Department of Economics
Spring 2009
University of California
Prof. Woroch
Economics 140:
Problem Set 4
SUGGESTED ANSWERS
Short Questions.
Answer each of the below questions about regression validity.
1.
This course has two midterm exams that are used to measure your knowledge of
econometrics.
Suppose that your performance, and that of your fellow students, on the day
of the first midterm measured knowledge imperfectly and with an error:
1
1
1
~
i
i
i
w
X
X
+
=
where
1
~
i
X
is first midterm score of student
i
,
1
i
X
is their true level of knowledge of econometrics,
and
1
i
w
is a random error with mean zero and variance
2
w
σ
.
For instance,
w
may depend on
whether the student had a headache that day, whether they had an especially good night’s
sleep, and so on.
A similar situation holds for the second midterm:
2
2
2
~
i
i
i
w
X
X
+
=
. What
concerns would you have about internal validity of a regression of scores from the second
midterm on the first midterm scores?
Answer
: Internal validity is violated because Measurement Error in the independent variable
causes a correlation between that variable and the regression error term which, in turn, results
in biased and inconsistent OLS estimate of the coefficient on that independent variable. The
OLS coefficient will be attenuated (smaller in absolute value, and therefore nearer to zero).
Measurement error in the dependent variable only increases the SSR and standard errors by
adding additional noise to the regression error, but does not lead to biased OLSEs.
2.
Assume that a simple economy could be described by the following system of Keynesian
equations:
01
tt
t
CY
u
β
=+
+
and
t
I
I
−
=
where
C
is consumption,
Y
is income, and
I
is
investment. Assume the presence of the GDP identity,
Y = C
+
I
.
If you estimated the
consumption function, what sort of problem involving internal validity may be present?
Answer
:
This is a case of simultaneous causality which is often also called “simultaneous
equations bias” because it arises when the researcher estimates one equation involving an
independent variable that is a dependent variable in another equation.
The second equation
here is the GDP identity in which GDP is determined by consumption plus an error term, say
v.
Substituting for C = Y  I from this identity into the consumption function gives an
expression that can be solved for Y in terms of the two error terms, in which case the
independent variable (Y) in the consumption function regression is correlated with the error
term (via v). The result is biased and inconsistent OLSEs.
3.
You have been hired as a consultant by building contractor, who have been sued by the
owners’ representatives of a large condominium project for shoddy construction work.
In
order to assess the damages for the various units, the owners’ association sent out a letter to
owners and asked if people were willing to make their units available for destructive testing.
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 Spring '08
 DUNCAN
 Economics, Econometrics, Regression Analysis, Final Exam Score

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