I'm currently analyzing the monetary effect of a country if his currency is pegged to another using shocks ( for example a group of African countries being pegged to dollars) my variables are Real GDP of each country(African countries and the US) , Gdp deflator of each country acting as a proxy of CPI and Real effective exchange rate African countries and Oil as exogeneous variable

All the variables are I(1) except the GDP deflator of US I(0)

Here are my questions:

- From the literature, I know what kind of restrictions I should apply to analyze the shocks but how to deal with multiple cointegrations do I have to apply my restrictions on the 3 cointegrations equations simultaneously or how do I choose

- From a paper, I read, they consider cpi as I(0) despite the fact that in their table it was I(1) and they justify this choice saying that from Macroeconomic perspectives Inflation and interest rates are stationary, can I do the same?