ECON 3200 Introduction to Econometrics
Answers for Problem Set 4
Problem 1 (Wooldridge 7.6)
In Section 3.3 – in particular, in the discussion surrounding Table 3.2 – we discussed
how to determine the direction of bias in the OLS estimators when an important variable
(ability, in this case) has been omitted from the regression.
As we discussed there, Table
3.2 only strictly holds with a single explanatory variable included in the regression, but
we often ignore the presence of other independent variables and use this table as a rough
guide.
If less able workers are more likely to receive training, then
train
and
u
are
negatively correlated.
If we ignore the presence of
educ
and
exper
, or at least assume that
train
and
u
are negatively correlated after netting out
educ
and
exper
, then we can use
Table 3.2:
the OLS estimator of
1
β
(with ability in the error term) has a downward bias.
Because we think
1
≥
0, we are less likely to conclude that the training program was
effective.
Intuitively, this makes sense:
if those chosen for training had not received
training, they would have lowers wages, on average, than the control group.
Problem 2 (Wooldridge 7.10)
1. Yes, simple regression does produce an unbiased estimator of the effect of the voucher
program. Because participation was randomized, we can write
0
1
,
score
voucher
u
=
+
+
where
voucher
is independent of
u
, that is, all other factors affecting
score
. Therefore, the
key assumption for unbiasedness of simple regression, Assumption SLR.3, is satisfied.
2. No, we do not need to control for background variables. In the equation from part 1,
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 Spring '08
 NEILSEN
 Statistics, Econometrics, Regression Analysis, Standard Deviation, Wooldridge, average looks, background variables

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