Questions from Econometrics

Q: Let W be an m * 1 vector with covariance matrix Σw

Let W be an m * 1 vector with covariance matrix Σw, where Σw is finite and positive definite. Let c be a non-random m * 1 vector, and let Q = c′W. a. Show t...

Q: Consider the regression model Yi = 0 + 1Xi +

Consider the regression model Yi = 0 + 1Xi + ui from Chapter 4, and assume that the least squares assumptions in Key Concept 4.3 hold. a. Write the model in the mat...

Q: Let PX and MX be as defined in Equations (19.

Let PX and MX be as defined in Equations (19.24) and (19.25). a. Prove that PXMX = 0n * n and that PX and MX are idempotent. b. Derive Equations (19.27) and (19.28). c. Show that rank (PX) = k + 1 and...

Q: Consider the regression model in matrix form, Y = X

Consider the regression model in matrix form, Y = X + W + U, where X is an n * k1 matrix of regressors and W is an n * K2 matrix of regressors. Then, as shown in Ex...

Q: Consider the regression model Yi = b1Xi + b2Wi + ui,

Consider the regression model Yi = b1Xi + b2Wi + ui, where for simplicity the intercept is omitted and all variables are assumed to have a mean of 0. Suppose that Xi is distributed independently of (W...

Q: Consider the regression model Yi = b0 + b1Xi + ui,

Consider the regression model Yi = b0 + b1Xi + ui, where u1 = u∼1 and ui = 0.5ui - 1 + u∼i for i = 2, 3 … n. Suppose that uâˆ&fra...

Q: This exercise shows that the OLS estimator of a subset of the

This exercise shows that the OLS estimator of a subset of the regression coefficients is consistent under the conditional mean independence assumption stated in Key Concept 6.6. Consider the multiple...

Q: Let x1, ……, xn denote a sequence of numbers; y1

Let x1, ……, xn denote a sequence of numbers; y1, ……, yn denote another sequence of numbers; and a, b, and c denote three...

Q: Suppose that Y1, Y2, ……, Yn are random variables with

Suppose that Y1, Y2, ……, Yn are random variables with a common mean Y; a common variance 2Y; and the same correlation ï&...

Q: Consider the problem of predicting Y using another variable, X,

Consider the problem of predicting Y using another variable, X, so that the prediction of Y is some function of X, say g(X). Suppose that the quality of the prediction is measured by the squared predi...