Lecture 4

Question 1

Under reasonable assumptions, what are OLS estimators

Answer 1

Efficient- they have the minimum variance of any linear unbiased estimators

Question 2

What is this property of efficiency called

Answer 2

The minimum variance property

Question 3

Why is an estimator with the minim variance property efficient

Answer 3

It achieves the same degree of accuracy with a smaller data set

Question 4

What is the homoskedasticity assumption

Answer 4

The error u has the same variance given any value of the explanatory variabke

Question 5

What does the distribution of y need to be to be homoskedastic

Answer 5

• centred around Y|X
• It needs to have a constant variance/ the same dispersion

Question 6

Is homoskedasticity likely for an example of looking at the effect of education on wage ( wage= b0 + b1education + u)

Answer 6

-NO- People with more education has a higher access to jobs
- The variability of wages is likely to increase with education

Question 7

Equation for variance of beta (hat) b^1

Answer 7

Question 8

What happens to variance of b^1 when sample size increases

Answer 8

Decreases

Question 9

What happens to the variance of b^1 when the variance of y increase

Answer 9

It increases as they are proportional

Question 10

What happens to variance of b^1 when sample size increases

Answer 10

Decreases

Question 11

As the variance in the stochastic component of Y increases, what happens to the variance of 𝛽̂1

Answer 11

As 𝜎^2, the variance in the stochastic component of 𝑦, increases, 𝑉𝑎𝑟(𝛽̂1 ) increases

Question 12

Diagram illustrating how an increase in disturbances (u) and thus higher variance in the error means the OLS estimators will be less accurate

Answer 12

Question 13

As variation in x increases what happens to the 𝑉𝑎𝑟(𝛽̂1 )

Answer 13

It decreases
“If “ 𝑥” doesn’t vary very much, it is difficult to reliably detect its effect on y”

Question 14

If there is more variation in X then what does that mean for accuracy of OLS estimators and why

Answer 14

They are likely to give a more accurate approximation to the true model as it easier to reliably detect its effect on Y

Question 15

What can be used to estimate this 𝜎^2, the variance of 𝑢𝑖

Answer 15

the variance of the observed residuals 𝑢̂𝑖, 𝜎̂^2, which we can calculate

Question 16

To calculate Var( 𝛽̂1 ), what do we need to know the value of that is paert of the true but unknown model

Answer 16

Unknown 𝜎^2

Question 17

What do the Var(𝛽̂1) and Var(𝛽̂0) measure

Answer 17

the dispersion of the OLS estimators in the SLR model

Question 18

What is it usual report in terms of these variances

Answer 18

The square root/ the standard errors

Question 19

What do the standard errors represent

Answer 19

estimates of the standard deviations of the sampling distributions of the OLS estimators

Question 20

Like the estimators 𝛽̂1 and 𝛽̂0, under reasonable assumptions, what characteristic does the estimator of 𝜎^2 have as well as the standard errors?

Answer 20

They are Unbiased

Question 21

Why is 𝜎̂=√(𝜎̂^2 ) of particular interest in its own right

Answer 21

It is a measure of the accuracy of the regression as a whole and we refer to 𝜎̂ as the standard error of the regression

Question 22

What are the standard erros of the OLS estimators for the SLR

Answer 22