Exam #1 Answer Key
Economics 435: Quantitative Methods Fall 2008
1
A few warmup questions
a) First note that: E(xu) = = = = E(E(xu|x) E(xE(u|x) E(xE(u) E(x)E(u) (by the law of iterated expectations) (by the conditioning rule) (since we are given E(u|x) =
Exam #1 Answer Key
Economics 435 Spring 2004
1
Airplanes
a) The probability is pL qL + pR qR . b) E(L ) p E(R ) p E() c c) E(|L reinf orced) c E(|R reinf orced) c = pR q R = pL q L pL (1 qL ) 1 pL q L pR q R pR (1 qR ) = 1 pL q L pR q R = pL q L + pR q R
Exam #2 Answer Key
Economics 435 Spring 2003
1
A few short questions
a) No. While high school grades satisfy relevance (they are correlated with university attendance),
they are not exogenous (they are associated with intelligence, patience, and hard work
Midterm Answer Key
Economics 435: Quantitative Methods
Fall 2010
1
Cluster samples
a) Yes.
E()
x
= E
=
=
=
1
nS
1
nS
1
nS
1
nS
n
S
xis
s=1 i=1
n
S
E(xis )
s=1 i=1
n
S
E( + vs + uis )
s=1 i=1
n
S
s=1 i=1
1
(Sn)
nS
=
=
b)
var(xis )
=
var( + vs + uis )
=
va
Exam #2 Answer Key
Economics 435: Quantitative Methods Spring 2006
1
Applications
There are a wide variety of correct answers, so your answer does not need to look like mine in order to be correct. By the way, I made our hypothetical data set into a panel
Exam #2 Answer Key
Economics 435 Spring 2004
1
A few issues in research design
a) You cannot. The reason is that while you have a panel data set, you are estimating the eect of one variable at a particular point in time on another variable at a particular
Exam #1 Answer Key
Economics 435: Quantitative Methods
Spring 2006
1
Fitted values and residuals (33 points)
a) No it isnt.
plim yi
plim (0 + 1 xi )
= plim 0 + plim 1 plim xi
= 0 + 1 xi
= yi u i = yi
=
b) Yes it is:
plim ui
= plim (yi yi )
= plim yi plim
Midterm Answer Key
Economics 435: Quantitative Methods
Fall 2009
1
Properties of expected values
a) We start with the denition, and then use a little algebra along with the linearity of expectations theorem:
cov(x, y)
= E (x E(x) (y E(y)
= E (xy xE(y) yE(
Exam #2 Answer Key
Economics 435: Quantitative Methods
Spring 2006
1
Ugly criminals
a) Teenagers with high family income can spend more on clothes, makeup, gym memberships, etc., all with
the intention of making themselves look better. So it is likely tha
Exam #1 Answer Key
Economics 435 Spring 2002
1
The lazy professor (12 pts)
a) Let actual understanding be u. The variance of u s is higher than the variance of u s. Ill
also accept a claim that s is not a consistent estimate of u, because the number of q
Exam #2 Answer Key
Economics 435: Quantitative Methods
Fall 2009
1
The xed eects IV estimator
a) First we note that:
yit = yit yit1
= (ai + 1 xit + uit ) (ai + 1 xit1 + uit1 )
= 1 xit + uit
We follow our usual procedure for proving consistency with one ex
Exam #1 Answer Key
Economics 435: Quantitative Methods
Spring 2006
1
Starter questions (20 points)
a)
cov(ax, b + cx + dy) = ac var(x) + ad cov(x, y)
b)
Yes.
Yes.
It is 1 =
0.23+0.77
2
= 0.5.
c) Suppose that E(u|x) = 0. The law of iterated expectations
Exam #1 Answer Key
Economics 435: Quantitative Methods
Spring 2005
1
Regression with standardized variables
a)
0 = 0
b)
2
R2 = 1
c)
corr(, x) = 1
y
d) Well, since we have shown that 1 = corr(, y ), and all correlations are between 1 and +1, the answer
Exam #2 Answer Key
Economics 435: Quantitative Methods
Fall 2010
1
Short answer questions
a)
1. If x and y are independent, then cov(x, y) = 0. TRUE.
2. If x and y are independent, then E(y|x) = E(y). TRUE.
3. If cov(x, y) = 0 then x and y are independent