Consider the Following Model Yt = β0 + β1Xt

question 10

Essay

Consider the following model Yt = β0 + β1Xt + β2Xt-1 + β3Yt-1 + ut,where Xt is strictly exogenous.Show that by imposing the restriction ,you can derive the following so-called Error Correction Mechanism (ECM)model
△Yt = β0 + β1△Xt - θ(Y - X)t-1 + ut
where θ = β1 + β2.What is the short-run (impact)response of a unit increase in X? What is the long-run solution? Why do you think the term in parenthesis in the above expression is called ECM?