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Economics 4261
Introduction to Econometrics
Fall 2010
HOMEWORK 5 : ASYMPTOTICS AND HETEROSKEDASTICITY
**Homework Policy Change**
There has been a change to the homework policy. Please read this message in its entirety.
Over the past two weeks, some homework assignments, which were handed in at the start of class, were missing when
grading began. It appears these assignments were some of the ﬁrst handed in. Both Randall and I are almost certain
these assignments were not lost in transport to or from the Department.
To correct this issue, homework will be collected at the end of class. Either Randall or I will go around the room
and collect assignments individually from you. Homework not turned in by this method will not be graded.
Please note that taking someone else’s work is a violation of the Student Conduct Code. Randall and I will report
any oﬀenders to the Director of Undergraduate Studies.
Question 1
Consider the linear model
y
X
β
u
. We say that the parameter(s)
β
is
identiﬁed
if
(1)
E
r
y

X
s
X
β
,
(2)
X
β
p
1
q
X
β
p
2
q
if and only if
β
p
1
q
β
p
2
q
.
(a) What do these conditions assert? That is, what does it mean in words for these conditions to hold?
(b) What are the assumptions needed for each condition to hold?
Question 2
The parameter(s)
β
is
consistent
if
plim
r
ˆ
β
s
β,
(1)
where ”plim” stands for probability limit. Phrased another way, (1) states that
ˆ
β
converges in probability to the
true parameter(s)
β
as the sample size increases to inﬁnity.
(a) Give an expression for
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 Spring '08
 Staff
 Econometrics

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