Heteroscedastic errors (no longer constant variance)

Question 1

Recall CLRA5

Answer 1

Errors have constant variance σ²

This is homoscedastic: we are looking at heteroscedacity, variance can be different!

Question 2

Heteroscedasticity says that

var (ε₁|X₁…Xk) =σ²i
i.e variances are different at given i

thus violating the classical assumption

Question 3

Income and savings example : homoscedastic vs heteroscedastic

Answer 3

Homoscedastic assumes equal variance for all X. (saving in this case)
This is saying that when income changes the variance/spread of saving stays the same.

unrealistic! people save less (LOW MPS) when low income since little left after buying necessities.

Heteroscedastic shows variation increases as X increases. More realistic

Question 4

Consequences of hetroscedastic errors

Answer 4

Unbiased still, but variance estimators incorrect.

(Just like autocorrelation - where we had to identify if exists by DW/BG and fix via GLS or CO)

Question 5

This is still not the best option that gives a lower variance.

Answer 5

Weighted least squares