Question: Exercise 5: MLE estimation in the Classical Normal Linear Model. Consider the Classical Normal Linear Model, 1. As we did in class, derive the log

Exercise 5: MLE estimation in the Classical Normal Linear Model. Consider the Classical Normal Linear Model,

1. As we did in class, derive the log likelihood function starting from the pdf of each data point and be precise about which assumption(s) you use at each step.

2. Take the FOC with respect to . Solve this FOC; that is, express that solves the equation as a function of . Substitute the expression for as a function of in the loglikelihood function and show that in the Classical Normal Linear Model, MLE = OLS.

3. A friend suggests to drop A5 Normality Assumption, that is, to find the MLE estimator for the Classical Linear Model. Could you compute the MLE estimator in the Classical Linear Model (i.e. Assumptions 1 through 4) without further assumption? If yes, how?

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