I state beforehand that my question may sound odd and captious (and maybe it is).
In regression theory basically we assume that explanatory variables and independent variable are joined togheter generally speaking with an unknown joint distribution.
All that we're looking for is a linear approximation (the best one) of the conditional expectation (CEF) $E[Y\mid\bf{x}]$ with $\bf{x}$ being the vector of regressors.
Clearly if we know the exact underlying distribution we're done (e.g. if $(Y,\bf{x})$ is MVN the conditional expectation is linear and it has a straighforward expression written on books) .
In OLS theory we look for a linear approximation of the CEF collecting a bunch of data $(y_1,{\bf{x}}_1 ),\ldots,(y_n,{\bf{x}}_n )$ that we suppose drawn from an identical underlying population (this is the standard assumption that the observations are identically distributed), in order for the coefficient $\beta=E[{\bf{xx}}^t]^{-1}E[{\bf{x}}y]$ to make sense.
My problem is how we can be sure that the joint underlying distribution exists, it's one and somehow fixed?
I mean, let's suppose that I want to make some prediction about $children's \; height$ using as regressors $parent's \; height $ (recalling the famous Francis Galton paper), who can assure us these assumptions?
If there's another variable which acts in an "odd manner", modifying the joint shape over time, is that analogous to an omitted bias problem?