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Online Econometrics Textbook - Regression Extensions - Assumption Violations of Linear Regression

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In the previous chapter we have discussed linear regression analysis under some specific assumptions. In this section we will investigate what can be done in case the assumptions of OLS or MLE are violated.

Suppose that

Online Econometrics Textbook - Regression Extensions - Assumption Violations of Linear Regression





which implies that the parameters are unbiased but inefficient.

A solution to this problem might be found by using Generalized Least Squares (GLS).

We know that


and therefore


In a first step we use the matrix P to transform y, X, and e as follows


It then follows


The unbiased GLS estimator can be written as




and an unbiased estimator for the variance



Suppose that


The log likelihood function is now equal to


Hence the GMLE estimator is


which is BLUE and


which is obviously biased. This problem can be solved by replacing T by T - K (cfr. eq. (III.I-10)).

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Restricted LS
Distributed Lags
Assumption Violations
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