Understanding Real Interest Parity and Purchasing Power Parity in Global Markets

1. Integrated MarketsPart III It’s the real thing

2. Real Interest Parity • Real interest rate (r) • Nominal interest rate (i) • i$ = r$ + p$e, p$e = expected inflation, and • i¥ = r¥ + p¥e

3. 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)

4. What arep$e & p¥e? • US inflation rate: p$e  2% • Jpn inflation rate: p¥e - 2% • Therefore, • (r$- r¥)  (2– (-2)- 4 • And r$- r¥ 0

5. 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

6. 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

7. 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?

8. 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(¥/$) = P¥/P$

9. 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

10. 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

11. 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

12. 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¥)

13. 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

14. 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?

15. (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?

16. 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?