4. This question studies how the term structure of nominal interest rates reflects inflation forecasts. Suppose that inflation evolves like this: t = 0.4 + 0.8t1 + t, where t is a mean-zero white noise. Suppose that the real interest rate takes a constant value of 1. The one-period, nominal interest rate is given by the Fisher relationship: i S t = 1 + Ett+1. 2 Meanwhile, the two-period, nominal interest rate i L t is given by the expectations hypothesis of the term structure.

(a) Find an expression for i S t . Will this interest rate move one-to-one with the current inflation rate?

(b) Find an expression for i L t .

(c) Under what circumstances will the yield curve slope up?

(d) At a very long horizon what are the expected values of the inflation rate and the short-term nominal interest rate?