L4 - Co-integration and ECM

Question 1

What is a Spurious regression?

Answer 1

Question 2

What is one rudimentary way we can test whether there is a spurious relationship between two variables?

Answer 2

• Regress y on x
  
  • High R-squared and statistically significant beta coefficient may indicate they are highly correlated
• The problem is we have two variables that should be independent
  
  • Based on their errors being generated by an independent process
  • Yet there is a significant relationship between them
    *

Question 3

What is Cointegration?

Answer 3

• • 𝐼(1) series should be differenced before they are used in regressions
• This limits the scope of the questions we can answer
• But… The notion of cointegration makes regressions involving 𝐼(1) variables potentially meaningful
• If we can find a beta that generates a stationary linear relationship between the two variables we can surmise they are cointegrated

Question 4

What is Superconsistency and how does it relate to a test for a cointegrating relationship?

Answer 4

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Question 5

What is the Engle-Granger test for cointegration?

Answer 5

• the null hypothesis is that they are unit root (non-stationary)
• the alternative is the residuals are stationary (they rate conitegrated)
• ONLY REJECT THE NULL IF TEST STATISTIC IS LOWER THAN THE ENGEL-GRANGER CRITICAL VALUE
  
  • if we don’t reject the null their is a spurious relationship and the long-run relationship is not valid
  • if they arent cointegrated we have to take first differences

What is one or both series have a trend?

• Add trend to the cointegration regression
• • i.e. 𝑦𝑡 = 𝛼 + 𝛿𝑡 + 𝛽𝑥𝑡 + 𝑢𝑡
• • and follow the steps below
• • considering the respective critical values with trend

Question 6

EG Test: Using ADF test to find the residuals?

Answer 6

Question 7

How to do you interpret the Output from Stata of the Engel-Granger test?

Answer 7

• the spread will mean revert to its average value (0)

Question 8

How to test for the Cointegration of multiple variables?

Answer 8

Question 9

What are some problems that may arise with the Engel-granger test?

Answer 9

• EG test finds its hard to reject values that close to one but arent it
  
  • we know its stationary but we cant reject the null under this test

Question 10

What is the Error Correction Model?

Answer 10

Question 11

What is the other reparameterisation of the ECM?

Answer 11

• In this form all variables are stationary (I(0))
• speed of adjustment parameter shows how facts the model revert back to normal after a disequilibrium
  
  • (how much of the disequilibrium disappears every period)

Question 12

How do you use the ECM to test for Cointegration?

Answer 12

Question 13

Advantage of the ECM approach over EG?

Answer 13

• Advantage of this approach:
  
  • – ECM is a better dynamic specification than the static regression used to generate the residuals in the EG test
  • – This test can also be shown to be more powerful than the Engle-Granger test
    
    • so is the Johansen test

Question 14

How do you use the reparameterised ECM to test for Cointegration?

Answer 14

• Dont need to constant as we are looking at the long-run relationship
• Test the coefficient on the lag of the residuals
  
  • Still 4 parameters
    
    • If you include alpha and beta as well from the first regression to find the residuals

Question 15

How do you interpret the reparametised ECM results?

Answer 15

Question 16

What is the Johnansen Test?

Answer 16

• rank –> the number of rows or columns that are linearly independent
  
  • Cant not write these rows or columns as a linear function of any other roes or columns in the matrix
  • In this case, we only have one row that is linearly independent (where the values are different from zero)
• Eigenvalues
  
  • Characteristic equations = det(M -λI) = 0
    
    • Check if λ is different from 0
  • trace of a matrix –> sum of all the values on the main diagonal

Question 17

What are the advantages of the Johnansen test?

Answer 17

• it allows for multiple cointegrating vectors when we have more than two variables in the model –> flexible when we have more that two variables
• – It has better power than the Engle-Granger test
• – it avoids the normalisation restriction necessary for both the EngleGranger and ECM approaches
  
  • • In both cases, we impose that the coefficient on the current value of 𝑦 is equal to one
  • • the result of the respective tests may be sensitive to this restriction
  • • there is no need to make such an assumption when we use the Johansen approach

Question 18

How do we perform the Johnansen test for Cointegration?

Answer 18

Question 19

Example of the Johnansen test?

Answer 19

Question 20

Johnansen Test when we have more than two variables?

Answer 20

• if rank 0 –> they are all stationary - I(0)