Economics 382
Instructor: Jing Sun
Homework #7
This homework is due on Tuesday April 8
th
at the time of the class.
1.
(Complete using calculator) Wooldridge Chapter 3, problem 3.10, page 114.
Answer:
3.10
(i)
Because
1
x
is highly correlated with
2
x
and
3
x
, and these latter variables have large
partial effects on
y
, the simple and multiple regression coefficients on
1
x
can differ by large
amounts. We have not done this case explicitly, but given equation (3.46) and the discussion
with a single omitted variable, the intuition is pretty straightforward.
(ii) Here we would expect
1
β
%
and
1
ˆ
β
to be similar (subject, of course, to what we mean by
“almost uncorrelated”).
The amount of correlation between
2
x
and
3
x
does not directly effect
the multiple regression estimate on
1
x
if
1
x
is essentially uncorrelated with
2
x
and
3
x
.
(iii) In this case we are (unnecessarily) introducing multicollinearity into the regression:
2
x
and
3
x
have small partial effects on
y
and yet
2
x
and
3
x
are highly correlated with
1
x
.
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 Spring '08
 Sun
 Economics, Regression Analysis, Poverty, Wooldridge Chapter, multiple regression estimate

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