Questions from Econometrics

Q: This exercise fills in the details of the derivation of the asymptotic

This exercise fills in the details of the derivation of the asymptotic distribution of b^1 given in Appendix 4.3. a. Use Equation (18.19) to derive the expression Where vi = (Xi - mX) ui. b. Use the c...

Q: Show the following results: a. Show that /

Show the following results: a. Show that Where a2 is a constant, implies that ^1 is consistent. b. Show that Implies that

Q: Suppose that W is a random variable with E (W4)

Suppose that W is a random variable with E (W4) < ∞. Show that E (W2) < ∞.

Q: Show that if ^1 is conditionally unbiased, then it is

Show that if ^1 is conditionally unbiased, then it is unbiased; that is, show that if E (^1  X1, Xn) = 1, then E (^1) = 1.

Q: Suppose that X and u are continuous random variables and (Xi

Suppose that X and u are continuous random variables and (Xi, ui), i = 1… n, are i.i.d. a. Show that the joint probability density function (p.d.f.) of (ui, uj, Xi, Xj) can be written as f(ui , Xi) f(...

Q: This exercise provides an example of a pair of random variables,

This exercise provides an example of a pair of random variables, X and Y, for which the conditional mean of Y given X depends on X but corr (X, Y) = 0. Let X and Z be two independently distributed sta...

Q: Consider the regression model in Key Concept 18.1, and

Consider the regression model in Key Concept 18.1, and suppose that assumptions 1, 2, 3, and 5 hold. Suppose that assumption 4 is replaced by the assumption that var (ui | Xi) = θ0 + θ1 |Xi|, where ...

Q: Prove Equation (18.16) under assumptions 1 and 2

Prove Equation (18.16) under assumptions 1 and 2 of Key Concept 18.1 plus the assumption that Xi and ui have eight moments. Data from Equation 18.16:

Q: Consider the population regression of test scores against income and the square

Consider the population regression of test scores against income and the square of income in Equation (8.1). a. Write the regression in Equation (8.1) in the matrix form of Equation (19.5). Define Y,...

Q: Let C be a symmetric idempotent matrix a. Show that

Let C be a symmetric idempotent matrix a. Show that the eigenvalues of C are either 0 or 1. b. Show that trace(C) = rank(C). c. Let d be an n * 1 vector. Show that d′Cd >= 0.