Christopher Dougherty

EC220 - Introduction to econometrics (chapter 11)Slideshow: the error correction model

 

 

 

 

Original citation:

Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 11). [Teaching Resource]

© 2012 The Author

This version available at: http://learningresources.lse.ac.uk/137/

Available in LSE Learning Resources Online: May 2012

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License. This license allows the user to remix, tweak, and build upon the work even for commercial purposes, as long as the user credits the author and licenses their new creations under the identical terms. http://creativecommons.org/licenses/by-sa/3.0/

 

 http://learningresources.lse.ac.uk/

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 Yt*is the level of Y that would correspond to the level of Xt in a long-run relationship.

ttt uXY 21*

THE ERROR CORRECTION MODEL

2

ttt uXY 21*

tttt

ttttt

ttttt

uYXX

uXXYX

uXYYY

1121

11121

1*1

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

THE ERROR CORRECTION MODEL

3

ttt uXY 21*

tttt

ttttt

ttttt

uYXX

uXXYX

uXYYY

1121

11121

1*1

ttttt uXYXY 141321

2 13 24

Hence we have a specification in which Yt is determined by Xt, Yt–1, and Xt–1, with the definitions of the new parameters as shown.

11

THE ERROR CORRECTION MODEL

4

ttt uXY 21*

tttt

ttttt

ttttt

uYXX

uXXYX

uXYYY

1121

11121

1*1

ttttt uXYXY 141321

2 13 24

= 2 is the short-run effect of X on Y, and = 1 – 3 is the speed of adjustment relating to the discrepancy.

11

THE ERROR CORRECTION MODEL

5

ttt uXY 21*

tttt

ttttt

ttttt

uYXX

uXXYX

uXYYY

1121

11121

1*1

ttttt uXYXY 141321

11 2 13 24

In this form, it is an ADL(1,1) model since it includes Xt–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

6

ttt uXY 21*

tttt

ttttt

ttttt

uYXX

uXXYX

uXYYY

1121

11121

1*1

ttttt uXYXY 141321

2 13 24

This way of representing the process will be particularly useful when we come to cointegration in Chapter 13.

11

Copyright Christopher Dougherty 2011.

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/.

Individuals studying econometrics on their own and 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

or the University of London International Programmes distance learning course

20 Elements of Econometrics

www.londoninternational.ac.uk/lse.

11.07.25