Hi Sharmila,

The OLS regression model only gives you the best "line" with least amount of quadratic residuals sum. If your model is correctly (and completely) specified, then the normally distributed residual is logical to assume. However, perfect specification is extremely difficult to achieve, assuming the linear relationship is true at all.

There are a lot of reasons why regression model does not have normal distributed residuals in practice. Some of them are:

1) there exist omitted important explanatory variables

2) the linearity is not true

3) your data is probably truncated

4) heteroscedasticity

and many others.

In most projects, the goal is not to completely explain bank performance (through risk), but at least to show that there is a significant drive from credit or market risk towards performance. So normally distributed residuals were never required in this particular case.

Note further that credit risk measures are usually estimated at 99,9%-level, i.e. during very bad financial crisis, while bank performance measures do not have this condition. So it is very likely to get a skewed result, if you specify your model that way.

In summary, there are a lot of reasons why your residuals are not normal. Depending on your goal, this may not matter a lot. Depending on your data availability and what variables you use to represent risks, other methods are surely possible but too broad to answer to.

Christopher Paulus Imanto Thank you very much for you explanation. Can I know the methods that I can use instead of OLS, so I can try them too.

Short answer is that you can use OLS, just statistical inference (i.e. significance, p-value, standard errors) should be based on robust standard errors.

There are small sample corrections available in any standard textbook of Econometrics.

S.K.Mallick

Dear Sharmila Ramanayaka,

Thank you very much for making very important inquiries on the Research Gate portal and inspiring important discussions on particularly important issues.

In my opinion, it is good that there was a discussion in the question of this query.

This is a very interesting and scientifically important topic.

Because the topic is very important so I still read the answers, I follow the interesting discussion.

Question:

Is that possible to have a model without normality while satisfying all other OLS assumptions? If so how we want to justify it?

this is a very important issue that requires scientific research.

The issues of risk management in the context of determinants of the global financial crisis are described in the publications:

https://www.researchgate.net/publication/323244391_Determinants_of_credit_risk_management_in_the_context_of_the_development_of_the_derivatives_market_and_the_cyclical_conjuncture_economic_processes

https://www.researchgate.net/publication/327201116_Importance_and_implementation_of_improvement_process_of_prudential_instruments_in_commercial_banks_on_the_background_of_anti-crisis_socio-economic_policy_in_Poland

https://www.researchgate.net/publication/327201132_The_role_and_application_of_Keynesian_macroeconomic_anti-crisis_theories_in_the_context_of_development_of_the_financial_system_in_Poland

https://www.researchgate.net/publication/320074785_THE_SHADOW_BANKING_AS_AN_EXAMPLE_OF_INEFFICIENCIES_IN_THE_FUNCTIONING_OF_THE_BANKING_SYSTEM_IN_POLAND

I invite you to discussion and cooperation. Greetings