Integrated Markets Part III

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Integrated MarketsPart III

• Its the real thing

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Real Interest Parity

• Real interest rate (r)
• Nominal interest rate (i)
• i r pe, pe expected inflation, and
• i r pe

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Dont You Just Love Math!

• If (i - i) 4, as before
• Then, r pe - r - pe 4
• Or, (r - r) (pe - pe) 4
• So, (r - r) 4 - (pe - pe)

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What are pe pe?

• US inflation rate pe ? 2
• Jpn inflation rate pe ? - 2
• Therefore,
• (r - r) ? (2 (-2) - 4
• And r - r ? 0

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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

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Purchasing Power Parity

• The Law of One Price (LOOP)
• Gold, silver, oil, and securities with identical
  risk return each have the same price everywhere
• Thats common sense
• Actual applications may require considerable
  disentangling of tariffs local taxes,
  transportation costs

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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?

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Back to PPP

• PPP is also common sense, but isnt that simple
• What is a representative market basket of
  goods?
• Absolute PPP ER relative prices
• Very strong assumption.
• ER(/) P/P

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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

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Relative PPP

• Using the above equation and a little
  mathematics,
• Ln(/) ln(P) ln(P),
• Taking derivatives with respect to time,
• ?(/) ?P - ?P
• This equation says that the per cent appreciation
  of the dollar should equal the Japanese inflation
  rate minus the US inflation rate

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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
  JPNs rates of inflation
• Lets use that knowledge

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Long-Run Exchange Rate Changes

• In general, MV Py. Hence,
• MV Py, MV/y, P,
• MV Py MV/y P
• OK, rearrange terms to get
• R(/) P/P (M/M)(V/V)(y/y)

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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

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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?

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(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?

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Lets 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?