Use the data in PHILLIPS to answer these questions.

(i) Estimate the models in (18.48) and (18.49) using the data through 1997. Do the parameter estimates change much compared with (18.48) and (18.49)?

(ii) Use the new equations to forecast unem1998; round to two places after the decimal. Which equation produces a better forecast?

(iii) As we discussed in the text, the forecast for unem1998 using (18.49) is 4.90. Compare this with the forecast obtained using the data through 1997. Does using the extra year of data to obtain the parameter estimates produce a better forecast?

(iv) Use the model estimated in (18.48) to obtain a two-step-ahead forecast of unem. That is, forecast unem1998 using equation (18.55) with a^ 5 1.572, r^ 5 .732, and h 5 2. Is this better or worse than the one-step-ahead forecast obtained by plugging unem1997 5 4.9 into (18.48)?