conflicting lag selection and cointegrating rank

[na8393a]

Hello,

I am having conflicting results between -varsoc- and -vecrank- results


I have annual data from 1959 to 2013; using DFGLS for unit root testing , it has estimated a maximum lag of 10 using Schwert Criterion. Taking that maximum lag and applying it to -varsoc- command gives that optimal lag selection for my VAR model through the AIC, HQIC, and SBIC at 10 lags as well. Now, when i use the -vecrank- and choose that the maximum lag should be 10, the results state that the maximum lag has been reduces to 9 because of collinearity, and then 8. This process repeats in -vecrank- until i choose a maximum lag of five.

Which lag should I choose for my VAR model and which lag should I choose for my cointegrating rank? can they be different? or am i misunderstanding the results.

Below you will find the results of DFGLS, followed by results of varsoc, followed by results of vecrank. I would appreciate any input or advice you can provide me. Thanking you in advance for your time and consideration.


Regards,

Nayef


please note edu1 = log of education spending; edu2 = first difference of edu1


. dfgls edu1, ers

DF-GLS for edu1 Number of obs = 43
Maxlag = 10 chosen by Schwert criterion

DF-GLS tau 1% Critical 5% Critical 10% Critical
[lags] Test Statistic Value Value Value
------------------------------------------------------------------------------
10 -1.666 -3.755 -3.177 -2.878
9 -1.916 -3.755 -3.177 -2.878
8 -1.586 -3.755 -3.177 -2.878
7 -1.860 -3.755 -3.177 -2.878
6 -1.611 -3.755 -3.177 -2.878
5 -1.582 -3.755 -3.177 -2.878
4 -1.565 -3.755 -3.177 -2.878
3 -1.358 -3.755 -3.177 -2.878
2 -1.307 -3.755 -3.177 -2.878
1 -1.153 -3.755 -3.177 -2.878

Opt Lag (Ng-Perron seq t) = 1 with RMSE .208624
Min SC = -2.959504 at lag 1 with RMSE .208624
Min MAIC = -3.021442 at lag 1 with RMSE .208624



. dfgls edu2, ers

DF-GLS for edu2 Number of obs = 43
Maxlag = 10 chosen by Schwert criterion

DF-GLS tau 1% Critical 5% Critical 10% Critical
[lags] Test Statistic Value Value Value
------------------------------------------------------------------------------
10 -2.072 -3.755 -3.177 -2.878
9 -2.056 -3.755 -3.177 -2.878
8 -1.789 -3.755 -3.177 -2.878
7 -2.192 -3.755 -3.177 -2.878
6 -1.894 -3.755 -3.177 -2.878
5 -2.218 -3.755 -3.177 -2.878
4 -2.334 -3.755 -3.177 -2.878
3 -2.454 -3.755 -3.177 -2.878
2 -3.006 -3.755 -3.177 -2.878
1 -3.454 -3.755 -3.177 -2.878

Opt Lag (Ng-Perron seq t) = 0 [use maxlag(0)]
Min SC = -2.96635 at lag 1 with RMSE .2079111
Min MAIC = -2.263437 at lag 3 with RMSE .2070669





. varsoc edu1 hlth1 dfs1 inf1 econ1 oilrev1, maxlag(10)

Selection-order criteria
Sample: 1970 - 2013 Number of obs = 44
+---------------------------------------------------------------------------+
|lag | LL LR df p FPE AIC HQIC SBIC |
|----+----------------------------------------------------------------------|
| 0 | -88.5693 3.0e-06 4.29861 4.38883 4.5419 |
| 1 | 126.421 429.98 36 0.000 8.8e-10 -3.83731 -3.20573 -2.13422 |
| 2 | 170.243 87.643 36 0.000 6.8e-10 -4.19285 -3.0199 -1.02997 |
| 3 | 218.487 96.488 36 0.000 5.0e-10 -4.74939 -3.03508 -.12672 |
| 4 | 320.54 204.11 36 0.000 4.3e-11 -7.75182 -5.49615 -1.66935 |
| 5 | 403.458 165.84 36 0.000 1.6e-11 -9.88444 -7.08741 -2.34219 |
| 6 | 610.671 414.43 36 0.000 8.5e-14 -17.6669 -14.3285 -8.66483 |
| 7 | 4496.7 7772.1 36 0.000 3.0e-85* -192.668 -188.789 -182.206 |
| 8 | 7091.41 5189.4 36 0.000 . -310.337 -306.367 -299.632 |
| 9 | 7347.44 512.05 36 0.000 . -321.974 -318.004 -311.269 |
| 10 | 7382.47 70.066* 36 0.001 . -323.567* -319.597* -312.862* |
+---------------------------------------------------------------------------+
Endogenous: edu1 hlth1 dfs1 inf1 econ1 oilrev1
Exogenous: _cons




vecrank edu1 hlth1 dfs1 inf1 econ1 oilrev1, trend(constant) lags(10)
maximum lag reduced to 9 because of collinearity
maximum lag reduced to 8 because of collinearity

Johansen tests for cointegration
Trend: constant Number of obs = 46
Sample: 1968 - 2013 Lags = 8
-------------------------------------------------------------------------------
5%
maximum trace critical
rank parms LL eigenvalue statistic value
0 258 . . . 94.15
1 269 . 1.00000 . 68.52
2 278 . 1.00000 . 47.21
3 285 . 1.00000 . 29.68
4 290 . 0.00000 . 15.41
5 293 . -0.00000 . 3.76
6 294 . -0.00000
-------------------------------------------------------------------------------

[Jorge Eduardo Perez Perez]

You do not have enough degrees of freedom to fit a VAR(10) model. You have at most 54 observations, and a VAR(10) model with 6 variables will have at least 60 parameters per equation excluding constants.

[na8393a]

Thank you Jorge, but what should be done then? I cannot increase the number of observations because that is the oldest data on record. Should I reduce the number of variables then? or disregard that maximum lag bit and go with lower number of lags? I am still confused.

Thanks for your time and reply.

[Jorge Eduardo Perez Perez]

Try first testing all of your variables for stationarity, not only edu1. When using varsoc you should be using stationary variables, so you should not be using edu1 which seems not stationary. Then reduce the maximum number of lags you allow for the tests, as they are not informative for large numbers of lags since those models can not be fit anyway.

[Sebastian Kripfganz]

Sorry, Jorge Eduardo, but I have to correct you: varsoc can be used with non-stationary variables. To quote the help file:

the lag-order selection statistics discussed here can be used in the presence of I(1) variables.

[Jorge Eduardo Perez Perez]

Thanks, I did not know that. I am used to thinking of VAR models as intended for stationary variables unless the variables in the system are cointegrated.