Consider the following model: Aggregate supply:
yt = γ (Pt - Et-1Pt ) + γ (Pt - Et-2Pt ) Aggregate demand:
yt = Mt - Pt + μt μt = μt-1 + ηt
where y, P and M have the usual meanings and are in logs. η is a serially uncorrelated error with mean zero and variance σ 2.
(i) How would you justify the above aggregate supply function and how does it differ from the Lucas one?
(ii) Suppose that the central bank can observe μt-1 but not μt when it sets the money supply. Is there then a role for systematic monetary policy?
(iii) Given (ii), suppose that the central bank wants to set the money supply to minimize the variance Et-1(yt - yf )2 of output about its full-employment level? What monetary policy would it follow?
(iv) If the policy in (iii) has always been followed, is there any way of using econometric evidence to differentiate between the pattern shown by this economy and one in which the economy had a Lucas supply function?