In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teachers and students were randomly assigned to be in a regular-sized class or a small class. The outcome of interest is a student’s score on a math achievement test (MATHSCORE). Let SMALL = 1 if the student is in a small class and SMALL = 0 otherwise. The other variable of interest is the number of years of teacher experience, TEXP. Let BOY = 1 is the child is male and BOY = 0 if the child is female.

a. Write down the econometric specification of the linear regression model explaining MATHSCORE as a function of SMALL, TEXP, BOY, BOY x TEXP, with parameters β1, β2,

i. What is the expected math score for a boy in a small class with a teacher having 10 years of experience?

ii. What is the expected math score for a girl in a regular-sized class with a teacher having 10 years of experience?

iii. What is the change in the expected math score for a boy in a small class with a teacher having 11 years of experience rather than 10?

iv. What is the change in the expected math score for a boy in a small class with a teacher having 13 years of experience rather than 12?

b. Modify the model in part (a) to include SMALL x BOY.

i. What is the expected math score for a boy in a small class with a teacher having 10 years of experience?

ii. What is the expected math score for a girl in a regular-sized class with a teacher having 10 years of experience?

iii. What is the expected math score for a boy? What is it for a girl?