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Assuming PPP holds and that real exchange rate doesn´t change. Additionally we assume fully mobile internationally capital and consumption growth its the same among countries. i) Show by using Fisher equation - r(t) = i(t) - E(t) (π (t+1)) that standard expression for Uncovered interest rate parity (UIP) follos from previous assumptions; ii) Considering a test of UIP with the follow regression: E (e (t+1))- e(t) = α + β (i (t) - i* (t)) + v(t). The i* (t) its given and p*(t) = E(p*(t+1))=0 where p* its the log of the foreign price level and p the domestic prices. The domestic policy makers set i (t) according to a price targeting rule, i(t) = r*(t) + µ p(t) + u(t) where u is serially uncorrelated and independent of v. Demonstrate that β will biased away from 1 if µ its different from zero; iii) Demosntrate the condition under which β <0.
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