- Exercise 4 in Wooldridge Chp 10

Answer:

Use the R-squared form of the F-stat and ignore the information on . The 10% critical value with 3 and 124 degrees of freedom is about 2.13. The F-stat is

which is well below the 10% critical value. Therefore, the event indicators are jointly insignificant at the 10% level. This is another example of how the (marginal) significance of one variable (afdec6) can be masked by testing it jointly with two very insignificant variables.

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- Exercise 2 in Wooldridge Chp 11

Answer:

(i)

Because the are independent, they are uncorrelated. Since for all ,

(ii)

since has zero mean,

Similarly, because only one of the nine terms has expectation not equal to zero.

(iii)

for because for , depends at most on for , while depends on .

(iv)

Yes, because terms more than two periods apart are actually uncorrelated, and so it is obvious that as .

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- Exercise 5 in Wooldridge Chp 11

Answer:

(i)

Neither of these depends on

(ii)

We assume , when we obtain . Then

because is an uncorrelated sequence (it is an independent sequence and is uncorrelated with for all ). From (i) we know that and do not depend on and we have shown that depends on neither nor . Therefore, is covariance stationary.

(iii)

From (i) and (ii)

(iv)

No. Actually, the correlation between and is the same positive value obtained in (iii) for any . In other words, no matter how far apart and are, their correlation is always the same. This is because of the presence of the time-constant variable .

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