# Inflation - Output Trade-off in the Adaptive and Rational Expectations Philips Curve

In the Adaptive Philips Curve, $E(\pi_t|I_{t-1})=\pi_{t-1}$. I'm reading a macro book, and the authors state that there is no long-term trade-off, i.e., when making the economy run at a level other than the equilibrium level of output, the policy makers must allow for inflation growth in the same direction, meaning $sign(\Delta \pi_t)=sign(y_t-y_e)$.

However, the way they write in the book is as if some sort of trade-off could still be allowed by this adaptive Philips Curve, if not in the long-run, then at short/medium-run. How could this possible?

Also, in the Rational Expectations Phillips Curve, we have $E(\pi_t|I_{t-1})=\pi_{t}$. How can we deduce this equality just by using $\pi_{t}=E(\pi_t|I_{t-1})+\alpha(y_t-y_e)+\epsilon_t$, where $\epsilon_t$ is the error/shock term, and $E(\epsilon_t|I_{t-1})=0$?

Any help would be appreciated.

• The assumption $E(\pi_t|I_{t-1})=\pi_{t}$ is the "perfect foresight" assumption. Too strong and only for educational purposes, in my opinion. – Alecos Papadopoulos Nov 26 '15 at 13:44
• @AlecosPapadopoulos Yes, I agree with you. The manual I'm reading now is called 'Macroeconomics: Institutions, Instability, and Financial System'. Have you ever heard of it? or read it? – An old man in the sea. Nov 26 '15 at 15:40
• No, I have no opinion on it. But I will have to read it in any case, since it is too close to what preoccupies me. – Alecos Papadopoulos Nov 26 '15 at 15:54