Q: Suppose that C is an n * n symmetric idempotent matrix with
Suppose that C is an n * n symmetric idempotent matrix with rank r, and let V ∼ N (0n, In). a. Show that C = AA′, where A is n * r with A′A = Ir. b. Show that A′V ∼ N (0r, Ir). c. Show that V′CV ∼ x2r...
See AnswerQ: a. Show that B∼Eff.GMM is the efficient
a. Show that B∼Eff.GMM is the efficient GMM estimator—that is, that B∼Eff.GMM in Equation (19.66) is the solution to Equation (19.65). b. Show...
See AnswerQ: Consider the problem of minimizing the sum of squared residuals, subject
Consider the problem of minimizing the sum of squared residuals, subject to the constraint that Rb = r, where R is q * (k + 1) with rank q. Let B∼ be the value of b that solves the...
See AnswerQ: Consider the regression model Y = XB + U. Partition X
Consider the regression model Y = XB + U. Partition X as [X1 X2] and B as [B′1 B′2]′, where X1 has k1 columns and X2 has k2 columns. Suppose that...
See AnswerQ: Consider the panel data model Yit = Xit + i
Consider the panel data model Yit = ï¢Xit + ï¡i + uit, where all variables are scalars. Assume that assumptions 1, 2, and 4 in Key Concept 10.3 hold and strengthen ass...
See AnswerQ: This exercise takes up the problem of missing data discussed in Section
This exercise takes up the problem of missing data discussed in Section 9.2. Consider the regression model Yi = Xib + ui, i = 1 … n, where all variables are scalars and the constan...
See AnswerQ: Suppose Yi is distributed i.i.d. N (
Suppose Yi is distributed i.i.d. N (0, ï³2) for i = 1, 2, …, n. a. Show that E (Y2i /ï€ ï³2) = 1 b. Show that c. Show that E(W) = n...
See AnswerQ: Consider the regression model in matrix form Y = XB + WG
Consider the regression model in matrix form Y = XB + WG + U, where X and W, are matrices of regressors and B and G are vectors of unknown regression coefficients. Let X∼ = MWX and...
See AnswerQ: Consider the homoskedastic linear regression model with two regressors, and let
Consider the homoskedastic linear regression model with two regressors, and let rX1, X2 = corr(X1, X2). Show that as n increases.
See AnswerQ: Suppose that a sample of n = 20 households has the sample
Suppose that a sample of n = 20 households has the sample means and sample covariances below for a dependent variable and two regressors: a. Calculate the OLS estimates of ï¢0, ï&...
See Answer
