Equilbrium Approach

Equilbrium Approach - ); ln * (ln ln ≥ − − = c Y Y c...

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Brigham Young University Department of Economics Economics 459 - International Monetary Theory Deriving the Equilibrium Approach to Exchange Rates Start with our definition of the real exchange rate, P eP q / * , and solve for the nominal rate: * / P qP e = Use domestic and foreign money market equilibria, ) , ( / Y i L P M = , solve for price levels and substitute to get: ) , ( *) *, ( * Y i L Y i L M M q e = Suppose the money demand function is log-linear, Y b ai L ln ln + = , then we can rewrite this as: Λ = Y Y i i M M q e * *, * , where 0 , ); / * ln( *) ( ln + = Λ b a Y Y b i i a Use the Fisher equations, } { } { π E r E i + = , to get: + + Λ = Y Y E r E E r E M M q e * *}), { *} { ( } { } { * Use real interest rate parity, ρ δ + = * r r , to get: + + Λ = Y Y E E E M M q e * , *} { } { } { * , where is the percentage growth of q . Use the quantity theory of money to get } { } { } { Y M g E g E E = + + Λ = Y Y g E g E g E g E E M M q e Y M Y M * , }) { } { ( } { } { } { * Finally assume that the real exchange rate depends on relative levels of GDP, ) / * ( Y Y q q = and that we can approximate this function with a log-linear version,
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Unformatted text preview: ); ln * (ln ln ≥ − − = c Y Y c q . This gives ) ( * Y Y g g c − − = . Taking logs and substituting for ln q and gives: Λ + − + = ln * ln ln ln ln M M q e ) ln * (ln *) ( * ln ln ) ln * (ln ln Y Y b i i a M M Y Y c e − + − + − + − − = ) ln * (ln ) } { } { } { } { ) ( ( * ln ln ) ln * (ln ln * Y Y b g E g E g E g E g g c a M M Y Y c e Y M Y M Y Y − + + + − − + − − + − + − − = ] } { } { }) { } { )( 1 [( * ln ln ) ln * )(ln ( ln * + − + − − + − + − − = M M Y Y g E g E g E g E c a M M Y Y c b e a g aE g aE g E c a g E c a M M Y c b Y c b e M M Y Y + − + − − − + − + − − − = } { } { } { ) 1 ( } { ) 1 ( * ln ln ln ) ( * ln ) ( ln *...
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This note was uploaded on 02/29/2012 for the course ECON 459 taught by Professor Phillips,k during the Winter '08 term at BYU.

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