Econ B: L10

Question 1

How to do an interaction between 2 dummy variables?

Answer 1

Add in another variable on top of the two dummy variables that is x1.x2 (see example notes)
eg. if testing whether married males have a different average wage to married females

Question 2

How to do an interaction between a dummy variable and a normal explanatory variable?

Answer 2

Again multiply them together (see example notes and 2 graphs)
May be able to factorise them aswell

Question 3

Given examples in notes, how would you test if returns to education is the same for men and women?

Answer 3

If the coefficient for the variable ‘female’ is tested and found not to be significantly different to 0, then we can assume this variable has no impact on log(wage) tf conclude no difference in returns to education

Question 4

See eg2)

Answer 4

Now

Question 5

When might we use the Chow statistic? Give an example

Answer 5

If we wanted to test the null hypothesis that 2 populations or groups follow the SAME regression function, against the alternative that one or more slopes differ across groups

eg) if wanting to test if any difference in RM between male and female grade point avg.s for college students

Question 6

How would we test if there is any difference in RM between male and female grade point avg.s for college students?

Answer 6

Need to use a model where intercept and ALL slopes can be different across the 2 groups:
Tf (using example in notes):

gpa=β0+δ0female+β1sat+δ1female.sat+β2hsperc+δ2female.hsperc+β3tothrs+δ3female.tothrs+u

Tf: H0: δ0=δ1=δ2=δ3=0
with few variables (eg. example above) can simply add all of interactions to test for group differences (F-test)

Question 7

What happens if we have too many explanatory variables?

Answer 7

Can’t do this since we will lose too many degrees of freedom tf use a Chow statistic technique

Question 8

What does the Chow stat. method do?

Answer 8

Creates 2 groups, g=1 and g=2, and tests the null that there is no difference between the groups on corresponding variables (see notes for full explanation and stuff!!!)

Question 9

How many degrees of freedom are there in the Chow statistic method?

Answer 9

n-2(k+1)

Question 10

What is SSR1, SSR2 and tf SSRu?

Answer 10

SSR1: sum of squared residuals obtained from estimating 1st group (n1 obs.)
SSR2: sum of squared residuals obtained from estimating 2nd group (n2 obs.)
SSRu: sum of squared residuals for unrestricted model, given by:
SSRu=SSR1+SSR2

Question 11

How do you calculate the restricted SSR?

Answer 11

Calculated by pooling the 2 groups and estimating the single equation (=SSR)

Question 12

Final step of Chow stat. method?

Answer 12

Compute the F-statistic (equation on my eqn sheet)

Question 13

What does it mean if the F test is significant on the Chow method?

Answer 13

That one or more of the slopes differ across the groups