Suppose the Home central bank commits to and announces the interest rate policy: t + Tt...

  

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Suppose the Home central bank commits to and announces the interest rate policy: ît + Têt with T > 0. (2) This means that the Home central bank commits to shadowing the policy of the Foreign central bank and to increasing the interest rate ît if the currency weakens (êt rises) or lowering the interest rate it if the currency strengthens (êt falls). The central bank announces this commitment and is completely credible. Furthermore, assume that the Home central bank and government are fully and credibly committed to the fact that they would never let the currency become worthless. (This means that the Home central bank and government would never accept a situation in which êt = ∞. Drastic actions would be taken such that êt remains finite.) • Use the UIP condition (1), the policy rule (2), the fact that these two equations must hold in each period (t, t+1, t + 2, and so on), and the fact that we assumed policy commit- ments to be fully credible to prove that the policy rule (2) will deliver êt = 0 in all pe- riods. (In developing this proof, you will have to use the Law of Iterated Expectations: Under rational expectations, the expectation today of the expectation tomorrow of some- thing the day after tomorrow is equal to the expectation today of that something. Formally, Et [Et+1 (xt+2)] = Et (x+2) for any variable x. Note that this applies also to longer horizons: Et [Et+1 [Et+2 [Et+3 [...Et+T (Xt+T+1)]]]] = Et [Et+T (Xt+T+1)] = Et (t+T+1).) • What happens to ît versus it if the Home central bank has been successful with its policy? • If the policy commitment has been successful, does the Home central bank actually need to exercise its threat of adjusting it in response to exchange rate movements? Suppose the Home central bank commits to and announces the interest rate policy: ît + Têt with T > 0. (2) This means that the Home central bank commits to shadowing the policy of the Foreign central bank and to increasing the interest rate ît if the currency weakens (êt rises) or lowering the interest rate it if the currency strengthens (êt falls). The central bank announces this commitment and is completely credible. Furthermore, assume that the Home central bank and government are fully and credibly committed to the fact that they would never let the currency become worthless. (This means that the Home central bank and government would never accept a situation in which êt = ∞. Drastic actions would be taken such that êt remains finite.) • Use the UIP condition (1), the policy rule (2), the fact that these two equations must hold in each period (t, t+1, t + 2, and so on), and the fact that we assumed policy commit- ments to be fully credible to prove that the policy rule (2) will deliver êt = 0 in all pe- riods. (In developing this proof, you will have to use the Law of Iterated Expectations: Under rational expectations, the expectation today of the expectation tomorrow of some- thing the day after tomorrow is equal to the expectation today of that something. Formally, Et [Et+1 (xt+2)] = Et (x+2) for any variable x. Note that this applies also to longer horizons: Et [Et+1 [Et+2 [Et+3 [...Et+T (Xt+T+1)]]]] = Et [Et+T (Xt+T+1)] = Et (t+T+1).) • What happens to ît versus it if the Home central bank has been successful with its policy? • If the policy commitment has been successful, does the Home central bank actually need to exercise its threat of adjusting it in response to exchange rate movements?

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Answer 1 In order to prove that the policy rule 2 will deliver t 0 in all periods we must use the UIP condition 1 the policy rule 2 and the fact that these two equations must hold in each period The U... View the full answer