Monetary economics: What is the causality between nominal and real interest rates?

I am very much confused about the causality between real and nominal interest rates, in monetary policy.

So we know the Fisher equation: $$i_t = r_t + E \pi_{t+1}$$

Now imagine that the central bank sets an interest rate rule where $$i_t = f(y, \pi, ...)$$, i.e., some function of important economy parameters like output and inflation.

So far, so good. Now imagine the central bank increases the rates, as $$i_t = f(y, \pi, ...) + \epsilon$$. This will affect the economy parameters, so the future interest rate will change as a result of its own increase.

But how?

I think there are two ways of measuing that change, and I don't know which one is correct.

1. The first measure is to first calculate the effect of $$i$$'s change on all economy parameters: $$y$$, $$r_t$$, $$\pi$$, etc, etc. Then, plug all those changes back into the rule $$i_t = f(y, \pi, ...)$$ to figure out the interest rate.

2. The second way is to again calculate the interest rate increase's affect on the entire economy, on $$y_t, r_t, \pi$$, etc. And then ... simply use the Fisher equation: $$i_t = r_t + E\pi$$ and calculate the new $$i_t$$.

I'm thinking the second way is correct, since the first seems to assume that the Central Bank "constantly" increases the rates, ... but it probably doesn't right? The "rule" is only in affect when it decides, and the rest of the time, I need to use the Fisher equation, like in 2?

• Your question is unclear - what do you mean by "measure"? Is this an attempt to empirically measure the effect of actual interest rate changes to actual economic variables, or is it an attempt to quantify the effect in some model economy? – Starfall Dec 9 '18 at 15:20