Question

In a paragraph, explain what bias is, what OLS assumptions are necessary to guarantee a non-biased estimate, and an example of how bias may enter into the model.

Answer 1

The bias of an estimator is the difference between the expected value and the true value of the parameter being estinated.

The following assumptions are necessary to give an unbiased OLS estimator-

i) The regression model should be linear in parameters

ii) The conditional mean should be zero i.e. the expected value of the mean of the parameter should be zero.

iii) There should be no multi collinearity.

iv) No autocorrelation between the variable and the error term

v) No heteroscedasticity

vi) Error term should be normally distributed

vii) No specification bias/error

If suppose one of the assumption is not satisfied, lets say autocorration, this means that the error term and the variable is correlated. In that case, the OLS estimators are no more Best Linear Unbiased Estimators - BLUE. Rather, they will only be unbiased and linear but will no more have minimum variance.