- The relationship between the Generalized Least Squares estimator & the Weighted Least Squares estimator is that:
- They are the same.
- They are the same if the errors have a known and observable form of heteroskedasticity.
- They are the sane if the errors follow an AR(1) process.
- They are the same as long as the GLS estimator is "feasible".

- The GLS estimator is BLU (by the Gauss-Markhov Theorem) if:
- The errors are normally distributed.
- The covariance matrix of the errors is non-singular.
- The covariance matrix of the errors is known and observable.
- The regressors are non-random and the errors have a zero mean and a covaraince matrix that is known and observable.

- Consider the linear regression model,
*y*=*Xβ*+*ε*, where E(*ε*) = 0 and E(*εε*') =*Σ*, and*X*is non-random.- The OLS estimator of
*β*is biased, and inefficient, unless*Σ*is a "scalar" matrix. - The GLS estimator of β is biased, but efficient.
- The OLS estimator of
*β*is unbiased, but inefficient, unless*Σ*is a "scalar" matrix. - The "feasible" GLS estimator of
*β*is unbiased, and consistent.

- The OLS estimator of
- White's estimator of the covariance matrix of the OLS estimator of β in the linear regression model is used:
- To ensure that the standard errors of the estimated coefficients are consistent, even if the error term is heteroskedastic of some unknown form.
- To ensure that the the estimated coefficients are consistent, even if the error term is heteroskedastic of some unknown form.
- To ensure that the standard errors of the estimated coefficients are consistent, even if the error term is autocorrelated of some unknown form.
- To ensure that the standard errors of the estimated coefficients are unbiased, even if the error term is heteroskedastic of some unknown form.

- The difference between the GLS estimator and the "feasible" GLS estimator is:
- The GLS estimator uses the known non-scalar covariance matrix of the errors, while the "feasible" GLS estimator uses an unbiased estimator of this covariance matrix because it is unobservable.
- The GLS estimator uses the known non-scalar covariance matrix of the errors, while the "feasible" GLS estimator uses a consistent estimator of this covariance matrix because it is unobservable.
- None - if the error term has a scalar covarince matrix,
- Both B & C.

- White's test for homoskedasticity in the linear regression model is:
- An asymptotically valid test in which the null hypothesis is that the errors follow some arbitrary form of heterokedasticity, and the alternative hypothesis is that the errors are homoskedastic.
- An asymptotically valid test in which the null hypothesis is that the errors are homoskedastic, and the alternative hypothesis is any arbitrary form of heteroskedasticity.
- The UMP test against any arbitrary form of heteroskedasticity.
- Valid in finite samples, but more powerful if the sample size is very large.

- The Goldfeld-Quandt test is used:
- To test if the variance of the regression model's error term is constant over two sub-samples, when it is known that the coefficient vector is constant.
- To test if the coefficient vector of the regression model is constant over two sub-samples, when it is known that the model's error term is constant.
- To test if the variance of the regression model's error term is constant over two sub-samples.
- To test if the variance of the regression model's error term is homoskedastic.

- The Goldfeld-Quandt test for homoskedasticity is:
- An asymptotically valid F-test if the model satisifes ALL of the usual assumptions, including normally-distributed errors.
- An exact F-test if the model satisifes ALL of the usual assumptions, including normally-distributed errors.
- An exact F-test if the model satisifes all of the usual assumptions, except for normally-distributed errors.
- Usually applied as a two-sided test as we don't know if

*σ*_{1}^{2}>*σ*_{2}^{2}, or if*σ*_{1}^{2}<*σ*_{2}^{2}.

- The Breusch-Pagan test is used:
- To test the null of homoskedastic errors against the alternative of heteroskedastic errors, when the heteroskedasticity is of a specified form, and the errors are normally distributed.
- To test the null of homoskedastic errors against the alternative of heteroskedastic errors, when the heteroskedasticity is of an arbitrary form, and the sample is relatively large.
- To test the null of homoskedastic errors against the alternative of heteroskedastic errors, when the heteroskedasticity is of a specified form, and the sample is relatively large.
- To test the null of homoskedastic errors against the alternative of heteroskedastic errors, when the heteroskedasticity is of a specified form, and the regressors are non-random.

- The connection between the Breusch-Pagan test for homoskedasticity and Harvey's test for homoskedasticity is:
- They are both examples of Wald tests.
- Harvey's test is just a special case of the Breusch-Pagan test, with the error variance being a particular function of some variables, under the alternative hypothesis.
- The Breusch-Pagan test is just a special case of Harvey's test, with the error variance being an exponential function of some variables, under the alternative hypothesis.
- They are both Lagrange Multiplier (LM) tests.

- If we have linear regression model that is "standard", except that the errors follow the process
*ε*, then:_{t}= ρ ε_{t-1}+ u_{t}- The OLS estimator of
*β*will be unbiased and consistent, but inefficient. - The OLS estimator of
*β*will be biased and inefficient, but consistent. - The OLS estimator of
*β*will be inefficient but unbiased and consistent, as long as the regressors do not include any lagged values of*y*. - The OLS estimator of
*β*will be consistent but inefficient and biased and inconsistent, if the regressors include any lagged values of*y*.

- The OLS estimator of
- The LM test for serial independence of the regression model's error term is:
- An asymptotically valid test.
- Appropriate even if the model includes lagged values of
*y*as regressors. - Appropriate even if the errors are non-normal.
- All of A, B, & C.

- The Cochrane-Orcutt estimator for the coefficients of a regression model with AR(1) errors is:
- Just a convenient way of implementing the Maximum Likelihood Estimator (MLE) of
*β*. - An approximation to the MLE of
*β*- the approximation arises because a term is actually omitted from the full likelihood function. - Slightly different from the MLE in finite samples, but asymptotically equivalent to the MLE.
- Used to obtain unbiased estimates of these coefficients.

- Just a convenient way of implementing the Maximum Likelihood Estimator (MLE) of
- Check the EViews regression output located here. The following is true:
- We reject the hypothesis that the errors for the model estimated on page 1 are serially independent, against the alternative hypothesis that they follow a first-order moving average process, at least at the 5% significance level, & this has been dealt with adequately on page 2 by re-estimating the model allowing for errors that follow this process.
- The residuals for the model estimated on page 1 exhibit first-order autocorrelation, at least at the 5% significance level, & this has been dealt with adequately on page 2 by re-estimating the model allowing for errors that follow a first-order autoregressive process.
- The residuals for the model estimated on page 1 exhibit first-order autocorrelation, at least at the 5% significance level, & this has been dealt with adequately on page 2 by re-estimating the model allowing for errors that follow a first-order moving average process.
- Answer C would be correct if we had a larger sample size, but we really can't conclude much at all in the case of only 15 observations.

- Check the EViews regression output located here. The following is true:
- The residuals for the model estimated on page 1 exhibit fourth-order autocorrelation, at least at the 5% significance level, & this is still a problem on page 2 after re-estimating the model allowing for errors that follow a (restricted) ARMA(4,4) process.
- The residuals for the model estimated on page 1 exhibit fourth-order autocorrelation, at least at the 5% significance level, but this problem has been resolved on page 2 by re-estimating the model allowing for errors that follow a (restricted) ARMA(4,4) process.
- The residuals for the model estimated on page 1 exhibit fourth-order autocorrelation, at least at the 5% significance level, & this is still a problem on page 2 after re-estimating the model allowing for errors that follow a fourth-order autoregressive process.
- None of the above.