Sja

0 Time

FIGURE 17.10 Hypothetical lag structures.

Time a. Using the preceding formula, find the variance of ßi expressed as

ßi = ä o + ä i i + ä 2i2 ßi = ä 0 + ä i i + ä 2 i2 + ä 3 i3

b. If the variances of cii are large relative to themselves, will the variance of ßi be large also? Why or why not?

17.19. Consider the following distributed-lag model:

Yt = a + ßo Xt + ßi Xt-i + ß2 Xt-2 + ß3 Xt-3 + ß4 Xt-4 + ut

Assume that ßi can be adequately expressed by the second-degree polynomial as follows:

How would you estimate the ß's if we want to impose the restriction that ßo = ß4 = 0?

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