Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui....
Consider a simple linear regression model with nonstochastic regressor: Yi = β1 + β2Xi + ui. 1. [3 points] What are the assumptions of this model so that the OLS estimators are
BLUE (best linear unbiased estimates)?
2. [4 points] Let βˆ and βˆ be the OLS estimators of β and β .
Derive βˆ and βˆ.
12 1212
3. [2 points] Show that βˆ is an unbiased estimator of β .22
Homework Answers
For OLS estimators to be BLUE following assumptions are made:
1) The regression model must be linear in the parameters.
2) The explanatory variable Xi must be uncorrelated with the disturbance term ui.
3) Given the value of Xi , the expected value of the disturbance term is zero.
4) The variance of each ui is constant or homoscedastic.
5) There is no correlation between two error terms.That is no autocorrelation.
6) Errors are normally distributed.
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Consider the linear model: Yį = ao + Q1(X; - X) + Ui. Find the OLS estimators of do and a1. Compare with the OLS estimators of Bo and B1 in the standard model discussed in...
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