Econ 456 Question Sheet 4 Question 1. Take the new Keynesian model yt = Etyt+1 - (it - Etrt+1 - rt) Tit = EtBut+1 + Xy't + ut it = 8 + 0Tit + Ut The first equation is the IS curve. The second equation is the Phillips curve, and the third equation is the policy rule. There are three shocks - the shock to rt, the 'natural interest rate', the shock to ut, the 'cost push' shock, and the shock to vt, the monetary shock. Assume that all shocks have persistence p and are driven by i.i.d. shocks. That is, assume rt = prt-1 + ret, Et-1ret = 0 Ut = put-1 + Wet, Et-1Wet = 0 Ut = put-1 + Vet, Et-1Vet = 0 a) Solve the above model for the effect of each shock on inflation and the output gap. Does each shock drive inflation and the output gap in the same direction? b) Now ask is there a particular monetary rule (value of 0) that can eliminate the effects of these shocks on both inflation and the output gap? Does this depend on which shock it is