Consider the following model Y_t = β₀ + β₁X_t + β₂X_t_-₁ + β₃Y_t_-₁ + u_t, where X_t is strictly exogenous. Show that by imposing the restriction $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$ , you can derive the following so-called Error Correction Mechanism (ECM)model
△Y_t = β₀+ β₁△X_{t -}θ(Y - X)_t_-₁ + u_t
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?

Question

Consider the following model Y_t = β₀ + β₁X_t + β₂X_t_-₁ + β₃Y_t_-₁ + u_t, where X_t is strictly exogenous. Show that by imposing the restriction

\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1

, you can derive the following so-called Error Correction Mechanism (ECM)model
△Y_t = β₀+ β₁△X_{t -}θ(Y - X)_t_-₁ + u_t
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?

Quizplus · Accepted Answer

The Answer of Consider the following model Y_t = β₀ + β₁X_t + β₂X_t_-₁ + β₃Y_t_-₁ + u_t, where X_t is strictly exogenous. Show that by imposing the restriction $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$ , you can derive the following so-called Error Correction Mechanism (ECM)model △Y_t = β₀+ β₁△X_{t -}θ(Y - X)_t_-₁ + u_t 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?

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

Consider the Following Model Y_t = β₀ + β₁X_t $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$