Use the data in PHILLIPS.RAW for this exercise. (i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form inft = 0

Use the data in PHILLIPS.RAW for this exercise.
(i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form
Δinft = β0 + β1 unemt + et,
where Δinft = inft - inft-1. In estimating this equation by OLS, we assumed that the supply shock, e, was uncorrelated with unem. If this is false, what can be said about the OLS estimator of β1?
(ii) Suppose that et is unpredictable given all past information E(et|inft-1, unemt-1,....,) = 0. Explain why this makes unemt-1 a good IV candidate for unemt.
(iii) Regress unemt on unemt-1. Are unemt and unemt-1 significantly correlated?
(iv) Estimate the expectations augmented Phillips curve by IV. Report the results in the usual form and compare them with the OLS estimates from Example 11.5.