Econ 141: Problem Set 2: Answers
Fall 2007
Due Wednesday, September 26th in Class
Example SAS code appended at the end.
The intention of this exercise is to get you to interpret the regression coefficient estimates
and standard errors in a context where you know the underlying population model. When
you move to real world data, you will not know the underlying population model, and you
will need to be able to use economic and statistical intuition to predict whether the coefficient
estimates are biased and to generate precise estiamtes.
This entire problem set is to be done in SAS (or an equivalent data analysis software).
The first section sets up the data that you will adapt for later questions.
You will likely
want to have four distinct sections to your SAS code, one for each section of the problem set.
These problems draw from the SAS code presented in section 3, which is posted on bspace.
The Model Setup
You will generate the data for this anaylsis yourself, so there is no data to upload. Start by
generating 100 observations of a random variable, x, that is distributed uniformly between
0 and 1 and a random variable, u, that has the standard normal distribution. Also generate
a variable,
y
= 10
*
x
+
u
. Then answer the following questions:
1. What is the mean of the variable
x
in your sample?
What is it’s variance in your
sample? What should the mean of
x
be in the population?
The mean of x in the sample is 0.53 and the variance is 0.084. The mean of x in the
population should be 0.50 .
2. What is the mean of the variable
u
in your sample?
What is it’s variance in your
sample? What should the mean and variance of
u
be in the population?
The mean of u in the sample is 0.004 and the variance is 0.755. The mean of u in the
population should be 0 and the variance should be 1.
3. What is the covariance between the variables
x
and
y
in your sample?
The covariance between x and y in the sample is 0.833.
1
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4. If you were to run a regression of
y
on
x
with no intercept,
y
=
βx
+
u
, what should
the true value of
β
be? What should
σ
2
(the variance of
u
i
) be?
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 Spring '08
 MCCULLOUGH
 Normal Distribution, Variance, Interest Rates, 98 percent, 99 degrees, model setup

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