# Levels versus Growth Rates

You are confusing something. If collinearity arises after using the steady_state operator, what you have done is exactly to remove the capability of the model to determine the steady state of that variable as a function of the parameters.

Take again the example of the Fisher equation and steady state inflation. If you exogenously provide the steady state inflation pibar (which cannot be endogenously determined), you can endogenously compute the steady state nominal interest as the product of real interest and inflation in steady state. Because this works in the model, you can use a Taylor rule like

``r/steady_state(r)=(pi/pibar)^1.5``

This equation will uniquely pin down the steady state of pi and r, because pi now needs to be equal to pibar in steady state. Therefore, in any other equation you can use the steady_state operator as you see fit. No problem in determining anything.

Similarly when you exogenously specify the steady state nominal interest rate, you can endogenously compute the steady state inflation rate and use

``r/rbar=(pi/steady_state(pi))^1.5``

This equation will again uniquely pin down the steady state of pi and r. Therefore, in any other equation you can use the steady_state operator as you see fit.

The problem arises when you try to simultaneously compute the steady state of inflation and the nominal interest endogenously from the model and use

``r/steady_state(r)=(pi/steady_state(pi))^1.5``

This cannot work, because any steady state combination satisfying the Fisher equation is a steady state and there are infinitely many such combinations. In contrast, in the two other examples, either picking rbar or pibar solves this indeterminacy by picking one particular combination.

Summarizing: if the steady state is uniquely determined within the model, there is no problem with using the steady state operator. The problem only arises when you use it to replace an exogenous relation by an endogenous one. The model then will be underdetermined.

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