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University of California
D. Steigerwald
Department of Economics
Economics 140A
Exercise 1
1.
You are interested in purchasing a home in Santa Barbara.
To determine if it is a good
time to buy, you collect the selling prices of all homes in the city over the past three
years, giving you 497 observations.
Let us denote observation
t
as
P
t
,
t=1,.
..,497
.
a)
We assume that
497
1
}
{
t
t
P
is a sequence of independent and identically distributed
random variables.
Construct an estimator of the mean and median of
P
t
.
b)
Are your estimators unbiased?
What is the variance of each estimator?
c)
Suppose that you grouped the sales according to years, so you could estimate the
mean and median sale price of a home in each of the three years.
Suppose
further, that our assumption that
497
1
}
{
t
t
P
is an i.i.d. sequence is erroneous.
In fact,
there are two types of homes, call them nice with mean price
N
and average
with mean price
A
, where
A
N
.
If the composition of sales over time has
shifted toward nice homes, which estimator would shift more over time?
Carefully explain your logic.
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This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff
 Economics

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