Topic 6B Price Levels and the Exchange Rate in the Long Run

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Topic 6BPrice Levels and the Exchange Rate in
the Long Run

• Textbook Chapter 15

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Learning objectives

• Learn the purchasing power parity, the goods
  market condition in determining the equilibrium
  exchange rate in the long run
• Introduce the monetary approach to the exchange
  rate
• Learn the general model of the exchange-rate
  determination that combine asset market and goods
  market.

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The law of one price

• In competitive markets free of transportation
  costs and barriers of trade, identical goods sold
  in different countries must sell for the same
  price when the prices are expressed in the same
  currency. Formally, we have
• PiUS(E/)?(PiE).

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Purchasing power parity (PPP)

• All countries price levels are equal when
  measured in terms of the same currency.
• PUS(E/)?(PE).
• Alternatively, a unit of all currencies must have
  the same real value in every country
• (E/)/ PUS1/(PE).

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Absolute PPP v.s. relative PPP

• Absolute PPP states that exchange rates equal
  relative price levels
• (E/)/ PUS1/(PE).
• Relative PPP states that prices and exchange
  rates change in a way that preserves the ratio of
  each currencys domestic and foreign purchasing
  powers.

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Absolute PPP v.s. relative PPP

• That is,
• (E/)/ PUS1/(PE)
• ? 11/(PE)/(E/)/ PUS,
• ? (E/,t- E/,t-1)/ E/, t-1 ?US,t-?E,t .

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Monetary approach to exchange rate

• In the long run, PPP holds and money demand and
  supplies determine the price level, therefore,
• E/PUS/PE
• MsUS/L(R,YUS)/MsE/L(R,YE)
• (MsUS/MsE)?L(R,YE)/L(R,YUS)

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Monetary approach to exchange rate

• Three predictions from PPP and monetary approach
• The larger the money supply, the lower the
  exchange value of the currency.
• The higher the interest rate, the lower the
  exchange value of the currency.
• The higher the output level, the higher the
  exchange value of the currency.

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One-time money supply change v.s. money growth
change

• One-time increase in the level of money supply
  has no effect on the long-run value of the
  interest rate.
• Continuing money supply growth (or permanent
  increase in inflation rate) eventually results in
  ongoing inflation so that the interest rate must
  increase accordingly.

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Fisher effect

• A rise (fall) in a countrys expected inflation
  rate will eventually cause an equal rise (fall)
  in the interest rate denominated in that
  countrys currency.

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Ongoing inflation, interest parity, and PPP

• Given that the IRP holds both in the short and
  long run, if people expect relative PPP to hold,
  the difference between R and R will equal the
  difference between ?eUS and ?eE.
• Formally, we have
• R - R ?eUS - ?eE.
• where ?e is expected inflation rate.

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Figure 15-1 Long-run time paths of U.S. economic
variables after a permanent increase in the U.S.
money growth rate
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Real exchange rate

• Using the reference commodity baskets to measure
  the price level, real dollar/euro exchange rate,
  q/, is the dollar price of the European basket
  relative to that of the American.
• q/ (E/ ?PE)/PUS.

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An example

• If the European basket costs 100, the U.S.
  basket costs 120, and the nominal exchange rate
  is 1.20 per euro, then,
• q/ (1.20 per euro)?(100 per European
  basket)/(120 per U.S. basket)
• (120 per European basket)/(120 per U.S.
  basket)
• 1 U.S. basket per European basket

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Real exchange rate

• Real depreciation of the dollar against the euro
  (q/?) means a fall in the dollars purchasing
  power over European goods relative to its
  purchasing power over U.S. goods.
• 1/ (E/ ?PE)/(1/PUS) ?
• which occurs when either E/? or PE?or PUS ?.

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An example (continued)

• A 10 nominal dollar depreciation to E/ 1.32
  per euro causes q/ to rise to 1.1 U.S. baskets
  per European basket (real dollar depreciation)
  the same change in could result from a 10 rise
  in PE or 10 fall in PUS.

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Real exchange rate

• Real appreciation of the dollar against the euro
  (q/ ?) means a rise in the dollars purchasing
  power over European goods relative to its
  purchasing power over U.S. goods.
• 1/ (E/ ?PE)/(1/PUS) ?
• which occurs when either E/ ? or PE ? or PUS
  ?.

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Factors that change real exchange rate

• A change in world relative demand for American
  products
• An increase (fall) in world relative demand for
  U.S. output causes a long-run real appreciation
  (depreciation) of the dollar against the euro,
  i.e., a fall (rise) in
• q/ .

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Factors that change real exchange rate

• A change in relative output supply.
• A relative expansion of U.S. (European) output
  causes a long-run real depreciation
  (appreciation) of the dollar against the euro,
  i.e., a rise (fall) in q/ .

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Why exchange rate differs from PPP?

• From the real exchange rate expression, we can
  get
• E/ q/ ?(PUS/PE).
• the absolute PPP q/ 1
• the relative PPP q/ is constant.
• The exchange rate differs from PPP because the
  real exchange rate changes over time.

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Beyond PPP a general model

• The exchange rate will rise (the dollar will
  depreciate against the euro) if
• the relative U.S. money supply increases
• the relative U.S. money growth rate rises
• the relative world demand for U.S. products
  increases
• the relative U.S. output supply increases so that
  the real exchange rate effect exceeds the money
  demand effect.

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Figure 15-5 The Real Dollar/Yen Exchange Rate,
1950-1996
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Summary

• Under the law of one price, the purchasing power
  of any currency is the same in any country
  (absolute PPP).
• Absolute PPP implies that percentage changes in
  exchange rates equal difference in inflation
  rates (relative PPP).
• The monetary approach uses PPP to explain
  long-term exchange rate behavior exclusively in
  terms of money supply and demand, finding that a
  rise in a countrys interest rate leads to a
  depreciation of its currency.

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Summary

• The long-run determination of nominal exchange
  rate can be analyzed by combining the theory of
  the long-run real exchange rate and the monetary
  approach.
• When all disturbances are monetary in nature,
  exchange rates obey relative PPP in the long run
• When disturbances occur in output markets, the
  exchange rate is unlikely to obey relative PPP,
  even in the long run.