## From Cointegration to estimation

Econometrics questions and discussions

### From Cointegration to estimation

Hi everyone

I am looking your help because without your help I can not overcome the following problems.

I have 12 variables in one equation. Three variables are stationary at level and nine variables are stationary in first difference. I make all 12 variables first difference (same order) and I did Johansen co-integration test. I find the results that seven are co-integrated and five are not co-integrated. I am looking your help how do I estimate this equation i.e., I will consider to estimate all variables at level or first difference. Please help me.

With Regard
Babul
alim

Posts: 11
Joined: Mon Jun 25, 2012 8:05 am

### Re: From Cointegration to estimation

alim wrote:Hi everyone

I am looking your help because without your help I can not overcome the following problems.

I have 12 variables in one equation. Three variables are stationary at level and nine variables are stationary in first difference. I make all 12 variables first difference (same order) and I did Johansen co-integration test. I find the results that seven are co-integrated and five are not co-integrated. I am looking your help how do I estimate this equation i.e., I will consider to estimate all variables at level or first difference. Please help me.

With Regard
Babul

If you do a Johansen co-integration test on the data in differences, you should be getting that the cointegrating rank is 12 since all the series are supposed to be stationary according to your first statement. You might have some variables that are I(2) instead, so you should test for that. At any rate, you don't want to difference the series before doing the cointegration test since that's defeating the whole purpose---cointegration is a relationship among the levels, not the differences. Note also that every stationary series in your list of variables adds 1 to the cointegrating rank. Trying to disentangle the meaning of very high dimension cointegrating spaces is difficult---it's what CATS is designed to do.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Dear TomDoan

Thank for your reply and advice. If I do in Johansen co-integration test at level data, the results show that three are co-integrated and nine are not co-integrated. How do I estimate this data (at level or 1st difference or I need to do something else) in one equation. I am waiting for your great help.

Thanking you

With Kind
Babul
alim

Posts: 11
Joined: Mon Jun 25, 2012 8:05 am

### Re: From Cointegration to estimation

What are you trying to estimate? If your dependent variable is stationary, but you have I(1) regressors, those regressors can only have non-zero coefficients asymptotically if they are cointegrated and enter into the regression in an "error correction" form.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Dear TomDoan

Thank you for your quick reply and try to help me. I really appreciate your help. In my equation the dependent variable is Australian Steam Coal Export and it is 1st difference stationary. In my regression have 10 independent variables. Among them two are at level stationary and other eight are 1st difference stationary. When I am doing Johansen Co-integration test by considering all the 11 variables at level; it shows that three are co-integrated and eight are non-co-integrated. I request you to please tell me in one regression, some are co-integrated and some are not co-integrated. In this situation, what should we need to do or how do we estimate this regression?

Thanking you

With Kindly

Babul
alim

Posts: 11
Joined: Mon Jun 25, 2012 8:05 am

### Re: From Cointegration to estimation

If you run a static regression (no lags) on a set of data like that, you are likely to get a result which makes little sense. You need to pay careful attention to the dynamics and cast it into some type of error correction form which is neither levels nor differences, but somewhere in between.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Dear TomDoan

Thank you for your help and guideline. I like to request you to give me the following two questions:

1. If I use Engle-Granger two step procedure or one step procedure as an estimator then the result will be appropriate or not or I have to do something else.

2. If the co-integration results show that in one equation 11 variables are not co-integrated and 1 variable are co-integrated then we can consider the data 1st difference to estimate (all 12 variables are stationary at 1st difference)

I am looking your help and co-operation.

Thanking you

with kinds
babul
alim

Posts: 11
Joined: Mon Jun 25, 2012 8:05 am

### Re: From Cointegration to estimation

alim wrote:Dear TomDoan

Thank you for your help and guideline. I like to request you to give me the following two questions:

1. If I use Engle-Granger two step procedure or one step procedure as an estimator then the result will be appropriate or not or I have to do something else.

Have you tried running an Engle-Granger regression? The famous rule of thumb is that if the R^2 is bigger than the Durbin-Watson, you have a "spurious regression".

alim wrote:2. If the co-integration results show that in one equation 11 variables are not co-integrated and 1 variable are co-integrated then we can consider the data 1st difference to estimate (all 12 variables are stationary at 1st difference)

Nothing bad will happen if you run some regressions and see what happens. Based upon your description, however, you don't want to end up with a static regression in levels, but instead, want some type of error correction.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Dear Tom　Doan,

Could you help me?
I have a similar problem.
In my regression, the dependent is I(1), one independent is I(0), and the others are I(1).
All data are in level and I do not want to use their difference if possible.

My queations are:

(1) Is it possible to use Baysian regression to avoid spurious regression?
** In baysian, I think we can not have such a asymptotic problem.

(2) If I use ECM, how do I make the regression equation?
** As you said, it is neither level nor difference. But I have no image for this.

(3) Do you have any other idea to resolve this?

I am happy if you gve me any suggestion.

T_FIELD
T_FIELD

Posts: 21
Joined: Sat May 15, 2010 8:03 pm

### Re: From Cointegration to estimation

T_FIELD wrote:Dear Tom　Doan,

Could you help me?
I have a similar problem.
In my regression, the dependent is I(1), one independent is I(0), and the others are I(1).
All data are in level and I do not want to use their difference if possible.

My queations are:

(1) Is it possible to use Baysian regression to avoid spurious regression?
** In baysian, I think we can not have such a asymptotic problem.

The problem with the spurious regression is that you are running a static regression, ignoring the fact that the data are dominated by the unit root dynamics. The model is so severely misspecified (dynamically) that the end result is garbage. If you use a Bayesian estimation procedure with the same badly misspecified likelihood function, you will similarly end up with really bad estimates.

T_FIELD wrote:(2) If I use ECM, how do I make the regression equation?
** As you said, it is neither level nor difference. But I have no image for this.

Try reading an early paper on error correction models like Davidson, Hendry, Srba, Yeo(1978), "Econometric Modelling of the ....", Economic Journal. That came out before the original cointegration paper, so they weren't obsessed with the I(x)-ness of the data. Start with the economics of the model, not the statistics.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: Estimation of non-contigrated variables

Dear Tom　Doan,

I need quick help from you. I have 4 variables. They are non-stationary at level but 1st difference, they are stationary. At level they are not cointegrated. It means, they have not long run relationship. Can you please help me what methods I will employ to estimate these variables.

With Regard

Ali
alim

Posts: 11
Joined: Mon Jun 25, 2012 8:05 am

### Re: From Cointegration to estimation

If the variables aren't cointegrated, then you can run the regression in differences. You might also have to deal with some short-term dynamics, but the first difference regression would be the place to start.
moderator

Posts: 306
Joined: Thu Oct 19, 2006 4:33 pm

### Re: From Cointegration to estimation

Dear tom
I run Engle-Granger regression and the R^2 (0.9768) is greater than the Durbin-Wastson (0.0488). From the rule of thumb method of interpretation, the result is spurious. What is the solution to such problem, given that both the dependent and independent variables are I(1).
menykeko

Posts: 2
Joined: Thu Dec 27, 2012 6:21 am

### Re: From Cointegration to estimation

Figure out a dynamic model rather than a static model. Again, I would recommend reading the DHSY paper.
TomDoan

Posts: 2722
Joined: Wed Nov 01, 2006 5:36 pm

### Re: From Cointegration to estimation

Thanks Tom! I will look for the paper you recommended.
menykeko

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Joined: Thu Dec 27, 2012 6:21 am

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