Heteroskedasticity Flashcards
Heteroskedasticity
error varaince is non- constant across observation
types/causes of het
1) due to scale/ proportionality factor
2) omitted variables
3) ARCH (auto regressive conditional het)
diff types of testing het
eyeball, the park, white, breusch pagan, goldfeld quandt
implications of het
1) hyp, t-test, p-value is not valid
2) OLS won’t be efficient
larger variances create larger dispersion
3) larger dispersion of error terms will average out over multiple sample
Eye ball test
squared residual for each observation
Park test
(steps)
squared fitted residual
Steps:
1) run regression model, square them and take logs
2) run auxiliary regression
3) conduct t -test for significance of a1 coefficient
4) conclusion:
a1 is significant, the regression has heteroskedasticity
Issues with Park Test
1) requires suspected casual variable z
2) z need not be included in the original regression
3) If Ho is rejected, specific culprit is in mind which will aid solving het. problem
White test
(steps)
- uses more flexible auxiliary regression,
which includes all variable in the orig model & linear and nonlinear combinations of X
Steps:
1) run regression model, square them and take logs
2) run auxiliary regression
3) conduct t -test for significance of a1 coefficient
4) conclusion:
a1 is significant, the regression has heteroskedasticity
Issues with White Test
1) Avoids a problem of needing a suspect variable
2) Aux reg includes only variables in the orig model
3) An orig model with many x var have many aux coefficient
4) results don’t tell you the exact cause
Breusch Pagan Test
- relies on LM test
- squared residuals are standardized by the est error variance
Steps:
1) run regression model, square them and take logs
2) construct estimated of sigma squared
3) run aux test with standardized squared residuals
4) construct LM test
5) Test null that all coefficients in test eq’n are zero
Goldfeld quandt Test
Steps:
1) sort data by increasing values of Z
2) split into three subsamples
3) run same model. on 1st and 3rd samples
4) construct LM test
5) conclude base on RSS
Solutions for Het
1) Respecify your model
2) use weighted Least Squares instead of OLS
3) use alternative formulation for SE
(Robust SE)
Respecify your model
- use per capita if population is the scale factor
- scale expenditure by income level
Weighted Least Square
- same as scaling
- reduce weight placed on observations
Robust Standard Error
- SE and t-stat can be modified to be valid
- only use if you are sure there’s heteroskedasticity
- changes in robust SE translate to changes in t-stat and p-value
but no change in coef
