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ECO 120
Practice Problems for Midterm
Fall 2007
1. This question is to get you a bit more comfortable with the idea of instrumental variables.
(a) Similar to the Thomas et al. (2006) paper that we studied in class, a researcher
is interested in estimating the impact of iron supplements on labor supply.
The
researcher conducts a randomized evaluation in which a treatment group is given
supplements but the control group is not. However, only 95% of the treatment group
ends up taking the supplement (nobody in the control group takes the supplement),
which means that comparing outcomes for those
sampled
for treatment to those
sampled for the control group would end up counting the 5% of people that did not
actually take the supplement.
Assuming that the 5% of people that did not take
the supplement did not bene&t at all, such an estimate (which is called the Intent
toTreat estimate) will give a lower bound on the impact of the program.
The
researcher therefore proposes using an instrumental variables approach. He proposes
using being sampled for treatment as an instrument for actually taking the drug.
That is, the equation of interest is
LS
it
=
&
0
+
1
TS
it
+
"
it
(1)
where
LS
it
is labor supply for individual
i
at time
t
and
TS
it
is a dummy variable
for whether that person took the drug (
"
it
is the error term).
i. Why is regressing (1) directly likely to be a biased estimate?
ii. The instrumental variables approach is to instrument
TS
it
with
S
it
, an indicator
for whether the person was sampled to take the drug. That is, the relationship
between taking the drug and being sampled for treatment is of the form
TS
it
=
±
0
+
±
1
S
it
+
u
it
(2)
1
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This note was uploaded on 05/04/2008 for the course ECON 120 taught by Professor Robinson during the Spring '08 term at University of California, Santa Cruz.
 Spring '08
 robinson
 Economics

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