HANDOUT 10

Question 1

How does non-normality affect OLS?

Answer 1

Our estimators are NOT t-distributed anymore

Question 2

What tests do we do when €i is not normal? Why?

Answer 2

We can do approx. normal tests via central limit theorem if n > 30 instead of t-tests.

Do chi-squared tests instead of F tests.

Question 3

Does non-normality affect E(bj) and V(bj)?

Answer 3

NO - E(bj) = Bj as only needs CLRM 1

V(bj) = same as normal as only needs CLRM 1,2 and 3.

Question 4

How can we test for non-normality?

Answer 4

Test the skewness and kurtosis of the residuals.

Question 5

Define mj =

Answer 5

mj = 1/n sum (ei^j) for j=1,2,3,4

Question 6

Skewness formula

Answer 6

S = m3 / m2 ^3/2
S = 0 for normal distribution.

Question 7

Kurtosis formula

Answer 7

K = m4 / m2^2
K = 3 for normal distribution

Question 8

Jarque-Bera Test of normality

Answer 8

JB = n/6 [S^2 + (K - 3)^2]
H0: JB = 0 - normal
H1: JB ≠ 0 - not normal

Question 9

What other problem can make the error term appear non-normal?

Answer 9

Outliers - to solve this include impulse dummy variables.