Cointegration analysis in practice

1. Cointegration analysis in practice Engle-Granger 2 step, and 1 step, estimation procedures

2. Applications Of Engle-Granger Two-Step Procedure Cointegration in Practice

3. Testing For Cointegration • Pretest the variables for their order of integration • Estimate the Long Run Equilibrium Relationship • Estimate the Error Correction Model • Assess Model Adequacy

4. Pretest the variables for their order of integration • By definition cointegration necessitates that the variables be • integrated of the same order • Use DF or ADF tests to determine the order of integration • If variables are I(0) - Standard Time Series Methods • If the variables are integrated of different order • (one I(0), one I(1) or I(2) etc) than it is possible to conclude • that the two variables are not cointegrated • If the variables are I(1), or are integrated of the same order, • go on

5. Estimate the Long Run Equilibrium Relationship Estimate the long run relationship If the variables are cointegrated, an OLS regression yields a “super-consistent” estimator of the cointegrated parameter 0 and 1. There is a strong linear relationship. Use the residual (e) of the estimated long run relationship. If (e) is STATIONARY (according to DF criteria) than we can conclude that the series are COINTEGRATED

6. Estimate the Error Correction Model If the variables are cointegrated, the residual from the equilibrium regression can be used to estimate the Error Correction Model Using the saved residual from the estimation of the long-run relationship, we can estimate the ECM as: Granger’s representation theorem: if a set of variables are cointegrated then there always exists an error correcting formulation of the dynamic model and vice versa

7. Assess Model Adequacy Asses if the ECM model you have estimate is appropriate using a General - Specific modelling approach

8. Problems With Engle-Granger Two Step Procedure

9. Some authors are uncomfortable with the two stage approach. Any mistake introduced in the first step, is carried forward in the second step. As long as the equation is balanced, an unrestricted ECM model can be at least as efficient as a two step EG method in defining long run relationships and short run dynamics This means estimating the following ECM model

10. Consider for example the Consumption-Income model analysed in a previous lecture. Modelling LC by OLS Variable Coefficient Std.Error t-value t-prob PartR^2 Constant 0.013285 0.080615 0.165 0.8696 0.0004 LYd 0.98530 0.011002 89.557 0.0000 0.9925 DW = 0.322 First step: Second Step:

11. Same Estimation with Free Parameters Does it make a difference?

12. In this case not very much From the long term relation estimation: Inserting this term in the dynamic equation we have estimated: Substituting the first in the second we have

13. Therefore with EG two step we obtain With the standard ECM procedure we have: Sometimes the second way is more efficient

14. Second Problem We have assumed that Economic Theory can guide in determining the dependent and the independent variable, like in the Consumption Function. What if this is not possible?

15. Given three variables (y,w,z) you have three possible long run relationship, and three possible ECM models

16. These weaknesses limit the applicability of the EG two step procedure. We need to introduce a technique that considers cointegration not only between pairs of variables, but also in a system This technique is the ML approach of Johansen