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Journals and books about the Johansen cointegration test suggest that only I(1) variables should be put into a cointegration test. However many journals modelling economic growth and inflation use two I(0) variables in the cointegration test. Is this an acceptable procedure?

What is then the interpretation of the residual if two I(0) variables are used in the cointegrating regression?

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Could you please suggest us a link to the paper? In case of I(0), there is no rationale for using co-integration.

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Quote from Lütkepohl and Krätzig, Applied Time Series Econometrics, 2004.

"Occasionally it is convenient to consider systems with both I(1) and I(0) variables. Thereby the concept of cointegration is extended by calling any linear combination that is I(0) a cointegration relation, although this terminology is not in the spirit of the original definition because it can happen that a linear combination of I(0)variables is called a cointegration relation."

So yes, it seems like an acceptable procedure.

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I think you should consider using ARDL test. However, there is no opensource implementation of ARDL test. You can consider using eViews. Link:

ARDL test in eViews:

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