Chapter 5
1. Which of the following assumptions are required to show the consistency, unbiasedness
and efficiency of the OLS estimator?
(i) E(ut) = 0
(ii) Var(ut) = δ2
(iii) Cov(ut, ut-j) = 0
(iv) ut ~ N(0, δ2)
(ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv) only
All of the assumptions listed in (i) to (iii) are required to show that the OLS estimator has the
desirable properties of consistency, unbiasedness and efficiency. However, it is not necessary
to assume normality (iv) to derive the above results for the coefficient estimates. This
assumption is only required in order to construct test statistics that follow the standard
statistical distributions – in other words, it is only required for hypothesis testing and not for
coefficient estimation.
2. Which of the following may be consequences of one or more of the CLRM assumptions
being violated?
(i) The coefficient estimates are not optimal
(ii) The standard error estimates are not optimal
(iii) The distributions assumed for the test statistics are inappropriate
(iv) Conclusions regarding the strength of relationships between the dependent and
independent variables may be invalid.
(ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv)
If one or more of the assumptions is violated, either the coefficients could be wrong or their
standard errors could be wrong, and in either case, any hypothesis tests used to investigate
the strength of relationships between the explanatory and explained variables could be
invalid. So all of (i) to (iv) are true.
3. What is the meaning of the term “heteroscedasticity”?
The variance of the errors is not constant
The variance of the dependent variable is not constant
The errors are not linearly independent of one another
The errors have non-zero mean
By definition, heteroscedasticity means that the variance of the errors is not constant.
1. Which of the following assumptions are required to show the consistency, unbiasedness
and efficiency of the OLS estimator?
(i) E(ut) = 0
(ii) Var(ut) = δ2
(iii) Cov(ut, ut-j) = 0
(iv) ut ~ N(0, δ2)
(ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv) only
All of the assumptions listed in (i) to (iii) are required to show that the OLS estimator has the
desirable properties of consistency, unbiasedness and efficiency. However, it is not necessary
to assume normality (iv) to derive the above results for the coefficient estimates. This
assumption is only required in order to construct test statistics that follow the standard
statistical distributions – in other words, it is only required for hypothesis testing and not for
coefficient estimation.
2. Which of the following may be consequences of one or more of the CLRM assumptions
being violated?
(i) The coefficient estimates are not optimal
(ii) The standard error estimates are not optimal
(iii) The distributions assumed for the test statistics are inappropriate
(iv) Conclusions regarding the strength of relationships between the dependent and
independent variables may be invalid.
(ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv)
If one or more of the assumptions is violated, either the coefficients could be wrong or their
standard errors could be wrong, and in either case, any hypothesis tests used to investigate
the strength of relationships between the explanatory and explained variables could be
invalid. So all of (i) to (iv) are true.
3. What is the meaning of the term “heteroscedasticity”?
The variance of the errors is not constant
The variance of the dependent variable is not constant
The errors are not linearly independent of one another
The errors have non-zero mean
By definition, heteroscedasticity means that the variance of the errors is not constant.
