lecture 10

Question 1

Why do we need to impose restrictions onto a regression model?

Answer 1

unrestricted regression will always fit at least as well as the restricted one.
So the question will be how much improvement in the fit do we get by relaxing the restrictions relative to the loss of precision that follows. The distribution of the test statistic will give us a measure of this so that we can construct a decision rule.

Question 2

What is RRSS?

Answer 2

the residual sum of squares obtained from estimating the restricted model.

RRSS = URSS/(1-R2)

Question 3

What is URSS?

Answer 3

This is simply RSS, as we dont restrict any values of the mod

Question 4

how do you test linear restrictions

Answer 4

Estimate the model without any restrictions
Estimate the model with the restrictions
Test the restrictions using an F test based on the residual
sums of squares.

Under the null hypothesis that the restrictions are true:

Question 5

what is the quantity theory of money

Answer 5

𝑀𝑉̄=𝑃𝑌⇒Δ𝑃/𝑃=Δ𝑀/𝑀−Δ𝑌/𝑌

so when you restrict you will look at B2=1 and B3=-1

Question 6

what are some issues with multivariate regression

Answer 6

. Increasing the number of right-hand side variables will always
increase the R-squared for the regression.

2. If the right-hand side variables are highly correlated with each
   other then the standard errors of the OLS coefficients will
   become large.
3. If we omit relevant variables then the OLS estimates will be
   biased.
4. If we include irrelevant variables the OLS estimates will be
   unbiased but inefficient.

Question 7

what is adjust R squared

Answer 7

alternative to combat the issue of adding too many regressors to increase R2

-This penalises the loss of degrees of freedom when we add
extra regressors.

Question 8

what is multicollinearity

Answer 8

when one independant variable on the RHS is correlated with another independat variable

Question 9

what are the usual signs of collinearity

Answer 9

For individual variables the standard errors are large and the
t-ratios are low.

For the regression as a whole the F-statistic is highly significant.

The R2 will tend to be high.

Some degree of multicollinearity is almost always present in
econometric models.

Question 10

when taking linear restriction what is the general form

Answer 10

R B = r

Question 11

why is the unrestricted always at least as effective as the restricted one

Answer 11

When estimating the model we minimise the residual sum of squares. In the unrestricted model, we can always choose the combination of coefficients that the restricted model chooses. Hence the restricted model can never do better than the unrestricted one.