Homework # 1
ECO 7427
ANSWER KEY
Prof. Sarah Hamersma
1.
This was a hard question.
I gave substantial partial credit for wrong answers that were
well thoughtout.
But please do make sure you read this so you know the right answer.
Outline of answer:
a)
clustering standard errors is still needed, even with dummies
b)
explanation of what dummies can and cannot successfully fix
c)
explanation of why clustering will make SEs bigger even if it’s unneeded
John Lott’s analysis uses countylevel data from several states and looks at the impact of
statelevel treatments.
Note that he does not use individual data at all – the unit of
observation is the county.
This means when he refers to using county fixed effects, this is
equivalent to an “individual” fixed effect from the perspective of his sample where each
observation is a county.
He argues that including county fixed effects implicitly includes
state fixed effects.
This argument is correct.
However, this only moves us one step closer to
the real question:
Does including state fixedeffects mean you don’t need clustering at the
state level?
The answer is that you still may need clustering.
State fixed effects are an important component of an analysis that uses statelevel treatments.
As noted in the example above, there may be correlated outcomes Y within a state that are
not picked up by observable X’s.
This can be thought of as an omitted variables
(endogeneity) problem – so if this is the case, and we do not include state fixed effects, our
estimates of the treatment effect will be biased and inconsistent (not to mention the standard
errors!).
Including a state fixed effect allows us to explain some of this variation.
Econometrically, it will force the expected value of the residuals within each state to be zero
(if they averaged something else, this would have been incorporated into the estimate of the
fixed effect by construction).
Suppose that these state fixed effects properly fix the point estimates (i.e. there is no longer
an omitted variables problem).
What does the error structure look like now?
Well, within
each state there are several counties.
We can estimate a regression and look at the residuals
within each state – they will average zero (as noted above) but depending on the state they
might be spread widely or distributed narrowly around zero.
This is a heteroskedasticity
problem – solve it with the “robust” function to fix your standard errors.
Where does the
clustering come in?
It is worth noting that the clustering problem would have been HUGE
if we ignored the fixed effects to start with, and so including them does make the problem
smaller (which is why some of our intuition suggested that it could fix the problem).
However, it may still remain.
The issue is that we have controlled only for a very specific
form of correlation among observations within a state – we have controlled for a form of
correlation in which every observation in the state has a common (statelevel) component of
1
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 Spring '06
 HAMERSMA
 Standard Deviation, Variance, labor force, standard errors, EITC

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