Your Textbook Used a Distributed Lag Model with Only Current $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + u _ { t }$

Essay

Your textbook used a distributed lag model with only current and past values of Xt-1
coupled with an AR(1)error model to derive a quasi-difference model, where the error
term was uncorrelated. (a) Instead use a static model $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + u _ { t }$ here, where the error term follows an AR(1). Derive the quasi difference form. Explain why in the case of the infeasible GLS estimators you could easily estimate the $\beta s$ by OLS.