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Consider the Following Model Yt = β0 + β1Xt i=13βi=1\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1

Question 46

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Consider the following model Yt = β0 + β1Xt + β2Xt-1 + β3Yt-1 + ut, where Xt is strictly exogenous. Show that by imposing the restriction i=13βi=1\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1 , 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?

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Starting with Yt = β0 + β1Xt + β2Xt-1 + β3Yt-1 + ut, ...

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