16.2 One version of the expectations theory of the term structure of interest rates holds that a long-term rate equals the average of the expected values of short-term interest rates into the future, plus a term premium that is I(0). Specifically, let Rkt denote a k-period interest rate, let R1t denote a one-period interest rate, and let et denote an I(0) term premium. Then Rkt = 1k gk - 1 i = 0 R1t + it + et, where R1t + it is the forecast made at date t of the value of R1 at date t + i. Suppose that R1t follows a random walk so that R1t = R1t - 1 + ut.

a. Show that Rkt = R1t + et.

b. Show that Rkt and R1t are cointegrated. What is the cointegrating coefficient?

c. Now suppose that ΔR1t = 0.5ΔR1t - 1 + ut. How does your answer to

(b) change?

d. Now suppose that R1t = 0.5R1t - 1 + ut. How does your answer to

(b) change?