Tutorial 2: RCTs
The University of Queensland ECON7360
Instructor: Rigissa Megalokonomou
1 OLS Estimator in an RCT
The data for the following exercises comes from the Project STAR: A Randomized Exper- iment of the Impact of Class Size Reductions on Pupil Achievement. This was a 4-year experiment in Tennessee designed to evaluate the effect of class size on learning. Each participating school had at least one control group class and one treatment group.
Use the data in star.dta to estimate the following regression models.
(1) The dummy variable ¡±sck¡± indicates whether students were in a small class. Find the mean, standard deviation, max and min values.
(2) Run a regression of the test score in kindergarten on that dummy variable that indicates whether students were in a small class.
score=¦Ä0 +¦Ä1sck+¦Å
(3) Show that the OLS estimate of the intercept in this regression will be the sample mean of the test score for those who are in the control group and that the coefficient on sck (small class indicator) will be the difference between the sample mean test score for those in treatment and control groups.
(4) What does this regression say about the impact of class size reductions on students¡¯ performance? Estimate the regression, but now use robust standard errors. Why does the coefficient remain the same? Why does the standard error change?
2 The role of other covariates in RCT
Use the data in star.dta to estimate the following regression models.
score = ¦Á0 + ¦Á1sck + ¦Á2Boy + ¦Á3freelunk + ¦Á4totexpk + u (1)
1
(1) Then run the following regression:
score = ¦Â0 + ¦Â1sck + ¦Â2Boy + ¦Â3freelunk + ¦Â4totexpk + schidkn + v (2)
where schidkn is school identification dummy variables.
(2) Generate a set of dummies for the school ID (schidkn), put it in the other covariates
and run the regression again.
(3) What would you expect to happen to the estimate of the treatment effect for small
class (¦Â1) in equation (2) compared to ¦Á1 in equation (1)? Is this what happens?
(4) Consider the following equation:
sck = ¦Ä0 + x1¦Ä + ¦Å1 (3)
where x1=(Boy, freelunk, totexpk).
Now consider a hypothesis test of ¦Ä = (¦Ä1, ¦Ä2, ¦Ä3)=0. Does F-test reject the null of ¦Ä1 = ¦Ä2 = ¦Ä3=0. What does this test imply for the estimation of ¦Á1 ?
(5) Consider the following equation:
sck = ¦Ä0 + x2¦Ã + ¦Å2 (4)
where x2=(Boy, freelunk, totexpk, schidkn)
Now consider a hypothesis test of ¦Ã=0. Does F-test reject the null of ¦Ã1 = ¦Ã2 = … = ¦Ãp=0.
Is assignment to a small class random?
(6) Now consider the estimation of equation (1) and the one that you used in part (2). How does the OLS estimate and its standard error for the coefficient on sck change by the addition of the school dummies?
3 Regression with interaction terms
Use the data in star.dta to estimate following regression models.
(1) Generate the interaction of the treatment dummy variable with boy, freelunk and totexpk. What is the mean, standard deviation, minimum and maximum values for each interaction term?
2
(2) Estimate the regression excluding the school dummies but including these interac- tions. Interpret the coefficients.
(3) Use an F-test to test the hypothesis that there is the same treatment effect for everyone. Do you accept or reject the test of homogeneity?
3