Homework 2

c) Is there a discontinuous jump in the distribution of x2 at the RDD threshold ¯x1 = 0.2?
How could one implement a test for this?
d) Now assume that the treatment effect α is random with E(α) = 3 and the distribution of
α is independent of (x1, x2). Show that the conditions for a sharp RDD are satisfied here
as well, i.e. the RDD estimator identifies α. Consider the assumptions put forward in Van
der Klaauw (2002) and check formally that they are satisfied in this case. Motivate the
identification result. What is the control function k(S) in this context? Be as specific as
possible.
Remark: This is a theoretical exercise. To solve this problem, it is not necessary to implement a
TSP program for estimation purposes.
[ 7 credits ]
5.) (Fuzzy RDD: Angrist and Lavy 1999, Maimonides Rule, PC Pool Problem Set 3, Problem 4)
Use the programs and the data provided as part of the third PC Pool Problem Set. For the
problem analyze only math scores as outcome variables for the fourth grade.
a) Analyze whether the variable ’percent disadvantaged’ shows discontinuous jumps at the
tresholds used to split classes. What do these results imply regarding the question as to
whether it is necessary to control for the variable ’percent disadvantaged’ when estimating
the RDD estimate of the treatment effect of class size?
b) Implement the 2SLS estimate of the effect of class size on math scores in the fourth grade
controlling for enrollment using an appropriate polynomial specification of enrollemnt and
percent disadvantaged as control variables. Discuss the results.
c) Implement the local Wald estimator for the RDD based on a local linear regression (using
a rectangular kernel) of class size on expected class size on both sides of each threshold.
Use these nonparametric estimates from the first stage to estimate in a second stage the
fuzzy RDD estimate of the effect of class size
E(Yi|
ˆρs = lim
∆→0
¯ Ss < S < ¯ Ss + ∆) − E(Yi| ¯ Ss − ∆ < S < ¯ Ss)
E(Di| ¯ Ss < S < ¯ Ss + ∆) − E(Di| ¯ Ss − ∆ < S < ¯ Ss)
for the s th threshold ¯ Ss (using the notation in the lecture). Discuss the differences in
methods and results in comparison to part b).
Remark: The solutions to the problem should include the TSP–programs, which you wrote to
solve the problems, together with the output on paper. The discussion of the results should make
reference to the computer output.
5
[ 6 credits ]