Week 6 Tutorial Exercises
Review Questions (these may or may not be discussed in tutorial classes)
How would you test hypotheses about a single linear combination of parameters?
We may re
‐
parameterise the regression model to isolate the “single linear combination”. Then
the OLS on the re
‐
parameterised model will provide the estimate of the “single linear
combination” and the related standard error. See the example in the textbook and lecture slides
What are exclusion restrictions for a regression model?
Exclusion restrictions are the null hypothesis that a group of x
‐
variables have zero coefficients in
the regression model.
What are restricted and unrestricted models?
When the null hypothesis is a set of restrictions on the parameters, the regression under the null
is called the restricted model, while the regression under the alternative (which simply states
that the null is false) is called the unrestricted model.
How do you compute the F
‐
statistic, given that you have SSRs?
Clearly, the general F
‐
stat is based on the relative difference between the SSRs under the
restricted model and unrestricted model: F = [(SSR
r
– SSR
ur
)/q]/[SSR
ur
/(n
‐
k
‐
1)], where you should
be able to explain the meanings of various symbols.
What are general linear restrictions on parameters?
These are linear equations on the parameters. For example,
β
1
– 2
β
2
+ 3
β
3
= 0.
What is the test for the overall significance of a regression?
This is the F
‐
test for the null hypothesis that all the coefficients of x
‐
variables are zero.
How would you report your regression results?
See the guidelines in Section 4.6 of the textbook.
Why would you care about the asymptotic properties of the OLS estimators?
When MLR.6 does not hold, the finite
‐
sample distribution of the OLS estimators is not available.
For reasonably large samples (large n), we use the asymptotic distribution of the OLS estimators,
which is known from studying the asymptotic properties, to approximate the finite
‐
sample
distribution of the OLS estimators, which is unknown.
Comparing the inference procedures in Chapter 5 with those in Chapter 4, can you list the
similarities and differences?
It is beneficial to make a list by yourself.
Under MLR.1
‐
MLR.5, the OLS estimators are consistent, asymptotically normal, and
asymptotically efficient. Try to explain these properties in your own words.
This is really a test on your understanding of these notions in econometrics.
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 One '11
 yang
 critical value, OLS estimators, P‐value

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