Homework 2

Remark: The solutions to the problem 2c) 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.
[ 7 credits ]
3.) For a panel of length T = 2, recall that the first differences (FD) estimator for the outcome
equation
(0) yit = θt + zitγ + δ1progit + ci + uit
yields the conditional difference–in–differences (CDiD) estimator of the treatment effect δ1, when
the policy is introduced in period 2, i.e. progi1 = 0, and participation takes only place in period
2, i.e. progi2 = 0, 1. This estimator accounts for the possibility that progit is correlated with ci.
a) Motivate and describe the FD estimator above in detail. Why does it provide a consistent
estimate of the treatment effect δ1?
b) Discuss and describe a semiparametric matching estimator as an extension of the CDiD
estimator for the model
(S) yit = θt + g(zit) + δ1progit + ci + uit .
under the above setup, where the policy is introduced in period 2. Assume that zit is a
scalar regressor. Be as specific as possible.
[ 4 credits ]
4.) (Sharp RDD with simulated Data, PC Pool Problem Set 3, Problem 3)
Assume that a sample of N observations is simulated based on the following regression model
yi = 1 + α · Di + x1i − 0.1x 2 1i + x2i − 0.2x1ix2i + ϵi ,
where x1i, x2i, and ϵi are three independent random variables following a standard normal distribution.
The treatment dummy is given by
Di = I(x1i > 0.2) .
a) First assume that the treatment effect α = 3 is a fixed constant. Show that the conditions
for a sharp RDD are satisfied here, 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.
b) Why is it not necessary that the RDD estimator controls for x2?
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