Answer to Question #101598 in Macroeconomics for Jorge Ferreira

Question

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.

Answer 1

i) E (t) (π (t + 1))= r (t) - i (t);

ii) if µ=1, то E (e (t + 1)) - e (t) = α + β ((r * (t) + p (t) + u (t))- i * (t)) + v (t);

iii) E (e (t + 1)) - e (t) = α + v (t).