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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
6   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 dj follow a relatively simple pattern. For concreteness, consider a model with four lags:
yt  5 a0  1 d0zt  1 d1zt21  1 d2zt22  1 d3zt23  1 d4zt24  1 ut.
Now, let us assume that the dj  follow a quadratic in the lag, j:
dj 5 g0 1 g1 j 1 g2 j 2,
for parameters g0, g1, and g2. This is an example of a polynomial distributed lag (PDL) model.
(i)      Plug the formula for each dj into the distributed lag model and write the model in terms of the parameters gh, for h 5 0,1,2.
(ii)    Explain the regression you would run to estimate the gh.
(iii)   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 F test.)
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