# Econometrics: diagnostic test for regression model

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#1
https://imgur.com/a/hRwRrlj

Hi, I managed to deduce in e that there is a structural change after conducting the F test for the restricted and unrestricted models. My conclusion is that the restriction doesn't hold which I believe answers what e asks for.

I don't quite get f and g at this point. Part f is asking for what test that can be used to test for this significant change in K and L. I can't think of any diagnostic test for this; I believe t-test is the best way to solve the but I am not sure. I also don't know which one of the two unrestricted regression to test this on; what can we work this out?

To add on: I am struggling to work out what test to run. Both unrestricted models pass the reset test, BG test and JB test. I think I am unsure about what the question means by 'significant change in capital and labour. I think t-test will be the answer but how can we identify which regression models to test on?

g asks for how model can be improved, so I am thinking about multicollinearity and using IVF to test for it. Since they have already included the lagged variable; I am just guessing the inclusion of dummy variable is also required to test for seasonal variation. What more can I add here?

Thanks a lot.

Gregorius
Last edited by coconut64; 1 year ago
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1 year ago
#2
Can you post the rest of the question? There are an awful lot of symbols there that are undefined, so it's hard to interpret what's going on!

Hi, I managed to deduce in e that there is a structural change after conducting the F test for the restricted and unrestricted models. My conclusion is that the restriction doesn't hold which I believe answers what e asks for.
I don't know what you mean by "restricted" and unrestricted" models. It looks to me that you're doing a "change-point analysis". The standard approach here is to compare the log-likelihood of the model without change-point, to the sum of the log-likelihoods of the two models with the change-point, using the likelihood ratio test. I can see that an F-test will also do (if a bit old-fashioned).

I don't quite get f and g at this point. Part f is asking for what test that can be used to test for this significant change in K and L. I can't think of any diagnostic test for this; I believe t-test is the best way to solve the but I am not sure. I also don't know which one of the two unrestricted regression to test this on; what can we work this out?
As I say, I don't know what your symbols mean, but it looks to me that they want you to compare the estimates of K (and L) before and after the change-point. You have the estimates, you have their standard errors, so you could use a t-test to compare them. The question is hopelessly obscure as it stands, so I would guess that you're expected to refer back to your lecture notes (or textbook) to go through a standard procedure. I can think of some more fiendish ways of doing this, but I don't want to lead you too far away from your syllabus!

To add on: I am struggling to work out what test to run. Both unrestricted models pass the reset test, BG test and JB test. I think I am unsure about what the question means by 'significant change in capital and labour. I think t-test will be the answer but how can we identify which regression models to test on?
You always do your analysis on the better model. Incidentally, there's a different set of diagnostic tests reported on the change-point model to the original. Why is this, and what is "h"?

g asks for how model can be improved, so I am thinking about multicollinearity and using IVF to test for it. Since they have already included the lagged variable; I am just guessing the inclusion of dummy variable is also required to test for seasonal variation. What more can I add here?
Gregorius
Again the question is vague without context. I'd do the standard battery of tests of each linear regression. I would also wonder if a time-series analysis might be more appropriate to this data - but I'd have to know a bit more about the data to tell - how many data points do you have, for example?
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