Dependent I(0) variable with I(1) regressors

[kipfilet]

I am currently undertaking some work on time series analysis and, while specifying a model and testing the dependent and independent variables for unit-roots and order of integration I got the following results:

Dependent Variable ~ I(0)
Two independent variables ~ I(0)
Two independent variables ~ I(1)

I am a bit at a loss, as I am used to work with macroeconomic variables which are all I(1), and my (potentially stupid) question is: I know that variables of different orders of integration cannot be cointegrated, but what about the dependent variables and the two I(0) regressors? Can there be cointegration between variables which are integrated of order zero? My supervisor is not sure, but he believes that I can just run a simple linear regression in this specific case, and that I won't have to bother with including a ECM term to correct for cointegration.

Thanks in advance

[theologos]

I suggest you to check further whether your I(1) variables are truly I(1) processes! They may be stationary around a time trend, once broken trend or twice broken tend etc. If something like this is true, then you can proceed, after de-trending your series, to the usual OLS inference. If now your series consistently prove to be I(1) after all the implemented stationarity tests, read carefully the following forum discussion : (pay attention to tcfoot comment)
http://forums.eviews.com/viewtopic.php? ... ardl#p3390

if all the above do not help let me know

[kipfilet]

First of all, I would like to thank you for your swift and insightful reply :)

I have indeed tested for every kind of trends, to see if I could detect any kind of trend-stationarity, but the ADF tests always led me not to reject the hypothesis of unit roots in the series.

Regarding tcfoot's comment, I reckon that I won't probably be getting the whole message, as I am not someone who is very deep into econometrics. However, doing some research on ARDL models I reached the conclusion that I am using precisely what appears to be a partial adjustment model, including all contemporary regressors (in their level values) and one lagged term for the regressand. While checking some scientific papers on the issue, I got the impression this would be a correct way to safeguard against cointegration. Is this true or am I misreading and misinterpreting? Should I nonetheless apply first differences to the I(1) variables? The residuals so far appear to be very well-behaved... (no serial correlation, completely stationary).

[theologos]

Hello again,

Of course you can use first differences in order to create stationary variables but the problem in such cases is that sometimes this kind of transformations are not supported by economic theory. If you are in a position to justify your transformation, then yes you may proceed with OLS. To implement a partial adjustment model, still requires stationary variables, otherwise estimates are inconsistent. I suggest you to try the ARDL approach to cointegration which is quite straightforward method to establish cointegration in such cases. If now it is tough for you to apply the ARDL approach to cointegration let me know!

regards

[kipfilet]

Thank you very much for your reply. Indeed, the use of first differences is not very well supported by economic theory and, in this particular case, it makes the model's interpretation a bit awkward. Would it be a case of bad specification if I allowed the I(1) variables to remain in levels, while adding a AR(1) term in order to correct for serial correlation (and then rewrite the long-run model by dividing all coefficients by 1-beta, where beta is the coefficient for the AR(1) term)?

[theologos]

Hello,

I think that your specification is incorrect since you continue to incorporate non-stationary variables. OLS inefficiencies are still present!

regards