Lecture 7.2 Trends in Regressors Examples

Question 1

State the case for which Grenander conditions are satisfied when there are trends in the regressors.

Answer 1

Question 2

State the case for which Grenander conditions are NOT satisfied when there are trends in the regressors.

Answer 2

Question 3

State the case for which Grenander conditions are satisfied when there are trends in the regressors, and prove that they are satisfied.

Answer 3

Question 4

State an example of regressors that Grenander conditions are not satisfied. Are both conditions unsatisfied?

Answer 4

Question 5

Show whether or not the first Grenander condition is satisfied in our example where not both conditions of Grenander are satisfied.

Answer 5

Question 6

Show whether or not the second Grenander condition is satisfied in our example where not both conditions of Grenander are satisfied.

Answer 6

Question 7

In the example where not both of the Grenander conditions are satisfied, impose that u_i s are iid. Show what assumption we would need to make on the u_is to be able to make the statement we want.

Answer 7

Question 8

If the u_i s are normally distributed, do we need to use L-F CLT to make a claim regarding X_n?

Answer 8

Question 9

Consider X_n below, where u_i is iid(0,1), E(u_i ^3) = /mu , and E(u_i ^4) exists. Show that the second Grenander condition is not satisfied.

Answer 9

Question 10

Consider the case where z_i = 1/i. Is the estimator consistent? Is it AN? Relate the AN to the distribution of the errors.

Answer 10