1. In Example 10.4, we saw that our estimates of the individual lag coefficients in a distrib- uted lag model were very imprecise. One way to alleviate the multicollinearity problem is to assume that the djfollow a relatively simple pattern. For concreteness, consider a model with four lags:

yt5a0 1d0 zt1d1 zt21 1d2 zt22 1d3 zt23 1d4 zt24 1ut.

Now, let us assume that the djfollow a quadratic in the lag, j:
dj5 g01 g1j1 g2j2,

for parameters g0, g1, and g2. This is an example of a polynomial distributed lag(PDL) model.

1. Plug the formula for each djinto the distributed lag model and write the model in terms of the parameters gh, for h5 0,1,2.

2. Explain the regression you would run to estimate the gh.

3. The polynomial distributed lag model is a restricted version of the general model. How many restrictions are imposed? How would you test these? ( Hint:Think Ftest.)