1
University of California, Davis
Managerial Economic(ARE) 106, Summer 2009
Instructor: John H. Constantine
Problem Set #3: Due Monday, August 24, 2009
Problem 1
:
This problem requires the use of SHAZAM.
Consider the problem of estimating a production function that expresses the relationship between the level
of output of a product (
y
) and the level of an input, or factor of production (
x
).
The SHAZAM command
file is given below.
When necessary, assume
α
= 5%.
sample 1 15
read(are106/table3-2.dat) x y
print x y
plot
ols y x
stop
(a)
Assume that the data can be described the simple linear regression model:
y
=
β
1
+
β
2
x
+
e
.
Use SHAZAM estimate b
1
and b
2
.
State the associated
t
statistics.
(b)
Give an economic interpretation of the estimated parameters.
(c)
Draw your estimated OLS line through the data plot.
(d)
(i)
Find the confidence interval for b
2
.
(ii)
Draw a picture and show the regions of “Reject H
0
” and “Do Not Reject H
0
”.
(iii)
Clearly explain what this confidence interval means.
(e)
Using the Confidence Interval approach, you are to test the following hypotheses.
Draw
β
2
HO
on
your picture in part (d, ii) for each hypothesis.
(i)
H
0
:
β
2
= 0
(ii)
H
0
:
β
2
= 0.30
(iii)
H
0
:
β
2
= 0.50
(f)
Now, conduct the three hypotheses of part (e), but this time using the t-test approach.

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