Economics 241B
Exercise 4
1.
Asymptotic Normality to Consistency
You undertake a research project on carbon sequestration with a colleague from
the geology department.
He defers to you as the expert on statistics.
a.
In one discussion, you note that the estimator you are using is consistent
and asymptotically normal.
He then asks the natural question, "What are the
advantages of using an estimator that is consistent and asymptotically normal?"
Please respond.
b.
Several weeks later, the geologist proposes an estimator that is common in
his °eld, but with which you are not familiar. He proudly notes that the estimator,
^
°
n
, is asymptotically normal (a concept he learned from you) and displays an
equation he copied down
p
n
°
^
°
n
°
°
0
±
d
!
N
²
0
; ±
2
³
:
He is puzzled, however, by the fact that he could not °nd out if the estimator is
consistent for the population value
°
0
.
Please show why the asymptotic normality
result does, or does not, establish consistency.
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 Fall '08
 Staff
 Economics, Normal Distribution, standard errors, geologist

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