Stats - Gauss-Markov PDF

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Gauss-Markov...

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Gauss-Markov Theorem 1. Zero conditional mean of errors (if we do have a violation “endogeneity in model)have bias in OLS estimatorsserious violation because if you have bias in model cannot trust output of OLS estimators because they won’t be indicative of what is going on in the population 2. No perfect Collinearity amongst regressors we cannot even estimate our regression equationjust beak down and come up with error messageput two or more regressors telling you essentially the same thingimpossible to differentiate between one’s effect from anothernot going to be possible – a. If however the two independent variables are correlated, then the variance of the estimate of the coefficient increases. This results in a smaller t-value for the test of hypothesis of the coefficient. In short, multicollinearity results in failing to reject the null hypothesis that the X variable has no impact on Y when in fact X does have a statistically significant impact on Y. Said another way, the large standard errors of the estimated coefficient created by multicollinearity suggest statistical insignificance even when the hypothesized relationship is strong.

b. 3. No serial correlationdoesn’t lead to bias in OLS estimators but it does lead to OLS estimators being inefficientother estimators that take into account this extra information (inefficiency)can’t rely on normal and std errors 4. Homoskedasticity...