CATS rank test statistics

[yebina]

Dear Tom,

I was trying to replicate results from Juselius' "The Cointegrated VAR Model".
I have been fine until page 199 on Chapter 11 for Tests of cointegration rank with exogenous variables.

Code: Select all

source CATSHandbook_DataRead.src

source c:\cats2\cats.src


*****************************************************************
* Chapter 11 - Restrictions on alpha                            *
* - The model with an unrestricted constant                     *
* - The model with an unrestricted constant and Rb as w.e.      *
*****************************************************************

* Unrestricted constant

*
* Illustration 11.1.1. Use unrestricted constant model.
*
@cats(lags=2,noexo,shift,dum,dettrend=drift) 1973:1 2003:1
# lm3rc lyr dpy Rm Rb
# Ds831
# Dt754 Dp764
*
* (a) Use I(1)--Set Rank of Pi and choose 3 cointegrating vectors.
*
* Test for Rb as weakly exogenous.
* (b) Use I(1)--Test for Weak Exogeneity. Input 1 as the number of
*     weakly exogenous variables. Set the R value to 1.0 on DRB.
*
* Automated test for weak exogeneity.
* (c) Choose Automated Tests--West Exogeneity. This will produce table 11.1
*
* Joint test of weak exogeneity of yr and db
* (d) Choose I(1)--Test for Weak Exogeneity. Input 2 as the number of weakly
*     exogenous variables. For the R matrix, enter a 1.0 in the DRB column
*     on the first row, and in the DLYR column on the second row.
* (e) Exit CATS
*
* Illustration 11.2.1. Run CATS with unrestricted constant and Rb as weakly exogenous
*
@cats(lags=2,exo,shift,dum,dettrend=drift) 1973:1 2003:1
# lm3rc lyr dpy Rm
# Rb
# Ds831
# Dt754 Dp764
*
* (a) Do I(1)--Rank Test Statistics
* (b) Do I(1)--Set Rank of Pi and set r=3. Normalize on DPY, LM3RC and RM in that order.
* (c) Do Misc--Short Run Parameters to get the short-run matrices needed to fill in the bottom of
*     page 199.
* (d) Do Misc--Residual Analysis to get table 11.3
* (e) Exit CATS

But this code does not provide the result as written out in the book. P-values are very small for rank r=3 where as it is supposed to be large p-value to accept as in the book. Do you possibly know what is going on with this test?
Or did I do something wrong?
Thank you in advance for your thought/advice.

[TomDoan]

If you're talking about the original test for cointegrating rank, the results are:

Code: Select all

I(1)-ANALYSIS
 p-r r Eig.Value  Trace  Trace*  Frac95 P-Value P-Value*
  5  0     0.346 118.979 111.567 69.611   0.000    0.000
  4  1     0.228  68.379  64.130 47.707   0.000    0.001
  3  2     0.193  37.567  34.062 29.804   0.005    0.014
  2  3     0.084  12.065  10.923 15.408   0.155    0.220
  1  4     0.014   1.670   1.522  3.841   0.196    0.217

which would have you accept r=3. Note, r (cointegrating rank) is the second column. p-r (number of unit roots) is the first.

[ateeb]

Hey,

I(1)-ANALYSIS
p-r r Eig.Value Trace Trace* Frac95 P-Value P-Value*
4 0 0.641 252.137 249.028 40.095 0.000 0.000
3 1 0.364 96.305 95.478 24.214 0.000 0.000
2 2 0.153 27.610 27.476 12.282 0.000 0.000
1 3 0.016 2.378 2.375 4.071 0.144 0.1443

I hope you are fine. So this would be a case of Full Rank and no cointegration among the variables right?

[TomDoan]

Note---"full rank" means all the series are stationary. By those results, you seem to have one unit root, but that last row is only barely above the critical value, so you're probably closer to having four stationary series than to having any meaningful cointegration.

[ateeb]

I have tested all series with and without trend in ADF tests and the results are that all of them are non-stationary in log-levels or levels. So given this result of cointegration, do you mean all variables are stationary or the relationships that have been found are stationary, because that is what the cointegration test is checking i.e. the linear combination of the non-stationary series to be stationary?