HANDOUT 4/5

Question 1

STRUCTURAL CHANGE REFERS TO

Answer 1

The coefficients in our model may NOT be constant over the entire sample of observations.

Question 2

What happens if we just estimate one model when we actually have structural change?

Answer 2

Biased coefficients

Some weighted average of both groups = not representative of either

Question 3

Unrestricted model for structural change

Answer 3

2 x models
One for North one for south
differing intercepts and slope parameters

Question 4

H0 for structural change

Answer 4

Parameters equal (intercept and all slopes)

Question 5

restricted for structural change

Answer 5

We just have one UK-wide model

Constant paramters

Question 6

dof for 1st chow test

Answer 6

dof = from unrestricted model
dof = n -2(K + 1) as consider both north and south equations

Question 7

RSS^U for 1st chow test

Answer 7

U = from 2 models north and south

RSS^U =RSS north + RSS south

Question 8

Efficiency vs accuracy

Answer 8

Efficient model = Uk wide model with fewer paramters

But accurate model = north/south - unbiased

Question 9

How do we introduce dummy variables for 1st chow test?

Answer 9

Instead of 2 separate equations for unrestricted model, make 1 with additive dummy variable for intercept shift and multiplicative for different slopes.

Question 10

What is H0 and restricted model in 1st chow test with dummies

Answer 10

H0: coefficient on the dummies = 0

Restricted model = no dummies

Question 11

Unrestricted model 2nd chow test

Answer 11

Unrestricted = model holds over i=1 to n only

Question 12

H0 for 2nd chow test

Answer 12

Model holds for n1 additional observations

i=n+1 to n+n1

Question 13

restricted model 2nd chow test

Answer 13

Model restricted to hold over all observations, including new ones.
i=1,…,n,n+1,…,n+n1

Question 14

What is d for 2nd chow test?

Answer 14

d = n1 - the number of new observations

Question 15

RSS R for 2nd chow test

Answer 15

RSS R = RSSn + RSS for new observations

Question 16

What are dummy variables called that take value 1 for one observation only?

Answer 16

IMPULSE dummy variables

Question 17

What do impulse dummy variables do to the regression line?

Answer 17

Allow regression line to shift so that for these new observations the prediction error is zero. An additive dummy variable for one data point exactly explains that data point.

Question 18

Through OLS minimising RSS what do we find about the coefficient on the impulse dummy?

Answer 18

RSS = RSSn + e^2 n+1
d/db
b = yn+1 - yn+1 hat = en+1

Question 19

So the coefficients on the impulse dummy variables =

Answer 19

The prediction error en+1

Question 20

Hence what is our unrestricted model 2nd chow test with dummies

Answer 20

Model with original explanatory variables plus impulse dummies for new observations - we need the intercept shifts as prediction error ≠ 0

Question 21

What is H0 2nd chow test dummies?

Answer 21

H0: coefficients on dummies = 0
This means prediction error = 0
Model perfectly predicts new observations

Question 22

SO what is our restricted model 2nd chow test with dummies

Answer 22

Normal model with NO impulse dummy variables. i=1,…,n,n+1,n+2 …
The model holds for all observations including the new ones and perfectly so we don’t need an intercept shift.

Question 23

How do we solve outliers problem?

Answer 23

Include an impulse dummy for every outlier point –> ensures unbiased.
equivalent to discarding them.