I have question relating to how to interpret an Impulse response function in a system of 5 endogenous non-stationary variables (GDP, Investment, Uncertainty index, Interest rate and inflation rate) with two stationary exogenous variable which reflect world impact. All variables is in log except inflation and interest rate. The model is done through an co integration investigation. I have only put restrictions on the long-run matrix. I have 2 common trends and 3 co-integrated relationships.
The IRF function has been divided into permanent shock and transitory shocks. GDP and Investment cause permanent shocks and Uncertainty, Interest rate and inflation cause transitory shocks to the system.
How shall I interpret the shocks if I include other exogenous variables such as oil prices and world GDP? An scenario is that an uncertainty shock in the baseline model (only the endogenous variables) shows a positive response for inflation. But in the extension of model with exogenous variables such as DLog(Oil prices) and GDP growth rate causes it to respond negatively and significant. Does this mean that by controlling for Dlog(Oil prices) and GDP growth rate that uncertainty shock can now be "revealed"? I really have problems understanding the combined effect on the shock from an endogenous variable to the other variables in to system with the inclusion of exogenous variables which influence the impact. Is the effect of the exogenous variables simultaneously shocking including the uncertainty shock? How shall I formulate by interpretation? I also want to pinpoint that the exogenous variables is not weakly exogenous. Impulse response functions is really not by strong suit!
I am really lost on this one! Have spent days on figuring it out but no luck!
(The uncertainty is a index triggered by news coverage)
Best regards, Johan