Use the data in PHILLIPS for this exercise.

(i) Estimate the models represented in equations (18.48) and (18.49) using the data through 2015. Do the parameter estimates change much compared with (18.48) and (18.49)?

(ii) Use the new equations to forecast unem₂₀₁₆; round to two decimal places. Which equation produces a better forecast?

(iii) Use the equation that includes inf_t-1, estimated in part (i), to forecast unem₂₀₁₇. You will need to obtain the 2016 values for unem and inf. Next, reestimate the parameters using the data through 2016, and use the updated estimates to forecast unem₂₀₁₇. Does using the extra year of data to obtain the parameter estimates produce a better forecast?

(iv) Use the equation that includes inf_t-1, estimated in part (i), to obtain a two-step-ahead forecast of unem. You will need the forecast of unem₂₀₁₆ from part (ii). Also, use an AR(1) model for inflation, using the data through 2015, to forecast 2016 inflation.