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I am estimating a 5 variable equation: gdp, cpi, monetary policy rate, money, exchange rate

My focus is on short run dynamics, and will allow cointegrating relationships in the data (dataset is short).

Every variable is non-stationary. First differences achieves stationarity for gdp, monetary policy rate & money. However, cpi and exchange rate requires 2nd-differences for stationarity.

Is there any issue differencing the variables as needed to achieve stationarity and proceed with the VAR estimation? I.e., having a mixture of differences?
Thanks.

Thanks for the reply, very helpful, but raises a different question.
The link to the forum justifies estimating a VAR in levels. However, is it still reasonable to estimate a VAR in differences?

I am confused. There are two IMF papers which are based on similar models however justify a levels ("Transmission Mechanisms of Monetary Policy in Armenia: Evidence from VAR Analysis") vs. differences ("Unraveling the Monetary Policy Transmission Mechanism in Sri Lanka") solution.

Does the decision of whether to use levels vs. differences open for debate / interpretation or is one preferred over the other? Just want to be sure I understand.