Questions from Econometrics

Q: a. Suppose that E (ut | ut - 1,

a. Suppose that E (ut | ut - 1, ut – 2 …) = 0, that var (ut ut - 1, ut - 2, …) follows the ARCH (1) model 2t = a0 + a1u2t -...

Q: Consider the regression model without an intercept term, Yi = b1Xi

Consider the regression model without an intercept term, Yi = b1Xi + ui (so the true value of the intercept, b0, is 0). a. Derive the least squares estimator of b1 for the restricted regression model...

Q: Let θ^ be an estimator of the parameter θ, where

Let θ^ be an estimator of the parameter θ, where θ^ might be biased. Show that if Then

Q: Suppose that X and Y are distributed bivariate normal with the density

Suppose that X and Y are distributed bivariate normal with the density given in Equation (18.38). a. Show that the density of Y given X = x can be written as Where b. Use the result in (a) to show tha...

Q: Suppose you have some money to invest, for simplicity $1

Suppose you have some money to invest, for simplicity $1, and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 - w, into a mutual fund. Suppose that $1 invested in...

Q: a. Suppose that u∼N (0, 2u

a. Suppose that u∼N (0, 2u). Show that E (eu) = e1/22u. b. Suppose that the conditional distribution of u given X = x is N (0, a + bx2), where a, and b are positive constants. Show that E (eu | X =...

Q: Consider the heterogeneous regression model Yi = b0i + b1i Xi +

Consider the heterogeneous regression model Yi = b0i + b1i Xi + ui, where b0i and b1i are random variables that differ from one observation to the next. Suppose that E (ui | Xi) = 0 and (ï&...

Q: Suppose that Yi, i = 1, 2 … n,

Suppose that Yi, i = 1, 2 … n, are i.i.d. with E (Yi) = m, var (Yi) = 2, and finite fourth moments. Show the following:

Q: Z is distributed N (0, 1), W is distributed

Z is distributed N (0, 1), W is distributed x2n, and V is distributed x2m. Show, as n --- ∞ and m is fixed, that a. b. Use the result to explain why the t ∞ distrib...

Q: Suppose that (Xi, Yi) are i.i.

Suppose that (Xi, Yi) are i.i.d. with finite fourth moments. Prove that the sample covariance is a consistent estimator of the population covariance—that is, that Where sXY is define...