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Unformatted text preview: ilibrium, we have: ¯ Y ¯ ¯ ¯ = β1 + β2 Y + β3 X + β4 X Rearranging we get the following long run relationship: ¯ Y = β1 β3 + β4 ¯ + X 1 − β2 1 − β2 47 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Stationary Difference for Nonstationarity Cointegration F Trend Regressions Testing Stationary Difference Stationary We would like to uncover long run relationships as well. Suppose we have the following ADL(1,1) model: Yt = β1 + β2 Yt −1 + β3 Xt + β4 Xt −1 + εt in equilibrium, we have: ¯ Y ¯ ¯ ¯ = β1 + β2 Y + β3 X + β4 X Rearranging we get the following long run relationship: ¯ Y = β1 β3 + β4 ¯ + X 1 − β2 1 − β2 48 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Stationary Difference for Nonstationarity Cointegration F Trend Regressions Testing Stationary Difference Stationary We can try to uncover both long and short run relationships by having estimating an error correction model. We rearrange the ADL(1,1) (see Prof Dougherty’s notes) to get ∆Y t = (β2 − 1)(Yt −1 − β3 + β4 β1 − Xt −1 ) + β3 ∆Xt + εt 1 − β2 1 − β2 The ﬁrst term in brackets contains the long run relationship and the latter term shows the error correction term. We cannot estimate this model straightaway. We could instead use the Engle-Granger 2 step procedure. Error Correction Model. 49 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Stationary Difference for Nonstationarity Cointegration F Trend Regressions Testing Stationary Difference Stationary We can try to uncover both long and short run relationships by having estimating an error correction model. We rearrange the ADL(1,1) (see Prof Dougherty’s notes) to get ∆Y t = (β2 − 1)(Yt −1 − β3 + β4 β1 − Xt −1 ) + β3 ∆Xt + εt 1 − β2 1 − β2 The ﬁrst term in brackets contains the long run relationship and the latter term shows the error correction term. We cannot estimate this model straightaway. We could instead use the Engle-Granger 2 step procedure. Error Correction Model. 50 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Stationary Difference for Nonstationarity Cointegration F Trend Regressions Testing Stationary Difference Stationary run the long run regression (regress Y on X and a constant) grab the residuals which should be stationary since X and Y are cointegrating regress ∆Yt on these residuals and ∆Xt 51 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Stationary Difference for Nonstationarity Cointegration F Trend Regressions Testing Stationary Past Exam Error Correction Model Stationarity Nonstationarity; Difference Stationarity, Trend Stationarity Cointegration, Cointegration factor 52 / 52 Introduction Omitting Relevant Variable Including Irrelevant Variables EC220 Revision Lectures Lecture 1 Can Celiktemur London School of Economics 27 April 2010 Past Exam Practice Question Introduction Omitting Relevant Variable...
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