Lecture_08_2007

# Lecture_08_2007 - International Finance FINA 5331 Lecture 8...

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International Finance FINA 5331 Lecture 8: Purchasing Power Parity William J. Crowder Ph.D.

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Purchasing Power Parity Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP
Purchasing Power Parity in a Perfect Capital Market Purchasing power parity (PPP) is built on the notion of arbitrage across goods markets and the Law of One Price. The Law of One Price is the principle that in a PCM setting, homogeneous goods will sell for the same price in two markets, taking into account the exchange rate. £ / \$ wheat UK, wheat US, S P P × =

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Purchasing Power Parity • Let P US and P UK represent the weighted average price level for goods in the U.S. and U.K. market baskets respectively. Absolute PPP predicts that these two price measures will be equal after adjusting for the exchange rate: P US = S \$/£ × P UK Absolute PPP requires that the consumption baskets are identical across the two countries.
Purchasing Power Parity and Exchange Rate Determination The exchange rate between two currencies should equal the ratio of the countries’ price levels: S (\$/£) = P £ P \$ S (\$/£) = P £ P \$ £150 \$300 = = \$2/£ For example, if an ounce of gold costs \$300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be:

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Suppose absolute PPP is violated. Introduce K so that: P US, t +1 = K × S \$/£, t +1 × P UK, t +1 ( a ) P US, t = K × S \$/£, t × P UK, t ( b ) p US = %Δ s + %Δ p UK + %Δ s × p UK \$/£, 1 \$/£, US, 1 US, UK, 1 UK, US UK \$/£, US, UK, % , % , % t t t t t t t t t S S P P P P s p p S P P + + + - - - ∆ = ∆ = ∆ = For small % changes, or when continuous rates are used, the cross-product term %Δ s × p UK can be ignored. % exchange rate = % U.S.prices – % U.K.prices Relative Purchasing Power Parity
Relative Purchasing Power Parity Note that p = π, the rate of inflation Relative PPP states that the rate of change in the exchange rate is equal to the differences in the rates of inflation: %Δs = (1 + π £ ) ( π \$ π £ ) π \$ π £ If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or approximately 3%.

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Ex-Ante PPP Ex-Ante PPP says that relative PPP will hold in an expected value sense, i.e. * 1 1 1 (% ) ( ) ( ) t t t E s E E π + + + ∆ = - Where E is the expectations operator signifying that E (·) is an expected value.
Purchasing Power Parity The real exchange rate is calculated by correcting the nominal exchange rate for the price levels in the two countries. When absolute PPP holds: \$1.50/£ = \$1,500/US good . £ 1,000/British good LHS = 1 US good / British good RHS When PPP holds, the real exchange rate is constant.

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Purchasing Power Parity An index of the real exchange rate is defined as: Spot (Real, t ) = Spot (Nominal, t ) . Spot (
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Lecture_08_2007 - International Finance FINA 5331 Lecture 8...

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