Model assumptions and reality
from Lars Syll
In a previous article posted here — What are the key assumptions of linear regression models? — yours truly tried to argue that since econometrics doesn’t content itself with only making optimal predictions, but also aspires to explain things in terms of causes and effects, econometricians need loads of assumptions — and that most important of these are additivity and linearity.
Let me take the opportunity to cite one of my favourite introductory statistics textbooks on one further reason these assumptions are made — and why they ought to be much more argued for on both epistemological and ontological grounds when used (emphasis added):
In a hypothesis test … the sample comes from an unknown population. If the population is really unknown, it would suggest that we do not know the standard deviation, and therefore, we cannot calculate the standard error. To solve this dilemma, we have made an assumption. Specifically, we assume that the standard deviation for the unknown population (after treatment) is the same as it was for the population before treatment.
Actually this assumption is the consequence of a more general assumption that is part of many statistical procedure. The general assumption states that the effect of the treatment is to add a constant amount to … every score in the population … You should also note that this assumption is a theoretical ideal. In actual experiments, a treatment generally does not show a perfect and consistent additive effect.
Additivity and linearity are the two most important of the assumptions that most applied econometric models rely on, simply because if they are not true, your model is invalid and descriptively incorrect. It’s like calling your house a bicycle. No matter how you try, it won’t move you an inch. When the model is wrong — well, then it’s wrong.