Questions from Econometrics

Q: (i) Find the product AB using / (

(i) Find the product AB using (ii) Does BA exist?

Q: Use the data in DISCRIM to answer this question. (See

Use the data in DISCRIM to answer this question. (See also Computer Exercise C8 in Chapter 3.) (i) Use OLS to estimate the model Log(psoda) = 0 + 1prpblck + 2log(income) + 3prppov + u, and report...

Q: Let X be an n * k matrix partitioned as X =

Let X be an n * k matrix partitioned as X = (X1 X2), where X1 is n * k1 and X2 is n * k2. (i) Show that What are the dimensions of each of the matrices? (ii) Let b be a k * 1 vector, partitioned as wh...

Q: Let X be any n * k matrix. Show that X’X

Let X be any n * k matrix. Show that X’X is a symmetric matrix.

Q: (i) Use the definition of inverse to prove the following

(i) Use the definition of inverse to prove the following: if A and B are n * n nonsingular matrices, then (AB)-1 = B-1A-1. (ii) If A, B, and C are all n * n nonsingular matrices, find (ABC)-1 in terms...

Q: Let A be an n * n symmetric, positive definite matrix

Let A be an n * n symmetric, positive definite matrix. Show that if P is any n * n nonsingular matrix, then P’AP is positive definite.

Q: Let a be an n * 1 nonrandom vector and let u

Let a be an n * 1 nonrandom vector and let u be an n * 1 random vector with E(uu’) = In. Show that E[tr(auu’a’)] = Σni=1a2i .

Q: Let xt be the 1 * (k + 1) vector

Let xt be the 1 * (k + 1) vector of explanatory variables for observation t. Show that the OLS estimator ^ can be written as Dividing each summation by n shows that ...

Q: Let ^ be the OLS estimate from the regression of y on

Let ^ be the OLS estimate from the regression of y on X. Let A be a (k + 1) * (k + 1) nonsingular matrix and define zt ; xtA, t = 1, . . . , n. Therefore, zt is 1 * (k + 1) and is a nonsingular linea...

Q: Assume that the model y = X + u satisfies the

Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let ^ be the OLS estimator of . Let Z = G(X) be an n * (k + 1) matrix function of X and assume that Z’X[a (k + 1) * (k + 1...