(b) Consider the following loglinear Cagan money demand function: m₁ - St=-n[Et$t+1-St] where m₁ = natural log of money stock at date t and st = natural log of the spot exchange rate (home currency/foreign currency), and the money demand semi elasticity, n>0. Let the money supply follow a process: m₁ = &t − 0₁&t-1 - 02&t-2 where 0< 0₁ <1, 0< 0₂<1 and &t is a white noise. Derive the rational expectation solution for St. What kind of data generating process does the exchange rate follow? How does this differ from a random walk and why?
(b) Consider the following loglinear Cagan money demand function: m₁ - St=-n[Et$t+1-St] where m₁ = natural log of money stock at date t and st = natural log of the spot exchange rate (home currency/foreign currency), and the money demand semi elasticity, n>0. Let the money supply follow a process: m₁ = &t − 0₁&t-1 - 02&t-2 where 0< 0₁ <1, 0< 0₂<1 and &t is a white noise. Derive the rational expectation solution for St. What kind of data generating process does the exchange rate follow? How does this differ from a random walk and why?
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D1.
![(b) Consider the following loglinear Cagan money demand function:
m, – St = -n[Eps4+1- $t]
where m = natural log of money stock at date t and st = natural log of the spot exchange rate (home
currency/foreign currency), and the money demand semi elasticity, n>0. Let the money supply follow a
process: m; = E; – 01Et-1 – 02ɛt-2 where 0< 0,<1, 0< 02<1 and &t is a white noise. Derive the
rational expectation solution for St. What kind of data generating process does the exchange rate follow?
How does this differ from a random walk and why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcb19559-1f65-4a28-a8c7-6c994065c737%2F519de6a3-fc90-4107-beb4-036e7225b3f6%2Fw5f05cc_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Consider the following loglinear Cagan money demand function:
m, – St = -n[Eps4+1- $t]
where m = natural log of money stock at date t and st = natural log of the spot exchange rate (home
currency/foreign currency), and the money demand semi elasticity, n>0. Let the money supply follow a
process: m; = E; – 01Et-1 – 02ɛt-2 where 0< 0,<1, 0< 02<1 and &t is a white noise. Derive the
rational expectation solution for St. What kind of data generating process does the exchange rate follow?
How does this differ from a random walk and why?
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