Lecture 4

Question 1

What is a dummy variable and what values do they take up?

Answer 1

Dummy variables are categorical variables which can only take a value of 0 or 1 e.g X1=0 if female, X1=1 if non female

Question 2

Consider a regression model Y=Bo+B1X1 + e, how would you interpret Bo and B1 based on X being able to tale a value of 0 or 1

Answer 2

Taking the expectation given X=0, you find out the awnser is Bo which shows that:

Bo- Represents the average of Y e.g wages given X=0 e.g non female

Taking the expectation given X=1, leaves you with Bo + B1, in order to get an interpretation of just B1 we minus E(Y|X=1)-E(Y|X=0) which gives us B1

B1- represents the differences in averages between Y when X=1 and Y when X=0

Question 3

What makes dummy variables special?

Answer 3

In order to interpret dummy variables we are not able to use differentiation, as dummy variables are categorical and not continuous variables.

This is because categorical variables have a finite number of values e.g 0,1 therefore we cannot make X really small as we do with differentiation, so we cannot differentiate.

Question 4

In an additive dummy variable such as Y= Bo + B1X1 +B2X2, with X1 being the dummy variable how would we interpret the coefficient B1

Answer 4

We would have to take the expectation of Y|X=1 - e(Y|X=0) and then we would have to fix X2 which is a continious variable to a certian number e.g 5 for both cases.

After this you will be left with 1. Bo+5B2 2. Bo+B1+16B2, doing 2-1, gives u B1.

B1 is the average difference between the two groups

Question 5

Interpret the different B by taking the expectation Y=Bo+B1X1 + B2X2 + B3X1X2 + e, for when X= O,1 and Y=0,1

Answer 5

1. E[Y|X1=0, X2=0]=Bo
2. E[Y|X1=1, X2=0]=Bo + B1
3. E[Y|X1=0, X2=1]=Bo
4. E[Y|X1=1, X2=1]=Bo+B1+B2+B3
   - Bo- Average wage for non female non hispanic workers
   - B1- Differences in average wage between non hispanic female/ male
   - B2- Difference in average wage between non female hispanic and non hispanic
   - B3- Differences of differences, the first difference is between male and female for hispanic and non hispanic. Now we take the differences of differences B3+B1-B1(the difference)