Heteroscedasticity

 What is heteroskedasticity?

There are two words homeoskedasticity means equal spread and heteroskedasticity means unequally spread. In economics tricks the major use for spread is the variance and heteroskedasticity deals with unequal variances.

Mathematically equation

VAR(ui) =(VAR)

Yi=a+BXi+ui

Consequence of heteroskedasticity for OLS estimators

The OLS estimators for the B's are still  unbiased and consistent.this is because none of the explanatory variables is correlated with the error term.So a correctly specified equation that suffers only from the presence of heteroskedasticity will give us value of beta that are relatively good.

heteroskedasticity  affects the disturbance of the beat  increasing the variance of the distributions and therefore making the estimators of the OLS method inefficient.

Heteroskedasticity also affects the variants of the estimated B's.in fact the presence of heteroscedasticity causes the OLS method to understand the variance.

Defecting heteroskedasticity

There are two ways of detecting heteroskedasticity first known as the informal way is the inspections of the different graph while the second is applying appropriate tests

The informal way

In the informal way and in the two variable case that we have seen before heteroskedasticity can easily be detected by simple inspection of the scatter plot. However this cannot be done in the multiple regression case.in this case useful information about the possible presence of heteroskedasticity can be given by plotting the squared residue was against the dependent variable and all the explanatory

 variable.

Appropriate tests

The Brevsch-Pagan LM test

The Glesjer LM test

The Harvey-Godfrey LM test

The Park LM test