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Re: st: more regressor in cointegration context

From   Christoph Birkel <>
Subject   Re: st: more regressor in cointegration context
Date   Tue, 03 Jan 2006 17:09:30 +0100

PodestÓ schrieb:

Dear all

I am writing you because I would like to have some advices about the multivariate analysis in the cointegration context
Let me explain my problem via a simple example.
Suppose that you have a cross-sectional data set and that want to estimate the effect of X on Y. So you can run a simple regression model. Nevertheless, if you want estimate the net effect of X on Y you have to include unless a control variable which affect both Y and X. In fact, if the inclusion of Z does not alter the relationship between X and Y, you can assert that their relationship is not spurious.
By contrast, if you have a time series data set and X and Y are two integrated process, you risk to observe a spurious relationship. So you could decide to include a time linear trend such a control variable. Nevertheless by so doing you will are not able to capture the long-run relationship. Consequently, you may decide to test for cointegration. So, if your results signal cointegration, you will be able to say that the relationship is not spurious without loosing any long-run effect. However, you could decide to include Z in the cointegration test. Nevertheless, I wonder whether you are still able to capture the long-run effect of X on Y - if Z is I(1), i.e. trending.
I think this because Z produces de facto the same impact of time linear trend inclusion.
Thus, if one obtains confirmations about cointegration using two (or more) regressors, is he still able to assert that X produces a long-run effect on Y or can only assert that Y, X and are cointegrated?

There should be no problem as long as the regressors are not cointegrated with each other (in this case, the regression is not longer "balanced" in the sense of Banerjee et al. 1993; then it might preferable to turn to the Johansen procedure) . If only the results of a multivariate tests point to the existence of a cointegration relationship, but not the bivariate tests, it is indeed not possible to say that X causes Y, but only that there exists a long-run relationship between X, Y and Z. In this case, Z might be thought of as an analogue to a suppressor variable in cross-section regressions. Nonetheless, it might be possible to use the Johansen procedure to figure out if the regressors are weakly exogenous (not influenced by Y on the long run).

Then if one can only assert that Y, X and are cointegrated, cannot we use control variables like in the cross-sectional context?
Finally there are any differences with respect to this topics if one uses single-equation ECM approach rather than two steps approach proposed by Engle and Grange?
See above.

how can I see this in Stata?

You might use "vec" and "vecrank" for the Johansen approach. Residual-based tests are not implemented in STATA, but there is a user-written routine (coint) (in Becketti's Time Series Library (tslib)).

Thanks a lot in advance for your hel and happy new year!

Federico PodestÓ

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Christoph Birkel, M.A.
Martin-Luther-Universitńt Halle-Wittenberg
Institut fŘr Soziologie
D-06099 Halle (Saale)
Tel.: ++ 49 3 45 / 55 24 22 5
Fax.: ++ 49 3 45 / 55 27 14 9

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