Question

Consider the following regression model Yi = ? Xi + ui, i = 1, ..., n. The error term has a zero mean, variance equal to ?^2 / Xi^2, and E(ui uj) = 0 for i ? j. You are given a sample of observations {(Yi, Xi)}_{i=1}^n. You may treat Xi as being non-stochastic. Clearly annotating your answers: (a) (5 marks) Derive the OLS estimator of ?. In the presence of heteroskedasticity, the OLS estimator remains unbiased (you are not asked to show this). Derive the variance of the OLS estimator of ?. (b) (3 marks) Discuss how you can obtain the Best Linear Unbiased Estimator (BLUE) of ? given the heteroskedasticity.

          Consider the following regression model
Yi = ? Xi + ui, i = 1, ..., n.

The error term has a zero mean, variance equal to ?^2 / Xi^2, and E(ui uj) = 0 for i ? j. You are given a sample of observations {(Yi, Xi)}_{i=1}^n. You may treat Xi as being non-stochastic. Clearly annotating your answers:

(a) (5 marks) Derive the OLS estimator of ?. In the presence of heteroskedasticity, the OLS estimator remains unbiased (you are not asked to show this). Derive the variance of the OLS estimator of ?.

(b) (3 marks) Discuss how you can obtain the Best Linear Unbiased Estimator (BLUE) of ? given the heteroskedasticity.

Consider the following regression model
Yi = ? Xi + ui, i = 1, ..., n.

The error term has a zero mean, variance equal to ?^2 / Xi^2, and E(ui uj) = 0 for i ? j. You are given a sample of observations (Yi, Xi)i=1^n. You may treat Xi as being non-stochastic. Clearly annotating your answers:

(a) (5 marks) Derive the OLS estimator of ?. In the presence of heteroskedasticity, the OLS estimator remains unbiased (you are not asked to show this). Derive the variance of the OLS estimator of ?.

(b) (3 marks) Discuss how you can obtain the Best Linear Unbiased Estimator (BLUE) of ? given the heteroskedasticity.

Added by Daryl K.

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