INTEREST PARITY CONDITIONS

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INTEREST PARITY CONDITIONS

• Define s (units of domestic currency/one unit
  of foreign currency)
• Uncovered Interest Parity
• i i ?se
• Implication
• ? If i gt i, then we expect depreciation of
  domestic currency
• ? If i lt i, then we expect appreciation of
  domestic currency

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• Explanation
• ? If i gt i, then there will be capital inflow
• ? Domestic currency appreciates
• ? Exchange rate will return to its long-run
  equilibrium in the future (see graph)
• ? We expect the exchange rate to return to its
  long-run level domestic currency will depreciate
  in the future

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• Real Interest Parity
• r r (i - ?pe) (i - ?pe)
• where r is real interest rate, p is price level
• Decompose as follows
• r r (i - i - fd) (fd - ?pe ?pe)
• where fd is the forward discount

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• Two terms
• Covered Interest Differential (CIP) this is the
  political or country premium
• ? This term captures barriers to integration of
  financial markets across countries
• ? Transaction costs, information costs, capital
  controls, discriminating tax laws, default risk,
  risk of future capital controls

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• Currency Premium
• ? Captures differences in assets based on their
  currency denomination not country of issuance
• Decompose currency premium
• fd - ?pe ?pe (fd - ?se) (?se - ?pe ?pe)
• Two terms
• Exchange Risk Premium
• ? Changes in the forward rate should reflect
  expected changes in spot rate

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• Expected Real Depreciation (Ex ante PPP)
• ? Expected changes in nominal exchange rates
  must reflect expected differential in inflation
  rates

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PURCHASING POWER PARITY

• Law of One Price (LOOP) Assuming no tariffs,
  non-tariff trade barriers and transportation
  costs, then arbitrage will ensure that
• Pi sPi
• Absolute PPP For identical baskets of goods
• P sP
• Relative PPP
• ?P ?s ?P

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PPP AND REAL EXCHANGE RATES

• Real Exchange Rate Broad summary measure of the
  prices of one countrys goods and services
  relative to anothers
• q sP/P
• ? If q ? ? real exchange rate depreciation
  (increased competitiveness)
• ? If q ? ? real exchange rate appreciation
• Real exchange rate is equivalent to terms of
  trade (? PM/PX)

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• If ? ? ? deterioration in our terms of trade
  (loss of purchasing power)
• Implication of PPP
• ? If PPP always holds, then real exchange rate
  must be constant through time
• q sP/P k
• We can test the PPP hypothesis by examining the
  time series properties of real exchange rates

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EMPIRICAL EVIDENCE ON LOOP

• In general, LOOP does not hold
• Some pieces of evidence
• ? Empirical evidence from homogeneous
  manufacturing commodities (screws, nuts, botls)
  between U.S. and Japan shows price differentials
• ? Evidence from cities within one country vs.
  cities across borders border effect equivalent
  to adding 2,500 to 23,000 miles

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• Evidence from historical data series Froot, Kim,
  Rogoff (1995) annual prices for grains and dairy
  products in Holland and England from 14th to 20th
  centuries show poor support for LOOP

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REASONS FOR FAILURE OF LOOP

• Transportation costs
• Significant non-traded components in production
  of goods (e.g. rent, labor costs, taxes,
  insurance, etc.)
• Tariffs
• Non-tariff trade barriers Knetter (1994) claims
  they are important for explaining failure of PPP

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• Pricing to market Firms set prices with a eye
  more on the prices of competing products in the
  customers market than on the price of the
  product in its country of origin
• ? BMWs in mid-1980s prices in U.S. did not
  decrease after appreciation of
• ? Different standards on cars, dealer service
  and waranties, etc.

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DOES PPP HOLD?

• Empirical tests of PPP followed three stages
• ? Regression Analysis
• ? Univariate Time Series Analysis (Does real
  exchange rate follow a random walk?)
• ? Multivariate Time Series Analysis (Are the
  real exchange rate and the ratio of prices
  cointegrated?)

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STAGE ONE TESTS REGRESSION ANALYSIS

• Early tests in mid-1970s used regression analysis
• ln st ? ? ln(Pt/Pt) ?t
• Testable Hypothesis ? 1
• Frenkel (1978) found ? .9 ? PPP must hold
• Data from high-inflation interwar period
• Frenkel (1981) found that PPP did not hold during
  1970s
• Problems with regression analysis stationarity
  of time series (spurious correlation)

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STAGE TWO TESTS DOES REAL EXCHANGE RATE FOLLOW
RANDOM WALK?

• If PPP holds ? q is constant
• Implication Time series data of real exchange
  rate must exhibit mean reversion
• Real exchange rate should behave as a stationary
  process
• Stationary variable constant mean and finite
  variance

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• Implication variable is occasionally disturbed
  from its mean by a shock, but eventually returns
  to its long-run value
• If it does not, then PPP does not hold (time
  series of real exchange rate is non-stationary
  process)
• Variable has undefined mean and infinite variance

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• Simplest non-stationary process is random walk
• xt1 xt ?t1
• Implication best forecast of future value of
  variable x is todays value
• Variable x could move in any direction with no
  tendency to return to its present value
• Testing PPP hypothesis Testing if real exchange
  rate behaves as random walk

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• If q is random walk ? PPP does not hold
• If q is not random walk ? q exhibits mean
  reversion and PPP holds
• Testing random walk hypothesis
• ? Run regression
• qt ?qt-1 ?t
• ? Impose, rather than estimate, that ? 1
• ? Test, rather than imposing, hypothesis that q
  is stationary

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• Testing of stationarity (unit root) is done
  through Dickey-Fuller and augmented Dickey-Fuller
  tests
• Numerous empirical studies in the 1980s failed to
  reject random walk hypothesis
• Some studies with data from fixed and floating
  rates found mixed support of PPP
• Does PPP not hold? Not necessarily.
• Problem with unit root tests low power

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• Power of test It is the probability that it will
  correctly lead to a rejection of a false null
  hypothesis
• For unit root tests, time span of data is more
  important than number of obseravtions
• Use longer series of low frequency data (annual
  data) rather than shorter series of high
  frequency data (monthly data)
• Use panel data (cross section time series)

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• Why? If deviations from PPP dump out slowly ?
  longer time span will capture mean reversion
• Recent evidence finds support for PPP
• ? Frankel (1986, 1990) long series of annual
  data 1869-1984 for dollar-pound rate ? rejection
  of random walk
• ? Frankel and Rose (1995) panel data for 150
  countries for period 1948-1992 ? reject random
  walk even for post-1973 data

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• Conclusion of empirical evidence Half-life of
  deviations from PPP is between 2.5 and 4.6 years
• Criticism of studies with long-run data mixing
  of fixed and floating exchange rate regimes