Tuesday, January 03, 2006

st: more regressor in cointegration context

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? 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? how can I see this in Stata?

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

Federico Podestà

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