Consider the cointegration example given in (14.14) and (14.15). (a) Verify equations ( 14.16)-(14.21). (b) Show that the OLS estimator of obtained by regressing

Consider the cointegration example given in (14.14) and (14.15).

(a) Verify equations ( 14.16)-(14.21).

(b) Show that the OLS estimator of β obtained by regressing Ct on Yt is superconsistent, i.e., show that plim T (βOLS

− β) → 0 as T →∞.

(c) In order to check the finite sample bias of the Engle-Granger two-step estimator, let us perform the following Monte Carlo experiments: Let β = 0.8 and α = 1 and let ρ vary over the set {0.6, 0.8, 0.9}. Also let σ11 = σ22 = 1, while σ12 = 0, and let T vary over the set

{25, 50, 100}. For each of these nine experiments, generate the data on Yt and Ct as described in (14.14) and (14.15) and estimate β and α using the Engle and Granger two-step procedure.

Do 1000 replications for each experiment. Report the mean, standard deviation and MSE of

α and β. Plot the bias of β versus T for various values of ρ.