ(¥/$) = %ΔP¥ - %ΔP$
This equation says that the per cent
appreciation of the dollar should equal the
Japanese inflation rate minus the US
inflation rate
THE REAL EXCHANGE
RATE
 RXR[¥/$] = ER[¥/$]*P$/P¥
 In percentage change terms, this
means that
 %∆RXR[¥/$] = %∆R[¥/$] + %∆P$ - %∆P¥
 We know much about those last two
terms: US & JPN’s rates of inflation
 Let’s use that knowledge
Long-Run Exchange Rate Changes
 In general, MV = Py. Hence,
 M$V$ = P$y$, & M$V$/y$, = P$,
 M¥V¥ = P¥y¥ & M¥V¥/y¥ = P¥
 OK, rearrange terms to get:
 R(¥/$) = P¥/P$ =
(M¥/M$)(V¥/V$)(y$/y¥)
Reality Check
R(¥/$) = P¥/P$ = (M¥/M$)(V¥/V$)(y$/y¥)
Is this equation valid?
LHS: R(¥/$), has fallen recently, 120
to 110 (yen appreciation)
P¥/P$ has also fallen due to minor
deflation in Japan & minor
inflation in USA
So R(¥/$) = P¥/P$ is OK
What About the RHS?
 Is (M¥/M$)(V¥/V$)(y$/y¥) falling?
 We know that (M¥/M$) is rising
due to Japanese use of monetary
policy to stimulate the economy
 We also know that (y$/y¥) is rising
due to faster growth rate in USA
 Two of the terms are rising?
(M¥/M$)(V¥/V$)(y$/y¥)
 This means that (V¥/V$) must be
falling rapidly enough to offset
the other two terms
 What do we know about velocity
that could lead to that
conclusion?
Let’s Talk About
 R(d/$) = Pd/P$ =
(Md/M$)(Vd/V$)(y$/yd)
 d, of course, stands for dong
 What about the currencies of
Korea, China, Europe?