Answer to Question #275123 in Economics for lee kuek

Question

a)   Explain thoroughly, with examples, the following:

i.              Heteroscedasticity

ii.             Perfect multicollinearity

iii.            Unbiasedness

Answer 1

i. Heteroscedasticity refers to the error variance, or dependence of scattering, within a minimum of one independent variable within a particular sample.

A classic example of heteroscedasticity is that of income versus expenditure on meals. As one's income increases, the variability of food consumption will increase. Those with higher incomes display a greater variability of food consumption.

ii. Perfect multicollinearity occurs when two or more independent variables in a regression model exhibit a deterministic (perfectly predictable or containing no randomness) linear relationship.

Examples: including the same information twice (weight in pounds and weight in kilograms), not using dummy variables correctly (falling into the dummy variable trap), etc.

iii. Unbiasedness refers to whether the expected value of the sampling distribution of an estimator is equal to the unknown true value of the population parameter.

For example, the OLS estimator bk is unbiased if the mean of the sampling distribution of bk is equal to βk.