Lecture notes 4 structural change Flashcards
What is a structural change test?
What can it also be called?
Testing that all parameters are constant over the sample.
H0 intercepts and coefficients are all the same
H1 intercepts and coefficients all differ.
First estimate equation 1, which is the unrestricted model
Chow’s 1st Test
What is an example for the need to use structural change?
When the data can be split into two sub-samples.
For both samples we observe the same variables.
We are looking to see if they have separate regression functions or if really it is the same
How do we do the structural change test?
What is important when calculating the F-statistic?
-H0 all slopes and coefficients are all equal.
Model 1 is using the same regression
Model 2 is splliting it
Model 3 is splitting it
B0A = B0B , B1A = B1B etc
RSSU = Model 2 RSS + Model 3 RSS
RSSR = model 1
F-statistics = RSSR- RSSU / d // RSSU / DOF
THE DOF subtraction must be multiplied by 2
2(K+1) AS THERE ARE TWO MODELS!!!!
Then find F value and compare
When doing a structural change with dummy variables what is the difference?
You fix the dummies and then collect like terms then compare that to the original model.
What is a predictive failure test and what else is it known as?
Also known as 2nd Chow test
Use when one of the samples is smaller than the other and to check.
Tests if the regression that holds over n observations also holds over n1 observations.
What is an outliar?
This is an observation that it is a mistake
What is the impact of an outliar graphically also?
It can bias the estimation as it can pull the estimation too up or to down from where it should be.
What are the ways of looking for the impact of an outliar?
Try different sub-samples and see how they impact the estimation and thus conclusions
From a regression persepective how can you see the impact of an outliar?
You add an impulse dummy variable for that where j = i when the jth observation is being looked at .
This is the same as dropping the observation.
if the coefficient of the outliar is large then it should it shows it has a big impact on the dependent variable.
tilda hat = Y - b0 - b1Xj
How do you conduct a predictive failure test with dummy variables
Null hypothesis is that all the dummy j’s are = 0 so it is the same regression model
Alternative is that all the dummy coefficients are not the same.
Unrestricted model with dummy for the 12 months where there was a different trend
Unrestricted model: Expenditure = B0 + B1Income + Sum12 gamma dij + epsilon
Restricted model: Expenditure = B0 + B1income + epsilon
F stat = RSSR -RSSU / n1 (extra observation) // RSSU/ DOF
Then find F distribution with 12 restrictions and DOF
What is important about the DOF in a predictive failure test in the denominator?
Only use n without the observations that were in the smaller sample.
How do you conduct a predictive failure test without dummy variables
H0 : yi = β0 + β1x1i + β2x2i + . . . + βkxki + εi i = n + 1, . . . , n + n1
in which case imposing the null hypothesis on the unrestricted equation (8), yields the restricted
model:
yi = β0 + β1x1i + β2x2i + . . . + βkxki + εi i = 1, 2 . . . , n + n1
F stat d = additional observations n1
DOF is the unrestricted model observations - k+1
