Dear Professors/Research
I have estimated the aggregate export supply function but i observed the difference between R-square and Adjusted R-square is very high. but other hand all other diagnostic tests are up to mark. i have paste the results of the model below please guide me what is logic behind it i am very thankful
R-square 0.57 adjusted R-square 0.39
thanks and best regards
Irshad
It is completely ok. R2 measures how good is the total fit of the model, independently of number of parameters you used. Adjusted R2 penalizes for number of parameters you used. Larger difference between R2 and adjusted R2 means simply that you used relatively a lot of explanatory variables. It might be completely ok, but you might also consider model with less variables.
Ok thanks a lot Professor Peter.
One more question. THe R-square value is range between 45-70 in most case when we estimating the conditional ARDL model. but when we estimate the long run model in the level of variables then the r-square value is more than 90%. what is the reason behind this. Either it is due to we use the difference variable in conditional ARDL model or other reason
regards
irshad
Supporting the Professor Peter, ARDL models are using a large number of variables, exacerbating the case. In another word, the structure of ARDL models includes a large number of explanatory variables which leads to decrease the value of Adjusted R2. Normally, the A.R2 is much lower than R2 in the ARDL models.
Am I right Professor Peter?
I actually do not know what is an ARDL model. The size of the R2 depends on particular problem. Sometimes it is possible to explain even more than 90% of the variation. However, is some problems, for example predicting stock returns, it is completely common to have R2 smaller than 5%. Therefore, absolute magnitude of R2, or adjusted R2, is not very useful. It really depends on the particular problem/data.
Sayed -
You have correctly answered your own question about why R2 is bigger in the levels equation. Levels of macroeconomic variables are often trended, which causes larger R2 values.
I take a different view - this largish drop suggest that you are (at least in part) modeling idiosyncratic noise and not clear and reproducible signal. Any problem would produce a R2 of 100 when the number of parameters equals the number of observations, but the R2 adjusted would drop towards zero. It is a sign of the Texas sharp shooter fallacy- the problem of rampant induction
https://en.wikipedia.org/wiki/Texas_sharpshooter_fallacy
It would be sensible to use techniques such as cross validation to see how complex a model can be supported by the data and of course theoretical insights and diagnostics to evaluate the assumptions of the model.
It may also be that the outcome is changing slowly and we can get good fits and predictions because of this . The length of my hair today is very much like it was yesterday. the more frequently I measure it the more auto-correlated it is!
However, I do not have subject specific knowledge of your area and what the norms and expectations are..
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