Using the data file phillips5_aus, estimate the equation

a. Find the first eight lag weights (delay multipliers) of the infinite distributed lag representation that corresponds to this model. What is the total multiplier?

b. Using a \(5 \%\) significance level, test the hypothesis that the error term in the infinite distributed lag representation follows the \(\mathrm{AR}(4)\) process \(e_{t}=\theta_{1} e_{t-1}+\theta_{4} e_{t-4}+v_{t}\).

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INF = 8+0INF-1+04INF-4 +80DU, + e