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I know expected inflation plays a key role in both the Phillips curve equation and the Fisher equation, but does it also play a key role in Taylor's Monetary Policy Rule?

I'm asking this as I have an assignment question which requires me to derive the DAD curve, with a different expected inflation, and I am unsure if I have to change the expected inflation in the monetary policy rule as well.

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Important details are missing, but just think: whose expectations about inflation are included in the monetary policy rule? Model consistency should help you answer your question.

If you provide more details on your model, I will be happy to expand.

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The effect of the Fed's (nominal) policy rate depends on the real interest rate, which is the difference between the nominal interest rate and the expected inflation, as you noted from the Fisher equation.

For example, suppose the Fed's policy rate is set at 8%. On one hand, suppose that people expect prices to rise at 1%, then the real interest rate is 7%. This implies a very tight monetary policy. On the other hand, if expected inflation is very high at 7%, then the policy rate at 8% is quite accommodative. This is why monetary policy rules have to account for inflation expectation.

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