I think the model is not structurally stable so you can respecify the model. Also, check for serial correlation and endogeneity bias.

Dear Prince Fosu

Thank you!

Best

Ibrahim

Dear Ibrahim,

Have you already checked for first order serial correlation and heteroskedasticity?

You can include the lag of the dependent variable as part of your explanatory variables. I think that will help address the serial correlation.

Dear Elvis Munyaradzi Ganyaupfu

Yes, the model does not have a heteroskedasticity problem and serial correlation is absent.

Best

Ibrahim

Thank you dear Prince Fosu

I will give it a try.

Best

Ibrahim

It seems to point to some problem with the model specification (i.e. functional form), eventhough the line returns into the band.

So Generate the residuals from the regression and test for linearity or otherwise using BDS independence test

Thank you dear Nana Akosah

I agree with Prince Fosu that the model is perhaps not stable. But you have yearly data and not many years so adding a break on one of the explanatory variables may not be wise .

Dear Ibrahim,

Kindly respecify the model and extend your data to cover more duration of time.

Regards

thank you dear Kehinde Mary Bello

Unfortunately, I don't have the flexibility to expand the data range but I can respecify the model.

Best

Ibrahim

I presume that your data is quarterly or monthly as otherwise, you have too few observations to make any reasonable inferences.

If you are trying to make causal inferences (e.g. you have an economic model that implies that x causes y and you wish to measure that effect). the CUMSUMSQ is one test that indicates that your model is not stable. Either the coefficients or the variance of the residuals is not stable. You have indicated that there is no heteroskedasticity so it is possible that the model coefficients are the problem. The test itself only indicates that there's instability and does not say what the instability is or what causes it. There are many possible causes of instability, (omitted variables, functional form, heteroskedasticity, autocorrelation, varying coefficients etc.) Your best procedure is to return to your economics and work out how your theory might lead to stability problems. Are there possible breaks in your data caused by policy changes, strikes, technological innovations, and similar. that might be covered with a dummy variable or a step dummy.

If you are doing forecasting (or projections) I would not be too concerned about specification tests. It is very unlikely that an unstable model will forecast well. You may achieve good forecasting results with a very simple model that need not be fully theory compliant.

Dear John C Frain

Thank you for your valuable and detailed answer. It will surely guide me throughout the estimations.

Best

Ibrahim

You can explain the reasons of instability by explaining the data during that period .

Lacking appropriate dummy data. The data suggest that something happened before the position where the line went of the critical boundary.

Theoretical underpinnings, literatures or apriori expectation could be used to explain these out of bound 95% CI