Questions from Econometrics

Q: Two samples of 50 observations each produce the following moment matrices.

Two samples of 50 observations each produce the following moment matrices. (In each case, X is a constant and one variable.) a. compute the least squares regression coefficients and the residual var...

Q: Suppose that in the group wise heteroscedasticity model of section 9.

Suppose that in the group wise heteroscedasticity model of section 9.7.2, Xi is the same for all i. What is the generalized least squares estimator of ? How would you compute the estimator if it were...

Q: The model / satisfies the group wise heteroscedastic

The model satisfies the group wise heteroscedastic regression model of section 9.7.2 All variables have zero means. The following sample second-moment matrix is obtained from a sample of 20 observat...

Q: The following table presents a hypothetical panel of data:

The following table presents a hypothetical panel of data: a. Estimate the group wise heteroscedastic model of section 9.7.2. Include an estimate of the asymptotic variance of the slope estimator. U...

Q: This and the next two exercises are based on the test statistic

This and the next two exercises are based on the test statistic usually used to test a set of J linear restrictions in the generalized regression model, where  is the GLS estimator...

Q: Now suppose that the disturbances are not normally distributed, although

Now suppose that the disturbances are not normally distributed, although / is still known. Show that the limiting distribution of the previous statistic is (1/J) times a chi-squared variable with J...

Q: Finally, suppose that / must be estimated

Finally, suppose that / must be estimated, but that assumptions (9-22) and (9-23) are met by the estimator. What changes are required in the development of the previous problem?

Q: In the generalized regression model, if the K columns of X

In the generalized regression model, if the K columns of X are characteristic vectors of
, then ordinary least squares and generalized least squares are identical. (The result is actually a bit broa...

Q: In the generalized regression model, suppose that /

In the generalized regression model, suppose that / is known. a. What is the covariance matrix of the OLS and GLS estimators of ? b. What is the covariance matrix of the OLS residu...

Q: Using the Box–cox transformation, we may specify an alternative

Using the Box–cox transformation, we may specify an alternative to the cobb– Douglas model as Using Zellner and Revankar’s data in Appendix Tabl...