Doing an empirical econometrics project, I have managed to confuse myself on one of the basics and wonder if you could lead me on the right track. What I wonder about is the normality assumption of the regression errors. For what do we need to assume this and how can we get around it if this is not the case?
Am I right in saying that although exogeneity and zero mean are part of the Gauss Markov assumptions, together with homoskedasticity, normality as per se is not? Which means that we should be able to obtain unbiased/consistent estimates without regression errors being normal? (And heteroskedasticity can be accounted for with robust errors?)
However, am I also right in thinking that our tests of significance, such as t and F, but also test of homoskedasticity and functional form, are only valid under normality of the errors? If my regression errors are non-normal (rejected at 1% by Jarque-Bera) is there any test I can apply to my OLS regression which would be valid? Or will I need to consider some form of transform?
Many thanks in advance, and apologies if this is really basic!