For the simple dynamic model given in (6.18), let the disturbances follow an MA(1) process t = t + t1 with t IIN(0, 2

For the simple dynamic model given in (6.18), let the disturbances follow an MA(1) process

νt = t + θt−1 with t ∼ IIN(0, σ2 ).

(a) Show that plim(βOLS

− β) = δ(1 − β2)

1 + 2βδ

where δ = θ/(1 + θ2).

(b) Tabulate this asymptotic bias for various values of |β| < 1 and 0 < θ < 1.

(c) Show that plim(

1 T

T t=2 ν2 t) = σ2 [1 + θ(θ − θ

∗)] where θ

∗ = δ(1 − β2)/(1 + 2βδ) and νt =

Yt − βOLSYt−1.