Introduction to Econometrics. Lecture 7 Heteroskedasticity and some further diagnostic testing. Topics to be covered. Heteroskedasticity Some further diagnostic testing Normality of the disturbances Multicollinearity. Econometric problems. Heteroskedasticity.
Introduction to Econometrics
some further diagnostic testing
Topics to be covered
What does it mean? The variance of the error term is not constant
What are its consequences?The least squares results
are no longer efficient and t tests and F tests results may be misleading
How can you detect the problem?Plot the residuals against each of the regressors or use one of the more formal tests
How can I remedy the problem? Respecify the model – look for other missing variables; perhaps take logs or choose some other appropriate functional form; or make sure relevant variables are expressed “per capita”
Consumption function example (cross-section data): credit worthiness as a missing variable?
The Homoskedastic Case
The Heteroskedastic Case
The consequences of heteroskedasticity
Plot residuals against one variable at a time
Goldfeld-Quandt test (JASA, 1965)
i.e. the error variance is proportional to the square of one of the X’s
where these RSS are based on regressions using the first and last [n-c]/2 observations [c is a central section of data usually about 25% of n]
Normality of the disturbances
What does it mean? A high degree of correlation amongst the
What are its consequences?It may be difficult to separate out
the effects of the individual regressors. Standard errors may
be overestimated and t-values depressed.
Note: a symptom may be high R2 but low t-values
How can you detect the problem?Examine the correlation
matrix of regressors - also carry out auxiliary regressions
amongst the regressors.
Look at the Variance Inflation Factors
Variance Inflation Factor (VIF)
Multicollinearity inflates the variance of an estimator
VIFJ = 1/(1-RJ2)
where RJ2 measures the R2 from a regression of Xj on the other X variable/s
serious multicollinearity problem if VIFJ>5