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ECON 140, Fall 2008  10/23
Alex Rothenberg
Practice Problems: Omitted Variables, Errors
in Variables, Randomized Experiments
Problem 1
Suppose you were interested in understanding how corruption aﬀects the provision of driver’s
licenses in India. There are two competing hypotheses that we’d like to distinguish empirically:
•
Hypothesis I
: Paying bribes might help to eliminate red tape and “grease the wheels” of
a slow, ineﬃcient bureaucracy. Bribes represent a transfer between good drivers who are
willing to pay for a license and bureaucrats. There is no social loss.
•
Hypothesis II
: Corruption has damaging eﬀects to society. Those who pay bribes to
obtain a license are typically less likely to be good drivers. As a result, corruption makes
the streets unsafe for everyone who drives.
How might we test these hypotheses? Suppose we collected data on a random sample of people
who tried to obtain drivers licenses in India. Let
D
i
be an indicator equal to 1 if individual
i
got a license, 0 otherwise. Let
B
i
denote the amount of bribes paid by individual
i
in trying to
obtain the license. Let
A
i
denote the driving ability of individual
i
, measured by their score on
an objective driving exam.
1. Suppose we were trying to decide between estimating two possible linear probability
models:
D
i
=
α
0
+
α
1
B
i
+
ε
i
(1)
D
i
=
β
0
+
β
1
B
i
+
β
2
A
i
+
ε
i
(2)
Which of these models would be most interesting to estimate for the purpose of
determining which of our hypotheses is more plausible?
2. Suppose the true model is (2) but we estimate (1) with ordinary least squares. Derive an
expression for the omitted variable bias.
3. (Optional) Explain the diﬀerences between estimating model (2) and the following model:
D
i
=
γ
0
+
γ
1
B
i
+
γ
2
A
i
+
γ
3
(
B
i
×
A
i
) +
ε
i
How do we interpret
γ
3
, the coeﬃcient on the interaction term?
1
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View Full DocumentECON 140, Fall 2008  10/23
Alex Rothenberg
4. Suppose we tried to estimate (1) but we mismeasure
B
i
. Our true model is the following:
D
i
=
α
0
+
α
1
B
i
+
ε
i
But instead, we have a noisy measure of
B
i
:
e
B
i
=
B
i
+
υ
i
So, the regression we actually run takes the following form:
D
i
=
α
0
+
α
1
e
B
i
+
ε
i
Here, we assume that the
υ
i
’s are
iid
, with
E
[
υ
i
] =

1000. That is, on average,
individuals underreport the bribes they pay by Rs 1000. Assuming that
υ
i
⊥
ε
i
, work
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