Find the value that e will take in the new long-run

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Reference no: EM132402526

International Monetary Economics

Asset Approach to Exchange Rate

Consider the asset model of exchange rate determination studied in class. The money demand is given by the equation

M^t_d / P_t = Y_t / i_t

The uncovered interest parity is given by the equation

i_t = i_t ∗ + (E^e_t+1 − E_t )/ E_t

Suppose that investors form their expectations following the equation

E^e_t+1 = θE_t + (1 − θ)E^e_t

where θ is a parameter, 0 ≤ θ ≤ 1.

(a) In period t = 1, the following information is provided: θ = 0, P₁ = 1, M^s₁= 100, Y₁ = 4, i^∗₁ = .02, and E^e₀ = E₀ = 1. Find E₁.

(b) Given part (a), suppose the Central Bank applies a contractionary monetary policy in period t= 2 under static exchange rate expectations: M₂^s = 50 and θ is still 0. Find E₂.

period t = 2 under changing exchange rate expectations: M₂^s = 50 and θ is now 0.5. Find E₂.

(d) Compute the magnitude of the undershooting and explain (intuitively and graphically) your result.

(e) Find the value that E will take in the new long-run equilibrium.

(f) Repeat part (d) if θ changes from θ = 0 to θ = θ^{^}. Compute the following sensitivity:

[d(undershooting)/ dθ^{^}]

Explain the impact from θ^{^} to the magnitude of undershooting.

Note: undershooting is calculated as the difference between the exchange rate under dynamic expectations and the exchange rate under static expectations (given that a change in monetary policy has occurred).

Reference no: EM132402526

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