1. THE ERROR CORRECTION MODEL 1 The error correction model is a variant of the partial adjustment model. As with the partial adjustment model, we assume a long-run relationship between Y and X as shown, where Y t *is the level of Y that would correspond to the level of X t in a long-run relationship.

2. 2 In the short run,  Y t, the change in Y t from Y t–1, is determined by two components: a partial closing of the discrepancy between its previous appropriate and actual values, Y* t–1 – Y t–1, and a straightforward response to the rate of change in X,  X t. THE ERROR CORRECTION MODEL

3. 3 Hence we have a specification in which Y t is determined by X t, Y t–1, and X t–1, with the definitions of the new parameters as shown. THE ERROR CORRECTION MODEL where

4. 4  =  2 is the short-run effect of X on Y, and = 1 –  3 is the speed of adjustment relating to the discrepancy. THE ERROR CORRECTION MODEL where

5. 5 In this form, it is an ADL(1,1) model since it includes X t–1 as an explanatory variable. The ADL(1,0) model is a special case with the testable restriction  4 =  2 –  = 0. THE ERROR CORRECTION MODEL where

6. 6 This way of representing the process will be particularly useful when we come to cointegration in Chapter 13. THE ERROR CORRECTION MODEL where

7. Copyright Christopher Dougherty 2013. These slideshows may be downloaded by anyone, anywhere for personal use. Subject to respect for copyright and, where appropriate, attribution, they may be used as a resource for teaching an econometrics course. There is no need to refer to the author. The content of this slideshow comes from Section 11.4 of C. Dougherty, Introduction to Econometrics, fourth edition 2011, Oxford University Press. Additional (free) resources for both students and instructors may be downloaded from the OUP Online Resource Centre http://www.oup.com/uk/orc/bin/9780199567089/http://www.oup.com/uk/orc/bin/9780199567089/. Individuals studying econometrics on their own who feel that they might benefit from participation in a formal course should consider the London School of Economics summer school course EC212 Introduction to Econometrics http://www2.lse.ac.uk/study/summerSchools/summerSchool/Home.aspx http://www2.lse.ac.uk/study/summerSchools/summerSchool/Home.aspx or the University of London International Programmes distance learning course 20 Elements of Econometrics www.londoninternational.ac.uk/lsewww.londoninternational.ac.uk/lse. 2013.01.20