Questions from Econometrics

Q: The expression for the restricted coefficient vector in (5-23

The expression for the restricted coefficient vector in (5-23) may be written in the form b* = [I - CR]b + w, where w does not involve b. What is C? show that the covariance matrix of the restricted l...

Q: Prove the result that the restricted least squares estimator never has a

Prove the result that the restricted least squares estimator never has a larger covariance matrix than the unrestricted least squares estimator.

Q: Prove the result that the R2 associated with a restricted least squares

Prove the result that the R2 associated with a restricted least squares estimator is never larger than that associated with the unrestricted least squares estimator. conclude that imposing restriction...

Q: An alternative way to test the hypothesis RB - q = 0

An alternative way to test the hypothesis RB - q = 0 is to use a Wald test of the hypothesis that L* = 0, where L* is defined in (5-23). Prove that Note that the fraction in brackets is the ratio of t...

Q: Use the test statistic defined in Exercise 7 to test the hypothesis

Use the test statistic defined in Exercise 7 to test the hypothesis in Exercise 1.

Q: Prove that under the hypothesis that RB = q, the estimator

Prove that under the hypothesis that RB = q, the estimator where J is the number of restrictions, is unbiased for s2.

Q: A regression model with K = 16 independent variables is fit using

A regression model with K = 16 independent variables is fit using a panel of seven years of data. The sums of squares for the seven separate regressions and the pooled regression are shown below. The...

Q: Reverse regression continued. This and the next exercise continue the analysis

Reverse regression continued. This and the next exercise continue the analysis of Exercise 2. In Exercise 2, interest centered on a particular dummy variable in which the regressors were accurately me...

Q: The data in Appendix Table f5.2 may be used to

The data in Appendix Table f5.2 may be used to estimate a small macroeconomic model. Use these data to estimate the model in Example 10.5. Estimate the parameters of the two equations by two-stage and...

Q: The two-variable regression. For the regression model y =

The two-variable regression. For the regression model y = a + bx + e, a. show that the least squares normal equations imply iei = 0 and ixiei = 0. b. show that the solution for the constant term is...