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 5a0 1d0zt 1d1zt21 1d2zt22 1d3zt23 1d4zt24 1ut. now, let us assume that the dj follow a quadratic in the lag, j: dj 5g0 1g1j1g2j2, 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