Question

4. What are the characteristics that we seek the OLS estimator to meet?

5. What are the main assumptions that we make about the data in order for the OLS estimator to have the properties we desire?

6. In the context of multivariate regression analysis, what type of bias might affect our ability to properly estimate the value of a parameter? How can we solve it?

Answer 1

Take the model for example:

,

The parameters are and . The parameters are to be estimated for which the the disturbance term is minimum. The method used is Ordinary Least Square (OLS) to estimate the parameters. The characteristics of OLS estimators are:

i) Linear ii) Unbiased iii)Least variance iv)Consistent

The assumptions made about the data in order make OLS estimators to have above properties are:

i) The mean value of disturbance term is zero.

ii) There is no autocorrelation among disturbance terms.

,   

iii)There is zero correlation between regressor and disturbance term.

iii) The disturbance term is homoscedastic.

Bias occurs in a model when .i.e. the regressor and disturbance term is correlated. Basically the the mean value of parameter becomes biased. Then it is no more fulfilling OLS characteristics. This occurs due to specification errors. One important variable must have been omitted which has important implication in the model. One can solve the problem by including all kind of regressor that has high influence on the regressand.