I’ve noticed that many posts on this forum have the problem of collinearity and especially when people try to identify the levels of prices. I understand that business cycle models cannot exactly identify the price level from a theoretical point of view, but I don’t understand exactly how it creates collinearity given that one could set the initial level to say unity.
For example, take the standard Euler equation:
Assuming that R is identified by a Taylor rule, the above Euler equation identifies the expected change in the price level PI(+1). If this is a simplified framework where STEADY_STATE(PI)=1, then the price level can be entered as an endogenous variable:
STEADY_STATE(P)=1, then the model checks out with the steady state model block and it provides a solution and impulse response functions for a price level that is nice and smooth. However, the model_diagnostics shows the usual message that all the equations containing PI are subject to collinearity.
Why is this happening, what is the intuition and should we be worried? Thank you.