Questions from Econometrics

Q: Consider two random variables, X and Y. Suppose that Y

Consider two random variables, X and Y. Suppose that Y takes on k values y1, ……., yk and that X takes on l values x1, ……...

Q: Prove the following results about conditional means, forecasts, and forecast

Prove the following results about conditional means, forecasts, and forecast errors: a. Let W be a random variable with mean W and variance 2w, and let c be a constant. Show that E [(W – c)2] = 2w...

Q: In this exercise, you will conduct a Monte Carlo experiment to

In this exercise, you will conduct a Monte Carlo experiment to study the phenomenon of spurious regression discussed. In a Monte Carlo study, artificial data are generated using a computer, and then t...

Q: Suppose Yt follows the stationary AR (1) model Yt =

Suppose Yt follows the stationary AR (1) model Yt = 2.5 + 0.7Yt - 1 + ut, where ut is i.i.d. with E (ut) = 0 and var (ut) = 9. a. Compute the mean and variance of Yt. b. Compute the first two autocova...

Q: Suppose Yt is the monthly value of the number of new home

Suppose Yt is the monthly value of the number of new home construction projects started in the United States. Because of the weather, Yt has a pronounced seasonal pattern; for example, housing starts...

Q: The moving average model of order q has the form Yt

The moving average model of order q has the form Yt = 0 + et + 1et - 1 + 2et - 2 + ……+ q...

Q: Increases in oil prices have been blamed for several recessions in developed

Increases in oil prices have been blamed for several recessions in developed countries. To quantify the effect of oil prices on real economic activity, researchers have run regressions like those disc...

Q: Consider the ADL model Yt = 5.3 + 0.

Consider the ADL model Yt = 5.3 + 0.2Yt - 1 + 1.5Xt - 0.1Xt - 1 + u∼t, where Xt is strictly exogenous. a. Derive the impact effect of X on Y. b. Derive the first five dynamic multipliers. c. Derive th...

Q: Suppose that a(L) = (1 - L

Suppose that a(L) = (1 - L), with |1| < 1, and b(L) = 1 + L +2L2 +3L3 ……. a. Show that the product b(L)a(L) = 1, so that b(L) = a(L)-1. b. Why is the restriction |1| < 1 important?

Q: Suppose Yt = 0 + ut, where ut follows a

Suppose Yt = 0 + ut, where ut follows a stationary stationary AR (1) ut = 1ut - 1 + u∼t with u∼t i.i.d. with mean 0 and va...