Question

4. Consider the regression model, y1B22+ BKiK+ei -.. where errors may be heteroskedastic. Choose the most incorrect statement (a) The OLS estimators are consistent and unbiased (b) We should report the OLS estimates with the robust standard errors (c) The Gauss-Markov theorem may not apply (d) The GLS cannot be used because we do not know the error variances in practice (e) We should take care of heteroskedasticity only if homoskedasticity is rejected Consider the regression model, +BKIK+et e pet-1+ with 1<p Yt B1B22 +. .. independent rdom error termswith mean zero and variance a where 's are Choose the wrong statement (a) OLS is unbiased, consistent, aeffic (b) We may use the OLS emates with the HAC Sdard errors (c) The errors follo an AR(1) process if p 0. (d) Var(e) 1- p) and Cov(et, e k) po/(1-) for The Breusch-Godfrey test considers Ho p 0 6. For each observation i 1,,n, the regressor i2 indicates "female," and i3 are similar, but indicates lipstick not the same. That is, in the sample, there are some women not using a lipstick, and there are some men users. From the data, it is confirmed that ri2 and ri3 using a lipstick. Now, suppose that an econometrician regresses yi on all the regressors including ri2 and ri3 and finds that the standard errors of the OLS estimates are large. Choose the wrong statement (a) This is called the near multicollinearity (b) One should find a way to reduce the standard errors to have significant estimates (c) The large standard errors arise naturally due to the difficulty to disentangle the effect of ri2 on yi from the effect of ri3 on yi C (d) The OLS is unbiased and consistent. (e) None of the above is wrong.

Answer 1

4)

The most incorrect statement is We should take care of heteroskedasticity only if homoskedasticity is rejected.

Because, Test for heteroskedasticity under the assumption that the errors are independent and identically distributed (i.i.d.). You can perform the test using the fitted values of the model, the predictors in the model and a subset of the independent variables.

F Test for heteroskedasticity under the assumption that the errors are independent and identically distributed (i.i.d.). You can perform the test using the fitted values of the model, the predictors in the model and a subset of the independent variables.

6)

The wrong statement is One should find a way to reduce the standard errors to have significant estimates.

Because, reducing the variability of your data decreases the standard deviation and, thus, the standard error for the estimate. Although it can be difficult to reduce variability in your data, you can sometimes do so by adjusting how you collect data for significant estimates.