(Two-Step Estimation) In Example 20.5, we noted that OLS with the LHS variable $y_t$ and the RHS variables $x_t$ and $x_{t-1}$ will deliver consistent estimators of $\beta_{01}$, $\beta_{02} + \phi_1\phi_0$, $\phi_0\cdot \beta_{01}$, and $\phi_0\beta_{02}$.

(a) Compare this estimator to Durbin's initial estimator (p. 469) for the static regression model with AR serial correlation.

(b) Given the initial consistent estimator for $\beta_{01}$ describe a second step OLS estimator for $\beta_{02}$

and $\phi_0$ based on the partitioning

(c) What sources of asymptotic inefficiency are present in this estimator for $\beta_{02}$?

31-% = 234-1+(-1)-2-2+